## 1 Introduction  
As the demand for power quality from distribution network users increases, power quality has become a pressing concern for the power system. In recent years, improving power quality in low-voltage distribution networks has been a major focus for the power system in China. One critical research topic is to identify and mitigate three-phase load imbalances in low-voltage distribution networks in order to enhance network management. However, distribution networks are challenging to manage due to their vast geographic spread, complex loads, and numerous single-phase loads with strong randomness and unbalanced spatiotemporal distributions. These factors can lead to three-phase imbalance phenomena in distribution systems [1; 2; 3], causing increased energy losses during transmission, reduced electric energy utilization efficiency, and severe consequences on power supply security, power quality, and the economic operation of the power system. Therefore, it is essential to adjust the phase sequence in low-voltage station areas not only to conserve energy and reduce losses within distribution networks but also to ensure the efficient use of electric energy [4; 5]. Currently, the primary solutions for addressing the three-phase load imbalance issue in distribution systems include manual phase adjustment, reactive power compensation [6], asymmetric compensation, and distribution system controller management [7; 8]. Reactive power compensation and asymmetric adjustment can partially improve the performance of distribution transformers. However, they cannot effectively solve the three-phase imbalance issue in distribution system lines. The manual phase adjustment and automatic commutation via smart commutation switches are the principal methods for regulating unbalanced loads in distribution systems. The manual phase adjustment involves manually adjusting the phase sequence of three-phase load access using power system operators to address unbalanced three-phase load distribution issues in distribution systems. This approach is time-consuming, labor-intensive, and unable to timely track load fluctuations, thus limiting its application scenarios. With the maturation of automatic load commutation device technology and decreasing equipment costs, automatic commutation devices have been widely adopted and applied in recent years. Nonetheless, with the increasing penetration of renewable energy sources within the distribution network [9], there has been a growing proportion of nonlinear and impact loads, leading to changes in power supply concerning both magnitude and direction on transmission lines. Therefore, it is crucial to study reasonable control strategies for automatic load commutation devices that fully consider uncertainties related to renewable energy output and load demand within the power system. In order to ensure the relative balance of loads distributed across three phases to reduce line loss, numerous scholars have conducted research on load commutation algorithms and the uncertainty of user loads. In [10], a load adjustment method based on the historical power data for each phase in the distribution system and the electricity consumption information of each user in the substation is proposed. This approach avoids misadjustment problems caused by the access or fluctuations of transient random loads when adjusting the load through on-site current detection. A three-phase unbalance mitigation model considering the three-phase unbalance degree is proposed in [11], and a mixed-integer linear programming model is formulated. In [12], a load commutation strategy that considers the threshold of a three-phase imbalance is proposed to alleviate the phenomenon of three-phase load imbalances in distribution systems effectively.