Transmission-Constrained Residual Demand Derivative In Electricity Markets

The residual demand derivative plays a central role in constructing the best response to competitors' strategies in widely used strategic models such as the Cournot model and the supply function model. In the absence of transportation or transmission constraints, the residual demand derivative is obtained straightforwardly by taking the derivative of the residual demand function with respect to price. However, in an electricity market, the market is embedded in a transmission network. When there is no transmission congestion, the residual demand derivative can be calculated as usual, but when there is transmission congestion, the residual demand derivative is more difficult to calculate.