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This project has received funding from the European
Union’s Horizon 2020 research and innovation
programme under grant agreement No 768619
The RESPOND Consortium 2019
Integrated Demand REsponse
SOlution Towards Energy
POsitive NeighbourhooDs
WP4 ICT enabled cooperative demand
response model
T4.2 INTEGRATION OF DEMAND RESPONSE WITH
SUPPLY/DEMAND SIDE MANAGEMENT
D4.2 Demand response optimization
model
Ref. Ares(2019)6063634 - 30/09/2019
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PROJECT ACRONYM RESPOND
DOCUMENT D4.2 Demand response optimisation model
TYPE (DISTRIBUTION LEVEL) ☐ Public
☒ Confidential
☐ Restricted
DELIVERY DUE DATE 30.09.2019.
DATE OF DELIVERY 30.09.2019.
STATUS AND VERSION FINAL, 1.0
DELIVERABLE RESPONSIBLE IMP
CONTRIBUTORS DEXMA
AUTHOR (S) Marko Jelić, Nikola Tomašević (IMP)
OFFICIAL REVIEWER(S) Iker Esnaola (TEK)
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DOCUMENT HISTORY
Version ISSUE DATE CONTENT AND CHANGES
V0.1 15.8.2019. Draft version
V0.2 25.9.2019. Reviewer comments
V1.0 26.9.2019. Final version with reviewer comments integrated
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This deliverable describes a linear programming-based methodology for solving the optimization
problem with special regard to DR related optimizations. Namely, with the addition of load
management variables and constraints and formulated around the Energy Hub concept of
modelling energy distribution through transmission and conversion, the proposed system has the
capabilities of considering demand forecasts, renewable generation forecasts and grid supply
limitations and to facilitate either DR events implied by variable pricing profiles or by explicitly
defining instances of time in which any load deviation is to be penalized in addition to the cost
function that minimizes costs for end users.
The proposed methodology is instantiated for a single-household model for each pilot site, and
with one of them assumed as a reference, the methodology is tested using implied DR with slightly
modified pricing and synthetized load forecast and renewable generation forecast. This example
successfully demonstrated that both load and power import manipulations can be performed by
defining the aforementioned DR events.
EXECUTIVE SUMMARY
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TABLE OF CONTENTS
EXECUTIVE SUMMARY _____________________________________________________________ 4
TABLE OF CONTENTS ______________________________________________________________ 5
LIST OF FIGURES __________________________________________________________________ 6
LIST OF TABLES ___________________________________________________________________ 7
ABBREVIATIONS AND ACRONYMS __________________________________________________ 8
1. INTRODUCTION __________________________________________________________________ 9
2. ENERGY HUB MODELING________________________________________________________ 11
2.1 MODELING FUNDAMENTALS _____________________________________________________________ 11
2.2 FUNDAMENTAL (ENERGY MANAGEMENT) CONSTRAINTS _______________________________________ 13
2.3 SUPPLEMENTARY (LOAD MANIPULATION) CONSTRAINTS _______________________________________ 15
2.3.1 VARIANT 1 – INDIVIDUAL LOADS _________________________________________________________________ 16
2.3.2 VARIANT 2 – AGGREGATED LOADS________________________________________________________________ 18
2.4 BOUNDARY CONDITIONS ________________________________________________________________ 20
2.4.1 VARIANT 1 ___________________________________________________________________________________ 20
2.4.2 VARIANT 2 ___________________________________________________________________________________ 21
2.5 OBJECTIVE FUNCTION ___________________________________________________________________ 21
3. INDIVIDUAL USER PILOT MODELS _____________________________________________________ 23
3.1 AARHUS ______________________________________________________________________________ 23
3.2 MADRID ______________________________________________________________________________ 25
3.3 ARAN ISLANDS _________________________________________________________________________ 26
4. OPTIMIZATION USE CASES ___________________________________________________________ 29
4.1 IMPLICIT DR EVENT _____________________________________________________________________ 29
5. CONCLUSION ___________________________________________________________________ 33
6. REFERENCES___________________________________________________________________ 34
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LIST OF FIGURES
FIGURE 1 - RESPOND OPTIMIZATION LOOP .................................................................................................. 9
FIGURE 2 – ENERGY HUB STRUCTURE WITH OVERLAID CONSTRAINTS (VARIANT 1) ................................. 14
FIGURE 3 – ENERGY HUB STRUCTURE WITH OVERLAID CONSTRAINTS (VARIANT 2) ................................. 15
FIGURE 4 - EXAMPLE OF LOAD SHIFTING IN TIME FROM NOMINAL LOAD SCHEDULE (TOP) WITH SHIFTING
WINDOWS TO THE OPTIMIZED LOAD SCHEDULE (BOTTOM) ..................................................................... 17
FIGURE 5 - ILLUSTRATION OF A DR EVENT LOAD DEVIATION ..................................................................... 19
FIGURE 6 - AN EXAMPLE OF MODELING A SINGLE USER WITH A SINGLE ENERGY HUB............................. 23
FIGURE 7 - AARHUS PILOT SITE TOPOLOGY ................................................................................................. 23
FIGURE 8 - MADRID PILOT SITE TOPOLOGY................................................................................................. 25
FIGURE 9 - ARAN PILOT SITE TOPOLOGY (TYPE 1 TOP, TYPE 2 MIDDLE AND TYPE 3 BOTTOM) ................. 28
FIGURE 10 - PRICE PROFILES USED FOR DEFINING AN IMPLICIT DR EVENT................................................ 30
FIGURE 11 – PREDICTED AND OPTIMIZED LOAD PROFILES ......................................................................... 31
FIGURE 12 – NOMINAL AND OPTIMIZED INDIVIDUAL CARRIER IMPORT PROFILES ................................... 32
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LIST OF TABLES
TABLE 1 – VARIABLE DESCRIPTIONS FOR THE CORE ENERGY MANAGEMENT ENERGY HUB CONSTRAINTS
..................................................................................................................................................................... 11
TABLE 2 – VARIABLE DESCRIPTIONS FOR THE ENERGY HUB’S LOAD MANIPULATION (VARIANT 1)
CONSTRAINTS .............................................................................................................................................. 12
TABLE 3 – VARIABLE DESCRIPTIONS FOR THE ENERGY HUB’S LOAD MANIPULATION (VARIANT 2)
CONSTRAINTS .............................................................................................................................................. 12
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ABBREVIATIONS AND ACRONYMS
DR Demand response
LP Linear programming
MILP Mixed-integer linear programming
RES Renewable energy source
DHW Domestic hot water
STC Solar thermal collector
PV Photovoltaic
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1. INTRODUCTION
As residential Demand Response (DR) programmes are yet to be explored in depth, there are
not that many solutions for this problem in related literature. In this regard, the RESPOND project
proposes a novel solution through the use of optimization in a control loop presented in Figure 1.
It takes into consideration day-ahead energy prices, the forecasted renewable production and the
predicted loads from individual users aggregated into a neighborhood profile. Using the supposed
demand flexibility, the optimizer shifts the loads in intensity and in time to generate a profile that
is the most cost-effective for end users and most stable for the grid operator. However, given that
the RESPOND project is all about maintaining grid stability and making use of the untapped
potential of residential DR capacities, the DR events hold a special place in the optimization
process. The system allows for load shifting to occur both in cases where the convenience is
dictated by current pricing (low prices drive loads up, and soaring prices drive loads down) and
by direct requests from the utility company or DR aggregator by means of predefined DR events.
