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Predictive Demand Side Management Strategies for Residential Building Energy Systems

Hassan Harb

This thesis presents a generalized methodology, supported by a software framework, for modeling and assessing mathematical programming based predictive demand side management (DSM) strategies that exploit thermal and electrical flexibilities of residential building energy systems (BES) to enhance the integration of renewable energy sources. The modeling and simulation platform is formulated in Python and includes a set of forecasting methods as well as a discrete mixed inte-ger linear programming (MILP) modeling library based on the Gurobi optimizer API. The platform further integrates a nonlinear BES simulation model in Dymola/Modelica as a functional mock-up unit (FMU). The investigated scheduling models for individual buildings consist of a deterministic MILP strategy and a multi-stage stochastic programming approach that extends the MILP model while incorporating the uncertainties of the electrical and domestic hot water demands. The city district DSM strategies comprise a centralized approach, which serves as a benchmark, as well as distributed formulations based on decomposition techniques. The distributed DSM approaches considered are Dantzig-Wolfe decomposition based column generation algorithm as well as an integrated Lagrangian decomposition column generation approach.

ISBN 978-3-942789-50-9

Predictive Demand Side Management

Strategies for Residential Building Energy

Systems

Vorausschauende Demand Side Management

Strategien für Wohngebäudeenergiesysteme

Von der Fakultät für Maschinenwesen der Rheinisch-Westfälischen Technischen Hochschule

Aachen zur Erlangung des akademischen Grades eines Doktors der

Ingenieurwissenschaften genehmigte Dissertation

vorgelegt von

Hassan Harb

Berichter: Univ.-Prof. Dr.-Ing. Dirk Müller

Univ.-Prof. Antonello Monti, Ph.D.

Tag der mündlichen Prüfung: 09. November 2017

Diese Dissertation ist auf den Internetseiten der Universitätsbibliothek online verfügbar.

Bibliographische Information der Deutschen NationalbibliothekDie Deutsche Nationalbibliothek verzeichnet diese Publikation in der DeutschenNationalbibliografie; detaillierte bibliografische Daten sind im Internet überhttp://dnb-nb.de abrufbar.

D 82 (Diss. RWTH Aachen University, 2017)

Herausgeber:Univ.-Prof. Dr.ir. Dr.h.c. Rik W. De DonckerDirektor E.ON Energy Research Center

Institute for Energy Efficient Buildings and Indoor Climate (EBC)E.ON Energy Research CenterMathieustr. 1052074 Aachen

E.ON Energy Research Center | 51. Ausgabe der SerieEBC | Energy Efficient Buildings and Indoor Climate

Copyright Hassan HarbAlle Rechte, auch das des auszugsweisen Nachdrucks, der auszugsweisen odervollständigen Wiedergabe, der Speicherung in Datenverarbeitungsanlagen und derÜbersetzung, vorbehalten.

Printed in Germany

ISBN: 978-3-942789-50-91. Auflage 2017

Verlag:E.ON Energy Research Center, RWTH Aachen UniversityMathieustr. 1052074 AachenInternet: www.eonerc.rwth-aachen.deE-Mail: post_erc@eonerc.rwth-aachen.de

Hassan Harb

"Predictive Demand Side Management Strategies for Residential Building Energy

Systems"

Dedicated to my parents, Ali & Fattouma

and to my wife, Tanja.

Acknowledgments

First and foremost, I would like to thank my supervisor Univ.-Prof. Dr.-Ing. Dirk Müller

for giving me the possibility and freedom to work on this thesis and for his confidence

and excellent guidance. I would also like to thank Univ.-Prof. Antonello Monti, P.h.D for

his support and for reviewing this thesis as well as being the co-examiner on my doctoral

examination.

Further, I would like to thank my colleagues at the Institute for Energy Efficient Buildings

and Indoor Climate for the unbounded cooperation, great working atmosphere and the

beautiful memories. Especially, I would like to thank Peter Matthes for being a pleasant

office mate and a great friend, for the interesting discussions and valuable advice. I

also want to thank Ana Constantin and Thomas Schütz for the cheerful and successful

cooperation in the projects we worked on together and for their support in the preparation

for the doctoral examination. Henryk Wolisz, Roozbeh Sangi and Moritz Lauster, thank

you for the memorable moments within and outside of the institute and unforgettable,

adventurous and enjoyable conference trips.

In addition, I would like to thank all the students, Jan-Niklas Paprott, Alexander Hoffmann,

Joel Kröpelin, Hossam Houta, Jöran Hahn, Katja Rieß, Marc Baranski, Christian Schwager,

Jan Reinhardt, Neven Boyanov, Thomas Rosen, Markus van Hünsel, Lukas Körnich, Lennart

Weitz and Lennart Böse, whom I had the chance to supervise, for the amazing collaboration

and their valuable contribution to this thesis.

Finally, I would like to express my deepest and sincerest gratitude to my family especially

my parents Ali and Fattouma, thank you for your sacrifices, you are by far the two best,

kindest, generous, supportive and cheerful people I know, my reliable brothers Rabih,

Hussein, Abbas and Hassanein, my dear and selfless sister Abir and her husband Tarek

Ghaddar thank you for always supporting me, my kind and beautiful wife Dr. Rer. Nat.

Tanja Vajen and my best friends, μαλάκας Kostas Saxonis, "yellowjacket" Ali Zaraket and

"Bekh" Bahaa Berjewei, thank you for being part of my life and always there for me.

Aachen, November 2017

Hassan Harb

ix

Abstract

This thesis presents a generalized methodology, supported by a software framework,

for modeling and assessing mathematical programming based predictive demand side

management (DSM) strategies that exploit thermal and electrical flexibilities of residential

building energy systems (BES) to enhance the integration of renewable energy sources.

The modeling and simulation platform is formulated in Python and includes a set of

forecasting methods as well as a discrete mixed integer linear programming (MILP)

modeling library based on the Gurobi optimizer API. The platform further integrates a

non-linear BES simulation model in Dymola/Modelica as a functional mock-up unit (FMU).

The evaluation of the forecasting algorithms shows that the lowest forecast error for

predicting electrical and space heating demands is provided by SVR and for predicting

the weather variables, i.e. temperature and solar irradiation, by ARMA, respectively. The

persistence method is selected for predicting the strongly stochastic domestic hot water

demand.

The introduced scheduling HEMS models for individual buildings consist of a deterministic

MILP strategy and a multi-stage stochastic programming (SP) approach that extends the

MILP model while incorporating the uncertainties of the electrical and domestic hot

water demands. The city district DSM strategies comprise a centralized approach, which

serves as a benchmark, as well as distributed formulations based on decomposition

techniques. In this work, two distributed DSM approaches are formulated, Dantzig-

Wolfe decomposition based column generation (CG) algorithm as well as an integrated

Lagrangian decomposition column generation (LRCG). The performance of the scheduling

algorithms for individual buildings is evaluated for different BES configurations. The

results indicate that predictive HEMS with perfect information enhance the integration of

locally generated electrical power from PV units and enables a significant potential of load

shifting and cost reduction with respect to a reactive control strategy. Employing point

forecasts of weather and energy demand variables within the deterministic scheduling

model reduces this potential but further allows for a higher integration of PV power

as well as cost reduction compared with a reactive strategy. The multi-stage SP model

outperforms the deterministic approach but induces larger modeling and computation

effort. The analysis of the DSM strategies for city districts shows that the CG approach

provides comparable coordination performance as the centralized model while significantly

reducing the computation time. Further, the integrated LRCG approach enables a faster

convergence compared with the standard CG formulation.

xi

Zusammenfassung

Diese Arbeit stellt eine Methodik und ein Software-Framework vor, um prädiktive Demand-

Side-Management-Strategien (DSM) zu modellieren und zu evaluieren. Das Ziel dabei

ist es, die thermische und elektrische Flexibilität von Gebäudeenergiesystemen (GES)

auszuschöpfen, um die Integration von erneuerbaren Energiequellen zu fördern. Die

Modellierungs- und Simulationsplattform ist in Python formuliert und enthält verschiedene

Prognosemethoden sowie eine GES-Modellierungsbibliothek auf Basis der Gurobi-Optimizer-

API. Des Weiteren ist ein nicht-lineares GES-Dymola/Modelica-Modell als Functional

Mock-Up-Unit (FMU) in die Plattform integriert.

Die Evaluierung der Vorhersagemethoden zeigt, dass Support-Vector-Regression den ger-

ingsten Prognosefehler bei der Vorhersage des elektrischen und des Raumwärmebedarfs

erlaubt. ARMA liefert das beste Ergebnis für die Vorhersage der Wettervariablen, wie

Temperatur oder Sonnenstrahlung. Die Persistenz-Methode wird für die Vorhersage des

Warmwasserbedarfs verwendet.

Die vorgestellten Heimenergiemanagementsysteme (HEMS) für einzelne Gebäude beste-

hen aus einer deterministischen GGLP-Strategie sowie einem mehrstufigen stochastischen

Programmierungsansatz (SP), der das GGLP-Modell erweitert und dabei die Unsicherheit-

en der elektrischen und thermischen Anforderungen berücksichtigt. Die DSM-Strategien

für Stadtquartiere umfassen einen zentralisierten Ansatz, der als Benchmark dient, sowie

verteilte Formulierungen auf Basis von Dekompositionsverfahren. In dieser Arbeit werden

zwei verteilte DSM-Ansätze formuliert: Dantzig-Wolfe-Decomposition basierte Column-

Generation-Algorithmen (CG) sowie eine integrierte Lagrange-Decomposition-Column-

Generation (LRCG). Die Ergebnisse zeigen, dass prädiktive HEMS mit perfekter Informa-

tion die Einbindung von lokal erzeugtem PV-Strom erhöhen und ein großes Potenzial der

Lastverschiebung und Kostenreduzierung gegenüber einer reaktiven Steuerstrategie er-

möglichen. Der Einsatz von Prognosen der Wetter- und Energiebedarfsvariablen innerhalb

des deterministischen Scheduling-Modells reduziert dieses Potenzial, ermöglicht aber

dennoch eine höhere Einbindung von PV-Strom sowie eine Kostenreduzierung gegenüber

der reaktiven Strategie. Das SP-Modell übertrifft den deterministischen Ansatz, bewirkt

aber einen größeren Modellierungs- und Berechnungsaufwand. Die Analyse der DSM-

Strategien für Stadtquartiere zeigt, dass der CG-Ansatz eine vergleichbare Koordination

wie das zentrale Modell bietet und gleichzeitig den Rechenaufwand deutlich reduziert.

Darüber hinaus ermöglicht der integrierte LRCG-Ansatz eine schnellere Konvergenz

gegenüber der standard CG-Formulierung.

xiii

Contents

Nomenclature xviii

List of figures xxiii

List of tables xxviii

1 Introduction 1

1.1 Background: Trends and challenges . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 "Energiewende": Energy transition and consequences . . . . . . . . . . . . . . . 1

1.1.2 Building energy systems: Decentralization and flexibility . . . . . . . . . . . . . 2

1.2 Demand side management: Review . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Classification: Triggering criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.2 Objectives for scheduling strategies . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.3 Target devices in DSM concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.4 Approaches: Decision scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.5 Forecast models in predictive scheduling . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.6 Scheduling algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.7 Architecture of DSM strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3.1 Modeling of heating energy systems . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3.2 Flexibility and extensibility of the modeling approach . . . . . . . . . . . . . . . 10

1.3.3 Uncertainty of underlying forecast models . . . . . . . . . . . . . . . . . . . . . . 11

1.3.4 Scalability of the DSM strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.4 Thesis statement and contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.5 Structure of this work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Methodology: Framework 17

2.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Software configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.1 Framework programming language . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.2 MILP optimization solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3.3 Dynamic simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

xv

3 Inputs: Synthesis and Forecast 25

3.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Forecasting methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.1 Persistence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.2 ARMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.3 SVR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.4 Performance indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.5 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4 Modeling of Building Energy Systems: Mathematical Programming

Formulation 35

4.1 Heat pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Micro combined heat and power unit . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3 Electrical heating element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.4 Gas boiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.5 Photovoltaic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.6 Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.7 Water tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.7.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.7.2 Definition of SoC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.7.3 Experimental evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.8 Building wall mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.8.1 Modeling: Grey-box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.8.2 Model identification approach: Parameterization . . . . . . . . . . . . . . . . . . 59

5 Scheduling Algorithms 61

5.1 Mathematical optimization: Fundamentals . . . . . . . . . . . . . . . . . . . . . . 61

5.2 Single building scheduling approaches . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2.1 Deterministic MILP model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2.2 Scheduling under uncertainty: Multi-stage stochastic programming . . . . . . 64

5.3 City district scheduling approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.3.1 Centralized scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.3.2 Distributed scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6 Analysis: Results and Discussion 79

6.1 Scheduling for single buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.1.1 Design and configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.1.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.2 Distributed scheduling for neighborhoods . . . . . . . . . . . . . . . . . . . . . . 90

6.2.1 Design and configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.2.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

7 Conclusion and Outlook 99

7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

A Appendix 105A.1 Single building evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105A.1.1 PV-HP-EH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105A.1.2 PV-HP-EH-Bat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106A.1.3 PV-CHP-EH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108A.1.4 PV-CHP-EH-Bat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110A.1.5 PV-CHP-B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111A.1.6 PV-CHP-B-Bat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Bibliography 115

Nomenclature

Symbols and Units

Symbol Description Unit

af absorption coefficient (short-wave) of the exterior surface -

A area m2

cw specific heat capacity of water for constant pressure J/(kgK)

cgas specific gas price ct/kWh

cbuy specific price for bought electricity ct/kWh

csell specific price for sold electricity ct/kWh

C area specific thermal capacity in Grey-Box model Wh/(m2 K)

C pn cost of a proposal p by a subproblem n e

COP coefficient of performance -

DoD depth of discharge %

E energy J

I current A

L length m

Lmod modulation level %

m mass flow kg/s

p autoregression order -

q moving average order -

P power W

Q energy content Wh

Q heat flow W

R area specific thermal resistance in Grey-Box model (m2 K)/W

s scenario -

SoC state of charge %

t time index s

tH moving window horizon s

T temperature K, °C

u binary on/off status -

uc electricity consuming unit -

continued on next page

xix

Nomenclature Nomenclature

Symbols and Units

Symbol Description Unit

ug electricity generation unit -

U voltage V

V volume m3

V volume flow m3/s

m mass flow kg/s

xloss,∆t thermal loss coefficient %

y prediction value W

y measurement value W

zl layer height in water storage m

Greek Symbols

Symbol Description

α PV temperature coefficient %/K

αA heat transfer coefficient W/(m2 K)

εi forecasting error W

η efficiency %

∆t time step length or resolution s

γ quotient between the area of interior or exterior walls and

floor area

-

φ support vector regression kernel -

ksto storage thermal transmittance W/(m2 K)

λ thermal conductivity of water W/(m2 K)

π shadow price ct/kWh

πs probability %

σ CHP power to heat ratio -

ρ volumetric density kg/m3

v binary variable -

w binary variable -

Nomenclature

Indices and Abbreviations

Acronym Description

a ambient

AIC akaike information criterion

amb ambient

ANN artifical neural network

API application programming interface

AR auto regression

ARMA auto regression moving average

ARMAX auto regression moving average with exogenous input

BAT battery

BES building energy system

CHP combined heat and power

CG column generation

CS cross sectional

dem demand

DHW domestic hot water

DP dynamic programming

DR demand response

DSM demand side management

DWD Dantzig-Wolfe decomposition

E expected value

EA evolutionary algorithm

EH electrical heater

el electrical

env environment

eq equivalent

FMI functional mock-up interface

FMU functional mock-up unit

GA genetic algorithm

GHG greenhouse gas emissions

GUI graphical user interface

HEMS home energy management system

HP heat pump

HiL hardware in the loop

continued on next page

Nomenclature Nomenclature

Indices and Abbreviations

Acronym Description

in interior

ia indoor air

init inital

l storage water layer

LB lower bound

LD Lagrangian decomposition

LP linear program

LR Lagrangian relaxation

MAPE mean absolute percentage error

MAS multi-agent system

MILP mixed integer linear program

MINLP mixed integer non linear porgram

MPC model predictive control

noct nominal operation cellt temperature

NAC non-anticipativity constraint

NP non-deterministic ploynomial-time

NRMSE normalized toot mean squared error

PV photovoltaic

RBF Radial Basis Function

RE renewable energy

ret return

s scenario

SA simulated annealing

SARIMA seasonal auto regression integrated moving average

SH space heating

SLP standard load profile

SP stochastic programming

sto storage

SVR support vector regression

tap tapping

th thermal

TRY test reference year

TS thermal storage

UB upper bound

List of Figures

1.1 Development of renewable energy sources in Germany with regard to the share

in gross electricity generation based on the data from [Federal ministry for

economic affairs and energy, 2015b] . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Potential of buildings within the energy transition: Energy consumption by

the field of application in Germany in 2014; data from [Federal ministry for

economic affairs and energy, 2015a] . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Illustration of discrepancy between electrical demand and local PV generation

as well as load shifting strategies through demand modification and storage

management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Overview on the characterizing features of DSM concetps . . . . . . . . . . . . . 4

1.5 Descriptive illustration of the thesis outline . . . . . . . . . . . . . . . . . . . . . . 15

2.1 Overview on the individual components and basic formulation of a predictive

HEMS. The inputs comprise weather, space heating, domestic hot water, electri-

cal demand, PV generation and occupancy. The building energy system includes

battery, CHP, electrical, building wall mass, HP and water storage tanks . . . . 17

2.2 Simplified illustration of the concept of the rolling horizon algorithm. The

rescheduling interval denotes the time between the scheduling steps or schedul-

ing re-initialization whereas the scheduling horizon defines the length of

scheduling step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 System testing and evaluation within the PyMPC framework. The left box rep-

resents the scheduling model which uses forecast and linearized BES models,

whereas the right box represents the realization platform which includes actual

weather and demands as well as non-linear BES dynamic simulation models

(integrated as a FMU) or HiL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 PyMPC framework structure and task diagram . . . . . . . . . . . . . . . . . . . . 20

2.5 Simplified overview on the space heating supply system within the dynamic

simulation models [Müller et al., 2015]. The main components are the thermal

zone which represents the thermal behavior of the building, the hydraulic

connection, the heat generation system e.g. HP and CHP and thermal storage

units as well as the rule-based control strategy . . . . . . . . . . . . . . . . . . . 22

2.6 Integration of the Modelica/Dymola dynamic BES simulation model within the

PyMPC framework as co-simulation Python FMU based on the FMI interface . 24

xxiii

List of Figures

3.1 Interconnection of weather, occupancy, demand and PV profiles. Occupancy

is only influenced by weather conditions and used to derive the electrical

and domestic hot water demands. PV generation is determined based on the

weather variables. Space heating is influence by the internal thermal gains

from active occupancy, electrical consumption and weather . . . . . . . . . . . 25

3.2 Stochastic occupancy based generation of demand profiles. The depicted

profiles, from top to bottom, are the electrical demand, occupancy and domestic

hot water demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Input data for the single building evaluation. The depicted profiles, from top

to bottom, are the domestic hot water, electrical demand, PV generation and

space heating demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4 Illustration of the transformation process from the input space to the high-

dimensional feature space, by applying the kernel function φ, within a SVR

model [Hong, 2013] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.5 Electrical demand forecast results for the 5th of May using the daily persistence,

ARMA and SVR methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.6 Domestic hot water forecast results for two consecutive days, 5th and 6th of

May, using the daily persistence, ARMA and SVR methods . . . . . . . . . . . . 32

4.1 Illustrative overview of possible energy demand, generation and storage units

as well as their thermal and electrical interactions within a residential building

energy system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 COP and heat generation power development with respect to the ambient

temperature of an ASHP ’Dimplex A/W LA6TU’ for different application tem-

peratures [Dimplex, 2017] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.3 Characteristic voltage, current and electrical power trends during the charging

process of a Li-Ion battery storage system . . . . . . . . . . . . . . . . . . . . . . . 42

4.4 Illustration of the energy balance for a middle layer; the heat flows represent

the charging heat from the heat generation unit, the heat conduction between

neighboring layers, the drawn heat from the consumer cycle and losses to the

tank surrounding environment [Schütz et al., 2015a] . . . . . . . . . . . . . . . . 45

4.5 Generic representation of the different states for the SoC of the empirical

approach. The black solid line depicts the temperature profile [Harb et al., 2017] 47

4.6 Consideration of the usable and unusable amount of energy for the determina-

tion of the SoC [Harb et al., 2017] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.7 Experimental scehme depicting the supply unit for the storage during the

charging cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

List of Figures

4.8 SoC comparison of the storage modeling approaches with the respect to mea-

surement data for use case 1; The stratified storage model comprises 5 layers

while Cunusabl e is represented by the factor f and set to the value 0.5 . . . . . . 52

4.9 Comparison of the development of the temperature profile for the measured

data and the stratified storage model in use case 1 . . . . . . . . . . . . . . . . . 53

4.10 SoC comparison of the storage modeling approaches with the respect to mea-

surement data in use case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.11 SoC comparison of the storage modeling approaches with the respect to mea-

surement data in use case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.12 4R2C model structure [Harb et al., 2016a] . . . . . . . . . . . . . . . . . . . . . . 57

5.1 Derivation of the scenarios’ probabilities π(s) from the root to the leaf nodes

within the scenario tree of multi-stage stochastic programming . . . . . . . . . 65

5.2 Uncertainty characterization of DHW demand. In the left diagram, the expected

value is depicted as a black solid line and the scenarios in grey color. In the

right diagram, the reduced scenario set is depicted stage-wise. Three scenarios

(states) are chosen to represent every stage [Harb et al., 2016b] . . . . . . . . 66

5.3 Uncertainty characterization of electrical demand: scenario samples and re-

duced set [Harb et al., 2016b] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.4 Scenario tree structure for a four-stage problem with three states respectively

[Harb et al., 2016b] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.5 Structure of a Dantzig-Wolfe decomposition model as well as the interactions

between the master- and subproblems based on shadow prices and proposals

[Bradley et al., 1977] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.6 Procedural description of the column generation algorithm [Harb et al., 2015] 73

5.7 Relation between column generation and Lagrangian relaxation [Nishi et al.,

2009] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.8 Procedural description of the integrated Lagrangean relaxation - column gen-

eration algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.1 State-based representation of HP-EH-Bat reactive control strategy; The transi-

tions are defined in function of the thermal storage and battery status . . . . . 81

6.2 Dynamic performance of the thermal side for PV-HP-EH under the Ref strategy.

The depicted profiles, from top to bottom, are the space heating and domestic

hot water demands, the thermal power of the HP, the On/Off operation status of

the HP, the thermal generation of the auxiliary EH and the state of charge of

the water storage tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

List of Figures

6.3 Dynamic performance of the thermal side for PV-HP-EH under the DPI strategy.

The solid lines represent the operation status delivered by the MILP scheduling

algorithm whereas the dashed lines represent the operation within the dynamic

simulation model formulated in Dymola/Modelica . . . . . . . . . . . . . . . . . . 83

6.4 Dynamic performance of the electrical side for PV-HP-EH under the DPI strategy.

Pdemand denotes the elctrical demand, Pimport and Peyport the electrical import

and export from the public grid, PPV the local PV electricity generation, PHP

and PEH the electrical consumption of the HP and EH units . . . . . . . . . . . . 84

6.5 Dynamic performance of the thermal side for for PV-HP-EH under the DF strategy 86

6.6 Computation time comparison between DPI, DF and SP scheduling models; The

values denote the average time for computing one day-ahead schedule; The

arrow indicate the increase of computation time in percentage of SP models

compared to DF; The simulations were carried out on a work-station with 12

active cores Intel Xeon CPU E5-26670@2.9 GHz and 32 GB of RAM . . . . . . . 89

6.7 Schedule profiles for a random day in February using the centralized and dis-

tributed approaches. ’D-R’ denotes the residual load, with ’D’ as the aggregated

electrical demand of lights and appliances for the participating buildings and

’R’ the renewable energy from wind and PV units; large negative value indicate

high availability of renewable energy. ’I-E’ represents the cluster’s interaction

with the public grid, with I and E as the electricity imported to and exported

from the cluster, respectively [Harb et al., 2015] . . . . . . . . . . . . . . . . . . . 91

6.8 Grid interaction (I-E) for the centralized and distributed scheduling approaches

over one year with respect to the residual load (D-R) [Harb et al., 2015] . . . . 92

6.9 Influence of including/excluding the production costs in the buildings’ proposals

on the grid interaction, over one year with respect to the hour of the day, within

the distributed approach. The green range indicates the desired self-sufficient

status, the blue range denotes electricity exports from the mircogrid whereas

the yellow to red range denotes electricity import [Harb et al., 2015] . . . . . . 93

6.10 Computation time analysis of the centralized and CG distributed scheduling

models for the coordination of two clusters comprising 34 and 102 buildings.

The arrow represents the computation time reduction achieved by the dis-

tributed approach compared with centralized. The other percentage ratios

denote the increase of the computation time when increasing the cluster size

within every approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

6.11 Convergence assessment of the CG (in black) and integrated LRCG (in red)

algorithms for a random day in March. The solid lines represent the develop-

ment of the linearly relaxed primal solution of the master problems whereas the

dashed lines depict the development of the lower bounds. The cross markers

denote the integer solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

List of Figures

6.12 Assessment of the primal zLRDW and integer zRDW solution, as well as the

computation time of the CG and integrated LRCG distributed scheduling ap-

proaches. Within the boxplot, the bottom and top of the box are the first and

third quartiles (25 % and 75 %), while the band inside is the median. The

whiskers represent a 1.5 multiple of the interquartile range. The ’+’ markers

denote the outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

A.1 Dynamic performance of the thermal side for PV-HP-EH under the SPdhw strategy105

A.2 Dynamic performance of the thermal side for PV-HP-EH under the SPel strategy106

A.3 Dynamic performance of the thermal side for PV-HP-EH-Bat under the Ref

strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

A.4 Dynamic performance of the thermal side for PV-HP-EH-Bat under the DPI

strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

A.5 Dynamic performance of the thermal side for PV-HP-EH-Bat under the DF strategy107

A.6 Dynamic performance of the electrical side for PV-HP-EH-Bat under the DF

strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

A.7 Dynamic performance of the thermal side for PV-CHP-EH under the DPI strategy108

A.8 Dynamic performance of the electrical side for PV-CHP-EH under the DPI strategy109

A.9 Dynamic performance of the thermal side for PV-CHP-EH under the DF strategy109

A.10 Dynamic performance of the thermal side for PV-CHP-EH-Bat under the DPI

strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

A.11 Dynamic performance of the electrical side for PV-CHP-EH-Bat under the DPI

strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

A.12 Dynamic performance of the thermal side for PV-CHP-EH-Bat under the DF

strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

A.13 Dynamic performance of the thermal side for PV-CHP-B under the DPI strategy 111

A.14 Dynamic performance of the electrical side for PV-CHP-B under the DPI strategy112

A.15 Dynamic performance of the thermal side for PV-CHP-B under the DF strategy 112

A.16 Dynamic performance of the thermal side for PV-CHP-B-Bat under the DPI

strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

A.17 Dynamic performance of the electrical side for PV-CHP-B-Bat under the DPI

strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

A.18 Dynamic performance of the thermal side for PV-CHP-B-Bat under the DF strategy114

List of Tables

3.1 Summary of the performance of the daily persistence, ARMA and SVR models

for forecasting the HEMS input profiles over an assessment period of 30 days

with a time resolution of 15 min and a forecast horizon of 24 h . . . . . . . . . . . 32

4.1 Parameters of ECOPower 3.0 [Vaillant, 2017] . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Parameters of a Schott PV module [Schott, 2017] . . . . . . . . . . . . . . . . . . . 41

4.3 Parameters of the battery model [Sundstrom O., 2010] . . . . . . . . . . . . . . . . 43

4.4 Configuration within the investigated use cases . . . . . . . . . . . . . . . . . . . . 51

4.5 Specific parameters boundaries [DIN - German Institute for Standardization,

2005, Recknagel et al., 2009, Association of Engineers, 2012a] . . . . . . . . . . 60

6.1 BES configurations: The characteristics of the primary heat generators, Dimplex

air-to-water LA9TU HP (QA2W35 = 7.5 kW) and Vaillant EcoPower 3.0 CHP (P =

3 kW, Q = 8 kW) are presented in Chapter 4 . . . . . . . . . . . . . . . . . . . . . . 80

6.2 Assessment results of the scheduling strategies for all BES configurations during

the months March, September and December. The optimization time resolution

is 15 min, the rolling horizon’s rescheduling interval and scheduling horizon are

24 and 48 h, respectively. The MIP gap is set to 1 % for DPI and DF and 1.5 %

for SPel and SPdhw. The costs are weekly averaged. Negative VS, VPI and VU

indicate a cost reduction whereas positive values denote an increase with respect

to the costs of the Ref , DPI and DF, respectively . . . . . . . . . . . . . . . . . . . . 87

xxix

1 Introduction

1.1 Background: Trends and challenges

1.1.1 "Energiewende": Energy transition and consequences

The impact of increased social awareness and concern about the potential consequences

of greenhouse gas (GHG) emissions is reflected in the energy and climate policy targets of

the German government, mainly, within the set of decisions taken in 2011 known as the

"Energiewende" or energy transition. This transition refers to a fundamental reformation

of the electricity sector to a decarbonized energy system mainly based on renewable

energy (RE) i.e. wind and solar, with emphasis on increased energy efficiency.

