Modeling Time of Use Pricing for Load Aggregators Using New Mathematical Programming with Equality Constraints

Demand Response (DR) and Time of Use (TOU) pricing for retail electricity market is the key to reduce total system costs in smart grids. In this paper, a bi-level optimization model for the time of use pricing problem is presented. The interactions between electricity Load Aggregators (LAs) and end-users in the smart grid is applied to obtain optimal TOU in the retail market. For the LAs, there is a revenue maximization problem (upper level), and for end-users there is a cost minimization problem (lower level). The proposed method defines a novel concept of the Retail Market Clearing Price (RMCP) by modeling DR at the lower level. It is proven that at the demand side, there is a unique marginal cost price, which will fulfill the end-user cost minimization problem. The proposed algorithm defines adequate TOU mechanism by presenting mathematical model of end-users response to electricity prices. To solve the lower level problem, a new Mixed Integer Linear Programming (MILP) problem is presented, which uses the Karush-Kuhn-Tucker (KKT) conditions and Mathematical Programming with Equality Constraints (MPEC). To validate the proposed model, three different competitive LAs were considered.