Small-gain Stability of P-HIL for Evaluating Grid-Connected Converters During Asymmetric Grid Faults

Power-hardware-in-the-loop (P-HIL) offers a highly effective method to bridge the gap between theoretical research and practical application, avoiding the complexity and reduced flexibility often encountered in field testing, particularly under grid fault conditions. However, P-HIL presents its own challenges, including model fidelity and closed-loop instability due to the intrinsic loop delays. Moreover, asymmetric grid faults induce a paradigm shift in the P-HIL model, transforming it into a multiple-input multiple-output (MIMO) system. The need to define a robustness margin for MIMO-based P-HIL becomes evident, as the conventional margins do not adequately evaluate the robust stability. In this paper the small-gain theorem is used for stability assessment, and the H∞-norm is established as robustness indicator in P-HIL based on ideal transformer methods with stabilizing low-pass filters (LPF). A robust stability analysis addressing uncertain fault severity conditions, variable converter power references under fault-ride-through scenario and uncertain loop delays is presented, and the analytical findings are validated in Matlab/Simulink environment. The paper delineates a robust design of the LPF, by considering parameter deviations in the LCL filter damping resistance of the converter under test. Finally, the analytical findings are experimentally validated.