Short-range hydrothermal scheduling by parametric equation approach - Camaclang, Sixto C. (1976)
Short range hydrothermal problem is formulated as two optimization problems. One problem deals with the optimization of the thermal schedule and having hourly cost minimization as the objective function. The other problem, on the other hand, concerns with the optimization of the hydro schedule wherein the aim is to increase the weighted output of the hydro system. Formulations of both optimization problems are done using parametric equation approach as suggested by LONG and BARRIOS (14). The technique is basically gradient search method because the decision variable are moved along the directional derivative of the objective function except for the dependent variable : the solution technique classifies the variables of a problem into one dependent variable and the rest as independent variables. Since the dependent variable is computed from the equality constraint of the problem, after computation of trial values for the independent variables, its presence provides facility for handling the constraint of the problem. Computation is carried out iteratively and starts from an initial solution, which must only be feasible but not necessarily near the optimum. Computation fro trial schedules is continued as long as improvement is realized on the objective function, otherwise, the solution arrived at is considered the optimum solution. In this study, the performance equations of thermal and hydro plants are assumed continuous and readily differentiable, wherein convexity is a must for the thermal performance equation and concavity is likewise required for the hydro performance equations. Meanwhile, both equations are considered to have the form of the general cubic equation. Variation in head for the hydro plants is neglected in this study. It is assumed that all the hydroplants are of the large pondage type such that the drawdown in the pond elevation is negligible over the optimization period. With this assumption then, hydro power generation is no more a function of head. Furthermore, pond refill also ceases to be time dependent because of negligible head consideration. Therefore, water inflows are assumed to have reached the pond at the start of the optimization period. The transmission system is duly represented in the modeling of the problem. Its effect in the scheduling problem is taken into account with the aid of loss formula, using Kron's B-coefficient matrix. Included in this report is the algorithm developed to solve this scheduling problem. The computer program has basically two parts - hydrothermal optimization routine and B-matrix computation routine. The first routine contains the two subroutines for the optimization of the hydro and thermal scheduling process, while the second part has the loadflow computation subroutine and the elements of B-matrix computation subroutine. Needless to say, the optimization routines utilized the essayed formulation; but, Newton's method and Tinney's table of factors are used in the solution of the loadflow problem and in the computation of the elements of the system B-matrix, respectively.