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IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
Models, Optimization and Control of CollectivePhenomena in Power Grids
Michael (Misha) Chertkov
Center for Nonlinear Studies & Theory Division,Los Alamos National Laboratory
& New Mexico Consortium
KITP/UCSB, Apr 7, 2011
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
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IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
Outline
1 IntroductionSo what?Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
2 Predicting Failures (Static Overloads) in Power GridsModel of Load SheddingError Surface & InstantonsInstantons for Wind Generation
3 Control of Reactive Flows in Distribution NetworksLosses vs Quality of VoltageControl & Compromises
4 An Optimization Approach to Design of Transmission GridsMotivational Example
Network OptimizationMichael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
http://find/http://goback/8/13/2019 Chertkov Turbulence KITP
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IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
So what?Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
So What? Impact! Savings!
30b$ annually is the cost of power losses10% efficiency improvement - 3b$ savings
cost of 2003 blackout is 7 10b$80b$ is the total cost of blackouts annually in US
further challenges (more vulnerable, cost of not doingplanning, control, mitigation)
Grid is being redesigned[stimulus]
The research is timely:
2T$ in 20 years (at least) in US
Renewables - Desirable but difficult to handle
Integration within itself, but also with Other Infrastructures,e.g. Transportation (Electric Vehicles)
Tons of Interesting (Challenging) ResearchProblems!
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
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I t d ti S h t?
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IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
So what?Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Introduction So what?
http://find/8/13/2019 Chertkov Turbulence KITP
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IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
So what?Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Introduction So what?
http://find/8/13/2019 Chertkov Turbulence KITP
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IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
So what?Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
Preliminary Remarks
The power grid operates according to the laws of electrodynamics
Transmission Grid (high voltage) vs Distribution Grid (lowvoltage)
Alternating Current (AC) flows ... often considered inlinearized (DC) approximation
No waiting periods power constraints should be satisfiedimmediately. Many Scales.
Loads and Generators are players of two types (distributed
renewable will change the paradigm)At least some generators are adjustable - to guarantee that ateach moment of time the total generation meets the total load
The grid is a graph ... but constraints are (graph-) global
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Introduction So what?
http://find/http://goback/8/13/2019 Chertkov Turbulence KITP
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IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
So what?Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
Many Scales InvolvedPower & Voltage
1KW - typical household;103KW = 1MW- consumption of a medium-to-largeresidential, commercial building;106KW = 1GW-large unit of a Nuclear Powerplant (30GW is the installed wind capacity of Germany =8% of total, US windpenetration is 5%- [30% by 2030?]); 109KW = 1TW - US capacity
Distribution -4 13KV. Transmission -100 1000KV.
Spatial Scales
1mm 103km; US grid = 3 106km lines (operated by 500 companies)
Temporal Scales[control is getting faster]
17ms-AC (60Hz) period, target for Phasor Measurement Units sampling rate(10-30 measurements per second)
1s- electro-mechanical wave [motors induced] propagates 500km
2-10s- SCADA delivers measurements to control units
1 min- loads change (demand response), wind ramps, etc (toughest scale tocontrol)
5-15min- state estimations are made (for markets), voltage collapse
up to hours- maturing of a cascading outage over transmissiongridsMichael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Introduction So what?
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IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
So what?Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
Basic AC Power Flow Equations (Static)The Kirchhoff Laws(linear)
a G0 :
baJab= Ja for currents(a, b) G1 : Jabzab=Va Vb for potentials
(a, b) G1 : Ja =
bG0YabVb
Y = (Yab|a, b G0), {a, b}: Yab=
0, a=b, a byab, a=b, a b
cac=a yac, a= b.{a, b}: yab=gab+iab= (zab)1, zab=rab+xab
Complex Power Flows [balance of power, nonlinear]
a G0 : Pa =pa+ iqa =VaJa =Va
baJab
= Va
baVa V
bz
ab
= baexp(2a)exp(a+b+iaib)
zab
Flows on graphs, but very different from transportation networksNonlinear in terms of Real and Reactive powersReactive Power needs to be injected to maintain reasonably stable voltageQuasi-static (transients may be relevant on the scale of seconds and less)Different (injection/consumption/control) conditions on generators (p, V) andloads (p, q)(, ) are conjugated (Lagrangian multipliers) to (p, q),energylandscape
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Introduction So what?
