Voltage stability analysis using quadratic objective function taking into account equality constraints

Calculation of maximum loading condition boundaries is an essential task for voltage stability margin evaluation. The current tendency is connected with the continuation method for maximum loading condition evaluation. As this method depends on the expert evaluation, it is known to be computationally burden. Therefore direct methods are actively developed for static stability margin assessment. The author group proposes quadratic objective function consisting of the squared residuals sum of node voltage equations to evaluate maximum loading condition. The paper presents the development of research devoted to the searching maximum loading condition with the accounting for equality constraints. The constraint under consideration is the condition of constant load factor. Proposed constraint is described and calculated by the usage of Lagrange method and penalty function method. The convergence of the iterative process to the extremum of the objective function which corresponds maximum loading condition is achieved by using a modified Newton method. Test calculations were made to evaluate maximum loading condition on example of PQ bus - the infinite bus system, two PQ buses - infinite bus system, PQ-bus - PV-bus - infinite bus system and 7 buses system taking into account power factor constraints of load nodes. The proposed objective function and algorithm of searching maximum loading condition boundary allow to identify accurately power system security margin. The algorithm implemented in the software package can be used for the modification of software for monitoring system security margin and for determining the maximum allowable power flows on the sections under control.