中文摘要：

电压源型换流器（vsc）谐波产生是由其交直流侧电压电流通过电力电子器件之间的非线性相互作用引起的，其机理复杂。为能直观展示VSC的谐波产生机理，提出了利用稀疏矢量法求解线性代数方程中的道路树分析VSC交直流侧谐波相互作用关系的方法，从而用赋权有向因子图展示VSC谐波产生机理。首先简化VSC的序分量动态相量谐波分析模型为线性代数方程，引入稀疏矢量求解线性代数方程组的方法对谐波分析模型进行求解。其次，利用谐波分析模型的变量定义和系数矩阵的特点，定义线性代数方程组稀疏矢量求解过程中的前代运算和回代运算为VSC交直流侧谐波电压电流之间的相互作用关系。然后，利用赋权有向因子图表示前代运算和回代运算的求解道路树，从而直观描述VSC的谐波产生机理。最后，通过仿真分析可知，由三相不对称产生的基波负序电流或背景谐波均能在直流侧产生相应的低次非特征谐波电压，从而验证了方法的有效性。利用稀疏矢量法求解线性代数方程，并通过用赋权有向因子图展示求解道路树，能直观全面地展示VSC谐波产生的机理和交直流侧的相互作用，同时验证了VSC交直流侧谐波相互作用的相对独立性。

英文摘要：

The harmonic of voltage source converter （VSC） is produced due to the nonlinear interactions between AC harmonic currents and DC harmonic voltages through solid-state switches, which is very complicated. In order to discover and describe the mechanisms of the harmonic generation in VSC directly, we put forward an approach to analyze the in- teraction of VSC with path set in sparse vector method to solve the linear algebraic equation. The weighted directed factor graph describing the path set can display the harmonic generation mechanism of VSC well. Firstly, the harmonic analysis model of VSC based on the dynamic sequence components can be simplified as a linear algebraic equation. The sparse vector method is applied to solve the equation. Secondly, with the physical significance of the coefficient matrix and gtate variables, the forward and backwards substitutions can be defined as the interactions of the harmonic currents on AC side and the harmonic voltages on DC side of VSC. Thirdly, the weighted directed factor graph is used to present the solution path sets which can describe the harmonic generation mechanisms of VSC directly. Finally, the simulation results show that the fundamental negative sequence current and background harmonic currents on AC side will generate the corres- ponding low order non-characteristic harmonic voltages on DC side. The effectiveness of the approach is testified. By analyzing path sets and the description of weighted directed factor graph, this approach can discover the reason of the harmonics production of VSC and describe the interactions between AC side and DC side in VSC directly. At the same time, this approach can testify that the harmonic interactions between the AC and DC side in VSC have some independence.