Evaluation of Alternative Market Structures and Compensation Schemes for Incenting Transmission Reliability and Adequacy Related Investments

Transcription

1 Evaluation of Alternative Market tructures and Compensation chemes for Incenting Transmission Reliability and Adequacy Related Investments hi-jie Deng H. Milton tewart chool of Industrial and ystems Engineering eorgia Institute of Technology Atlanta, eorgia Project Tele-eminar, eptember 16, 2008 For members only

2 Project Team Academic Team: eorgia Tech: Dr. hi-jie Deng (Lead), Dr. akis Meliopoulos (ECE), Haibin un, Jieyun Zhou. Cornell: Dr. Tim Mount, Jaeuk Ju. UC Berkeley: Dr. hmuel Oren, Enzon auma, Kory Headman Industry Advisors: ABB (Xiaoming Feng), Entergy Corporation (Floyd alvan), E Industry Advisors: ABB (Xiaoming Feng), Entergy Corporation (Floyd alvan), E Energy (Mark anford), NYIO (Jonathan Mayo), and PJM (Jianzhong Tong)

3 Outline Power system simulation i modeling Econometric modeling of Transmission Congestion Contracts Forward price risk premium and implications for transmission investments Nonparametric modeling of the Hub-and-poke Representation of a Network Inherent inefficiency of FTR auctions 3

4 Power system simulation Built on Perc project M-6. Market dispatch optimal power flow formulation Computations based on IEEE- RT 24 ystem 4

5 Power system simulation LMPs and evaluation of reliability constraints Incorporating constraints on transmission reliability margin (TRM) and generation reserve margin lity Density Probabi LMP at Bus 10 ρ T =0% ρ T =10% ρ T =20% Probability distributions of LMPs at bus 10 over the sample year with different TRMs requirements 0% TRM 10% TRM 20% TRM Averaged spatial volatility of LMPs over the sample year when imposing different TRM requirements in the market dispatch ($/MWh) 5

6 Power system simulation Identification of transmission adequacy and reliability needs ensitivity of reliability index for system transmission reliability margin 6

7 Power system simulation Effectiveness of Transmission Compensation A case study: allocation of incremental FTRs st s.t. Max b δ δ FP T F ( P δ ) T b : bid preference parameter, b 20, 23 = 60, b 22, 21 = 10 F and F : system PTDF matrices before and after expansion T and T : transmission capacity limits P : existing amounts of FTRs, P , P 300 δ : amounts of incremental FTRs 20,23 = 22,21 = 7

8 Power system simulation Effectiveness of Transmission Compensation Increase the capacity between bus 20-bus 23 to 150%, so reliability index is above Optimal incremental FTRs solved: δ 264.8, δ 22 = ,23 =,21 Fully allocate capacities: bus 20-bus 23, bus 22-bus 21 FTR revenues collected: bus 20-bus 23 increases 4%, bus 22-bus 21 increases 16% The magnitude of incentives depends on Amount of incremental FTRs Bid values Transmission network topology Initial configuration of the allocated FTRs 8

9 Econometric modeling of TCCs Introduction Price of electricity is a function of The corresponding load Price of natural gas A set of seasonal and daily variables Multivariate time-series models were estimated for Daily temperature in different locations Average daily loads in different zones conditional on HDD, CDD, seasonal cycles and dummy variables Prices of electricity in different zones 9

10 Econometric modeling of TCCs Data used Daily Temperature Data for Three Locations in New York tate Daily Load Data for Four Locations in New York tate 10

11 Econometric modeling of TCCs The Econometric Results Use the estimated models to predict the average daily prices in New York for the summer of 2006 imulated Payouts from Four Different ix-month TCCs for the ummer 2006 imulation Results ($/MW) im1 (Hedgers) Zones A- Zones A-J Zones -J Zones J-K Actual payout LBMP 60, , , ,281.1 May-October 2006 Loss 1, , C.C. 58, , , ,140.8 imulated payouts max 72, , , , LBMP mean 52, , , ,333.1 median 52, , , ,461.4 min 37, , , ,908.9 im2 (peculators) A- A-J -J J-K Actual payout LBMP 60, , , ,281.1 May-October 2006 Loss 1, , C.C. 58, , , ,140.8 imulated payouts max 67, , , ,000.7 LBMP mean 48, , , ,236.2 median 48, , , ,405.5 min 34, , , ,

