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.