Learning From Past Bids to Participate Strategically in Day-Ahead Electricity Markets

Abstract

We consider the process of bidding by electricity suppliers in a dayahead market context where each supplier bids a linear non-decreasing function of her generating capacity with the goal of maximizing her individual profit given other competing suppliers' bids. Based on the submitted bids, the market operator schedules suppliers to meet demand during each hour and determines hourly market clearing prices. Eventually, this game-theoretic process reaches a Nash equilibrium when no supplier is motivated to modify her bid. However, solving the individual profit maximization problem requires information of rivals' bids, which are typically not available. To address this issue, we develop an inverse optimization approach for estimating rivals' production cost functions given historical market clearing prices and production levels. We then use these functions to bid strategically and compute Nash equilibrium bids. We present numerical experiments illustrating our methodology, showing good agreement between bids based on the estimated production cost functions with the bids based on the true cost functions. We discuss an extension of our approach that takes into account network congestion resulting in locationdependent prices.

Inverse optimization for the recovery of constraint parameters

“…Similarly, a bidder may seek to impute several unknown parameters which can be used in the process of deciding her bid. These parameters include cost coefficients of rivals' models (Chen et al, 2019); rival bids, which are objective function coefficients in the facilitator's problem (Ruiz et al, 2013); and parameters that describe the routing of energy through the network and the capacity of transmission lines, which are left-hand-side constraint parameters in the facilitator's problem (Birge et al, 2017).…”

Inverse Equilibrium Analysis of Oligopolistic Electricity Markets

“…If an inverse model is a good fit to the data, we can insert the fitted parameters in the original problem to obtain good predictive power [3]. Although this is a nice feature, we limit this paper to only consider formulating and solving inverse equilibrium problems, and refer the interested reader to [10] and [20] that use inverse optimization for prediction.…”

“…Applications include the investigation of price response of consumers [5], [6], estimation of offer prices from rival producers [7], and investigation of the parameters of transmission constraints in electricity markets based on locational marginal prices [8]. Relevant work on inverse equilibrium models include [9] and [10], which use the variational inequality approach of [3] to estimate bid curves of competing firms that employ strategic bidding.…”

“…The inverse demand function (9) sets the price λ i at a particular bus i ∈ N , where N is the set of nodes, with respect to total quantity q i , slope a i and intercept b i . Equation (10) denotes the linear marginal cost for a producer p, where x p is its generation.…”

Simulation of day-ahead electricity market prices using a statistically calibrated structural model

“…In addition, we use a scarcity factor similar to [5] in order to account for strategic bidding. Complementary approaches to infer aggregated supply curves [6] and electricity suppliers' cost functions [7] have also been proposed recently.…”