Stray flux in a transformer enters the outer packages of a core perpendicularly and induces significant eddy currents that cause ohmic losses. Local thermal conditions near the core are affected by these losses that are dissipated as heat and can cause local overheating in the oil near the outer packages. Stray losses in the outer packages should be considered during the power transformer design process, and it is, therefore, important to model them properly. This type of loss can be solved using 3-D FEM; however, that approach is time-consuming, which makes it impractical for the loss calculation in real time. Another approach is 2-D modeling, which is faster, but it is limited to axisymmetric and planar geometries only. Due to its complex geometry, a transformer cannot be modeled using a single 2-D model. Instead, each quantity of interest, such as a magnetic field or eddy currents, can be obtained from a suitable model. These models include certain simplifications, which should not affect the accuracy of the results. In this article, a hybrid approach that utilizes various 2-D models for the calculation of stray losses in the outer packages is proposed. The advantage of the proposed methodology is in obtaining the same level of accuracy while considerably reducing the calculation time when comparing to the 3-D FEM approach. The estimation of the temperature rise of the outer packages, based on the calculated losses, will be a part of further research.

中文翻译：

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快速混合法计算垂直杂散磁通引起的变压器铁心外包装损耗

变压器中的杂散磁通量垂直进入铁心的外包装，并感应出大量涡流，从而导致欧姆损耗。铁心附近的局部热状况会受到这些损耗的影响，这些损耗会随着热量散发，并可能导致外包装附近的机油局部过热。在电源变压器的设计过程中，应考虑外包装中的杂散损耗，因此，对其进行正确建模很重要。可以使用3-D FEM解决这种类型的损耗。但是，这种方法很耗时，因此对于实时的损失计算来说是不切实际的。另一种方法是二维建模，速度更快，但仅限于轴对称和平面几何。由于其复杂的几何形状，因此无法使用单个二维模型来建模变压器。取而代之的是，每个感兴趣的数量，诸如磁场或涡流之类的信息可以从合适的模型中获得。这些模型包括某些简化，这些简化不应影响结果的准确性。在本文中，提出了一种混合方法，该方法利用各种二维模型来计算外包装中的杂散损耗。与3-D FEM方法相比，所提出方法的优势在于可以获得相同级别的精度，同时大大减少了计算时间。根据计算得出的损失估算外包装的温度升高将是进一步研究的一部分。提出了一种混合方法，该方法利用各种二维模型来计算外包装中的杂散损耗。与3-D FEM方法相比，所提出方法的优势在于可以获得相同级别的精度，同时大大减少了计算时间。根据计算得出的损失估算外包装的温度升高将是进一步研究的一部分。提出了一种混合方法，该方法利用各种二维模型来计算外包装中的杂散损耗。与3-D FEM方法相比，所提出方法的优势在于可以获得相同级别的精度，同时大大减少了计算时间。根据计算得出的损失估算外包装的温度升高将是进一步研究的一部分。