Bifurcation Analysis Based Control Design for Virtual Negative Inductance

Previous studies have already introduced a variable active-passive reactance (VAPAR) to be used as virtual inductance in power circuits. Its most remarkable feature of generating a negative virtual inductance can be used to cancel an undesired existing inductance. It has found applications in the rapid power flow control of power systems, for flexible AC transmission systems, where the power flow is essentially restricted by a line inductance. Therefore, the operation of VAPAR has been investigated within the frame of an RL configuration. The present paper aims to contribute to the control design of VAPAR, which has to avoid the occurrence of any bifurcation within the intended range of the parameters. A stability analysis is carried out by modelling the periodic steady-state operation of the variable-structure piecewise-linear system by a stroboscopic map. Determining the eigenvalues of the Jacobian matrix of the stroboscopic map, evaluated at its fixed point, reveals bifurcation behaviour as a result of varying the control parameters, as well as the effect on the overall system dynamics. The approach allows convenient and accurate identification of the control domain in the parameter space of the virtual negative inductance and the control parameters, which guarantee stable operation and good transient performances.