Generation of Synthetic Series for Long-Term Analysis of Optimal Operation Policies of a Cascade Hydroelectric Dam System

Abstract

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.