Nonconvex dynamic economic dispatch of genaration via valve-point loading

One of the biggest gains that technology brings to electrical engineering is the increase in energy consumption around the world. As the number of electrical appliances and the use of them have increased, they have also increased their power consumption to provide more advanced technology. These increases, and the fact that the software systems become more preferred, reveal the need for extra energy. The increase in energy demand is pushing the sufficiency of electric energy production systems day by day and we need to build more and more qualified electric energy production plants. With the increase in the amount of electric energy produced, the economic load dispatch, which is one of the optimization processes in production, becomes more important. Economic load dispatch is the calculation of the number of generators to be loaded to meet the demanded energy minimum fuel cost using the cost generated by the sum of the fuel-power curves of all the generators used in the production system. By distributing economic loads between generators, the same amount of energy is obtained at a lower fuel cost than for plants without economic load dispatch. The fact that the amount of electricity demanded by consumers from power systems differs during certain time periods during the day caused the economic load dispatch problems to be inadequate. According to the changing demand power values, dynamic economic load dispatch problems have been established in order to determine in which period of time, which generators will produce in output power. Today, the greatest amount of energy demanded is met by production plants that use fossil fuels. This leads to an increase in environmental pollution in the region where production is being carried out. In addition to the economic load dispatch, environmental load dispatch can also be achieved in order to minimize the amount of gas emissions emitted to the environment. When an economic load dispatch operation is performed, the total production cost of the system is equal to the sum of the costs of all production units. There is an output power range that each generator can produce. The minimum and maximum output power values must be considered in order to keep the generator output powers within this range in the load distribution to be made. The sum of the generator output powers must meet the demand power when the load distribution operation in which transmission losses are neglected. When performing the load distribution operation in which transmission losses are included, the sum of the generator output powers must meet both the transmission losses and the demand power. By including the valve-point effect on the fuel cost of the production unit, the display of the fuel cost is made more convenient. Due to the valve-point effect, the total fuel cost function includes higher nonlinear components. When distributing economically, it is necessary to select the most appropriate values among the forces that the generators produce based on the fuel costs. Fast, reliable and effective optimization methods are used to solve economic dispatch problems in energy systems. In power systems, classical optimization methods are used first. However, heuristic optimization methods have been developed for problem solving in which these methods are insufficient. Classical and heuristic methods have different advantages and disadvantages. For proper optimization, the power system must be handled correctly and a suitable method must be selected. Inspired by Darwin's theory of evolution, Genetic Algorithm (GA) was developed by John Holland in 1975. It is artificially imitated in Genetic Algorithm that the birth of the creatures, their disappearance with the repose and the natural selection. Through the genetic processors, each individual is transferred to a new population, which is a potential solution, from the population of older individuals, and a fitness value that determines the quality of that individual is assigned to all the individuals in the population. The fitness value reflects the quality of that individual. As a basic optimization procedure, it extracts individuals with high fitness values and creates individuals with higher fitness for these individuals. Particle Swarm Optimization (PSO) is a population-based, intuitive method designed by J. Kennedy and R.C. Eberhart in 1995 for solving nonlinear problems, inspired by the behavior of bird and fish swarms. PSO is a kind of evolutionary algorithm based on simulating the social behavior of the most appropriate individual survival. Similar to other population-based evolutionary algorithms, it is initiated with a random solution population. The PSO method is more advantageous in terms of simplicity of content, ease of implementation, and computational efficiency compared to mathematical and other heuristic optimization methods. The Tabu Search Algorithm (TSA) is an iterative research algorithm developed by F. Glover in 1986 for solving optimization problems. The basic approach in the TSA is to prohibit or punish again in the next cycle in order to prevent circular movements of the step leading to the final solution. In this way, the solutions that are ahead of the best solution are being investigated. The tabu list is created by taking the best solution in each loop. If the tabu list is full, the first solutions saved in the list are dropped from the list and the solutions reached in the last loop are included in the list. The algorithms developed in this thesis are terminated when a solution satisfying the desired criteria is reached, when the maximum number of iterations is reached, the given time is exceeded, the iterations where good results are not obtained, or combinations of these occur. The aim of the study is to emphasize the importance of generating energy at low cost and to explain how to make economic load distributions for optimization of energy production with Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Tabu Search Algorithm (TSA) methods using MATLAB. In this study, economic load dispatch problems, mathematical expressions and optimization methods used for this purpose are explained and examples of applications are given. Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Tabu Search Algorithm (TSA) were used as the heuristic optimization methods. All these algorithms are created by writing MATLAB code. Toolbox or ready code is not used. With these algorithms created, dynamic economic load dispatch operations have been realized including transmission losses on 3 units test system, 5 units test system and 10 units test system. Valve-point effect is taken into consideration when providing dynamic economic load dispatch on 5 units test system and 10 units test system. Since the valve-point effect coefficients (e_i and f_i) are not available for the 3 units test system, the valve-point effect can not be considered in the load distribution process. In addition to all these, a load distribution operation has been carried out on 10 units test systems, in which transmission losses are neglected. The results of the dynamic economic load dispatch with GA, PSO and TSA methods are compared with the minimum fuel costs and transmission losses obtained in previous studies. All three algorithms used in this study showed that algorithms are more accurate and more applicable to power systems than the literature. When the algorithms used in this study are evaluated among themselves, it is seen that the PSO algorithm gives the most optimal result.