optimal energy management of buildings and districts

| |

Georgios Darivianakis joint work with A. Georghiou, A. Eichler, R. S. Smith and J. Lygeros

Optimal Energy Management of Buildings and Districts

Tuesday, 1st March, 2016

Automatic Control Laboratory (IfA)

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Background

Energy Strategy 2050

Wind, 0.10% Solar, 0.80%

Fossil, 5.70%

Nuclear, 39.10% Hydro, 54.20%

Electricity mix 2014!

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Background

Energy Strategy 2050

Wind, 7.40%

Solar, 19.30%

Fossil, 6.00%

Nuclear, 0.00%

Hydro, 67.40%

Electricity mix 2050!

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Motivation

Opportunities •  Sharing energy efficient equipment

(e.g. heat pumps, batteries) •  Shifting of energy between residen-

tial and commercial buildings

Challenges •  Regulation of energy exchange

between hub devices and buildings •  Operation under uncertain condi-

tions (e.g. weather, occupancy)

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Control scheme

Plant Controller -

+ reference input

measurements

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Weather forecast

Prediction model &

Operational Constraints

Electricity

Gas Boiler

Heat PumpChiller

Battery

Transf.

Photovoltaics

Electricity

Cooling

Heating

Energy Hub

Buildings

Energy Efficient Buildings & DistrictsComputation

Measurements

Comfort bounds, Electricity/Gas Prices

System Dynamics Modelling

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Control Scheme

Stochastic Optimization Problem

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Energy Hub Topology

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Outline

System Modelling

Stochastic Optimization

Problem

Simulation Results

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Energy Hub Topology

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Outline •  Input Streams •  Devices (conversion, storage,

production) •  Output Streams

Stochastic Optimization

Problem

Simulation Results

System Modelling

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Energy hub topology

Battery Photovoltaic

Chiller

Heat pump

Hot Water Tank

Boiler (electric)

Electrical grid

Electrical demand

Cooling demand

Heating demand

Buildings

Energy Hub

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Energy Hub Topology

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Outline

System Modelling

Stochastic Optimization

Problem

Simulation Results

•  EH devices dynamics •  Buildings dynamics •  Buildings – EH Coupling

Constraints •  Disturbance handling

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Energy hub devices dynamics

Battery Photovoltaic

Chiller

Heat pump

Hot Water Tank

Boiler (electric)

Electrical grid

Electrical demand

Cooling demand

Heating demand

Buildings

Energy Hub

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control variables

states

11

Energy hub devices dynamics

xt+1,i = Aixt,i +Bin

i uin

t,i +Bout

i u

out

t,i + Ci⇠t,

(xt,i,uin

t,i,uout

t,i , ⇠t) 2 Ht,i,

uin

t,i, uout

t,i :

xt,i :

⇠t :Ht,i :

disturbances operational constraints

where

We model the -th energy hub device with the following linear dynamical system, i

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uint,HWT

uoutt,HWT

(e.g. water’s temperature) (e.g. power flows)

(e.g. ambient temperature) (e.g. operation limits)

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Building dynamics

Battery Photovoltaic

Chiller

Heat pump

Hot Water Tank

Boiler (electric)

Electrical grid

Electrical demand

Cooling demand

Heating demand

Buildings

Energy Hub

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Building dynamics

Type: Floor area:

Location:

Swiss office building 600 m2

Allschwill, Basel

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[1] Sturzenegger, D., Gyalistras, D., Semeraro, V., Morari, M., Smith, R. S., ”BRCM Matlab Toolbox: Model Generation for Model Predictive Building Control”, American Control Conference, 2014.

