Exploring Market Properties of Policy-based Reserve Procurement for Power Systems

Abstract

This paper proposes a market mechanism for co-optimization of energy and reserve procurement in dayahead electricity markets with high shares of renewable energy. The single-stage chance-constrained day-ahead market clearing problem takes uncertain wind in-feed into account, resulting in optimal day-ahead dispatch schedule and an affine participation policy for generators for the real-time reserve provision. Under certain assumptions, the chance-constrained market clearing is reformulated as a convex quadratic program. Using tools from equilibrium modeling and variational inequalities, we explore the existence and uniqueness of a Nash equilibrium. Under the assumption of perfect competition in the market, we evaluate the satisfaction of desirable market properties, namely cost recovery, revenue adequacy, market efficiency, and incentive compatibility. To illustrate the effectiveness of the proposed market clearing, it is benchmarked against a deterministic cooptimization of energy and reserve procurement. Biased and unbiased out-of-sample simulation results for a power systems test case highlight that the proposed market clearing results in lower expected system operations cost than the deterministic benchmark, without the loss of any desirable market properties.

An equivalent mathematical program for games with random constraints

“…The first term of the payoff function of player i is linear in ith player's strategies for a fixed strategy profile of rest of the players and the second term only depends on the strategies of player i and is quadratic in nature. Such a payoff function appears in various applications, e.g., it represents the mean-variance model in portfolio optimization [11,26,27] and in electricity market the second term can be the production cost [19] and the first term represents the payoff received due to the interaction among all the players.…”

“…The games considered in these papers are deterministic in nature, i.e., the players' strategy Email addresses: vikassingh@iitd.ac.in (Vikas Vikram Singh), abdel.lisser@l2s.centralesupelec.fr (Abdel Lisser), monika@iiitd.ac.in (Monika Arora) sets and payoff functions are defined using real valued functions. However, in practical situations the decision making process usually faces various types of uncertainties due to which payoff functions or strategy sets are modeled using random variables [7,17,19]. The expected value approach is used to model the uncertainties when the decision makers are risk neutral [20].…”

“…The first term of a player's payoff function is multi-linear in all the players strategies and second term is a quadratic concave function of the player's strategies. Such types of payoff functions are often encountered in practical situations [11,19,26,27]. We propose an equivalent mathematical program for this class of games and show the one-to-one correspondence between a Nash equilibrium of the game and a global maximizer of the mathematical program.…”

Inertia Pricing in Stochastic Electricity Markets

“…High price volatility caused by stochastic RES injections and market uncertainty, see [6], has raised the interest of the academic community in electricity pricing under uncertainty. The work in [7]- [10] showed that wholesale electricity market designs can efficiently internalize the uncertainty of renewable generation resources and the reliability requirements of the system operator in the price formation process using chance constraints. In contrast to previously proposed scenario-based stochastic electricity market approaches, see, e.g., [11]- [14], chance-constrained market clearing avoids issues related to computational tractability, transparency, and per-scenario trade-offs and provides insights into commitment, energy and reserve pricing [8].…”

“…In contrast to previously proposed scenario-based stochastic electricity market approaches, see, e.g., [11]- [14], chance-constrained market clearing avoids issues related to computational tractability, transparency, and per-scenario trade-offs and provides insights into commitment, energy and reserve pricing [8]. However, the approaches in [7]- [10] do not consider inertia services and requirements, which are important for RES-rich power systems because of their influence on commitment and dispatch decisions and, thus, on the resulting prices [15].…”