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Four algorithms for estimation of the parameters of models used in optimal economic operation of electric power systems, are proposed. The details of the formulations for estimating the parameters of the fuel cost expression, the loss formula coefficients, and the active-reactive power loss models are highlighted. Critical performance evaluation of each of the proposed algorithms is carried out using some practical test systems. The first evaluation criterion is based on the familiar modeling error-comparison. Further evaluation is carried out on the basis of the optimal strategies resulting from the use of each estimated model. Optimal costs as well as overall network performance (based on load flow analysis) resulting from the implementation of each model, provide the basis for our comparisons.