Abstract
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.