基于复线性最小二乘法的谐波责任定量划分

Determining Harmonic Contributions Based on Complex Least Squares Method

定量划分各主要谐波源在特定母线上的谐波责任是电能质量管理的一项重要任务。该文提出一种基于复线性最小二乘原理的等效谐波阻抗和背景谐波电压计算方法,由此可定量划分谐波源对关注母线谐波责任。不同于传统的将复数实部和虚部分开计算方法,复线性最小二乘法通过直接在复数域内求解误差模的平方和最小值,得到了真实的最小二乘解。在此基础上,利用基于内积理论推导谐波责任定量划分的计算公式,量化了谐波源对关注母线的谐波责任。对IEEE14节点系统进行仿真计算,并与现有方法相比,证明了所提方法计算更简单,结果更准确,易于在工程中实现。

Determining harmonic contributions in quantitative of the main harmonic sources in a particular bus is an important task for power quality management.Based on the complex least squares,a method for calculating the equivalent harmonic impedance and the background harmonic voltage was presented,and then identifying harmonic contributions in quantitative of the harmonic sources on the bus of concern was deduced.Contrast to the traditional binary linear regression method,by which the result was calculated by real or imaginary part regression respectively,complex least squares method could get the real least squares solution by directly solving the squares of error in the complex domain.On this basis,the quantitative harmonic contribution of the harmonic source on the bus of concern could be calculated based on equation deduced by the inner product theory.A case study based on the IEEE 14-bus test system was conducted,which shows that the proposed method is easier for computation and more reliable results can be given by comparing with the existing methods.