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IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
So hat?Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
Energy Functional Landscape (Static)
Transmission Networks(resistance is much smaller than inductance, rab xab)Q(,) =
{a,b}G1
exp(2a)+exp(2b)2 exp(a+b) cos(ab)2xab
aG0
apa
aGloads
aqa
Single Load (p1, q1)and Slack Bus (0 =0 = 0)
Q= 1+exp(21 )2 exp(1) cos(1 )2x
1p1 1q1
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Introduction So what?
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Predicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
DC [linearized] approximation (for AC power flows)
(0) The amplitude of the complex potentials are all fixed to the same number(unity, after trivial re-scaling): a: a = 0.
(1) {a, b}: |a b| 1 - phase variation between any two neighbors on thegraph is small
(2) {a, b}: rabxab - resistive (real) part of the impedance is much smallerthan its reactive (imaginary) part. Typical values for the r/x is in the1/27 1/2 range.
It leads to
Linearized relation between powers and phases (at the nodes):
a G0 : pa =
ba
ab
xab
Losses of real power are zero in the network (in the leading order)
apa = 0
Reactive power needs to be injected (lines are inductances - only consumereactive power=accumulate magnetic energy per cycle)
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionModel of Load Shedding
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Predicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Model of Load SheddingError Surface & InstantonsInstantons for Wind Generation
Our Publications onGrid Stability
21. M. Chertkov, M. Stepanov, F. Pan, and R. Baldick , Exact and EfficientAlgorithm to Discover Stochastic Contingencies in Wind Generation overTransmission Power Grids, invited session on Smart Grid Integration ofRenewable Energy: Failure analysis, Microgrids, and Estimation at CDC/ECC2011.
16. P. van Hentenryck, C. Coffrin, and R. Bent , Vehicle Routing for the LastMile of Power System Restoration, submitted to PSCC.
15. R. Pfitzner, K. Turitsyn, and M. Chertkov , Statistical Classification ofCascading Failures in Power Grids , arxiv:1012.0815, accepted for IEEE PES2011.
14. S. Kadloor and N. Santhi , Understanding Cascading Failures in Power Grids, arxiv:1011.4098 submitted to IEEE Transactions on Smart Grids.
13. N. Santhi and F. Pan , Detecting and mitigating abnormal events in largescale networks: budget constrained placement on smart grids , proceedings ofHICSS44, Jan 2011.
8. M. Chertkov, F. Pan and M. Stepanov, Predicting Failures in Power Grids,arXiv:1006.0671, IEEE Transactions on Smart Grids 2, 150 (2010).
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Introduction Model of Load Shedding
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Predicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Model of Load SheddingError Surface & InstantonsInstantons for Wind Generation
Outline
1
IntroductionSo what?Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
2 Predicting Failures (Static Overloads) in Power GridsModel of Load SheddingError Surface & InstantonsInstantons for Wind Generation
3 Control of Reactive Flows in Distribution Networks
Losses vs Quality of VoltageControl & Compromises
4 An Optimization Approach to Design of Transmission GridsMotivational Example
Network OptimizationMichael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionP di i F il (S i O l d ) i P G id
Model of Load Shedding
http://find/8/13/2019 Chertkov Turbulence KITP
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Predicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Model of Load SheddingError Surface & InstantonsInstantons for Wind Generation
MC, F. Pan (LANL) and M. Stepanov (UA Tucson)
Predicting Failures in Power Grids:The Case of Static Overloads, IEEETransactions on Smart Grids2, 150(2010).
MC, FP, MS & R. Baldick (UT Austin)
Exact and Efficient Algorithm toDiscover Extreme StochasticEvents in Wind Generation overTransmission Power Grids, invitedsession on Smart Grid Integrationof Renewable Energy at CDC/ECC
2011.Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionP di ti F il (St ti O l d ) i P G id
Model of Load Shedding
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Predicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
S gError Surface & InstantonsInstantons for Wind Generation
Normally the grid is ok (SAT) ... but sometimes failures
(UNSAT) happensHow to estimate a probability of a failure?
How to predict (anticipate and hopefully) prevent the systemfrom going towards a failure?
