Stochastic Dynamic Programming (SDP) has been used to solve reservoir management problems in different parts of the world; specifically in Mexico, it has been used to obtain operating policies that optimize a given objective function. By simulating the operation of the system with a comprehensive model, the behavior of such policies can be accurately evaluated. An optimal policy involves, on the one hand, the selection of the volume of water to extract from each reservoir of the system that guarantees the maximum expected benefit from electricity generation in the long term; and, on the other hand, an optimal policy should reduce the occurrence of unwanted events such as spills, deficits, as well as volumes exceeding the guide curves imposed by the operators of the dams. In the case of the Grijalva river dam system, SDP was applied to determine optimal operating policies considering three alternative guide curves proposed by different agencies; however, since the simulation of the operation of the system under the three alternatives with the historical record of dam inflows found that none of them showed deficits or spills, it was considered necessary to use synthetic series of inflows to increase the stress of the system. Records of synthetic biweekly series of 1000 years were then generated to simulate the behavior of the Grijalva river dam system using the optimal operation policies obtained for each alternative. By stressing the dam system by simulating its behavior with synthetic series longer than the historical record but preserving the same statistical characteristics of the historical series on the synthetic ones, it was possible to realistically evaluate each operating policy considering the frequency and magnitude of spills and deficits that occurred at each dam. For the generation of the synthetic series, a fragment method was used; it was adapted to simultaneously generate the inflow volumes to the two regulating dams (modified Svanidze method), which preserves the statistical characteristics of the historical series, including both the autocorrelations of each series and the cross-correlation. It was also verified that simulating the operation of the dam system with the generated series also preserves the average conditions, such as the average biweekly generation at each dam, which were obtained in the simulations with the historical record. Finally, an optimal policy was obtained (Test 4) by combining the guide curves used in the previous tests. Such a policy attained an average energy production of 474 GWh/fortnight, the lowest average total spills in the system (30,261.93 hm3), and limited deficits (5973.17 hm3) in the long term. This represents a relative increase of 16% in energy generated compared to the balanced historical operation scenario with respect to the few events of spills and deficits.
The objective of the present study was to develop a genetic algorithm capable of establishing optimal operating policies for monthly extractions from the three main reservoirs of the Cutzamala System, which supply drinking water to the Mexico City metropolitan area. In previous studies, annual water extraction defined with an annual Z curve in terms of the total water storage in the reservoirs on November 1 was optimized using genetic algorithms. In this study, a percentage of total annual extraction for each reservoir was also optimized, but monthly water extractions were adjusted too, when the water level fell outside the upper or lower limits of guide curves stablished for each reservoir. The capabilities of the genetic algorithms combined with a detailed simulation of reservoirs operation were used to optimize the levels of the guide curves and also to optimize the adjusted monthly programed extractions as linear functions of the difference between the actual storage level at the beginning of each month and the corresponding level of the guide curves. Therefore, 90 parameters were established: four to define the Z curve, two to establish the percentage assigned to each reservoir, 72 to establish the monthly levels of the guide curves and 12 to define the parameters of the linear functions used to adjust the monthly programed extractions when the actual water level exceeds the limits of the guide curves. For each alternative of the 90 parameters, a detailed simulation is done using the last 20 years of hydrological data on the inflow of water to the three main reservoirs, including the net contributions of five diversion dams, and the objective function sought to maximize water delivery to the treatment plant, while penalizing possible spills and deficits in the system is evaluated. The optimal policies found in this research resulted in smaller spills than those that occurred during the historical operation of the reservoir system. Therefore, the optimal monthly operating decisions required for each reservoir are provided by the genetic algorithm.
En este estudio se obtuvieron políticas de operación del tipo curvas Z, usando dos métodos de optimización: el de gradiente reducido 2022, Instituto Mexicano de Tecnología del Agua Open Access bajo la licencia CC BY-NC-SA 4.0
Stochastic dynamic programming (SDP) is an optimization technique used in the operation of reservoirs for many years. However, being an iterative method requiring considerable computational time, it is important to establish adequate convergence criterion for its most effective use. Based on two previous studies for the optimization of operations in one of the most important multi-reservoir systems in Mexico, this work uses SDP, centred on the interest in the convergence criterion used in the optimization process. In the first trial, following the recommendations in the literature consulted, the difference in the absolute value of two consecutive iterations was taken and compared against a set tolerance value and a discount factor. In the second trial, it was decided to take the squared difference of the two consecutive iterations. In each of the trials, the computational time taken to obtain the optimal operating policy was quantified, along with whether the optimal operating policy was obtained by meeting the convergence criterion or by reaching the maximum number of iterations. With each optimization policy, the operation of the system under study was simulated and four variables were taken as evaluators of the system behaviour. The results showed few differences in the two operation policies but notable differences in the computation time used in the optimization process, as well as in the fulfilment of the convergence criterion.
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