# Practical Submodule Capacitor Sizing for Modular Multilevel Converter Considering Grid Faults
## 1 Introduction  
Several commercial modular multilevel converter (MMC) projects have been deployed in the past few decades [1; 2; 3]. Compared with the traditional line-commutated converter (LCC), the MMC has many competitive advantages, e.g., low switching frequency, high conversion efficiency, strong scalability and reduced harmonic distortion [4; 5; 6; 7; 8; 9]. As a key part in the MMC, the SM capacitors must achieve high reliability in industrial projects, due to their high-voltage and high-power operating environment. Moreover, according to the national grid code shown in [10], the ability of grid-fault-ride-through is required for grid-tied MMCs. Especially in countries such as Germany and Canada, the converters must stay connected to the grid when a 100% voltage dip [11; 12] appears. These unexpected grid fault operation will bring extra voltage stress on SM devices (IGBTs and capacitors), which is one of the critical reasons leading to system-level failure [13; 14; 15; 16]. To avoid this problem, the SM capacitor is normally over-designed in practical cases, causing the rise of size and cost of the overall system. Thus, an optimized SM capacitor sizing method considering grid fault conditions is necessary for the practical MMC design. Some efforts have been devoted to the SM capacitor sizing to ensure the steady-state operation of MMCs [17; 18; 19; 20]. For instance, an SM capacitor sizing method is given in [17], based on the energy storage requirement of each SM. Dimensioning of SM capacitors considering energy fluctuation, ripple voltage is given in [18]. The minimum size for the SM capacitors to keep their voltage fluctuation is given in [19]. A computational design procedure in the aspects of maximum SM voltage, SM ripple voltage, and current stress is given in [20], considering the impact of the modulation index and the instantaneous power output. However, these methods assume that the system operates in steady-statewith normal grid conditions, which cannot be used to predict the SM voltage during grid faults. To solve this problem, the control method of the MMC under unbalanced grid conditions is discussed in [21] and the literature [22] gives the mathematical model of the SM voltage, considering the positive- and negative-sequence of grid voltages and the MMC arm currents. The above solutions can be used for SM capacitor sizing when the system operates in steady-state. However, the SM voltage is also affected by other factors, such as control strategies, modulation methods, circuit configurations, etc. For instance, the impact of the circulating current suppresion control (CCSC) on SM capacitor voltage ripples under different unbalanced AC grid conditions is discussed in [23]. With a second-order circulating current control [24], the SM voltage ripple can be reduced, i.e., a lower SM capacitance is required. An improved DC-loop regulator is proposed in [25] to suppress the capacitor voltage fluctuations. Considering unbalanced grid conditions, the DC-link voltage ripple is regulated through an arm voltage feed-forward control [26]. The interaction between the MMC modulation methods and the SM voltage stress is discussed in [27]. By applying a power decoupling circuit to each SM, the voltage ripple can be suppressed [28]. Hence, the sizing of SM capacitor should take the system control schemes into consideration. In addition, the SM capacitor sizing should also consider the transient state of the MMC during grid faults, which may induce catastrophic damage to the SM. To study the transient behavior of MMC system, a few literature works have been conducted [16; 29; 30]. A time-domain transient SM voltage analysis is shown in [16]. By taking the grid current control into account, the transient SM voltage response during grid faults is discussed in [29]. In Ref. [30], the transient response of CCSC and its impact on SM voltage are analyzed. Considering the impact factors above, the aim of this paper is ensure the reliability of SM capacitors when the system operates both in normal and grid fault states.