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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
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