Modified Benders Decomposition for Solving Transmission Investment Game With Risk Measure

This paper proposes a mathematical model for transmission investment game where there are several transmission planners (TPs). The model is developed assuming a simultaneous-move game between TPs. Each TP maximizes the total surplus (producers', consumers', and transmission surplus) minus the investment cost of its region given the investment decisions of rival TPs. The transmission investment risk is also considered using the probability-of-shortfall measure. We assume one market operator who dispatches the generators in all TP's regions. The risk-constrained Nash equilibria model is formulated as a mixed-integer linear program (MILP). To solve the proposed MILP, a solution algorithm is proposed that combines the standard branch-and-bound algorithm (BB) with a proposed modified benders decomposition algorithm (MBD). The proposed BB-MBD algorithm is also parallelized to improve the computation performance. To improve the coordination between TPs, a supporting budget mechanism is also mathematically modeled in the MILP. The numerical results are carried out using the 9-bus 3-area and the IEEE Three Area RTS-96 networks. The computational performance of proposed BB-MBD is compared with standard BB algorithm.