1990

1995

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

Year

0

5

10

15

20

25

30

35

Share

of

RE e

lect

rici

ty g

enera

tion in %

3.65.4

7.0 7.18.3 8.0

9.8 10.611.6

14.214.816.116.8

20.4

22.923.9

25.8

30.0

Hydro + biomass

PV

Wind

Figure 1.1: Development of renewable energy sources in Germany with regard to theshare in gross electricity generation based on the data from [Federal ministryfor economic affairs and energy, 2015b]

This resulted in a significant increase of the share of renewable electricity generation

1

Introduction

which reached 30 % in 2015, corresponding to double the share of 2010. Figure 1.1 shows

the development of RE in Germany over the past 25 years. The intermediate goal of

reaching 35 % by 2020 is foreseen to be exceeded. The long-term goal is set to increase

the RE contribution to 80 % by 2050.

This rapid increase led to concerns with regard to the grid stability and supply security as

the accommodation of the rising share of volatile RE has proven to be a major challenge

[Stoyanova et al., 2013]. In contrast to conventional power plants, RE sources are

only partially dispatchable and characterized by distributed and uncertain generation.

Consequently, an adaptation of the energy system is required, mainly flexibility from other

parts of the system is required to achieve the balancing needs and ensure the network

reliability. These increased balancing needs may be addressed by a number of strategies

that include energy storage and increased flexibility of the demand side.

1.1.2 Building energy systems: Decentralization and flexibility

Buildings account for more than one third of the total primary energy consumption.

Mainly, the space heating share amounts to around to 30 % as shown in Figure 1.2. Hence,

buildings can play an important role in the energy transition.

2%3%

5%

22%

27%

2% 39%

ICT

Lighting

Domestic hot water

Other process heat

Spaceheating

Other process refrigeration

Mechanical energy

Figure 1.2: Potential of buildings within the energy transition: Energy consumption bythe field of application in Germany in 2014; data from [Federal ministry foreconomic affairs and energy, 2015a]

The promotion of RE and energy efficiency as part of the "Energiewende" strategy has

led to an increased installation of photovoltaics (PV) panels and modern heating systems

i.e. heat pumps (HPs) and micro combined heat and power (µCHP) units in residential

buildings. This resulted in the following trends:

2

1.2 Demand side management: Review

. electricity generation, through distributed PVs and (µCHPs), is switching from a

power plants based centralized structure towards a decentralized structure which

poses a challenge for the grid stability

. passive consumers are transforming into prosumers 1 that can participate directly in

the energy market

. flexibility in energy generation and consumption on the demand side is emerging.

This is achieved by coupling modern heating systems, HPs and CHPs with thermal

storage, PVs with electrical storage units i.e. batteries or through management of

electric vehicles or shiftable home appliances. Notably, the potential of the electrical

flexibility generated from heating systems is significant when considering the share

of space heating in the total energy consumption. The operational flexibility provided

by buildings can be exploited by intelligent control strategies to enable load shifting

which represents the "backbone" of the future concept of smart grid 2 and provide

the balancing needs for stabilizing the grid. These strategies are widely known as

demand side management.

1.2 Demand side management: Review

Demand side management (DSM) is generally defined as the modification of energy

demand of consumers through different methods such as financial incentives. The main

implementation mechanisms of DSM are short-term demand response (DR) and long-term

energy efficiency programs. According to [Albadi and El-Saadany, 2008], DR is defined

as “intentional electricity consumption pattern modifications by end-use customers that

are intended to alter the timing, level of instantaneous demand, or total electricity

consumption”. There are two general approaches to DR programs:

. direct load control which employs a load signal

. indirect load control respectively pricing-based approach which employs a price

signal e.g. time-of-use or real-time pricing

Recently, home energy management systems (HEMS) have emerged for local load man-

agement at the consumer side. According to [Beaudin and Zareipour, 2015], HEMS

are defined as residential DR tools that shift or curtail demand to improve the energy

consumption and production profile of a building on behalf of a consumer by providing

optimal operation schedules.

1This term denotes a new class of consumers that both consume and produce electrical energy throughlocally installed µCHPs or PVs

2The smart grid concept refers to an increased use of digital information and controls technology to integratecentralized and decentralize electricity generators, consumers and storage units and improve reliability,security, and efficiency of the electric grid.

3

Introduction

𝑡

Demand

PV generation

Storage management Demand modification

Figure 1.3: Illustration of discrepancy between electrical demand and local PV generationas well as load shifting strategies through demand modification and storagemanagement

Figure 1.3 exemplary depicts the discrepancy between a consumer’s electrical demand

and local PV generation. Further, it illustrates the strategies i.e. storage management and

demand modification, employed by a HEMS for adapting the consumption to enhance the

integration of PV. Storage management targets the surplus of PV generation while demand

modification adjusts the electrical demand according to the availability of PV generation.

DSMfeatures

Classification

Objectives

Targetdevices

Decisionscope

Forecastmodels

Schedulingalgorithms

Architecture

Figure 1.4: Overview on the characterizing features of DSM concetps

Numerous works in the literature provide in-depth reviews on HEMS or building energy

4

1.2 Demand side management: Review

management systems [Javaid et al., 2013, Khan et al., 2015, Vega et al., 2015, Beaudin

and Zareipour, 2015, Lee and Cheng, 2016], scheduling in buildings [Lazos et al., 2014,

Cardozo, 2014], and DR concepts [Albadi and El-Saadany, 2008, Barbato et al., 2013, Kosek

et al., 2013, Ansari, 2014, Adika and Wang, 2014, Siano, 2014, Müller et al., 2015, Vardakas

et al., 2015, Olatomiwa et al., 2016]. Accordingly, the main characteristic features of DSM

concepts are identified and illustrated in Figure 1.4.

1.2.1 Classification: Triggering criteria

DR programs can be categorized according to economic or reliability drivers [Siano, 2014].

Reliability programs target high-voltage connected customers e.g. large commercial and

industrial entities, and yield to technical objectives that are services to the grid, such

as frequency and voltage control, and power quality. The economic category addresses

customers available at low-voltage networks while providing economic incentives.

1.2.2 Objectives for scheduling strategies

The objectives for operation scheduling in HEMS vary depending on the consumer, the

application and DR framework. The list includes:

. energy costs reduction e.g. minimization of energy wastage

. increase consumer comfort and well-being

. environmental concerns e.g. GHG emissions’ reduction

. load profiling which evaluates the desirability of the load profile to some party such

as:

• reducing grid dependency for the consumer

• reducing peak demand for the utility

• adapting to the variations in power supply from renewable energy sources to

reduce the undesirable power imbalance (smart grid application).

1.2.3 Target devices in DSM concepts

According to the survey provided in [Beaudin and Zareipour, 2015], the majority of

HEMS and DR studies in the literature typically target electrical appliances or white

goods such as time-shiftable loads notably washing machines, dryers and dishwashers

as well electrical storage systems mainly stationary batteries and electric vehicles. The

underlying models of these electrical components are, to a certain extent, simple to

5

Introduction

formulate in the scope of mathematical optimization. In contrast, the scheduling of

heating systems, aside from electrical heater is scarcely addressed in the literature.

[Gunkel et al., 2012, Shaneb et al., 2012, Bakker, 2012, Di Zhang et al., 2013, Zapata

et al., 2014] formulated scheduling strategies for distributed µCHPs while [Adika and

Wang, 2014, Fink et al., 2015] incorporated a simplified HP model into a HEMS concept.

1.2.4 Approaches: Decision scope

HEMS can be classified into reactive and predictive approaches. Reactive HEMS are

typically heuristics, i.e. knowledge based techniques, that approximate solutions based

on certain prescribed rules for the actual system state, uniquely, with no consideration

of predictions. Hence, reactive HEMS are also referred to as online scheduling [Fohler,

2011]. An example of this approach for energy management in residential building is

provided in [Moshövel et al., 2015]. The development of heuristics require extensive

experience and knowledge about the considered system and are case-specific strategies

that cannot be generalized for other systems. The main advantage of a well-designed

heuristic is the low computational effort required for generating a good solution. Yet,

heuristics are difficult to derive for complex architectures including different components.

However, reactive HEMS have been recently formulated as multi-agent system (MAS)

concepts. MAS is a negotiation based framework which is characterized by a flexible and

extensible architecture. A notable example is provided by the ’PowerMatcher’ model in

[Kok et al., 2005].

Predictive HEMS incorporate forecasts for estimating states to provide an optimal sched-

ule under future conditions. Predictive HEMS are also known as proactive scheduling as

well as unit commitment. They are also referred to as preventive scheduling when infor-

mation about the behavior of uncertainties is considered in the formulation. Predictive

HEMS rely on a mathematical program or meta-heuristic for the scheduling model.

Typically, in the literature [Castro et al., 2010, Beaudin et al., 2012, Kopanos and Pis-

tikopoulos, 2014, Fang and Lahdelma, 2016] predictive scheduling is implemented in

a moving window framework, also referred to as sliding window, rolling or receding

horizon algorithms, which is similar to a model predictive control (MPC) methodology.

This framework is used to reduce the computational effort and increase the accuracy

of the scheduling by updating the forecasts in a cyclic manner which allows for react-

ing to disturbances, depending on the rescheduling rate, which is a feature of reactive

scheduling.

Through embedding forecasts, preventive HEMS and DR are expected to hold an advan-

tage over classical reactive approaches for the accommodation of volatile RE especially in

scenarios with a large share of renewable generation capacity.

6

1.2 Demand side management: Review

1.2.5 Forecast models in predictive scheduling

Proactive HEMS or scheduling incorporates several forecasts as inputs. These include

predictions of weather conditions e.g. solar irradiation and outdoor temperature, PV and

wind power generation, occupancy, as well as energy consumption behavior i.e. space

heating, domestic hot water and electrical demand.

Forecast models have been heavily investigated in the literature [Suganthi and Samuel,

2012, Veit et al., 2014] but still continue to evolve. Prediction methods are broadly

grouped in:

. black box models which are data driven formulated and require no knowledge about

the physical characteristics of the system. These comprise regression and machine

learning techniques as well as modified formulations i.e. adaptive and stochastic

models. These models are widely used in the literature [Hong, 2013, Suganthi

and Samuel, 2012]. The field of applications includes price, weather variables, PV

generation, electrical and thermal demand prediction among many others

• regression based methods include: (a) Statistical time series techniques which

use historical data as the basis of estimating future outcomes such as exponen-

tial smoothing, Holt-Winters method [Hoverstad et al., 2015], autoregressive

model i.e. ARMA, ARIMA, SARIMA (b) Causal methods which embed an ex-

ogenous input in the forecast model such as ARMAX and multiple regression

models [Bacher and Madsen, 2011]

• machine learning algorithms mainly artificial neural networks (ANN) [Frausto

and Pieters, 2004] and support vector regression (SVR) are the most known

black box models. These methods are widely applied to tackle complex defined

problems due to their strong non-linear learning ability and potential to be

made adaptive and self-learning

. white box models which are based on detailed physical representation of a specific

system [Li and Wen, 2014]. This approach is exhaustively applied for predicting the

building thermal behavior i.e. space heating demand or indoor air temperature

. grey-box models [Kristensen et al., 2004] that denote an intermediate stage between

white and black models and are typically applied to predict the thermal behavior as

well.

It is worthwhile to note that despite the advances in formulating complex forecast methods,

the naive prediction model remains a hard to beat approach for many applications [Veit

et al., 2014]. This is emphasized by the almost non-existing modeling and computational

burden. A naive prediction is a persistence routine based on cycle pattern i.e. prediction

for today is yesterday (daily persistence) or the corresponding day of past week (weekly

persistence).

7

Introduction

1.2.6 Scheduling algorithms

Several approaches have been proposed in the literature to schedule residential energy

systems. These can be categorized into:

. Mathematical optimization or programming:

• linear programming (LP) [Shaneb et al., 2012], quadratic programming (QP),

dynamic programming (DP) [Chang et al., 2012, Nguyen et al., 2012], mixed

integer linear programming (MILP), mixed integer non-linear programming

(MINLP) [Zhang et al., 2012]

• decomposition techniques such as Lagrangian Relaxation (LR) or Lagrangian de-

composition (LD) [Zelazo et al., 2012, Zhang et al., 2013, Diekerhof et al., 2014],

Benders decomposition and Dantzig-Wolfe decomposition (DWD) [Dantzig, 1965]

combined with the column generation algorithm [Gauthier et al., 2014]

• robust optimization [Ferreira et al., 2012] and stochastic programming.

. Meta-heuristic [Hutterer et al., 2010, Rahman et al., 2014, Huang et al., 2015,

Gamarra and Guerrero, 2015]: bio inspired evolutionary algorithms (EA), population

based genetic algorithm (GA) and particle swarm optimization (PSO), trajectory

based simulated annealing (SA) and tabu-search method (TSM).

. Heuristics: rule based or knowledge based techniques [Moshövel et al., 2015] and

priority listing [Delarue et al., 2013].

In LP, all decision variables are continuous, hence, on/off decisions, which are formulated

as binary variable, cannot be modeled. Hence, the suitability of LP for scheduling problems

is quite limited. MILP extends LP to allow for binary or integer variables modeling which

makes the problem then NP-hard 3. MILP based unit commitment is the most widely

used approach for formulating scheduling problems for HEMS and DR e.g. [Bozchalui

et al., 2012, Zhu and Chin, W.M Fan,Z., 2012, Gunkel et al., 2012, Beaudin et al., 2012, Di

Zhang et al., 2013, Wakui et al., 2014, Zapata et al., 2014, Tenfen and Finardi, 2015, Fink

et al., 2015]. MINLP and metaheuristic enable non-linear modeling, however, they tend

to face convergence problems or get stuck in local optima. MILP provides a higher

chance of achieving a globally optimal solution compared with MINLP and meta-heuristics

as well as direct measure of the optimality a solution, the MIP gap. More importantly,

several powerful solver packages have been established and optimized for tackling such

problems, such as IBM CPLEX [IBM, 2017] and Gurobi [Gurobi Optimization, 2017]

optmizers. Yet, MILP restricts the model to a linear formulation which depending on the

linearization scheme adopted can greatly affect the validity or reliability of the solution

3Non-deterministic polynomial-time hard which increases the computational effort to find an optimal solution

8

1.3 Challenges

despite achieving global optimality conditions. Therefore, robust formulation should be

adopted to allow for minimal loss of performance information.

1.2.7 Architecture of DSM strategies

[Scattolini, 2009, Law et al., 2012, Kosek et al., 2013] provide an overview of control

and DR system architectures. The arrangements comprise centralized, decentralized and

hybrid or distributed architectures.

In centralized architectures, the central component has access to all information. The-

oretically, a centralized approach allows for achieving the best solution. However, the

difficulty in this approach lies in application bottlenecks such as scalability, computation

tractability, data privacy concerns and communication infrastructure.

Decentralized architectures eliminate several disadvantages of a centralized approach

on the cost of stability and optimality. In a decentralized architecture, the centralized

problem is decomposed into sub-systems with no direct coupling between them.

Hybrid or distributed architectures are formulated based on a trade-off between stability

and information exchange. In non-hierarchical distributed architectures, subsystems with

similar or opposite goals, interact directly with each other in a cooperative or competitive

manner. An example for non-hierarchical distributed architecture is provided in [Barbato

et al., 2013], which apply a game theory based scheduling model for residential DSM.

Hierarchical distributed architectures employ a multi-layer structure with a coordinator or

aggregator entity which coordinates the negotiation across the subsystems. Hierarchical

distributed structures are typically applied to MAS [Harb et al., 2014]. Further, it is well

suited for mathematical optimization decomposition methods such as LR and DWD [Harb

et al., 2015].

1.3 Challenges

Despite the numerous research activities in the field of DR and HEMS shown in the prior

review, several challenges persist to exist for the development and implementation in

residential building and neighborhoods [Baharlouei and Hashemi, 2013, Beaudin and

Zareipour, 2015]. The main challenges include:

. Modeling of heating energy systems

. Flexibility and extensibility of the modeling approach

. Uncertainty of underlying forecast models

. Scalability of the DSM strategy

9

Introduction

1.3.1 Modeling of heating energy systems

The majority of HEMS papers consider batteries or white goods as flexibility source

[Beaudin and Zareipour, 2015, Olatomiwa et al., 2016]. In the context of predictive

scheduling, the underlying mathematical optimization model complexity, specifically MILP

based, of heating units within building energy systems (BES) mainly the operational

dynamics of air-to-water heat pumps (AW-HPs), µCHPs and water storage tanks remains

taxing and not fully explored.

The MILP models of AW-HPs in the literature are simplified with no consideration of

part load operation or dynamic development of the coefficient of performance (COP),

heat output and electical consumption with respect to the evaporator and condenser

temperatures. The widespread formulation represents the COP as a fix value, for example

[Molitor et al., 2013, Diekerhof et al., 2014] or simple linear dependency of the outdoor air

temperature. This approach doesn’t allow for a robust representation of the HP operation,

which directly impacts the scheduling reliability.

Another critical gap is found in the modeling of thermal water storage tanks. [Schütz et al.,

2015a, Schütz et al., 2015b] indicate that the most widespread MILP representation of

thermal water storage tank is based on a single capacity model for example in [Di Zhang

et al., 2013, Wakui et al., 2014, Zapata et al., 2014, Molitor et al., 2013, Diekerhof et al.,

2014]. Further, the investigations [Schütz et al., 2015a, Schütz et al., 2015b] show that

this modeling approach is unable to deliver an accurate representation of the state of

charge of the storage which leads to scheduling infeasibilities .

1.3.2 Flexibility and extensibility of the modeling approach

The installation of PVs, solar thermal panels, modern heating supply systems such as

HPs and µCHPs, thermal storages, stationary batteries and electric vehicles has led to

an unprecedented heterogeneity of units, that are subject to different unique charac-

teristics and dynamics, within residential building energy systems. As a result, future

configurations may include a combination of different flexibilities such as two electricity

generators i.e. PVs and CHPs as well as both thermal and electrical storage units. Further,

the modification of pre-existing setups by replacing or additionally installing units is quite

probable.

This heterogeneity and variability of thermal and electrical systems’ configurations is

challenging for the modeling of HEMS and DR. This requires a flexible and extensible

modeling framework which can easily integrate different as well as additional new systems.

10

1.3 Challenges

1.3.3 Uncertainty of underlying forecast models

The main advantage of predicitve sheduling is the incorporation of forecasts to anticipate

future states and provide an optimal operation under these conditions. However, these

forecasts represent a crucial source of uncertainty which can lead to scheduling infea-

sibilities. In a benchmark of state-of-the-art methods for household electricity demand

forecasting, [Veit et al., 2014] showed that the mean absolute percentage error for day-

ahead forecast ranges between 20 and 150 %. The forecast error increases with higher

time resolution considered i.e. small time steps. Yet, the majority of studies of HEMS

focus solely on scheduling and assume perfect forecasts. This approach is referred to as

deterministic unit commitment.

Scheduling under uncertainty, also referred to as preventive scheduling, is a framework

for modeling optimization problems that involves uncertainty. [Grossmann, 2012] and

[Cardozo, 2014] deliver a good overview on the integration of uncertainty in scheduling

models. Uncertainty can be characterized through a probability distribution description, or

in a bounded form if this distribution is not available and instead only error bounds can be

obtained. Accordingly, stochastic optimization also referred to as stochastic programming,

and robust optimization are applied for preventive scheduling.

Robust optimization incorporates the bounded range of the uncertainty, and focuses mainly

on minimizing the impact of the worst-case scenario. This approach is mostly suited for

risk-adverse consumers and may not be the most cost effective approach. [Conejo et al.,

2010] and [Chen et al., 2012] used the method proposed by [Bertsimas and Sim, 2001]

to tackle price uncertainty in real-time demand response strategies. [Wang et al., 2015]

used a robust optimization approach for day-ahead load scheduling in smart homes while

considering uncertainties from locally installed PV systems.

Stochastic programming (SP) is a systematic approach for dealing with uncertainty. In

SP, uncertainty is represented by a discretized scenario tree according to decision stages.

The basic idea is to make ’here and now’ decisions at the first stage and then take some

corrective ’wait and see’ actions in the future when the uncertainty is revealed [Grossmann,

2012]. The objective in SP is to optimize the cost of the ’here and now’ decisions and

the expected cost of the recourse action. [Chen et al., 2012] proposed a DR strategy

based on a two-stage stochastic MILP approach for residential appliances by considering

uncertainty in price forecast. The model is formulated as a rolling procedure in which the

two-stage, scenario based stochastic optimization is performed for every 5 minutes. The

appliances considered comprise white good as well as electric heaters. [Chen et al., 2012]

further compared the SP model with a robust counterpart and deduced that the SP model

achieves better performance. [Cau et al., 2014] integrated the probability distribution of

solar irradiation, wind speed and electrical and applied a 3-stage stochastic programming

approach for short-term scheduling in a microgrid. The focus lied on electricity generators

11

Introduction

i.e. PV and wind turbines as well as electrical batteries and hydrogen storage systems.

Similarly, [Huang et al., 2014] formulated a DR model based on a two-stage stochastic

MILP by considering the uncertainty of renewable wind and solar power generation.

In general, few studies have addressed scheduling under uncertainty in HEMS or DR

concepts. The focus lies on price and PV generation uncertainties with focus on electrical

appliances. Hence, the field remains not fully unexplored. Mainly, the integration of

thermal units and uncertainty in thermal demand remains untackled.

1.3.4 Scalability of the DSM strategy

The size of the scheduling model for a DR strategy inreases with increasing number

of participating buildings and their corresponding units to coordinate simultaneously.

Centralized MILP approaches for coordinating electro-thermal units yield theoretically

an optimal value for the coordination problem but display limitations with respect to

scalability. The traditional methods for solving generalized MILP, the branch-and-bound

and cutting planes algorithm as well their conjuction, the branch-and-cut algorithm, have

greatly enhanced solving the MILP, however the problem remains NP-hard. Another

drawback of centralized approaches is the assumption that the central controller has

access to all the information which rises the issue of information privacy.

The scalability restriction has been tackled in the literature by applying a special designed

hierachical architecture comprising a centralized controller as well as aggregators such as

the TRIANA [Bakker, 2012] concept. Another approach consists of applying traditional de-

composition techniques to reformulate the large scale MILP into a hierachical optimization

structure and facilitate the solution process. It should be noted that, branch-and-bound,

cutting planes and branch-and-cut can also be considered as decomposition algorithms as

they split a problem in its linear relaxation and integrality constraints.

For Problems with complicating constraints, Lagrangian relaxation (LR) and Lagrangian

decomposition (LD) are the most common decomposition techniques for MILP problems

[Grossmann, 2012]. The basic idea consists of relaxing the original problem and splitting

into a sequence of smaller subproblems which are then solved by employing an iterative

algorithm like the subgradient method [Fisher, 2004]. If the Lagrangian relaxation splits

the problem into independent subproblems, it is referred to as Lagrangian decomposition.

In the context of a DR strategy for the coordination of residential heating systems, [Diek-

erhof et al., 2014] applied the Lagrangian relaxation (LR) method for coordinating heat

pumps. The main limitations of [Diekerhof et al., 2014] is that the algorithm convergence

is not fully addressed especially when incorporating both consumption and generator

flexible units.

12

1.4 Thesis statement and contribution

Dantzig-Wolfe decomposition [Dantzig and Wolfe, 1961] is a well established method

for problems with complicating constraints, which exploits special structured problems

i.e. block-angular constraint matrix structure and decomposes the original problem into

dynamically decoupled subsproblems and a master problem with coupling and convexity

constraints. A column generation algorithm is then used to iteratively solve the problem.

This decomposition method is quite suitable for the formulation of DR coordination

startegies since the problem has a block-angular structure. [Mc Namara and McLoone,

2013] and [Altay and Delic, 2014] applied a DWD for designing a hierachical demand

response strategy. However, both models are strictly linearly formulated and don’t

consider heating systems as a source of flexibility.

1.4 Thesis statement and contribution

This thesis delivers a mathematical programming based generalized, flexible and extensi-

ble software framework which enables the implementation of robust predictive HEMS

and distributed DR strategies that exploit hybrid thermal and electrical flexibility for local

load optimization or the integration of RE in residential building energy systems.

The underlying formulation is an MILP scheduling problem, that is coupled with a rolling

horizon algorithm or model predictive control. Several forecasting methods e.g. ARMA

and SVR are implemented for predicting weather and demand profiles. Data-driven grey-

box modeling approaches are integrated for incorporating the building wall mass as a

thermal flexibility within the optimization problem.

The framework enables the extension of the deterministic MILP problem to a stochastic

programming approach for coping with demand forecasts’ uncertainties on a building

level. Further, the framework allows for reformulating the MILP problem for a city district

based on inner decomposition methods to tackle the scalability and information privacy

issues in coordinating multiple BESs within a cooperative DR strategy. Moreover, the

framework employs dynamic simulation models for the verification and evaluation of the

scheduling strategies on a building level.

The contribution of this thesis addresses the challenges introduced in Section 1.3 for the

development of HEMS and DR strategies and presents a methodology for:

. Integration of thermal and electrical flexibility of BES in energy management strate-

gies

. Advanced MILP models of heating supply systems

. Novel approach for modeling thermal water storage systems and validation through

measurement data

13

Introduction

. Stochastic programming scheduling approach to cope with forecast uncertainty

. Evaluation of the performance of the scheduling models based on non-linear dynamic

simulation models

. Scalable formulation of DR strategies for residential city districts based on hybrid

decomposition techniques

1.5 Structure of this work

The structure of this work is mapped in Figure 1.5. In Chapter 1, the motivation for

this work is reviewed and the novelty as well as the objectives of the thesis are defined.