When the optimization engine has completed its run, an “optimal neighborhood profile” is available
for the next day. If this profile is upheld by the end users, lowest cost and maximum stability are
obtained. However, as the day progresses, the aggregated demand may slightly or more
significantly differ from what the optimizer has deemed best. That’s where the energy monitoring
service comes in. It looks at the optimized profile and the aggregated profile of an entire
neighborhood that is continuously being measured. Whenever a deviation is noticed, for example
when actual load levels are higher than optimal, this service looks at data from individual
households, scans for currently active appliances that are considered to be large energy
FIGURE 1 - RESPOND OPTIMIZATION LOOP
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consumers, and issues notifications trough the RESPOND dashboard and mobile app that
suggest to the end user that the activation of that appliance should be deferred to a later time. By
doing this, the user may obtain a monetary reward and maintain grid stability. Thus, the energy
management process is semi-automatized resulting in a minimal additional burden for the end
user, while maintaining full control since actions are not performed without explicit user
authorization.
This deliverable describes the core methodology behind the optimization process, the model that
was used to depict the topology of the system in all three pilot sites, and some variations of that
model that are introduced for individual and aggregate load management purposes. It also
describes a potential use case in which a DR event is induced using peak pricing in order to force
load decreases.
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2. ENERGY HUB MODELING
2.1 MODELING FUNDAMENTALS
A mixed-integer linear programming (MILP) model is most commonly defined as a problem where a vector of variables
𝑥 = [𝑥1 𝑥2 ⋯ 𝑥𝑚]𝑇 ∈ ℝ𝑚
is to be determined as an argument that optimizes (most commonly minimizes) a product with a predefined objective function 𝑓 as given by
𝑥opt = arg𝑥{min{𝑓𝑇𝑥}}.
At the same time, the optimal solution vector 𝑥opt must also adhere to a set of constraints. These constraints are split into five different categories being equality and inequality constraints, lower and upper bounds and integer constraints. Since a mixed-integer programming problem is being discussed, an
integer subvector 𝑥int of 𝑥 is defined as
𝑥𝑖𝑛𝑡 = [𝑥1int 𝑥2
int ⋯ 𝑥𝑚𝑖𝑛𝑡int ]
𝑇
and with a lower 𝑙b bound and upper 𝑢b bound vectors given as
𝑙b = [𝑙1 𝑙2 ⋯ 𝑙𝑚]𝑇
𝑢b = [𝑢1 𝑢2⋯ 𝑢𝑚]𝑇
the aforementioned constraints can be posed as
𝐴eq𝑥 = 𝑏eq
𝐴ineq𝑥 ≤ 𝑏ineq
(∀𝑖)(𝑙𝑖 ≤ 𝑥𝑖 ≤ 𝑢𝑖) (∀𝑖)(𝑥𝑖
int ∈ 𝑍, 𝑍 ⊂ ℤ).
The vector of variables 𝑥 is formed by arranging a set of all variables (input power, export power,
etc.) required for model simulation at each time step during the simulated horizon.
The variables used within the model are summarized in Table 1, Table 2 and Table 3.
TABLE 1 – VARIABLE DESCRIPTIONS FOR THE CORE ENERGY MANAGEMENT ENERGY HUB CONSTRAINTS
Label Variable name Variable type
𝑃in Imported power (from renewable sources, grid, etc.) Float
𝑃cin Power sent to the conversion stage Float
𝑃cout Power obtained from the conversion stage Float
𝑄in Power flow to or from the input stage storage Float
𝑄out Power flow to or from the output stage storage Float
𝐿 Load (demand) Float
𝑃out Power sent to the output stage Float
𝑃exp Exported power Float
𝑞in Converted power flow to or unconverted flow from input storage Float
𝐸in Input stage storage state of charge (available energy) Float
𝑞out Converted power flow to or unconverted flow from output storage Float
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𝐸out Output stage storage state of charge (available energy) Float
TABLE 2 – VARIABLE DESCRIPTIONS FOR THE ENERGY HUB’S LOAD MANIPULATION (VARIANT 1) CONSTRAINTS
Label Variable name Variable type
𝑦 Device ON/OFF indicator Boolean (0/1)
𝑧 Device start indicator Boolean (0/1)
𝑑+ Positive load (power) deviation Float
𝑑− Negative load (power) deviation Float
𝐼(𝑑+) Indicator of positive load (power) deviation Boolean (0/1)
𝐼(𝑑−) Indicator of negative load (power) deviation Boolean (0/1)
TABLE 3 – VARIABLE DESCRIPTIONS FOR THE ENERGY HUB’S LOAD MANIPULATION (VARIANT 2) CONSTRAINTS
Label Variable name Variable type
Δ𝐿+ Positive load (power) deviation Float
Δ𝐿− Positive load (power) deviation Float
𝐼(Δ𝐿+) Indicator of positive load (power) deviation Boolean (0/1)
𝐼(Δ𝐿−) Indicator of negative load (power) deviation Boolean (0/1)
To be operated programmatically, the variable values must be reordered into a flattened format.
Accordingly, what was, for example, natively considered as a 2D matrix like the imported power
that spans over time trough columns and over carriers over rows, written as
𝑃in = [
𝑃in(𝑖 = 1, 𝑘 = 1) 𝑃in(𝑖 = 1, 𝑘 = 2) ⋯ 𝑃in(𝑖 = 1, 𝑘 = 𝑛)
𝑃in(𝑖 = 2, 𝑘 = 1) 𝑃in(𝑖 = 2, 𝑘 = 2) ⋯ 𝑃in(𝑖 = 2, 𝑘 = 𝑛)⋮
𝑃in(𝑖 = 𝑛c, 𝑘 = 1)⋮
𝑃in(𝑖 = 𝑛c, 𝑘 = 2)⋱⋯
⋮𝑃in(𝑖 = 𝑛c, 𝑘 = 𝑛)
]
where 𝑖 represents the carrier counter, 𝑛c the total number of carriers, 𝑘 the time counter and 𝑛
the time horizon length (number of time steps during the simulation), is reordered into a vector of
format
𝑃in = [𝑃in(𝑖 = 1, 𝑘 = 1), 𝑃in(𝑖 = 2, 𝑘 = 1), ⋯ , 𝑃in(𝑖 = 𝑛c, 𝑘 = 1), 𝑃in(𝑖 = 2, 𝑘 = 1), ⋯ , 𝑃in(𝑖 = 𝑛c, 𝑘
= 𝑛)]𝑇 .
