Transmission-Constrained Inverse Residual Demand Jacobian Matrix in Electricity Markets

A generation firm in an electricity market may own multiple generators located at multiple locations. This paper generalizes the concept of transmission-constrained residual demand from a single generator´s perspective to that of a generation firm. We calculate the derivative of a generation firm´s inverse residual demand function, i.e., the Jacobian matrix, based on a multi-parameter sensitivity analysis of the optimal power flow solution, and characterize some of its properties. This Jacobian matrix provides valuable information, such as in characterizing a generation firm´s profit maximizing strategy. We apply the bundle-Newton method utilizing the Jacobian matrix to find a generation firm´s maximum profit. The effectiveness and performance of the algorithm is demonstrated with the IEEE 118-bus system example. The Jacobian matrix and the profit maximizing algorithm are helpful for market participants to bid into electricity markets, and for market monitors to analyze firm-based strategic behaviors.