This paper focuses on the finite element method in the complex frequency domain(CFD-FEM)for the transient electric field.First,the initial value and boundary value problem of the transient electric field under the ele...This paper focuses on the finite element method in the complex frequency domain(CFD-FEM)for the transient electric field.First,the initial value and boundary value problem of the transient electric field under the electroquasistatic field in the complex frequency domain is given.In addition,the finite element equation and the constrained electric field equation on the boundary are derived.Secondly,the indirect algorithm of the numerical inverse Laplace transform is introduced.Based on it,the calculation procedures of the CFD-FEM are illustrated in detail.Thirdly,the step response,zero-state response under the positive periodic square waveform(PPSW)voltage,and the zero-input response by the CFD-FEM with direct algorithm and indirect algorithm are compared.Finally,the reason for the numerical oscillations of the zero-state response under the PPSW voltage is analyzed,and the method to reduce oscillations is proposed.The results show that the numerical accuracy of the indirect algorithm of the CFD-FEM is more than an order of magnitude higher than that of the direct algorithm when calculating the step response of the transient electric field.The proposed method can significantly reduce the numerical oscillations of the zero-state response under the PPSW voltage.The proposed method is helpful for the calculation of the transient electric field,especially in the case of frequency-dependent parameters.展开更多
针对油浸式变压器瞬态流固耦合温度场求解存在模型自由度高导致耗时长达小时级的缺陷,构建了变压器数字孪生降阶模型,基于该模型可快速求解瞬态温度场。首先建立基于物联网(internet of things,IoT)的变压器数字孪生实现架构,搭建瞬态...针对油浸式变压器瞬态流固耦合温度场求解存在模型自由度高导致耗时长达小时级的缺陷,构建了变压器数字孪生降阶模型,基于该模型可快速求解瞬态温度场。首先建立基于物联网(internet of things,IoT)的变压器数字孪生实现架构,搭建瞬态流固耦合温度场伽辽金有限元全阶模型。其次,提出将本征正交分解(properorthogonal decomposition,POD)与有限元结合建立瞬态温度场降阶模型,并结合实测数据给出数字孪生建模与降阶计算流程。最后,开展实际变压器温升试验确保全阶模型准确性,并应用不同阶数降阶模型快速计算温度场分布,比较各阶模型的计算误差与时间。结果表明:计算值与实测值的温升误差绝对值满足在1.5℃以内;3阶模型计算结果与全阶模型结果符合POD误差规范要求;降阶模型与全阶模型相比其计算时间由小时级降至秒级。研究结果验证了降阶模型的准确性与时效性,可以在保证数字孪生模型求解精度的同时最大限度提高求解效率。展开更多
基金supported by the National Natural Science Foundation of China(No.52077073).
文摘This paper focuses on the finite element method in the complex frequency domain(CFD-FEM)for the transient electric field.First,the initial value and boundary value problem of the transient electric field under the electroquasistatic field in the complex frequency domain is given.In addition,the finite element equation and the constrained electric field equation on the boundary are derived.Secondly,the indirect algorithm of the numerical inverse Laplace transform is introduced.Based on it,the calculation procedures of the CFD-FEM are illustrated in detail.Thirdly,the step response,zero-state response under the positive periodic square waveform(PPSW)voltage,and the zero-input response by the CFD-FEM with direct algorithm and indirect algorithm are compared.Finally,the reason for the numerical oscillations of the zero-state response under the PPSW voltage is analyzed,and the method to reduce oscillations is proposed.The results show that the numerical accuracy of the indirect algorithm of the CFD-FEM is more than an order of magnitude higher than that of the direct algorithm when calculating the step response of the transient electric field.The proposed method can significantly reduce the numerical oscillations of the zero-state response under the PPSW voltage.The proposed method is helpful for the calculation of the transient electric field,especially in the case of frequency-dependent parameters.
文摘针对油浸式变压器瞬态流固耦合温度场求解存在模型自由度高导致耗时长达小时级的缺陷,构建了变压器数字孪生降阶模型,基于该模型可快速求解瞬态温度场。首先建立基于物联网(internet of things,IoT)的变压器数字孪生实现架构,搭建瞬态流固耦合温度场伽辽金有限元全阶模型。其次,提出将本征正交分解(properorthogonal decomposition,POD)与有限元结合建立瞬态温度场降阶模型,并结合实测数据给出数字孪生建模与降阶计算流程。最后,开展实际变压器温升试验确保全阶模型准确性,并应用不同阶数降阶模型快速计算温度场分布,比较各阶模型的计算误差与时间。结果表明:计算值与实测值的温升误差绝对值满足在1.5℃以内;3阶模型计算结果与全阶模型结果符合POD误差规范要求;降阶模型与全阶模型相比其计算时间由小时级降至秒级。研究结果验证了降阶模型的准确性与时效性,可以在保证数字孪生模型求解精度的同时最大限度提高求解效率。
