Ordinary Differential Equations Mathematical Modelling of a Power Hardware-in-the-Loop Platform to Evaluate Photovoltaic Inverter IEEE 154 7.1 Unintentional Islanding Tests

The rise of distributed energy resources (DERs)., coupled with rigorous ride-through requirements and the integration of grid support functions (GSF)., has raised concerns about the effectiveness of inverter-based DERs in detecting and addressing unintentional islanding (UI) incidents. Inverters linked to power grids must accurately detect and respond to islanding events. The UI test., designed specifically for power inverters., utilizes the resonant parallel RLC load method., connecting an electric power source (EPS)., a power inverter or Equipment Vnder Test (EUT)., and an RLC load through a point of common coupling. The traditional discrete method uses a physical RLC load bank for the UI test implementation. Technological advancements have introduced the Power Hardware-in-the-Loop (PHIL) method., offering a faster and more suitable approach. Despite its potential., limited literature exists on implementing and validating the UI IEEE P1547 standard tests using PHIL. The integration of the inverter's GSF during PHIL UI testing also remains unexplored. This study proposes developing a dynamic mathematical model that represents the PHIL UI testbed to evaluate its performance and stability. The proposed mathematical model includes the inverter's GSF dynamic combined with a detailed DQ frame circuit of the UI test implemented with PHIL that allows a system's performance study through analysis techniques based on state variable representation and a MATLAB numerical method.