STOCHASTIC AND DYNAMIC PROGRAMMING MODELS FOR WATER RESERVOIRS WITH APPLICATION ON RUSIERIS DAM

Abstract

Water storage is carried out in wide basins constructed along the river course or on rain or floods accumulating points. The main purpose is to store accumulated water resources for later utilization. Hydroelectric power generation is one of the most important objectives. Rusieris dam is one of the important storage facilities of the Sudan. It is used to irrigate Gezira Agricultural scheme and contributes 95% of generated hydroelectric power in the Sudan. The primary conceptual framework of this thesis emanates from the hypothesis that there is a minimized utilization of the potential capacity of Rusieris dam. Additionally, that there are greater amounts of wastage of stored water. The student has used stochastic as well as dynamic models to measure the present mode of utilization and to reach an optimal use of the potentials of the water storage capacity of the Rusieris dam under specific conditions. That achieves an originality in the work considering that there are no similar previous studies for optimal water resources utilization in the Sudan. The present research also presents stochastic as well as dynamic maximization of hydroelectric power from Rusieris dam and thus introduces pivotal questions: is it possible to apply such stochastic models on other Sudanese water storage facilities and would that produce better utilization modes for their potentials. One of the axial hypotheses represented in this research postulates that there is a wastage in the water resource of the Rusieris dam, i.e., that is represented in the input–output relation, that relation follows the Markov chain. Time series data during the period 1967-2002 were accumulated from the National Electricity Corporation, interviews with engineers of the Ministry of Irrigation were conducted and more records were utilized to establish the empirical analysis. Considering the unavailability of ready computer packages for analyzing or applying the thesis models, enhanced the student to build up a specialized computer program based on Q-Basic language. The program was primarily used for the application of the thesis models of the Rusieris dam data. Statistical tests were conducted for the descriptive analysis as well as the application of stochastic model based on Markov chain. The most important results obtained were: the maximum generated hydroelectric power of the Rosieres dam is achieved when 45-78% of stored water is used. That means an amount of 2.2 milliard cubic meters can generate 1,563,693 megawatt/hour and 1,563,711 megawatt/hour in both stochastic and dynamic programming models, respectively. Summer months i.e., July, August, September and October is the highest productivity period where the average generated power reaches up to 208,320 megawatt/hour per month. There is solid proof of applied similarities in the results produced in both used models; the stochastic and dynamic programming under the different stored water levels of Rusieris dam. The empirical models proved to be highly efficient; this can be tested when applied to the 2003 year’s data. The study recommended the National Electricity Authority is called for to consider using the models in the future cascaded Dams. It is important to make greater efforts for the elevation of Rusieris dam to reach 491 meters which can potentially achieve the maximum possible generated hydroelectric power. It is important to conduct more studies specially when the relation between the input-output becomes non-linear and that enhances the necessity to test it on other dams like Sennar dam.