Journal of ELECTRICAL ENGINEERING, VOL. 58, NO. 4, 2007, 214–219 OPTIMAL SHORT TERM HYDRO SCHEDULING OF LARGE POWER SYSTEMS WITH DISCRETIZED HORIZON Ahmed Bensalem* — Abdallah Miloudi** Salah Eddine Zouzou*** — Belgacem Mahdad*** Abdelmalik Bouhentala**** In this paper, we present a new algorithm based on the discrete maximum principle for determining the optimal short- term operating policy of hydroelectric power systems consisting of multi-reservoirs, where the objective is to maximize the potential energy while satisfying all operating constraints over a short-term planning horizon. In order to improve the performance of the proposed algorithm, we have suggested subdividing the short-term planning horizon to shorter study horizons so shorter study periods are embedded in a longer one. Afterward, the objective becomes maximizing the value of potential energy stored at the end of the shorter horizon. The final state of the shorter horizon will be regarded as the initial state of the next shorter horizon and so on. Hence, a reduced size problem is solved in each shorter horizon. Consequently, the calculation effort is decreased considerably and moreover the adjustment of the parameters of the methods used is facilitated. Keywords: short-term scheduling, potential energy, discrete maximum principle, augmented Lagrangian method, discretized horizon 1 INTRODUCTION The short-term optimal operating policy of hydroelec- tric power systems is a deterministic problem [1, 2] which consists of choosing the quantity of water preliminary se- lected to release from each reservoir of the system over the short term planning horizon in order to meet an hourly electric power demand assigned in advance. The prime objective here is to perform the operation policy with the lowest use of water. This is achieved by avoiding spilling and by maximizing the hydropower generation, besides satisfying all operating constraints. Maximization of elec- trical power production is achieved by maximizing the heads. Consequently, this allows maximizing the reser- voirs content. In order to improve the performances of the pro- posed algorithm, we have suggested subdividing the short term planning horizon into shorter study horizons so that shorter study periods are embedded in a longer one. Afterward, the objective becomes maximizing the value of potential energy stored at the end of the shorter horizon. The final state of a shorter horizon will be re- garded as the initial state of the next shorter horizon and so on. Hence, a reduced size problem is solved in each short period. When modelling the problem, and for more accuracy, the following factors which make the problem more com- plex are taken into consideration: – Significant water travel time between reservoirs. – The multiplicity of the input-output curve of hydro- electric reservoirs that have variable heads. – The maximum generation of the hydro power plant (HPP) varies with the hydraulic head. In fact, the quantity of water required for a given power output decreases as the hydraulic head increases. – The water stored in the upstream reservoir is more valuable than that stored in the downstream reservoir. – Whether the reservoirs have very different storage ca- pacity. – Whether the system has quite complex topology with many cascaded reservoirs. To solve the short-term operating policy problem, we use the discrete maximum principle [3 ,4]. While solving equations related to the discrete maximum principle, we use the gradient method [3]. However, to treat the equal- ity constraint we use Lagrange’s multiplier method. To treat the inequality constraint we use the augmented La- grangian method [5]. Furthermore, the present paper is particularly con- cerned with treating the state variable constraints, which are of two-sided inequalities. The augmented Lagrangian method is proposed to deal with this type of inequalities. The hydroelectric power system considered in this pa- per consists of ten reservoirs hydraulically coupled, ie , the release of an upstream reservoir contributes to the inflow of downstream reservoirs. All reservoirs are located on the same river. The time taken by water to travel from one reservoir to the downstream reservoir [8–10] and the water head variation are taken into account. The natural *Electrical engineering department. University of Batna, Algeria Email: a bensalem dz@yahoo.com **University of Saida, El-Nasr, 20000 Saida, Algeria *** LGE, University of Biskra, B.P. 145 - 07000 Biskra, Algeria **** LAM Reims University, Champagne, Ardennes, France ISSN 1335-3632 c  2007 FEI STU