The methodology comprising the concept, architecture and software configuration is

introduced in Chapter 2. The inputs i.e. user behavior, weather variables’ synthesis

and forecast are presented in Chapter 3. The MILP based modeling of the individual

components within a BES is formulated in Chapter 4. The algorithms used for self-

scheduling under uncertainty and distributed coordination of multiple buildings are

formulated in Chapter 5. In Chapter 6, the performance of the algorithms is evaluated for

building and city district use cases. The thesis is then concluded by a summary and an

outlook to future perspectives.

14

1.5 Structure of this work

Chap.2Methodologyframework

Chap. 3Inputs

Synthesis

Forecastmethods Chap. 4

MILPmodelsof BES

GeneratorsStorage

units

Chap. 5Schedulingalgorithms

Deterministic

Stochasticprogramming

Decompositionapproaches

Chap. 6Analysis

HEMS ina building

DSMin citydisticts

Figure 1.5: Descriptive illustration of the thesis outline

15

2 Methodology: Framework

This chapter defines the methodology, also referred to as PyMPC [Harb et al., 2017]

framework, developed in this work. This comprises the concept as well as the software

architecture and configuration.

2.1 Concept

An overview of the basic formulation of a predictive HEMS for an individual building is

illustrated in Figure 2.1. The scheduling problem is formulated as a discrete MILP opti-

mization model in which the operation costs, respectively expected costs, are minimized

subject to the constraints that describe the technical setup and operational behavior of

the individual units of the building energy system and their interaction. The forecasted

inputs comprise weather related variables such as the outdoor temperature and solar

irradiation, PV generation as well as resident related variables such as occupancy, electri-

cal, domestic hot water and space heating demands. The synthesis and forecast of the

inputs is introduced in Chapter 3. The optimization model of the building energy system

is presented in Chapter 4.

Operation and capacity

constraints

Energy import/export

from/to the grid

Storage dynamics

(charging/discharging)

s.t.

HP

+-Minimize costs

CHP

Inputs Building energy systemAlgorithm

Figure 2.1: Overview on the individual components and basic formulation of a predictiveHEMS. The inputs comprise weather, space heating, domestic hot water,electrical demand, PV generation and occupancy. The building energy systemincludes battery, CHP, electrical, building wall mass, HP and water storagetanks

The scheduling model is integrated within a rolling horizon algorithm that allows the re-

duction of the computational effort and the impact of prediction uncertainties by updating

17

Methodology: Framework

the forecasts in a cyclic manner. The rolling horizon approach is illustrated in Figure

2.2. It is characterized by a rescheduling interval which defines the time between two

scheduling processes and a horizon that represents the length of the scheduling interval.

The concept of the PyMPC framework is to enable a modular, flexible and extendable for-

mulation of the scheduling problems of residential buildings. This comprises the building

energy system, i.e. energy generation and storage units, and scheduling approach.

time steps 1 2 3 4 5 6

rescheduling interval scheduling horizon

run 2

run 3

run 1

Figure 2.2: Simplified illustration of the concept of the rolling horizon algorithm. Therescheduling interval denotes the time between the scheduling steps orscheduling re-initialization whereas the scheduling horizon defines the lengthof scheduling step

The basic formulation of the scheduling model for a single building is a deterministic

MILP model which can be inherited by robust optimization or stochastic programming

approaches for embedding uncertainties into the scheduling model. Moreover, the MILP

model of a single building can be integrated within a decomposition optimization approach

i.e. Dantzig-Wolfe decomposition method for the formulation of a city district DSM model.

The scheduling algorithms are described and formulated in Chapter 5.

The system evaluation is enabled by coupling the scheduling model with a dynamic simu-

lation model based or hardware-in-the-loop (HiL) setup in which hardware components

are embedded in a simulation environment. The assessment takes into consideration the

impact of the forecast, the linearized models of the units within the BES and finally the

scheduling algorithms. The evaluation approach is illustrated in Figure 2.3.

The first method makes use of dynamic simulation models which depict the non-linear

behavior of the units. In this approach, the dynamic simulation model is integrated as a

functional mock-up unit (FMU) based on the functional mock-up interface (FMI) standard

[Modelica Association, 2016]. The second approach allows a closer to reality assessment

but necessitates the availability of the investigated hardware and hence large investment

and installation effort.

18

2.2 Architecture

Input: Actual data

Model: Dynamic non-linear

simulation models – FMU

Real units - HiL

Input: Forecast

Model:

Discrete linearized

optimization model

Schedule Actual

operation

Initialization

Figure 2.3: System testing and evaluation within the PyMPC framework. The left boxrepresents the scheduling model which uses forecast and linearized BESmodels, whereas the right box represents the realization platform whichincludes actual weather and demands as well as non-linear BES dynamicsimulation models (integrated as a FMU) or HiL

2.2 Architecture

The task diagram in Figure 2.4 delivers a comprehensive overview of the architecture of

the PyMPC framework. The latter consists of three layers, source, library and run-time.

Source layer

The source layer includes:

. a database of the weather and demand profiles which are used for training the

forecasting algorithms, as well as the characteristics of energy conversion units

. a user interface for configuring and characterizing the desired use case. This

comprises:

• the building energy system considered i.e. which unit and its corresponding

MILP model

• the forecasting methods for every application i.e. which method and its parame-

ters as well as the source of training data

• the scheduling algorithm

• the rolling horizon parameters as well as the simulation/optimization general

setup e.g. time resolution, simulation start and end time

19

Methodology: Framework

Ru

n-t

ime

Sou

rce

Configuration:• Components’ identification• Algorithm selection• Execution parameters• Inputs’ configuration

Lib

rary

Constructor

BES components:• Heat Pump• µCHP• PV• Battery• Water storage• Building wall mass

Forecasting methods:• Persistence • ARMA• SVR

DesignBuilding

Main model

For each run

Update inputsInstantiate

main modelCompute schedule

PyFMIsimulation

Scheduling algorithms:• Deterministic• Robust• Decomposition

methods• Stochastic

Programming

Database:• Components’ datasheets• Measurement data• Results logging

Update intialsof next run

Inputs

Run time controller

Figure 2.4: PyMPC framework structure and task diagram

20

2.3 Software configuration

Library layer

The library includes the forecasting methods, the individual MILP models of the different

BES components i.e. energy generation and storage units and the scheduling algorithms

as well as different meta-classes that are employed by a constructor to build up the BES

optimization model. The constructor creates a design object based on the configuration

set by accessing the database content.

The design object is then used to instantiate the building model i.e. the available units and

the corresponding capacities and data sheets, and the inputs i.e. the forecasting method

employed and the corresponding parameters, based on the BES components and forecast

methods libraries, respectively.

The building model and the inputs’ object are aggregated along with the interconnecting

electricity energy balance constraint and an objective function e.g. cost minimization

into a main model which is forwarded to the Gurobi solver [Gurobi Optimization, 2017],

within the run-time layer, for computing and determining the optimal schedule within the

dynamic run-time layer.

Run-time layer

The run-time module involves the iterations of the moving window algorithm. In each

iteration, all inputs are updated mainly forecasts from the current time index up to the

predefined horizon are generated. The constructor is then called upon to generate the

main model. Thereafter, the main model is optimized by the Gurobi solver for determining

the schedule which is passed to a corresponding FMU that simulates the corresponding

time period. In the case of stochastic programming, the simulation results are reported

back into the controller which decides which strategy should be adopted according the

the uncertainty realization. The final values of the simulations are set as initial values for

the next iteration.

2.3 Software configuration

2.3.1 Framework programming language

Python is the programming language applied for formulating the framework. Python is an

interpreted, object-oriented, programming language. Python is developed and distributed

based on an open source license and provides a large portfolio of generic and domain

specific modules, packages and libraries. Several libraries are employed within the PyMPC

framework, mainly, GurobiPy [Gurobi Optimization, 2017], Matplotlib, NumPy, Pandas,

21

Methodology: Framework

Scikit-learn [Scikit-learn development team, 2016], SciPy [SciPy development team, 2014]

and Statsmodels [Statsmodels development team, 2016].

2.3.2 MILP optimization solver

The Python application programming interface (API) "Gurobipy" provided by the optimizer

Gurobi [Gurobi Optimization, 2017] is employed for formulating the MILP optimization

model.

2.3.3 Dynamic simulation model

The BES dynamic simulation models are formulated based on the in-house developed

library within the project dual demand side management (2DSM) [Müller et al., 2015] with

the programming language Modelica [Modelica Association, 2012] in the environment

Dymola [Dassault Systemes, 2016].

Pressure Loss(Pipes)

Controller

M

Heat Delivery(Radiator)

Supply System ThermalZone

Consumer System

T

Heat Generator

Pressure Loss(Pipes)

Pressure Loss(Pipes)

Buffer Storage

Tank

M

Figure 2.5: Simplified overview on the space heating supply system within the dynamicsimulation models [Müller et al., 2015]. The main components are the thermalzone which represents the thermal behavior of the building, the hydraulicconnection, the heat generation system e.g. HP and CHP and thermal storageunits as well as the rule-based control strategy

The models comprise the building envelope, its interaction with the ambient conditions

22

2.3 Software configuration

and user behavior as well as the heating supply and delivery system as exemplary depicted

in Figure 2.5. The building is modeled based on [Lauster et al., 2014] which extends the

German industry guideline VDI 6007 [Verein Deutscher Ingenieure, 2012] also known as

two capacitor (2-C) low order thermal network model. [Lauster et al., 2014] provides a

detailed description of the corresponding modeling approach.

The heating supply system comprises a heat generation unit and a buffer storage tank. The

space heating mass flow is drawn out of the storage unit into a radiator delivery system

with thermostatic valves. The domestic hot water is drawn out of the buffer storage tank

as well.

The heat generators are formulated as black box models with non-linear behavior. This

allows for reducing the computational effort while preserving the model behavior accuracy.

A detailed modeling approach is adopted to a level that hydraulic cycles with specific media

properties are computed. The HP model consists of two heat exchangers connected by the

HP circuit. Given a specific electrical power, the mean temperature of the evaporator and

condenser will adjust according to the attached hydronic systems and their power demand.

Tabulated values for electrical and thermal powers are taken from the manufacturer data

sheets. In all simulations, the HP is assumed as non-modulating and can only be switched

on or off.

The CHP is a table based black box model as well. An internal controller will set the

power level of the CHP to reach a target flow temperature. This corresponds to a mean

temperature of maximum device temperature and the current heating curve temperature

or domestic hot water tap temperature. In this manner, the system energy losses are

reduced and the efficiency of the CHP is increased at partial load conditions. According

to the power level of the CHP, controllable between 30 % and 100 %, the thermal and

electrical power output are calculated.

The storage tank model consists of a discrete number of layers that make up the total

water volume. The internal control of the heat generators will ensure that there is always

a sufficiently high flow temperature so that the user’s comfort will not be affected by the

demand side management strategy.

The models are exported as co-simulation FMU based on the FMI standard and imported

within the framework using the python library PyFMI [Modelica Association, 2016], as

illustrated in Figure 2.6. The FMI standard allows for tool independent exchange of

dynamic models on binary format. FMUs can be exported for both model exchange and

co-simulation applications. A co-simulation FMU extends the model exchange standard

to include a solver. This allows for solving the dynamic model independently within a

coupled heterogeneous system.

23

Methodology: Framework

Dymola

Figure 2.6: Integration of the Modelica/Dymola dynamic BES simulation model within thePyMPC framework as co-simulation Python FMU based on the FMI interface

24

3 Inputs: Synthesis and Forecast

This section introduces the synthesis of the input data and the forecasting methods

implemented in the PyMPC framework. Demand profiles are commonly formulated based

on representative standard load profiles (SLP) which deliver an average profile that is

devoided from significant individual demand characteristics. The assessment results of

an energy management strategy greatly depend on the input data used. Therefore, it is

critical to make use of high resolution measurement data or generate synthetic demand

profiles that provide a realistic pattern or approximation of the representing load. The goal

in this section is to present a method to generate realistic profiles as well as identifying

and formulating suitable forecasting method for the individual variables and evaluate the

resulting forecasting error or uncertainty.

3.1 Synthesis

The input data for a HEMS comprise weather variables, electrical demand, domestic hot

water, space heating demand, active occupancy, as well as PV generation. These profiles

are interdependent and impact each other as illustrated in Figure 3.1.

Domestic

hot water

Active

occupancy

PV

generationSpace

heating

Electricity

demand

Figure 3.1: Interconnection of weather, occupancy, demand and PV profiles. Occupancyis only influenced by weather conditions and used to derive the electricaland domestic hot water demands. PV generation is determined based on theweather variables. Space heating is influence by the internal thermal gainsfrom active occupancy, electrical consumption and weather

25

Inputs: Synthesis and Forecast

It can be seen that the basis is the active occupancy model, according to, an electrical

as well as a domestic hot water demand is derived. The occupancy profile as well as the

electrical and DHW consumption is influenced by weather variables. Further, based on the

weather conditions a PV generation profile can be approximated as well as a space heating

demand. The space heating demand mainly depends on the physical thermodynamic

characteristics of the building considered but is significantly influenced by the occupant

behaviour i.e. presence and electrical demand, that impacts the ventilation and internal

gains.

Based on this approach, a high resolution occupancy generation developed by [Richardson

et al., 2008] is adopted and implemented in the PyMPC framework. The occupancy profile

generator is coupled with an electricity demand profile as introduced in [Richardson et al.,

2010]. The occupancy is then used as input for the domestic hot water model which is

formulated based on the model developed by [Jordan and Vajen, 2003]. The resulting

synthetic profiles for, exemplary, 3rd of March are depicted in Figure 3.2.

0 .00 .51 .01 .52 .02 .53 .0

kW

Pdemand

0 .00 .51 .01 .52 .02 .53 .0

#reside

nts

Activ e occupancy

00 :0003 -Mar

03 :00 06 :00 09 :00 12 :00 15 :00 18 :00 21 :00

Date

0 .00 .51 .01 .52 .02 .53 .0

kW

Qdhw

Figure 3.2: Stochastic occupancy based generation of demand profiles. The depictedprofiles, from top to bottom, are the electrical demand, occupancy anddomestic hot water demand

This methodology is critical in evaluating DSM strategies for a city district energy system

26

3.2 Forecasting methods

with several buildings since measurement data for such a scale are hardly available. The

assessment of HEMS for a single building later introduced in Section 6.1 is carried based

on measurement data for domestic hot water and electricity demand provided from the

project [Osterhage et al., 2015]. The weather data is derived from the test reference year

(TRY) weather data for the respective geographical location of the dwellings considered in

the project [Osterhage et al., 2015]. The TRY data is used to generate a space heating

demand profile based on a design driven grey-box model [Lauster et al., 2014] implemented

in Dymola/Modelica as well as PV generation profile based on the model later introduced

in Chapter 4. An overview on the resulting raw input data is exemplary depicted in Figure

3.3 .

0 .00 .20 .40 .60 .81 .01 .2

kW

Qdhw

0 .00 .51 .01 .52 .02 .53 .0

kW

Pdemand

0 .0

0 .5

1 .0

1 .5

2 .0

kW

PPV

00 :0003 -Mar

03 :00 06 :00 09 :00 12 :00 15 :00 18 :00 21 :00

Date

1 .01 .52 .02 .53 .03 .54 .0

kW

Qspace heating

Figure 3.3: Input data for the single building evaluation. The depicted profiles, from topto bottom, are the domestic hot water, electrical demand, PV generation andspace heating demand

3.2 Forecasting methods

The forecasting models implemented in the PyMPC framework comprise persistence,

ARMA, and SVR models. Further, a time-series additive decomposition model is formulated

27

Inputs: Synthesis and Forecast

using the Statsmodels package [Statsmodels development team, 2016] to cope with non-

stationary time series. In an additive decomposition model, the time series consists of a

trend, a seasonality/periodicity and a remainder component. Accordingly, the trend and

the remainder are forecasted using an ARMA or a SVR model while the seasonality is

forecasted using a persistence model.

3.2.1 Persistence

A persistence or naive forecast model is a simple prediction method in which measured

values are assumed to reoccur in the future. A persistence model is characterized by

its cycle e.g. daily or weekly, re-occurrence of the measured value. Accordingly, a daily

persistence sets the prediction yi for the next day as the measured values yi−n of the

previous day and a weekly persistence prediction is the measured values a from the day

one week before.

yi = yi−n (3.1)

The corresponding amount of time steps n for a given cycle is determined depending on

the time resolution ∆t .

3.2.2 ARMA

ARMA is a widely used forecasting model that combines an autoregressive (AR) with

a moving average (MA) model. An AR process forecasts a random variable as a linear

function of its past values. A MA model is a weighted sum of the historic model errors.

Consequently, the ARMA process is a linear function predicting yi based on the past

measurements and the past forecasting errors:

yi =AR︷ ︸︸ ︷

ρ0 +ρ1 · yi−1 + . . .+ρp · yi−p +MA︷ ︸︸ ︷

α0 +α1 ·εi−1 + . . .+αq ·εi−q

with εi = yi − yi

(3.2)

ARMA is implemented based on the Statmodels package. An ARMA(p,q) model is deter-

mined by the choice of the orders p and q. This process is called model selection and

introduced in [Zucchini, 2000]. The parameters ρp and αq are determined by minimizing

the sum of squared errors. The latter step is referred to as model fitting. The order of the

ARMA(p,q) model is determined by fitting the model to the measurement data through

a grid search while minimizing the Akaike information criterion (AIC) [Akaike, 1974]

based on a "brute force" method using the SciPy brute optimizer [SciPy development

team, 2014]. The AIC couples the model error to the amount of model parameters so that

the quantity of model parameters and thereby the model complexity does not increase

28

3.2 Forecasting methods

infinitely. Big grids can lead to a decrease in the model error but also to an increase

in the computation time needed to determine the model order with the lowest AIC. The

ARMA model is configured within the PyMPC framework by setting the time resolution

∆t , the forecast horizon, the fitting window i.e. the time range of past observation to be

considered for the model fitting, the fitting cycle i.e. the cycle for re-determining the

orders p and q.

In the following investigations, the time resolution ∆t and the forecast horizon are re-

spectively set to 15 minutes and 24 hours analogously to the intra-day also referred to as

day-ahead energy market.

3.2.3 SVR

Support Vector Regression (SVR) is a machine learning or computational intelligence

model. The idea behind SVR is that input data generated by a non-linear function can be

mapped by a kernel φ into a high-dimensional feature space in which the relation between

input and output becomes linear as indicated in Figure 3.4.

set) fðxi; yiÞgNi¼1 into a so-called high-dimensional feature space (Fig. 2.3), which

may have infinite dimensions, <nh . Then, in the high-dimensional feature space,

there theoretically exists a linear function, f, to formulate the nonlinear relationship

between input data and output data (Fig. 2.4a, b). Such a linear function, namely,

SVR function, is as Eq. (2.47):

f ðxÞ ¼ wTφðxÞ þ b; (2.47)

where f(x) denotes the forecasting values and the coefficients w (w 2 <nh ) and

b (b 2 <) are adjustable. As mentioned above, using SVM method one aims at

minimizing the empirical risk as Eq. (2.48):

Rempðf Þ ¼ 1

N

XNi¼1

Θεðyi;wTφðxiÞ þ bÞ; (2.48)

whereΘεðy; f ðxÞÞ is the ε-insensitive loss function (as thick line in Fig. 2.4c) and isdefined as Eq. (2.49):

Θεðy; f ðxÞÞ ¼ f ðxÞ � yj j � ε; if f ðxÞ � yj j � ε0; otherwise

�: (2.49)

In addition, Θεðy; f ðxÞÞ is employed to find out an optimum hyperplane on the

high-dimensional feature space (Fig. 2.4b) to maximize the distance separating the

training data into two subsets. Thus, the SVR focuses on finding the optimum

hyperplane and minimizing the training error between the training data and the

ε-insensitive loss function.Then, the SVR minimizes the overall errors, shown as Eq. (2.50):

Minw;b;ξ�;ξ

Rεðw; ξ�; ξÞ ¼ 1

2wTwþ C

XNi¼1

ðξ�i þ ξiÞ; (2.50)

with the constraints

Input space

a

(x)ϕ

Feature space

b*iξ

iξ

0ε+

ε−

-insensitive loss functionε

ε+ε−

*iξc

Hyper plane

Fig. 2.4 Transformation process illustration of an SVR model

2.7 Support Vector Regression Model 33

Figure 3.4: Illustration of the transformation process from the input space to the high-dimensional feature space, by applying the kernel function φ, within a SVRmodel [Hong, 2013]

In the feature space the relation between input and output is described by a hyperplane.

This relation is determined by optimizing, respectively, minimizing the model error. Based

on the assumption that the input data is subject to noise, the optimization constraints are

relaxed by using soft margins whose width is given by the parameter ε [Cristianini and

Shawe-Taylor, 2000]. All data elements inside these margins are not considered while

calculating the model error. The errors above +ε are denoted as ξ∗i , whereas erros below

-ε are denoted as ξi . The influence of the model error on the optimization is determined

by the parameter C . The accuracy of the SVR model highly depends on how well the

non-linear relationship between input and output is captured by the kernel function φ.

Common kernels are the linear kernel, the polynomial kernel and the radial basis function

29

Inputs: Synthesis and Forecast

(RBF) kernel [Cristianini and Shawe-Taylor, 2000]. The choice of the kernel is decided

based on prior knowledge about the data or by trial and error. Depending on the kernel

different parameters have to be set. The linear and polynomial kernels includes the

aforementioned parameters C and ε, whereas the RBF kernel further includes a specifiv

parameter γ which defines how far the influence of a single training example reaches.

The SVR model is implemented in the PyMPC framework based on the scikit-learn library

[Scikit-learn development team, 2016]. The optimal model configuration is determined by

applying the "GridSearchCV" algorithm [Scikit-learn development team, 2016]. Since the

amount of parameters for a SVR model is fixed, the AIC is no a suitable for assessing the

goodness of fit. Instead the coefficient of determination (R2) [Nagelkerke, 1991] is used.

It is calculated by training the model with a subset of the training data and evaluating the

forecast against the remaining training data based on a cross-validation process.

3.2.4 Performance indicators

The quality of a forecast is typically determined by a posteriori evaluation i.e. comparison

of predicted yi and observed values yi . Several accuracy indicators are available for

evaluating the performance of time series forecasting methods e.g. mean absolute error

(MAE), mean absolute percentage error (MAPE), root mean squared error (RMSE) and

mean absolute scaled error (MASE). Every indicator has advantages and disadvantages.

Therefore, it is advisable to use several indicators to assess the prediction accuracy. The

error measures considered in this work are:

. Mean absolute percentage error (MAPE):1

N

∑Ni=1 |

yi − yi

yi| ·100%

. Normalized root mean squared error (NRMSE):

√1

N

∑Ni=1(yi − yi )2√

1

N

∑Ni=1(yi )2

·100%

The MAPE indicator is adopted since it does not depend on the series’ mmagnitude or unit

of measurement, thus allowing for a representative measure of the overall forecast quality.

However, MAPE has the disadvantage of being infinite or undefined if the measurement

values are equal to zero. Therefore, NRMSE is further employed as a forecast accuracy

measure.

3.2.5 Evaluation

The dynamic performance of the forecasting methods for predicting the electrical demand

is exemplary depicted in the Figure 3.5 for the 5th May. The measurement values are

derived from consumption data for a single family house [Osterhage et al., 2015]. The

30

3.2 Forecasting methods

results show the stochastic nature of the consumption profile. Mainly, the upper subplot of

the naive forecast indicates that the electrical consumption at the evening hours for this

specific day is significantly lower than the consumption at the same period the previous

day. The ARMA and SVR models outperform the persistence method and exhibit similar

NRMSE of 52.39 and 49.39 %, respectively. These values are comparable to the results

presented in the forecast assessment studies found in the literature [Veit et al., 2014].

However, the SVR forecast allows for a better estimation of the dynamic behavior of the

demand profile.

456

Meas urem entDda tapers is tentD-DNRMSE:D1 1 0 .1 9

0 .01 .0

0 .00 .51 .01 .52 .02 .53 .03 .5

Meas urem entDda taARMAD-DNRMSE:D5 2 .3 9

0 0 :0 00 5 -May

0 3 :0 0 0 6 :0 0 0 9 :0 0 1 2 :0 0 1 5 :0 0 1 8 :0 0 2 1 :0 0

Date

0 .00 .51 .01 .52 .02 .53 .03 .5

Meas urem entDda taSVRD-DNRMSE:D4 9 .3 9

2 .03 .0

.0.0.0

Ele

ctri

calDd

eman

dDin

DkW

Figure 3.5: Electrical demand forecast results for the 5th of May using the daily persis-tence, ARMA and SVR methods

Table 3.1 summarizes the performance results of the forecast model for the ambient

temperature Tamb, solar irradiation Isolar, electrical Pdemand, space heating Qspace heating

and domestic hot water Qdhw demands. The prediction period is 30 days whereas the

model fitting interval is set to the past 4 weeks. The rescheduling (model re-fitting)

interval is one week. The forecasting horizon is a day-ahead or 24 hours and the time

resolution is 15 minutes.

31

Inputs: Synthesis and Forecast

Table 3.1: Summary of the performance of the daily persistence, ARMA and SVR modelsfor forecasting the HEMS input profiles over an assessment period of 30 dayswith a time resolution of 15 min and a forecast horizon of 24 h

Persistence ARMA SVR

Tamb 26.06 13.68 14.97 MAPE [%]28.89 17.05 18.58 NRMSE [%]

Isolar 49.67 353.05 431.95 MAPE [%]53.58 45.53 47.08 NRMSE [%]

Pdemand 108.48 100.73 76.73 MAPE [%]83.14 65.12 61.7 NRMSE [%]

Qspace heating 5245.61 3980.67 3201.73 MAPE [%]68.33 69.86 57.41 NRMSE [%]

Qdhw 131.17 67.18 70.94 MAPE [%]130.1 94.82 94.88 NRMSE [%]

0 .0

0 .5

1 .0

1 .5

2 .0

2 .5Meas urem entVda tapers is tentV-VNRMSE:V1 4 9 .9 8

0 .0

0 .5

1 .0

1 .5

2 .0Meas urem entVda taARMAV-VNRMSE:V9 5 .0 4

0 0 :0 00 5 -May

0 0 :0 00 6 -May

0 6 :0 0 1 2 :0 0 1 8 :0 0 0 6 :0 0 1 2 :0 0 1 8 :0 0

Date

0 .0

0 .5

1 .0

1 .5

2 .0Meas urem entVda taSVRV-VNRMSE:V9 9 .3 9D

omes

ticVh

otVw

ater

Vdem

andV

inVk

W

Figure 3.6: Domestic hot water forecast results for two consecutive days, 5th and 6th ofMay, using the daily persistence, ARMA and SVR methods

32

3.2 Forecasting methods

It is important to note that the forecast models’ accuracy strongly depends on the con-

figuration assumed for the model fitting interval, rescheduling frequency, forecasting

horizon and time resolution. The model fitting interval describes the data window of past

observations included in the training phase. The value adopted depends on the available

data set. Typically, this parameter is more influential in machine learning algorithms

such as ANN and SVR than in statistical models such as ARMA. Furthermore, the impact

of this parameter depends on the specific time series or application. The value of 30

days was determined for the considered data sets through a sensitivity analysis within

the interval 7 to 60 days. The rescheduling interval denotes the frequency at which the

model is refitted to redetermine its parameters e.g. ρp and αq within ARMA. A higher

refitting frequency generally results in decreasing the forecast error but resuls with an

increasing computation effort. Moreover, the forecast typically improves with lower time

resolution e.g. increasing ∆t from 15 to 60 min as the dynamic behavior of the time series

becomes more smooth, due to the loss of high granularity information, which is then

more easily captured by the model characterization process and consequently results in

better predictions. The forecast performance is also expected to improves with shorter

forecasting horizon since the uncertainty development is reduced.

