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.

The issues of improving of methods and algorithms for power system short-term mode optimal planning are considered. The main disadvantages and calculation difficulties typical for traditional algorithms are described. An effective algorithm for power system mode optimization based on a piecewise- linear approximation of nonlinear dependencies is proposed. Application of the proposed algorithm can effectively increase the accuracy and overcome many calculation difficulties associated with discontinuity of energy characteristics of power plants and various constraints in the form of equality and inequality.

In the article the problem of power system optimization under partial uncertainty of initial information is considered. The possibilities of using the methods of determinization to solve the problem of power system optimization taking into account the regime and technological constraints in the form of equality and inequality are researched. In basis of performed calculation studies using the example of the test scheme of power system, it was found that the optimization algorithm by the method of determinization can be effectively used for this proposes.

Optimal planning of short-term modes of power systems is a complex nonlinear programming problem with many simple, functional and integral constraints in the form of equalities and inequalities. Especially, the presence of integral constraints causes significant difficulties in solving of such problem. Since, under such constraints, the modes of power system in separate time intervals of the considered planning period become dependent on the values of the parameters in other intervals. Accordingly, it becomes impossible to obtain the optimal mode plan as the results of separate optimization for individual time intervals of the period under consideration. And the simultaneous solution of the problem for all time intervals of the planning period in the conditions of large power systems is associated with additional difficulties in ensuring the reliability of convergence of the iterative computational process. In this regard, the issues of improving the methods and algorithms for optimization of short-term modes of power systems containing thermal and large hydroelectric power plants with reservoirs, in which water consumption is regulated in the short-term planning period, remains as an important task. In this paper, we propose the effective algorithm for solving the problem under consideration, which makes it possible to quickly and reliably determine the optimal operating modes of the power system for the planned period. The results of research of effectiveness of this algorithm are presented on the example of optimal planning of daily mode of the power system, which contains two thermal and three hydraulic power plants..

Many existing methods and algorithms for optimization of short-term modes of power systems provide in calculations the introduction of a slack bus station, which ensures the balance of active power and, accordingly, the permissible frequency. In cases where the real load deviates from the planned one, determined by forecasting, the power system mode may turn out to be not optimal, and sometimes even not acceptable. This factor is especially noticeable in conditions of partial uncertainty of initial information about loads of nodes. To overcome this problem, planning of power system mode should be carried out taking into account the frequency change and, accordingly, the regulatory capabilities of all stations. This paper proposes an algorithm for optimization of modes of power systems in terms of partial uncertainty of initial information about loads, taking into account the frequency change. On the basis of computational experiments using the proposed algorithm, it is shown that taking into account the frequency change when planning modes of power systems with partially undefined loads of nodes can give a significant economic effect.

Based on the improvement of existing algorithms, an effective algorithm and program for taking into account the network factor have been developed for optimal planning of short-term modes of power systems with control of the load of power consumers, based on the restructuring of the dependences of the relative gains of losses on the power of nodes with settlement stations and regulated power consumers. As a result, it is possible to determine the optimal short-term modes of power systems, taking into account the network factor in terms of load management of power consumers.

Optimization of modes of electrical networks provides for the determination of rational values of reactive powers of controlled sources, voltages of reference nodes and transformation coefficients of adjustable loop transformers, at which the minimum costs associated with the production, transmission and distribution of electricity are ensured and all the specified operating and technological constraints are met. As a result of a lot of work performed by specialists from all over the world on the development of methods and algorithms for optimization the modes of electrical networks, at present, the methods for optimization of reactive powers and voltages of nodes are quite developed. At the same time, the algorithms for optimization of transformation coefficients of transformers, taking into account the provision of permissible voltage levels and minimum energy losses in closed electric networks by ensuring the optimal distribution of power flows in them, requires corresponding improvement. In this regard, this work proposes a new algorithm for optimization of modes of electrical networks on transformation coefficients of adjustable loop transformers. The results of researched the effectiveness of the proposed algorithm are presented.

The problem of optimization the modes of electrical networks pro- vides determination the optimal values of reactive power of sources, voltages of reference nodes and transformation ratios of controlled transformers. At pre- sent, methods and algorithms for optimization of reactive power and node volt- ages are sufficiently developed. However, the development of new efficient optimization algorithms of transformation ratios remains as a important topic. In this case, the issues of optimization of transformation ratios of transformers included in closed networks have a particular importance. This paper provides an effective algorithm for optimization the modes of electrical networks on transformation ratios of controlled transformers. The results of research of its efficiency in the presence of transformers with phase-rotary and longitudinal control in the circuit are presented. It is shown that minimization of losses in closed electrical networks when optimizing transformation ratios occurs due to the rational distribution of power flows in the branches.