A probability model for the electricity price duration curve under an oligopoly market

In this paper, we propose a new formulation for the "price duration curve" (PDC) using probability considerations and provide a procedure for constructing it. This curve is expected to be useful in the long-term prediction of market prices and is similar in spirit to the load duration curve. It shows the proportion of time over a given time horizon during which the real-time market price of electricity is expected to exceed specified dollar amounts. The price over a long term is a stochastic quantity that depends on physical factors such as production cost, load, generation availability, unit commitment, and transmission constraints. It also depends on economic factors such as strategic bidding and load elasticity. We illustrate a procedure for constructing a stochastic system-based model for the PDC, taking into account the randomness associated with load and generator outages. The effects of unit commitment, transmission congestion, and transmission outages are not considered. We use two economic models. One is due to Bertrand and represents perfect competition. The other model is due to Rudkevich et al. who have given a closed-form expression for the market-clearing price in an oligopoly consisting of several identical firms.