This paper presents a dynamic phasor-based state-space modelling framework for modular multilevel converters (MMCs) using multiple dq reference frames (DQsym). The main contribution is the development of a numerically stable state-space 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 converter-dominated grids.

Modern power systems with high penetration of inverter-based resources (IBRs) exhibit fast dynamics and complex harmonic interactions that challenge conventional modelling tools. Electromagnetic transient (EMT) simulations provide high fidelity but are computationally demanding for large-scale studies due to small time-step requirements, whereas conventional phasor-domain models neglect harmonic and higher-frequency effects to allow for larger time-steps. This paper proposes a unified dynamic-phasor-based framework (DQsym), implemented as a MATLAB/Simulink library, that combines dynamic phasors with multiple rotating reference frames and defines explicit algebraic rules for harmonic-domain operations compatible with state-space formulations, enabling systematic assembly of interconnected system-level models beyond isolated component representations. The formulation supports modelling across multiple harmonic orders and is expressed in state space, providing a natural pathway for future integration with small-signal analysis and control design tools, although such extensions are outside the scope of this paper. The approach is validated through: 1) benchmark case demonstrating higher-order harmonic modelling capability and 2) simulations of an IEEE 9-bus system expanded with point-to-point HVDC transmission based on a modular multilevel converter (MMC), where the framework reproduces fundamental and second-harmonic dynamics indicating that DQsym reproduces the overall harmonic pattern and closely matches the fundamental component compared with EMT results. The proposed framework provides a structured and accurate harmonic-domain modelling tool for the analysis of IBR-rich power systems.