Impact of virtual bidding on financial and economic efficiency of 1 wholesale electricity markets

4 Virtual bidding is a financial mechanism that allows participants to speculate on the price spread 5 between day-ahead and real-time wholesale electricity markets. We employ statistical learning methods 6 to show that virtual bidding improves financial efficiency by narrowing the room for arbitrage. We 7 then formulate a two-settlement market model and use it to analyze market data. We find that virtual 8 bidding improves economic efficiency by reducing the system generation cost. Notwithstanding the 9 empirical evidence of its effectiveness, virtual bidding has not fully eliminated market inefficiency, and 10 we propose strategies that extract profits beyond those of the actual virtual bids. Lastly, we conduct 11 a game-theoretic analysis based on the two-settlement model to develop the theory of virtual bidding. 12 The analysis leads to the interpretation of spread as a measure of the average forecast accuracy of the 13 market participants, and implies that introducing more qualified virtual bidders into the market can 14 improve market efficiency. 15 The restructured electricity markets in the United States feature a two-settlement system at the whole16 sale level, consisting of a day-ahead (DA) forward market and a real-time (RT) spot market. Systematic 17 nonzero spreads, defined as the differences between DA locational marginal prices (LMPs) and RT LMPs, 18 are routinely observed, and signify market inefficiency. Virtual bidding was introduced as a financial 19 mechanism to allow market participants including outside financial entities to speculate on the spread, 20 without physically consuming or producing power. While the statistics of spreads across different regional 21 markets and over different time horizons has been studied [1–11], the impact of virtual bidding on market 22 efficiency has not been explored until recently. It is acknowledged that virtual bidding has improved price 23 convergence [12]. A statistical framework is developed in [13] to test the existence of profitable bidding 24 strategies. In [14], a hidden Markov model is proposed to characterize the stochastic process of the spread 25 and to solve for optimal bidding strategies. 26 The aforementioned work focuses on price convergence, which we refer to as financial efficiency. Fol27 lowing a statistical learning approach, we propose a couple of measures that test the financial efficiency 28 of the market, before and after the implementation of virtual bidding, and we design bidding strategies 29 that outperform the actual virtual bids. Thus our findings agree with prior work that virtual bidding 30 has reduced but not eliminated arbitrage opportunities. More fundamentally, we investigate the impact 31 of virtual bidding on economic efficiency, which refers to generation cost minimization. To that end, we 32 Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA. Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA. e-mail: tangwenyuan@berkeley.edu 1 formulate a two-settlement market model that captures the flexibility of generation, and addresses various 33 phenomena observed from market data, in contrast with existing models [15–17]. Our proposed model 34 provides a theoretical framework for understanding the interactions between DA and RT markets, and 35 suggests a methodology for estimating the system generation cost. We then provide empirical evidence 36 of the effectiveness of virtual bidding. Lastly, we conduct a game-theoretic analysis based on the two37 settlement model, and develop the theory of virtual bidding. Our study interprets the spread as a measure 38 of the average forecast accuracy of the market participants, and implies that introducing more qualified 39 virtual bidders into the market can improve market efficiency. 40 Exploring market data 41 Our work is based on market data from the California independent system operator (CAISO) and PJM 42 Interconnection (PJM). CAISO implemented the DA market in April 2009, and the virtual bidding mech43 anism in February 2011. This allows us to compare price performance before and after the implementation 44 of virtual bidding. In particular we use the DA and RT LMPs at the CAISO NP15 trading hub for 2010 45 and 2012. PJM implemented the DA market and the virtual bidding mechanism concurrently in June 46 2000. We use PJM regional level data from the years 2012–2015, including DA and RT LMPs, DA and RT 47 load, forecast load, and virtual bids. The additional data from PJM allows more sophisticated statistical 48 analysis. 49 Summary statistics of DA and RT LMPs are shown in Fig. 1. While the DA and RT LMPs are very 50 close on average, the standard deviation of the RT LMP is considerably larger than that of the DA LMP, 51 indicating higher volatility in the RT market. Fig. 2a plots the time series of the spread for an off-peak 52 hour (3–4 AM) and an on-peak hour (5–6 PM). The spread is large positive when the price spike occurs 53 in the DA market, and large negative when the price spike occurs in the RT market. The distribution 54 of the spread is shown in Fig. 2b. While the mean is close to zero, the distribution is heavy-tailed. It 55 is also left-skewed, since price spikes are more likely to occur in the RT market than in the DA market. 56 In general, the spread is difficult to forecast, and the characterization of its statistics is challenging. For 57 example, it can be shown that the recent data from PJM does not support the classic Bessembinder and 58 Lemmon model [15], which states that the spread is negatively related to the variance of the RT LMP, and 59 positively related to the skewness of the RT LMP. 60 There are two types of virtual bids: incremental (INC) bids and decremental (DEC) bids. An INC 61 bid is submitted as a supply bid in the DA market. It opens a short position in the DA market, with the 62 obligation to be closed out in the RT market. The holder is paid the DA LMP and pays the RT LMP per 63 cleared MWh. On the other hand, a DEC bid is submitted as a demand bid in the DA market. It opens a 64 long position in the DA market, with the obligation to be closed out in the RT market. The holder pays 65 the DA LMP and is paid the RT LMP per cleared MWh. Given the virtual bids and the LMPs, we obtain 66 the cleared INC and DEC volumes, and then the net INC volumes as their difference. When the net INC 67 volume and the spread have the same sign, the virtual bids make a net profit on aggregate, as shown in 68 Fig. 3. The net INC volume is predominantly negative, which suggests that the virtual bidders speculate 69 on negative spreads most of the time. The reason for this may be the left-skewness of the distribution of 70 the spread: when the spread is large in magnitude, it is more likely to be negative than positive. 71 To take a closer look at the profit pattern of the virtual bids, we divide the 8760 hours in a year (or 72