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§  Bi-linear model

§  Comfort and input constraints

14

Building dynamics

xt+1,i = Aixt,i +Biut,i + Ci⇠t +X

j2Dbi

(Di,j⇠t + Ei,jxt,i)ut,i,j ,

where

21oC x

room

t,i

25oC

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Dbi

xt,i

ut,i

⇠t,i

: states (e.g. room and wall temperatures) : inputs in the set (e.g. radiators, AHU, TABS) : disturbances (e.g. solar radiation, ambient temperature)

ut,i 2 Uiand

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Buildings – Energy Hub Coupling

Battery Photovoltaic

Chiller

Heat pump

Hot Water Tank

Boiler (electric)

Electrical grid

Electrical demand

Cooling demand

Heating demand

Buildings

Energy Hub

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Buildings – Energy Hub Coupling

Heating demand dheatt

dheat

t =X

i2But,i,radiator +

X

i2But,i,TABS

Heating energy balancing:

Similarly for other sources: electricity, cooling, etc.

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Disturbance handling

Battery Photovoltaic

Chiller

Heat pump

Hot Water Tank

Boiler (electric)

Electrical grid

Electrical demand

Cooling demand

Heating demand

Buildings

Energy Hub

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Disturbance handling

ε1

ε2

The uncertainty set for the stochastic process is defined as, ⇠t

ft

ebt

dbt dbt

ebt

where

,

,

: forecast

: bounds on error : bounds on error correlation

⌅ =

8><

>:

⇠ 2 Rk s.t ⇠t = ft + ✏t, t = 1, . . . , T,

✏t 2 [ebt, ebt], t = 1, . . . , T,

✏t+1 � ✏t 2 [dbt, dbt], t = 1, . . . , T � 1,

9>=

>;.

✏1

✏2T : prediction horizon

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Energy Hub Topology

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Outline

System Modelling

Stochastic Optimization

Problem

Simulation Results

•  Problem formulation •  Solution methods

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minimize E X

t2Tctpt

!

such that Energy Hub Constraints,

i-th Building System, i 2 B ,

Coupling Constraints .

9>=

>;8 ⇠t 2 ⌅

20

Optimization problem

where ct

BT

: time-varying prices : (decision variable) Energy purchased from the grid : time horizon : set of buildings

pt

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Disturbances (e.g solar rad., temp.)

Cost of energy purchased from grid

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Solution method

Methodologies Issues

minimize E X

t2Tctpt

!

such that Energy Hub Constraints,

i-th Building System, i 2 B ,

Coupling Constraints .

9>=

>;8 ⇠t 2 ⌅

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Solution method

Methodologies •  Linearization around current

operating point and forecasts

Issues •  Nonlinear Building Dynamics

xt+1,i = Aixt,i +Biut,i + Ci⇠t +X

j2Dbi

(Di,j⇠t + Ei,jxt,i)ut,i,j ,

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Solution method

Methodologies •  Linearization around current

operating point

•  Constraint relaxation using slack variables

Issues •  Nonlinear Building Dynamics

•  Infeasibility for some initial conditions

21oC x

room

t,i

25oC

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Solution method

Methodologies •  Linearization around current

operating point

•  Constraint relaxation using slack variables

•  Robust Optimization methods

Issues •  Nonlinear Building Dynamics

•  Infeasibility for some initial conditions

•  Constraint satisfaction for every disturbance realization

minimize E X

t2Tctpt

!

such that Energy Hub Constraints,

i-th Building System, i 2 B ,

Coupling Constraints .

9>=

>;8 ⇠t 2 ⌅

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Control methodology

Method Information Structure

Decision variables Structure Disturbances

Affine Decision Rules

Open Loop Policies

Certainty Equivalent Problem

⇠

T time0

⌅

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Control methodology

Method Information Structure

Decision variables Structure Disturbances

Affine Decision Rules

Open Loop Policies

Certainty Equivalent Problem

t

⇠

T time0

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Control methodology

Method Information Structure

Decision variables Structure Disturbances

Affine Decision Rules

Open Loop Policies

Certainty Equivalent Problem

It = (1, ⇠1, . . . , ⇠t) ⇠t 2 ⌅pt = pt,0 +tX

s=0

pt,s ⇠s

⇠

T time0

pt = 3pt = 2

t

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Control methodology

Method Information Structure

Decision variables Structure Disturbances

Affine Decision Rules

Open Loop Policies

Certainty Equivalent Problem

It = (1, ⇠1, . . . , ⇠t)