However, some of the variables represent individual appliances and not individual carriers. For
example, the device on/off status variable 𝑦 that might be natively considered as a 2D matrix like
𝑦 = [
𝑦(𝑖 = 1, 𝑘 = 1) 𝑦(𝑖 = 1, 𝑘 = 2) ⋯ 𝑦(𝑖 = 1, 𝑘 = 𝑛)
𝑦(𝑖 = 2, 𝑘 = 1) 𝑦(𝑖 = 2, 𝑘 = 2) ⋯ 𝑦(𝑖 = 2, 𝑘 = 𝑛)⋮
𝑦(𝑖 = 𝑛a, 𝑘 = 1)⋮
𝑦(𝑖 = 𝑛a, 𝑘 = 2)⋱⋯
⋮𝑦(𝑖 = 𝑛a, 𝑘 = 𝑛)
]
where 𝑖 represents the appliance number, 𝑛a the total number of appliances, 𝑘 the time counter
and 𝑛 the horizon length, is reordered into a new flattened-out form of
𝑦 = [𝑦(𝑖 = 1, 𝑘 = 1), 𝑦(𝑖 = 1, 𝑘 = 2), ⋯ , 𝑦(𝑖 = 1, 𝑘 = 𝑛), 𝑦(𝑖 = 2, 𝑘 = 1), ⋯ , 𝑦(𝑖 = 𝑛𝑎, 𝑘 = 𝑛)]𝑇 .
In further text, depending on the appropriate contexts, variables are used as both matrices and
vectors where such an application is deemed more suitable.
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2.2 FUNDAMENTAL (ENERGY MANAGEMENT) CONSTRAINTS
The fundamental constraints of the Energy Hub system depict energy flow and energy transformations through a set of stages:
• Input (raw) energy storage
• Input energy transformation
• Energy conversion
• Energy export
• Output energy transformation
• Output (user) energy storage
• Loads
Let 𝑃in(𝑘) be the imported power from a certain energy carrier (for example thermal (hot water) energy obtained by a solar thermal collector system as will be described in D4.4 or electric energy imported from the grid). The imported power can then be either stored within the input storage stage or sent further to the rest of the system using appropriate transformers and convertors. According to the law of conservation of power for the input stage, the balance
(∀𝑘)(𝑃in(𝑘) = 𝑆in𝑄in(𝑘) + 𝐹in𝑃cin(𝑘))
must hold. In this equation, 𝑄in depicts the instantaneous power that is being sent or obtained from the
input storage and 𝑃cin(𝑘) is the instantaneous power being dispatched to the conversion stage. Furthermore, the power dispatched to the storage system is converted into energy with a charge/discharge rate of 𝑞in through the expression
(∀𝑘) (𝑄in(𝑘) = 𝑆qin𝑞in(𝑘)).
The available energy (state of charge, SOC) of the storage system is given by an integral
expression that accumulates input and output energy
(∀𝑘 < 𝑁𝑇𝑠)(𝐸in(𝑘 + 1) = 𝐸in(𝑘) + 𝑞in(𝑘)𝑇𝑠)
with an initial condition given by
𝐸in(1) = 𝐸in1
defining the SOC in the first timestep which is most commonly set to zero unless the optimization
is being performed on consecutive time intervals where the final condition of one interval
influences the initial condition of the next one. The energy that is not being stored within the input
system is sent to the energy conversion stage as is given by
(∀𝑘)(𝑃cout(𝑘) = 𝐶𝑃cin(𝑘))
The output power 𝑃cout of the conversion stage can be exported back to the grid or sent to the
output stage. This routing is given by
(∀𝑘)(𝑃out(𝑘) = 𝑃cout(𝑘) − 𝑃exp(𝑘))
with the option of setting certain carrier’s export power to a predefined value (most commonly
used to block exporting power imported from the grid back to the grid) by
(∀𝑘)(𝐷exp𝑃exp(𝑘) = 𝑅exp)
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where 𝐷exp is a matrix that defines what carrier is to have a restricted export and 𝑅exp sets those
fixed values.
The power 𝑃out that is left over from the export process is sent to the output transformation stage
defined by a matrix 𝐹out that aggregates all the carriers into a given number of values depending
on the number of load types. This operation is obtained through the equation
(∀𝑘)(𝐿(𝑘) = 𝐹out𝑃out(𝑘) − 𝑆out𝑄out(𝑘))
where 𝐿 is the demand vector that needs to be fulfilled and 𝑄out is the power that can be stored
for later use within the output storage system. As was the case with the input, the output can also
feature a storage option. The charge/discharge rate 𝑞out is calculated using
(∀𝑘)(𝑄out(𝑘) = 𝑆qout𝑞out(𝑘)).
Analogous to the input stage, the output storage energy availability is calculated using an integral
expression
(∀𝑘 < 𝑁𝑇𝑠)(𝐸out(𝑘 + 1) = 𝐸out(𝑘) + 𝑞out(𝑘)𝑇𝑠)
and an initial condition is set with
𝐸out(1) = 𝐸out1
which concludes the set of equations governing the energy management aspect of the Energy
Hub system. However, additional equations must be added for load management mechanisms.
This document analyses two use cases for load management: one in which the loads are
FIGURE 2 – ENERGY HUB STRUCTURE WITH OVERLAID CONSTRAINTS (VARIANT 1)
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managed individually on a per-appliance basis and one in which the loads are managed jointly,
as would be the case when viewing multiple users from a neighbourhood perspective or when
individual appliances for a single user are not accessible through sensors and actuators. Figure
2 illustrates the constraints that govern energy flow through the Energy Hub model with overlaid
formulas in accordance with the first load management variant. Here, the equality constraints are
denoted with a blue outline while the inequality constraints are denoted with an orange outline.
On the other hand, Figure 3 illustrates the second variant of energy management, with core
constraints being denoted with a blue outline and the load management constraints denoted with
a red outline.
2.3 SUPPLEMENTARY (LOAD MANIPULATION) CONSTRAINTS
The following subsections go into detail about how load manipulations are modelled. Generally,
there are to main types of approach in this regard. The first one (variant one) is where each
appliance’s activation are managed individually i.e. the appliance activations shifts in time and in
power value are traceable meaning that an optimal schedule can be obtained on a per appliance
basis. Such an approach is convenient when users are willing to provide detailed information
regarding the ways in which they use their appliances: the appliance’s nominal power draw, power
deviations if applicable, nominal activation timeframes and appropriate shifting windows in which
the appliances are to be moved around in time in order to optimize a given criterion function. The
second one (variant two) regards loads as an aggregate value, whether it be an aggregate of
multiple appliances within a single household (as will be discussed in this deliverable) or an
aggregate of multiple households that form a neighbourhood (as will be discussed in D4.3). Such
an approach is considered as more feasible because the variations and data uncertainty of the
baseline load are levelled out when the aggregation is performed
Since the data available for the RESPOND project does not assume any appliance specific
scheduling in this regard, the latter approach is selected as the method of choice for the
RESPOND services. However, for the sake of describing the potentials of the proposed
methodology, both methods will be briefly described.
FIGURE 3 – ENERGY HUB STRUCTURE WITH OVERLAID CONSTRAINTS (VARIANT 2)
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2.3.1 VARIANT 1 – INDIVIDUAL LOADS
Load 𝐿 in this regard is considered as either 𝐿fix which cannot be shifted in time and cannot be
shifted in value or 𝐿flex which can theoretically be shifted in both time and value. What’s more, the
individual appliance activations for some appliances which are named dispersible can be split into
multiple time instances. The modelling of this process starts with the introduction of the activation
indicator, i.e. an on/off state variable 𝑦𝑖 defied for each appliance 𝑖 by
𝑦𝑖(𝑘) ≜ { 0, appliance 𝑖 is off at 𝑡 = 𝑘𝑇𝑠
1, appliance 𝑖 is on at 𝑡 = 𝑘𝑇𝑠.
