Investigating stability of power configuration including virtual negative inductance

Since power circuits are significantly influenced by inductances, a variable active-passive reactance (VAPAR) has previously been introduced in order to generate a virtual negative inductance, which has found applications in the rapid power flow control of power systems. It is used to cancel an existing undesired inductance, since the power flow through a simple power system of two voltage buses connected by an inductive power line is essentially restricted by the line inductance. These studies also indicated that the stability of the system could be compromised by the presence of stray capacitances. The present paper aims to offer a more accurate stability assessment of this RLC configuration, estimated so far by linear approximation, by essentially ignoring the switching process within VAPAR. The normal periodic steady-state regime leads to a fixed point in the stroboscopic map used to model the variable-structure piecewise-linear nonlinear system. The stability is indicated by the eigenvalues of the Jacobian matrix of the stroboscopic map, evaluated at this fixed point. The analysis reveals bifurcation behaviour and allows accurate and convenient prediction of the stability boundary in the parameter space of the virtual negative inductance required by the application and the stray capacitance present in the power circuit.