The study of the static stability of complex electrical systems

The article shows the effectiveness of the joint application of the equations of node voltages (ENV) and the Lyapunov`s function in a quadratic form for the analysis of small oscillations of a power system, in the literature called method Allaev. The joint solution of the equations of node voltages and Lyapunov`s matrix equation allows to determine the stability conditions of the electrical system and identify the generator, which first approaches the stability limit. As will be shown below, studies of small oscillations of complex electrical systems can be carried out in full on the basis of matrix methods, successfully developed in recent decades. This is facilitated by the removal of memory limitations and a sharp increase in the speed of computing modern computers.