Phase space of possibilities is huge (finding the needle in thehaystack)
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Model of Load Shedding
http://find/8/13/2019 Chertkov Turbulence KITP
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Predicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
gError Surface & InstantonsInstantons for Wind Generation
Model of Load Shedding [MC, F.Pan & M.Stepanov 10]
Minimize Load Shedding = Linear Programming for DC
LPDC(d|G; x; u; P) = minf,,p,s
aGd
sa
COND(f,,p,d,s|G;x;u;P)
COND=CONDflow CONDDC CONDedge CONDpower CONDover
CONDflow =
a:
ba
fab=
pa, a Gp
da+ sa, a Gd0, a G0\ (Gp Gd)
CONDDC=
{a, b}: a b+xabfab= 0
, CONDedge=
{a, b}: uab fab uab
CONDpower=
a: 0 pa Pa
, CONDover=
a: 0 sa da
-phases; f -power flows through edges; x - inductances of edges
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
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IntroductionPredicting Failures (Static Overloads) in Power Grids
Model of Load Shedding
8/13/2019 Chertkov Turbulence KITP
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Predicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Error Surface & InstantonsInstantons for Wind Generation
Instanton Search Algorithm[Sampling]
Borrowed (with modifications) from Error-Correction studies:analysis of error-floor [MC, M.Stepanov, et al 04-10]
ConstructQ(d) =
P(d), LPDC(d)> 00 , LPDC(d) = 0Generate a simplex (N+1points) of UNSAT points
Use Amoeba-Simplex
[Numerical Recepies] tomaximizeQ(d)Repeat multiple times(sampling the space ofinstantons)
Point at the Error Surfaceclosest to normal operational point
normal operational point
demand1
demand2
demand...
Error Surface
load sheddingload sheddingload shedding
no load sheddingno load sheddingno load shedding
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Model of Load SheddingE S f & I
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Predicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Error Surface & InstantonsInstantons for Wind Generation
Example of Guam [MC, F.Pan & M.Stepanov 10]
The instantons are sparse (localized ontroubled nodes)
The troubled nodes are repetitive inmultiple-instantons
Instanton structure is not sensitive tosmall changes in D and statistics ofdemands
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Model of Load SheddingE S f & I t t
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g ( )Control of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Error Surface & InstantonsInstantons for Wind Generation
Example of IEEE RTS96 system [MC, F.Pan & M.Stepanov 10]
The instantons are well localized (but stillnot sparse)
The troubled nodes and structures arerepetitive in multiple-instantons
Instanton structure is not sensitive tosmall changes in D and statistics ofdemands
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Model of Load SheddingError Surface & Instantons
http://find/8/13/2019 Chertkov Turbulence KITP
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g ( )Control of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Error Surface & InstantonsInstantons for Wind Generation
Triangular Example (illustrating a paradox)
lowering demand may betroublesome [SAT UNSAT]develops when a cycle contains a
weak linksimilar observation was made inother contexts before, e.g. by S.Oren and co-authors
the problem is typical in realexamples
consider fixing it with extrastorage [future project]
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Model of Load SheddingError Surface & Instantons
http://find/8/13/2019 Chertkov Turbulence KITP
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Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
Error Surface & InstantonsInstantons for Wind Generation
Instantons for Wind Generation
SettingRenewables is the source of fluctuations
Loads are fixed (5 min scale)
Standard generation is adjusted according to a droop control
(low-parametric, linear)
Results
The instanton algorithm discovers most probable extremestatistics events
The algorithm is EXACT and EFFICIENT (polynomial)
Illustrate utility and performance on IEEE RTS-96 exampleextended with additions of 10%, 20% and 30% of renewablegeneration.