If we let 𝑃𝑖 be the power draw of 𝑖-tha appliance, the flexible load at the 𝑘-th time sample can be
written as
𝐿flex(𝑘) = ∑ 𝑃𝑖(𝑘)𝑦𝑖(𝑘)
𝑖
with the total load being expressed as
𝐿(𝑘) = 𝐿flex(𝑘) + 𝐿fix(𝑘)
However, the product being summed in the equation that defines the flexible load would
represents a nonlinear operation between two variables and as such cannot be incorporated
within a mixed-integer model in its previously defined format. To mitigate this issue, 𝑃𝑖 is divided
into three sperate values: nominal power draw 𝑃𝑖nom, positive power deviation 𝑑𝑖
+ and negative
power deviation 𝑑𝑖− from the nominal value, or in other words
𝐿flex(𝑘) = 𝑃𝑖nom𝑦𝑖(𝑘) + 𝑑𝑖
+(𝑘)𝑦𝑖(𝑘) + 𝑑𝑖−(𝑘)𝑦𝑖(𝑘).
However, this equation still cannot be incorporated into the MILP model because it also
incorporates a product between two variables. nevertheless, if 𝑑𝑖+ and 𝑑𝑖
− are constrained to
having nonzero values only when the appliance is turned on, this last expression can be
shortened to
𝐿flex(𝑘) = 𝑃𝑖nom𝑦𝑖(𝑘) + 𝑑𝑖
+(𝑘) + 𝑑𝑖−(𝑘).
Now, total load can be expressed as
(∀𝑘) (𝐿(𝑘) = ∑(𝑃𝑖nom𝑦𝑖(𝑘))
𝑖
+ ∑(𝑑𝑖+(𝑘) + 𝑑𝑖
−(𝑘)) + 𝐿fix(𝑘)
𝑖
).
Having in mind that 𝑃𝑖nom is set before the model is optimized, it can be deduced that this
expression now represents a linear combination of subvectors of 𝑥 and can therefore be
implemented as a MILP constraint.
Related literature [1] provides a classification in which elastic loads are either classified as being
energy-based, meaning that they must consume a predefined amount of energy within a specified
time window, or comfort-based, researched previously in [2], meaning that they must control an
environmental variable within a desired range. However, comfort-based appliances are not
treated by the RESPOND services as the appliances’ operations that are supposed to be
optimized only allow on/off controls. Therefore, only energy-based elastic appliances are
considered for the aspect of demand side management with an option to elastically adjust their
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power within given power tolerances. Accordingly, a set of windows (activation cycles) is defined
for each appliance 𝑖 with one of them
𝑤𝑖(𝑛)
(𝑘) ≜ { 0, 𝑘 is not in the window 𝑛, 𝑘 is in the window
defining the 𝑛-th window of 𝑖-th appliance by having nonzero values equal to 𝑛 at time instances
that belong to that window. This type of implementation provides the possibility for windows to be
discontinuous i.e. they can be split into a given number of segments. Having in mind that these
windows are also defined prior to problem optimization just like the nominal power, they can be
used to form an energy constraint
(∀𝑖, ∀𝑛) ( ∑ 𝑃𝑖nom
𝑤𝑖(𝑛)
(𝑘)=𝑛
𝑇𝑠 ⋅ 𝑦𝑖(𝑘) = 𝑃𝑖nom𝛥𝑡𝑖
(𝑛))
that states how a specific appliance 𝑖 must only be active a given amount of time so that the
amount of energy it spends during that activation cycle 𝑛 is equal to the product between nominal
power 𝑃𝑖nom and the length 𝛥𝑡𝑖
(𝑛) of nominal activation belonging to that window. Nevertheless,
FIGURE 4 - EXAMPLE OF LOAD SHIFTING IN TIME FROM NOMINAL LOAD SCHEDULE (TOP) WITH
SHIFTING WINDOWS TO THE OPTIMIZED LOAD SCHEDULE (BOTTOM)
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deviations in power also affect the total energy consumed, and so it is also stated that the sum of
power deviations must be equal to zero during a given window, as given by
(∀𝑖, 𝑘, 𝑛) ( ∑ (𝑑𝑖+(𝑘) + 𝑑𝑖
−(𝑘))
𝑤𝑖(𝑛)
(𝑘)=𝑛
= 0)
thus, finalizing the set of equality constraints required for the model. Nonetheless, these relations
are not sufficient for the model and some additional conditions must be applied in form of bounds.
2.3.2 VARIANT 2 – AGGREGATED LOADS
When the load is considered as an aggregated value it is not separated into individual appliances
but rather viewed through its nominal value and the appropriate positive and negative deviations.
In this context, the deviation is defined as the difference between the realized load value 𝐿 and a
predefined load profile 𝐿required, as would be defined by
Δ𝐿 = 𝐿required − 𝐿.
The general idea here is that at certain instances of time, some segments of the criterion function
would force the load profile 𝐿 to resemble the required one 𝐿required. This can be performed by
penalizing the load deviation in these time instances. However, when the load deviation is
positive, such a penalty should be positive and if the when the load deviation is negative, such a
penalty should be negative. However, it is impossible to know in advance when the difference
between the optimized load profile and the required one will be positive and when it will be
negative. This poses an issue because the criterion function is defined before the model is
optimized, and so these instances of time have to be known beforehand. However, this issue can
be mitigated by splitting the load deviation into positive and negative (in a similar manner as the
individual appliance power draw values are modelled using positive and negative deviations in
variant one). The last equation is now rewritten as
Δ𝐿(𝑘) = Δ𝐿+(𝑘) + Δ𝐿−(𝑘) = 𝐿required(𝑘) − 𝐿(𝑘).
However, no constraints are implemented to force positive load deviations to actually be positive
and negative load deviations to actually be negative. Therefore, two binary variables are
introduced to illustrate when the positive load deviation is active and when the negative load
deviation is active. Since the load must be bounded on each side by an upper and lower bound,
these indicators are connected with the aforementioned bounds with the expressions
Δ𝐿+(𝑘) ≤ +𝐼(Δ𝐿+(𝑘)) ⋅ Δ𝐿max+ (𝑘)
Δ𝐿−(𝑘) ≤ −𝐼(Δ𝐿−(𝑘)) ⋅ Δ𝐿max− (𝑘).
Concretely, Δ𝐿max+ and Δ𝐿max
− define the largest possible (by absolute value) positive and negative
deviations between the total (aggregated) load and the required profile. However, implementing
these two relations by themselves allows for both positive and negative load deviations to exist
simultaneously. However, the binary nature of them can be exploited to restrict only one of them
to be allowed to assume a nonzero value at a given timestep. This is obtained by
𝐼(Δ𝐿+(𝑘)) + 𝐼(Δ𝐿−(𝑘)) ≤ 1.
