## 3 The Proposed Control System
### Improved CVB Method  
The capacitor voltage imbalance not only compromises the converter efficiency but can also lead to reduced system reliability and increased maintenance costs [28]. Therefore, the development of effective control strategies to mitigate and manage capacitor voltage imbalances is a key issue in the design and operation of MMCs [29]. Several research efforts have been conducted to address this challenge, focusing on various control strategies [30]. Previous works have explored traditional proportional-integral (PI) controllers [31] and model predictive control [32; 33; 34]. Nevertheless, these methods often depend on precise sensor feedback, which increases both the complexity and the cost of the overall system, necessitating additional hardware and sophisticated signal processing to ensure reliable performance [35]. To optimize capacitor voltage balancing algorithms, some researchers have proposed several solutions, including reducing the computational load on the processor or a new MMC topology that has the ability to self-balance the capacitor voltage. By using auxiliary circuits and not requiring information about the voltage of each SM capacitor, voltage sensor and processor computational loads are reduced. Reference [36] proposed a new MMC topology with capacitor voltage self-balancing capabilities, relying on three voltage sensors and eliminating the need for sorting algorithms. However, while this method reduces control complexity, it needs auxiliary circuits and three voltage sensors. Reference [37] proposed a new method for estimating the SM capacitor voltage using one voltage sensor per arm and one current sensor at the converter output. The method is based on a Kirchhoff voltage law and circuit relations governing the AAMC; however, it needs six voltage sensors and three current sensors to realize the voltage balancing. A sensorless capacitor voltage balancing technique was proposed in [38]; it uses a logical permutation sequence for capacitor voltage balancing in a five-phase MMC. Nevertheless, this strategy does not target a simple three-phase MMC configuration with less control complexity. Using a reduced number of voltage sensors and an estimation technique, reference [39] proposed an approach for monitoring the condition of SM capacitors in MMCs. Nonetheless, one voltage sensor is required for each set of SMs in each arm. Reference [40] proposed a method for estimating the voltages of SM capacitors in an MMC using a Kalman filter with one voltage sensor per arm. The computational complexity of this method is relatively high, requiring significant processing power and real-time resources, which can increase the overall cost and latency of the control system. A technique for balancing capacitor voltages was proposed in [41], using an algorithm for sorting the measured capacitor voltages and selecting the SMs to insert according to the current direction. However, a voltage sensor is required for each SM in each arm. The above methods reduce the number of sensors to varying degrees, but our proposed CVB method is unique in that it eliminates the need for external sensors, relying on estimation techniques based on mathematical models to predict capacitor voltages [20]. This approach not only simplifies the system architecture by eliminating the need for additional physical components but also enhances cost efficiency and reduces potential points of failure, relying solely on the robustness of algorithmic computations. By eliminating the influence of measurement noise, this technique offers significantly better accuracy than the above methods, as well as improved responsiveness to rapid load variations. This is because it optimizes the insertion of SMs via dynamic current-based classification, which limits unnecessary switching and reduces the associated losses.