The values marked in green in Table 3.1 highlight the lowest forecasting error for every

application. It can be seen that SVR performs best for forecasting electrical and space

heating demands. ARMA provides the best prediction results for the strongly seasonal

weather variables, ambient temperature and solar irradiation as well as the domestic

hot water demand. However, the dynamic evaluation of Figure 3.6 shows that the do-

mestic hot water demand strong stochasticity could not be captured by SVR and ARMA.

Hence, the computational effort is not justified and accordingly the persistence method is

recommended for this application.

Based on these result, the forecast setup for the assessment of the scheduling algorithms

in Section 6.1 is determined. ARMA is employed for predicting the weather variables, SVR

for electrical and space heating demand and persistence for domestic hot water demand.

Furthermore, it can be noticed that the forecasting errors are the highest in the case of

domestic hot water and electrical demand that strongly depend on the resident’s behavior

which has a strong stochastic nature. Accordingly, the uncertainty of these two demands

is integrated in the formulation of the stochastic programming scheduling approach.

33

4 Modeling of Building Energy Systems: Mathematical

Programming Formulation

The setup of a building energy system determines its HEMS compatibility and load shifting

potential. In this chapter, the discrete mathematical optimization models of the individual

BES components are introduced in the framework of mixed inter linear programming

(MILP). These components can be mainly categorized into energy generation and storage

systems. Figure 4.1 delivers an overview on the possibly existing components and their

interaction on both the thermal and electrical side within a BES.

ECOS 16 | Hassan HarbFolie 3

Buidling Energy System: Generation and Flexibility

Folie 3

+-

HEMS

thermal side electrical side

PV

EH

EHHP

CHP

CHPHP

Boiler

Figure 4.1: Illustrative overview of possible energy demand, generation and storageunits as well as their thermal and electrical interactions within a residentialbuilding energy system

4.1 Heat pump

Residential heat pumps for HVAC, mainly space heating and domestic hot water applica-

tions are compression HP and can be categorized according to the operation, respectively,

evaporator heat source, into ambient or exhaust air source (AS), ground water or soil

source (GS), exhaust air (EA) and water source (WS) heatpumps. The most common type

is ASHP followed by GSHP.

The performance of a HP unit is determined by the source/evaporator temperature and

the condenser inlet temperature and is characterized by the coefficient of performance

(COP) which is the ratio of the heating energy provided to the work required. Figure

35

Modeling of Building Energy Systems: Mathematical Programming Formulation

4.2 depicts the performance of an ASHP i.e. the generated heat power and COP based

on the evaporator air temperature for three discrete application temperatures, 35, 45

and 55 °C. The condenser inlet temperature is a dynamic variable which depends on the

hydraulic connections as well as the storage type and status. The COP increases with

higher evaporator temperature as well as lower condenser temperature. The notable bend

in the curve corresponds to the typical defrost loss at air temperatures just above the

freezing point.

20 15 10 5 0 5 10 15 20Ambient temperature in ◦ C

1

2

3

4

5

6

7

8

9

Therm

al pow

er

in k

W

Q (Tset=35)

Q (Tset=45)

Q (Tset=55)

1

2

3

4

5

6

CO

P

COP (Tset=35)

COP (Tset=45)

COP (Tset=55)

Figure 4.2: COP and heat generation power development with respect to the ambienttemperature of an ASHP ’Dimplex A/W LA6TU’ for different applicationtemperatures [Dimplex, 2017]

The characteristic diagram in Figure 4.2 is extracted for the data sheets of a HP system

provided by the manufacturers e.g. [Dimplex, 2017]. Accordingly, the HP MILP model is

formulated as:

QHP(t ) = PHP(t ) /COP (t ) ∀ t (4.1)

COP (t ) = QUBHP (t ) / PUB

HP (t ) ∀ t (4.2)

PHP(t ) = uHP(t ) ·PUBHP (t ) ∀ t (4.3)

36

4.2 Micro combined heat and power unit

uHP(t ) is a binary variable which describes the operation status of the HP; 1 corresponds

to ’on’ and 0 to ’off’.

The values for QUBHP (t ) and PUB

HP (t ) are extracted from the data sheets based on interpolation,

using the ambient air temperature Tamb(t ) as source temperature and the flow set tem-

perature of the consumer cycle T flowset (t ). T flow

set (t ) is determined according to Equation 4.4.

The value of T flow, SHset (t ) is derived from the heating curve of the space heating distribution

system based on Tamb(t ) and the heat distribution system characteristics.

T flowset (t ) =

T flow, dhwset (t ), if Qdhw(t ) ≥ 0

T flow, SHset (t ), if Qdhw(t ) = 0

(4.4)

A modulation behavior can be realized by substituting the Equation 4.3 through:

PHP(t ) ≥ uHP(t ) ·Lmod ·PUBHP (t ) ∀ t (4.5)

PHP(t ) ≤ uHP(t ) ·PUBHP (t ) ∀ t (4.6)

with Lmod as the modulation level ranging between 0 and 1. In the investigations later

introduced in Chapter 6, the HP models considered are non-modulating or on-off systems.

Hence, the modulation level is set to one, Lmod = 1.

In order to reduce wear and tear of the device, a frequent change of operation status must

be avoided. This can be modeled through the following equations:

v(t )−w(t ) = uHP(t )−uHP(t −1) ∀ t ≥ 2 (4.7)

t∑i=t−t run

min

v(i ) ≤ uHP(t ) ∀ t ≥ t runmin (4.8)

t∑i=t−tdown

min

w(i ) ≤ 1−uHP(t ) ∀ t ≥ tdownmin (4.9)

v(t ) and w(t ) are binary variables, that account for startup and shutdown transitions,

respectively. The system has a startup at time step t if v(t ) equals one, and has a shutdown

at time t if w(t ) equals one. t runmin and tdown

min represent the minimum run and shut down

time, respectively. Both parameters are set to 30 min according to expert opinion from

manufacturing companies .

4.2 Micro combined heat and power unit

Micro combined heat and power (µCHP) units cogenerate heat and power using gas as

fuel thus enabling a high energy conversion efficiency. The performance of a CHP unit is

37

Modeling of Building Energy Systems: Mathematical Programming Formulation

characterized by a power-to-heat ratio σ, electric efficiency ηel, thermal efficiency ηth and

an overall efficiency ηtotal.

σ= PCHP /QCHP (4.10)

ηel = PCHP /QCHP, gas (4.11)

ηth = QCHP /QCHP, gas (4.12)

ηtotal = ηel+ηth (4.13)

The electric efficiency depends on the operation mode and decreases with the modulation

level. In contrast, the thermal efficiency increases at lower modulation level. Consequently,

the overall efficiency remains almost constant.

The MILP model of a CHP unit is formulated based on the following equations:

PCHP(t ) ≥ uCHP(t ) ·PminCHP ∀ t (4.14)

PCHP(t ) ≤ uCHP(t ) ·PmaxCHP ∀ t (4.15)

QCHP(t ) = c1 · (PCHP(t )−PminCHP ·uCHP(t ))+Qmin

CHP ·uCHP(t ) ∀ t (4.16)

QCHP, gas(t ) = c2 · (PCHP(t )−PminCHP ·uCHP(t ))+Qmin

CHP, gas ·uCHP(t ) ∀ t (4.17)

The parameters for the MILP equations can be extracted from the Table 4.1 and calculated

according to the stationary equations:

c1 =Qmax

CHP−QminCHP

PmaxCHP−Pmin

CHP

(4.18)

c2 =Qmax

CHP, gas−QminCHP, gas

PmaxCHP−Pmin

CHP

(4.19)

QmaxCHP, gas = Pmax

CHP/ηmax (4.20)

QminCHP, gas = Pmin

CHP/ηmin (4.21)

Frequent startup and shutdown can be limited by introducing Equations 4.7 - 4.9.

38

4.3 Electrical heating element

Table 4.1: Parameters of ECOPower 3.0 [Vaillant, 2017]

Parameter Value Unit

Pmax 3 kWPmin 1.5 kWQmax 8 kWQmin 4.7 kWηmax

el 25 %ηmin

el 17 %ηtot 90 %σ 0.375 -

4.3 Electrical heating element

Electrical heating elements are commonly used as instantaneous flow auxiliary heaters

within a mono-energetic HP system or as main heating systems such as night storage

heaters or integrated surface heaters.

The MILP model of an electrical heating element can be formulated as:

PEH(t ) ≥ uEH(t ) ·Lmod ·PmaxEH ∀ t (4.22)

PEH(t ) ≤ uEH(t ) ·PmaxEH ∀ t (4.23)

QEH = PEH(t ) ·ηEH ∀ t (4.24)

with Lmod as the modulation level ranging between 0 and 1, and ηEH as the energy

conversion efficiency. In this work, the efficiency is set equal to one (ηEH = 1) and the

operation is restricted to on-off. Hence, the modulation level is set to one (Lmod = 1).

Some EH can only operate at discrete modulation levels P iEH with i ∈ [1,n]. This behavior

can be formulated by introducing a set of binary variables uiEH for every modulation level

using the following equations:

PEH(t ) =n∑

i=1ui

EH(t ) ·P iEH ∀ t (4.25)

n∑i=1

uiEH(t ) ≤ uEH(t ) ∀ t (4.26)

39

Modeling of Building Energy Systems: Mathematical Programming Formulation

4.4 Gas boiler

Gas-fired boilers are the most widespread installed heat generator. Boilers are used as

primary heaters, instantaneous flow heater or auxiliary heater within a mono-energetic

µCHP system. The MILP model of a boiler is formulated as:

QBoiler(t ) ≥ uBoiler(t ) ·Lmod ·QmaxBoiler ∀ t (4.27)

QBoiler(t ) ≤ uBoiler(t ) ·QmaxBoiler ∀ t (4.28)

QBoiler(t ) = QBoiler, gas(t ) ·ηBoiler ∀ t (4.29)

4.5 Photovoltaic

The operation of a PV system is restricted as only power throttling is possible to avoid

network over-voltage but it is at the same not desirable since it means that energy is lost.

Consequently, a HEMS can only decides on the utilization of the generated electricity but

not the power output of the PV system itself.

A PV system is defined by the installed peak power Ppeak and the module specifications

provided by the manufacturer. Typically, the installed PV power ranges from 3 to 5 kWp for

a single-family house. A maximum power point tracker (MPPT) within the power inverter

ensures that the system is operated optimally.

The power output is formulated based on [Cau et al., 2014] as:

PPV(t ) = Isolar(t ) · APV ·ηPV(t ) ∀ t (4.30)

PPV(t ) ≤ Ppeak ∀ t (4.31)

where Isolar(t ) denotes the solar global irradiation.

The area of PV system APV and the temperature dependent module efficiency ηPV(t ) are

determined according to the following equations:

APV = Ppeak

P refmodule

· Amodule (4.32)

ηPV(t ) = ηref−α · (Tcell(t )−Tref) ·Pref (4.33)

Tcell(t ) = Tamb(t )+ (Tnoct−Tamb, noct) ·Isolar(t )

Inoct∀ t (4.34)

40

4.6 Battery

Table 4.2: Parameters of a Schott PV module [Schott, 2017]

Parameter Value Unit

Amodule 1.673 m2

P refmodule 240 Wp

ηrefPV 13.4 %α 0.4 %/K

Tamb, noct 20 °CTnoct 47 °CInoct 800 W/m2

ηref is the nominal module efficiency under reference conditions. α is the temperature

coefficient in [%/K] that defines the power decrement due to cell temperatures above

25 °C. The cell temperature Tcell can be derived by linear interpolation based on the

nominal operation cell temperature (NOCT) conditions. An overview of the parameters

employed for the PV module is presented in Table 4.2.

4.6 Battery

The battery model is based on Lithium-Ion (Li-Ion) type with a characteristic current curve

from [Sundstrom O., 2010]. Since the self-discharging rate of Li-Ion batteries usually

amounts to less than 2 %/month [Johnson and White, 1998], it is neglected in this model.

Furthermore, aging effects of the Li-Ion cells are not considered as well.

The MILP model is mainly based on an energy balance equation which represents the

development of the state of charge (SoC) with respect to the charging or discharging

power.

Ebat(t ) =Ebat(t −1)+(ηbat ·Pcharge(t )− 1

ηbat·Pdischarge(t )

)·∆t ∀ t (4.35)

Pcharge(t ) & Pdischarge(t ) ≥ 0 ∀ t (4.36)

SoCbat(t ) = Ebat(t )

Emax∀ t (4.37)

SoCbat(t ) ≤ 1 ∀ t (4.38)

SoCbat(t ) ≥ 1−DoD ∀ t (4.39)

Ebat(t ) represents the actual energy content of the battery storage. The parameter ηbat

is the charging/discharging efficiency which considers the cell and inverter losses of

the AC circuit connected battery system. A maximal depth of discharge (DoD) of 90 %

is allowed for discharging the battery to maintain the unit lifetime. Discharging below

41

Modeling of Building Energy Systems: Mathematical Programming Formulation

the specified DoD results in fast aging due to volume dilatation, respectively, internal

mechanical stress.

Pcharge(t ) ≤ Pmaxcharge ∀ t (4.40)

Pdischarge(t ) ≤ Pmaxdischarge ∀ t (4.41)

During the operation of battery storage systems, the rates of charging and discharging

rates have be limited due to the power limitation of the inverter and to prevent the battery

cells from overheating. Furthermore, with higher charging or discharging currents the

energy losses due to the internal resistance increase.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1

Sp

ecif

ic r

ates

in

A/A

h o

r k

W/k

Wh

Vo

ltag

e in

V

SoC

U_oc

Datenreihen6

U_charge

I_discharge_max

Icharge,max

Linear fit

Uoc

Udischarge

Ucharge

Idischarge,max

Icharge,max

Linear fit

Figure 4.3: Characteristic voltage, current and electrical power trends during the charg-ing process of a Li-Ion battery storage system

Figure 4.3 shows the typical voltage trend of a Li-Ion battery at highest possible charging

rate. The charging voltage Ucharge lies above the open circuit voltage UOC, because of the

internal resistance of the battery cells. Consequently, the maximal charging current must

be further reduced by the end of the charging process to enable a full state of charge.

Hence, a second constraint for the charging rate must be considered.

Pcharge(t ) ≤ (α ·SoCbat(t )+β)

·Ebat(t ) ∀ t (4.42)

This effect is approximated by a linear fit of the descending part of the specific power trend

as a function of the battery state-of-charge, which results in a decreasing upper bound

42

4.7 Water tank

Table 4.3: Parameters of the battery model [Sundstrom O., 2010]

Parameter Value Unit

Emax 2 kWhPmax

charge 4.6 kW

Pmaxdischarge 4.6 kW

ηbat 97.47 %DoD 90 %α -5.8531 kW

kWhβ 5.8675 kW

kWh

of the charging rate towards the end of the charging process as indicated in Equation

4.42. The parameters α and β represent the linear fit coefficients. Table 4.3 provides an

overview of the parameters for the battery model.

4.7 Water tank

Up to now, the investment costs of batteries are relatively high, hindering a widespread

installation of electric storage systems on building level. Residential water storage tanks

are considerably less expensive and allow for desynchronizing a thermal unit’s generation

and building’s heating demand without affecting the residents’ comfort, consequently

providing a large potential for load shifting.

4.7.1 Modeling

It is evident that the modeling or representation of the storage capacity greatly impacts the

scheduling reliability since it is the core flexibility source. Different modeling approaches

for water thermal storage tanks have been proposed in the literature. The most common

MILP representation is based on a simplified single capacity model which assumes that

the storage is homogeneously (fully) mixed or ideally stratified 1, for example in [Di

Zhang et al., 2013, Wakui et al., 2014, Zapata et al., 2014, Zidan et al., 2015, Harb et al.,

2015, Renaldi et al., 2016]. [Schütz et al., 2015a, Schütz et al., 2015b] investigated

the impact of this representation of thermal storage systems and showed that it greatly

decreases the scheduling reliability. The main drawbacks of the single capacity model

are the missing representation of the thermal stratification [Shin et al., 2003, Fan and

Furbo, 2009, Arteconi et al., 2012] within the storage and a noncompliance with the

entropy balance. Mainly, the energy content, regardless of its corresponding temperature,

is always considered as a usable energy. However, the storage layers’ energy content

1The two different assumptions are only relevant for the calculation of the storage losses to the environment

43

Modeling of Building Energy Systems: Mathematical Programming Formulation

can only be considered usable when the corresponding layer’s temperature is equivalent

or above the required flow temperature on the sink side. When a layer’s temperature is

below the flow temperature energy content is considered unusable. Consequently, the

state of charge in single capacity models are expected to overestimate the real value.

Consequently, the thermal losses to the environment cannot be accurately estimated.

A less common approach for MILP applications is layered stratified storage model, which

represent the storage based on a discrete number of layers with corresponding capacities,

for example in [Schütz et al., 2015a, Schütz et al., 2015b]. This allows for a better estima-

tion of the usable energy content and thermal losses but results in high computational

effort due to the increased number of state variables.

In this section, both models for the single capacity and stratified storage are presented.

Furthermore, a novel empirical modeling approach that allows for considering both usable

and unusable energy contents based on the thermocline effect is introduced.

Single capacity

The simplified singe capacity model is formulated based on an energy balance around the

storage considering heat losses proportional to the storage energy content. A concrete

temperature distribution is not calculated, so there is no distinction between usable and

unusable energy based on the temperature level of the stored energy. The time-discrete

equation of this model is introduced Equation 4.43.

Q(t ) =Q(t −1) · (1−xloss,∆t )+ (Qcharge(t )−Qdrawn(t )

)·∆t ∀ t ≥ 1 (4.43)

Q represents the energy content of the storage. Qdrawn(t ) is the drawn heat at time t and

may comprise domestic hot water Qdhw(t ) and space heating Qspace heating(t ) demand.

Qdrawn(t ) = Qdhw(t )+Qspace heating(t ) ∀ t (4.44)

Qcharge(t ) is the charging thermal flow from a heat generation system e.g. HP, CHP, boiler

or auxiliary electrical heater.

Qcharge(t ) =QHP(t )+QEH(t ), for HP-EH systems

QCHP(t )+QBoiler(t ), for CHP-Boiler systems(4.45)

xloss,∆t is a thermal loss coefficient which is empirically determined for a certain time

period ∆t according to 4.46.

44

4.7 Water tank

xloss,∆t =κsto

ρ ·cω·

Asto

Vsto·∆t ∀ t (4.46)

with ρ and cw as the volumetric density and heat capacity of water, respectively. Asto is

the surface area, ksto the thermal transmittance and Vsto the volume of the storage tank.

Layer-based stratification

The stratified or layered storage model is based on a spatially discretized consideration

of the vertical temperature distribution of the storage medium. An energy balance is

formulated for each layer l . The total energy balance is presented in Equations 4.47 - 4.50

by taking into consideration the conduction between the layers, losses to the surroundings

and convective heat fluxes due to the cross section velocity. This formulation is derived

from [Schütz et al., 2015a, Schütz et al., 2015b].

ሶ𝑚charge(𝑡, 𝑙) · 𝑐w · 𝑇charge(t, 𝑙˗1)

ሶ𝑚charge(𝑡, 𝑙) · 𝑐w · 𝑇sto t, 𝑙

ሶ𝑚drawn(𝑡, 𝑙) · 𝑐w · 𝑇sto(𝑡, 𝑙)

ሶ𝑚drawn(𝑡, 𝑙) · 𝑐w · 𝑇ret(t, 𝑙˖1)

𝑇𝑠𝑡𝑜(𝑡, 𝑙) 𝑘sto · 𝐴sto 𝑙 · [𝑇sto 𝑡, 𝑙 − 𝑇env]

𝜆 · 𝐴cs · [𝑇sto 𝑡, 𝑙˗1 − 𝑇sto 𝑡, 𝑙

0.5 · [𝑧 𝑙 + 𝑧 𝑙˗1 ]]

𝜆 · 𝐴cs · [𝑇sto 𝑡, 𝑙˖1 − 𝑇sto 𝑡, 𝑙

0.5 · [𝑧 𝑙 + 𝑧 𝑙˖1 ]]

Figure 4.4: Illustration of the energy balance for a middle layer; the heat flows representthe charging heat from the heat generation unit, the heat conduction betweenneighboring layers, the drawn heat from the consumer cycle and losses tothe tank surrounding environment [Schütz et al., 2015a]

The equation for the top layer is formulated as:

msto(l ) ·cω ·Tsto(t , l )−Tsto(t −1, l )

∆t= mdrawn(t ) ·cω · [Tsto(t , l +1)−Tsto(t , l )]

+mcharge(t ) ·cω · [Tcharge(t )−Tsto(t , l )]−ksto · Asto(l ) · [Tsto(t , l )−Tenv]

+λ · Acs ·

[Tsto(t , l +1)−Tsto(t , l )

0.5 · [z(l )+ z(l +1)]

],∀ t

(4.47)

with mdrawn(t ) as the drawn mass flow rate through the heating distribution system which

45

Modeling of Building Energy Systems: Mathematical Programming Formulation

is determined according to Equation 4.48.

mdrawn(t ) =mnom

drawn, if Qdrawn(t ) > 0

0, if Qdrawn(t ) = 0(4.48)

Tsto is the vector for the vertical temperature distribution and Acs is the cross-sectional

area. The value for the heat generator temperature Tcharge depends on the installed unit.

mcharge(t ) is the mass flow rate through the heat supply system and has a nominal value in

case the unit is on or set equal to zero if it is off, similar to mdrawn(t ) in Equation 4.48. z

is the height of one storage layer. The term ksto · Asto(l ) represents the heat losses over

the surface and the term λ · Acs denotes the heat conductance between the layers. The

parameter λ is the thermal conductivity of water.

The equation for any middle layer is based on the energy balance depicted in Figure 4.4

and is formulated as:

msto(l ) ·cw ·Tsto(t , l )−Tsto(t −1, l )

∆t= mdrawn(t ) ·cw · [Tsto(t , l +1)−Tsto(t , l )]

+mcharge(t ) ·cw · [Tcharge(t , l +1)−Tsto(t , l )]−ksto · Asto(l ) · [Tsto(t , l )−Tenv]

+λ · Acs ·

[Tsto(t , l −1)−Tsto(t , l )

0.5 · [z(l )+ z(l −1)]+ Tsto(t , l +1)−Tsto(t , l )

0.5 · [z(l )+ z(l +1)]

],∀ t

(4.49)

The equation for the bottom layer is:

msto(l ) ·cw ·Tsto(t , l )−Tsto(t −1, l )

∆t= mdrawn(t ) ·cw · [Tret(t )−Tsto(t , l )]

+mcharge(t ) ·cw · [Tsto(t , l −1)−Tsto(t , l )]−ksto · Asto(l ) · [Tsto(t , l )−Tenv]

+λ · Acs ·

[Tsto(t , l −1)−Tsto(t , l )

0.5 · [z(l )+ z(l −1)]

],∀ t

(4.50)

Empirical thermocline

We propose a novel empirical approach for modeling water storage that extends the energy

balance of the capacity model by differentiating between usable and unusable energy

content. The formulation is presented in Equation 4.51 - 4.58. The usable energy amount

for the consumer cycle is determined by quantifying and subtracting an unusable amount

from the storage energy content. Under the assumption that the temperature profile of the

storage medium is linear at all times along the height of the tank, the storage is considered

to be empty when the tapping water temperature drops down to the flow temperature. At

this point, no further energy can be extracted from the tank. The temperature can only

decrease due to environmental losses. In this case, the drawn water temperature is below

46

4.7 Water tank

𝑇𝑟𝑒𝑡 𝑇𝑐ℎ𝑎𝑟𝑔𝑒𝑇𝑓𝑙𝑜𝑤 𝑇𝑟𝑒𝑡 𝑇𝑐ℎ𝑎𝑟𝑔𝑒𝑇𝑓𝑙𝑜𝑤 𝑇𝑟𝑒𝑡 𝑇𝑐ℎ𝑎𝑟𝑔𝑒𝑇𝑓𝑙𝑜𝑤 𝑇𝑟𝑒𝑡 𝑇𝑐ℎ𝑎𝑟𝑔𝑒𝑇𝑓𝑙𝑜𝑤

ℎ𝑒𝑖𝑔ℎ𝑡

𝑓𝑢𝑙𝑙𝑦 𝑐ℎ𝑎𝑟𝑔𝑒𝑑 ℎ𝑎𝑙𝑓 𝑐ℎ𝑎𝑟𝑔𝑒𝑑 𝑓𝑢𝑙𝑙𝑦 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒𝑑 𝑏𝑒𝑙𝑜𝑤 𝑓𝑢𝑙𝑙𝑦 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒𝑑

Figure 4.5: Generic representation of the different states for the SoC of the empiricalapproach. The black solid line depicts the temperature profile [Harb et al.,2017]

the consumer flow temperature and the storage must be charged to reach a usable SoC

of zero again. The behavior of the temperature distribution for the assumptions of this

model, and the corresponding states of charge, are exemplary shown in Figure 4.5.

Q(t ) =Q(t −1) · (1−xloss,∆t )+ (Qcharge(t )−Qdrawn(t )) ·∆t ∀ t ≥ 1 (4.51)

Qusable(t ) =Q(t −1) · (1−xloss,∆t )−Qunusable, bottom−Qunusable(t ) ∀ t ≥ 1 (4.52)

Qusable(t )/∆t +Qcharge(t ) ≥ Qdrawn(t ) ∀ t (4.53)

Qusable(t ),Qunusable(t ) ≥ 0 ∀ t (4.54)

The amount of unusable energy due to mixing effects in the storage Qunusable(t ) depends on

the consumer flow Tflow and return Tret temperature as well as the storage volume. Tflow

can be extracted from the heating curve of the corresponding heat distribution system

while Tret can be roughly approximated based on the heat exchanger characteristic while

assuming a constant mass flow rate. Both Tflow and Tret are assumed to be constant for

the considered time sequence, since the changes of the outside temperature are very slow

compared to the characteristic time scales in which the storage is (dis-)charged.

Qunusable(t ) is determined based on the assumption that the temperature distribution of

the storage medium depends not only on the SoC but also on the dynamic development of

the mixing zone between the hot and cold section area in the tank as observed in [Nelson

et al., 1999]. The authors in [Chung and Shin, 2011] observe a proportionality between

the thermocline thickness and the square-root of time. Hence, a saturation behavior of

the development of the mixing zone can be assumed. Since mixing of hot and cold water

47

Modeling of Building Energy Systems: Mathematical Programming Formulation

causes a loss of exergy, a part of the unusable energy is assumed to have a saturation

behavior as well, which is approximated in Equation 4.55.

Qunusable(t ) = Qunusable(t −1)+(Qmax

unusable−Qunusable(t −1))·Cunusable, thermo ·∆t ,∀ t ≥ 1

(4.55)

The coefficient Cunusable, thermo is an empirical value that is approximated by means of the

measurement data. Qmaxunusable is the upper bound for Qunusable and is defined in Equation

4.56.

