Optimal reservoir operation for hydropower production using particle swarm optimization and genetic programming

Abstract

Water is one of the most valuable natural resources in the world. Optimal utilization of limited water resources, therefore, would help in building a strong economy for any country. Water availability varies spatially and temporally from location to location. Further, the growth in population, urbanization, deforestation and industrialization has increased the demand of water day-by-day. In recent times, it is also noted that the global warming became a threat that effects availability of water resources both spatially and temporally in several parts of the world. Thus, optimal management of surface water reservoirs plays a key role in sustainable development of a region. Many times, the reservoir operation is carried out by using conventional rule curve policies in several countries (for e.g., in Nepal). The rule curve policies may be easy to use, but it has several demerits. To improve the performance of reservoir systems, optimal operation policies should be evolved by using scientific approaches. Also, for field application, efficient real-time operation models need to be explored. The reservoir inflow is the most uncertain variable that has high influence on implementation of reservoir operation policies. Considering these issues, this study focused on developing optimal operational policies for two case studies, namely, Hirakud reservoir system in India, and Upper Seti reservoir system in Nepal. The first case study, Hirakud reservoir system is a multipurpose project serving flood control, irrigation and hydropower production. The study presented reservoir operation models for hydropower optimization for monthly and ten-daily periods after fulfilling the requirements for irrigation and flood control. Initially, the formulated reservoir operation models for monthly and ten-daily period are solved by using elitist-mutated particle swarm optimization (EMPSO) and genetic algorithms (GA) methods, and their results are compared with historical records. From the obtained results, it is noticed that the EMPSO solutions (for both monthly and ten-daily models) have resulted in higher annual hydropower than GA and historical records for all the years. However, hydropower production trend from both monthly and ten-daily model results followed similar trend to that of historical records. Later, the models (monthly and ten-daily) are solved for different inflow scenarios (that correspond to different inflow exceedance probabilities α of 0.5, 0.6, 0.7, 0.8 and 0.9). To represent the uncertainty in inflows, generalized extreme value (GEV) distribution is found be the best model for most of the time periods. The best-fit probability distribution is employed to estimate the inflows at various exceedance probabilities. The reservoir operation models are solved for different inflow scenarios and optimal operational policies are evolved. The results indicate that the amount of annual power production generated decreases as the value of inflow exceedance probability increases. To develop real-time reservoir operation models for Hirakud reservoir system, regression techniques such as linear genetic programming (LGP) and multiple linear regression (MLR) are explored for inflow forecasting and generalization of reservoir releases, and the best performing models are used for real time reservoir operation. For generalization of reservoir releases, the solutions of ten-daily operation model obtained using EMPSO for 39 years data are used to generalize reservoir releases as a function of previous time periods releases (R), inflows (Q), and initial storages (S). The available 39 years data are used for training and testing of LGP/MLR models. For real-time reservoir operation, various models are explored, which are broadly grouped into two categories (i) the real-time release model without considering inflow forecasts, and (ii) the real-time release model considering inflow forecasts. First, the reservoir inflow forecasting models for ten-daily period are developed by using LGP method. Out of several models tested for inflow forecasting, the model having inflow function, Qt = f(Qt-4, Qt-3, Qt-2, Qt-1) resulted in better performance than others. Subsequently, for generalization of reservoir releases, several models are explored for each case. For the first category models (i.e., release models without considering inflow forecasts), the best performing model is found to be the model having functional relation Rt=f( Qt-2, Qt-1, Rt-2, Rt-1, St) for ten-daily operation. Whereas for the second category models (i.e., models which use inflow forecasts), the best performing model is found to be the model having functional relation Rt= f(Qt, Rt-1, St) for ten-daily operation. Thereafter, a simulation model is developed for real time reservoir operation by integrating the models for reservoir inflow forecasting and generalization of reservoir releases for Hirakud reservoir system. The real time simulation model helps to take the release