## 5 Discussion and Conclusions  
This paper has proposed an SG-DDPG-based voltage control method that integrates safety constraints into the reinforcement learning framework and leverages graph-based state representations to capture the topological characteristics of power networks. Four strategies have been compared: Without RPO (a baseline without any reactive power control), DDPG (without GCN), TD3, and the proposed SG-DDPG. DDPG served as a fundamental deterministic policy gradient algorithm for continuous control, while TD3 improved upon DDPG by incorporating a double Q-network and delayed policy updates to mitigate overestimation bias. However, neither DDPG nor TD3 explicitly enforced action constraints, which often resulted in non-zero voltage violation rates, even after convergence. In contrast, SG-DDPG incorporated a dual-variable safety layer that penalized voltage deviations exceeding \(\pm 5\%\) of the nominal value, thereby guiding the learned policy to maintain all bus voltages within the [0.95, 1.05] p.u. range. The DDPG method (without GCN) reduced both power losses and voltage violations but still exceeded voltage limits in 4.9% of time steps. The TD3 algorithm further improved the stability but failed to eliminate violations entirely, resulting in a 5.1% violation rate. In comparison, the proposed SG-DDPG achieved zero violations and the lowest active power loss (11.5 MW), demonstrating the effectiveness of combining safety constraints with graph-based feature representations. The experimental results confirmed the critical role of constraint-awareness, with DDPG and TD3 serving as representative DRL baselines. The No-RPO case further quantified the fundamental benefits of reactive power control. Moreover, the integration of GCN enhanced the spatial generalization capability, while the dual-variable mechanism ensured operational safety. Future work will explore dynamic graph partitioning and multi-agent coordination to further improve scalability and robustness.  
Conceptualization, X.Z. and X.G.; methodology, X.G.; software, P.S.; validation, X.G., P.S. and X.L. ([PERSON]); formal analysis, X.Z.; investigation, X.Z.; resources, X.L. ([PERSON]); data curation, Y.Z.; writing--original draft preparation, X.Z.; writing--review and editing, X.G.; visualization, X.W.; supervision, C.D.; project administration, X.Z.; funding acquisition, X.L. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Natural Science Basic Research Program of Shaanxi Province under Grant 2023-JC-ZD-38, and in part by the National Key Research and Development Program of China under Grant 2022 YFB3305502 and Grant 2022 YFB3305503.  
Not applicable.  
The data used to support the findings of this study are included in the article.  
The authors appreciate the comments and suggestions by the editors and anonymous reviewers.  
[PERSON], [PERSON], [PERSON] and [PERSON] were employed by the company Gansu Tongxing Intelligent Technology Development Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.