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Abstract-Deregulated electricity markets use an auction mechanism to select offers and their power levels for energy and ancillary services. A settlement mechanism is then used to determine the payments resulting from the selected offers. Currently, most independent system operators (ISOs) in the United States use an auction mechanism that minimizes the total offer costs but determine payment costs using a settlement mechanism that pays uniform market clearing prices (MCPs) to all selected offers. Under this setup, the auction and settlement mechanisms are inconsistent since minimized costs are different from payment costs. Illustrative examples in the literature have shown that for a given set of offers, if an auction mechanism that directly minimizes the payment costs is used, then payment costs can be significantly reduced as compared to minimizing offer costs. This observation has led to discussions among stakeholders and policymakers in the electricity markets as to which of the two auction mechanisms is more appropriate for ISOs to use. While methods for minimizing offer costs abound, limited approaches for minimization of payment costs have been reported. This paper presents an effective method for directly minimizing payment costs. In view of the specific features of the problem including the nonseparability of its objective function, the discontinuity of offer curves, and the maximum term in defining MCPs, our key idea is to use augmented Lagrangian relaxation and to form and solve offer and MCP subproblems by using the surrogate optimization framework. Numerical testing results demonstrate that the method is effective, and the resulting payment costs are significantly lower than what are obtained by minimizing the offer costs for a given set of offers.Index Terms-Augmented Lagrangian relaxation, deregulated electricity markets, market clearing price (MCP), offer cost minimization, payment cost minimization, surrogate optimization.

In this paper, we provide mathematical formulations for the offer cost and MCP payment cost minimizations for optimal auctions in the ISO/RTO electricity market, and summarize the newly developed solution methodology using augmented Lagrangian relaxation and surrogate optimization for solving the optimal auction with the MCP payment objective function. Data has been used to test the method based on a simplified energy market, and for a given set of offers, the testing result demonstrates significant potential savings for electricity consumers if the MCP payment cost minimization is implemented in the ISO/RTO electricity markets. More importantly, this paper addresses economic implications of the objective function choice, including whether maximizing social welfare should be one of objectives of electricity industry deregulation. We conclude that an objective to maximize social welfare, even if it were determined to be desirable, is not achievable based on current bidding rules after moving from traditional vertically integrated utilities to a market approach, and is certainly not achieved by the offer cost minimization approach in use today.Other implications such as the inconsistency between the actual payment and the cost function minimized, and bidding behaviors are also discussed.Index Terms − Deregulated electricity markets, offer cost minimization, payment cost minimization, market clearing price, augmented Lagrangian relaxation, and surrogate optimization.1 Offer cost minimization of the CAISO is the same as the Pay-as-Bid cost minimization or Pay-as-Bid cost minimization. Pay-as-Offer is a new term for "Pay-as-Bid." This is consistent with Standard Market Design terminology under which bids are related to demand and offers to supply. He is interested in planning, scheduling, and coordination of design, manufacturing, supply chain; configuration and operation of building elevator and HVAC systems; schedule, auction, portfolio optimization, and load/price forecasting for power systems and decision-making under uncertain or distributed environments. He is a Fellow of IEEE,

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