Using Bifurcation Analysis for Control Design of Virtual Negative Inductance

Document Type

Conference Proceeding


Faculty of Computing, Health and Science


School of Engineering




Dranga, O., Funato, H., Ogasawara, S., Hamar, J., & Nagy, I. (2004). Using bifurcation analysis for control design of virtual negative inductance. In 11th International Power Electronics and Motion Control Conference (EPE-PEMC’04). Riga, Latvia.


A variable active-passive reactance (VAPAR) has already been proposed for applying as virtual variable inductance in power circuits. One of its most remarkable features is the capability of generating a negative virtual inductance. VAPAR has found applications in the rapid power flow control of power systems, the power flow being essentially restricted by a line reactance. Therefore, the system under investigation is represented by a series RL configuration including VAPAR. One basic aim of the design of the feedback loop controlling VAPAR is to avoid instability or bifurcations that can be detected when the loop gain is varied. The stability analysis performed uses the stroboscopic map to model the operation of the variable-structure, piecewise-linear, non-linear system. The nonlinearity stems from the dependence of the switching instant of VAPAR on state variables. The eigenvalues of the Jacobian matrix of this map, evaluated at its fixed point, are employed for the stability assessment. The results allow convenient and accurate identification of the control domain ensuring stable operation and good transient performances in the parameter space of the virtual negative inductance and the loop gain.

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