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Finally, if the mode described above where to be optimized using a price-based objective function,
the optimizer would drop all load levels to their lowest possible values. Therefore, an additional
integral window constraint must be enforced to maintain the integral level of load to a value related
to the predicted energy consumption. Such a constraint is defined as
∑ 𝐿(𝑘)
𝑘2
𝑘=𝑘1
= ∑ 𝐿predicted(𝑘)
𝑘2
𝑘=𝑘1
where 𝑘1 and 𝑘2 represent the beginning timestep and ending timestep of the window for which
the constraint is to be applied. This constraint can be applied for the full-time horizon but can also
be applied, if required, multiple times for day/night consumption use cases and/or peak hour
consumption use cases.
Figure 5 illustrates a case where an Energy Hub with three types of loads is employed to enforce
a requested load profile during a DR event. Here, the load deviations between the load variable
and the requested profile (which equals 80% of the predicted load during the DR event) are
separately penalized and so the optimized load follows the requested profile during the DR event
and remains otherwise unconstrained in this regard.
FIGURE 5 - ILLUSTRATION OF A DR EVENT LOAD DEVIATION
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2.4 BOUNDARY CONDITIONS
To fully define the model, the equality and inequality constraints are supplemented with a set of boundary constraints that define upper and lower limits for the aforementioned variables. Since the imported power values cannot be negative, a limit is imposed in form of
(∀𝑘)(0 ≤ 𝑃cin(𝑘), 𝑃cout(𝑘), 𝑃out(𝑘), 𝑃exp(𝑘) ≤ ∞).
On the other hand, the portion of imported power 𝑃in that comes from renewable sources 𝑃renew
has to be exactly equal the amount of energy that is being generated, while the power imported
from the grid can be viewed as virtually unlimited (lower than the highest power that can be
delivered)
𝑃renew(𝑘)0
} ≤ 𝑃in(𝑘) ≤ {𝑃renew(𝑘), from renewables
∞, from the grid.
At both the input and output stages, storage levels must be between the lowest possible (zero)
and highest possible (battery capacity) SOC and so
(∀𝑘)(0 = 𝑆𝑂𝐶inmin ≤ 𝐸in(𝑘) ≤ 𝑆𝑂𝐶in
min),
and
(∀𝑘)(0 = 𝑆𝑂𝐶outmin ≤ 𝐸out(𝑘) ≤ 𝑆𝑂𝐶out
max),
with 𝑄in and 𝑄out being limited by
(∀𝑘)(−𝑄inmax ≤ 𝑄in(𝑘) ≤ 𝑄in
max )
and
(∀𝑘)(−𝑄outmax ≤ 𝑄out(𝑘) ≤ 𝑄out
max)
where 𝑄max is the highest achievable charge rate, and thus also bounding 𝑞in and 𝑞out.
2.4.1 VARIANT 1
In the case of managing load through individual appliance, the total load 𝐿 only has a defined
lower bound equal to the value of fixed load since the flexible load is non-negative and thus
(∀𝑘)(𝐿fix(𝑘) ≤ 𝐿(𝑘)).
As mentioned before, both positive and negative deviations 𝑑𝑖+(𝑘) and 𝑑𝑖
−(𝑘) also have bounds
that are equal to a predefined upper and lower deviation limit, respectively, applied during
specified windows as follows
(∀𝑘, 𝑖, 𝑛) (0 ≤ 𝑑𝑖+(𝑘) ≤ {
0, 𝑤𝑖(𝑛)
(𝑘) ≠ 𝑛
𝑃dev+𝑖
max , 𝑤𝑖(𝑛)
(𝑘) = 𝑛)
(∀𝑘, 𝑖, 𝑛) (0, 𝑤𝑖
(𝑛)(𝑘) ≠ 𝑛
𝑃dev−𝑖
max , 𝑤𝑖(𝑛)
(𝑘) = 𝑛} ≤ 𝑑𝑖
−(𝑘) ≤ 0).
As for the indicator variables, the device starts 𝑧𝑖 has a lower bound of zero and upper bound of
one for all time samples i.e.
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(∀𝑘, 𝑖)(0 ≤ 𝑧𝑖(𝑘) ≤ 1)
while the on/off state 𝑦𝑖 has the same bound within windows and both bounds set to zero outside
(∀𝑖, 𝑘, 𝑛) (0 ≤ 𝑦𝑖(𝑘) ≤ {0, 𝑤𝑖
(𝑛)(𝑘) ≠ 𝑛
1, 𝑤𝑖(𝑛)
(𝑘) = 𝑛).
A similar logic is employed as to limit the deviation indicators
(∀𝑖, 𝑘, 𝑛) (0 ≤ 𝐼(𝑑𝑖+(𝑘)), 𝐼(𝑑𝑖
−(𝑘)) ≤ {0, 𝑤𝑖
(𝑛)(𝑘) ≠ 𝑛
1, 𝑤𝑖(𝑛)
(𝑘) = 𝑛).
Finally, since the indicator variables should only assume a value of either zero or one, thus
rendering this problem to be classified as MILP rather than LP, we specify
(∀𝑘)(𝑦𝑖(𝑘), 𝑧𝑖(𝑘), 𝐼(𝑑𝑖+(𝑘)), 𝐼(𝑑𝑖
+(𝑘)) ∈ {0,1}).
2.4.2 VARIANT 2
As for the case in which the load is managed through its aggregated profile, a load tolerance limits
are imposed in form of two margins (upper and lower margin) between which the loads can be
adjusted. This is obtained by enforcing a limiting constraint as
(∀𝑘) ((1 + tol−)𝐿predicted(𝑘) ≤ 𝐿(𝑘) ≤ (1 + tol+)𝐿predicted(𝑘)).
In this regard, the load tolerance is mentioned in literature [3] to be in the range of −tol− = tol+ =
20%, however as research related to this topic is relatively scarce, other load tolerance values
will be tested within the RESPOND platform as well. Having in mind that the load difference
between the optimized profile and the required one is modeled using positive and negative load
deviations, these variables must also be limited using
(∀𝑘)(Δ𝐿+(𝑘) ≥ 0) and (∀𝑘)(Δ𝐿−(𝑘) ≤ 0).
Finally, the indicator variables that depict the activity of the aforementioned load deviations must
be equal to either one or zero thus rendering this problem also to be classified as MILP rather
than LP, as set by
(∀𝑘)(𝐼(Δ𝐿+(𝑘)), 𝐼(Δ𝐿−(𝑘)) ∈ {0,1}).
After adequate transformations, the given expressions can be morphed into the 𝐴eq, and 𝐴ineq
matrices and 𝑏eq, 𝑏ineq, 𝑙b and 𝑢b vectors defining the constraints from the MILP problem
definition. What remains to be set in order to complete the model used for optimization is the
objective function 𝑓.
