Smart dispatch of controllable loads with high penetration of renewables

This paper presents a bi-level aggregator-utility optimization model to schedule an energy consumption pattern of controllable loads in a power system with a high penetration of renewables. The upper level is an aggregator's problem which aims to minimize the electricity payment by managing the energy consumption of three types of controllable loads. On the other hand, the lower level is a utility's problem which is assumed to be a follower. The utility's problem is a market-clearing model which provides a spot price to the aggregator's problem. We derive the Karush-Kuhn-Tucker (KKT) optimality conditions of the lower-level utility's problem as the equilibrium constraint in the upper-level aggregator's problem. Therefore, the bi-level formulation is converted into a form of mathematical program with equilibrium constraints (MPECs) which can be solved analytically. A numerical example is conducted to demonstrate the performance of the proposed model.