Implications of cost and bid format on electricity market studies: linear versus quadratic costs

One important assumption in a model of an electricity market is the format of bids and costs. Most literature on electricity markets uses piecewise linear or quadratic functions to represent cost and bid. Economic theory holds that a firm in a perfectly competitive market maximizes its profit when it sells at marginal cost. This implies that profit-maximizing generators bid at marginal cost. Different markets have varying rules regarding bid formats. Piecewise linear bid curves are compatible with physical characteristics of electricity generators, but cause difficulties in certain analysis techniques. Quadratic bid curves provide smooth dispatch, revenue, and profit curves that facilitate calculus-based analysis. In profit calculations, bids and marginal costs may either be coupled or independent of each other. The relation between bids and marginal costs impacts the profit-maximizing bid, and thus impacts generator strategies. These assumptions arc particularly important for marginal generators, since different bid structures may yield different dispatch results, especially if the system is constrained. We compare markets with all piecewise linear bids, all quadratic bids, and a mixture of bids, and study the impacts of bid format and profit calculation on market outcomes in different scenarios.