DERIVATION OF THE BALERIAUX FORMULA OF EXPECTED PRODUCTION COSTS BASED ON CHRONOLOGICAL LOAD CONSIDERATIONS

Production simulation models ave extensively used in the electric powe r industry. In these models, the expected energy produced by each unit is commonly calculated using a method due to Baleriaux. This formulat ion ignores the chronological sequence of load levels and performs the computations based on the load duration curve (LDC). This paper reder ives this formula first based on a deterministic chronological load di stribution, It is shown that in order for the Baleriaux formula to hol d, it is necessary that the distributions of the operating states of t he generating units have reached a steady state. When the chronologica l load is itself distributed as a stochastic process, the Baleriaux fo rmula is shown to hold with a different definition of the LDC; it is s hown to be related to the time average of the cumulative distribution functions of the loads.