| 引用本文: | 廖小兵,魏寒琪,李自成,等.考虑相关性的配电网切比雪夫仿射潮流计算方法[J].电力系统保护与控制,2026,54(01):1-16. |
| LIAO Xiaobing,WEI Hanqi,LI Zicheng1,et al.Chebyshev affine power flow calculation method for distribution networks considering correlation[J].Power System Protection and Control,2026,54(01):1-16 |
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| 摘要: |
| 为了解决现有泰勒展开仿射潮流的仿射系数求解问题，提出了考虑相关性的配电网切比雪夫仿射潮流计算方法。首先利用切比雪夫多项式来构造仿射算子，在输入区间变量范围内抽取若干个内插值点来求解仿射系数，以此建立切比雪夫仿射模型。根据切比雪夫仿射模型建立待求变量的仿射形式，并将待求变量的仿射形式代入到原始潮流方程中，重构潮流方程，得到关于待求变量噪声元的仿射优化模型。采用混合盒式-椭球集合描述分布式风电出力的相关性，通过坐标变换将混合盒式-椭球集合转换为新的仿射约束嵌入仿射优化模型中进行联立求解。通过2个配电网的算例仿真结果表明，所建立模型与泰勒展开仿射模型相比，具有更高的计算精度和效率，并且更适合于较大波动区间下的区间潮流分析场景。同时混合盒式-椭球集合可以很好地反映不同相关性水平对计算结果的影响。 |
| 关键词: 配电网 区间潮流 切比雪夫多项式 仿射优化模型 区间相关性 |
| DOI：10.19783/j.cnki.pspc.250131 |
| 分类号: |
| 基金项目:国家自然科学基金项目资助(52107122) |
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| Chebyshev affine power flow calculation method for distribution networks considering correlation |
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LIAO Xiaobing1, WEI Hanqi1, LI Zicheng1, ZHANG Yiming1, YANG Meng2, CHEN Xinyun3
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1. College of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430073, China;2. Economic Research Institute of State Grid Hubei Electric Power Company, Wuhan 430000, China;3. College of Information Engineering, Nanchang University, Nanchang 330031, China
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| Abstract: |
| To address the problem of solving affine coefficients in existing Taylor expansion-based affine power flow methods, a Chebyshev affine power flow calculation method for distribution networks considering correlation is proposed. First, Chebyshev polynomials are used to construct affine operators, and several interpolation points are extracted within the interval ranges of the input variables to solve for the affine coefficients, thereby establishing a Chebyshev affine model. Based on this model, the affine form of the variables to be solved is constructed and substituted into the original power flow equations to reconstruct the equations, obtaining an affine optimization model with respect to the noise elements of the target variables. The correlation of the distributed wind power output is described using the hybrid box-ellipsoid set, and through coordinate transformation, the hybrid box-ellipsoid set is converted into new affine constraints and embedded into the affine optimization model for simultaneous solution. Simulation results on two distribution network examples show that, compared with the Taylor expansion affine model, the proposed model has higher calculation accuracy and efficiency, and is more suitable for interval power flow analysis scenarios under larger fluctuation ranges. Meanwhile, the hybrid box-ellipsoid set effectively reflects the impact of different correlation levels on the calculation results. |
| Key words: distribution network interval power flow Chebyshev polynomial affine optimization model interval correlation |
