Modeling Lyapunov Control-Based Selective Harmonic Compensated Single-Phase Inverter in the Dynamic Phasor Domain

Single-phase grid-forming inverters are commonly used in uninterruptible power supply (UPS) systems that feed single-phase critical loads in homes, data centers, and hospitals. With the increasing use of power electronics-interfaced loads, single-phase UPS inverters are being designed to exhibit characteristics such as low total harmonic distortion (THD) in output voltage, fast dynamic response, and strong robustness against large changes in load, to ensure a seamless operation of critical loads. The Lyapunov-function-based control strategy is a popular method to provide these characteristics in UPS inverters. However, most studies and designs related to Lyapunov-function-controlled single-phase UPS inverters are conducted by using detailed switching models. While detailed switching models accurately represent the true dynamics of power converters, simulating these models with nonlinear control schemes requires small time steps to produce accurate results. To address this limitation, we propose a new model of Lyapunov-function-based single-phase grid-forming inverter using the dynamic phasor (DP) method. The DP method transforms time-domain signals into slow-varying signals, enabling the use of larger time steps in simulations, which results in shorter simulation times. In the proposed DP model, the Lyapunov energy function is constructed in the DP domain using the dominant harmonics of the inverter output voltage and output current as state variables. The high accuracy and superior computational speed of the proposed DP model are validated through comparison with results obtained from a detailed model with natural-frame-based Lyapunov-function control. Experimental test results confirm the validity and high accuracy of the proposed DP-based method of modeling Lyapunov-function-controlled single-phase grid-forming inverter.