decision one time step-ahead, by using input data of previous time periods releases, inflows, and initial storage. The developed models are employed for real-time operation of Hirakud reservoir for twelve years’ data and its efficacy is tested by comparing with the results of standard operating policy (SOP). On estimating performance indicators, such as reliability, resilience, vulnerability, and sustainability index (SI) for the solutions of real time operation and SOP models, it is found that the real time model that uses inflow forecast information has resulted in best performance, and recommended for practical applications. The second case study, Upper Seti reservoir system in Nepal is a single purpose reservoir system serving hydropower production. Initially, an optimization model is formulated considering maximizing hydropower as main objective subject to satisfying environmental, physical and technical constraints, for monthly/fortnightly/weekly operation of Upper Seti reservoir system. The EMPSO and GA methods are applied for monthly, fortnightly, weekly operation of Upper Seti reservoir system and evaluated their performances by comparing with historical records. It is found that the EMPSO technique gave best performance by yielding higher hydropower production (585.43 GWh, 584.06 GWh, 574.30 GWh for monthly, fortnightly and weekly operation respectively) when compared with the planned hydropower of 558 GWh. It is also noticed that, the EMPSO method has the capability of handling large number of variables and constraints, and gives good quality optimal solutions in fewer numbers of iterations. On evaluating the performance of the reservoir system to meet specified target demands, it is found that there exist higher variations in weekly hydropower generation. To determine optimal hydropower target, a modified reservoir operation model is formulated with an objective of minimizing the sum of squared deviation of generated hydropower from target hydropower over a year. The model is solved for a set of target demands and their sustainability is analyzed by estimating reliability, resilience, vulnerability, and sustainability index. On performing sustainability analysis, it is found that higher sustainability of the system is achieved at a target hydropower of 4.8 GWh per week. However, this target power has resulted in reduced average annual hydropower of 545 GWh, which is about 2.3 percent less than that of the planned hydropower. To develop real-time operation model for Upper Seti reservoir, the optimization model results of EMPSO are used to generalize reservoir releases as a function of previous time periods releases, inflows, and initial storages. Here also the performance of two category models (i.e., model considering with and without inflow forecasts) are tested. For forecasting weekly reservoir inflows, LGP based regression models are developed, using the information of on various sets of lagged inflows. Among the several models tested for inflow forecasting, the LGP model that is having functional relation Qt = f(Qt-4, Qt-3, Qt-2, Qt-1), resulted in best performance as compared to other models. Subsequently, LGP method is applied to develop generalized reservoir releases, and explored various models by using different sets of inputvariables. From performance measures, it is found that the release models that have functional relations of Rt=f( Qt-1, Rt-1, Et-1, St) and Rt= f(Qt-1, Qt, Rt-1, St) resulted in best performances for reservoir release models without and with inflow forecast information respectively. For real time operation of Upper Seti reservoir, a simulation model is developed by integrating the models for reservoir inflow forecasting and reservoir releases. The performance of the developed models is evaluated by applying for real-time operation of Upper Seti reservoir for few years’ data, and compared with the results of SOP. On estimating the performance indicators, such as reliability, resilience, vulnerability, and sustainability index (SI) for the solutions of developed real time models and SOP model, it is found that the real time model that uses inflow forecast information has resulted in best overall performance, and is recommended for practical application. From the results of the two case studies, the following inferences are drawn: (1) On comparing the performance of EMPSO and GA methods for reservoir operation problems, the EMPSO is giving better performance than GA method; (2) The uncertainty in inflows is best represented by generalized extreme value distribution model; (3) On solving the reservoir operation model for different inflow scenarios, the study found that the amount of annual hyropower produced decreases as the value of inflow exceedance probability increases; (4) LGP method is found to be giving better performance than MLR method for inflow forecasting and generalization of reservoir releases; (5) For real time reservoir operation, the real-time release model that uses inflow forecast information is giving better performance than the models without inflow forecasts and SOP.