On the other hand, as with most conventional converters, the MMC has specific control requirements. For instance, the voltage-balancing of the submodule (SM) capacitors in the converter is critical. However, due to the series of cascaded SMs which are used to construct the converter, the reliability of the MMC is an important challenge [5]. In one example of a real application based on the MMC is presented in [6], where hundreds of SMs per leg were used. This also requires a great many voltage sensors in order to achieve the voltage-balancing of the system. This problem has been extensively investigated in recent research [3,7]; but many voltage sensors are always used in such studies. However, it would be preferable if this issue could be resolved with lower cost and complexity.Several proposals have been attempted to minimise the number of voltage and current sensors required. For instance, successful simulation and practical results have been achieved with fewer current sensors [8][9][10]. However, no reductions in voltage sensor number were discussed in those studies. Another attempt based on an open-loop scheme has been suggested, where fixed PWM signals were applied to the converter [11]. Although, this proposed scheme does not use any sensors since it does not require any form of feedback control, the wellknown disadvantages of open-loop control schemes may threaten the performance of the system. In some recent studies, online observers have been introduced to estimate individual SM voltages [12,13]. For example, fewer voltage sensors could be achieved based on a sliding mode where the proposed method merely monitors the total input voltage and arm current of the converter [12]. This technique has been proposed for fault detection scheme. However, variations in SM capacitance were not considered in this study. In an attempt to ameliorate this problem, the estimation of capacitance values for each individual SM was considered in [13]. This improvement provides an important solution against concerning capacitance; however, in all observer-based methods the effect of variations associated with arm inductor values was not included in the design. In very recent research [14,15], the voltage-balancing of a seven-level MMC has been achieved with important reductions in the number of voltage sensors required, where the lowest number of voltage sensors needed is two when sevenlevel MMC is used. Two sensors are contributed to measure total arm voltage of the converter. On the other hand, the main UK

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Different schemes of modified conventional sorting algorithms with low complexity are proposed in order to balance the voltages of submodule (SM) capacitors for the modular multilevel converter (MMC). Two different procedures are investigated in this study. The main idea is to achieve voltage balance within the MMC arms with fewer current sensors. The two different methods are examined under different operating conditions; for instance, with a sudden change in the DC-source or when different load values are applied. The advantage of such sensor-less control methods is to simplify hardware communications in general. Moreover, the reliability of the MMC is also improved. Simulation analyses of a single-phase four-level MMC are conducted to show the effectiveness of the proposed methods.