含光伏电网的电压–无功雅可比矩阵结构特征及电压稳定性分析  

Structural Properties of V-Q Jacobian Matrix and Voltage Stability Analysis of Power Network With Photovoltaic Penetration

作　　者：郝文清 黄志光 陆建宇 周毅 廖圣文 王雪一 陈民权 甘德强[1] HAO Wenqing;HUANG Zhiguang;LU Jianyu;ZHOU Yi;LIAO Shengwen;WANG Xueyi;CHEN Minquan;GAN Deqiang(College of Electrical Engineering,Zhejiang University,Hangzhou 310027,Zhejiang Province,China;East China Branch of State Grid Corporation of China,Pudong New District,Shanghai 200120,China)

机构地区：[1]浙江大学电气工程学院,浙江省杭州市310027 [2]国家电网有限公司华东分部,上海市浦东新区200120

出　　处：《中国电机工程学报》2023年第5期1719-1729,共11页Proceedings of the CSEE

基　　金：国家电网有限公司华东分部科技项目(SGTYHT/20-JS-221)。

摘　　要：该文推导出含光伏电网的电压-无功雅可比矩阵,发现存在特定结构特征,进一步结合特殊矩阵理论,分析光伏机组接入后的电网电压稳定特性。相关解析结果表明,单节点的电压-无功灵敏度与广义短路容量的倒数相一致,而多节点的电压-无功雅可比矩阵则与节点阻抗矩阵的虚部具有一致性。同时,借助矩阵论以及代数图论,明确电压-无功雅可比矩阵符号全正与分块对角占优,解释了现有工程认识:增加光伏机组无功出力,所有节点电压均会抬升,且对近区电压幅值的影响要远远大于远区。通过论证电压-无功雅可比矩阵元素值与电气距离之间的衰减关系,指出随着节点之间电气距离的增加,电压-无功的相互影响程度减弱。最后,结合实际电网算例结果验证该文理论分析的有效性。In this paper,the V-Q Jacobian matrix expression of a grid containing photovoltaics(PVs)is derived and found to have structural properties.The grid voltage stability characteristics after large-scale integration of PVs are analyzed using matrix theory.The correlation analytical results showed that the V-Q sensitivity of a single PV node grid is consistent with the inverse of the generalized short-circuit capacity,while the V-Q Jacobian matrix of multiple PV nodes grid is consistent with the imaginary part of the nodal impedance matrix.Meanwhile,with the help of matrix theory as well as algebraic graph theory,it was clear that the V-Q Jacobian matrix is block diagonally dominant and its entries are all positive.These properties explain the existing engineering understanding that increasing the reactive power output of a PV unit rose the voltage at all nodes and had a much greater impact on the voltage magnitude in the near area than in the far area.By demonstrating the decay relationship between the entries of V-Q Jacobian matrix and electrical distance,it was pointed out that with the increase of the electrical distance between PV nodes,the interaction between voltage and reactive power will decrease.Finally,the theoretical analysis in this paper was validated by actual grid examples.

关 键 词：光伏发电 电压–无功雅可比矩阵 电压稳定 分块对角占优 电气距离 

分 类 号：TM712[电气工程—电力系统及自动化]