2.5 OBJECTIVE FUNCTION
The main objective that is being considered within the RESPOND optimization process is the minimization of costs that would ultimately fall on the end users. Therefore, the most beneficial factor to the cost function are the costs of individual energy types. These values are modelled by setting the objective function 𝑓’s
values to the corresponding energy import/export prices. Since the energy import (𝑃in) usually costs money if it is being imported from the grid, the corresponding values of those elements of 𝑓 are set to positive
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values that depict electricity prices at the given time. Also, if the local legislative allows for renewable energy generation subsidies, the elements of 𝑓 that correspond to energy imports from renewable sources are set to negative values that are given by the acting generation tariff. Furthermore, the user can also receive monetary gains by exporting excess energy back to the grid (𝑃exp) and so the corresponding values
should also be set to negative values dictated by the acting feed-in tariff program. If 𝑖 and 𝑗 represent import and export power energy carriers, 𝛼 represents the costs of importing energy and 𝛽 represents the costs of exporting energy, the overall operational cost can be obtained as
𝐶 = ∑ ∑ 𝛼𝑖(𝑘)𝑃in(𝑖, 𝑘) +𝑘
∑ ∑ 𝛽𝑗(𝑘)𝑃exp(𝑖, 𝑘)𝑘𝑗
.𝑖
However, to enable simultaneous optimizations that include specific DR events in order to force the load to uphold the requested profile, the mentioned cost function is extended with the addition of load deviation penalization as is given by
𝐶′ = ∑ ∑ 𝛼𝑖(𝑘)𝑃in(𝑖, 𝑘) +𝑘
∑ ∑ 𝛽𝑗(𝑘)𝑃exp(𝑖, 𝑘)𝑘𝑗
+ ∑ (𝑤d+(𝑘)Δ𝐿+ + 𝑤d
−Δ𝐿−)𝑘
.𝑖
In this mixed criterion, the penalization factors 𝑤d+ and 𝑤d
− are supposed to have non-zero values only
when a specific DR event is active, with 𝑤d+ being strictly positive and 𝑤d
− being strictly negative in those
cases in order to force the deviations into their minimum optimal value. When defining these values, a balance should be made between the raw operational costs as given by 𝐶 and the additional factor
introduced in 𝐶′, i.e. the load penalization should not be significantly greater or smaller than the operational costs.
Besides the cost or running the system, other criteria are to be monitored as well. One of them is a renewable energy source (RES) share in the imported power and it can be calculated from
𝑅𝐸𝑆share =∑ 𝑃in(renewables, 𝑘)𝑘
∑ 𝑃in(all carriers, 𝑘)𝑘⋅ 100%.
Another interesting indicator of the ecological impacts of running the system are the effective CO2
emissions of running the system. This value can be estimated using the corresponding grid power fuel mix
and life cycle emissions provided by [4] through the expression
CO2 emiss = ∑ ∑ 𝑐𝑖𝑃𝑖𝑛(𝑖, 𝑘)
𝑖𝑘
where 𝑐𝑖 represents the carbon footprint value of the 𝑖-th energy carrier. These values can even be
included within the cost criterion in order to create a multi-criteria optimization function that would include
multiple factors.
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3. INDIVIDUAL USER PILOT MODELS
The RESPOND project is to be deployed in three pilot sites: Aarhus (Denmark), Madrid (Spain)
and Aran Islands (Ireland). In the context of this deliverable, the process of modelling individual
users using the Energy Hub structure is described in detail. Figure 6 provides an illustration of
how a multi-carrier single-user energy system (household) is effectively replaced by the Energy
Hub structure that manages energy imports, conversions, exports and loads.
3.1 AARHUS
The Aarhus pilot site in Denmark is located in a public housing district that consists of around 30
residential buildings. RESPOND focuses on four of those buildings, with around 20 preselected
apartments that will be used as demonstrators of the RESPOND platform. There are three primary
energy carriers (from the aspect of the end consumers): electric energy that can be imported from
the grid, electric energy that is being generated by the shared photovoltaic (PV) panel array and
thermal energy contained within hot water that is being obtained from the district heating system.
The electricity imported from the grid passes through a transformer as is usually the case in
FIGURE 6 - AN EXAMPLE OF MODELING A SINGLE USER WITH A SINGLE ENERGY HUB
FIGURE 7 - AARHUS PILOT SITE TOPOLOGY
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electricity distribution systems, while an inverter is used to adapt PV production to the AC
electricity that can be used by end users. Furthermore, the hot water from the district heating
system is directly dispatched to the heating system while, on the other hand, a heat exchanger is
employed to heat the secondary water loop and provide the domestic hot water supply. It is worth
mentioning that the excess of electricity generated by PV panels can be exported to the grid. The
model that correspond to this description, as depicted in Figure 7, is defined by
𝑆qin = [0 0 00 0 00 0 0
] , 𝑆in = [1 0 00 1 00 0 1
] , 𝐹in = [1 0 0 000
1 0 00 1 1
] , 𝐶 = [
0.98000
00.95
00
00
1.000
000
0.98
],
and
𝐷exp = [
1 0 0 00 0 0 000
00
1 00 1
] , 𝑅exp = [
0000
] , 𝐹out = [1 1 0 000
0 1 00 0 1
] , 𝑆qout = [0 0 00 0 00 0 0
] , 𝑆out = [1 0 00 1 00 0 1
]
with all storage capacities set to zero as no storage facilities are present within this pilot. The
aforementioned matrices are populated with multiple efficiency factors 𝜂transformer = 0.98,
𝜂inverter = 0.95 and 𝜂heatexch = 0.98, whose value ranges can be found in related literature [5],
[6], [7] and [8].
When modelling individual users, a rough estimate of how much electric energy coming from the
PV array can be distributed to each household can be obtained by dividing the total power
generation capacity of 622 kWp by the total number of households that, according to D1.1, equals
592 total apartments. Therefore, it can be assumed that each household has
622 kWp592
⁄ = 1.05 kWp
at its disposal. Since this value is used in this deliverable for the sole purpose of theoretical
demonstration, more precise figures regarding the aggregated PV availability for the considered
neighbourhood by the RESPOND project will be discussed in D4.3. D1.1 also states that the total
yearly electricity consumption of the entire public housing estate equals 1800 MWh while the total
heating demand is 6700 MWh. This allows for a rough estimate of
1800 MWh592⁄ = 3.04 MWh
total yearly electricity consumption per household and
6700 MWh592⁄ = 11.32 MWh
total yearly heating demand. When these values are distributed averagely for each day of the
year, the values of 8.3 kWh of daily electricity demand and 31.0 kWh of daily thermal demand are
obtained and can be used to generate an average demand profile. The daily DHW demand is
assumed to be equal to 23% of daily thermal demand in accordance with the analysis from [9]
with the leftover 77% corresponding to space heating demand.
As for the pricing scheme, the tariff is fixed at around 2.0 DKK/kWh = 0.27 EUR/kWh for electric
energy and 0.5 DKK/kWh = 0.067 EUR/kWh for thermal energy obtained from the district heating
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system. Excess electricity produced by the PV array can be exported back to the grid for
0.6 DKK/kWh = 0.08 EUR/kWh
3.2 MADRID
Over on the Madrid pilot in Spain, the RESPOND project tackles shared areas and 24 preselected
dwellings among the total 69 individual households in three identical residential buildings. On the
roof of one of the buildings considered, a solar thermal collector (STC) system has been installed
with the capabilities of converting solar energy (irradiation) into thermal energy. In this way, the
water is heated and will be later used to fulfil the domestic hot water load. In addition, the tenants
have the ability of importing gas through the residential pipeline, which is then burnt in one of the
two gas boilers. The resulting hot water is either used to fulfil the heating demand or the DHW
demand (as a supplemental energy carrier to the energy obtained from the STC system). The
DHW loop is also equipped with two hot water tanks: the first one with the total capacity of
630 kWh that can be filled only by the hot water that is being heated within the STC, and another
with the total capacity of 420 kWh that can be filled by both the hot water from the STC and the
hot water that is being heated by the secondary gas boiler. This pilot does not have the ability of
exporting any types of energy back to the grid. The schema of the appropriate Energy Hub that
models one of the households is presented in Figure 8 with the model being instantiated using
the following structural matrices
𝑆qin = [0 0 00 0 00 0 1
] , 𝑆in = [1 0 00 1 00 0 0.98
] , 𝐹in = [100
00.97
0
00.97
0
001
] , 𝐶 = [
0.98000
00.98
00
00
0.980
000
0.98
],
and
𝐷exp = [
1 0 0 00 1 0 000
00
1 00 1
] , 𝑅exp = [
0000
] , 𝐹out = [1 0 0 000
1 0 00 1 1
] , 𝑆qout = [0 0 00 0 00 0 1
] , 𝑆out = [1 0 00 1 00 0 0.98
]
FIGURE 8 - MADRID PILOT SITE TOPOLOGY
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with relevant DHW reservoir storage limits set to the appropriate capacities mentioned earlier.
