Dynamic Phasor State-Space Solver For Hybrid Ac/dc Systems

This paper presents a dynamic phasor-based statespace modelling framework for modular multilevel converters (MMCs) using multiple dq reference frames (DQsym). The main contribution is the development of a numerically stable statespace solver tailored to multi-dq dynamic phasor models. The solver employs integration and a systematic matrix update mechanism to consistently incorporate switching events within the unified state-space formulation, allowing harmonic interactions and topology changes to be captured without manual reconfiguration. The proposed framework is implemented as a standalone MATLAB/Simulink library to facilitate time-domain simulation and to provide a structured basis for future eigenvalue-based small-signal stability studies. The approach is validated on a point-to-point HVDC system and benchmarked against an EMT model. Results demonstrate that the DQsym-based implementation achieves EMT-level fidelity while maintaining state-space structure suitable for scalable, system-level analysis of converterdominated grids.