Time-Varying Model and Boundary Model of Differential Mode Circulating Switching Harmonics Among Multiple Inverters

Multiple inverters connected at the same point of common coupling (PCC) will generate the differential mode circulating switching harmonics (DM-CSHs), which can worsen the output current quality and threaten the inverter safety. The behavior of DM-CSH is dominated by PWM phase shift values, quantity of inverters, and grid impedance, where the time-varying output current harmonics and its boundary are hard to be estimated. To fill this gap, this article first builds the time-varying model that can precisely describe the rms trajectory of output current harmonics. Then, the time-varying model is deeply analyzed by employing the particle swarm optimization (PSO) to obtain the boundary model for different quantities and grid impedances. After that, the boundary model is further analyzed by the limit theory to obtain the extreme boundary for any quantity and grid impedance. Finally, the experimental results and measured field results verified the theoretical analysis. This article could help to estimate the amplification of current harmonics before installing the multiple inverters, where the possible overcurrent operation can be avoided.