**1. Introduction**

To date, modular multilevel converter (MMC) is a preferred technology for high-power medium/high-voltage distribution and transmission applications due to ease of scalability, modularity, reduced power losses, and high-quality ac and dc side waveforms [1]. However, the use of submodules (SMs) with floating distributed capacitors in MMC results in complex internal dynamics, which necessitates the adoption of a complex multi-layer control system compared to that of conventional voltage source converters.

Typically, the common-mode current of balanced MMC consists of dc and harmonic components, and its dc component acts as a link between the dc power and the power flowing through SMs, which constitute the MMC arms. The harmonic components of the common-mode current circulate between the arms, which are widely referred to as circulating currents representing undesirable parasitic components that add losses and increase SM capacitor voltage ripples [1]. In contrast, the differential-mode currents of an internally balanced MMC are the fundamental output currents that flow in the ac side and responsible for power transfer between the MMC arm and ac-side output

circuit. Normally, the SM capacitor voltages affect the synthesis of ac and dc side voltages of the MMC, i.e., the differential- and common-mode voltages, respectively. To reduce such couplings, several control methods exist in the open literature for suppression of the circulating current and regulation of the capacitor voltages independent of dc-link voltage [2].

SM, arm, and phase-leg voltages/energies represent three important elements or layers that must be controlled to minimize MMC internal dynamic interactions during normal and abnormal conditions. To manage the voltage differences between SMs within each arm, SM voltage balancing algorithms based on either centralized sorting or distributed control are employed [3,4]. Generally, MMCs with de-coupled internal-external dynamics respond faster to active power and dc voltage set-points; exhibit reduced output voltage distortion during major transients and overall impacts of cross-modulation on ac and dc side waveforms [5,6]. Wide-ranging research efforts have been invested into high-level controllers (capacitor voltage/energy sum controllers in arm and phase-leg levels) [7,8], in which predominantly ideal (identical) passive components are usually assumed. Although a large number of SMs may reduce the adverse effects of capacitance tolerances, passive component tolerances remain a prevalence issue, particularly, for MMCs, with a relatively low number of SMs per arm as anticipated in medium-voltage (MV) applications. Therefore, it is imperative to account for uncertainties due to passive component tolerances during MMC design and maintenance stages [9–12]. In this line, the adverse effects of asymmetrical cell capacitances on the ac output voltage of MMC that employs three-level flying capacitor SMs have been identified when the energy-based balancing approach was used in the high-level controllers that regulate the MMC internal dynamics [10]. The work in [11] has revealed the inducement of fundamental frequency ripple in the dc-link current of the MMC with asymmetrical arm inductances and proposed a voltage-based active control method to suppress the induced fundamental frequency ripple from the dc-link current.

On the other hand, a fault that happened in MMC SMs may cause operational issues ranging from distortion of ac and dc side voltages and currents to total disruption of power transfer. Methods for SMs fault detection and identification are proposed in [13–15], while increased MMC resiliency to SM faults through the concept of redundant SMs are discussed in [16] and [17]. With regard to the SM fault tolerance capability of the MMC, several SM-fault control methods have been discussed [18–21]. Two approaches are proposed, and the respective features are presented in [18]. The fundamental common-mode current ripple during SM faulty has been claimed in [19], and a dq-frame-based control method is proposed. However, this method depends on phase lock-loop for the ripple. Further research in [20,21] has proposed proportional resonant (PR) based control methods to suppress the fundamental ripple, but the control effects on the overall operation are not analyzed. Besides, in most previous works, the predominant assumption is that the number of faulty SMs is less than the number of redundant SMs or within a hot redundancy configuration, while the extreme condition, in which the number of faulty SMs is larger than the redundant SMs, is seldom discussed. In these cases, SM capacitor voltages would be increased, within a safe margin, for continuous operation.

Based on the preliminary findings in [22], this paper considered the adverse effects of MMC asymmetry caused by SM fault on both dc and ac sides when mainstream balancing control methods are employed. The differential-mode voltage balancing control method reduces the fundamental component in the common-mode and dc-link currents of the MMC with significant passive component tolerances. However, its effectiveness is limited since it is not direct control but via minor ripple injection, and its control objective is to nullify the differential-mode capacitor voltage sums. Considering the random nature of the passive component tolerance distribution within one phase-leg of an MMC-based power conversion system, the proportional-resonant (PR)-based controller that operates at the fundamental frequency was studied to suppress any fundamental circulating component that may arise in the three-phase common-mode currents. Comparatively, control effects on both ac and dc side performances were investigated in this paper. This paper is organized as follows. Section 2 provides a brief review of MMC operation fundamentals, and Section 3 discusses the issues that arise due to component tolerance and SM fault. Section 4 introduces the internal control methods against internal imbalance. Section 5 verifies the effectiveness and assesses the performances of control methods. Finally, Section 6 summarizes this paper.

#### **2. MMC Basic Operation**

Figure 1 shows a three-phase half-bridge MMC, with *Vdc* and *Idc* representing dc bus voltage and current, respectively. Each phase-leg consists of upper and lower arms, and each arm comprises a reactor with nominal inductance *LARM* and *N* series-connected SMs. Each SM consists of a capacitor with nominal capacitance *CSM* and an IGBT-based half-bridge circuit. The term circulating current represents the ac component of the common-mode current, *icm*. The *icm* is mainly caused by cross-modulation of the upper and lower arms or, simply, the interaction of the arm voltages, currents, and switching functions. Strategies of the inner-arm SM voltage balancing and the second-order circulating current suppression have been widely discussed [2–5]. Figure 1 also shows a generic MMC connected into the ac grid through an interfacing transformer.

**Figure 1.** Modular multilevel converter (MMC) topology configuration.

Under the ideal condition, each MMC arm has an equivalent capacitance *CARM*, which can be calculated as:

$$\mathbb{C}\_{ARM} = \frac{\overline{\mathbb{C}\_{SM}}}{N} \tag{1}$$

As the arm equivalent capacitance is alternatively charging and discharging, the MMC internal power can be dynamically balanced as it transfers power between ac and dc sides.

Figure 2 visualizes the MMC power paths, which can be divided into ac and dc loops. The dc loop depicted in Figure 2 represents the conduction path through dc output to MMC phase-leg, in which the common-mode current of each phase follows, which consists of ac and dc components (*icm* = *Id* + *ih*, where *Id* and *ih* are dc and harmonic components of *icm*). In a three-phase MMC, the dc components of the common-mode currents of the phase legs add to the dc-link currents that flow in the positive and negative dc poles at the upper/positive and lower/negative dc nodes. In this way, the MMCs exchange power with the dc side. The ac components of the common-mode currents of the MMC phase legs are predominantly second-order harmonics and add to zero at upper and lower dc-link nodes; they represent parasitic currents, which increase the MMC SM capacitance requirement for a given voltage ripple and semiconductor losses. In contrast, the depicted ac loop represents the conduction path through which each MMC phase-leg exchanges active power with ac side and

fundamental frequency ac current flows. The output phase current represents the differential-mode current; for example, for a phase A, *ia* = *iau* − *ial*, where *ia*, *iau,* and *ial* are output and upper and lower arm currents. In a balanced three-phase MMC, the fundamental frequency components of the currents add to zero at positive and negative dc nodes; while in an internally unbalanced MMC with asymmetrical ac and dc loops in the phase-legs, the asymmetries introduce zero and negative sequence fundamental frequency components in the common-mode currents of the phase-legs, which may leak into dc side and appear as fundamental frequency ripples in the dc current.

**Figure 2.** Diagram of MMC internal dynamics (phase A).
