Analysis of modal interaction in power systems with FACTS controllers using normal forms

In this paper, an analytical procedure based upon normal form (NF) theory and the Kronecker product, is proposed for the analysis of second-order modal interaction in power systems with multiple static VAR compensators (SVCs). The approach used is based on a flexible representation of the power system and may be used to study higher-dimensional systems. First, an analytical derivation is developed which is utilized to investigate the effects of nonlinear modal interaction on system dynamic performance. Next, analytical expressions are derived that provide approximate solutions near a singularity and techniques for interpreting these solutions in terms of modal functions are given. The analysis methodology is demonstrated on a practical 46-machine, 189-bus test system in which several SVCs are used to support system voltage. Results of the second-order normal form study are presented and techniques for implementing each phase of the method are discussed. The analysis results are compared with the detailed step-by-step time-domain simulations (SBSS) of the system to test the validity of the analysis.