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

Context

Controlling Air Conditioners

Direct Control for Demand Response

Architecture

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 ∆)?

Two Layer Block Diagram

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)

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)] .

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)

Simulation: 500 homes + ERCOT DA price

How Can the LSE Price A Contract

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.

Thank You

Backup Slides

First Layer: "discretize-then-optimize"

Numerical challenges for MILP and LP

Solution: continuous time PMP w. state inequality constraints

First Layer: "discretize-then-optimize"

Numerical challenges for MILP and LP

Solution: continuous time PMP w. state inequality constraints

Differential Privacy Preserving Sensing

Houston Data for August 2015

5 PM

Limits of Control Performance

⇡0.000