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... certain nodes and branches. The graphs thus obtained have much fewer trees, from which the trees of the initial graph can be obtained by adding the removed branches and nodes. This algorithm of determining all possible trees of a graph was tested against the circuit of a 220 kV network section of the power system of the Republic of Kazakhstan (Fig. 1) in [6], where the number of possible trees was equal to 85. The circuit had n = 9 nodes and m = 11 ...
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Citations
... Calculations of the powers of compensating devices can be obtained on the basis of a topological model of the formation of steady-state modes. After replacing the setting currents � with powers, the equation of the steady-state mode is written as follows [12,13]: ...
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
... In [7], an analytical approach to determining the topological content of current distribution coefficients is proposed. The essence of the approach is that an analytical proof of the formation of specific trees of a directed graph is obtained, without determining 2-trees of the graph, based on all its possible trees [8]. Then, the value of the distribution coefficient in a branch from the node current is determined by the topological expression: (2) where is ∑ the total value of all possible trees in the graph; �� is the algebraic sum of the values of specific trees in the graph of the i -th branch. ...
... The remaining elements of the first six rows will be as follows: at column 7, the same as that of column 5, since node 7 is connected to node 5. At columns 6 and 7, the same as that of column 1, and the remaining columns 8,9,10,11 are the same as that of column 4, since node 4 is a connecting node of the second "hanging" circuit with nodes 8,9,10,11. The seventh row, corresponding to the seventh branch, will be zero, with the exception of the 5th element, where the value -1 will be located. ...
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.
