Modified penalty function method for optimal social welfare of electric power supply chain with transmission constraints

• Present a modified supply chain model with transmission limits for optimal social welfare (OSW).
• The OSW is then formulated as a variational inequality problem (VIP).
• Present modified penalty function (MPF) method to compete with extragradient (EG) method for VIP.
• Comparisons show MPF is much more effective to solve OSW than QP-based EG method.
• MPF is at least 3 times faster than QP-based EG method for 57-, 118-, 300-bus test systems.

Many power system application problems utilize optimal social welfare model as a decision-making tool. In this paper, we tackle the optimal social welfare problem based on a mathematic modeling framework capable to capture the interactions among decision-makers in an electric power supply chain network with consideration of transmission power flows and constraints which are neglected in previous literature, and present a generalized electric power supply chain network equilibrium model. In this model, each player tries to maximize its own profit and competes with others in a noncooperative manner. The Nash equilibrium conditions of these players form a finite-dimensional variational inequality problem (VIP). A modified penalty function (MPF) method is then used to replace conventional extragradient method for solving VIP by transforming VIP into a nonlinear programming problem. Numerical tests are conducted to demonstrate the effectiveness of the MPF for solving the VIP-based social welfare maximization model in the context of an electric power supply chain network.