Valuation and optimal operation of electric power plants in competitive markets

We present an algorithm for the valuation and optimal operation of hydroelectric and thermal power generators in deregulated electricity markets. Real options theory is used to derive nonlinear partial-integro-differential equations (PIDEs) for the valuation and optimal operating strategies of both types of facilities. The equations are designed to incorporate a wide class of spot price models that can exhibit the same time-dependent, mean-reverting dynamics and price spikes as those observed in most electricity markets. Particular attention is paid to the operational characteristics of real power generators. For thermal power plants, these characteristics include variable start-up times and costs, control response time lags, minimum generating levels, nonlinear output functions, and structural limitations on ramp rates. For hydroelectric units, head effects and environmental constraints are addressed. We illustrate the models with numerical examples of a pump storage facility and a thermal power plant. This PIDE framework can achieve high levels of computational speed and accuracy while incorporating a wide range of spot price dynamics and operational characteristics.