\r赵志刚^{1, 2}，魏 乐^{1, 2}，郭 莹^{1, 2}，刘 佳^{1, 2}，杨 凯^{1, 2}，尹赛宁\r^{1, 2}\r
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AuthorsHTML:\r赵志刚^{1, 2}，魏 乐^{1, 2}，郭 莹^{1, 2}，刘 佳^{1, 2}，杨 凯^{1, 2}，尹赛宁\r^{1, 2}\r
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AuthorsListE:\rZhao Zhigang^{1, 2}，Wei Le ^{1, 2}，Guo Ying ^{1, 2}，Liu Jia^{1, 2}，Yang Kai^{1, 2}，Yin Saining\r^{1, 2}\r
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AuthorsHTMLE:\rZhao Zhigang^{1, 2}，Wei Le ^{1, 2}，Guo Ying ^{1, 2}，Liu Jia^{1, 2}，Yang Kai^{1, 2}，Yin Saining\r^{1, 2}\r
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Unit:\r1. 省部共建电工装备可靠性与智能化国家重点实验室，天津 300132；
2. 河北省电磁场与电器可靠性重点实验室，天津 300132\r
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Unit_EngLish:\r1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment，Tianjin 300132，China；
2. Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province，Tianjin 300132，China\r
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Abstract_Chinese:\r针对谐波激励下变压器磁损耗计算问题，对传统Bertotti 模型进行改进，使其适应于复杂谐波工况下损耗计算，并完全按照实际变压器的要求，设计制造了变压器叠片铁心模型，搭建了谐波激励下变压器磁损耗测试平台，对改进的Bertotti 模型的正确性及精确性进行验证，并对谐波激励下磁滞损耗和涡流损耗的分布规律进行研究．首先，基于简化的Bertotti 模型，采用铁心工艺系数，获得了正弦激励下变压器磁损耗分离数据，并通过对不同频率下磁滞损耗和涡流损耗的确定，发现低频段磁滞损耗占绝大部分，随着频率的增加，磁滞损耗所占比例降低，涡流损耗占据了主导地位；其次，引入修正因子，综合考虑谐波相位、谐波含量以及谐波阶次的影响，对磁滞损耗和涡流损耗进行修正，实现了谐波激励下磁损耗的计算．通过测量与计算结果的对比分析，损耗误差保持在5%以内，满足工程所需的精度要求，验证了模型的正确性．所得结果和结论有助于谐波激励下磁损耗的研究，为变压器的优化设计以及产品性能的提高提供了必要的数据支撑．\r
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Abstract_English:\rIn recent years，owing to the development of power electronics and the high-voltage direct current(HVDC)transmission system，harmonic pollution has attracted considerable attention．Simultaneously，the emergence of harmonic pollution also poses a major challenge to the efficient operation of the HVDC transmission system．As one of the core pieces of equipment in the transmission system，the converter transformer has problems of partial overheating and the increasing loss and reduced service life of its structural parts，which also results in a large waste of power．Therefore，it is particularly important to accurately calculate the loss experienced by the converter transformer under harmonic conditions．To calculate the transformer magnetic loss under harmonic excitation，herein，we improve the traditional Bertotti model by adapting it to calculate the loss experienced under complex harmonic conditions．We also design and construct a transformer laminated core model based on the requirements of the actual transformer and build a platform for testing the transformer magnetic loss under harmonic excitation．These changes improve the correctness and accuracy of the traditional Bertotti model．In addition，we investigated the distributions of hysteresis loss and eddy current loss under harmonic excitation．First，based on the simplified Bertotti model，we obtain data on the transformer magnetic loss separation under sinusoidal excitation using core process coefficients．By determining the hysteresis and eddy current losses at different frequencies，we found that hysteresis loss accounts for the majority of the transformer magnetic loss at low frequencies．With increases in frequency，the proportion of hysteresis loss decreases，and the eddy current loss begins to occupy the dominant position．Secondly，the correction factor is introduced．Considering the influences of the harmonic phase，harmonic content，and harmonic order，we correct the hysteresis loss and eddy current loss to realize the calculation of magnetic loss under harmonic excitation．A comparison and analysis of the measurement and calculation results shows that the loss error is within 5%，which meets the engineering accuracy requirement and verifies the correctness of the model．The results and conclusions are helpful to the study of magnetic loss under harmonic excitation and provide the data support necessary for the optimal design of transformers and the improvement of product performance．\r
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Keyword_Chinese:变压器；谐波激励；损耗分离；涡流损耗；磁滞损耗；损耗模型\r

Keywords_English:transformer；harmonic excitation；loss separation；eddy current loss；hysteresis loss；loss model\r


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