Abstract:This article investigates the voltage rise problem induced by regenerative braking in heavy-load electrified railways with long gradients and proposes a stability evaluation method based on the rise mechanism. An iterative model is formulated by deriving vector relationships among no-load voltage, rise voltage, load voltage, and braking current, revealing the formation of overvoltage during braking. The effects of power factor, regenerative power, load position, and system instability on voltage stability are analyzed. Results show that a higher power factor facilitates voltage balance under combined traction and braking, significantly mitigating voltage rise, while the influence of regenerative power variation is limited. Voltage rise is most severe when the load is located at the end of the power supply arm and weakest near the substation. Parallel power supply enhances system redundancy and suppresses fluctuations. Further analysis indicates that no-load voltage level plays a dual role, which is that higher values improve adaptability to regenerative power but increase overvoltage risk. However, lower values reduce rise but constrain traction capacity. A recommended range of 27.5~28.5 kV is suggested. In addition, introducing inductive loads is shown to effectively suppress voltage rise by enlarging the no-load voltage angle and reducing the load voltage angle. An engineering application requires dynamic adjustment of inductive loads between regenerative and traction states. This study provides theoretical and practical guidance for voltage stability regulation in long-gradient electrified railways.