Qmaxunusable =

1

2· (Tflow−Tret) · Acs · Hsto ·ρcw ·Cunusable (4.56)

Qunusable, bottom = (Tret−Tenv) ·cw ·ρ ·Vsto (4.57)

Cunusable denotes an empirical scaling factor for the amount of unusable energy that is

depicted in Figure 4.5. It ranges between 0 (for no mixing at all) and 1 (for the assumption

of a linear temperature profile). Furthermore, an additional unusable amount of energy is

defined in Equation 4.57 by considering the energy under the level of Tret with reference

to the environmental temperature Tenv, based on the storage volume which corresponds

to the product of the storage height Hsto and cross-sectional area Acs, to approximate

the environmental losses correctly. The amount of unusable energy is reset to the initial

amount when the TS is completely charged or after a longer standstill. Furthermore, the

whole storage content is considered to be unusable after longer time periods without

charging phases. The temperature level of the hot water section Ttap is approximated by

Equation 4.58. Ctap is an empirical scaling factor.

Ttap(t ) = Ttap(t −1)− (Ttap(t )−Tenv

)·xloss,∆t ·Ctap ∀ t ≥ 1 (4.58)

When Ttap drops down under Tflow the storage is considered to be empty. The remaining

energy is unusable. The content can be made usable by charging the storage another

time.

4.7.2 Definition of SoC

The thermal energy content of the storage is defined using a dimensionless factor, state of

charge (SoC). In this work, the SoC for water tank is defined as in Equation 4.59.

SoC = Qusable

Qmax(4.59)

The maximal storable energy Qmax corresponds to the state at which the whole storage

medium has the heat generator temperature Tcharge. Qusable denotes the usable amount of

48

4.7 Water tank

energy and is defined as the thermal energy that is available at a temperature level equal

or above the consumer flow temperature Tflow, with reference to the consumer return

temperature. Figure 4.6 shows exemplary the consideration for Qusable. The stored energy

at a level of L > Lsto−Lcrit is considered usable. The usable amount of energy is spatially

𝑇𝑟𝑟𝑟 𝑇𝑐𝑐𝑐𝑟𝑐𝑟 𝑇𝑓𝑓𝑓𝑓

L

usable storage content

unusable storage content

𝐿𝑠𝑟𝑓 − 𝐿𝑐𝑟𝑐𝑟

Figure 4.6: Consideration of the usable and unusable amount of energy for the determi-nation of the SoC [Harb et al., 2017]

discretized and evaluated according to Equation 4.60. Nl denotes the total number of

layers discretization within the storage.

Qusable =

Vsto ·ρ ·cw ·∆L

L

Nl∑l=1

(Tl −Tret), for Tl ≥ Tflow

0, for Tl < Tflow

(4.60)

With this definition of the SoC, the usable energy content in the tank is estimated very

conservatively. Energy that is available on a temperature level slightly below consumer

flow temperature is considered to be completely unusable. This definition allows for

determining the point in time when an additional heat generation is required.

4.7.3 Experimental evaluation

In this section, the performance of the above formulated modeling approaches for thermal

water storage tanks is evaluated based on measurement data from an experimental setup.

49

Modeling of Building Energy Systems: Mathematical Programming Formulation

Setup

The experimental setup comprises a water tank Logalux PNR 500E [Buderus, 2017] which

has capacity of 500 l and a thermal transmittance, ksto = 1.01805W/(m2 K). 5 rods made

of stainless steel are vertically inserted into the tank for measuring the temperature

profile. In each rod, 10 thermocouples are equidistantly installed with a gap of 150 mm.

Consequently, each temperature value along the 10 levels (vertically) is measured over 5

points (radially).

The built-in heat exchanger inside of the water tank has been removed, so that it is directly

charged and discharged. A diffuser is installed to reduce the mixing of the water influx

during both the charging and the discharging cycle. The setup comprises two supply units

each connected to a heat exchanger which allow for heating and cooling the tank. The

cooling is achieved by circulating the tank’s medium from the upper layer through the

cooling exchanger and reintroducing it into the inlet at the bottom of the storage. The

heating is carried out by circulating the tank’s medium from the bottom layer over the

heating exchanger and reintroducing it at the upper inlet of the tank.

T

T

T

TES

Figure 4.7: Experimental scehme depicting the supply unit for the storage during thecharging cycle

Figure 4.7 illustrates the instrumental scheme of measurement and control for the charg-

ing cycle. The setup of the cooling cycle is analogous to the setup introduced in Figure

4.7. The control of the inlet temperatures and flow rates are decoupled in both cycles

by integrating 2 bypasses in each supply unit. Thus, the dead time between changes in

the valve position and the control temperature can be kept constant and reduced to a

minimum. The temperature in the supply unit is measured by PT100 elements. A magnetic

inductive flow meter is installed for measuring the flow rate.

50

4.7 Water tank

Results

In the following sections the results of the experimental assessment of the storage model-

ing approaches based on three use cases are presented.

Table 4.4: Configuration within the investigated use cases

Parameter Use case 1 Use case 2 Use case 3 Unit

Tcharge 65 60 50 °CTenv 22 22 22 °CTret 30 35-45 35 °CT init 32 32 36 °C

Across the use cases, the storage is charged and discharged with different temperature

levels for both consumer return and heat generator flow temperatures to represent typical

energy system configurations in residential buildings. Furthermore, several standstills of

the tank are realized between the operation phases (charging/discharging) to examine

and evaluate the heat losses to the surroundings. Table 4.4 gives an overview on the

configuration of the use cases.

Use case 1 The goal of this use case is to examine the mixing between the hot and

the cold water fronts and the time-dependent development of the temperature profile in

general for non-operating tanks. Furthermore, the heat loss transmission coefficient to

the environment can be investigated based on the data of the standstill periods. At the

beginning, the storage is entirely cooled down. The initial temperature of the storage

medium is quite homogeneous and equivalent to the return temperature. After an effective

partial charging, the storage is operated in a standstill mode for a time period of 6 days.

Thereafter, the tank is charged again then put in standstill for 4 days.

The SoC for the measured data (mSoC) and the three modeling approaches is depicted in

Figure 4.8. The mSoC falls continuously during the standstill after the charging phase.

The development is relatively linear. After a standstill of three days, the mSoC rapidly falls

towards 0. At this point, the temperature level of the hot section area drops under the

defined flow temperature, so the remaining energy is considered to be unusable.

The single capacity approach greatly overestimates the energy content of the storage

through the whole test. The mixing of hot and cold water is not considered in the model

and, therefore, the usable storage potential is overestimated from the very beginning of

the test. Due to the expansion of the mixing zone, the difference between the SoC of the

capacity model and the mSoC increases. The drop under the flow temperature cannot

be depicted. Furthermore, the approximation for the environmental losses is not well

51

Modeling of Building Energy Systems: Mathematical Programming Formulation

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Time in min

0.0

0.2

0.4

0.6

0.8

1.0SoC

measured datacapacity approachstratified approach - 5empirical approach - f. 0.5

measured datacapacity approachstratified approach - 5empirical approach - f. 0.5

Figure 4.8: SoC comparison of the storage modeling approaches with the respect tomeasurement data for use case 1; The stratified storage model comprises 5layers while Cunusabl e is represented by the factor f and set to the value 0.5

represented. There is no proportionality between the energy content of the storage and

the losses unless the return temperature Tret is on the same level as the environmental

temperature Tenv which would be unrealistically low.

In the stratified storage model, the SoC is slightly underestimated after the first operational

phase. During charging or discharging, the energy balance of a discretized layer for direct-

loaded tanks contains a convective term on account of the cross section velocity. Water

that goes from one layer to another is considered to be totally mixed as it enters the new

layer. For this reason, mixing effects due to operational phases are overestimated in this

model. This miscalculation becomes more evident when the storage is being charged

and discharged in parallel since the flow rates of the heat source and consumer are

considered autonomously. Figure 4.9 depicts the deviation of the calculated and the

measured temperature profiles. The deviation gets lower with increasing operational

time, as depicted in Figure 4.9d. The temperature difference between measurements and

simulation in the top layer is caused the missing consideration of the natural convection

phenomenon in the modeling approach. Therefore, the calculated temperature distribution

52

4.7 Water tank

is not strictly decreasing and interpolating over temperatures may lead to discontinuities

for the SoC approximated by the stratified storage model during a standstill. The drop

under the flow temperature is well depicted.

2 0 3 0 4 0 5 0 6 0 7 0 8 0tem peraturecin ◦ C

1

2

3

4

5

6

7

8

9

1 0

mea

sure

men

tcpo

ints

s im ula tionm eas uredcdata

2 0 3 0 4 0 5 0 6 0 7 0 8 0tem perature inc ◦ C

1

2

3

4

5

6

7

8

9

1 0

2 0 3 0 4 0 5 0 6 0 7 0 8 0tem perature cin ◦ C

1

2

3

4

5

6

7

8

9

1 0

2 0 3 0 4 0 5 0 6 0 7 0 8 0tem perature cin ◦ C

1

2

3

4

5

6

7

8

9

1 0

tcc=c16cmin tcc=c23cmin tcc=c100cmin tcc=c4300cmincccccccccccc(a) cccccccccccc(b) cccccccccccc(c) cccccccccccc(d)

Figure 4.9: Comparison of the development of the temperature profile for the measureddata and the stratified storage model in use case 1

In the empirical approach, the SoC is approximated sufficiently. The deviation from the

mSoC is relatively low, both at the beginning after the charging and during the standstill.

The drop of the temperature of the hot water section under the flow temperature is only

roughly approximated.

Use case 2 The goal of use case 2 is to examine the development of the temperature

profile during operational phases in comparison to the development during standstills

investigated in use case 1. The storage is partially charged and subsequently set in

a standstill of 21.5 h. Thereafter, the storage is continuously charged and discharged

alternately over a period of 5.5 h. Finally, the storage is charged and discharged another

time over a period of 3 hours and then completely discharged. During this period,

charging and discharging are done in parallel. The SoC for the measured data and

the three modeling approaches for use case 2 are shown in Figure 4.10. The SoC for

the capacity approach shows an increasing deviation from the mSoC. Furthermore, the

SoC is overestimated from the very beginning where the inaccurate approximation of

environmental losses has only a low influence on the deviation. In the stratified approach,

the SoC is underestimated at the beginning of the test. After the second operational phase,

the stratified approach gives a better approximation for the SoC. The storage content

53

Modeling of Building Energy Systems: Mathematical Programming Formulation

0 1000 2000 3000 4000 5000 6000

Time in min

0.0

0.2

0.4

0.6

0.8

1.0SoC

measured datacapacity approachstratified approach - 5empirical approach - f. 0.5

measured datacapacity approachstratified approach - 5empirical approach - f. 0.5

Figure 4.10: SoC comparison of the storage modeling approaches with the respect tomeasurement data in use case 2

is more mixed due to the influx of water over the diffusers. This effect is not explicitly

described by the stratified approach. However, it is indirectly considered as the convective

flows between the discrete layers result in a certain mixing. For a higher degree of mixing

in the water tank, the solution of the stratified approach gets better. The temperature

drop of the storage medium under the consumer flow temperature is well depicted. In the

empirical approach, the SoC is well approximated, especially at the beginning of the test.

Time-dependent mixing effects are simulated. However, the effects due to inlet mixing

characteristics are not represented. For that reason, the deviation of the model predicted

SoC from the mSoC rapidly changes during the second operational phase (t ~1300 min).

However, mixing due to the influx of water can be statistically represented through time

by adapting Cunusable, thermo. The temperature drop under the consumer flow temperature

is roughly simulated.

Use case 3 The goal of this use case is to generate typical conditions for a storage oper-

ation in connection with a heat pump resulting in a relatively low charging temperature.

The initial temperature of the storage medium is set close to a typical consumer return

54

4.7 Water tank

temperature. The storage is simultaneously charged and discharged for a period of 10 h

then set in a standstill of 24 h.

0 500 1000 1500 2000

Time in min

0.0

0.2

0.4

0.6

0.8

1.0

SoC

measured datacapacity approachstratified approach - 5empirical approach - f. 0.5

measured datacapacity approachstratified approach - 5empirical approach - f. 0.5

Figure 4.11: SoC comparison of the storage modeling approaches with the respect tomeasurement data in use case 3

The results of use case 3 are depicted in Figure 4.11. Due to a low temperature differ-

ence between Tflow and Tret, the unusable energy, with regard to the stored energy, is

relatively low compared with the other use cases. Thus, the temporal development of

the unusable energy has a lower influence on the SoC. For this reason, the deviation of

the capacity model is at the beginning of the test lower than it is for the previous use

cases. Nevertheless, the inaccurate approximation for the environmental losses results

in an increasing difference. The stratified storage model underestimates the SoC at the

beginning. For a discretization of 5 and 10 layers the stratified approach shows similar

results. An increase of the layers’ number considered does not improve the results. The

initial development of the SoC in the empirical approach accurately matches the mSoC.

The temporal development of the amount of usable energy calculated by the model is

low compared to the other use cases indicating that Qmaxunusable is overestimated for this

configuration.

55

Modeling of Building Energy Systems: Mathematical Programming Formulation

Conclusion The results indicate that the widely adopted simplified capacity storage

model greatly overestimates the usable energy content especially for high temperature

differences in the storage. Further, the approximation of the environmental losses within

this approach is insufficient.

The stratified storage approach provides a solution with general applicability for different

temperature ranges. However, the mixing due to convection between the discrete layers

caused by charging and discharging of the tank is highly overestimated in this modeling

approach.

The introduced empirical approach allows for representing the dynamic development of

the unusable energy content and delivers the best approximation of the storage’s state of

charge. Furthermore, this representation comprises less decision variables compared with

the stratified formulation which represents a decisive advantage for the implementation

and computational effort in the scope of MILP models.

4.8 Building wall mass

Building thermal wall mass provides a flexible heat capacity which can be effectively used

for load shifting, thus enabling demand side management. The most crucial barrier for

a practical application of buildings as short term heat storage is the lack of knowledge

about the building physical properties. The challenge lies in accurately estimating the

building thermal dynamics and response to avoid affecting the residents comfort. The

modeling concepts of building thermal behavior can be categorized into data driven and

design driven [Li and Wen, 2014]. Design driven models require extensive information on

the physical characteristics of the buildings, that are typically not available for existing

building stock. Data-driven models are an inverse modeling approach that explore his-

torical measurement data to estimate the building thermal behavior. This approach has

gained a lot of interest with the recent roll out of smart meters which led to increased

availability of sensors’ data.

Data-driven models comprise black-box and grey-box models. Black box models don’t

require fundamental knowledge of the building physical properties and comprise autore-

gression models with exogenous inputs, multiple regression, exponential smoothing and

machine learning algorithms i.e. artificial neural networks and support vector machines.

Autoregression models are frequently used in the literature for simulating the thermal

building behaviour to enable HVAC predictive control [Loveday and Craggs, 1993, Love-

day and Craggs, 1992]. However, these models do not allow for capturing non-linear

effects and are therefore only valid for a limited range of values [Kristensen et al., 2004].

Machine learning algorithms allow for modeling non-linear relation and have been ex-

tensively applied in the literature [Lundin et al., 2004, Lundin et al., 2005, Mustafaraj

56

4.8 Building wall mass

et al., 2011, Frausto and Pieters, 2004, Ruano et al., 2006]. However, the performance

of these algorithms is limited to the extent and quality of the data used for the model

training so that long periods of data from different seasons of the year are needed to

generate a robust building model. Grey-box denotes an intermediate stage that combines

the data based system identification of black-box models and partially physical relations

of white-box models.

4.8.1 Modeling: Grey-box

The structure of grey-box-models is developed based on knowledge of the physical effects

of the system. This structure is represented as xR yC networks with lumped parameters

in analogy to an electrical circuit with x as the number of thermal resistances and y of

thermal capacities. The choice of a proper model structure is critical for the ability of the

model to reproduce the building thermal behavior in an accurate way without increasing

the model complexity.

Te

Ce

Re,a

Exterior Ambience

Ta,eq

Tin

Cin

Interior

Ria,a

Ta

Rin,ia Ria,e

Indoor Air

Tia

Φsol, in

Φh, in

Φh, ia

Φsol, ia

Φh, e

Figure 4.12: 4R2C model structure [Harb et al., 2016a]

In [Harb et al., 2016a], four grey-box model structures were compared in their ability to

forecast the indoor temperature behavior in occupied buildings based on single zone rep-

resentation. The analysis revealed that a two-capacity model structure with an additional

consideration of the indoor air as a mass-less node (4R2C) enables the most accurate

qualitative prediction of the indoor temperature.

Figure 4.12 illustrates the 4R2C model structure. This structure comprises two capacities

summarizing the interior Cin and exterior Ce building components respectively. The indoor

57

Modeling of Building Energy Systems: Mathematical Programming Formulation

air is considered as a separate temperature node with no thermal capacity. The heat

dynamics are expressed by the following differential equations:

dTin = 1

Rin, ia ·Cin(Tia−Tin)d t + 1

Cin(Φh,in+ (1− fconv) ·Φsol)d t +dωin (4.61)

dTe = 1

Ria, e ·Ce(Tia−Te)d t + 1

Re, a ·Ce(Ta, eq−Te)d t + 1

CeΦh, ed t +dωe (4.62)

As well as the algebraic equation around the indoor air Tia node.

0 = 1

Rin, ia(Tin−Tia)+ 1

Ria, e(Te−Tia)+ 1

Ria, a(Ta−Tia)

+ fconv ·Φsol+Φh, ia

(4.63)

The infiltration heat resistance Ria, e connects the indoor air node with the outdoor air.

Rin, ia and Ria, e represent the convective heat exchange between the walls and indoor air.

Radiation heat transfer between interior and exterior is neglected. The heat flux from

the heating system is partly transferred directly to the indoor air. According to a rule

of thumb, presented in DIN EN ISO 13790 [DIN - German Institute for Standardization,

2008b], the convective contribution of the solar heat gains through transparent surfaces

i.e. windows can be assumed at fconv = 9%. The allocation of the heat supply Φh to the

indoor air Φh, ia as well as the interior Φh, in and exterior Φh, e wall is carried out according

to Equations 4.64-4.66:

Φh, ia =Φh · (1− fheat, rad) (4.64)

Φh, in = (Φh−Φh, ia) · (1− fheat,rad,ext) (4.65)

Φh, e = (Φh−Φh, ia) · fheat, rad, ext (4.66)

with fheat, rad = 0.2 representing the radiation contribution of the heat flux from the heater

and fheat, rad, ext = γe, floor/γin, floor as the share of the radiation contribution to the exterior

walls. γin, floor is the quotient between the area of interior walls and floor area while

g ammae, floor is the quotient between the area of external walls and floor area. γin, floor

and γe, floor are assumed as 2.5 and 1.5 respectively.

Ta, eq = Ta+Qirradaf

αA(4.67)

Ta, eq is an equivalent outdoor temperature at the exterior surfaces by considering the

influence of short-wave radiation calculated based on the VDI 6007 [Association of Engi-

58

4.8 Building wall mass

neers, 2012b] to allow for a more precise representation of the heat exchange between

the building exterior and the environment. The impact of long-wave radiation is neglected

as a simplification. Ta, eq is calculated as indicated in Equation 4.67 with a short-wave ab-

sorption coefficient of the exterior surface af = 0.5 and an exterior heat transfer coefficient

αA = 25Wh/(m2 K). Ta is the outdoor air temperature and Qirrad denotes the global solar

radiation on a horizontal surface. Ta, eq applies only for the transmission heat exchange

between building envelope and ambiance. The infiltration heat losses over the thermal

resistance Rin, a use further Ta as reference outdoor air temperature.

Φsol represents the solar heat gains absorbed by the interior building components and is

determined according to:

Φsol = fsol ·Qirrad (4.68)

fsol is a factor ranging between 0 and 0.25, which is empirically defined based on [Bacher

and Madsen, 2011]. The value of fsol is determined during the fitting process.

4.8.2 Model identification approach: Parameterization

The goal of the model identification process is to determine the set of the parameters

which reproduces the building thermal behavior most accurately during the training

period ttrain.

f (x) =ttrain∑

t(T (t )−T (t ))2 (4.69)

This is achieved by formulating an non-linear optimization problem that minimizes the

objective function f (x) in Equation 4.69 subject to the grey-box model structure equations

4.61 - 4.63 as constraints. x is a vector of the model parameters, T (t ) the simulated indoor

air temperature at the time step t and T (t ) the measured indoor air temperature vector

over the training period. Interior point method [Waltz et al., 2006] is useful to handle

large non-linear optimization problems with inequality constraints and therefore employed

as solver. Alternative solvers are metaheuristics such evolutionary algorithms or mixed

integer non-linear program.

The boundaries of the model parameters are defined based on several norms and guide-

lines [DIN - German Institute for Standardization, 2003, DIN - German Institute for

Standardization, 2005, DIN - German Institute for Standardization, 2008a, Recknagel

et al., 2009, Association of Engineers, 2012c, Association of Engineers, 2012a]. The

boundaries are defined as specific values to the building floor area and are then multiplied

by it during the simulation. An overview is provided in Table 4.5.

59

Modeling of Building Energy Systems: Mathematical Programming Formulation

Table 4.5: Specific parameters boundaries [DIN - German Institute for Standardization,2005, Recknagel et al., 2009, Association of Engineers, 2012a]

Parameter LB Initial value UB Unit

1/Re, a 0.77 1 2.0 W/(m2 K)1/Rin, ia 0.5 2.5 25 W/(m2 K)1/Ria, a 0.15 0.5 1.5 W/(m2 K)1/Ria, e 0.5 2.5 25 W/(m2 K)

Ce 10 50 200 Wh/(m2 K)Cin 30 70 500 Wh/(m2 K)

60

5 Scheduling Algorithms

This section delivers an overview on the fundamentals of mathematical programming

discrete optimization. Thereafter, the formulation of a deterministic MILP scheduling

model for a single building is presented, followed by a scheduling under uncertainty model

based on stochastic programming. Finally, distributed scheduling algorithms for city

districts or microgrids are formulated based on decomposition methods.

5.1 Mathematical optimization: Fundamentals

Linear programming: Mathematical programming optimization problems are formu-

lated based on an objective function zP comprising the decision variables’ vector ~x that

is maximized or minimized subject to restrictions known as constraints [Bradley et al.,

1977, Bertsimas and Tsitsiklis, 1997, Castillo, 2002]. The simplest form of a mathematical

optimization problem is a linear program (LP) where the dependencies between decision

variables in both the objective function and the constraints are linear and the decision

variable are continuous as in Equation 5.1. LPs are solved using two main classes of

methods, simplex method which is a gradient descent method that moves along the edge

or vertices of the feasible region i.e. solution space and interior point methods (IPM)

that move through the interior of the feasible region. Dual simplex method is an evolved

version of the simplex algorithm that takes advantage of the duality theory.

min zP = cT ·~x

s.t.: A~x ≤ b

~x ≥ 0

(5.1)

Duality theory: Given any LP in the form of Equation 5.1, which is known as primal

problem, there exists another corresponding problem called dual problem which is for-

mulated according to Equation 5.2. The latter is referred to as the dual of problem 5.1

and vice versa. The variables ~y are called dual variables or dual multipliers. For every

constraint in the primal problem there is a variable in the dual problem and for every

variable in the primal problem there is a constraint in the dual problem.

61

Scheduling Algorithms

max zD = bT~y

s.t.: AT~y ≥ c

~y ≥ 0

(5.2)

Let z∗P be the optimal solution to the primal problem and z∗

D be the optimal solution to the

dual problem. The duality gap is defined as z∗P − z∗

D. A problem is said to hold weak duality,

if this gap is greater than zero and it holds strong duality, if the duality gap is equal to

zero [Bradley et al., 1977]. Hence, it is possible to solve the primal problem by solving its

dual counterpart which is exploited by the dual simplex algorithm [Bradley et al., 1977].

Furthermore, the solution of the dual problem gives several information about the primal

problem regarding sensitivity e.g. through shadow prices.

Shadow prices: The dual theory properties are significant for sensitivity analysis in

mathematical economic problems. Analyzing incremental changes in the primal LP

problem allows for an economical interpretation of the dual solution vector. It can be

shown that a small change d in the right-hand side vector of a primal equality constraint

i results in a change equal to πi ·d in the optimal primal cost, with πi being part of the

optimal solution to the dual problem [Bertsimas and Tsitsiklis, 1997]. Therefore, the

optimal dual solutions can be interpreted as the marginal cost per unit increase of a

requirement associated with a particular constraint. This vector is referred to as shadow

prices vector. Shadow prices are determined automatically when using a modern solver

like the Gurobi [Gurobi Optimization, 2017] or CPLEX [IBM, 2017] optimizers.

MILP: Most practical optimization problems, e.g. scheduling, require integer decision

variables. A program, where the decision variables x are integer and continuous variables,

is called mixed integer linear program (MILP). The general method to solve a MILP is

the branch-and-bound algorithm. The branch-and-bound algorithm solves a MILP by

linearly relaxing the integrality conditions (LP-relaxation). Thereafter, a decision tree is

spanned called branch-and-bound tree which comprises all possible states of the integer

variables. Every new integer variable that is introduced to the problem results in an

additional node in the branch-and-bound tree. The algorithm sets up lower and upper

bounds of the optimal solution. Every optimal solution to the LP relaxation provides a

lower bound and every feasible integer solution provides an upper bound. The branching

strategy sequentially refines these bounds. An improved version of this method is the

branch-and-cut algorithm which is a combination of the branch and bound algorithm and

cutting planes. Cutting planes are constraints that are added to the problem with the aim

to reduce the size of the solution space. Therefore, previous solutions are "cut" from the

62

5.2 Single building scheduling approaches

branch-and-bound tree in case they lay outside the current UB. Thereby, non promising

nodes in the branch-and-bound tree can be dropped thus reducing the size of the problem

and the computation time [Castillo, 2002].

Convex-hull pricing model: The definition of shadow prices is based on assumptions

that hold only for LP problems. To attain the optimal shadow prices when solving MILP

problems, a linear relaxation of the MILP problem has to be introduced that allows the

integer variables to take every value from within the convex hull of the integer solution

space. Therefore the optimal dual solution to this problem is called convex hull price.

5.2 Single building scheduling approaches

5.2.1 Deterministic MILP model

The deterministic formulation of the scheduling problem for a single building employs

point forecasts for both the weather variables and consequently PV generation as well as

DHW, electrical and space heating demands. Hence, a single scenario (s) is investigated

which corresponds to the expected values from the corresponding forecasts.

The scheduling problem minimizes the objective function formulated in Equation 5.3

subject to a power balance constraint shown in Equation 5.5 as well as the corresponding

energy generation and storage units presented in Chapter 4. The objective function is a

balance of the costs of the electricity bought from the grid and profit from remuneration

for electricity feed-in Psellug

(t , s) from PV or CHP surplus fed into the grid.

C (s) =tH∑

t=t0

cbuy ·Pbuy(t , s) ·∆t +tH∑

t=t0

cgas ·Qgas(t , s) ·∆t −tH∑

t=t0

∑ug∈Ug

csellug

·Psellug

(t , s) ·∆t ∀ s (5.3)

tH is the horizon of the moving window algorithm. cgas, cbuy and csellug

are constant

coefficients that define the specific cost of gas and imported energy from the public grid

as well as the feed-in compensation from the corresponding unit. Pbuy(t , s) and Psellug

(t , s)

are optimization variables. The simultaneous import from and export into the public power

grid is not allowed. Qgas(t , s) is the combined gas cosumption from available CHPs or

boilers as indicated in Equation 5.4.

