Application of the particle swarm method in optimization problems of energy.

The article considers the application of the particle swarm method in energy domain. The problem of effective load distribution of energy-generating capacities under the conditions of minimum fuel consumption is one of those that arises most often. The economic expediency of the operation of one or another power plant at the appropriate capacity determines the distribution of generating capacities in the power system. It is no secret that power units of thermal power plants, which were built in different time periods, differ in their cost characteristics. This makes it necessary to find optimal configurations of the power system, in which the relevant energy objects are involved. Particle Swarm Optimization (PSO) is a computational optimization method inspired by the social behavior of birds in a flock or fish in a shoal. This method was first proposed by Kennedy and Eberhart in 1995. In PSO, a population of possible solutions, called particles, moves through the search space according to a set of mathematical rules. The motion of each particle affects its own bestknown position and the global best-known position of the entire population. The basic idea is that each particle adjusts its position based on its own experience and that of the entire swarm. This correction takes place with the help of two main components: 1. Cognitive component (personal best result): The particle remembers the best solution it found before. 2. Social component (global best result): A particle also takes into account the best solution found by any other particle in the swarm. These components are used to update the particle's velocity and position iteratively, with the goal of converging to an optimal solution. PSO is widely used in various optimization problems, including engineering design, robotics, finance, and data analysis. It is known for its simplicity, ease of implementation, and ability to solve non-linear, non-convex optimization problems. However, like any optimization algorithm, its performance can be sensitive to the parameters and the nature of the problem to be solved. The article solves a typical problem of distributing the total load between two thermal power plants under the conditions of minimum fuel consumption. The obtained values of the solutions confirm commonly known the statements about the achievement of adequate indicators in the range from 10 to 30 particles, in our case - 20.Analyzing the obtained results, one can see that the objective function changes almost linearly from the very beginning until the 30th iteration, after which the improvement in the result is almost imperceptible. The main reason is that at this moment the result of the algorithm is as close as possible to the reference value, namely 250. That is, in fact, it can be considered that the solution comes at the 31st iteration. Carrying out a comparison with the solution of such a problem using the genetic algorithm from the previous work, it can be seen that when solving such a problem, the algorithms demonstrate similar performance with comparable accuracy of the result. From the above studies, it can be concluded that evolutionary algorithms can be used to solve similar energy problems.