Reducing the cost of implementing phasor measurement units (PMUs) can be achieved by determining the minimum number of devices needed to provide the electrical network observability. This article describes the optimal PMU placement algorithm, based on the analysis of the topological properties of the electrical network. It was shown that the optimal placement of PMUs can be achieved by dividing the nodal admittance matrix into four submatrices, one of them will be a band submatrix, which can be reduced to a lower triangular matrix of maximum rank by elementary transformations. Results reflecting the number of installed PMUs were obtained for IEEE test bus systems with 9, 14, 19, 30 and 57 nodes. For all test bus systems, the proposed PMU placement algorithm provides complete observability of the system with the same or fewer nodes of installation in comparison with the results of other authors. There were carried out computations with the help of the algorithm accelerated calculations of state estimation performance in power systems, in order to confirm the correctness of this approach. There were determined conditions under which the equations of nodal voltages were solved linearly and nonlinearly (iteratively).