Spatially-Explicit Prediction of Wholesale Electricity Prices

Transcription

1 Spatially-Explicit Prediction of Wholesale Electricity Prices J. Wesley Burnett and Xueting Zhao Intern l Assoc for Energy Economics, NYC 2014 West Virginia University Wednesday, June 18, 2014

2 Outline Motivation 1 Motivation

3 Problem Statement Transmission constraints lead to interaction effects Wholesale electricity markets We use this spatial information to better predict spot prices

4 Restructuring of the Electricity Industry Concerns over non-competitive behavior led to significant restructuring PURPA (1978) Public Utility Regulatory Policies Act Utilities to buy power from independent producers

5 Regulatory Reform Energy Policy Act (1992) Federal Energy Regulatory Commission (1996) Orders 888 and 889 Regulatory acts designed to encourage competition

6 Deregulation and Restructuring Many states began to deregulate Restructuring differs by state In these markets electricity has become commoditized Transmission and distribution is regulated, generation is not Independent system operators (ISOs) or regional transmission organizations (RTOs) manage market activity

7 Status of Restructuring by State

8 Peculiar Properties of Electricity Markets Unlike other commodities, electricity is non-storable Generation and demand must be matched on a minute-by-minute basis The RTO s role is to balance the system Supply and demand are balanced through day-ahead and hour-ahead markets

9 Market Operations Generator submits a bid to the RTO Prices vary over a node zone, or multiple nodes RTO select the lowest bids by hour-of-day to match supply with projected demand

10 Transmission System Node Grid Zone Bus

11 Challenge to RTOs Challenge to RTO is balance supply with demand Balance is subject to the physical limits within the system Transmission system only allows so much thermal constraints

12 Spatial Patterns in Restructured Markets Electricity markets provide the framework for constantly changing spatial patterns of pricing Theoretical price at each node will reflect the shadow price of the constrained amount of power Locational marginal pricing (LMP) or nodal pricing

13 Spatial Panel Data Econometrics Latest spatial panel data models to forecast spot prices PJM is a RTO that coordinates the movement of wholesale electricity in all or parts of 13 states Douglas and Popova (2011) did a similar analysis of wholesale electricity prices in the PJM

14 Zones within the PJM Interconnect

15 Criticisms Motivation Some specifications of spatial econometrics has come under criticism recently It is hard to separate out the effects of what causes prices to fluctuate locally versus what causes prices to fluctuate in neighboring regions

16 Alternative Validation Strategy We agree that there are potential problems of endogeneity So rather than appealing to causality, we focus primarily on an alternative validation strategy of prediction In other words, we take the spatial panel models as a black box

17 Looking Ahead Motivation We find spatial panel data models outperform non-spatial models in terms of out-of-sample forecasts Dynamic, spatial panel data model provide the best out-of-sample predictions among all models Forecasting prices is useful for market participants as well as market operators Spatial panel data forecasting is a useful decision-making support tool for estimating nodal prices Market participants can use such models for strategy improvement

18 Past Literature Motivation Previous Analysis Abstracted away from details within the transmission system Given more detailed examinations of the transmission system We provide a simple theoretical model We use the theoretical model to help motivate the empirical model

19 Network of Zonal Market Prices and Shadow Prices Figure: Source: Li, Liu, and Salazar (2006)

20 Engineering Model Subject to, z l = N 1 i=1 z = Hy h li y i z l z l z l, l z l Hy z l.

21 Economic Model Motivation Cost minimization subject to two constraints: min C i (y i ) yi i Subject to, Hy z, yi = 0. (Second constraint is Kirchoff s Current Law total charge flowing into a node must be equal to the total charge flowing out.)

22 Linear Optimization FOCs: L = i ( ) C i (y i ) p y i λ l C / i (y i ) = p + i ( N 1 i=1 h li y i z l ) M λ l h li, i = 1,..., N 1, (1) l=1 C / 1 (y 1) = p (swing bus). (2),

23 Interpretation Motivation p optimal nodal spot price λ l shadow price...optimal spot price at a node is the average of the prices at all other nodes (Bushnell and Stoft, 1996) Thus, we use a spatial weighting matrix as a proxy for the system constraints

24 Motivation In replacement of the transfer admittance matrix, we use a spatial weighting matrix as a proxy to represent the spatial location of each node within the system: w i,j = W i j i indicates a geographic point of injection into the system j indicates a neighboring point of injection

25 Data Motivation Consists of PJM s real-time market, which is a spot market for current LMPs (nodal prices) PJM provides hourly aggregated valued Historical values are listed hourly by zone Day-ahead prices We examine data for 18 zones with the PJM

26 Econometric Models Standard panel data model: p it = βx it + µ i + η t + ε it Spatial panel data model (SAR): N p it = ρ w i,j p jt + βx it + ε it, ε it N(0, σ 2 ) j=1

27 Dynamic, Spatial Panel Data Model N N p it = ρ w ij p jt + γp j,t 1 + λ w ij p j,t 1 + βx it + µ i + η t + ε it j=1 n=1

28 Within-Sample Regression Results

29 Highlights Motivation We find consistent evidence of statistically significant spatial autocorrelation Suggests spillovers in prices Implies that the spatial models may control for transmission constraints

30 Out-of-Sample Forecasting Metrics MAE = MAPE = RMSE = T N t=1 i=1 T N t=1 i=1 { T 1 N T 1 N T N t=1 i=1 F(t) A(t), 1 N T F(t) A(t) A(t), [F(t) A(t)]2 } 1/2

31 Theil s U Statistic (Scale Free Metric) U = { T N t=1 i=1 1 N T [F(t) A(t)]2} 1/2 { T } 1/2 { N t=1 i=1 1 T } 1/2 N T F(t)2 + N t=1 i=1 1 N T A(t)2 Previous metrics measure the fit of the predictive models Theil U measures how well the models perform against naïve models, such as random walk Statistic is similar to the measure of R 2

32 Forecasting Error Performance

33 Highlights Motivation Dynamic, spatial panel data model provides the best forecast For one day forecasts, DSPD and POLS model perform similarly DSPD outperforms POLS for a majority of one-day-ahead forecasts DSPD provides superior seven-day-ahead and thirty-day-ahead forecasts

34 Implications Motivation We exploited the geographic nature of PJM to better predict spot prices Zonal prices display spatial autocorrelation We used the spatial econometric model as a proxy Market operators can use spatial econometric models Trading strategies may be improved

35 Questions? Motivation Thank you.