This paper investigates the dynamic behavior of a modular multi-level converter (MMC)-based HVDC link. An overall state-space model is developed to identify the system critical modes, considering the dynamics of the master MMC and slave MMC, their control systems, and the HVDC cable. Complementary to the state-space model, an impedance-based model is also derived to obtain the minimum phase margin (PM) of the system. In addition, a relative gain array (RGA) analysis is conducted to quantify the level of interactions among the control systems of master and slave MMCs and their impacts on stability. Finally, with the help of the results obtained from the system analysis (eigenvalue, phase margin, sensitivity, and RGA), the system dynamic performance is improved.3 of 19 an eigenvalue and participation factors analysis in Section 6. Moreover, the system minimum PM is calculated through an impedance-based analysis using the Nyquist plot, and the level of interactions among control loops is studied using a frequency-dependent relative gain array (RGA) analysis. Finally, in Section 7, based on the results achieved from the system analyses, the stability of the system is improved by tuning the DC voltage control loop.
System DescriptionA typical HVDC link between two AC networks is shown in Figure 1. In such configuration, the master MMC regulates DC voltage while the slave MMC controls active power exchange [27]. Either AC voltage or reactive power can be regulated at both ends. AC network 1 HVDC cable AC network 2 Master Slave V dc control P control