Analytical Estimation of MMC Short-Circuit Currents in the AC In-Feed Steady-State Stage

Modular multilevel converters (MMCs) are vulnerable to DC short-circuit faults. Analytical estimation of the AC and DC short-circuit currents in the AC in-feed steady-state stage is essential to reveal fault mechanisms and design protections. However, the nonlinearity of the MMC has brought significant difficulties to the calculation. This paper proposes a novel analytical calculation method for the steady-state AC and DC short-circuit currents. First, various working modes of the MMC in the AC in-feed stage are specified, and the relations between the arm current and the short-circuit current in each mode are studied. Subsequently, the arm current is divided into multiple sub-intervals, and the analytical expressions of the steady-state AC and DC fault current are deduced by solving the arm current in the sub-intervals one by one. Moreover, the derived expressions are further optimized considering the resistive-inductive (R/X) characteristic of AC grids, making them applicable for various scenarios. These analytical expressions intuitively show the relations between the system parameters and the short-circuit currents, thus can guide the rating and tuning of protection devices and power equipment. Finally, the effectiveness of the derived expressions is verified, and the influences of the system parameters on the fault currents are discussed.