Stability analysis of power circuit comprising virtual inductance

The concept of a variable active-passive reactance (VAPAR), which can generate a virtual variable inductance in power circuits, including negative values, has already been proposed. Since it has found application in the power flow control of power systems, where the power flow is essentially restricted by a line inductance, the aim of the paper is to report on the stability of this virtual inductance in an RL circuit. The periodic steady-state operation of the variable-structure, piecewise-linear, nonlinear system is modeled by its Poincare map. The stability criterion employs the position of the eigenvalues of the Jacobian matrix of the Poincare map, evaluated at its fixed point. Bifurcation behaviour when varying the virtual inductance is revealed. Such an analysis allows accurate prediction of stability boundaries and facilitates the selection of parameter values to guarantee stable operation.