Improvement of Algorithms of the Topological Model of the Steady Mode of Electric Power Systems

Abstract

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 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).