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Model of Load SheddingError Surface & Instantons
http://find/8/13/2019 Chertkov Turbulence KITP
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Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
Error Surface & InstantonsInstantons for Wind Generation
Simulations: IEEE RTS-96 + renewables
10% of penetration -localization, longcorrelations
20% of penetration -worst damage, leadinginstanton is delocalized
Instanton1
Instanton2
Instanton3
30% of penetration -spreading anddiversifying decreasesthe damage, instantonsare localized
Instanton1
Instanton2
Instanton3
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
C l f R i Fl i Di ib i N k
Model of Load SheddingError Surface & Instantons
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Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
Error Surface & InstantonsInstantons for Wind Generation
Path Forward (for predicting failures)
Path Forward
Many large-scale practical tests, e.g. ERCOT wind integration
The instanton-amoeba allows upgrade to other (than LPDC)
network stability testers, e.g. for AC flows and transients
Instanton-search can be accelerated, utilizing LP-structure of thetester (exact & efficient for example of renewables)
This is an important first step towards exploration of next level
problems in power grid, e.g. on interdiction [Bienstock et. al 09],optimal switching [Oren et al 08], cascading outages/extremes[Dobson et al 06], and control of the outages [Ilic et al 05,Bienstock 11]
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
C t l f R ti Fl i Di t ib ti N t kLosses vs Quality of VoltageC t l & C i
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Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
Control & Compromises
Our Publications onGrid Control
20. K. Turitsyn, S. Backhaus, M. Ananyev and M. Chertkov , Smart Finite State Devices: A ModelingFramework for Demand Response Technologies, invited session on Demand Response at CDC/ECC 2011.
19. S. Kundu, N. Sinitsyn, S. Backhaus, and I. Hiskens, Modeling and control of thermostaticallycontrolled loads, submitted to 17th Power Systems Computation Conference 2011, arXiv:1101.2157.
16. P. van Hentenryck, C. Coffrin, and R. Bent , Vehicle Routing for the Last Mile of Power SystemRestoration, submitted to PSCC.
12. P. Sulc, K. Turitsyn, S. Backhaus and M. Chertkov , Options for Control of Reactive Power byDistributed Photovoltaic Generators, arXiv:1008.0878, to appear in Proceedings of the IEEE, special issue
on Smart Grid (2011).11. F. Pan, R. Bent, A. Berscheid, and D. Izrealevitz , Locating PHEV Exchange Stations in V2G,arXiv:1006.0473, IEEE SmartGridComm 2010
10. K. S. Turitsyn, N. Sinitsyn, S. Backhaus, and M. Chertkov, Robust Broadcast-Communication Controlof Electric Vehicle Charging, arXiv:1006.0165, IEEE SmartGridComm 2010
9. K. S. Turitsyn, P. Sulc, S. Backhaus, and M. Chertkov, Local Control of Reactive Power by DistributedPhotovoltaic Generators, arXiv:1006.0160, IEEE SmartGridComm 2010
7. K. S. Turitsyn, Statistics of voltage drop in radial distribution circuits: a dynamic programming
approach, arXiv:1006.0158, accepted to IEEE SIBIRCON 20105. K. Turitsyn, P. Sulc, S. Backhaus and M. Chertkov, Distributed control of reactive power flow in aradial distribution circuit with high photovoltaic penetration, arxiv:0912.3281 , selected for super-session atIEEE PES General Meeting 2010.
2. L. Zdeborova, S. Backhaus and M. Chertkov, Message Passing for Integrating and Assessing RenewableGeneration in a Redundant Power Grid, presented at HICSS-43, Jan. 2010, arXiv:0909.2358
1. L. Zdeborova, A. Decelle and M. Chertkov, Message Passing for Optimization and Control of PowerGrid: Toy Model of Distribution with Ancillary Lines, arXiv:0904.0477, Phys. Rev. E80, 046112(2009)
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksLosses vs Quality of VoltageControl & Compromises
http://find/8/13/2019 Chertkov Turbulence KITP
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Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
Control & Compromises
Outline
1 IntroductionSo what?Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
2 Predicting Failures (Static Overloads) in Power GridsModel of Load SheddingError Surface & InstantonsInstantons for Wind Generation
3 Control of Reactive Flows in Distribution Networks
Losses vs Quality of VoltageControl & Compromises
4 An Optimization Approach to Design of Transmission GridsMotivational ExampleNetwork Optimization
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksLosses vs Quality of VoltageControl & Compromises
http://find/8/13/2019 Chertkov Turbulence KITP
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Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
