Stability Analysis of the Sinusoidal Orbits of a Nonlinear Proportional and Resonant Current Regulator for Islanded Microgrids

Conventional control of islanded microgrids employ power electronic inverters as voltage controllers. However, inverters can also be operated in current control mode with a number of desirable features. One proposed scheme is to use a proportional and resonant controller to regulate the inverter output current and use the phase estimate from a PLL as a nonlinear feedback signal. It was recently shown that for linear time-invariant loads this current control scheme has a family of sinusoidal orbits in its state space, producing a sinusoidal output at the inverter. However, it remained an open question as to whether this family of sinusoidal orbits is stable in the sense that it attracts nearby trajectories in the system’s state-space. In this work we establish stability theorems for the sinusoidal orbits, providing explicit conditions for their stability.