## 1 Introduction  
With the acceleration of the clean and low-carbon energy transition and the continuous advancement of new power system construction, the grid integration of a high proportion of new energy has become a development trend and characteristic of China's power system. The strong randomness and volatility of new energy outputs (e.g., the daily fluctuation of photovoltaic power can reach 80% of the rated capacity), when superimposed with the time-varying nature of load [1], have intensified the risk of frequent voltage limit violations at distribution network nodes. In power systems, reactive power plays a pivotal role in maintaining voltage stability, ensuring power quality, and enhancing grid reliability. Adequate reactive power support is essential to keep the voltage within acceptable limits, especially in distribution networks with high penetration of distributed energy resources (DERs). With the increasing integration of DERs such as photovoltaic power and wind power, the traditional reactive power optimization methods face new challenges due to the intermittent and uncertain nature of these sources. Events such as the 2003 power crises in North America and Europe have demonstrated that voltage instability has become a critical trigger for cascading failures in power grids [2]. There is an urgent need to conduct research on reactive power and voltage optimization and control for new energy grid-connected systems. In power systems, voltage violations at nodes caused by faults or other security factors often trigger cascading failures, which can lead to catastrophic accidents. Given the criticality of this issue, maintaining safe node voltage is of utmost importance for ensuring the safe and stable operation of power systems [3]. Recent studies have made significant progress in reactive power control. For instance, a three-phase shift power level controller (TPSPC) was proposed in [4], which can independently and effectively control active and reactive power in single-phase dual active bridge (DAB) DC-DC converters. This method demonstrates the potential for improving reactive power management in power systems. Another study [5] highlighted the importance of combining flexible alternating current transmission system (FACTS) devices and renewable energy sources (RES) for optimal reactive power dispatch (ORPD), aiming to reduce active power losses and enhance voltage profiles. Additionally, a reactive power controller for single-phase DAB DC/DC converters was presented in [6], which can regulate reactive power, while controlling the DC output voltage or active power. A comprehensive review of reactive power planning (RPP) methods was provided in [7], emphasizing the effectiveness of strategic RPP approaches in reducing power losses, minimizing equipment failures, and improving power quality. In response to the voltage instability problems arising from the integration of DERs, severe load fluctuations, and extensive deployment of power electronic devices, traditional reactive power optimization methods face three major challenges, as detailed below: First, centralized optimization based on static topology assumptions struggles to adapt to the time-varying network structure resulting from the random switching of DERs [8]. Second, conventional model predictive control (MPC) methods are constrained by the forecasting accuracy of renewable energy outputs, leading to insufficient regulation timeliness at the minute scale [9]. Third, the multi-timescale dynamic interactions among power electronic devices significantly increase control dimensionality [10], thereby posing a risk of dimensional explosion for traditional mathematical programming approaches. Current research on reactive power and voltage optimization (RPO) primarily focuses on three directions: deterministic mathematical programming (DMP), heuristic intelligent algorithms, and deep reinforcement learning methods.