Control & Compromises
K. Turitsyn (MIT), P. Sulc (NMC), S. Backhaus and M.C.
Optimization of Reactive Power by Distributed PhotovoltaicGenerators, to appear in Proceedings of the IEEE, special issueon Smart Grid (2011), http://arxiv.org/abs/1008.0878
Local Control of Reactive Power by Distributed Photovoltaic
Generators, proceedings of IEEE SmartGridComm 2010,http://arxiv.org/abs/1006.0160
Distributed control of reactive power flow in a radial
distribution circuit with high photovoltaic penetration, IEEEPES General Meeting 2010 (invited to a super-session),
http://arxiv.org/abs/0912.3281
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksLosses vs Quality of VoltageControl & Compromises
http://arxiv.org/abs/1008.0878http://arxiv.org/abs/1006.0160http://arxiv.org/abs/0912.3281http://arxiv.org/abs/0912.3281http://arxiv.org/abs/1006.0160http://arxiv.org/abs/1008.0878http://find/8/13/2019 Chertkov Turbulence KITP
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Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
Control & Compromises
Setting & Question & Idea
Distribution Grid (old rules, e.g.voltage is controlled only at thepoint of entrance)
Significant Penetration of
Photovoltaic (new reality)How to controlswinging/fluctuating voltage(reactive power)?
Idea(s)
Use Inverters.
Control Locally.Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksLosses vs Quality of VoltageControl & Compromises
http://find/8/13/2019 Chertkov Turbulence KITP
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Control of Reactive Flows in Distribution NetworksAn Optimization Approach to Design of Transmission Grids
Control & Compromises
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksLosses vs Quality of VoltageControl & Compromises
http://find/8/13/2019 Chertkov Turbulence KITP
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An Optimization Approach to Design of Transmission Gridsp
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksLosses vs Quality of VoltageControl & Compromises
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An Optimization Approach to Design of Transmission Gridsp
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksLosses vs Quality of VoltageControl & Compromises
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An Optimization Approach to Design of Transmission Grids
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power Grids
Control of Reactive Flows in Distribution NetworksO f G
Losses vs Quality of VoltageControl & Compromises
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An Optimization Approach to Design of Transmission Grids
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
A O ti i ti A h t D i f T i i G id
Losses vs Quality of VoltageControl & Compromises
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An Optimization Approach to Design of Transmission Grids
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimi ation Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
http://find/8/13/2019 Chertkov Turbulence KITP
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An Optimization Approach to Design of Transmission Grids
Our Publications onGrid Planning
18. R. Bent, A. Berscheid, and L. Toole , Generation and TransmissionExpansion Planning for Renewable Energy Integration, submitted to PowerSystems Computation Conference (PSCC).
17. R. Bent and W.B. Daniel , Randomized Discrepancy Bounded Local Searchfor Transmission Expansion Planning, accepted for IEEE PES 2011.
11. F. Pan, R. Bent, A. Berscheid, and D. Izrealevitz , Locating PHEV
Exchange Stations in V2G, arXiv:1006.0473, IEEE SmartGridComm 20106. J. Johnson and M. Chertkov, A Majorization-Minimization Approach toDesign of Power Transmission Networks, arXiv:1004.2285, 49th IEEEConference on Decision and Control (2010).
4. R. Bent, A. Berscheid, and G. Loren Toole, Transmission Network ExpansionPlanning with Simulation Optimization, Proceedings of the Twenty-Fourth AAAI
Conference on Artificial Intelligence (AAAI 2010), July 2010, Atlanta, Georgia.3. L. Toole, M. Fair, A. Berscheid, and R. Bent, Electric Power TransmissionNetwork Design for Wind Generation in the Western United States: Algorithms,Methodology, and Analysis , Proceedings of the 2010 IEEE Power EngineeringSociety Transmission and Distribution Conference and Exposition (IEEE TD2010), April 2010, New Orleans, Louisiana.