12 Econometric modeling of TCCs The Econometric Results imulated LBMP Payouts for a TCC between NYC and the Hudson Valley for May-October 2006 Hedgers using Actual Forward Prices for Natural as peculators using imulated Realizations of the Price for Natural as 12

13 Hub-and-poke Representation Local Linear Embedding (LLE) 13

14 Hub-and-poke Representation Low Dimensional pace Embedded three-dimensional Coordinates of the embedded 4 manifold after LLP smoothing dimensional manifold 1st dimension coordinates 2nd dimension coordinates rd coo ordinate nd coordinate st coordinate Feb03 Oct03 Jun04 Feb rd dimension coordinates -4-6 Feb03 Oct03 Jun04 Feb th dimension coordinates -10 Feb03 Oct03 Jun04 Feb05-4 Feb03 Oct03 Jun04 Feb05 14

15 Hub-and-poke Representation Low Dimensional pace Embedded 2-dimensional manifold after LLP smoothing LMP curve of New York IO: actual vs. forecast 15

16 Hub-and-poke Representation Each Coordinate in Low Dimensional pace Correlation coefficient of the four-dimensional Coordinates with the four FTRs Coordinate 1 st 2 nd 3 rd 4 th FTR Correlation Coefficient CENTRL to CAPITL CENTRL to NYC NORTH to LONIL WET to DUNWOD

17 Hub-and-poke Representation Each Coordinate in Low Dimensional pace Correlation coefficient of the four-dimensional Coordinates with the two FTRs Coordinate 1 st 2 nd 3 rd 4 th FTR Correlation Coefficient WET CENTRL CENTRL WET to to to to DUNWOD LONIL LONIL DUNWOD

18 Hub-and-poke Representation Parameter etting and ensitivity Analysis TRE vs. number of intrinsic dimensions TRE vs. number of data in training set TRE vs. number of nearest neighbors TRE(% %) TRE(% %) 1.9 1,8 TRE(% %) Intrinsic dimension The number of the neareast neighbors The length of the training data(days) 18

19 Forward price risk premium Problem Description Price ($/MWh) Price ($/MWh) Reference NY electricity market Forward Market Mar2005 Jul2005 Oct2005 Jan2006 May2006 Aug2006 pot Date Market Mar2005 Jul2005 Oct2005 Jan2006 May2006 Aug2006 Date tatistics of LBMPs in NYIO Zone Forward Market pot Market Forward Mean Volatility Mean Volatility Premium Ref. Bus CAPITL CENTRL DUNWOD ENEE HUD VL LONIL MHK VL MILLWD N.Y.C NORTH WET High volatility, especially in real-time spot market Existence of day-ahead forward risk premiums Transmission structure and transmission congestion To understand the composition of day-ahead forward risk premiums 19

20 Forward price risk premium Model Assumptions Two-stage model Forward market: uncertain load and spot price pot market: accurate forecast of load and price in the immediate future No speculators The wholesale market participants: ENs and LEs only Risk averse ENs and LEs: mean-variance utility functions U U F ( ) = E u π ( ω) A, i 2 F AL, Lj = E[ u( π ω )] = E[ π ( ω) ] Var π ( ω) 2 i L( Lj ) ( ) [ ( )] = E[ π ( ω) ] Var( π ( ω) ) ( ) DC power flow Transmission i network constraints t Fixed set of active transmission constraints 20

21 Forward price risk premium Time equence of the Decision Problems ENs Choose [ F ] F 1, 2 to maximize expected utility LEs Choose [ L F L ] F 2, 3 to maximize expected utility IO Bl Balance demand d and supply and determine forward prices F F F [ P1, P2, P3 ] ENs F * F* iven [ 1, 2 ] choose [ 1, 2 ] by maxing profit LEs Buy [ L 2, L ] 3 to serve residual demand IO Balance demand and supply and determine, P P spot prices [ P1 2, 3 ] [ F 1, 1 ] [ F ] L F L 2, 2 [ 3, 3 ] [ L F 2, L ] 2 21

