A Novel Lie Group Control Scheme for Off-Grid Operation of Dual-Mode Solar Microinverters

This article presents a novel Lie group-based control scheme for off-grid operation of single-phase microinverters. The off-grid operation of solar microinverters poses several challenges due to their small energy storage capacity, impacting their ability to handle sudden load transients. This article shows that the rotation groups, particularly the special orthogonal group ( $\text {SO}(2)$ ), is the natural framework to design the control system for off-grid operation. The proposed controller offers a fast transient response and reliable operation against severe load fluctuations. In the proposed methodology, $\text {SO}(2)$ group and its Lie Algebra $\mathfrak {so}(2)$ are used to generate the appropriate current reference and in turn control the voltage at the point of common coupling (PCC) for parallel microinverters. The control system is robust against variations in the output impedance, eliminating the need for virtual impedance compensation to maintain system stability. By avoiding the voltage reference drop caused by impedance compensation, the proposed controller can effectively regulate the output voltage with smaller deviations from the nominal voltage. Unlike conventional droop methods, the proposed controller can effectively handle any type of linear and nonlinear loads without requiring structural changes. Experimental results demonstrate the superior performance of the Lie group-based control technique compared with the conventional droop control.