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
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An Optimization Approach to Design of Transmission Grids
Outline
1 Introduction
So what?Smart Grid Project (LDRD DR) at LANLPreliminary Technical Remarks. Scales.Technical Intro: Power Flows
2 Predicting Failures (Static Overloads) in Power GridsModel of Load SheddingError Surface & InstantonsInstantons for Wind Generation
3 Control of Reactive Flows in Distribution Networks
Losses vs Quality of VoltageControl & Compromises
4 An Optimization Approach to Design of Transmission GridsMotivational ExampleNetwork Optimization
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
http://find/8/13/2019 Chertkov Turbulence KITP
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An Optimization Approach to Design of Transmission Grids
Grid Design: Motivational Example
Cost dispatch only(transportation,economics)
Power flows highly approximate
Unstable solutions
Intermittency in Renewables not
accounted
An unstable grid example
Hybrid Optimization - is currentengineering solution developed atLANL: Toole,Fair,Berscheid,Bent 09extending and built on NREL 20% by2030 report for DOE
Network Optimization
Design of the Grid as a tractableglobal optimization
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
http://find/8/13/2019 Chertkov Turbulence KITP
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An Optimization Approach to Design of Transmission Grids
Network Optimization (for fixed production/consumption p)
ming
p+ G(g)1 p minimize losses
convex overg
, Gab= 0, a
=b, a b
gab, a =b, a bcac=agac, a=b.
Discrete Graph Laplacian of conductance
Network Optimization (averaged over p)
mingp+
G(g)1
p = mingtr
G(g)1
pp+
=
ming
trG(g)1 P still convex
, P
covariance matrix of load/generation
Boyd,Ghosh,Saberi 06in the context of resistive networksalsoBoyd, Vandenberghe, El Gamal and S. Yun 01forIntegratedCircuits
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
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An Optimization Approach to Design of Transmission Grids
Network Optimization: Losses+Costs [J. Johnson, MC 10]
Costs need to account for
sizing lines - grows with gab, linearly or faster (convex in g)
breaking ground - l0-norm (non convex in g) but also imposesdesiredsparsity
Resulting Optimization is non-convex
ming>0
tr
G(g)
1P
+{a,b}
(abgab+ab(gab))
, (x) =
xx+
Tricks (for efficient solution of the non-convex problem)
annealing: start from large (convex) and track to 0(combinatorial)
Majorization-minimization (from Candes, Boyd 05) for current :
gt+1 = argming>0 tr(L) + .
g+.
(g
tab).
gab
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
http://find/8/13/2019 Chertkov Turbulence KITP
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p pp g
Single-Generator Examples (I)
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
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Single-Generator Examples (II)
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
http://find/8/13/2019 Chertkov Turbulence KITP
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Multi-Generator Example
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
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Adding Robustness
To impose the requirement that the network design should berobust to failures of lines or generators, we use the worst-casepower dissipation:
L\k
(g) = max{a,b}:zab{0,1}|
{a,b}zab=NkL(z. g))
It is tractable to compute only for small values ofk.
Note, the point-wise maximum over a collection of convex
function is convex.So the linearized problem is again a convex optimizationproblem at every step continuation/MM procedure.
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
http://find/8/13/2019 Chertkov Turbulence KITP
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Single-Generator Examples [+Robustness] (I)
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
http://find/8/13/2019 Chertkov Turbulence KITP
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Single-Generator Examples [+Robustness] (II)
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
http://find/8/13/2019 Chertkov Turbulence KITP
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Multi-Generator Example [+Robustness]
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
IntroductionPredicting Failures (Static Overloads) in Power GridsControl of Reactive Flows in Distribution Networks
An Optimization Approach to Design of Transmission Grids
Motivational ExampleNetwork Optimization
http://find/8/13/2019 Chertkov Turbulence KITP
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Conclusion (for the Network Optimization part)
A promising heuristic approachto design of power transmissionnetworks. However, cannot guarantee global optimum.
CDC10: http://arxiv.org/abs/1004.2285
Future Work:Applications to real grids, e.g. for 30/2030
Bounding optimality gap?
Use non-convex continuation approach to place generators
possibly useful for graph partitioning problems
adding further constraints (e.g. dont overload lines)
extension to (exact) AC power flow?
