Risk‐constrained expansion planning of wind integrated networks using innovative MPEC primal‐dual formulation for directly involving price‐based demand response in MILP problem

Abstract Price‐based demand response (PBDR) programs can push consumers to reconsider their electricity demand regarding the electricity price in the market. The load profile of the whole network can be reshaped in response, which can directly affect the network investment decisions. The decision‐maker had to consider this effect in order to reach an optimal plan for the network. Here, a mixed‐integer linear programming (MILP) model considering a price‐based demand response (PBDR) program is developed for transmission expansion planning (TEP) of wind‐integrated networks and the problem is constrained by the conditional value at risk (CVaR) measure to model the risk of planning and investments for both sides. The proposed model is an originally bi‐level problem with different objective functions in both layers. These objectives are as follows, minimizing the total cost of TEP, consumer payments, and wind curtailment in the first layer, and minimizing the network operational costs in the second layer. Then, using an innovative formulation to overcome the non‐linearities, and using KKT conditions of the second layer problem, the problem recast into a single‐layer mixed integer non‐linear program (MINLP) problem which is called a mathematical program with equilibrium constraints (MPEC) with primal‐dual formulation. The proposed model had been applied to IEEE standard 24‐bus RTS and IEEE standard 118‐bus test systems to show its efficiency.