大型电力变压器三维涡流场结构件损耗计算方法的研究
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摘要
准确计算变压器结构件的杂散损耗从而避免局部过热,对于提高变压器运行的可靠性和保证电力系统的安全运行具有十分重要的意义。由于漏磁场和杂散损耗分布的不合理性而造成的局部损耗集中,是局部过热和运行故障的直接原因。在结构复杂的大型电力变压器三维漏磁场和结构件损耗的计算中,由于存在庞大的求解区域和小透入深度的矛盾,若要考虑叠片铁心复杂的电磁特性(非线性、各向异性等)和铁心叠片材料的不连续性,采用传统方法计算时计算规模过大,且计算误差不可接受。本文针对这一问题,研究了提高变压器结构件损耗的计算精度并减小计算规模的几种方法。
为了计及场量(磁通密度B和涡流密度J)的高次谐波,本文提出了一种时域分析方法,将解析解与数值解相结合,对叠片铁心区域做均匀化处理,并计算了包含非线性各向异性的叠片铁心的三维漏磁场及结构件损耗。该方法能够在保证工程精度的条件下减少计算规模,可应用于大型电力变压器三维漏磁场及其结构件损耗计算。
已在三维涡流场计算中广泛应用的复频域运算具有其省时和简单性,但理论上不适于求解非线性问题。为了保留其优点并提高计算的精度,本文对传统复频域计算做了改进,推导了在复频域下分别考虑不同材料的非线性各向同性和各向异性电磁特性的三维涡流场有限元离散化公式,其中离散化得出的非线性代数方程组应用复数牛顿-拉夫逊法求解,得到了满足工程精度的计算结果。
区域分解法是另一种减小复杂问题计算规模的方法。本文将重叠型区域分解法应用于复频域三维非线性涡流场有限元分析中,将求解区域分解为互相重叠、互相影响的子区域,不同的子区域可以单独剖分,应用不同的离散化方式和不同的力法求解,有效地减小了计算规模并降低了计算的复杂性。
为了验证所提出的计算方法和所编制的计算机程序的正确性,本文采用了小模型测试和实际变压器产品测试的检验方法。制作了TEAM问题21的补充模型,对其磁场和损耗分布进行了测试,并应用所提出的叠片铁心均匀化处理的时域分析方法对该模型进行了仿真计算。此外还对两台大型电力变压器产品做了实例计算和实验值对照。计算结果与实验结果的比较验证了本文研究成果的正确性和有效性。
It is of great significance to accurately calculate stray losses of structural parts of a large power transformer thus to avoid the local overheating for improving the reliability of transformer operation and ensuring the safety operation of power system. The local losses concentration is the direct reason of local overheating and operational failure caused by the inappropriate distribution of the magnetic leakage fields and stray losses.
In the computation of three dimensional magnetic leakage field and its related structural part losses of large power transformer with a complex structure, when the complicated electromagnetic properties (anisotropy, nonlinearity, and so on) and discontinuity of laminated core material have to be considered, the computational scale will be too large to carry out the whole computation, or the calculated error become unacceptable if the conventional method is used, mainly because the contrast between the huge size of the computation region and very small skin depth. To treat with the problem, this thesis researches several methods of improving the calculation accuracy and reducing the calculation scale for these computations.
In order to consider the higher-order harmonics of the field quantities (flux density B, eddy current density J), a time domain analysis method combining analytical and numerical solutions for laminated core homogenization is proposed in the thesis to calculate3D magnetic leakage field and its structural parts stray losses including nonlinear and anisotropic laminated core. On the premise of guarantee engineering precision, this method can reduce the scale of calculation and make it feasible to calculate this kind of problems.
Although the calculation carried out in complex frequency domain is widely applied in3D eddy current field analysis due to its simplicity and time saving, it is not suitable for solving nonlinear problems. For preserving the advantages and improving calculation accuracy, the calculation method of traditional complex frequency domain is improved, and the discretized finite element equations of3D eddy current field are deduced considering the electromagnetic characteristics of different materials such as anisotropy, isotropy and nonlinearity in complex frequency domain. The nonlinear complex algebraic equations are solved by complex Newton-Raphson method, and the calculation results meeting engineering precision are obtained.
Domain Decomposition Method (DDM) is another method reducing calculation scale of complicated problem. Overlapping Domain Decomposition Method (ODDM) is applied to the nonlinear FE analysis of3D eddy current field in complex frequency domain in the thesis. The solved region is divided into different sub-regions which are overlapped and influenced on each other. Different sub-regions can be meshed independently and solved with different discretization mode and method. The calculation scale is reduced and the computational complexity is decreased effectively.
