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High-order Fitting Method of Boundary for Static Voltage Stability Region Based on Asymptotic Numerical Method
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State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China

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    Abstract:

    In order to calculate the static voltage stability boundary rapidly and precisely, an algorithm of fitting static voltage stability boundary based on asymptotic numerical method is proposed. By analyzing the equations formulated by the voltage collapse point, the general formula of the high-order partial derivatives of the static voltage stability boundary is obtained. Based on the asymptotic numerical method, the relationship between the fitting error and the boundary area is analyzed. The method avoids the multiple power flow calculations in traditional method, and has higher accuracy and lower time cost. On the other hand, the factor table of the existing coefficient matrices can be reused when calculating the high-order partial derivatives, which decreases the calculation burden. Finally, the related applications based on the method are presented. The cases based on IEEE 118 node system are established to verify the effectiveness of the proposed method.

    表 3 各阶导数值Table 3 Derivative values of different orders
    表 7 Table 7
    表 5 不同算法的时间对比Table 5 Time comparison of different algorithms
    图1 节点20与节点7的二维注入功率空间SVSR边界Fig.1 Two-dimensional SVSR boundary of injection power space based on node 20 and node 7
    图2 负荷节点20的二维注入功率空间SVSR边界Fig.2 Two-dimensional SVSR boundary of injection power space based on load node 20
    图3 不同阶数下的SVSR边界残差Fig.3 SVSR boundary residues with different orders
    图4 基于渐近数值法的三维注入功率空间SVSR边界Fig.4 Three-dimension SVSR boundary of injection power space based on asymptotic numerical method
    图 节点20有功与无功的二维注入功率空间SVSR边界Fig. Two dimensional injection of SVSR boundary in power space based on active power and reactive power of node 20
    图3 节点4与节点7的二维注入功率空间SVSR边界Fig.3 Two dimensional injection of SVSR boundary in power space based on active power of node 4 and active power of node 6
    表 4 二维边界算法时间对比Table 4 Time comparison of two-dimension boundary algorithms
    表 2 状态变量形成的雅可比矩阵最小奇异值Table 2 Minimum singular values of Jacobian matrix formed by state variables
    表 6 不同负荷增长方式下静态电压稳定指标Table 6 Static voltage stability indices with different load growth patterns
    图 渐近数值法构造SVSR边界流程图Fig. Flow chart using asymptotic numerical method for constructing SVSR boundary
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FENG Zhuocheng,WAN Kaiyao,JIANG Tong.High-order Fitting Method of Boundary for Static Voltage Stability Region Based on Asymptotic Numerical Method[J].Automation of Electric Power Systems,2020,44(7):100-106.DOI:10.7500/AEPS20190301001

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History
  • Received:March 01,2019
  • Revised:July 17,2019
  • Adopted:
  • Online: March 25,2020
  • Published: