Progressive Hedging for Stochastic Economic Dispatch with AC Power Flow

Transcription

1 hotos placed i horizotal positio with eve amout of white space betwee photos ad header rogressive Hedgig for Stochastic Ecoomic Dispatch with AC ower Flow Joh D. Siirola, Cesar A. Silva-Moroy 13 th Iteratioal Coferece o Stochastic rogramg Bergamo, Italy 1 July, 013 Sadia Natioal Laboratories is a multi-program laboratory maaged ad operated by Sadia Corporatio, a wholly owed subsidiary of Lockheed Marti Corporatio, for the U.S. Departmet of Eergy s Natioal Nuclear Security Adistratio uder cotract DE-AC04-94AL SAND NO. 011-XXXX

2 Outlie Operatig a ower Grid ACOF formulatio I rectagular rectagular polar Stochastic ACOF with Reewable Eergy Resources Computatioal Results Coclusios

3 Operatig the electric power grid Coceptually simple demad geeratio losses t T I practice, this is complicated by Dyamic costraits (ramp rates Trasmissio limitatios Security (reliability requiremets Market costraits

4 How do utilities implemet this i practice?

5 Day-Ahead Uit Commitmet (SCUC D-8h Day-Ahead Eergy Market (DAEM or DAM Clears demad bids ad supply offers at 1600h o the day prior to the operatig day roduces: Hourly schedules for the ext operatig day for market participats (i.e., geeratio ad demad Hourly iterchage schedules Hourly day-ahead Locatioal Margial rices (LMs Some markets optimize reserve requiremets simultaeously

6 Reliability Uit Commitmet RUC (SCUC D-h Reliability Assessmet (Reserve Adequacy Aalysis - RAA Miimize additioal start-up ad o load costs to provide sufficiet capacity to satisfy the forecasted load plus the operatig ad replacemet reserve requiremets Clears ISO forecasted load at 00h DAM commitmets are respected roduces: Additioal commitmets Updated geerator dispatch poits

7 Look-Ahead Ecoomic Dispatch (H-1h SCED with ability to brig olie fast start resources It s iteded to meet itra-hour power fluctuatios Update load ad variable geeratio forecasts It produces: Geerator setpoits Schedule of fast start uits

8 ower flow i a electric grid (Real ower ( is the itegrated product of voltage ( ad curret (I For AC circuits with oly resistive loads = RMS * I RMS Reactive loads (iductors & capacitors shift the I- phase; worst case: = 0 Apparet ower (S is RMS * I RMS Govers geeratio costs ad trasmissio costraits (S ½ is the Reactive ower (

9 Solvig Ecoomic Dispatch I practice, operators liearize the uderlyig system Basis of Stochastic UC preseted i previous talk DCOF Small agle assumptio for voltage agle Omit reactive power 1, = B ( θ θ 1 Yields suboptimal (ad frequetly ifeasible solutios Actual system voltage agles ca exceed 30 degrees

10 Formulatig the ACOF ACOF: Detere,,, I for every lie, geerator i grid Explicitly capture etwork topology Miimize total geeratio costs Multiplicity of formulatios Choice of basis (for etwork costraits sigificat: polar: rectagular: I rectagular: Rectagular basis,,, θ,, v r, v j,, i r, i j, v r, v j si(w+ θ = v r si(w + v j si(w+π/., I i the complex plae

11 ACOF- (polar cos si ( si cos (.. ( m m m d mk m mk m mk m d mk m mk m mk m B G B G s t c

12 ACOF- (rectagular * * arcta( arcta( ( ( (.. ( m r m j m r j m j j r r k mk mk d d v v v v s q p j Y j s t j c

13 ACOF-I (rectagular arcta( arcta( ( ( ( (.. ( m r m j m r j m j j r r k mk d j r r j d j j r r v v v v i i I I I I Y I s t j c

14 Stochastic ACOF Motivatio Icreased peetratio of reewable (odispatchable eergy impacts fossil-fuel plats, i particular uit cyclig. Sudde availability / loss of reewable geeratio must be absorbed by dispatchable geeratio Curtailig reewables frequetly disallowed by cotract / regulatio 0% ad 30% reewable peetratio for a easy week i July. Reproduced from NREL 010 Wester Wid ad Solar Itegratio Study

15 Stochastic ACOF Motivatio Uits that are desiged for base-load operatio are beig employed to help absorb reewable plats variability Results i icreased O&M costs ad higher forced outage rates How to dispatch geeratio to imize the cyclig of slow geerators while takig ito accout the stochastic ature of wid ad solar plats? 0% ad 30% reewable peetratio for a challegig week i April. Reproduced from NREL 010 Wester Wid ad Solar Itegratio Study

16 Addig Reewables to ACOF Reewable plats are a sigificat source of ucertaity They do ot use fuel to provide power No structural chages to objective fuctio (zero cost coefficiets Reewables are modeled as must-take resources egative real power loads gg where ww ll 0 " Î N,t Î T g w mm dd G are the geerators at ode W are the reewable geerators at ode L are the lies coected ito ode M are the lies out of ode l m d

17 Addig Reewables to ACOF Moder reewable power plats ca cotrol their reactive power output, thus is a variable Dispatchable å gîg w g + w + å l - å m - å d = 0 å wîw lîl durig periods whe geeratio is ormally off-lie. Additioally, reactive power limits are give by their power electroics iterface ratig (MA w + w MA ratig mîm reactive power capability. Some iverters have the capability to a power, if eeded, provided that curret ad teral voltage ratigs a Cosiderig that iverter cost is related to curret ratig, provisio of output meas that the iverter eeds to be larger for the same plat M a higher cost compared to existig idustry practice. Figure 6 shows iverter based o curret limits oly. Normally, this iverter would b power factor operatio (1 i Figure 6. Iverters would be able to p "w Î W,t Î T " Î N,t Î T power whe it operates at a power levels lower tha 1 (e.g.,. I provide dîd reactive power support at zero power, similar to a STATCOM fuctioality is ot stadard i the idustry. iverters are typicall grid at ight, i which case the iverter-based reactive power capabil practice could, of course, be modified, if site coditios dictate the us Figure 6. Reactive power capability of a iverter (red curve

18 Stochastic ACOF Formulatio Objective s. t. tt C gt gg ( t C gt a b ( g t 0 g g, ( t c ( g, ( t k( gt Add explicit rampig costs (k First-stage: geerator set poits ( g at the first time step Secod-stage: rampig of the uits through time Base load uits have high k values eakers have low k value

19 Case Studies IEEE Test cases 118-bus system 118 buses 186 lies 54 geerators 300-bus system 300 buses 411 lies 69 geerators 4 period model Implemetatio (rectagular yomo / ys Ipopt w/ MA7 4x Itel Xeo E (3 51 GB RAM

20 Extesive form ot tractable Target: <<300 secods Disclaimer: Sigificat tuig opportuities remai Warm-startig / iitializatio Model presolve (ot curretly available i yomo

21 rogressive Hedgig arallel solutio MI o sigle machie Weak scalig Extremely tight covergece costrait (1E-5 10x 80x improvemet i wall clock time

22 rogressive hedgig: tuig ρ Surprisigly high rho required (118 bus, 16 sceario, 1e-5 covergece

23 Impact of ocovexity

24 Impact of ocovexity (

25 Summary Stochastic ACOF has the potetial to sigificatly impact grid operatios Itegratio of reewable (odispatchable geeratio ricig rampig products? Extesive Form covergece a cocer rogressive Hedgig (with appropriate tuig effective at gettig high-quality solutios i tractable time Sigificat tuig, formulatio, ad algorithmic opportuities remai