The Market Impacts of Convergence Bidding

Transcription

1 The Market Impacts of Convergence Bidding Frank A. Wolak Director, Program on Energy and Sustainable Development (PESD) and Professor, Department of Economics Stanford University March 7, 2014

2 Convergence Bidding in Multi-Settlement Markets Anticpated Benefit Reduce the frequency and magnitude of price differences between day-ahead and real-time Suppliers will have an incentive to schedule their expected real-time output in day-ahead market because E(P DA P RT ) = 0. Load-serving entities have an incentive to schedule real-time expected demand in day-ahead market Allows system operator to penalize generation unit owners and load-serving entities for under-scheduling

3 Convergence Bidding in Multi-Settlement Markets Systemwide Benefit Reduce the total operating costs of meeting demand in real-time Virtual bidders that correctly anticipate that more real-time demand or supply is needed than was scheduled in the day-ahead market at a given location in transmission network will profit from their virtual bids. Virtual bidders that incorrectly anticipate real-time system conditions will lose money from their virtual bids Creates incentive for more accurate day-ahead scheduling of real-time system operation Jha and Wolak (2013), Testing for Market Efficiency with Transactions Costs, paper this talk is based on, examines validity of these two hypothesis for California wholesale electricity market.

4 Trading and Forward and Spot in Commodity Markets In the presence of risk neutral traders, we expect that E t [pt+k S pf t,t+k ] = 0, where p S t+k = spot price at time t+k p F t,t+k = forward price at time t for delivery at time t + k E t (.) = expectation conditional on information available at time t All commodity markets have non-trivial trading costs that invalidate this relationship. Profitable trading implies that E t [pt+k,t+k S pf t,t+k ] > c, where c = round-trip cost associated with trading price differences across the two markets Jha and Wolak (2013) develops a methodology for measuring the implicit average per MWh cost associated with trading the day-ahead and real-time price differences

5 Trading Day-Ahead and Real-Time Price Differences before Explicit Virtual Bidding A supplier that thinks P DA < P RT will sell less than anticipated real-time production in day-ahead market and sell remaining output in real-time market Reduces supply in day-ahead market and increases supply in real-time market, which causes day-ahead price to rise and real-time price to fall A load-serving entity that thinks P DA > P RT will buy less than anticipated real-time consumption in day-ahead market and purchase remaining consumption in real-time market Reduces demand in day-ahead market and increases demand in real-time market, which causes day-ahead price to fall and real-time price to increase Implicit virtual bidding as these activities are called can create significant system reliability consequences and increase the costs of meeting system demand

6 What is Explicit Virtual or Convergence Bidding? Virtual bids are identified as such to ISO. Incremental (INC) virtual bid is a purely financial transaction that is treated just like an energy offer curve in the day-ahead market. Amount sold in day-ahead market must be purchased in the real-time market as a price-taker Profit from day-ahead sale of 1 MWh INC bid is P DA P RT Decremental (DEC) virtual bid is a purely financial transactions that is treated just like an demand bid curve in day-ahead market. Amount purchased in day-ahead market must be sold in real-time market as a price-taker. Profit from accepted 1 MWh DEC bid is P RT P DA Market participants can now use these products to take advantage of expected price differences, rather than take costly actions to change their physical schedules.

7 Why Should Explicit Virtual Bidding Reduce Trading Costs and Improve Price Convergence? Generation unit owners have limited range of MWh over which they can implicit virtual bid from minimum operating level to maximum operating level of generation unit. Can only implicit virtual bid where own generation units. Load-serving entities can only bid within range of expected demand level. Load serving entities can only submit physical demand bids for their entire service area. ISO allocates this aggregate demand bid curve to nodes in service territory of load-serving entity using load distribution factors Significant deviations from day-ahead schedules are assessed financial penalties for deviations, which increases the cost of implicit virtual bidding

8 Why Should Explicit Virtual Bidding Improve Market Performance? If all expected nodal price differences are zero, no reason to take costly actions to exploit them There are many low-variable cost, long-start units that may not be started in day-ahead market because of implicit virtual bidding on supply or demand side of market If long-start units are not turned on in day-ahead market they are unlikely to run in real-time More expensive short-start unit likely to have to operate instead and set a higher real-time price Can submit a DEC virtual bid to increase day-ahead demand and cause unit to be taken in day-ahead market Lower prices potentially set in both day-ahead and real-time markets because long-start unit operates Conclusion Besides reducing price differences between day-ahead and real-time market, EVB can reduce actual cost to serve system demand