The aforementioned matrices are populated with multiple efficiency factors 𝜂transformer = 0.98,
𝜂inverter = 0.95, 𝜂boiler = 97%, 𝜂heatexch = 0.98, whose value ranges can be found in related
literature [5], [6], [7], [8] and [10].
Pilot characterization from D1.1 suggests that all 69 dwellings consume 215 MWh of yearly
electricity for personal use and 1198 MWh yearly energy through gas consumption (disregarding
the 12 MWh for cooking purposes). Therefore, the yearly consumption per household would
equate to
215 MWh69⁄ = 3.16 MWh
of electric energy and
1198 MWh69⁄ = 17.36 MWh
of thermal energy. When downscaled to daily consumption per household, on an average day, a
single household would consume 8.54 kWh of electric energy and 47.57 kWh of thermal energy.
As the total value of thermal energy was measured before the STC system had been installed,
the daily DHW demand in this case is again assumed to be equal to 23% of daily thermal demand
in accordance with the analysis from [9] with the leftover 77% corresponding to space heating
demand.
As for the pricing scheme, grid electricity can be imported under a fixed tariff of 0.165 EUR/kWh
whilst gas can be imported at a fixed cost of 0.54 cEUR/kWh.
3.3 ARAN ISLANDS
The Aran Islands pilot in Ireland site consists of multiple distributed houses in the region of three
islands called Inis Mór, Inis Meáin and Inis Oírr with a total of 448 individual dwellings. However,
unlike the two other pilot sites, different households within the Aran Islands pilot have different
topologies. The houses that participate in the project at the moment of writing this deliverable can
be grouped into three types:
• Type 1: Electric energy is obtained either by importing from the grid or by utilizing the
distributed PV generation (with installed capacity of 4 kWp) and PV energy can be locally
stored in a battery with of 20 kWh capacity (house internally referred to as H2 is of this
type);
• Type 2: Electric energy is obtained either by importing from the grid or by utilizing the
distributed PV generation (with installed capacity of 2 kWp) (house internally referred to as
H1 is of this type)
• Type 3: Electric energy is only obtained by importing from the grid.
The corresponding Energy Hub structures of these three household types are presented in Figure
9. These hubs can be instantiated using
𝑆qin = [0 00 1
] , 𝑆in = [1 00 1
] , 𝐹in = [1 00 1
] , 𝐶 = [0.98 0
0 0.95],
and
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𝐷exp = [1 00 0
] , 𝑅exp = [00
] , 𝐹out = [1 1], 𝑆qout = [0 00 0
] , 𝑆out = [1 00 1
]
and the storage limit set to the aforementioned value for type 1,
𝑆qin = [0 00 0
] , 𝑆in = [1 00 1
] , 𝐹in = [1 00 1
] , 𝐶 = [0.98 0
0 0.95],
and
𝐷exp = [1 00 0
] , 𝑅exp = [00
] , 𝐹out = [1 1], 𝑆qout = [0 00 0
] , 𝑆out = [1 00 1
]
for type 2 and finally
𝑆qin = [0], 𝑆in = [1], 𝐹in = [1], 𝐶 = [0.98],
and
𝐷exp = [1], 𝑅exp = [0], 𝐹out = [1], 𝑆qout = [0], 𝑆out = [1]
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for type 3. The aforementioned matrices are populated with multiple efficiency factors
𝜂transformer = 0.98, 𝜂inverter = 0.95, whose value ranges can be found in related literature [5], [6]
and [7].
The total electricity consumption of all dwellings for a year, as given by D1.1, equates to
approximately 3.94 MWh. When scaled by the total number of households, each of them would
consume
3.94 MWh448⁄ = 8.79 kWh
with most of the consumption being attributed to space heating for which large amounts of fossil
fuels are imported to the islands and burnt.
Two types of electricity tariffs are at play: a fixed one with a price of 0.18 EUR/kWh and a time-of-
use day/night tariff with a high value of 0.203 EUR/kWh and a low value of 0.10 EUR/kWh.
FIGURE 9 - ARAN PILOT SITE TOPOLOGY (TYPE 1 TOP, TYPE 2 MIDDLE AND TYPE 3 BOTTOM)
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4. OPTIMIZATION USE CASES
To demonstrate the methodology for a single-user (household/dwelling-level) hypothetical use
case, a topology is assumed in accordance with the model for the Aarhus pilot in Denmark that
was developed and previously described in Section 3.1. A single day is selected for the
optimization showcase, and a carrier availability and load profiles are synthetized whilst having in
mind the expected daily electric and thermal energy as well as the domestic hot water demand
requirement per household. All load types are modelled as functions that have two peak values:
one in morning hours and the other in the evening. These modelled demand levels are created
using Gaussian curves that have a mean value that correspond to the given peak time, and a
standard deviation that correspond to the dispersion intensity of that peak. The predicted electric
load is therefore defined as
𝐿elec(𝑘) = 8.3 (0.75 + 0.5𝑒
−(𝑘−7)2
2⋅12⁄+ 1.0𝑒
−(𝑘−18)2
2⋅32⁄
∑ (0.75 + 0.5𝑒−
(𝑖−7)2
2⋅12⁄+ 1.0𝑒
−(𝑖−18)2
2⋅32⁄)23
𝑖=0
) kW
while the predicted thermal load is defined as
𝐿thermal(𝑘) = 23.87 (0.50 + 0.5𝑒
−(𝑘−6)2
2⋅32⁄+ 0.5𝑒
−(𝑘−21)2
2⋅32⁄
∑ (0.50 + 0.5𝑒−
(𝑖−6)2
2⋅32⁄+ 0.5𝑒
−(𝑖−21)2
2⋅32⁄)23
𝑖=0
) kW
and the predicted DHW load as
𝐿DHW(𝑘) = 7.13 (0.25 + 0.5𝑒
−(𝑘−8)2
2⋅22⁄+ 0.5𝑒
−(𝑘−19)2
2⋅22⁄
∑ (0.25 + 0.5𝑒−
(𝑖−8)2
2⋅22⁄+ 0.5𝑒
−(𝑖−19)2
2⋅22⁄)23
𝑖=0
) kW.
