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In this paper, two different approaches to analyzing firm-based market power considering transmission constraints are proposed. One is an application of the transmission-constrained residual demand Jacobian, while the other is a generalization of the “residual supply index” to the case of transmission constraints. These two approaches provide complementary evaluations of market power. Medium- and large-scale system examples are provided to demonstrate computational efficiency, and both approaches could be applied to real-world electricity markets.