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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
6 Georgios Darivianakis
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
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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
Georgios Darivianakis
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
Georgios Darivianakis
[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
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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
Georgios Darivianakis
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
19 Georgios Darivianakis
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
31 Georgios Darivianakis
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
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• 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