9 Data Overview Use hourly prices from California s day-ahead and real-time markets from 4/1/ /31/2012. California switched to nodal pricing market on 4/1/2009 Analysis of prices at the Load Aggregation Point (LAP) level and nodal level. There are three large load-serving entities in California: Pacific Gas and Electric (PGE), Southern California Edison (SCE), and San Diego Gas and Electric (SDGE). They bid their demand in at the LAP level and pay the LAP price for their withdrawals The LAP price is calculated as a nodal load-weighted average of LMP s in each firm s service territory. All generation units are paid or pay their nodal price. Many more nodes (about 5,000) than generation units (about 400) in California. Summary Statistics

10 California s Load-Serving Entity Territories California's Electric Investor-Owned Utilities (IOUs) PacifiCorp PG&E Sierra Pacific Power Mountain Utilities PG&E SCE Bear Valley Electric SDG&E

11 The Location of California s Pricing Nodes Real-Time Dispatch [RTD] LMP Contour Map *Disclaimer: The data and prices provided on this page are preliminary and should not be relied upon for settlement or other purposes. The California ISO makes no representations or warranties regarding the correctness or veracity of the data and

12 Before Virtual Bidding Hour of Day After Virtual Bidding Before Virtual Bidding Hour of Day Before Virtual Bidding Hour of Day After Virtual Bidding After Virtual Bidding Average Hourly Price Differences: Before and After EVB 21:08 Saturday, April 6, CAISO Wholesale Electricity Day-Ahead - Real-Time Price Spread Time-weighted Means for PGE, By Hour of Day 21:08 Saturday, April 6, $/MwH CAISO Wholesale Electricity Day-Ahead - Real-Time Price Spread Time-weighted Means for SCE, By Hour of Day 21:08 Saturday, April 6, $/MwH $/MwH CAISO Wholesale Electricity Day-Ahead - Real-Time Price Spread Time-weighted Means for SDGE, By Hour of Day

13 Joint Null of Zero Expected Price Differences Table: Test Statistics for Joint Test of Zero Mean Price Differences Before EVB After EVB PG&E SCE SDG&E The upper α = 0.05 critical value for the χ 2 (24) distribution is Note that test statistics are smaller after explicit virtual bidding (EVB).

14 Motivation: The Trader s Problem with Transactions Costs Consider a trader that has access to 24 financial assets X (h) = P(h) RT P(h) DA for h = 1, 2,..., 24 with X = (X (1), X (2),..., X (24)) with mean vector µ and contemporaneous covariance matrix Λ. As mentioned previously, each asset is: Buy (sell) MWhs in hour h in the day-ahead market and sell (buy) back same number of MWhs in the real-time market. A profitable trading strategy exists if a trader can make a expected profits from trading these assets, after paying per-unit trading costs c Expected trading profits exist if a µ c 24 i=1 a i > 0 for some a R 24, subject to a normalization on the elements of a. Note that trading charge is assessed on absolute values of portfolio weights, a, because trader can buy or sell day-ahead price minus real-time price.

15 Test for the Existence of Profitable Trading Strategy Let X be the 24 x 1 vector of estimates of µ, estimated using N days of data. Let ˆΣ denote a consistent estimate of the variance of asymptotic distribution of N(X µ) calculated using Newey and West (1987) with lags up to 14 days. Three tests choose different portfolio weights a R 24 to maximize a µ c 24 i=1 a i subject to different restrictions on the elements of a. In all cases, hypothesis test is H : a µ > c versus K : a µ c for a that solves above maximization problem