The forecasted PV production is also synthetized using Gaussian curves as
𝑃in𝑃𝑉= 1.05 (
𝑒−
(𝑘−12)2
2⋅22⁄
∑ 𝑒−
(𝑖−12)2
2⋅22⁄23𝑖=0
) kW.
4.1 IMPLICIT DR EVENT
Namely, there are two main types of DR event enforcement methodologies: explicit and implicit.
Explicit DR events, on the one hand, are specified by directly arranging times and amounts of
energy that can be either increased or decreased over specific appliance activations over the
regular usage profile. On the other hand, implicit DR events can be induced by manipulating
carrier import and/or export prices to create time spans in which a certain carrier or carriers are
significantly more (or less) expensive than at other times, thus forcing the load to be reduced (or
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increased) at those times. As a showcase, an implicit DR event is created by means of price
profile manipulations in this theoretical demonstration.
Concretely, electric energy imports are set to be 25% higher from 17:00 to 21:00 (including both
timesteps) than at other times and thermal energy is set to be 30% higher from 00:00 to 06:00
(including both timesteps) and from 15:00 to 23:00 (including both timesteps). However, the price
profiles are normalized in such a way that, for this demonstration, the average price per each
carrier remains the same as it was in the nominal (real) scenario and no load deviation
penalization was introduced. The obtained price profiles are depicted in Figure 10, where the real
prices are denoted with a dashed line and the manipulated prices are denoted with a full line.
Note: the dashed orange line lays underneath the full line.
The Energy Hub model of the considered pilot was optimized twice: once without a load shifting
margin (i.e. the optimized load had to be equal to the predicted value) and once with a predefined
non-zero load shifting margin (20% was selected for this demonstration). This was done in order
to obtain a realistic baseline profile of what the load levels and imported power levels would look
like without any price manipulations and to therefore be able to validate that the mentioned price
FIGURE 10 - PRICE PROFILES USED FOR DEFINING AN IMPLICIT DR EVENT
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manipulations do have an effect of raising or lowering the load levels. The load profiles for the
predicted values (denoted in coloured dashed lines) optimized without any margin and those
optimized with a load margin (denoted in coloured full line), are presented in Figure 11. Here, one
can observe that the price manipulations did in fact have an effect on the final load profile in such
a way that the peak pricing drove all three load levels down at times where the system deems
that it is not cost-effective to consume energy because of high prices. At other times of day,
because of the integral energy constraints, the lowered load levels are shifted. This is most
noticeable during the mid-day period where the PV array is producing at its maximum capacity
and the district heating system’s hot water is the cheapest. It can also be noticed that the optimizer
did not completely reduce the thermal load in the evening peak period because the integral energy
constraint could not be met otherwise since the positive margin is used to its full extent during the
mid-day period.
FIGURE 11 – PREDICTED AND OPTIMIZED LOAD PROFILES
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Even though load manipulations were the primary objective of introducing DR, when viewed from
the grid standpoint, another important aspect of the DR programme is the manipulation of
individual carrier imports as that is what ultimately affects the stability of the system. The obtained
effects can be observed in the imported power profile in Figure 12, where it is abundantly clear
that the price increases in peak periods resulted in the reduction of the respective carrier
demands. This clearly indicates that the system, in its form defined in previous sections, has the
capabilities of performing both load and carrier import intensity manipulations. Note: the dashed
orange line once again lays underneath the full line.
Finally, it should be noted that the potential savings in both price and total energy imported,
although relatively minor in this discussed example, may be even greater depending on the
forecasted profiles, differences in price and load flexibility margins. These effects will be
discussed in more detail in D4.3
FIGURE 12 – NOMINAL AND OPTIMIZED INDIVIDUAL CARRIER IMPORT PROFILES
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33 | 34
5. CONCLUSION
This deliverable describes the development of a methodology that employs the Energy Hub
modelling concept specifically modified for load management applications. Two methodologies
were presented for load management applications: one in which individual appliance activations
are managed through the utilization of shifting windows and power tolerances, and another one
in which the loads are managed jointly as an aggregate value (a sum of either individual appliance
activations or multiple household’s aggregate load). Since RESPOND focuses on the
neighbourhood perspective, it makes use of the latter one.
The underlying model represents a mixed-integer linear programming problem that is solved
using IBM ILOG Optimization Studio’s CPLEX Python library. The output of the optimization
process are time series of model’s variables, being the most important ones the imported power
levels and the load levels. For each pilot site, appropriate Energy Hub models are defined for
individual households to credibly depict the ways in which different energy types are converted,
mixed and used to fulfil the required load.
Finally, in order to demonstrate the proposed methodology, the Hub for the Aarhus pilot is
instantiated with synthetized predicted load profiles and a slightly modified price profile to facilitate
an implicit DR event i.e. motivate load reduction by increasing prices in a peak period during the
afternoon for electric loads and night for thermal loads. Because of the differences in price, the
optimizer managed to lower the loads in the requested periods, but maintained the integral
demand for the entire simulated day.
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6. REFERENCES
Illustrations from freepik.com
[1] A. Barbato and A. Capone, “Optimization Models and Methods for Demand-Side Management of Residential Users: A Survey,” Energies, vol. 7, no. 9, pp. 5787–5824, Sep. 2014.
[2] M. Batić, N. Tomašević, G. Beccuti, T. Demiray, and S. Vraneš, “Combined energy hub optimisation and demand side management for buildings,” Energy and Buildings, vol. 127, pp. 229–241, Sep. 2016.
[3] “Achieving energy efficiency through behaviour change: what does it take?,” European Environment Agency. [Online]. Available: https://www.eea.europa.eu/publications/achieving-energy-efficiency-through-behaviour. [Accessed: 12-Aug-2019].
[4] Intergovernmental Panel on Climate Change, “Technology-specific Cost and Performance Parameters,” in Climate Change 2014: Mitigation of Climate Change: Working Group III Contribution to the IPCC Fifth Assessment Report, Cambridge University Press, 2015, pp. 1329–1356.
[5] T. Kubo, H. Sachs, and S. Nadel, “Opportunities For New Appliance and Equipment Efficiency Standards: Energy and Economic Savings Beyond Current Standards Programs,” p. 116.
[6] H. De Keulenaer, “The scope for energy saving in the EU through the use of energy-efficient electricity distribution transformers,” in 16th International Conference and Exhibition on Electricity Distribution (CIRED 2001), Amsterdam, Netherlands, 2001, vol. 2001, pp. v4-27-v4-27.
[7] “Inverter Efficiency - an overview | ScienceDirect Topics.” [Online]. Available: https://www.sciencedirect.com/topics/engineering/inverter-efficiency. [Accessed: 13-Aug-2019].
[8] “Elge Shell & Coil Heat Exchanger| WasteEnergy Recovery| AR MAC| GS Dunham.” [Online]. Available: http://www.gsdunham.com/heat.html. [Accessed: 13-Aug-2019].
[9] “Energy consumption in households - Statistics Explained.” [Online]. Available: https://ec.europa.eu/eurostat/statistics-explained/index.php/Energy_consumption_in_households. [Accessed: 13-Aug-2019].
[10] “Factsheet: Boiler Efficiency.” Departmant of the Environment and Energy, Australian Government.
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