OPTIMAL SEQUENCING AND OPERATING POLICIES OF MULTIPURPOSE MULTIRESERVOIR RIVER BASIN PROJECTS

Abstract

For the economy in hydroelectric projects planning, the problem of optimal sequencing of the expansion units at a minimum present cost becomes an important task. Once these projects are executed, the optimal operation of the interconnected reservoirs for maximizing the benefits (or minimizing the cost/loss) turns out to be an equally important feature for consideration and the present work is concerned with these aspects. A heuristic method for sequencing capacity expansion projects is that of Tsou, Mitten and Russell (TMR). In the work being presented, a less restrictive criterion for the optimality of the TMR approach has been obtained which can establish opti mality of resulting sequences for various demand curves conven iently. The conditions in which the TMR technique is found to yield sub-optimal results have been identified. An alternative heuristic approach is proposed which yields optimal results in many examples even with the 'odd1 types of growth curves. The method attempts a project under consideration at two most appropriate places in the existing (already decided) set of projects while minimizing the overall cost/capacity ratio of the project set at every stage. Case studies of interdependent projects have also been considered and reported. Inflation is unwanted but unavoidable in many countries under the present world economic conditions. The effects of inflationary economies are studied and analysed in the thesis. The optimal sequence and cost both are highly effected by this

parameter. Results have been obtained to bring out the facts. The heuristic sequencing rule by TMR does not work for sequencing of interdependent projects under inflationary situationsk dual version of the alternative heuristic approach is presented which yields optimal results in most of the cases- To be able to represent real life conditions, several parameters neglected so far have been considered in a simulation study of sequencing a set of interdependent hydroelectric projects. The realistic models incorporate (a) permitted delays with penal ties (PDP) with different growth curves and (b) allowances for the construction periods of the individual projects (with and without distributed funds intake during these intervals). The impacts due to varied inflationary situations throughout the time horizon i.e. the fixed inflation rates, deterministically reducing infla tion rates and stochastically varying inflation rates - have been brought out. The results are appropriately interpreted. Optimal sequencing of project set with due considerations to the irrigation benefits (returns) of the storage projects has been achieved by modifying the 'investment cost1 term in the existing dynamic programming (DP) algorithm and heuristics appro aches, including the one presented in this work. The modified algorithms are used to sequence a river basin interdependent project system. Effect of variations in irrigation return rate and nature of effective discounting on the optimal sequence and cost have been studied and the inferences have been drawn. Water for irrigation has also been considered as an additional demand projected over the same or different time span. For this, a multidimensional DP formulation has been developed which explicitly

incorporates interdependencies amongst the projects- A set of twelve interdependent hydroelectric projects on Ganga river basin in the northern India has been optimally sequenced minimizing the costs involved and feeding in 'completely1 the power demand of the region within a period of twenty years. Population growth rate, per capita power generation, deficiencies in generation etc. during the period 1960-80 have been used to estimate the total power demand growth v/s time relationship during the years 198V-200W. Impacts due to constant inflation/ interest rates, deterministically reducing inflation rates, stochastic changes in inflation rates and considerations of irrigation aspects on sequencing have been studied. Appropriate recommendations have been made. Any form of the DP formulations for solving the large sized problem for optimizing operating (discharge) policy encoun ters either major difficulty of computational burden or fail to yield optimal results. A sequential method has been developed in which the discharges are successively transferred between stages in one reservoir at a time (alone or with related discharges) within a number of constraints to optimize the objective function over the given time horizon. Discretization of the control varia bles is not needed, all series-parallel configurations are taken care of and any initial feasible policy converges to optimal one with very small computational effort. In case of linear objective functions, results can be obtained even without using a digital computer. Examples have been worked out with linear and nonlinear performance criteria and the results are compared.

The inflows to the reservoirs are, in fact, stochastic. Because of its appealing advantages, the aforementioned successive variation algorithm can be used for the stochastic optimization of the long range operating policy of an interlinked system of reser voirs. The operating policy of Ganga valley multiple reservoir system has been optimized under stochastic inflows. Operational bounds and the terminal storage requirements of the reservoirs have been accounted for. First order serial correlation between successive inflows is assumed. Aproposition has been made which gives very good results with a reduced computational burden in case where the inflows are poorly correlated.