As societal progress and advancements in productivity continue to unfold, the cable utilization of China's urban power distribution networks has progressively increased. The cable utilization rates in first and second-tier cities have surpassed 80%, with some cities exceeding 90%. However, this development has given rise to certain challenges. During periods of light load on the lines, the high capacitance and inductance of cable lines may lead to elevated voltages at the terminal ends of the distribution network. Furthermore, the widespread integration of distributed new energy sources in recent years introduces stochastic and fluctuating characteristics that may result in recurrent voltage violations, compromising power supply quality. Consequently, it becomes imperative to deploy reactive power compensation devices for line configuration. In recent years, scholars have proposed the integration of magnetically controlled reactors with transformers. By regulating the saturation level of the transformer core, the excitation reactance of the transformer can be altered, presenting a viable solution for reactive power control. This article conducts circuit theoretical analysis and MATLAB/Simulink simulation analysis for planar parallel and planar series-connected single-phase magnetically controlled transformers. The validity of the theoretical formulas is verified, and a comparative analysis of their compensatory effects is presented. This research holds significance in guiding the practical application and selection of magnetically controlled transformers.