22 Forward price risk premium Quantitative Model of Forward Premiums F ( [ ] P ) ( ( ϖ )) ( ( ϖ )) ( ( ϖ )) ( ( ϖ )) 2 E P2 AVar P1 AVar P2 AVar L P2 AVar L P3 = E[ [ ] F ( λ E λ ) ( ( ϖ )) ( ( ϖ )) ( ( ϖ )) ( ( ϖ )) AVar P1 AVar P2 AVar L P2 AVar L P3 Cov Var Cov Var ( ρ ( ) ( )) ( P1 ( ϖ )) ( ( ) ( ϖ )) ( P2 ( ϖ )) * * 1 ϖ, P1 ϖ Cov ρ2 ϖ, P2 L ( ρ ( ϖ ), P2 ( ϖ )) ( P2 ( ϖ )) Var Cov Var 2, L ( ρ3 ( ϖ ) P3 ( ϖ )) ( P3 ( ϖ )) 22

23 Forward price risk premium Empirical tudy with the New York Market Data Estimation of power transfer distribution factors Transmission congestion effect on forward premium Forecasting of out-of-sample spot market prices 23

24 Forward price risk premium Evidence of Transmission Congestion Effect Forward Pre emium ($/MWh) Forwa ward Premium ($/MW Wh) Mean F1 F2 F3 Media Zone-CAPITL Zone-CENTRL Zone-DUNWOD Zone-ENEE Zone-HUD VL Zone-LONIL Zone-MHK VL Zone-MILLWD Zone-N.Y.C Zone-NORTH Zone-WET Hour Hour Mean Media = F ( P E[ P ]) Ref Ref F ( λ E[ λ ]) I 1 ( l ) j = 1 * ( P ( ϖ )) j A L Var P ( ϖ ) i= 1 * A Var 1 ϖ g I J g, k k k k K i 1 * A = Var g I i= 1 Cov ( ρi ( ϖ ), Pg ( ϖ )) i ( P ( ϖ )) Var g i f i J i j ( ( )) j P 1 * ϖ A L Var P ( ϖ ) 1 l, k ( l ) = i j * J, j= 1 Cov L ( ρ j ( ϖ ) Pl ( ϖ )) ( ( )) j l ϖ j Var P f 24

25 Forward price risk premium Forecasting of Out-of-ample pot Market Prices Price ($/MWh) Historical Price Forecasted Price μ 95% CI of μ σ 95% CI of σ [8.97, 11.47] [15.85, 17.58] /01 08/06 08/11 08/16 08/21 08/26 08/31 μ 95% CI of μ σ 95% CI of σ 7.07 [5.96, 8.18] [12.81, 14.29] Price ($/MWh) /01 08/06 08/11 08/16 08/21 08/26 08/31 Date 25

26 Inherent inefficiency of FTR auctions Clearing Mechanism for the FTR Auction The FTR auction is equivalent to a virtual energy auction. Max Q C T Q s. t. s. t. e T r Q = 0 Q L r Q Qˆ Q 0 Q L T ( c1, c2, 2, c n ) T ( q1, q2, L, qn ) T ( qˆ, qˆ, L, qˆ ) = α Q Min λ, μ, μ, η T T T [( ) ( ) ] ˆ μr μr L Q η r r λ e r T r R T T [ ( μr ) ( μr ) ] r R μ 0, r R μ 0, r R r η 0 r T η I C = 1 L, λ, μ, μ, and η are dual var iables Q = Qˆ = 1 2 n r r C associated with 4 categories of constraint s in the primal formulation T c i E[ nodal price] = E[ nodal price] for for supplier demand bus bus 26

27 Inherent inefficiency of FTR auctions Market Clearing Nodal Prices The market clearing nodal price vector P of an FTR auction is given by Proposition P λ e T [ ( ) ( ) ] T T μr μr r R If none of the bid quantity constraint is binding FTR auction clearing prices match expected FTR settlements For a generation (load) bus, if the bid quantity constraint is binding market clearing nodal price is greater (less) than expected ex post nodal price r 27

28 Inherent inefficiency of FTR auctions A 6-Bus ystem DC power flow upply buses 1,2,4 Demand Buses 3,5,6 8 transmission lines Admittance B B = B = B = B46 j = B = j 5.0 The supply and demand functions at the 6 buses 45 = j

29 Inherent inefficiency of FTR auctions A6-Bus ystem Computational Results under Transmission Line and Load Contingencies Market Clearing Prices and Quantities FTR Price Comparison As α increases, the bid quantity constraints do not bind. The FTR market clearing prices converge to the expected ex post FTR prices 29

30 Inherent inefficiency of FTR auctions IEEE 24-Bus RT DC power flow 14 supply buses 10 demand buses Postulated tltdcontingency sets Load fluctuation Transmission line outage Conclusion: A much larger α is needed for the FTR market clearing prices converge to the expected ex post FTR prices