Virtual impedance based stability analysis for direct digital controlled single-phase grid-connected inverter with LCL filter having wide inductance variation

In this paper an approach to adapting virtual impedance based stability analysis method for direct digital controlled grid-connected inverters with LCL filters having wide non-linear variation in inductance is presented. The non-linear time-varying inductance is due to soft-saturation characteristics of powder-iron inductor core, whose magnetic permeability varies with current. A state-space switching average model of the system is derived considering time-varying filter inductance terms. An energy-based Lyapunov function is used to show that stability of the system at any operating point is independent of the time-varying filter inductance terms. The stability is then analyzed graphically from a simplified parameterized model in s-domain using the concept of virtual impedance with filter inductance in the third dimension. Experimental results from a 5 kW single-phase grid-connected inverter implementing direct digital control based on an anhysteretic filter inductance model have shown good agreement with analytical results for various LCL parameters. The effect of hysteresis on stability behavior is further postulated and verified from the experimental results.