Innovative dynamic models for the DC modular multilevel converter (DC-MMC) in rotating dq frame are presented in this paper, which are specifically designed to enhance converter design and stability analysis. Open-loop and closed-loop models are developed using three dq frames, providing a detailed examination of the impact of 2 ^nd and 3 ^rd harmonic components on the model accuracy. A novel contribution of this paper is the integration of a 2 ^nd harmonic current suppression controller (SHCSC) within the closed-loop model, offering new insights into its effects on system stability. The DC-MMC model is further extended by coupling it with high-voltage direct current (HVDC) cables on each side, forming an interconnected system model that accurately represents a more authentic scenario for future DC grids. The proposed model is rigorously validated against PSCAD benchmark model, confirming their precision and reliability. The interconnected system model is then utilized to analyze the influence of cable length on system stability, demonstrating practical applications. The closed-loop model is subsequently employed for stability assessment of the interconnected system, showcasing its applicability in real-world scenarios. Additionally, a damping controller is designed using participation factor and residue approaches, offering a refined approach to oscillation damping and stability optimization. The effectiveness of the controller is evaluated through eigenvalue analysis, supported by simulation results, underscoring its potential for enhancing system stability.