It = (1)

⇠t 2 ⌅

⇠t 2 ⌅

pt = pt,0 +tX

s=0

pt,s ⇠s

pt = pt,0

⇠

T time0

pt = 4

t

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pt = 1

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Control methodology

Method Information Structure

Decision variables Structure Disturbances

Affine Decision Rules

Open Loop Policies

Certainty Equivalent Problem

It = (1, ⇠1, . . . , ⇠t)

It = (1)

It = (1)

⇠t 2 ⌅

⇠t 2 ⌅

⇠t = E{⇠t}

pt = pt,0 +tX

s=0

pt,s ⇠s

pt = pt,0

pt = pt,0

⇠

T time0 t

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Receding horizon

Planning horizon Act time forecast

Planning horizon Act time forecast

Planning horizon Act time forecast

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Energy Hub Topology

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Outline

System Modelling

Stochastic Optimization

Problem

Simulation Results

•  Comparison of optimal control formulations

•  System performance over a simulated day

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Problem set up

Battery Photovoltaic

Chiller

Heat pump

Boiler (electric)

Electrical grid

Electricity

Cooling

Heating

Energy Hub

Buildings

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Problem set up

Buildings

Building specificationsNo. Area(m2) WFA BT CT Input Devices

1 420 30% SP heavy AHU, blinds, radiator2 228 50% SP light AHU, blinds, TABS3 276 80% SA light AHU, blinds, TABS4 516 50% SA heavy AHU, blinds, radiator5 324 50% SP heavy AHU, blinds, radiator

WFA: Window Fraction Area

BT: Building Type

CT: Construction Type

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Control of building temperatures

0 5 10 15 20 25 30 35 40 4518

20

22

24

26

0 5 10 15 20 25 30 35 40 450

10

20

30

40

50

34 Georgios Darivianakis

hours!

hours!

Room Temperatures!

Energy Purchased!

Tem

pera

ture

s (o C

)!

Affine Decision Rules!Open Loop Policies!Certain. Equival. Prob.!

•  Winter period, with the ambient temperature ranging around 5 oC.

Cost

(CH

F)!

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Comparison of Optimal Control Formulations

35

•  8 consecutive weeks (January 1st and June 29th)

Winter

Method Energy Purchased per Building (CHF)

Comfort Constraints Violations per Room (Kh)

Certainty Equivalent Problem (393, 6.7) (3.2, 0.2)

Open Loop Policies (453, 4.8) (0.6, 0.1)

Affine Decision Rules (426, 6.2) (0.5, 0.1)

Summer

Method Energy Purchased per Building (CHF)

Comfort Constraints Violations per Room (Kh)

Certainty Equivalent Problem (30, 2.1) (1.2, 0.1)

Open Loop Policies (54, 2.9) (0.4, 0.05)

Affine Decision Rules (49, 3.1) (0.2, 0.05)

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(mean, std.)

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References

[1] Darivianakis G., Georghiou A., Smith R. S. and Lygeros J. “A Stochastic Optimization Approach to Cooperative Energy Management via an Energy Hub”, IEEE Conference on Decision and Control, 2015.

[2] Sturzenegger, D., Gyalistras, D., Semeraro, V., Morari, M. and Smith, R. S., ”Model Predictive Climate Control of a Swiss Office Building: Implementation, Results and Cost-Benefit Analysis”, IEEE Transactions on Control Systems Technology, 2015.

[3] Sturzenegger, D., Gyalistras, D., Semeraro, V., Morari, M. and Smith, R. S., ”BRCM Mat-lab Toolbox: Model Generation for Model Predictive Building Control”, American Control Conference, 2014.

36 Georgios Darivianakis 01/03/2016