A cooperative game theory-based approach to formulation of distributed slack buses

Abstract

The conventional power flow formulation is based on a single slack bus model, which may not necessarily provide accurate values for minimum generation cost and minimum power losses. On the other hand, distributed slack buses, which are used to distribute the slack power (power mismatch) among different voltage-controlled buses, can overcome this problem. A cooperative game theory-based approach is proposed in this paper to calculate active power participation factors to distribute slack active power among different participating generators. In the first stage, the worth (or value) of individual participating generators and their coalitions are computed. In the second stage, the Shapley value, which is one of the solution concepts of cooperative game theory, is used to calculate the participation factors of individual participating generators. The participation factors are then used to distribute the mismatch power among different generators. The effectiveness of the proposed approach is demonstrated through case studies on the IEEE 14-bus, IEEE 30-bus, and IEEE 57-bus systems. The results show that the cost of generation and power losses are reduced in case of systems with distributed slack buses compared to that with a single slack bus.