基于模型修正方法和拓扑优化理论的电力变压器绕组变形状态逆向求解问题研究

Quantitative relation between the deformation of the power transformer winding and the measured frequency response is an important issue for the mechanical state evaluation of the winding. In this application, the model updating, frequency-dependent characteristic of winding materials, time harmonic electromagnetic field finite element and the adjoint network method will be used to calculate the sensitivity of the frequency response function to the element parameters in the equivalent circuit of the winding. The frequency dependent index (FDI) and parameter dependent index (PDI) are investigated respectively, which will be applied to deduce the approximate linear independent sensitivity matrix and its adjustment strategy. Therefore, the method to update the element parameters in the equivalent circuit by using the measured frequency response function can be achieved. With the topology optimization theory, the winding conductor surface topography and material property of finite elements are expressed by the level set-based approach, where the modified equivalent circuit parameters of deformed windings are taken as the optimization objective function. The sensitivity of element parameters of equivalent circuit with respect to the finite element material property are derived by the time harmonic electromagnetic field finite element method and adjoint variable method; Then, determine the zero level set function and study adjustment strategy of finite element material parameters. Finally, the fundamental theory and its implement of reverse solution for the deformation of power transformer winding according to the measured frequency response function are realized and verified by experiment. These theories may provide powerful support for the prediction and evaluation of winding deformation in transformer.

变压器绕组变形与其测量频率响应信号之间的定量关系对电力变压器绕组的力学状态评估至关重要。本申请拟借鉴模型修正方法，依据绕组材料的频变参数特性和时谐场有限元法，运用伴随网络法计算频率响应函数对绕组等效频变电路模型元件参数的灵敏度，在研究频率点之间及元件参数之间的相关度表达形式的基础上，推演近似线性无关灵敏度矩阵的构建与调整策略，实现依据绕组变形实验测量的频率响应函数修正等效电路元件参数的方法；基于拓扑优化理论，以修正的绕组变形等效电路元件参数为优化目标函数，研究绕组导体表面形貌和有限单元材料属性的水平集描述方法，基于时谐场有限元法和伴随变量法推导绕组等效电路元件参数对有限单元材料属性的灵敏度，确定零水平集函数及有限单元材料参数调整策略，建立并实验验证依据绕组频率响应函数逆向求解绕组变形状态的基本理论与实现方法,为变压器绕组变形预测和评估提供理论基础和方法支撑。

项目背景：.电力变压器是电力传输网络中能量转换的关键枢纽设备，确保变压器的正常运行对电力系统的安全性和可靠性意义重大。研究表明，目前，绕组变形仍然是直接或间接导致电力变压器损坏的主要原因之一。国内外学者在变压器绕组变形检测方面取得显著研究成果，但现有关于变压器绕组变形的判断大多仍然属于定性的范畴。如何更加准确、有效地对变压器内部绕组变形的位置和程度进行定量的判定已是当今变压器绕组故障诊断研究的一个焦点问题。.研究内容：.（1）变压器绕组等效电路模型及频率响应函数对元件参数的灵敏度计算方法.（2）基于频率响应函数的变压器绕组等效电路模型修正方法.（3）基于拓扑优化理论的变压器绕组变形的逆向求解方法.（4）变压器绕组变形逆向求解方法的实现与实验验证.重要结论：.（1）频率响应的中频段将是判断各种类型故障最为重要的频带。.（2）EE接线方式更适合且更易于发现与电感参数相关的短路故障以及铁芯故障。.（3）TF接线方式较EE接线方式更适合判断对称结构绕组变形位置。.（4）FRA频响曲线在各个谐振点和所有电路参数都同时相关。.（5）基于频率响应函数的变压器绕组等效电路模型修正方法能够有效地获得等效电路参数的变化量。.（6）水平集方法能够有效地确定线饼的鼓包变形形貌。.关键数据：.绕组等效电路中的电感参数随频率变化比较明显，当频率高于100kHz后，电感值可能减小至原来的10%左右。模型修正方法的仿真算例结果表明：一般经过四到六次的迭代修正就可得到满意的结果，电路参数的修正精度可达到97%以上。.科学意义：.本项目将模型修正方法和拓扑优化理论引入到变压器绕组变形定量分析中，解决了由实测频响数据得到绕组的真实变形状态定量诊断问题，丰富了变压器绕组变形状态分析与诊断方法和理论。