Research on Hybrid State Estimation of Distribution Networks with Renewable Energy Integration Based on Generalized Benders Decomposition

GAO Liping; YAN Jun; HENG Dongqiang; WANG Song; LI Jiang

doi:10.14044/j.1674-1757.pcrpc.2025.05.005

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Research on Hybrid State Estimation of Distribution Networks with Renewable Energy Integration Based on Generalized Benders Decomposition

Optimal Control Technology of Traction Power Supply System and New Power Distribution System | 更新时间：2025-10-30

- Research on Hybrid State Estimation of Distribution Networks with Renewable Energy Integration Based on Generalized Benders Decomposition
- Power Capacitor & Reactive Power Compensation Vol. 46, Issue 5, Pages: 45-53(2025)
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- DOI：10.14044/j.1674-1757.pcrpc.2025.05.005
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- Received：31 August 2025，
  
  Published：25 October 2025
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GAO Liping, YAN Jun, HENG Dongqiang, et al. Research on Hybrid State Estimation of Distribution Networks with Renewable Energy Integration Based on Generalized Benders Decomposition[J]. Power Capacitor & Reactive Power Compensation, 2025, 46(5): 45-53.
DOI：

GAO Liping, YAN Jun, HENG Dongqiang, et al. Research on Hybrid State Estimation of Distribution Networks with Renewable Energy Integration Based on Generalized Benders Decomposition[J]. Power Capacitor & Reactive Power Compensation, 2025, 46(5): 45-53. DOI： 10.14044/j.1674-1757.pcrpc.2025.05.005.

摘要

为解决分布式电源运行时离散和连续混合状态的不确定性给配电网状态估计运行带来的困难，本文提出了一种包含开关离散变量和电压连续变量的配电网混合状态估计方法。首先，该方法以最小二乘法为准则建立目标函数，考虑开关状态对节点导纳矩阵的作用机理，把节点电压和开关状态作为混合估计量构建复数的数学模型。针对复数变量求解的复杂性，通过坐标变换和实部虚部解耦将复变量转化为实变量，简化了数学模型的求解难度。然后，通过广义Benders分解的方法将数学模型分解成主问题和子问题，通过更新子问题求解结果，求解更新约束下的主问题，利用主-子问题交互迭代求解实现目标函数最优解。最后，在IEEE 33节点算例验证所提方法的有效性，通过与凸松弛求解的方法进行对比，显示了方法在计算速度和精度上的优越性。

Abstract

To address the challenges brought by the uncertainty of discrete and continuous hybrid state during distributed generation operation to distribution network state estimation，a hybrid state estimation method incorporting both discrete switch variales and continuous voltage variables is proposed in this paper. First，the target function is set up with the least squares method as the criterion，the action mechanism of switch state to the nodal admittance matrix is considered ，the node voltage and switch state are used as combined estimation to construct a complex mathematical model. Considering the complexity of solving complex variables，the complex variables is transformed into real variables by coordinating transformation and decoupling of real and imaginary parts. Then，the mathematical model is decomposed into master problem and a sunproblem using the generalized Benders decomposition method（GBD）. By updating the solution results of the subproblem，the master problem under the updated constraints is solved. The optimal solution of the objective function is achieved through the iterative solution of the master problem and subproblem in an interactive manner. Finally，the effectiveness of the proposed method is verified in the simulation is verified using the IEEE 33-node test case. The superiority of the method in calculation speed and accuracy is demonstrated by comparing with the convex relaxation solution method.

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references

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