  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.