In order to verify the validity of the proposed methods and the self-compiled computer programs, the computation examples of small models and the models of real transformer products are adopted. A supplementary model of TEAM Problem P21C-M1is made, and the magnetic field distribution and losses of this model are measured. A simulation calculation is executed for this model with the proposed time domain analysis method for laminated core homogenization. In addition, the calculated results are compared with measured results of two large power transformers. The comparison of the computed and measured results confirmed the validity and efficiency of the methods proposed in this thesis.
为了计及场量(磁通密度B和涡流密度J)的高次谐波,本文提出了一种时域分析方法,将解析解与数值解相结合,对叠片铁心区域做均匀化处理,并计算了包含非线性各向异性的叠片铁心的三维漏磁场及结构件损耗。该方法能够在保证工程精度的条件下减少计算规模,可应用于大型电力变压器三维漏磁场及其结构件损耗计算。
已在三维涡流场计算中广泛应用的复频域运算具有其省时和简单性,但理论上不适于求解非线性问题。为了保留其优点并提高计算的精度,本文对传统复频域计算做了改进,推导了在复频域下分别考虑不同材料的非线性各向同性和各向异性电磁特性的三维涡流场有限元离散化公式,其中离散化得出的非线性代数方程组应用复数牛顿-拉夫逊法求解,得到了满足工程精度的计算结果。
区域分解法是另一种减小复杂问题计算规模的方法。本文将重叠型区域分解法应用于复频域三维非线性涡流场有限元分析中,将求解区域分解为互相重叠、互相影响的子区域,不同的子区域可以单独剖分,应用不同的离散化方式和不同的力法求解,有效地减小了计算规模并降低了计算的复杂性。
为了验证所提出的计算方法和所编制的计算机程序的正确性,本文采用了小模型测试和实际变压器产品测试的检验方法。制作了TEAM问题21的补充模型,对其磁场和损耗分布进行了测试,并应用所提出的叠片铁心均匀化处理的时域分析方法对该模型进行了仿真计算。此外还对两台大型电力变压器产品做了实例计算和实验值对照。计算结果与实验结果的比较验证了本文研究成果的正确性和有效性。
It is of great significance to accurately calculate stray losses of structural parts of a large power transformer thus to avoid the local overheating for improving the reliability of transformer operation and ensuring the safety operation of power system. The local losses concentration is the direct reason of local overheating and operational failure caused by the inappropriate distribution of the magnetic leakage fields and stray losses.
In the computation of three dimensional magnetic leakage field and its related structural part losses of large power transformer with a complex structure, when the complicated electromagnetic properties (anisotropy, nonlinearity, and so on) and discontinuity of laminated core material have to be considered, the computational scale will be too large to carry out the whole computation, or the calculated error become unacceptable if the conventional method is used, mainly because the contrast between the huge size of the computation region and very small skin depth. To treat with the problem, this thesis researches several methods of improving the calculation accuracy and reducing the calculation scale for these computations.
In order to consider the higher-order harmonics of the field quantities (flux density B, eddy current density J), a time domain analysis method combining analytical and numerical solutions for laminated core homogenization is proposed in the thesis to calculate3D magnetic leakage field and its structural parts stray losses including nonlinear and anisotropic laminated core. On the premise of guarantee engineering precision, this method can reduce the scale of calculation and make it feasible to calculate this kind of problems.
Although the calculation carried out in complex frequency domain is widely applied in3D eddy current field analysis due to its simplicity and time saving, it is not suitable for solving nonlinear problems. For preserving the advantages and improving calculation accuracy, the calculation method of traditional complex frequency domain is improved, and the discretized finite element equations of3D eddy current field are deduced considering the electromagnetic characteristics of different materials such as anisotropy, isotropy and nonlinearity in complex frequency domain. The nonlinear complex algebraic equations are solved by complex Newton-Raphson method, and the calculation results meeting engineering precision are obtained.
Domain Decomposition Method (DDM) is another method reducing calculation scale of complicated problem. Overlapping Domain Decomposition Method (ODDM) is applied to the nonlinear FE analysis of3D eddy current field in complex frequency domain in the thesis. The solved region is divided into different sub-regions which are overlapped and influenced on each other. Different sub-regions can be meshed independently and solved with different discretization mode and method. The calculation scale is reduced and the computational complexity is decreased effectively.
In order to verify the validity of the proposed methods and the self-compiled computer programs, the computation examples of small models and the models of real transformer products are adopted. A supplementary model of TEAM Problem P21C-M1is made, and the magnetic field distribution and losses of this model are measured. A simulation calculation is executed for this model with the proposed time domain analysis method for laminated core homogenization. In addition, the calculated results are compared with measured results of two large power transformers. The comparison of the computed and measured results confirmed the validity and efficiency of the methods proposed in this thesis.
引文
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