Abstract
Each market agent (producer or consumer) in a power market pursues its own objective, typically to maximize its own profit. As such, the specific behavior of each agent in the market is conveniently formulated as a bi-level optimization problem whose upper-level problem represents the profit seeking behavior of the agent and whose lower-level problem represents the clearing of the market. The objective function and the constraints of this bi-level problem depend on the agent’s own decision variables and on those of other agents as well. Understanding the outcomes of the market requires considering and solving jointly the interrelated bi-level problems of all market agents, which is beyond the purview of optimization. Solving jointly a set of bi-level (or single-level) optimization problems that are interrelated is the purview of complementarity. In this paper and in the context of power markets, we review complementarity using a tutorial approach.
Highlights
W E DESCRIBE in this paper a number of mathematical models to represent the behavior of the agents of a power market, namely, producers, consumers and market operator
Each producer seeks to maximize its owns profit by submitting to the market operator a strategic offer consisting of prices and quantities
To identify its strategic offer, the producer solves a bi-level optimization problem whose upper-level problem represents its profit seeking behavior and whose lower-level problem represents the clearing of the market
Summary
W E DESCRIBE in this paper a number of mathematical models to represent the behavior of the agents of a power market, namely, producers, consumers and market operator. To identify its strategic offer, the producer solves a bi-level optimization problem whose upper-level problem represents its profit seeking behavior and whose lower-level problem represents the clearing of the market. To identify its strategic bid, the consumer solves a bi-level optimization problem whose upper-level problem represents its profit seeking behavior and whose lower-level problem represents the clearing of the market. The upper-level problem of this bi-level problem represents the profit seeking behavior of the agent, while the lower-level problem (inner box of the lower box of Fig. 2) represents the clearing of the market. Offering/bidding strategy (to be transferred to the lower-level problem), while the lower-level problem provides the market clearing price (as a dual variable) needed to compute the agent’s profit at the upper-level problem. Appendix A reviews the Karush-Kuhn-Tucker optimality conditions and Appendix B the diagonalization algorithm
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