Optimal Parameter Estimation for Hydro-Plant Performance Models in Economic Operation Studies

Optimal Economic Operational schedules in hydro-thermal electric power systems are obtained on the basis of models of the various subsystems involved. In this paper we are concerned with models of hydro-plant performance characteristics. Due to the diversity of plant types and installations, a number of models have been proposed in developing optimal operational strategies over the years. Here we choose four commonly used models. The problem of finding optimal estimates of model parameters is investigated for the Glimn-Kirchmayer model, the Hildebrand model, the Hamilton-Lamont model and the Arvanitidis-Rosing model. We develop the optimal estimator equations for each model using the weighted-least-squares approach. The result for three of the models is a set of nonlinear equations in the unknown parameters. We adopt Newton's method for actually implementing the optimal estimators. Due to the sensitivity of the algorithm's convergence characteristics to the initial guess of the unknowns, we explore and present procedures for generating initial guess values to improve the procedure's performance. Computational experience with the techniques is given in the paper to confirm its feasibility using test data from existing hydro-plants. The paper proposes and examines some extensions to the classical models to improve the accuracy of the modeling process.