We consider stylized constrained optimization problems for reserve market design in a power flow setting whose objectives are formed either as a combination of a convex quadratic involving discrete variables, and a surrogate function or as a bilevel optimization problem. In the first case, the simulation measuring the expected energy not served (EENS) has variables that are the capacities of each energy bid, and the capacity requirements in each of a given set of zones. The EENS can be evaluated using a simulation that takes 2 hours to complete for each given vector of capacity requirements. We show how to build a surrogate of EENS for use in a mixed integer optimization. The results of interest from solution of the optimization are prices that are formed from gradients of the surrogate function. We report on computations that use a Moreau-Yoshida approximation to generate these gradients, the challenges of this solution approach, and outline some results for use in a specific market problem. We also consider an alternative model that uses bilevel optimization to capture the effects of trade-offs between energy and reserve capacities. Joint work with Olivier Huber (University of Wisconsin).
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