Optimal volt/var Control

Masoud Farivar Steven Low Mani Chandy

Computing + Math Sciences Electrical Engineering

Caltech

June 2013

Christopher Clarke Russel Neal

Robert Sherick

T&D BU

SCE

Outline

Motivating example

Problem and solution

Simulation evaluation

Illustration: OPF based on convex relaxation

Motivation n  Static capacitor control cannot cope with rapid

random fluctuations of PVs on distr circuits n  A utility company needs $B infrastructure

investment to cope

Our proposal n  Optimize reactive output of

inverters

Example: distr volt/var control

Motivation n  Static capacitor control cannot cope with rapid

random fluctuations of PVs on distr circuits n  A utility company needs $B infrastructure

investment to cope

Our proposal n  Solve OPF in real time (mins) n  Overcome nonconvexity

Example: distr volt/var control

Control strategy

Two timescale coordinated control n  Capacitors: slow infrequent (hours) n  Inverters: fast frequent (mins)

Optimal capacitor control n  Dynamic programming

Optimal inverter control n  Real-time OPF

this talk

Power network

pjG,qj

G

input: solar power

control: var output

Vj

min riji~ j∑ Iij

2+ αi

i∑ Vi

2+ c0p0

G

Optimal volt/var control

real  power  loss   CVR  (conserva1on  voltage  reduc1on)    

fuel  cost  

min f x( )over x := qi

G, Vi , other variables( )s. t. voltage constraints: Vi

min ≤ Vi ≤Vimax

other constraints, e.g., line limits

AC power flow: g(x) = 0

Optimal volt/var control

min f x( )over x := qi

G, Vi , other variables( )s. t. voltage constraints: Vi

min ≤ Vi ≤Vimax

other constraints, e.g., line limits

AC power flow: g(x) = 0

Optimal volt/var control

Optimal volt/var control

DistFlow equations

min f x( )over x := qi

G, Vi , other variables( )s. t. voltage constraints: Vi

min ≤ Vi ≤Vimax

other constraints, e.g., line limits

AC power flow: g(x) = 0

Shorthand:

Optimal volt/var control

minx∈X

f x( )s. t. g(x) = 0 DistFlow equations

DistFlow equations

Sij − zij ij + sj = Sjkj→k∑

vi = vj + 2 Re zij*Sij( )− zij

2 ij

ijvi = Sij2

Baran  and  Wu  1989  Chiang  and  Baran  1990  

ij := Iij2

vi := Vi2

nonconvex (linear otherwise)

real & reactive power balance

AC Ohm’s law (magnitude sq’d)

apparent power

DistFlow equations

ij := Iij2

vi := Vi22nd-order

cone Convex !

real & reactive power balance

AC Ohm’s law (magnitude sq’d)

apparent power

Sij − zij ij + sj = Sjkj→k∑

vi = vj + 2 Re zij*Sij( )− zij

2 ij

ijvi ≥ Sij2

Baran  and  Wu  1989  Chiang  and  Baran  1990  

Shorthand:

Optimal volt/var control

minx∈X

f x( )s. t. g(x) = 0

nonconvex

Shorthand:

Optimal volt/var control

minx∈X

f x( )s. t. g(x) ≥ 0

convex ! SOCP relaxation

Why solve SOCP relaxation?

DC OPF not applicable n  Control reactive power to regulate voltage n  DC power flow ignores both !

Traditional nonlinear algorithms n  Why ? n  … when SOCP relaxation is (almost)

guaranteed to converge to a global optimal

Solution strategy

Solve  SOCP  relaxa1on  

heuris1cs  w/  guarantee  

Solu1on  sa1sfies      g x*( ) = 0 ?

global  op1mal  

Theorem Always works for practical networks ! •  radial nature •  parameters

minx∈X

f x( )s. t. g(x) ≥ 0

No

Yes

Simulations

SCE 47-bus Calabash distribution circuit 5 PV buses

Load  and  Solar  Varia1on  

Empirical  distribu1on    of  (load,  solar)  for  Calabash  

pic

pig

•  More  reliable  opera1on  •  Energy  savings  

Simulations

Simulations

SCE 56-bus (rural) distribution circuit 1 PV bus (5MW)

6 miles from substation

•  More  reliable  opera1on  •  Energy  savings  

Simulations

Under IEEE 1547: Volt at point of common coupling vs solar output (MW)

Simulations

Low load High load

Optimal inverer VAR injection (kVAR)

Papers

Application:

Inverter VAR control for distribution systems with renewables Farivar, Clarke, Low and Chandy IEEE SmartGridComm Conference, 2011 Theory:

Branch flow model: relaxations and convexification Farivar and Low IEEE Trans. Power Systems, 2013

Backup Slides