Derivation of the Baleriaux formula of expected production costs based on chronological load considerations

Abstract Production simulation models are extensively used in the electric power industry. In these models, the expected energy produced by each unit is commonly calculated using a method due to Baleriaux. This formulation ignores the chronological sequence of load levels and performs the computations based on the load duration curve (LDC). This paper rederives this formula first based on a deterministic chronological load distribution. It is shown that in order for the Baleriaux formula to hold, it is necessary that the distributions of the operating states of the generating units have reached a steady state. When the chronological load is itself distributed as a stochastic process, the Baleriaux formula is shown to hold with a different definition of the LDC; it is shown to be related to the time average of the cumulative distribution functions of the loads.