Gaussian Process-based Approach for Bilevel Optimization in the Power System -- A Critical Load Restoration Case

Bilevel optimization problems can be used to represent the collaborative interaction between a power system and grid-connected entities, called the followers, such as data centers. Most existing approaches assume that such followers' response behaviors are made available to the power system in the operation decision-making, which may be untenable in reality. This work presents a novel idea of solving bilevel optimization problems without assuming power systems' omniscience. The followers' responses will be represented by a function of the power system's decisions using Gaussian Process Regression. Then the two layers in the bilevel problem can be solved separately by the power system and its followers. This not only avoids the omniscience assumption, but also significantly increases the computational efficiency without compromising accuracy, especially for the problems with a complex lower layer. Moreover, a bilevel critical load restoration model is developed to test the proposed technique. Compared to the conventional methods, the proposed restoration model considers the load-side operation and the varying load marginal value, and can accurately estimate load-side loss and achieve better restoration solutions. Two case studies validate the advantages of the proposed approaches from different perspectives.