Qgas(t , s) = QgasCHP(t , s)+Qgas

Boiler(t , s) ∀ t , s (5.4)

The power balance links the electricity generation and consumption of the individual

generating Ug = {CHP,PV,Batdischarge

}and consuming Uc =

{HP,EH,Batcharge

}units to the

63

Scheduling Algorithms

interaction with the grid and local electricity demand Pdem(t , s) for lights and appliances.

The local electricity generated Pug (t , s) may flow into the internal circuit of the building,

denoted as self-consumption Pselfug

(t , s) or exported/sold to public grid Psellug

(t , s).

Pbuy(t , s)− ∑ug∈Ug

Psellug

(t , s)+ ∑ug∈Ug

Pselfug

(t , s) = ∑uc∈Uc

Puc (t , s)+Pdem(t , s) ∀ t , s (5.5)

Pug (t , s) = Psellug

(t , s)+Pselfug

(t , s) ∀ t , s (5.6)

Pbuy(t , s),Psell(t , s),Psellug

(t , s),Pselfug

(t , s),Puc (t , s) ≥ 0 ∀ t , s (5.7)

5.2.2 Scheduling under uncertainty: Multi-stage stochastic programming

As previously shown in Section 3.2.5, the forecasts of domestic hot water and electrical

demand, which are both significantly influenced by the stochastic behavior of the resi-

dents, exhibit large errors. Consequently, schedules generated based on such forecasts

are expected to be unreliable when the uncertainty is realized. Multi-stage stochastic

programming allows for coping with demand uncertainties by taking into account different

realizations of the uncertainty in terms of probability distribution functions in the predic-

itve scheduling phase. The basic idea behind stochastic programming problem is to make

some ’here and now’ decisions before the actual realization of the uncertainty during

the first stage, and to take some ’wait and see’ or corrective decisions, in the second

stage after revelation of the uncertainty [Grossmann, 2012]. In a stochastic problem, the

cost of the decisions and the expected cost of the recourse actions are optimized [Conejo

et al., 2010]. If there are only two stages then the problem corresponds to a two-stage

stochastic program, while in a multi-stage stochastic program the uncertainty is revealed

sequentially, i.e. in multiple stages or periods, and corrective actions are then decided

over a sequence of stages.

Objective function

The objective function of the stochastic program extends the objective function for the

deterministic MILP which correpsonds to a single scenario. Consequently, an SP can be

formulated as:

arg min E {C (s)} (5.8)

E {C (s)} =NS∑s=1

π(s) ·C (s) (5.9)

E {C (s)} denotes the expected value of the scenario s specific objective function C (s) . It

is calculated by the probability weighted sum of the respective cost functions of each

64

5.2 Single building scheduling approaches

s1 s2 s3 s4 s5 s6 s7 s8 s9

π1 π3

π11 π12 π13 π21 π22 π23

π2

π31 π32 π33

root

leaf

Figure 5.1: Derivation of the scenarios’ probabilities π(s) from the root to the leaf nodeswithin the scenario tree of multi-stage stochastic programming

scenario. The scenario probabilities π(s) are derived from the product of transition

probabilities from the root to the leaf node in the scenarios tree as illustrated in Figure

5.1

Scenario tree generation

The initial step for formulating an SP is to describe the uncertatinty. Electrical and

domestic hot water demand are set as a source of uncertainty as they result in the highest

forecasting error. On the basis that the uncertainty follows a discrete probability distri-

butions, a stochastic process can be represented with scenario trees. The probabilistic

information for the electrical and DHW demand can be extracted either from a stochastic

forecast model by Monte-Carlo sampling which generates a large set of equi-probable sce-

nario, or from historical observation respectively measurement data. The obtained sample

set denotes a discrete representation of the underlying stochastic model; process and its

distribution; of the corresponding uncertainty. The set is then reduced for decreasing

computational complexity in the targeted optimization problem. The scenario reduction is

carried out by the fast forward selection heuristic [Gröwe-Kuska et al., 2003] for solving

the Kantorovich distance problem. This algorithm aims to find the best approximation

of the original set by a predefined number of scenarios similar to supervised clustering

algorithms.

The left diagram in Figures 5.2 and 5.3 depicts the scenario samples for DHW and electrical

demands. The solid black line denotes the point forecast and the scenario samples are

65

Scheduling Algorithms

0 5 1 0 1 5 2 0 2 50

5 0 01 0 0 01 5 0 02 0 0 02 5 0 03 0 0 03 5 0 04 0 0 0

Mean: 3 8 6 0 .5 7SD: 1 2 6 2 .4 5

0 5 1 0 1 5 2 0 2 50

1 0 0 0

2 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

Mean: 1 7 0 4 4 .3SD: 3 1 4 0 .9 4

0 5 1 0 1 5 2 0 2 50

5 0 01 0 0 01 5 0 02 0 0 02 5 0 03 0 0 03 5 0 04 0 0 0

0 5 1 0 1 5 2 0 2 50

1 0 0 0

2 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

Time steps in h Time steps in h

Time steps in hTime steps in h

Pow

er in

WP

ower

in W

Pow

er in

WP

ower

in W

Figure 5.2: Uncertainty characterization of DHW demand. In the left diagram, theexpected value is depicted as a black solid line and the scenarios in greycolor. In the right diagram, the reduced scenario set is depicted stage-wise.Three scenarios (states) are chosen to represent every stage [Harb et al.,2016b]

illustrated in grey color. The right diagram depicts the reduced three representative

samples, respectively states, per demand period (Nstates = 3).

The demand periods are chosen based on the observed characteristics of the electrical

demand pattern [Harb et al., 2016b]: a very low demand during the night (0-5 h), followed

by a moderate demand in the morning (5-11 h). During 11-18 h, the active occupancy

in private households is usually low since inhabitants are at work. Yet, the distribution

still shows a small probability of a moderate demand during this period. Finally, a high

demand is observed in the evening between 18-24 h. Each demand period represents a

decision stage in the multi-stage framework. Hence, the number of stages Nstages is equal

to four. 0 5 1 0 1 5 2 0 2 50

5 0 01 0 0 01 5 0 02 0 0 02 5 0 03 0 0 03 5 0 04 0 0 0

Mean: 3 8 6 0 .5 7SD: 1 2 6 2 .4 5

0 5 1 0 1 5 2 0 2 50

1 0 0 0

2 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

Mean: 1 7 0 4 4 .3SD: 3 1 4 0 .9 4

0 5 1 0 1 5 2 0 2 50

5 0 01 0 0 01 5 0 02 0 0 02 5 0 03 0 0 03 5 0 04 0 0 0

0 5 1 0 1 5 2 0 2 50

1 0 0 0

2 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

Time steps in h Time steps in h

Time steps in hTime steps in h

Pow

er in

WP

ower

in W

Pow

er in

WP

ower

in W

Figure 5.3: Uncertainty characterization of electrical demand: scenario samples andreduced set [Harb et al., 2016b]

66

5.2 Single building scheduling approaches

The scenario tree construction algorithm [Harb et al., 2016b] transforms the reduced

set of stage-wise samples into a data matrix where each column represents a scenario.

Stage-wise stochastic independence requires the scenario set to contain every possible

combination of states, resulting in a scenario set with the cardinality (Nstates)Nstages = 81.

The scenario tree structure is illustrated in Figure 5.4.S

tage

1

Sta

ge 2

Sta

ge 3

Sta

ge 4

S1

S81

0 24 time5 11 18

Figure 5.4: Scenario tree structure for a four-stage problem with three states respectively[Harb et al., 2016b]

The scenario tree generation must be conform with the non-anticipative nature of the

decision framework, meaning that a decisions made in former stages does not depend

on the realisation of the uncertain process in later stages. This is assured by the non-

anticipativity constraint.

Non-anticipativity

The non-anticipativity constraint (NAC) states that all ’here-and-now’ decisions, corre-

sponding to the same branch of the scenario tree, are equal up to the node where the

branches fork out. The mathematical formulation is provided by Equation 5.10.

xa(t , s) = xa(t , s +1) if A ( s,k(t ) ) = 1,

∀s ∈ S, ∀ t ∈ tH ,∀ a ∈ AX = {HP, CHP}(5.10)

67

Scheduling Algorithms

A is the non-anticipativity matrix, in which the rows correspond to scenarios and the

columns correspond to time stages. It contains structural information about the scenario

tree. It has the property, A ( s,k(t ) ) = 1, for all pairs of decision variables x(t , s), x(t , s +1)

that correspond to the same branch, and is zero otherwise. The function k(t ) maps the

time steps to their corresponding time stages. NAC is required at all stages except for the

last one. The inter-scenario constraints are set with a so-called NAC-Matrix. It consists of

binary variables that induce constraint links between scenarios. Furthermore, the matrix

representation allows a straightforward conversion of the deterministic problem into the

SP counterpart and vice versa.

5.3 City district scheduling approaches

The increasing share of distributed energy as well as renewable volatile generation

is expected to lead to large discrepancies between generation and consumption and

consequently grid destabilization or curtailment of renewable energy. Such a situation

cannot be mitigated by individual independent local load optimization with no direct or

indirect interaction with other buildings or information about the grid status. Hence,

a coordination or DSM strategy which integrates the available energy generation and

storage flexibilities is required. Such coordination is ideally formulated as a centralized

architecture. However, the latter typically imposes a binding restriction as the computation

time increases exponentially with the number of involved systems. Therefore, hierarchical

distributed architecture which are based on reformulation techniques have gained a lot of

interest. The reformulation is based on decomposition methods which enable a scalable

optimization approach. The cost is a trade-off between solution computation time and

optimality.

In this section, the formulation of a centralized as well distributed architectures for city

disrict DSM strategies is introduced. The centralized model only serves as a reference to

assess the solution quality for the proposed reformulations.

5.3.1 Centralized scheduling

A centralized architecture mainly revolves around a coordinator which has access to all

information and generates the schedules of the electro-thermal heating systems. This

can be formulated as a MILP with the objective of minimizing the total costs of involved

buildings N as indicated in Equation 5.11.

min z =tH∑

t=t0

(P import(t ) ·∆t ·c import−Pexport(t ) ·∆t ·cexport+

N∑n=1

Qgasn ·∆t ·cgas

)(5.11)

68

5.3 City district scheduling approaches

P import(t ) and Pexport(t ) represent the imported into and exported electrical power from

the cluster which are penalized by c import and remunerated by cexport, respectively. Qgas

denotes the aggregated gas consumption from available CHP and boiler of all buildings as

indicated in Equation 5.12.

Qgas =N∑

n=1

(Qgas

CHP,n(t )+QgasBoiler,n(t )

)∀ t ,n (5.12)

The electricity balance for the cluster of buildings is formulated in Equation 5.13.

P import(t )+N∑n

Peln (t ) = Pexport(t ) ∀ t (5.13)

Peln (t ) is the electricity balance on a building n level as indicated in Equation 5.14.

Peln (t ) = Pdem,n(t )+ ∑

uc∈Uc

Puc ,n(t )− ∑ug∈Ug

Pug ,n(t ) ∀ t ,n (5.14)

Pug ,n(t ) and Puc ,n(t ) are bounded by the energy generation and storage units specific

restrictions introduced in Chapter 4. The thermal comfort requirements of the residents

are ensured by a further constraint which indicates that the space heating and DHW

demand must be covered at all times.

5.3.2 Distributed scheduling

The centralized scheduling approach, theoretically, provides the best coordination results

for a limited number of buildings, however, it leads to significant disadvantages, mainly,

the high computation time and accordingly limited extensibility, as well as data privacy

concerns.

Decomposition techniques allow for reformulating large scale optimization problems

which exhibit a special structure. The principle of a decomposition technique is to break a

problem down into a set of smaller problems. As a result, the reformulated optimization

model can be easily solved, thus, reducing the computational effort.

Two separate approaches are investigated in this work, the Dantzig-Wolfe decomposition

(DWD), as well as an integrated Langrangean relaxation columnn generation (LRCG)

approach.

Dantzig-Wolfe decomposition

DWD was proposed for LP problems in which the constraint matrix exhibits a primal block

angular structure. The main idea is to decompose the original problem into a master

69

Scheduling Algorithms

and several subproblems by substituting the variables in the original formulation with a

convex combination of the extreme points or feasible solutions of the subproblems. The

subproblems compute feasible solutions with respect only to the subproblem specific

constraints. The master problem strives to find the optimal weights for the subproblems

feasible solutions that minimize the objective function with respect to a coupling resource

constraint. Figure 5.5 illustrates the structure of the DWD model and the interactions

between the master- and subproblems.

Subproblem 1Generates proposals

based on reduced costs

Subproblem 2Generates proposals

based on reduced costs

Master problemIntegrates proposals and

determines shadow prices

Shadow prices π ProposalProposal

Figure 5.5: Structure of a Dantzig-Wolfe decomposition model as well as the interactionsbetween the master- and subproblems based on shadow prices and proposals[Bradley et al., 1977]

For large scale optimization problems, it is not practical to add every possible subproblem

extreme point to the master problem. Therefore, DWD is coupled with the column

generation (CG) algorithm. The latter restricts the master problem to a selection of

feasible solutions and includes, in an interative manner, additional feasible solutions or

columns only if they have potential to further improve the solution. This corresponds to

columns with negative reduced costs also known as opportunity costs.

Formulation Based on the DWD, the restricted master problem is formulated according

to Equations 5.15 - 5.19. The objective function and ressource constraint are reduced to

Equation 5.15 and 5.16, respectively.

min zLRDW =tH∑

t=t0

(P import(t ) ·c import−Pexport(t ) ·cexport

)∆t +

N∑n=1

(∑p

C pnλ

pn

)(5.15)

P import(t ) represents the electricity bought from public grid with c import = 27.94 ct/kWh

and Pexport(t ) is electrical energy exported into the public grid at cexport=12.00 ct/kWh.

70

5.3 City district scheduling approaches

N∑n

∑p

Pel,pn (t ) ·λp

n +P import(t )−Pexport(t ) = 0 ∀ t (5.16)

P import(t ), Pexport(t ) ≥ 0 ∀ t (5.17)

The master problem finds feasible solutions by linearly combining all known proposals by

the weighting factors λpn . One weighting factor exists for each subsystem and for each

proposal. The convexity of the linear combination of proposals is ensured by introducing

the constraints in Equation 5.19.

∑p∈P

λpn = 1 ∀ n (5.18)

0 ≤λpn ≤ 1 ∀ n, p (5.19)

Since the weights are defined as continuous variables λn ∈ [0,1], the restricted master

problem is considered as a linear relaxation (LRDW) of the original MILP problem.

In each iteration k, the restricted master problem is provided with a new proposal by each

subsystem. The generalized formulation of the objective within the subproblems or pricing

problems is presented in Equation 5.20 subject to device specific and comfort restrictions.

min νn =tH∑

t=t0

(Qg as

CHP,n +Qg asBoiler,n

)·cgas ·∆t︸ ︷︷ ︸

costs for production

+tH∑

t=t0

Peln (t ) ·π(t ) ·∆t︸ ︷︷ ︸

costs for grid interaction

−σn ∀ n (5.20)

A proposal p contains the consumed or produced electricity Pel,pn (t ) and the corresponding

production costs C pn of a subsystem n. C p

n reduce to zero for an electricity driven heating

generator i.e. HP and EH. A positive value for Pel,pn (t ) indicates electricity consumption

and a negative value indicates electricity production. Only proposals with, νn ≤ 0, provide

valid solutions and are therefore added to the base of the master problem. The shadow

prices (or marginal costs) π(t ), and σn are derived from the resource (Equation 5.16) and

convexity (Equation 5.19) constraints. The shadow price vector π(t ) can be interpreted as

the current price for exchanging electricity within the microgrid. The values of π(t ) are

bounded by the low price for exports cgrid and the high price for imports c import. Hence,

π(t ) serve as incentives for the subsystems to shift their operation to pursue the global

goal on a city district level. σn are scalar values that are individual for each subsystem n

and represent its marginal costs. Consequently, the total costs of each subsystem must be

lower or equal to the marginal costs σn to ensure optimality.

71

Scheduling Algorithms

Integering step The solution of the master problem is a linear relaxation that provides

a lower bound (LB) for an integer solution when considering a minimization problem. This

bound will slightly improve in every branching step until a termination criterion is reached.

Solving the master problem can result in fractional weighting factors λpn . However, to

provide each subproblem with an explicit index that indicates which proposal yielded the

optimal solution, the master problem needs to generate integer solutions for the weighting

factors λpn at least in the last iteration. One possible way to obtain integer solutions is to

branch-and-price [Desrosiers and Lübbecke, 2010]. Thereby, the same procedure as in

branch-and-bound algorithms is applied to systematically introduce further constraints in

a branching tree and solve the linear relaxation of the master problem in each node until

a solution satisfying the integrality constraints is found. This approach induces a high

computational effort. Therefore, the approach proposed by [Belov and Scheithauer, 2004]

is adopted. Thereby, the weighting factors λpn are declared in the last iteration as binary

variables in the final optimization step of the master problem using all the proposals

obtained in every iteration.

Algorithm description The restricted master problem is initialized by arbitrary propos-

als and computes an initial vector of shadow prices π(t ) that is sent to the subproblems.

Thereafter, the cycle depicted in Figure 5.6 is executed. Based on the current shadow

price vector π(t ), the subproblems or pricing problems are solved. The corresponding

schedules and production costs are provided to the coordinator and new proposals are

added to the restricted master problem. The coordinator computes new shadow prices

to optimize the overall costs of the city district. Based on the new shadow prices, the

individual buildings adjust their electricity generation/consumption, in order to enhance

the overall objective of the microgrid. This leads to increased costs on subproblem level,

while on microgrid level the solution is continuously improving, thus a convergence is

witnessed, where the sum of all the subproblem costs approaches the objective calculated

by the master problem. The base of the master problem increases with every iteration and

might become very large but it is still smaller and less complex than the original mixed

integer problem formulation. The algorithm is terminated when no significant change

in the value of the objective function of the master problem z occurs, when adding new

proposals. This condition is formulated as:

zk−1 − zk

zk−1≤ ε (5.21)

with k as an iteration index. The threshold ε is set to 0.001. Furthermore, additional

termination criteria are introduced by setting an iteration or time limit. Finally the index

of the optimal proposal is determined based on the integering step as indicated in Section

5.3.2.

72

5.3 City district scheduling approaches

Start

Solve master problem

Solve subproblem

Propose schedule

Update shadow prices

Send new shadow prices

to buildings

Termination criterion reached?

no

End

yes

Solve master problem with binary weighting

factors

Send index of optimal proposal to building

Building

Coordinator

Figure 5.6: Procedural description of the column generation algorithm [Harb et al., 2015]

Integrated decomposition model

In CG approaches, the Dantzig-Wolfe restricted master problem has to be solved in every

iteration to determine the optimal shadow prices. As the algorithm proceeds the master

problem gets bigger with each iteration which results in a increased computation time.

[Vanderbeck and Wolsey, 1996] and [Barnhart et al., 1998] anaylzed the convergence of

CG algorithms and identified a ’tailing-off’ effect. The analysis showed that after a few

initial iterations in which the objective value improves fast, the convergence tends to slow

73

Scheduling Algorithms

down in the final phase. As a result, a large number of iterations is required to achieve an

optimal solution for large scale problems.

[Barahona and Jensen, 1998] proposed a combined algorithm that exploits the strong

relation between column generation and Lagrangian relaxation illustrated in Figure

5.7. The relation states that the Langrangian dual (LD) problem, that derives from

the Lagrangian relaxation (LR) reformulation, is the dual of the linear relaxation of the

Dantzig-Wolfe (LDW) reformulation and vice versa.

EMS | Hassan HarbFolie 1

DLDWLD

LR

DWDLD

MILP

LDW

Dantzig-Wolfe

reformulation

Lagrangian

relaxation

Lagrangian

dual

dual dualdual

equivalent

equivalent

Original problem

linear

relaxation

Figure 5.7: Relation between column generation and Lagrangian relaxation [Nishi et al.,2009]

The approach introduced in [Barahona and Jensen, 1998] employs the Lagrangian relax-

ation formulation and subgradient optimization method [Fisher, 2004] to generate new

columns inexpensively without solving the DW master problem in each iteration. The

same approach has been also used by [Degraeve and Peeters, 2003] for the cutting stock

problem.

LR is a decomposition approach that exploits the structure of primal block-angular ma-

trices, similar to the DWD. In LR, complicating constraints linking the subproblems are

dualized into the objective function using a fixed vector of Lagrange multipliers π as

indicated in Equation 5.22. This leads to a formulation without any linking constraints.

min zLR(x,π) = cx +π(Ax −b) (5.22)

The Lagrangian problem zLR(π) will always provide a lower bound of the original minimiza-

tion formulation, since negative π are introduced into the objective function. The goal is to

maximize zLR(π) over π in order to achieve the original optimal solution. This is referred

74

5.3 City district scheduling approaches

to as the Langragean dual formulation zLD and corresponds to the master problem.

max zLD(π) = cx +π(Ax −b) (5.23)

The LD is solved to determine the optimal values of the Lagrangian multipliers using an

iterative procedure such as subgradient method. The latter iteratively generates dual

feasible points according to Equation 5.24.

πk+1 =πk + sk g k (5.24)

g k is the subgradient and sk is the step size which can be approximated as a constant

value. [Fisher, 2004] proposed a progressive method to update the step size based on

Equation 5.25

sk = αk(

f k − qk)

‖g k‖2, (5.25)

where 0 < αk < 2, f k is the best known upper bound of the optimal cost, qk is the best

known value of the dual cost and g k is the subgradient of the dual problem.

The integrated algorithm can be described as a nested double loop. In the outer loop,

the DW master problem is solved with a simplex algorithm to obtain the optimal dual

variables as known from the CG algorithm. In the inner loop, the subgradient optimization

method is applied on the LR formulation of the problem to iteratively update the shadow

prices. Since the LR subproblems are effectively the same as the pricing subproblems in

CG, the LR subproblem solutions are used as new columns for the DW master problem.

As a result, the speed of convergence for the dual solutions is enhanced. Furthermore,

the LR provides a lower bounds for the optimal value of the linear restricted master

problem, which can be used to estimate the quality of the solution and as termination

criterion. When applying the DWD to reformulate the original MILP problem, the two

problem formulations are actually equivalent problems and thus share the same optimal

solution zMILP and zDW. Relaxing the integer variables of the DW master problem leads

to an improved solution zLDW, because of the extended solution space. As previously

introduced, the Lagrangian dual problem is the dual of the linear relaxation of the DW

master problem. Hence, based on the strong duality theorem, the optimal objective value

zLD is equivalent to zLDW. On the other hand, the weak duality theorem indicates that this

optimal Lagrangian dual solution gives an upper bound for every other optimal solution of

the Lagrangian relaxation problem with non-optimal shadow prices.

zLR(π) ≤ zLD = zLDW ≤ zDW = zMILP (5.26)

The optimal solution of the restricted Dantzig-Wolfe master problem zLRDW can be inter-

preted as an upper bound on the optimal solution of the non-restricted master problem

75

Scheduling Algorithms

zLDW, because its solution space is only a subspace of the full master problem. With every

variable introduced in an iteration, the objective value of the restricted master problem is

improves or at least remaining constant due to the extension of the solution space until

the optimal solution is found.

zLDW ≤ zLRDW

zDW ≤ zRDW

(5.27)

Algorithm description Figure 5.8 depicts the procedural algorithm of the integrated

approach. The algorithm comprises three steps, initialization, pricing step and integering.

The restricted master problem is initialized with random proposals and solved for several

iterations based on the traditional DWD-CG algorithm. Thereby, the aim is to exploit the

good convergence properties of the DWD in the first few iterations. The initialization is

followed by the pricing step which involves an outer and inner loop. In the outer loop

level, the master problem is solved to generate the shadow prices π. Thereafter, the

inner loop runs for a defined number of iterations, during which new shadow prices are

calculated using the subgradient method. The number of inner loop iterations is increased

in a progressive manner. The algorithm is terminated when the difference between the

current upper and lower bound becomes smaller than a specified tolerance value ε or

when the maximum number of iteration or time limit is reached.

76

5.3 City district scheduling approaches

Start

Generate random shadow prices πCompute initial proposals

Solve relaxed, restrictedmaster zLRDW

zk−1LRDW−zk

LRDW

zk−1LRDW

≤ ε,Final outer iteration?Time limit reached?

Solve subproblems

False

Set lower bound zLR

Update shadow pricesusing subgradient method

πk (t )+ sk g k (t )

1− zLRzLRDW

≤ ε,Time limit reached?

Final inneriteration?

False

False

True

Set weights λi

as integers

True

True

Solve restrictedmaster zRDW

End

Figure 5.8: Procedural description of the integrated Lagrangean relaxation - columngeneration algorithm

77

6 Analysis: Results and Discussion

This section delivers an assessment of the formulated scheduling strategies for individual

buildings and city districts.

6.1 Scheduling for single buildings

The first evaluation of the scheduling algorithms considers a single building with no

regard to the grid interaction. The load shifting strategy is motivated by the residents’

goal to increase the local consumption of PV power and reduce the operation costs of their

building energy systems.

The aim of this evaluation is to assess the expected advantage of the predicitve scheduling

algorithms for individual buildings with respect to a reactive strategy as a benchmark.

The analysis is conceptualized by first determining the best possible solution of predic-

tive scheduling by employing perfect forecasts then evaluating the performance of the

deterministic approach based on point forecasts and finally assessing the impact of incor-

porating demand forecast uncertainty in the scheduling model based on the stochastic

programming approach.

The assessment is carried out based on a coupled simulation of the optimization program

with a BES dynamic simulation model. This allows to consider both the modeling and

input data uncertainty.

6.1.1 Design and configuration

BES configurations The impact of the scheduling strategy is mainly influenced by

the design of the BES. Therefore, six different configurations are considered for the

assessment. This allows to evaluate the impact of the different combinations of heat

generators as well as the thermal and electrical storage systems. Table 6.1 delivers an

overview on the design of the investigated BES.

The building considered is a single family house with three residents. The heated floor

area is 125 m2and the nominal heating load is 6.5 kW. The maximal domestic hot water

load amounts to 15 kW. The design power of the heat generators are determined based on

conventional design criteria to satisfy the nominal heating load and domestic hot water

79

Analysis: Results and Discussion

demand. Both the HP and EH are non-modulating. The characteristics of the HP unit are

presented in Section 4.1. The characteristics of the CHP unit are presented in Table 4.1.

The CHP as well as the auxiliary boiler can modulate down to 30 %. All BES configurations

comprise a PV system and a single thermal water storage (TS).

Table 6.1: BES configurations: The characteristics of the primary heat generators, Dim-plex air-to-water LA9TU HP (QA2W35 = 7.5 kW) and Vaillant EcoPower 3.0 CHP(P = 3 kW, Q = 8 kW) are presented in Chapter 4

Configuration PV HP CHP EH Boiler TS Battery

PV-HP-EH 4.8 kWp LA9TU - 11 kWel - 500 l -PV-HP-EH-Bat 4.8 kWp LA9TU - 11 kWel - 500 l 4.6 kWh

PV-CHP-B 4.8 kWp - EcoPower 3.0 - 12 kWth 500 l -PV-CHP-B-Bat 4.8 kWp - EcoPower 3.0 - 12 kWth 500 l 4.6 kWhPV-CHP-EH 4.8 kWp - EcoPower 3.0 11 kWel - 500 l -

PV-CHP-EH-Bat 4.8 kWp - EcoPower 3.0 11 kWel - 500 l 4.6 kWh

HEMS setups The anaylsis of the scheduling strategies’s performance is conceptualized

by defining and evaluating the following HEMS configuration:

. reactive (Ref) as a benchmark

. deterministic based on perfect information (DPI)

. deterministic based on forecasts (DF)

. multi-stage stochastic programing incorporating electrical demand uncertainty (SPel)

. multi-stage stochastic programing incorporation domestic hot water demand uncer-

tainty (SPdhw).

