optimal power flow + load control
TRANSCRIPT
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Optimal Power Flow + Load Control
Steven Low
Computing + Math Sciences Electrical Engineering
June 2013
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Acknowledgment Caltech Bose, Candy, Hassibi, Gan, Gayme, Li, Nicky,
Topcu, Zhao
SCE Auld, Clarke, Montoya, Shah, Sherick
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Motivations Uncertainty in supply/demand Need for closing control loops, nonconvex
physical flows
Uncertainty in data Unavailable, incomplete, inaccurate, dynamic
and outdated
Control timescales and market mechanism How to co-design for efficiency & security?
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Key messages Uncertainty in supply/demand Exploit convexity structure, sparsity, locality
Uncertainty in data Exploit (not fight) system dynamics for
robustness, scalability, simplicity
Control timescales and market mechanism How to co-design for efficiency & security?
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AC OPF
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Optimal power flow (OPF)
OPF underlies many applications Unit commitment, economic dispatch State estimation Contingency analysis Feeder reconfiguration, topology control Placement and sizing of capacitors, storage Volt/var control in distribution systems Demand response, load control Electric vehicle charging Market power analysis …
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ARPA-E GENI project Goal: overcome nonconvexity of AC OPF Status: new approach for AC OPF Theory convex relaxations
Algorithms SDP, chordal relaxation, SOCP
Simulations IEEE test systems, Polish systems, SCE circuits
Seek: real-world applications Distributed volt/var control
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Fast accurate AC OPF
Exploit convex relaxations of power flows Physical systems are nonconvex … … but have underlying convexity that should be exploited
Convexity is important for OPF Foundation of LMP, critical for efficient market theory Required to guarantee global optimality Required for real-time computation at scale
It’s not just about accuracy and scalability New/enhanced applications where
AC power flow is a must (reactive, voltage, loss) Guaranteed quality of solution is critical
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Advantages of relaxations
always converge, fast Nonlinear algorithms may not converge
Yes
global optimal No guarantee on solution quality
Algorithms based on convex relaxation
Traditional algorithms
feasible ?
heuristics w/ guarantee
DC OPF solution may not be feasible
No
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AC OPF: some details
simple resource & stability constraints
nonconvex physical law
simple model to focus on nonconvexity of power flow
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AC OPF: some details
simple resource & stability constraints
nonconvex physical law
simple model to focus on nonconvexity of power flow
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AC OPF: some details
simple resource & stability constraints
nonconvex physical law
how to deal with this nonconvexity ?
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AC OPF: some details
Kirchhoff law:
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AC OPF: some details
DC OPF
linear approximation
DC solution infeasible
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AC OPF: some details
DC OPF
linear approximation
DC solution local optimal
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AC OPF: some details
convex relaxation • Y is convex • Y contains X
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AC OPF: some details
relaxed solution lower bounds
convex relaxation • always lower bounds
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AC OPF: some details
relaxed solution globally optimal
convex relaxation • always lower bounds • often global optimal (checkable!)
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Advantages of relaxations
always converge, fast Nonlinear algorithms may not converge
Yes
global optimal No guarantee on solution quality
Algorithms based on convex relaxation
Traditional algorithms
feasible ?
heuristics w/ guarantee
DC OPF solution may not be feasible
No
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Advantages of relaxations
always converge, fast
Yes
global optimal
Algorithms based on convex relaxation
feasible ?
heuristics w/ guarantee
No
Radial networks • Guaranteed to work (almost) Mesh networks • Understand network structure needed for exact relaxation
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Examples
power flow solution X
SDP Y SOCP Y
Real Power Reactive Power
• Relaxation is exact if X and Y have same Pareto front
• SOCP is faster but coarser than SDP
[Bose, et al 2013]
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Examples
optimal solutions ! [Bose, et al 2013]
(secs)
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Examples
SDP
SOCP
[Lingwen Gan, Caltech]
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Examples
MatPower default nonlinear solver generally performs very well Fast, and computes global optimal (checked
using convex relaxation method!) Example difference: IEEE 39-bus 5% improvement in optimal network loss
over MatPower default nonlinear solver
[Lingwen Gan, Caltech]
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ARPA-E GENI project
Seek: real-world applications AC power flow is a must (reactive, voltage,
loss) Guarantee on solution quality is a must
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Key messages Uncertainty in supply/demand Exploit convexity structure, sparsity, locality
Uncertainty in data Exploit (not fight) system dynamics for
robustness, scalability, simplicity
Control timescales and market mechanism How to co-design for efficiency & security?
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Load control for freq regulation
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Motivation
OPF applications determine operating point Economic efficiency through markets Setpoints for generators, taps, switches, … Slow timescale: 5min – day
Fast timescale control tracks operating point Frequency regulations, AGC, PSS, … Fast timescale: <1 sec – min Supplement with load-side control ? Market to incentivize huge number of small
loads at fast timescale ?
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Synchronous network All buses synchronized to same nominal
frequency (US: 60 Hz) Supply-demand imbalance frequency
fluctuation
Frequency regulation Generator based Frequency sensitive (motor-type) loads
Freq-insensitive loads/generations Do not react to frequency deviation More & more: electronics Need active control – how?
Motivation
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swing dynamics
Network model
Suppose the system is in steady state, and suddenly …
small-signal (linear) model around setpoint
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Given: disturbance in gen/inelastic load How to control active load Re-synchronize frequencies Re-balance supply and demand Minimize disutility in heterogeneous load
reduction
Optimal load control
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Optimal load control (OLC)
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Theorem
network dynamics + frequency-based load control = primal-dual algorithm that solves OLC
Completely decentralized No need for explicit communication No need for accurate network data Exploit free global control signal
Punchline
… reverse engineering swing dynamics
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network dynamics
Punchline
active control
implicit load control
freq deviations provide the right info, but not the incentive (unlike prices) !
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Theorem
system trajectory converges to
: unique optimal load control
: re-synchronized frequency : re-balances gen-load
Punchline
Zhao, Topcu, Li and Low, 2012. (http://netlab.caltech.edu) Power system dynamics as primal-dual algorithm for optimal load control
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Key insights
freq deviations contain exactly right info on global power imbalance for local decisions
natural system frequency should be exploited for robustness (e.g. to data), simplicity, scalability
Punchline
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Simulations
optimal load control (this talk)
Automatic Generation Control (AGC)
16 buses nonzero resistances
load control + generator control
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Simulations
total power imbalance
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Simulations
bus 12
adding load control to AGC improves transient
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Key messages Uncertainty in supply/demand Exploit convexity structure, sparsity, locality
Uncertainty in data Exploit (not fight) system dynamics for
robustness, scalability, simplicity
Control timescales and market mechanism Challenge: fast timescale, large small loads Market + standards ?
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Simulations Dynamic simulation of IEEE 68-bus system
• Power System Toolbox (Chow) • Detailed generation model • Exciter model, power system stabilizer model • Nonzero resistance lines
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Simulations
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Simulations