16 Autocorrelation Across Days Before and After EVB Because day-ahead prices for following day are only known during the afternoon of current day, there can be unexploitable first-order autocorelation in vector of daily price differences Test for zero autocorrelation beyond first-order conditional on existence of non-zero first order autocorrelation Let Γ(τ) = E(X t µ)(x t τ µ) τ th order autocorrelation matrix Test joint null hypothesis H : Γ(2) = 0, Γ(3) = 0,..., Γ(L) = 0 Implement test as H : ξ vec(γ(2), Γ(3),..., Γ(L)) = 0 and compute estimate of asymptotic covariance of ˆξ using moving blocks bootstrap to allow for first-order autocorrelation in X t Test statistic is asymptotically distributed as chi-squared random variable with 24 2 (L 1) degrees of freedom

17 Multivariate Test for Autocorrelation Past First Lag for Daily Price Differences Table: Test Statistics for Autocorrelation (1 < L 10) in Daily Price Differences Before EVB After EVB PG&E SCE SDG&E The upper α = 0.05 critical value for the χ 2 (5184) for 5184 = distribution is

18 Zonal-Level Implied Trading Costs Before EVB After EVB PGE IU Test SCE SDGE PGE Square-Based Test SCE SDGE PGE Ellipsoidal Test SCE SDGE

19 Bootstrap Distribution of Implied Trading Costs: By LAP

20 Nodal-level White Noise Tests Table: Percentage of Tests that Fail to Reject (α = 0.05) Before EVB After EVB Non-Generation Node Generation Node Table: Sample Counts By Cell Before EVB After EVB Non-Generation Node 4,031 4,386 Generation Node

21 Regression Results Associated with Implied Trading Costs (1) (2) (3) Dep Var: Implied Trading Costs IU Square Ellipse Gen Node Indicator (0.241) (0.0745) (0.0230) Post EVB Indicator (0.164) (0.0388) (0.0102) Gen Node x Post EVB Indicator (0.345) (0.0888) (0.0276) Constant (0.110) (0.0313) ( ) Observations 9,780 9,780 9,773 R Heteroscedasticity-consistent standard errors in parentheses

22 Differences in Nodal Level Trading Cost Changes Between Generation Nodes and Non-Generation Nodes Average Implied Trading Costs falls for all nodes after introduction of explicit virtual bidding (EVB) Negative Coefficient on Post EVB Indicator Average Implied Trading Costs higher for non-generation nodes before EVB Gen Node Indicator Negative Average Implied Trading Costs at both types of nodes the same after EVB Gen Node x Post EVB Indicator positive and equal in absolute value to Gen Node Indicator Results consistent with higher cost to implicit virtual bid at load nodes before EVB and equal cost to virtual bid at all nodes (generation and non-generation) after EVB

23 P-values associated with the Absolute Difference Tests µ pre > µ post µ post > µ pre PGE SCE SDGE Results consistent with null hypothesis that trading profits fell after implementation of EVB.

24 Second Moment Implications of Explicit Convergence Bidding Virtual bidders are expected to reduce day-ahead uncertaintly about differences between day-ahead and real-time prices, as well as uncertainty in real-time prices Formally, the hypothesis test is H : Λ pre Λ post 0, the difference between pre-evb convariance matrix and post-evb covariance matrix is a positive semi-definite matrix Test is implemented as nonlinear multivariate inequality constraints test (described earlier) with null hypothesis that all 24 eigenvalues of Λ pre Λ post are greater than or equal to zero Compute estimate of asymptotic covariance matrix of eigenvalues of ˆΛ pre ˆΛ post using moving blocks boostrap that accounts for potential autocorrelation in vector of daily prices

25 P-values associated with Volatility Tests Price Difference Real-Time Price Pre - Post Post - Pre Do not reject null hypothesis that all 24 eigenvalues of Λ pre Λ post are greater than or equal to zero Consistent with EVB reducing price volatility

26 Overview In this section, we examine the effect of the introduction of EVB on three measures of market performance: TOTAL VC(t): is the total variable cost of all natural gas-fired generation units (240 of them) in hour t. TOTAL ENERGY (t): the total amount of energy consumed in hour t by natural gas-fired generation units. STARTS(t): total number of generation units started in an hour t. Controlling nonparametrically for thermal generation, intermittent generation, and natural gas prices, we find that the conditional means of STARTS(t) is higher after the introduction on EVB, while the conditional means of TOTAL ENERGY (t) and TOTAL VC(t) are lower after the introduction of EVB.

