Arman Akhmetbaev’s research while affiliated with Nizhny Novgorod State Technical University and other places

Calculations of steady-state modes of a complex electric power system are significantly simplified if we use the coefficients of distribution of the setting currents. The use of the theory of directed graphs for the formation of the matrix of the coefficients of distribution of the setting currents is directly related to the determination of the values of all possible and specific trees of the graph of a complex electric network. The authors have developed and implemented an improved algorithm. calculation of current distribution coefficients of the electric power system. The concepts of the “base” of the graph and the “hanging” contour are introduced. In this case, to calculate the current distribution coefficients, it is necessary to take into account all possible and specific trees of only the graph base. A method is indicated for supplementing the matrix of current distribution coefficients of the graph base to the current distribution matrix of the original graph. The paper proposes methods for simplifying the network topology based on the development of diacoptic principles.

Currently, the use of FACTS devices for voltage regulation and optimal control of electric power system modes is widely used. Controlled FACTS devices, based on power electronics, allow obtaining the desired characteristic of not only power transmission, but also a dedicated part of the electrical system. The paper presents the results of a study of the operating modes of a real distribution network, taking into account the installation of a static thyristor compensator (STC), in order to increase its operating reliability. The efficiency of distribution networks in and the area of existence of modes significantly depend on the installation location and the law of power control of compensating devices. To solve this problem, a systems approach based on graph theory methods is proposed. The conditions for stabilizing nodal voltages to reduce total active power losses in the electrical network are studied. The ranges of change in the required powers with the corresponding STC control laws are determined to ensure a minimum of total power loss in the network

The paper presents the results of a study of topological algorithms for the formation of a steady state of a complex electrical network, on the convergence of the iterative process. For a power transmission with distributed parameters, consisting of 5 nodes with a voltage of 500 kV, operating on a system of unlimited power, it is shown that there are two solutions and the need to introduce restrictions to obtain real solutions to nonlinear systems of equations. As the regime becomes heavier, the topological method ensures convergence and slow growth of the iterative process compared to the results obtained using the RASTR software package.

The work improves the algorithms for the formation of a steady state mode of electric power systems, developed on the basis of a topological model. The topological model is developed on the basis of the theory of directed graphs using a matrix of current distribution coefficients. Algorithms for the formation of a steady state provide for conducting calculations with respect to all independent nodes of a complex network of a power system, which leads to an increase in the number of operations of iterative processes. The paper proposes a transformation of the topological model of the system, in which, in the process of solving the transformed model, iteration is performed only over nodes that have non-zero load or generation powers. The rest of the nodal stresses are simply calculated through the stresses of the above nodes. The resulting transformation makes it possible to reduce not only the number of operations in each iteration, but also the number of iterations itself. In particular, when studying a 5-node test circuit [1], instead of four complex equations of the original system, it is sufficient to iterate only one equation (reduction by 25%), and for the New England test 39-node circuit [2], instead of 38 equations It is enough to iterate over 26 equations (32% reduction).

The paper proposes a new approach to determining the required powers of controlled compensating devices, in order to stabilize the desired node voltages from the standpoint of the synthesis of voltage modes. Optimal algorithms for searching and determining the values of all possible and specific trees of a complex directed network graph are given. Based on the values of all possible and specific trees, topological formulas for the distribution coefficients of the driving currents are determined, which are used to develop algorithms for the formation of established modes of the electrical system. By transforming the nodal equation, an analytical dependence of the powers of the compensating devices is es- tablished as a function of the complex of node voltages. The solution of the system of equations makes it possible to de- termine the required capacities of the compensation devices for stabilizing the voltages of the given nodes of the electri- cal network, from the standpoint of the synthesis of voltage modes.

The work was carried out on the basis of a topological model and the necessary parameters of the steady state were determined when specifying nodal loads with active and reactive powers. Equations of state of the electric power system are obtained with respect to the transformation ratios of transformers from the standpoint of the synthesis of voltage modes. An algorithm has been developed for the implementation of the formation and solutions of nonlinear equations of the transformation ratios of power transformers with an estimate of the tap changer control range that provides the desired voltage for a given network node. The calculations were carried out using the author's program and in the Mathcad Professional package using the example of a section of a real 220 kV network of Astana REC JSC. It is shown that when controlling the transformation ratios of a part of the supply network nodes, the operating parameters of other uncontrolled nodes remain the same as in a predetermined steady state.

The paper presents one of the possible variants of optimization of the algorithm for finding all spanning trees of the graph from the point of view of the application of the results of calculations in the topological study of complex electric power systems. The first stage of the topological analysis of the network is the search and determination of the values of all possible trees of the graph corresponding to a given energy system. The computational complexity of the algorithm for finding and determining the weights of all spanning graphs increases as the branches and nodes of the power grid network increase. The main idea of optimization is to build special classes of trees. At the same time, in the process of grouping, parts of future graphs that are "parent" for groups of graphs are allocated and corresponding graphs of significantly smaller dimension are constructed. If the analysis is time-consuming, the grouping process can be applied to each graph found.