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The paper presents the possibility of simplifying the algorithms for forming the parameters of the steady state mode of a complex electrical network, using the independence of the currents of its equivalent circuit. In this case, all independent currents of a complex circuit of an electrical network must be found in advance, which is, in the general case, a rather difficult task, since it requires additional calculations of the steady state. The matrix of current distribution coefficients, formalized on the basis of the topology of the electrical network, can be used to directly determine the currents in the branches of its equivalent circuit. This allows you to preliminarily estimate the values of pre-selected independent currents in the circuit branches of a complex electrical network and determine its simplified design scheme. In this case, a calculation model is established, consisting of some trees of a complex electrical network graph.

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).

A systematic approach to determining the control range of the on-load tap-changer of transformers from the standpoint of the synthesis of the voltage mode is proposed. Transformations of the equation of nodal voltages, formalized on the basis of the topology of a complex electrical network, with respect to the transformation ratios of transformers are given.