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
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Bottom Line
A lot of interestingcollective phenomenain the power grid settings for Applied
Math, Physics, CS/IT analysisThe research is timely (blackouts, renewables, stimulus)
Other Problems the team plans working on
Efficient PHEV charging via queuing/scheduling with and withoutcommunications and delays
Power Grid Spectroscopy (power grid as a medium, electro-mechanical wavesand their control, voltage collapse, dynamical state estimations)
Effects of Renewables (intermittency of winds, clouds) on the grid & control
Load Control, scheduling with time horizon (dynamic programming +)
Price Dynamics & Control for the Distribution Power Grid
Post-emergency Control (restoration and de-islanding)
For more info - check:
http://cnls.lanl.gov/~chertkov/SmarterGrids/
https://sites.google.com/site/mchertkov/projects/smart-grid
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
http://cnls.lanl.gov/~chertkov/SmarterGrids/http://cnls.lanl.gov/~chertkov/SmarterGrids/http://cnls.lanl.gov/~chertkov/SmarterGrids/https://sites.google.com/site/mchertkov/projects/smart-gridhttps://sites.google.com/site/mchertkov/projects/smart-gridhttp://cnls.lanl.gov/~chertkov/SmarterGrids/http://find/8/13/2019 Chertkov Turbulence KITP
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Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Statistical Classification of Cascading Failures Algorithm of the Cascade
Phase Diagram of Cascades
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Outline
5 Statistical Classification of Cascading FailuresAlgorithm of the CascadePhase Diagram of Cascades
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Statistical Classification of Cascading Failures Algorithm of the Cascade
Phase Diagram of Cascades
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Rene Pfitzner (NMC), Konstantin Turitsyn (MIT) & MC
Statistical Classification of Cascading Failures in Power Grids,accepted to IEEE PES 2011,http://arxiv.org/abs/1012.0815
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Statistical Classification of Cascading Failures Algorithm of the Cascade
Phase Diagram of Cascades
http://arxiv.org/abs/1012.0815http://arxiv.org/abs/1012.0815http://find/8/13/2019 Chertkov Turbulence KITP
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Objectives:
Have a realisticmicroscopicmodel of a cascade [not (!!) a
disease-spread like phenomenological model]Resolvediscrete eventsdynamics (lines tripping, overloads,islanding) explicitly
Address (first) thecurrent realityof the transmission grid
operation, e.g. automatic control on the sub-minute scaleConsider (first)fluctuations in demandas a source of cascadein the overloaded (modern) grid
Analyze the results, e.g. in terms of phases observed, onavailable power grid models [IEEE test beds]
Building on
I. Dobson, B. Carreras, V. Lynch, and D. Newman, Aninitialmodel for complex dynamics in electric power system
blackouts, HICSS-34, 2001Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Statistical Classification of Cascading Failures Algorithm of the Cascade
Phase Diagram of Cascades
Al i h f h C d
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Algorithm of the Cascade
Optimum Power Flowfinds (cost)optimal distribution of generation(decided once for 15 min - in betweenstate estimations)
DC power flow is our (simplest) choice
Droop Control= equivalent (pre set for
15 min) response of all the generators tochange in loads
Identify islandswith a proper connectedcomponent algorithm(s)
Discrete time Evolution of Loads= (a)generate configuration of demand from
given distribution (our enabling example= Gaussian, White); (b) assume that theconfiguration grow from the typical one(center of the distribution) in continuoustime, t [0; 1]; (c) project next discreteevent (failure of a line or saturation of agenerator)andjumpthere
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
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Statistical Classification of Cascading Failures Algorithm of the CascadePhase Diagram of Cascades
General Conclusions (3 phases)
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General Conclusions (3 phases)
Phase #0 The grid is resilient against fluctuationsin demand.
Phase #1 shows tripping of demands due totripping of overloaded lines. This has aoverall de-stressing effect on the grid.
Phase #2 Generator nodes start to become tripped,
mainly due to islanding of individualgenerators. With the early tripping ofgenerators the system becomes stressedand cascade evolves much faster (withincrease in the level of demandfluctuations) when compared with arelatively modest increase observed in
Phase #1.
Phase #3 Significant outages are observed. Theyare associated with removal from the gridof complex islands, containing bothgenerators and demands.
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
Statistical Classification of Cascading Failures Algorithm of the CascadePhase Diagram of Cascades
Path Forward (Cascades)
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Path Forward (Cascades)
From DC solver to AC solver
Mixed models - combining fluctuations in demands andincidental line tripping
More detailed study of effect of capacity inhomogeneity (e.g.on islanding)
Towards validated (derived from micro-) phenomenologicalmodel and theory of cascades [power tails, scaling, dynamic
mechanisms]
Michael (Misha) Chertkov [email protected] http://cnls.lanl.gov/chertkov/SmarterGrids/
http://find/