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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.