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Architecture and Algorithms for the LSEto Manage Thermal Inertial Loads
Abhishek Halder
Department of Electrical and Computer EngineeringTexas A&M University
College Station, TX 77843
Joint work with X. Geng, F.A.C.C. Fontes, P.R. Kumar, and L. Xie
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Context
Controlling Air Conditioners
Direct Control for Demand Response
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Architecture
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Research Scope
Objective: A theory of operation for the LSE
Challenges:
1. How to design the target consumption as a functionof price?
2. How to control so as to preserve privacy of the loads’states?
3. How to respect loads’ contractual obligations (e.g.comfort range width ∆)?
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Two Layer Block Diagram
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First Layer: Planning Optimal Consumption
minimize{u1(t),...,uN(t)}∈{0,1}N
∫ T
0
Pη
priceforecast
π̂ (t) (u1(t) + u2(t) + . . . + uN(t)) dt
subject to
(1) θ̇i = −αi
(θi(t)− θ̂a(t)
)− βiPui(t) ∀ i = 1, . . . , N,
(2)∫ T
0(u1(t) + u2(t) + . . . + uN(t)) dt = τ
·=
ηENP
(< T, given)
(3) Li0 ≤ θi(t) ≤ Ui0 ∀ i = 1, . . . , N.
Optimal consumption: P∗ref (t) =Pη
N
∑i=1
u∗i (t)
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Second Layer: Real-time Setpoint Control
optimalreference
P∗ref(t) =Pη
N
∑i=1
u∗i (t),
error
e(t) = P∗ref(t)−
measured
Ptotal(t) ,
v(t) =
PID velocity control
kpe(t) + ki
∫ t
0e(ς)dς + ki
ddt
e(t) ,dsidt
=
gain
∆i
broadcast
v(t) ,
Lit = Ui0 ∧ [Li0 ∨ (si(t)− ∆i)] , Uit = Li0 ∨ [Ui0 ∧ (si(t) + ∆i)] .
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Boundary Control: Deadband→ Liveband
0 2000 4000 6000 8000 10000 12000 14000
0
2
4
6
0 2000 4000 6000 8000 10000 12000 1400020
22
24
26
28
30
t (seconds)
Pow
er(kW
)
t (seconds)
Tem
perature
(◦C)
Lt
Ut
θ(t)
s(t)
U0
L0
P reftotal(t)
Ptotal(t)
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Simulation: 500 homes + ERCOT DA price
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How Can the LSE Price A Contract
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Details in1. A. Halder, X. Geng, G. Sharma, L. Xie, and P.R. Kumar, "A
Control System Framework for Privacy PreservingDemand Response of Thermal Inertial Loads",SmartGridComm, 2015.
2. A. Halder, X. Geng, P.R. Kumar, and L. Xie, "Architectureand Algorithms for Privacy Preserving Thermal InertialLoad Management by A Load Serving Entity", in revision,IEEE Trans. Power Systems, 2016.
3. A. Halder, X. Geng, F.A.C.C. Fontes, P.R. Kumar, and L.Xie, "Optimal Power Consumption for Demand Responseof Thermostatically Controlled Loads", under review, ACC,2017.
4. A. Halder, X. Geng, F.A.C.C. Fontes, P.R. Kumar, and L.Xie, "Deterministic and Stochastic Optimal Control ofThermal Inertial Loads", working manuscript, available uponrequest.
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Thank You
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Backup Slides
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First Layer: "discretize-then-optimize"
Numerical challenges for MILP and LP
Solution: continuous time PMP w. state inequality constraints
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First Layer: "discretize-then-optimize"
Numerical challenges for MILP and LP
Solution: continuous time PMP w. state inequality constraints
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Differential Privacy Preserving Sensing
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Houston Data for August 2015
5 PM
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Limits of Control Performance
⇡0.000