The optimization of the weekly operating policy of multireservoir hydroelectric power systems is a stochastic nonlinear programing problem. For small systems this problem can be solved by dynamic programing, but for large systems there is yet no method of solving this problem directly, so that one must resort to mathematical manipulations in order to solve it. This paper presents and compares two possible manipulation methods for solving this problem. The first, called the one-at-a-time method, consists in breaking up the original multivariable problem into a series of one-state variable subproblems that are solved by dynamic programing. The final result is an optimal local feedback operating policy for each reservoir. The second method, called the aggregation/decomposition method, consists in breaking up the original n-state variable stochastic optimization problem into n stochastic optimization subproblems of two-state variables that are also solved by dynamic programing. The final result is a suboptimal global feedback operating policy for t. he system of n reservoirs. The two methods are then applied to a network of six reservoir-hydroplant complexes, and the results obtained are reported. It is shown that the suboptimal global feedback operating policy gives better results than the optimal local feedback operating policy.

This paper presents a method for determining the weekly operating policy of a power system of n reservoirs in series; the method takes into account the stochasticity of the river flows. The method consists of rewriting the stochastic nonlinear optimization problem of n state variables as n -I problems of two state variables which are solved by dynamic programing. The release policy obtained with this method for reservoir i is a function of the water content of that reservoir and of the total amount of potential energy stored in the downstream reservoirs. The method is applied to a power system of four reservoirs, and the results obtained are compared to the true optimum.

This paper presents an algorithm based on the principle of progressive optimality for determining the optimal short-term scheduling of multireservoir power systems; the method takes into account water head variations, spilling, and time delays between upstream and downstream reservoirs. The method is computationally efficient and has minimal storage requirements. The convergence is monotonic and a global solution is reached. Contrary to dynamic programing, the state variables do not have to be discretized with this method. An example consisting of four hydroplants in series is solved, and the results are presented.

This paper describes a nonlinear disaggregation technique for the operation of multireservoir systems. The disaggregation is done by training a neural network to give, for an aggregated storage level, the storage level of each reservoir of the system. The training set is obtained by solving the deterministic operating problem of a large number of equally likely flow sequences. The training is achieved using the back propagation method, and the minimization of the quadratic error is computed by a variable step gradient method. The aggregated storage level can be determined by stochastic dynamic programming in which all hydroelectric installations are aggregated to form one equivalent reservoir. The results of applying the learning disaggregation technique to Quebec's La Grande river are reported, and a comparison with the principal component analysis disaggregation technique is given.

Abstract. The problem is to find the monthly operating policy of Hydro-Qudbec's 26 large reservoirs that maximizes the utility's expected profits over a period of several years. The problem is solved in a hierarchical way. First, the optimal operating policy of the whole system, represented by an aggregate model, is found by stochastic dynamic programming (SDP). This gives not only the hydroelectric energy to produce in a month but also, as is very important in a deregulated market, the expected marginal value of the hydroelectric energy produced. At the second level the expected marginal value of the potential energy stored in each river is determined by solving a SDP problem with two state variables: one for the energy content of the river and the other for the energy content of all the other rivers combined. These marginal values are used afterward to divide the hydroelectric production among the rivers. At the third level the production assigned to each river is distributed between the reservoirs so as to minimize the spillages first, and then the square of the deviations of the reservoir levels from the target level. The targets are adjusted to maximize the expected long-term production of the river. The monthly inflows to the reservoirs are the only random variables in this problem. IntroductionThis paper tackles the problem of determining a monthly releasing policy for Hydro-Qufibec's 26 seasonal and interannual reservoirs over a period of several years. The objective is to find a policy that maximizes the utility's profits while respecting all constraints. The policy must absolutely take into account the random behavior of the reservoir inflows, since these cannot be predicted long in advance and since they vary widely throughout the year. Ideally, the randomness of electricity demand should also be taken into account, but since a probability distribution cannot be obtained for future demand, we suppose that demand is known for the whole period and equal to the most probable scenario.The problem is not stationary, even though the inflows are on an annual basis, because electricity demand increases every year and new power plants must periodically be added to meet it. Whatever the investments made, however, we cannot, in a stochastic environment, guarantee that demand will be met all the time. At best, we can guarantee that demand will be met with a certain probability. The choice of a probability is not obvious, though, because it must take into account, on the one hand, the investment that will have to be made to meet it and, on the other, the losses incurred by the customers when demand is not met. Rather than trying to determine this probability, Hydro-Qufibec has chosen to build, from information gathered from its customers, a curve representing the economic and social costs of a shortage in terms of the number of gigawatt hours (GWh) not supplied in a month. This shortage cost curve is used in our model to penalize shortages.Copyright 1998 by the American Geophysical Union. Paper number 98WR02608.00...