Chronological Influences of the Variance of Electric Power Production Costs

The cost of producing electric power at a given time depends on the demand and the set of generating units that are available. We present a Markovian model of the generation system together with a deterministic, time-varying demand function that yields a stochastic integral for the production cost over a time interval. The variance of this integral may be computed exactly by enumerating states. An expression for the integrand is developed in which the deterministic time variation is decoupled from the stochastic variation. This expression is amenable to an asymptotic approximation that reduces the computation. When system state transition rates are high, little accuracy is lost. The exact and approximate results are compared for several parameter values in a small example system.