Versatile Converter Impedance Modeling with Matrix Signal Flow Graphs to Include Frequency Coupling

The behavior of grid-connected converters is defined by their control systems over a wide frequency band. Understanding the impact of the control design on the converter output impedance is thus essential. In the lower frequency range, asymmetric control elements such as the phase-locked loop (PLL) or DC link control introduce frequency coupling, resulting in a multiple-input multiple-output (MIMO) system structure. Deriving the MIMO converter impedance model can be a complex and demanding task. This paper presents a structured approach to model the converter output impedance based on its signal-flow graph that accounts for asymmetric control loops and frequency coupling. The technique is applied to analyze the impedance of a real converter system, focusing on the low-frequency range. The obtained analytical impedance curves are validated by experimental impedance measurements that capture frequency coupling. Finally, the validated converter impedance matrix is used to assess and mitigate a low-frequency instability observed in a power hardware-in-the-loop (PHIL) setup.