Formulation and Visualization of Power System Bus Voltage and Reactive Power Safety Region
Liu Chengxi1,2, He Zaiyu1,2, Lai Qiupin1,2, Luo Yongjian1,2
1. School of Electrical Engineering and Automation Wuhan University Wuhan 430072 China; 2. Hubei Engineering and Technology Research Center for AC/DC Intelligent Distribution Network Wuhan 430072 China
Abstract：With the rapid economic development and growing electric power demand, power systems tend to be operated under heavier loads and closer to their stability limits. Consequently, it is critical for system operators to monitor the voltage and reactive power (volt/var) status in real-time at each bus and promptly detect violations to initiate remedial control actions proactively. Traditional methods, requiring extensive repeated power flow calculations to assess volt/var status against safety regions at each bus, impose an excessive computational burden unsuitable for online applications. Furthermore, conventional power flow analysis only evaluates the current operating point and cannot directly anticipate violations without supplementary sensitivity analysis. To address these limitations, this paper proposes a novel method for defining volt/var safety regions and their visualization based on nonlinear network decomposition. The objective is to provide a computationally efficient framework for assessing bus voltage conditions and generator reactive power outputs, eliminating the need for repeated power flow solutions. This method facilitates the rapid identification of buses at risk of volt or var violations and supports proactive voltage stability assessment under foreseeable operating conditions. The proposed method begins by constructing a set of virtual two-bus channels through nonlinear network decomposition, effectively transforming the original multi-bus system. Each bus is modeled as a virtual equivalent channel, enabling localized analysis of volt-var characteristics. A complex-valued index is introduced to describe the coupled volt/var status. To trace the status under varying load conditions, the holomorphic embedding method (HEM) is employed to derive the status index trajectory (SIT), capturing the complex-plane trajectory of each bus's Volt and Var status. Leveraging the analytical properties of HEM, closed-form expressions for safety region boundaries are derived. Specifically, the voltage safety region (VoSR) and its boundary are characterized as a circular region in the complex plane, while the reactive power safety region (VaSR) is represented by a linear boundary. These boundaries are visualized concurrently with the SIT, providing a comprehensive and intuitive depiction of the margin information. The effectiveness of the proposed method is validated on multi-bus test systems of varying scales. Simulation results demonstrate that visualizing the VoSR and VaSR enables early detection of weak buses and potential reactive power limit violations. Compared to traditional dispatching procedures—requiring operators to perform repeated power flow calculations for each operating status—the proposed method significantly reduces computational burden and enhances online applicability. It enables continuous, real-time assessment of the system's voltage stability margins and supports more informed decision-making for system operation and control. Overall, this research introduces a physical-HEM-based, analytical, and computationally efficient method for visualizing voltage safety regions and reactive power safety regions in power systems. The method's ability to predict and prevent voltage violations and reactive power exceedances enhances the reliability and stability of modern renewable-integrated power systems. This work provides fundamental insights into volt/var coupling behavior and contributes an operationally practical tool for real-time system monitoring and voltage stability management.
刘承锡, 何再雨, 赖秋频, 罗永建. 电力系统节点电压-无功安全域的构建与可视化[J]. 电工技术学报, 2026, 41(1): 156-168.
Liu Chengxi, He Zaiyu, Lai Qiupin, Luo Yongjian. Formulation and Visualization of Power System Bus Voltage and Reactive Power Safety Region. Transactions of China Electrotechnical Society, 2026, 41(1): 156-168.
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2026, Vol. 41 