A reactive strategy is defined for every BES configuration to serve as reference for

evaluating the impact of employing a predicitve scheduling algorithm. Ref aims to

satisfy the space heating and DHW demand with no regard to the availability of local PV

generation. It consists of a conventional 2-point hysteresis control strategy which turns

on the primary heating unit i.e. HP or CHP, when the set temperature required by the

consumer heat cycle is not satisfied anymore. The primary heat generator is kept on

until the tapping temperature reaches the maximal heating system’s supply temperature.

The assumptions for the control strategies within the dynamic simulation model, which

emulates the reality, are crucial for the performance of the predictive energy management

strategies as well as the conventional operation of the BES. Figure 6.1 depicts the status

and transition conditions within the reactive control strategy for a HP-EH-Bat system.

80

6.1 Scheduling for single buildings

HP: OffEH: Off

HP: ONEH: Off

HP: ONEH: ON

Ttap ≤ Tmin orSOCBat > 98 % & Ttap < Tmax -5 K

Ttap ≥ Tmax orSOCBat ≤ 20 % & Ttap >= Tmin + 10 K

Ttap ≥ Tmin+ 5 K

Ttap < Tmin

Figure 6.1: State-based representation of HP-EH-Bat reactive control strategy; The tran-sitions are defined in function of the thermal storage and battery status

Ttap is the drawn temperature from the storage tank, Tmin is the minimum flow temperature

necessary for matching the heat demand determined according to the DHW supply

temperature requirements and the heating curve. Tmax is the maximum heat pump

condenser’s temperature. SoCbat denotes the battery’s state of charge. The transitions

are subject to further restrictions related to the operation time of the HP unit, namely, the

minimum shut down and run time which are set to 30 mins.

DPI assumes perfect forecast and allows for determining the best bound for cost op-

timization enabled by employing a predictive HEMS while considering the modeling

uncertainties of the linearized MILP BES model.

DF is based on a predefined configuration of forecasting models for the different input data

according to the evaluation results presented in Section 3.2.5. Namely, SVR is used for

electrical and space heating demands, naive for DHW demand and ARMA for forecasting

the solar irradiation and outdoor temperature. The DF setup allows for determining the

real potential for a deterministic scheduling model under consideration of both input data

forecast and BES MILP modeling uncertainties.

SPel and SPdhw allow for assessing the impact of incorporating the uncertainty from the

electrical and domestic hot water demand in the predictive scheduling model, respectively.

The forecast evaluation presented in Section 3.2.5 showed that the strong stochasticity

of the domestic hot water and electrical demand induce the highest perdiction error and

are therefore integrated as uncertainties within the stochastic programming scheduling

approach.

6.1.2 Evaluation

The dynamic performance of the Ref, DPI and DF strategies is depicted in Figures 6.2-

6.5 for the PV-HP-EH configuration during two consecutive days in March, that are

representative for the transition period. The dynamic performance of SPel and SPdhw are

included in Appendix A.1.1. The transition period is characterized by the availability of

space heating and DHW demand as well a significant solar irradiation and thereby PV

81

Analysis: Results and Discussion

generation. Whereas, the winter period is characterized by low solar irradiation and

high heating demand, which leads mostly to an uninterrupted, inflexible operation of the

heating systems. In summer, the non-existing space heating demand significantly reduces

the operation of the heating generators and thereby the flexibility potential for load

shifting. Therefore, the transition period is chosen to evaluate the dynamic performance

of the energy management strategies in matching or coordinating the operation of flexible

heating systems and PV electricity generation. The dynamic performance for the rest of

the BES configurations is found in Appendix A.1.

02468

kW

Dymola_Qspace Dymola_Qdhw

036912

kW

Dymola_QHP

0

1

OnO

ff

Dymola_uHP

036912

kW

Dymola_QEH

00 :0028 -Mar2008

00 :0029 -Mar

06 :00 12 :00 18 :00 06 :00 12 :00 18 :000

20406080100

%

Dymola_SoCST

Figure 6.2: Dynamic performance of the thermal side for PV-HP-EH under the Ref strategy.The depicted profiles, from top to bottom, are the space heating and domestichot water demands, the thermal power of the HP, the On/Off operation statusof the HP, the thermal generation of the auxiliary EH and the state of chargeof the water storage tank

Figure 6.2 shows the operation of the BES using the reference reactive strategy. This

strategy is implemented within the dynamic simulation model in Dymola as an internal

controller. The upper subplot displays the actual space heating Qspace and DHW Qdhw

demands. The second and third subplots depict the thermal generation QHP and on/off

82

6.1 Scheduling for single buildings

status uHP of the HP. The last two subplots show the heat generation of the auxiliary

electrical heater QEH and the state of charge of the thermal water storage tank SoCST.

The operation of the HP displays the expected hysteresis based On/Off operation in

function of the storage drawn temperature, respectively the resulting SoC. The HP is

turned on when the drawn temperature is below its set value and kept on until the storage

is almost full i.e. SoC of around 100 %. The auxiliary electrical heater is additionally

turned on when the set temperature cannot be achieved by the sole operation of the HP

and turned off when the storage drawn temperature exceed the set point by a predefined

offset.

02468

kW

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

036912

kW

QHP

Dymola_QHP

0

1

OnO

ff

uHP

Dymola_uHP

01234

kW

QEH

Dymola_QEH

00 :0028 -Mar

00 :0029 -Mar

06 :00 12 :00 18 :00 06 :00 12 :00 18 :000

20406080100

%

SoCST

Dymola_SoCST

Figure 6.3: Dynamic performance of the thermal side for PV-HP-EH under the DPI strat-egy. The solid lines represent the operation status delivered by the MILPscheduling algorithm whereas the dashed lines represent the operation withinthe dynamic simulation model formulated in Dymola/Modelica

Figures 6.3 and 6.4 depcit the thermal and electrical loads for the DPI predictive scheduling

strategy, respectively. The solid lines represent the operation status as foreseen in the

scheduling model. The dashed lines represent the realization of the schedule status within

the dynamic simulation model in Dymola. The dynamic simulation model comprises an

83

Analysis: Results and Discussion

internal controller which ensures that the schedule set points are overridden when the

thermal comfort standards, the heating generator or storage restrictions are violated,

analogously to the conditions declared within the reactive strategy illustrated in Figure

6.1. Such an intervention is seen in the 3rd subplot of Figure 6.3 on 28th of March at

around 13:00 o’clock. The internal controller detects that the thermal storage is full and

turns off the HP sooner than foressen by the scheduling algorithm which underestimates

the thermal storage state of charge. Another overriding action is also seen on the same

day at around 15:00 o’clock. The foreseen operation of the HP is ignored by the internal

controller since the thermal storage is full.

02468

kW

PdemandDymola_Pdemand

036912

kW

Pimpor tDymola_Pimpor t

Pexpor tDymola_Pexpor t

02468

kW

PPVDymola_PPV

01234

kW

PHPDymola_PHP

0

1

OnO

ff uHPDymola_uHP

00 :0028 -Mar

00 :0029 -Mar

06 :00 12 :00 18 :00 06 :00 12 :00 18 :0001234

kW

PEHDymola_PEH

Figure 6.4: Dynamic performance of the electrical side for PV-HP-EH under the DPI strat-egy. Pdemand denotes the elctrical demand, Pimport and Peyport the electricalimport and export from the public grid, PPV the local PV electricity generation,PHP and PEH the electrical consumption of the HP and EH units

Overall, the results show that the operation of the HP is more dynamic, displaying frequent

switching, compared with the operation seen in Figure 6.2 under the Ref strategy. This

frequent switching behavior is usually avoided to reduce the tear and wear of the unit.

The HEMS strives to shift the operation of the HP to the time slots characterized by PV

84

6.1 Scheduling for single buildings

generation availability as depicted in the 3rd and 4th subplots of Figure 6.4. Moreover, the

HEMS allows for avoiding the operation of the less efficient auxiliary heater compared

with reactive strategy as shown in the 4th subplots of Figures 6.2 and 6.3. Further, the

results show that the foreseen schedule from the predictive HEMS is well followed by the

dynamic simulation model. This indicates that the MILP model of the BES allow for a good

representation of the real dynamic performance of the corresponding BES.

DPI is formulated based on the assumption of perfect information or perfect forecasts.

Hence, the forecast values of the scheduling model and the real values in dynamic

simulation model for space heating and DHW demand forecast (1st subplot in Figure 6.3),

as well as the electrical demand and the PV generation (1st and 3rd subplots in Figure 6.4)

are mostly identical. The discrepancies between the perfect forecast and the real values

result from the modified dynamic operation of the BES simulation model as well as the

different discretization or time resolution considered. The scheduling optimization model

is computed with a 15 minutes resolution while the dynamic simulation model is solved

with variable time step at a much higher resolution.

Consequently, the results of the perfect forecast based DPI strategy represent an upper

bound for assessing the predictive HEMS that integrate weather and demand forecasts.

Figure 6.5 displays the scheduling performance of the DF strategy under real forecast

conditions. As a result, discrepancies are observed between the forecasts, for space

heating, DHW and electrical demand as well as PV generation, assumed by the scheduling

model and the actual values computed within the dynamic simulation model. The discrep-

ancies for the space heating and DHW demand are shown in the upper subplot of Figure

6.5. The space heating demand is greatly overestimated by the forecast model during

the afternoon period on the 28th of March. The DHW demand forecast delivers a bad

estimation of the real consumption. The impact of the forecasts’ inaccuracy is observed in

the operation of the HP when compared to the DPI based operation in Figure 6.3. Mainly,

the foreseen schedule is ignored several times. The state of charge of the thermal storage

is underestimated in the scheduling model at around 9:00 o’clock due the DHW demand

forecast. Consequently, the later, extended operation of the HP during the afternoon

starting from 13:00 o’clock which aims to take advantage of the availability of PV genera-

tion and satisfy the falsely predicted space heating demand is overridden by the internal

controller. Nevertheless, the operation of the HP is partially shifted towards the time slot

of PV generation and the EH operation is reduced, compared with the reactive reference

strategy. This implicitly indicates that, despite the forecast error, a cost reduction can

be achieved. The scheduling efficiency can be increased by increasing the rescheduling

rate e.g. reduce the rescheduling interval from 24 h to 6 h. This results in reducing the

forecast and consequently the deviations in the schedules’ realization.

85

Analysis: Results and Discussion

02468

kW

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

036912

kW

QHP

Dymola_QHP

0

1

OnO

ff

uHP

Dymola_uHP

01234

kW

QEH

Dymola_QEH

00 :0028 -Mar

00 :0029 -Mar

06 :00 12 :00 18 :00 06 :00 12 :00 18 :000

20406080100

%

SoCST

Dymola_SoCST

Figure 6.5: Dynamic performance of the thermal side for for PV-HP-EH under the DF

strategy

An overview of the performance of all HEMS setups for all introduced BES configurations

of Table 6.1, under all HEMS strategies, is presented in Table 6.2. The results are averaged

over the simulations for three months during the heating period in March, September

and December. The assessment is described by evaluating the resulting operating costs.

Furthermore, three indicators are defined to quantify the impact of employing predictive

scheduling, the influence of forecast error and the integration of uncertainty within the

scheduling model:

. Value of scheduling (VS)

. Value of perfect information (VPI)

. Value of uncertainty (VU)

The costs’ column represents the averaged weekly operation costs of the BES. VS defines

the costs increase or decrease in % of the resulting costs from employing a predictive

HEMS compared to the costs of the conventional reactive strategy. VPI defines the costs’

deviation of the predictive HEMS from the best bound possible when applying a HEMS

86

6.1 Scheduling for single buildings

with perfect forecasts. The value of uncertainty (VU) represents the impact of considering

uncertainty of either the electrical or DHW demand prediction in the scheduling algorithm

compared to the determinstic formulation with point forecasts.

Table 6.2: Assessment results of the scheduling strategies for all BES configurationsduring the months March, September and December. The optimization timeresolution is 15 min, the rolling horizon’s rescheduling interval and schedulinghorizon are 24 and 48 h, respectively. The MIP gap is set to 1 % for DPI andDF and 1.5 % for SPel and SPdhw. The costs are weekly averaged. NegativeVS, VPI and VU indicate a cost reduction whereas positive values denote anincrease with respect to the costs of the Ref , DPI and DF, respectively

BES Strategy Costs in e VS in % VPI in % VU in %

PV-HP-EH Ref 102.62DPI 90.85 -11.5DF 98.78 -3.7 8.7

SPel 95.99 -6.5 5.6 -2.8SPdhw 95.05 -7.4 4.6 -1.0

PV-HP-EH-Bat Ref 99.95DPI 92.33 -7.6DF 95.16 -4.8 3.1

SPel 92.64 -7.3 0.3 -2.8SPdhw 92.44 -7.5 0.1 -2.9

PV-CHP-B Ref 80.6DPI 75.77 -6.0DF 78.27 -2.9 3.3

SPel 77.64 -3.7 2.5 -0.8SPdhw 75.82 -5.9 0.1 -3.1

PV-CHP-B-Bat Ref 80.91DPI 77.03 -4.8DF 79.28 -2.0 2.9

SPel 77.71 -4.0 0.9 -2.0SPdhw 77.93 -3.7 1.2 -1.7

PV-CHP-EH Ref 86.10DPI 79.90 -7.2DF 84.22 -2.2 5.4

SPel 79.97 -7.1 0.1 -5.0SPdhw 80.39 -6.6 0.6 -4.5

PV-CHP-EH-Bat Ref 80.63DPI 76.57 -5.0DF 80.57 -0.1 5.2

SPel 76.84 -4.7 0.4 -4.6SPdhw 65.76 -4.8 1.3 -4.7

87

Analysis: Results and Discussion

The MIP gap for the Gurobi optimization solver is set, respectively, to 1 % and 1.5 % for

the deterministic (DPI and DF) and SP (SPel and SPdhw) models. The convergence from

1.5 % to 1 %, withing the SP approach1, showed an extremly slow pattern which often led

to exceeding the time limit of 10000 s.

The results show that employing a predictive scheduling algorithm under perfect infor-

mation condition enable a cost reduction in all considered BES configuration compared

with a rule-based reactive strategy. The value of scheduling amounts to -11.5 % and -7.6 %

for PV-HP-EH and PV-HP-EH-Bat, -6.0 % and -4.8 % for PV-CHP-B and PV-CHP-B-Bat, as

well as, -7.2 % and -5.0 % for PV-CHP-EH and PV-CHP-EH-Bat. The highest cost reduction

potential is provided in the HP based BES setup and the CHP-EH configuration. This can

be attributed to the more balanced capacities of electricity consuming units i.e. HP or EH

and generation units i.e. CHP or PV within these configurations. Moreover, the results

indicate that the cost reduction potential of the predictive scheduling algorithm under

perfect information condition is lower in the BES configurations employing a battery

storage. It is foreseen that increasing the rescheduling time resolution of the rolling

horizon algorithm results in reducing the uncertainty from the BES model and thereby

enhancing the performance of the scheduling realization and consequently the cost re-

duction achieved. The value of scheduling with the DF strategy is reduced from -11.5 %

to -7.6 % for the HP-EH BES system as well as from -6.0 % to -4.8 % and -7.2 % to -5.0 %

for the CHP-B and CHP-EH systems, respectively. The battery allows for balancing the

discrepancy between the electricity generation from PV or CHP and the electrical demand,

hence enabling load shifting or optimization without requiring demand forecasts. The bal-

ancing through the battery is further facilitated in the presence of electrically driven heat

generator i.e HP and EH. Furthermore, the results verify the hypothesized cost reduction

potential of predictive scheduling compared with the reactive operation strategy despite

the embedded forecasting errors. The value of scheduling with the DF strategy amounts

to -3.7 % and -4.8 % for PV-HP-EH and PV-HP-EH-Bat, -2.9 % and -2.0 % for PV-CHP-B and

PV-CHP-B-Bat, as well as, -2.2 % and -0.1 % for PV-CHP-EH and PV-CHP-EH-Bat. Hence, the

DF strategy allows in all configuration for a clear cost reduction compared to the reference

reactive strategy, except for PV-CHP-EH-Bat. Within the configuration PV-CHP-EH-Bat,

the forecast deviation results in non-optimal schedules which lead to similar costs with

the reactive strategy. The highest saving potential is achieved by the configuration based

on an HP unit. The integration of the electrical or DHW demand uncertainty in the SP

scheduling model enables an average cost reduction of 5.8 % ranging between 3.7 and

7.5 %, with respect to the reactive strategy, over all considered configurations. Within

PV-HP-EH-Bat, PV-CHP-B and PV-CHP-EH, a value of perfect information around zero is

achieved. Hence, the SP scheduling model achieves in these setups within the considered

investigation period, the best bound of cost reduction potential set by DPI. This can be

1The mutli-stage SP model is formulated based on three states and four stages resulting in 81 scenarios

88

6.1 Scheduling for single buildings

related to the effectiveness of incorporating the uncertainty in the scheduling model and

to the stage-wise schedule update within the dynamic simulation which compensates the

MILP BES modeling uncertainties that reduce the potential of the DPI strategy. The value

of uncertainty shows a negative value throughout all considered configurations indicating

that the SP HEMS outperforms the DF strategy. An average cost reduction of 3.0 % is

achieved ranging between 1.0 and 5.0 %.

However, the average computation time increases from around 200 s in the DF to over

2300 s in the SP approach. Figure 6.6 illustrates the computational effort across the

DPI, DF and SP approaches for the scheduling step only ; The simulation time within

the dynamic BES model is not included. The computational time for a single day-ahead

schedule within the DPI approach only amounts to one second; this corresponds to the pure

optimization solving time. The training of the forecasting algorithms employed by the DPI

increases the time required for the scheduling step to 200 s. It must be noted that this time

interval varies depending on the forecasting model and training configurations, mainly,

the model complexity, number of exogenous inputs and past measurements considered. It

is important to note that the computation time of the SP model depends on the number

of scenarios considered, which results from the number of states (branches) and stages

used to characterize the uncertainty. An increasing number of scenarios increases the

scheduling model ’s complexity and results in an exponentially higher computation effort.

DPI DF SP

0

0.5

1

1.5

2

2.5

1 s200 s

2.3 103 s

+1000 %

HEMS setup

Ave

rag

eco

mp

uta

tion

tim

ein

103s

Figure 6.6: Computation time comparison between DPI, DF and SP scheduling models;The values denote the average time for computing one day-ahead schedule;The arrow indicate the increase of computation time in percentage of SPmodels compared to DF; The simulations were carried out on a work-stationwith 12 active cores Intel Xeon CPU E5-26670@2.9 GHz and 32 GB of RAM

89

Analysis: Results and Discussion

6.2 Distributed scheduling for neighborhoods

The second evaluation involves a residential neighborhood. The DSM strategies’ goal is to

increase the integration of renewable energy internally within the microgrid of the city

district and optimize the interactions of the flexible electricity consuming and generating

units within the individual buildings.

The aim of this assessment is to evaluate the distributed coordination approaches with

regard to the quality of the generated schedules and consequently the coordination fitness

as well as the scalability potential.

6.2.1 Design and configuration

The performance of the distributed scheduling algorithms is assessed by considering a

cluster of 34 residential buildings.

The heating units are designed as bivalent systems according to conventional standards.

The CHP units are designed to run at least 4000 h/a while a bivalence temperature of

-2 °C is set for the heat pump units. The CHP units are supported by an additional gas

boiler while heat pumps are provided with an integrated electrical heater to cover peak

loads. All BESs comprise a PV system as well as a 300 l thermal storage tank to enable a

flexible operation. The ratio between installed capacity of µCHP units and HPs is roughly

set to 140 % to ensure that the µCHPs are able to cover both the electrical demand for

appliances and the electricity consumption of the HPs.

The demand profiles are generated synthetically for every building using the approach

introduced in Section 3.1 with respect to the number of residents assumed. The distributed

DSM strategies considered are the Dantzig-Wolfe decomposition based column generation

algorithm (CG) as well as the integrated Lagrangian relaxation column generation (LRCG).

A centralized approach is formulated to serve as a benchmark.

6.2.2 Evaluation

Comparison of CG and centralized approach

The goal of the following assessment is to evaluate the coordination performance and

scalability potential of the distributed CG approach with respect to the centralized formu-

lation.

Coordination Figure 6.7a and 6.7b exemplary show the schedules of the centralized

and distributed approaches, respectively, for a single day in February.

90

6.2 Distributed scheduling for neighborhoods

The upper subfigures illustrate the cluster’s internal microgrid status with respect to the

residual load. The residual load is represented by the dashed line and it is defined as the

difference of the total electrical demand of lights and appliances (D) and the electricity

generated by local wind and PV renewable energy sources (R). The solid line represents the

difference of electricity import (I) and export (E), which denotes the microgrid interactions

with the public grid.

The lower figure illustrates the scheduling results of both, HP and CHP units operating

within the cluster. The electricity consumption and production of all HP and CHP units,

respectively, are aggregated at each time step.

40

20

0

20

40

60

80

Po

we

rHin

HkW

DH-HR IH-HE

5 10 15 20

Tim eHinHhours

2030405060708090

100

Po

we

rHin

HkW

CHP HP

(a) Centralized

40

20

0

20

40

60

80

Po

we

rHin

HkW

DH-HR IH-HE

5 10 15 20

Tim eHinHhours

2030405060708090

100

Po

we

rHin

HkW

CHP HP

(b) Distributed

Figure 6.7: Schedule profiles for a random day in February using the centralized anddistributed approaches. ’D-R’ denotes the residual load, with ’D’ as theaggregated electrical demand of lights and appliances for the participatingbuildings and ’R’ the renewable energy from wind and PV units; large negativevalue indicate high availability of renewable energy. ’I-E’ represents thecluster’s interaction with the public grid, with I and E as the electricityimported to and exported from the cluster, respectively [Harb et al., 2015]

As expected, the centralized coordination is able to balance the load completely. However,

the distributed scheme is also able to balance a large amount of the residual load. The

operation of the HPs and CHPs is shifted according to the residual load development. In

the early morning hours around 4 h the HPs are operated to accommodate the available

wind energy while the CHPs’ employment is reduced. During the evening, around 20 h,

the electricity consumption is at its peak value. Accordingly, the operation of electricity

driven HPs is reduced while the electricity generating CHPs are maximally activated.

91

Analysis: Results and Discussion

0 50 100 150 200 250 300 350

Time in days

60

40

20

0

20

40

60

80

Pow

er

in k

W

D - R I - E

(a) Centralized

0 50 100 150 200 250 300 350

Time in days

60

40

20

0

20

40

60

80

Pow

er

in k

W

D - R I - E

(b) Distributed

Figure 6.8: Grid interaction (I-E) for the centralized and distributed scheduling ap-proaches over one year with respect to the residual load (D-R) [Harb et al.,2015]

Figures 6.8a and 6.8b illustrate the microgrid interaction over one year for the centralized

and distributed scheduling models, respectively. The observations in Figure 6.7 are further

affirmed. Mainly, the centralized approach achieves a high coordination level. This allows

for integrating the surplus of renewable energy indicated by a negative residual load, and

reducing the amount of imported electricity from the public grid. The grid interaction

(I-E) exhibit an export pattern only when the renewable generation is quite high e.g.

during the day 60 and 2500. In summer, the imports are reduced but cannot be balanced

effectively since the missing space heating demand restricts the employment of the flexible

heating generators mainly µCHP units. The optimal coordination is achieved during the

transition periods e.g. around day 100 and 280. During this period, a self-sufficient status

is achieved as the grid interaction (I-E) often reaches the value zero. The distributed

approach achieves a comparable coordination performance. Similar as in the centralized

setup, the renewable energy surplus integration within the microgrid is enhanced and the

imported electricity is reduced. However, the self-sufficient status during the transition

period, is reached less often compared with the centralized approach. This result is

expected when taking into consideration the formulation of the centralized model which

has access to all information on the individual building energy systems.

The impact of the coordination through the predicitive DSM strategies on the total

operation costs of the city district can be assessed by evaluating the resulting total gas

and electricity costs compared with a heat-driven reference scenario. Within this reference,

the heating generators are operated based on the conventional heat-driven mode. This

operation mode aims to satisfy the heat demand with no consideration of renewable energy.

The evaluation shows that for the considered city district with 34 buildings, the centralized

approach results in reducing the total yearly operation costs by 9% while the CG algorithm

allows for 4% reduction compared with the heat-driven scenario. These values are strongly

dependent on the amount of renewable energy available within, the feed-in electricity

92

6.2 Distributed scheduling for neighborhoods

tariffs for PV and CHP systems as well as the available flexibility capacities i.e. thermal

storage and battery units. With increasing share of renewable energy systems or size of

the microgrid, the cost reduction potential of the DSM strategies is foreseen to increase.

0 50 100 150 200 250 300 350

Time in days

0

5

10

15

20

Hour

of

day

120

80

40

0

40

80

120

Power in kW

(a) Grid interactions based on subproblems’ proposals with produc-tion costs

0 50 100 150 200 250 300 350

Time in days

0

5

10

15

20

Hour

of

day

120

90

60

30

0

30

60

90

120

Power in kW

(b) Grid interactions based on subproblems’ proposals without pro-duction costs

Figure 6.9: Influence of including/excluding the production costs in the buildings’ pro-posals on the grid interaction, over one year with respect to the hour of theday, within the distributed approach. The green range indicates the desiredself-sufficient status, the blue range denotes electricity exports from themircogrid whereas the yellow to red range denotes electricity import [Harbet al., 2015]

Data privacy One of the main drawbacks of the centralized approach is the amount of

information needed which hinders a real-life application. The distributed approach allows

93

Analysis: Results and Discussion

for greatly reducing the amount of sensible information that needs to be communicated

between the buildings and the coordinator. To recap, the proposal of a building with an

electrical driven heat generator comprises only the electrical demand while the proposal

of a building with a gas driven heat generator further includes the production costs. This

inclusion may arise privacy concerns. Hence, the impact of removing the production costs

from the proposal provided by the building to the master problem is investigated. Figure

6.9a and 6.9b display the grid interactions in the distributed approach while including

and excluding the production costs in the proposal, respectively. In general, the results

restate that the coordination degree is best during the transition period (indicated by the

green color). Moreover, the impact of the daily electricity demand, which is characterized

by a morning and an evening peak, on the grid interaction is shown by the large imports

exhibited by the mircogrid (indicated by the yellow color) at the same peak periods. With

regard to the proposal formulation, it can be seen that the exclusion of the production

costs results in slight shift towards an energy positive cluster or a virtual power plant.

Mainly the electricity export (blue color) during the transition seasons is increased as

shown in Figure 6.9b. Excluding the production costs which reveal implicitly the efficiency

of the µCHPs results in reducing the weight of the coordinator while the local goal fo the

individual building becomes more dominating. As a result, the coordination of balancing

the residual load within the cluster decreases.