27 Notation and Setup Let y t = W t α + X tβ + θ(z t ) + ɛ t, with E(ɛ t X t, W t, Z t ) = 0, where θ(z) is an unknown function of the vector Z. We consider three specifications, based on different dependent variables y t : Dependent variable y t is one of our three market efficiency measures: ln(total VC(t)), ln(total ENERGY (t)), or STARTS(t). Non-parametric controls Zt include total output from natural gas-fired generation units, the total output from all wind and solar generation units, and delivered natural gas prices in both Northern and Southern California. Wt includes hour-of-day and month-of-year fixed effects. We consider specifications both with Xt as a single indicator which is one if hour of sample t is after the introduction of EVB in 2/1/2011 and X t as a (24x1) vector with k th element X tk, which equals one if hour t is after 2/1/2011.

28 Semiparametric Coefficient Results Dependent variable ln(total ENERGY (t)) STARTS(t) β Standard error Dependent variable ln(total VC(t)) β Standard error Implied total annual variable cost savings of approximately $70 million and total annual CO 2 emissions reduction of 600,000 Tons.

29 Hour (Post) Point Estimate Upper Bound Lower Bound Hour (Post) Point Estimate Upper Bound Lower Bound Hour (Post) Point Estimate Upper Bound Lower Bound Hour-of-the-Day Percent Change Estimates 21:08 Saturday, April 6, Hour-of-the-Day Change Estimates for Hourly Total Energy With 95% Pointwise Confidence Intervals 21:08 Saturday, April 6, Coefficient Values Hour-of-the-Day Change Estimates for Hourly Total Starts With 95% Pointwise Confidence Intervals Coefficient Values 21:08 Saturday, April 6, Coefficient Values Hour-of-the-Day Change Estimates for Hourly Total Variable Costs With 95% Pointwise Confidence Intervals

30 Conclusions We derive three equivalence hypothesis tests for the existence of a profitable trading strategy between futures and real-time prices, potentially applicable to wide range of commodity markets. For all three procedures, implied trading costs decrease after EVB. Find this same result at nodal level. Find evidence consistent with hypothesis that trading profits fell after the introduction of EVB Find evidence that explicit virtual bidding reduced volatility in price differences and real-time prices. Evidence of economically sizeable market efficiency gains and environmental benefits from EVB

31 Questions or Comments? Related Papers at

32 Summary Statistics by Service Area and EVB Before EVB After EVB Area Variable Mean Std. Dev Mean Std. Dev DA Price PGE RT Price Price Diff HA Price SCE RT Price Price Diff HA Price SDGE RT Price Price Diff Back

33 Sketch of the IU Hypothesis Test Derivation Consider the one dimensional Null: µ > versus µ <. We know how to test the Null hypotheses µ < and µ >. The claim is that intersecting two size α tests of the above Null hypotheses (µ <, µ > ) gives us an asymptotic level α test for Null: µ >. The proof is an application of Berger (1982), but the intuition is that each of the one-sided tests The extension to the multivariate case is fairly trivial given this machinery. Back

34 Sketch of the Square-Based Hypothesis Test Derivation We begin with the assumption that N(X µ) d N(0, Σ). We apply Delta s Method: N(X sign(x ) µ sign(x )) d N(0, sign(x ) Σsign(X )). We let Nµ = λ in order to say that N(X ) d N( λ, V ), where V = sign(x ) Σsign(X ). This requires the technical assumption that the data generating process is quadratic mean differentiable (qmd). We then impose that we are at the least favorable place in our Null to get the needed test statistic: µ i = c for all i. Of course, we also have N µ i = Nc for all i. Back

35 Sketch of the Ellipsoidal Hypothesis Test Derivation We begin with the assumption that N(X µ) d N(0, Σ). We let Nµ = λ in order to say that NX d N(λ, Σ). This requires the technical assumption that the data generating process is quadratic mean differentiable (qmd). From there, NX Σ 1 X d χ 2 24 (λ Σ 1 λ). We can then impose that we are on the boundary of our Null ( least favorable ): µ Σ 1 µ = 24 i=1 Σ 1 µ. Of course, µ Σ 1 µ = λ Σ 1 λ Back