  Current state-of-the-art solution techniques for solving bilevel optimization
problems either assume strong problem regularity criteria or are
computationally intractable. In this paper 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.
