A game theoretic approach to risk based optimal bidding strategies for electric vehicle aggregators in electricity markets with variable wind energy resources
This paper proposes a stochastic optimization model for optimal bidding strategies of electric vehicle (EV) aggregators in day ahead energy and ancillary services markets with variable wind energy. The forecast errors of EV fleet characteristics, hourly loads, and wind energy as well as random outages of generating units and transmission lines are considered as potential uncertainties, which are represented by scenarios in the Monte Carlo Simulation (MCS) The conditional value at risk (CVaR) index is utilized for measuring EV aggregators' risks caused by the uncertainties. The EV aggregator's optimal bidding strategy is formulated as a mathematical programming with equilibrium constraints (MPEC) in which the upper level problem is the aggregators' CVaR maximization while the lower level problem corresponds to the system operation cost minimization. The bi level problem is transformed into a single level mixed integer linear programming (MILP) problem using the prime dual formulation with linearized constraints. The progressive hedging algorithm (PHA) is utilized to solve the resulting single level MILP problem. A game theoretic approach is developed for analyzing the competition among the EV aggregators. Numerical cases are studied for a modified 6 bus system and the IEEE 118 bus system. The results show the validity of the proposed approach and the impact of the aggregator's bidding strategies on the stochastic electricity market operation.