Solving Bilevel Optimal Bidding Problems Using Deep Convolutional Neural Networks

Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this article, we address power system problems of bilevel structure, commonly arising after the deregulation of the power industry. Such problems are predominantly solved by converting the lower level problem into a set of equivalent constraints using the Karush-Kuhn-Tucker optimality conditions at an expense of binary variables. Furthermore, in case the lower level problem is nonconvex, the strong duality does not hold rendering the single-level reduction techniques inapplicable. To overcome this, we propose an effective numerical scheme based on bypassing the lower level completely using an approximation function that replicates the relevant lower level effect on the upper level. The approximation function is constructed by training a deep convolutional neural network. The numerical procedure is run iteratively to enhance the accuracy. As a case study, the proposed method is applied to a price-maker energy storage optimal bidding problem that considers an ac power flow-based market clearing in the lower level. The results indicate that greater actual profits are achieved as compared to the less accurate dc market representation.