Modified Map of Variable Active Passive Reactance for Stability Evaluation with Consideration of Capacitor Mode

Variable active passive reactance (VAPAR) can generate virtual variable inductance in power circuits .There are two poincare maps for studying of stability in the switching systems. One of them is first order poincare map. It is suitable for the systems with one fixed point on every switching period however; if the system has low periodic response in steady state the first order poincare map can not analyze behavior of the systems. In this case modified poincare map can determine stability of the systems. In this paper VAPAR stability with ac source include capacitor mode by modified poincare map is investigated. The stability region for period of time varying system can be found by eigenvalues loci of modified Poincare map. For computing of Jacobian matrix, the fixed point on each period is calculated by averaging theory.