Centralized Distributed

0

2

4

6

-78 %

+140 %

+17 %

Scheduling architecture

Com

pu

tati

on

tim

ein

103s

34 buildings102 buildings

Figure 6.10: Computation time analysis of the centralized and CG distributed schedulingmodels for the coordination of two clusters comprising 34 and 102 buildings.The arrow represents the computation time reduction achieved by thedistributed approach compared with centralized. The other percentageratios denote the increase of the computation time when increasing thecluster size within every approach.

94

6.2 Distributed scheduling for neighborhoods

Scalability The scalability of the centralized and CG distributed approaches is investi-

gated by analyzing the development of the computation time required to generate the

daily schedules for one year in clusters comprising 34 and 102 buildings. Figure 6.10

shows the results of the average computation time for the considered clusters within

the centralized and distributed scheduling models. The computation time within the

centralized approach amounts to 2800 s for the cluster with 34 buildings. The increase in

the number of considered buildings results in a significant rise of the computation time to

over 6700 s, this corresponds to an increase of 140 %. In contrast, the computation time of

the distributed approach is around 600 s in the cluster with 34 buildings. This corresponds

to 22 % of the time needed by the centralized approach. The computation time increases

within the distributed scheduling approach to around 700 s when increasing the number

of considered buildings to 102. This corresponds to an increase of 17 %.

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0Tim e in s

2 0 0

2 5 0

3 0 0

3 5 0

4 0 0

4 5 0

5 0 0

Cos

t fu

ncti

on v

alue

in E

uro

CG: zLRDWCG: zLRCG: zRDWLRCG: zLRDWLRCG: zLRLRCG: zRDW

Figure 6.11: Convergence assessment of the CG (in black) and integrated LRCG (inred) algorithms for a random day in March. The solid lines represent thedevelopment of the linearly relaxed primal solution of the master problemswhereas the dashed lines depict the development of the lower bounds. Thecross markers denote the integer solutions

Comparison of CG and LRCG

The main challenge for implementing a DSM strategy on a city district level is the

scalability potential for including a large number of buildings. The goal of the following

assessment is to compare the performance of the integrated LRCG and standard CG

95

Analysis: Results and Discussion

algorithms. It is assumed that the integrated LRCG enables a faster convergence and

thereby a higher potential of scalability.

Figure 6.11 depicts the convergence development of the CG and LRCG algorithms for a

random day in February. zLRDW represents the linear relaxation primal solution of the

master problem, zLR the lower bound or dual solution and zRDW the integer solution of the

master problem. The primal problem is a minimization problem while the dual problem is

a maximization problem. Therefore, the primal solution should decrease in each iteration,

whereas the dual solutions increases. It can be seen that the integrated LRCG algorithm

allows for faster convergence compared with the traditional CG algorithm by updating the

dual solution or lower bound based on the subgradient method. The integer solution is

quite comparable in both approaches.

2 0 02 2 02 4 02 6 02 8 03 0 03 2 0

z LRDW

in E

uro

2 0 02 2 02 4 02 6 02 8 03 0 03 2 03 4 0

z RDW

in E

uro

CG LRCG2 0 02 5 03 0 03 5 04 0 04 5 05 0 05 5 06 0 0

Com

puta

tion

tim

e in

s

Figure 6.12: Assessment of the primal zLRDW and integer zRDW solution, as well as thecomputation time of the CG and integrated LRCG distributed schedulingapproaches. Within the boxplot, the bottom and top of the box are the firstand third quartiles (25 % and 75 %), while the band inside is the median.The whiskers represent a 1.5 multiple of the interquartile range. The ’+’markers denote the outliers

96

6.2 Distributed scheduling for neighborhoods

The boxplot in Figure 6.12 delivers an overview on the average performance of both CG

and LRCG approaches in the transition period in terms of primal and integer solution as

well the computation time. It can be seen that the observations in Figure 6.11 are affirmed.

The primal and integer solutions are similar. However, the average computation time is

significantly reduced from around 550 to 250 s. The outlier found in the bottom subplot of

Figure 6.12 is a result of a slower convergence at the subproblems level. Consequently,

the assumption that the integrated LRCG allows for faster convergence and a higher

scalability potential compared with the traditional CG algorithm is verified.

97

7 Conclusion and Outlook

7.1 Conclusion

This thesis presents a generalized methodology, supported by a software framework, for

modeling and assessing mathematical programming based predictive DSM strategies that

exploit thermal and electrical flexibilities of residential BES.

Chapter 1 delivers an overview on the motivation, classification and challenges of residen-

tial DSM strategies. The main challenges for formulating and developing DSM strategies

are identified as BES MILP modeling, extensibility and scalabiltiy of the architecture as

well as the uncertainty of the incorporated forecasts.

In Chapter 2, the methodology developed in this thesis is described. Mainly, the concept

as well as the software architecture and configuration are presented. The modeling and

simulation platform is formulated in Python and includes a set of forecasting methods as

well as a BES MILP modeling library based on the Gurobi optimizer API and integrates a

BES non-linear Dymola/Modelica simulation model. The main advantages of the methodol-

ogy are the modular structure of the forecasting and BES MILP libraries as well as the

defined interfaces for coupling the scheduling HEMS to dynamic simulation models based

on the FMI standard. The FMI standard allows for integrating the dynamic simulation

models independent of the modeling language as a black box. Consequently, the software

framework is solely written in the programming language Python. Thereby, the advantage

is eliminating the usage of multiple programming languages and simulation coupling

servers. Consequently, the methodology provides a software framework which enables a

flexible and extensible formulation of scheduling models as well as reliable evaluation of

the schedules’ realization.

In Chapter 3, the forecasting algorithms for predicting the weather and demand variables

are introduced and evaluated. The assessment showed that the machine learning algorithm

SVR results in the lowest forecasting error for electrical and space heating demand

prediction. ARMA delivered the best results for the strongly seasonal solar irradiation

and ambient temperature. The DHW demand strong stochasticity could not be captured

by SVR and ARMA. Hence, the persistence method is recommended for this application.

It must be noted that considering the negligible implementation effort and the plausible

prediction performance, the persistence method can be further used as a forecasting

model for the other variable as well.

99

Conclusion and Outlook

In Chapter 4, the discrete MILP optimization models of the individual building energy

systems components are formulated. The introduced modeling approach for the heat-

ing generators comprehensively integrate units’ specific dynamic characteristics from

manufacturer data sheets and enable a better representation compared to the tradition-

ally used simplified MILP models in the literature, that are formulated to averagely and

conservatively represent the units’ behavior. It is recommended to adopt this modeling ap-

proaches for short-term scheduling application since the modeling uncertainty is thereby

reduced. Furthermore, a novel empirical approach for modeling thermal storage systems

is introduced which allows for representing the dynamic development of the usable and

unusable energy content depending on time and operation, based on the thermocline

effect. This model was compared to the traditionally used capacity storage model and a

(layer-based) stratified model, based on measurement data from an experimental setup.

The results indicate that the capacity storage model greatly overestimates the usable

energy content especially for high temperature differences in the storage. This results in

decreasing the reliability of the scheduling model. The thermocline model delivered the

best representation of the storage thermal behavior and is the recommended modeling

approach especially when considering the lower computation effort compared with a

stratified storage model due to the lower number of state variables.

In Chapter 5, the concepts and formulation of the scheduling algorithms for individual

buildings HEMS and city districts DSM strategies are presented. The models for HEMS

consist of a deterministic MILP model and a multi-stage stochastic programming approach

that extends the MILP model while incorporating the uncertainties of the electrical and

domestic hot water demands. The city district DSM strategies comprise a centralized

approach, which serves as a benchmark, as well as distributed formulations based on

decomposition techniques. A decomposition approach separates a centralized problem

into a master and several smaller subproblems which allows for reducing the computation

effort. In this work, two distributed DSM approaches are formulated, Dantzig-Wolfe

decomposition based column generation algorithm as well as an integrated Lagrangian

decomposition column generation. The analysis results of the introduced scheduling

algorithms are presented in Chapter 6. On a single building level, the performance of the

predictive HEMS approaches was assessed based on coupling the scheduling models to

dynamic non-linear simulation models of the building energy system to enable a reliable

evaluation that integrates the uncertainties of the forecast input data as well as the

linearization error of the BES MILP model. The results show that predictive HEMS with

perfect information allowed for a significant potential of load shifting and cost reduction,

ranging between 4.8 and 11.5 %, with respect to the reactive control strategy. However,

the dynamic operation results in a frequent switching behavior which is usually avoided

to reduce the tear and wear of the unit. Further, the deterministic scheduling model,

employing point forecasts of the weather variables and space heating, DHW and electrical

100

7.1 Conclusion

demand, enabled a cost reduction with respect to the reactive strategy. The cost reduction

ranged between 2.8 and 4.8 %,for the considered BES configurations except for the PV-

CHP-EH-Bat system, in which similar costs where achieved as with the reactive strategy.

Based on the results of the perfect information HEMS, the improvement of the applied

forecasting methods is expected to enhance the performance of this scheduling model.

A further improvement is also foreseen when increasing the rescheduling rate within

the rolling horizon algorithm, which allows for reducing the uncertainty of the forecasts

as well as the BES modeling. The multi-stage SP model outperformed the deterministic

model and allowed for an average cost reduction of around 3.5 %. This comes on the

cost of an increased computationally effort due to the increased modeling complexity.

On the other hand, the usage of forecasting models becomes unnecessary if historical

measurement data based scenario generation is applied for characterizing the demand

uncertainties within the SP model. In general, it was shown that the cost reduction

potential of predictive scheduling algorithms, with respect to reactive control strategy is

higher in BES configurations wiht HP as in CHP based systems. The potential is enhanced

by including an electrical heater instead of a boiler as auxiliary unit within the CHP based

system. Furthermore, the relative cost reduction potential compared, with the reactive

setup, is reduced in the presence of a battery. Nevertheless, the hypothesized advantage

of predictive scheduling models compared with reactive control strategy is verified. Both

deterministic and SP scheduling enhance the local integration of PV generation and enable

cost reduction.

On a city district level, the comparison between the centralized and distributed CG

approaches showed that the former provides, as expected, better coordination results.

However, the computational time rises significantly by around 140 % while increasing

number of participants from 34 to 102 buildings. This indicates that a scheduling problem

for a large number of buildings is intractable for conventional solvers in a reasonable time.

On the other hand, the CG approach provides comparable coordination performance as

the centralized model while significantly reducing the computation time by almost 80 %.

The computational effort increases by 17 % when increasing the number of participating

buildings. This is attributed to the decomposed structure since the subproblems computa-

tional effort remains the same but only the master problem complexity slightly increases.

The distributed architecture further enables significant advantages with regard to the

model extensibitiy since the master problems requires no modifications when adjusting

the functions, constraints or the number of participating energy systems. Moreover, the

data privacy concerns that arise in a centralized approach are reduced through distributed

scheduling since the buildings’ specific subproblems can be solved by a local intelligence

thus limiting the amount of sensible information that needs to be shared with the master

problem. In the final assessment, the integrated LRCG approach enabled a faster con-

vergence compared with the standard CG formulation. Thereby, the computation time

101

Conclusion and Outlook

was reduced by almost 50 %. Consequently, the integrated approach based distributed

scheduling model is recommended for future investigation to develop predictive DSM

concepts for residential neighborhoods.

7.2 Outlook

The simulation based evaluation of scheduling algorithms, on a single building level, clearly

indicate the advantage of employing predictive HEMS. However, the implementation

within a hardware based environment is foreseen to impact the operation results. It is

expected that the schedules reliability is weakened due to the influence of BES modeling

uncertainty. Therefore, hardware-in-the-loop (HiL) based investigations are required to

assess the advantage of predictive HEMS and provide insights on its real potential. The

interface between the HEMS and hardware controller can either be established directly

or indirectly based on the smart grid (SG) interface. The challenge in integrating HEMS

within a HiL setup is expected to lie in the controller configuration of the heating systems.

Despite the fact that new HP and CHP systems are equipped with a SG-interface, the

internal system controller is not designed to integrate an external HEMS control signal.

The underlying concept is based on hystereses which restrict the desired flexible operation

of HEMS. Therefore, the system controller must be modified or extended to allow for an

HEMS compatible operation phase which enables an interruptible operation (as opposed

to a hysteresis based uninterruptible operation) bounded by the thermal storage state

according to the space heating and domestic hot water requirements. Furthermore, the

simulation time of a HiL setup is equivalent to real time e.g. a HiL coupled simulation

of one week requires one week in real time as well. This represents a limitation for a

HiL based assessment and hinders a long period evaluation. Consequently, a dynamic

assessment based on representative periods should be designed and employed. Similarly,

HiL based evaluation of the SP-model compared to the deterministic approach should be

carried out, with respect to the increased computational and implementation effort. The

analysis should consider the impact of increasing the rescheduling rate within the rolling

horizon on the performance of the deterministic model. Further investigations should also

focus on embedding HEMS on mini single-board computers, e.g. ’Rapsberry PI’, which

would pave the way for real life applications.

The concept of employing distributed small microgrids, to enable the integration of large

renewable energy capacity, provides a highly promising alternative to an infrastructure

development of the electric grid. Within this approach, the individual mircrogrids reduce

the imports and exports to the macrogrid and provide positive or negative load capacities

which can allow for compensating the fluctuations of renewables and ensuring grid stability.

The introduced simulation based results for distributed DSM strategies, in this work, can

102

7.2 Outlook

only be regarded as a proof of concept. However, it was shown that the predictive DSM

strategies for city districts provide a significant potential for BES coordination and residual

load balancing already in small microgrids comprising 34 buildings. Moreover, the DSM

strategies allowed for operation cost reduction of the whole microgrid. This can be used

to develop a business plan such as internal microgrid market regulations or contracting

based model which can promote the installation of the required flexible heat generators

i.e. HPs and CHPs and pave the way for the concept realization. Future research on

predictive DSM strategies for city districts should further address uncertainties with

regard to generation and demand profiles. Finally, future investigations should also be

focused on the implementation architecture to identify the bottlenecks, which are not

considered in simulation-based assessments. A cloud-based solution is recommended as a

testing platform.

103

Appendix

A Appendix

A.1 Single building evaluation

A.1.1 PV-HP-EH

0.00.51.01.52.02.53.03.54.0

kW

Thermal loads

Dymola_Qspace Dymola_Qdhw

0369

12

kW

Dymola_QHP

0

1

OnO

ff

Dymola_uHPDymola_uHP,PyMPC

02468

kW

Dymola_QEH

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

Dymola_SoCST

Figure A.1: Dynamic performance of the thermal side for PV-HP-EH under the SPdhw

strategy

105

Appendix

0.00.51.01.52.02.53.03.54.0

kW

Thermal loads

Dymola_Qspace Dymola_Qdhw

0369

12

kW

Dymola_QHP

0

1

OnO

ff

Dymola_uHPDymola_uHP,PyMPC

02468

kW

Dymola_QEH

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

Dymola_SoCST

Figure A.2: Dynamic performance of the thermal side for PV-HP-EH under the SPel

strategy

A.1.2 PV-HP-EH-Bat

0.00.51.01.52.02.53.03.54.0

kW

Thermal loads

Dymola_Qspace Dymola_Qdhw

0369

12

kW

Dymola_QHP

0

1

OnO

ff

Dymola_uHP

0369

12

kW

Dymola_QEH

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

Dymola_SoCST

Figure A.3: Dynamic performance of the thermal side for PV-HP-EH-Bat under the Refstrategy

106

A.1 Single building evaluation

02468

kW

Thermal loads

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

0369

12kW

QHP

Dymola_QHP

0

1

OnO

ff

uHPDymola_uHP

01234

kW

QEH

Dymola_QEH

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

SoCSTDymola_SoCST

Figure A.4: Dynamic performance of the thermal side for PV-HP-EH-Bat under the DPI

strategy

02468

kW

Thermal loads

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

0369

12

kW

QHP

Dymola_QHP

0

1

OnO

ff

uHPDymola_uHP

01234

kW

QEH

Dymola_QEH

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

SoCSTDymola_SoCST

Figure A.5: Dynamic performance of the thermal side for PV-HP-EH-Bat under the DF

strategy

107

Appendix

02468

kW

Electrical loadsPdemandDymola_Pdemand

0369

12kW

PimportDymola_Pimport

PexportDymola_Pexport

02468

kW

PPVDymola_PPV

01234

kW

PHPDymola_PHP

0

1

OnO

ff uHPDymola_uHP

01234

kW

PEHDymola_PEH

02468

kW

PBAT,chargeDymola_PBAT,charge

PBAT,dischargeDymola_PBAT,discharge

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

255075

100

%

SoCBATDymola_SoCBAT

Figure A.6: Dynamic performance of the electrical side for PV-HP-EH-Bat under the DF

strategy

A.1.3 PV-CHP-EH

02468

kW

Thermal loads

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

0369

12

kW

QCHP

Dymola_QCHP

0

1

OnO

ff

uCHPDymola_uCHP

0369

12

kW

QEH

Dymola_QEH

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

SoCSTDymola_SoCST

Figure A.7: Dynamic performance of the thermal side for PV-CHP-EH under the DPI

strategy

108

A.1 Single building evaluation

02468

kW

Electrical loadsPdemandDymola_Pdemand

0369

12kW

PimportDymola_Pimport

PexportDymola_Pexport

02468

kW

PPVDymola_PPV

01234

kW

PCHPDymola_PCHP

0

1

OnO

ff uCHPDymola_uCHP

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:00048

1216

kW

PEHDymola_PEH

Figure A.8: Dynamic performance of the electrical side for PV-CHP-EH under the DPI

strategy

02468

kW

Thermal loads

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

0369

12

kW

QCHP

Dymola_QCHP

0

1

OnO

ff

uCHPDymola_uCHP

0369

12

kW

QEH

Dymola_QEH

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

SoCSTDymola_SoCST

Figure A.9: Dynamic performance of the thermal side for PV-CHP-EH under the DF

strategy

109

Appendix

A.1.4 PV-CHP-EH-Bat

02468

kWThermal loads

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

0369

12

kW

QCHP

Dymola_QCHP

0

1

OnO

ff

uCHPDymola_uCHP

0369

12

kW

QEH

Dymola_QEH

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

SoCSTDymola_SoCST

Figure A.10: Dynamic performance of the thermal side for PV-CHP-EH-Bat under the DPI

strategy

02468

kW

Electrical loadsPdemandDymola_Pdemand

0369

12

kW

PimportDymola_Pimport

PexportDymola_Pexport

02468

kW

PPVDymola_PPV

02468

kW

PCHPDymola_PCHP

0

1

OnO

ff uCHPDymola_uCHP

048

1216

kW

PEHDymola_PEH

02468

kW

PBAT,chargeDymola_PBAT,charge

PBAT,dischargeDymola_PBAT,discharge

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

255075

100

%

SoCBATDymola_SoCBAT

Figure A.11: Dynamic performance of the electrical side for PV-CHP-EH-Bat under theDPI strategy

110

A.1 Single building evaluation

02468

kW

Thermal loads

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

0369

12kW

QCHP

Dymola_QCHP

0

1

OnO

ff

uCHPDymola_uCHP

0369

12

kW

QEH

Dymola_QEH

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

SoCSTDymola_SoCST

Figure A.12: Dynamic performance of the thermal side for PV-CHP-EH-Bat under the DF

strategy

A.1.5 PV-CHP-B

02468

kW

Thermal loads

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

0369

12

kW

QCHP

Dymola_QCHP

0

1

OnO

ff

uCHPDymola_uCHP

02468

kW

QBoiler

Dymola_QBoiler

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

SoCSTDymola_SoCST

Figure A.13: Dynamic performance of the thermal side for PV-CHP-B under the DPI

strategy

111

Appendix

02468

kW

Electrical loadsPdemandDymola_Pdemand

02468

kW

PimportDymola_Pimport

PexportDymola_Pexport

02468

kW

PPVDymola_PPV

01234

kW

PCHPDymola_PCHP

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

1

OnO

ff

uCHPDymola_uCHP

Figure A.14: Dynamic performance of the electrical side for PV-CHP-B under the DPI

strategy

02468

kW

Thermal loads

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

0369

12

kW

QCHP

Dymola_QCHP

0

1

OnO

ff

uCHPDymola_uCHP

048

1216

kW

QBoiler

Dymola_QBoiler

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

SoCSTDymola_SoCST

Figure A.15: Dynamic performance of the thermal side for PV-CHP-B under the DF strat-egy

112

A.1 Single building evaluation

A.1.6 PV-CHP-B-Bat

02468

kW

Thermal loads

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

0369

12

kW

QCHP

Dymola_QCHP

0

1

OnO

ff

uCHPDymola_uCHP

048

1216

kW

QBoiler

Dymola_QBoiler

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

SoCSTDymola_SoCST

Figure A.16: Dynamic performance of the thermal side for PV-CHP-B-Bat under the DPI

strategy

02468

kW

Electrical loadsPdemandDymola_Pdemand

02468

kW

PimportDymola_Pimport

PexportDymola_Pexport

02468

kW

PPVDymola_PPV

01234

kW

PCHPDymola_PCHP

0

1

OnO

ff uCHPDymola_uCHP

01234

kW

PBAT,chargeDymola_PBAT,charge

PBAT,dischargeDymola_PBAT,discharge

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

255075

100

%

SoCBATDymola_SoCBAT

Figure A.17: Dynamic performance of the electrical side for PV-CHP-B-Bat under the DPI

strategy

113

Appendix

02468

kW

Thermal loads

Qspace

Dymola_Qspace

Qdhw

Dymola_Qdhw

0369

12

kW

QCHP

Dymola_QCHP

0

1

OnO

ff

uCHPDymola_uCHP

048

1216

kW

QBoiler

Dymola_QBoiler

00:0028-Mar2008

00:0029-Mar

06:00 12:00 18:00 06:00 12:00 18:000

20406080

100

%

SoCSTDymola_SoCST

Figure A.18: Dynamic performance of the thermal side for PV-CHP-B-Bat under the DF

strategy

114

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126

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Thermal Sensation and

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Inhomogeneous Indoor

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Multi-phase, multi-species

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Four Essays related to Energy

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Impact of Carbon Capture and

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Multi-Resonant Converters as

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Lenke, R.

A Contribution to the Design of

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Brännström, F.

Einsatz hybrider RANS-LES-

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The Integrated Emitter Turn-

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Hoh, A.

Exergiebasierte Bewertung

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Köllensperger, P.

The Internally Commutated

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Achtnicht, M.

Essays on Consumer Choices

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Stated Preference Evidence

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Panašková, J.

Olfaktorische Bewertung von

Emissionen aus Bauprodukten

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Vogt, C.

Optimization of Geothermal

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Benigni, A.

Latency exploitation for

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Butschen, T.

Dual-ICT – A Clever Way to

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Li, W.

Fault Detection and

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Shen, J.

Modeling Methodologies for

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Flieger, B.

Innenraummodellierung einer

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Modelica

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Liu, J.

Measurement System and

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Experimentelle Untersuchung

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Thomas, S.

A Medium-Voltage Multi-

Level DC/DC Converter with

High Voltage Transformation

Ratio

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Tang, J.

Probabilistic Analysis and

Stability Assessment for Power

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Wind Generation and

Synchrophasor Measurement

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Sorda, G.

The Diffusion of Selected

Renewable Energy

Technologies: Modeling,

Economic Impacts, and Policy

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Rosen, C.

Design considerations and

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reserve energy markets for

distributed generation

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Ni, F.

Applications of Arbitrary

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Michelsen, C. C.

The Energiewende in the

German Residential Sector:

Empirical Essays on

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Space Heating Technologies

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Rolfs, W.

Decision-Making under Multi-

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for Long-Lived Energy

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Wang, J.

Design of Novel Control

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System-Level Multi-Physics

Power Hardware in the Loop

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Togawa, K.

Stochastics-based Methods

Enabling Testing of Grid-

related Algorithms through

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Huchtemann, K.

Supply Temperature Control

Concepts in Heat Pump

Heating Systems

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Molitor, C.

Residential City Districts as

Flexibility Resource: Analysis,

Simulation, and Decentralized

Coordination Algorithms

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Sunak, Y.

Spatial Perspectives on the

Economics of Renewable

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Cupelli, M.

Advanced Control Methods for

Robust Stability of MVDC

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Chen, K.

Active Thermal Management

for Residential Air Source Heat

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Pâques, G.

Development of SiC GTO

Thyristors with Etched

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Garnier, E.

Distributed Energy Resources

and Virtual Power Plants:

Economics of Investment and

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Calì, D.

Occupants' Behavior and its

Impact upon the Energy

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Isermann, T.

A Multi-Agent-based

Component Control and

Energy Management System

for Electric Vehicles

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ISBN 978-3-942789-38-7

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Wu, X.

New Approaches to Dynamic

Equivalent of Active

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Transient Analysis

1. Auflage 2016

ISBN 978-3-942789-39-4

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Garbuzova-Schiftler, M.

The Growing ESCO Market for

Energy Efficiency in Russia: A

Business and Risk Analysis

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Huber, M.

Agentenbasierte

Gebäudeautomation für

raumlufttechnische Anlagen

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Soltau, N.

High-Power Medium-Voltage

DC-DC Converters: Design,

Control and Demonstration

1. Auflage 2017

ISBN 978-3-942789-42-4

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Stieneker, M.

Analysis of Medium-Voltage

Direct-Current Collector Grids

in Offshore Wind Parks

1. Auflage 2017

ISBN 978-3-942789-43-1

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Bader, A.

Entwicklung eines Verfahrens

zur Strompreisvorhersage im

kurzfristigen Intraday-

Handelszeitraum

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Chen, T.

Upscaling Permeability for

Fractured Porous Rocks and

Modeling Anisotropic Flow

and Heat Transport

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Ferdowsi, M.

Data-Driven Approaches for

Monitoring of Distribution

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Kopmann, N.

Betriebsverhalten freier

Heizflächen unter zeitlich

variablen Randbedingungen

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ISBN 978-3-942789-47-9

E.ON ERC Band 49

Fütterer, J.

Tuning of PID Controllers

within Building Energy

Systems

1. Auflage 2017

ISBN 978-3-942789-48-6

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Adler, F.

A Digital Hardware Platform

for Distributed Real-Time

Simulation of Power Electronic

Systems 1. Auflage 2017

ISBN 978-3-942789-49-3

Input: Actual data

Model: Dynamic nonlinear

simulation model– FMU

Input: Forecast

Model: Discretelinearized

optimization model

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Predictive Demand Side Management Strategies for Residential Building Energy Systems

Hassan Harb

This thesis presents a generalized methodology, supported by a software framework, for modeling and assessing mathematical programming based predictive demand side management (DSM) strategies that exploit thermal and electrical flexibilities of residential building energy systems (BES) to enhance the integration of renewable energy sources. The modeling and simulation platform is formulated in Python and includes a set of forecasting methods as well as a discrete mixed inte-ger linear programming (MILP) modeling library based on the Gurobi optimizer API. The platform further integrates a nonlinear BES simulation model in Dymola/Modelica as a functional mock-up unit (FMU). The investigated scheduling models for individual buildings consist of a deterministic MILP strategy and a multi-stage stochastic programming approach that extends the MILP model while incorporating the uncertainties of the electrical and domestic hot water demands. The city district DSM strategies comprise a centralized approach, which serves as a benchmark, as well as distributed formulations based on decomposition techniques. The distributed DSM approaches considered are Dantzig-Wolfe decomposition based column generation algorithm as well as an integrated Lagrangian decomposition column generation approach.

ISBN 978-3-942789-50-9