The task of power systems mode optimization relates to the complex tasks of non-linear mathematical programming. Despite the development over the past few decades many methods and algorithms for solving this problem, questions of their improvement taking into account the current operating conditions of energy systems remain an important task. This article proposes a new algorithm for the optimization of short-term modes of power systems, taking into account frequency changes in terms of the probabilistic nature of initial information. A distinctive feature of the algorithm is associated with the elimination of the need to choose the single slack bus with balancing power plant in calculations, which is typical for many existing methods. It is shown that taking into account frequency change in the optimization of power system mode in terms of probabilistic nature of initial information can introduce significant changes in the calculation results and lead to a corresponding increase in the resulting economic effect.

Over the past decades, many publications on the use of genetic algorithms, which offer a new and powerful approach for solving the problem of power system mode optimization, have appeared. Despite this, the issues of effectively taking into account various constraints when solving such problems with genetic algorithms remain opened. In this regard, this article proposes an algorithm for optimizing power system modes by genetic algorithm, taking into account functional constraints in the form of equalities and inequalities by various penalty functions. The results of effectiveness research of the given algorithm in the example of optimization of 8-nodal power system with four thermal power plants and three lines with controlled power flows are presented.

In article discusses issues for solving optimization problems based on the use of genetic algorithms. Nowadays, the genetic algorithms for solving various problems. This includes the shortest path search, approximation, data filtering and others. In particular, data is being examined regarding the use of a genetic algorithm to solve problems of optimizing the modes of electric power systems. Imagine an algorithm for developing the development of mathematical models, which includes developing the structure of the chromosome, creating a started population, creating a directing force for the population, etc.

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A mathematical model is presented for optimizing power flows in an electric network with a flexible controlled alternating current power transmission device - FACTS. The range of questions on the problem of optimizing the power flow in electric networks with one of the FACTS devices, the SVC static power factor compensator, has been expanded and investigated. The Lagrange function for the SVC device is proposed, which serves as the basis for obtaining a linearized equation and determining the optimum of the objective function. The method and algorithm of the optimization problem in the electric power system containing devices of the FACTS technology have been synthesized. The mathematical model allows for flexible and reliable optimization of the electrical power system. Flexibility is explained by the universality of the model, and reliability is explained by the high convergence rate of the Newton method used.