Stability analysis of nonlinear power electronics systems utilizing periodicity and introducing auxiliary state vector

Variable-structure piecewise-linear nonlinear dynamic feedback systems emerge frequently in power electronics. This paper is concerned with the stability analysis of these systems. Although it applies the usual well-known and widely used approach, namely, the eigenvalues of the Jacobian matrix of the Poincare/spl acute/ map function belonging to a fixed point of the system to ascertain the stability, this paper offers two contributions for simplification as well that utilize the periodicity of the structure or configuration sequence and apply an alternative simpler and faster method for the determination of the Jacobian matrix. The new method works with differences of state variables rather than derivatives of the Poincare/spl acute/ map function (PMF) and offers geometric interpretations for each step. The determination of the derivates of PMF is not needed. A key element is the introduction of the so-called auxiliary state vector for preserving the switching instant belonging to the periodic steady-state unchanged even after the small deviations of the system orbit around the fixed point. In addition, the application of the method is illustrated on a resonant dc-dc buck converter

Stability analysis of nonlinear power electronic systems utilizing periodicity and introducing auxiliary state vector

Variable-structure piecewise-linear nonlinear dynamic feedback systems emerge frequently in power electronics. This paper is concerned with the stability analysis of these systems. Although it applies the usual well-known and widely used approach, namely, the eigenvalues of the Jacobian matrix of the Poincare/spl acute/ map function belonging to a fixed point of the system to ascertain the stability, this paper offers two contributions for simplification as well that utilize the periodicity of the structure or configuration sequence and apply an alternative simpler and faster method for the determination of the Jacobian matrix. The new method works with differences of state variables rather than derivatives of the Poincare/spl acute/ map function (PMF) and offers geometric interpretations for each step. The determination of the derivates of PMF is not needed. A key element is the introduction of the so-called auxiliary state vector for preserving the switching instant belonging to the periodic steady-state unchanged even after the small deviations of the system orbit around the fixed point. In addition, the application of the method is illustrated on a resonant dc-dc buck converter

Using Bifurcation Analysis for Control Design of Virtual Negative Inductance

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