Asymptotic Mean and Variance of Electric Power Generation System Production Costs via Recursive Computation of the Fundamental Matrix of a Markov Chain

The cost of producing electricity during a given time interval is a random variable that depends both on the availability of the generating units during the study horizon and on the magnitude of the load. Based upon a Markov model, we present a recursive scheme for estimating the asymptotic mean and variance of the production cost. These computations are difficult because the state space for a typical power generation system is very large and because the asymptotic variance depends upon the fundamental matrix. Its computation requires the inversion of a matrix whose dimension depends on the size of the state space. The recursion relations given here preclude the need for such matrix inversion and provide approximate estimates that compare very favorably with a realistic Monte Carlo simulation.