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工程设计学报  2026, Vol. 33 Issue (2): 213-222    DOI: 10.3785/j.issn.1006-754X.2026.06.103
优化设计     
基于多目标海星优化算法的干式配电变压器结构优化设计方法
项恩新1(),李航1,聂永杰1,管京荣2,王东阳2
1.云南电网有限责任公司 电力科学研究院,云南 昆明 650032
2.西南交通大学 电气工程学院,四川 成都 611756
Structural optimization design method for dry-type distribution transformer based on multi-objective starfish optimization algorithm
Enxin XIANG1(),Hang LI1,Yongjie NIE1,Jingrong GUAN2,Dongyang WANG2
1.Electric Power Science Research Institute, Yunnan Power Grid Co. , Ltd. , Kunming 650032, China
2.School of Electrical Engineering, Southwest Jiaotong University, Chengdu 611756, China
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摘要:

为了提高环氧树脂干式配电变压器的服役性能,以一台10 kV/0.4 kV环氧树脂干式配电变压器为研究对象,提出了一种基于多目标海星优化算法(multi-objective starfish optimization algorithm, MOSFOA)的干式配电变压器结构优化设计方法。首先,建立了电磁-热-力耦合的变压器模型并进行性能仿真,确定以高/低压绕组导体截面积、风道宽度和铁心半径为核心设计变量;其次,运用中心复合设计和响应面法构建了设计变量与高/低压绕组热点温升、损耗及单位体积短路电动力之间的高精度代理模型;最后,基于MOSFOA进行协同寻优,获得最优结构参数组合。优化结果表明:在保持绝缘安全的前提下,相较于初始方案,优化后高、低压绕组热点温升,损耗,高、低压绕组单位体积短路电动力分别降低了22.91%、33.37%、9.39%、42.82%、45.52%,验证了所提出优化方法的有效性。研究结果为干式变压器的优化设计提供了新方法,对提高干式变压器的设计效率和运行可靠性具有重要的参考价值。

关键词: 环氧树脂干式配电变压器结构优化响应面法多目标海星优化算法协同寻优    
Abstract:

In order to enhance the service performance of epoxy resin dry-type distribution transformer, taking a 10 kV/0.4 kV epoxy resin dry-type distribution transformer as the research object, a structure optimization design method for dry-type distribution transformer based on the multi-objective starfish optimization algorithm (MOSFOA) was proposed. Firstly, a transformer model coupling electromagnetic-thermal-mechanical fields was established for performance simulation. The cross-sectional areas of the high/low voltage winding conductors, the width of the air ducts, and the radius of the core were determined as the core design variables. Subsequently, high-precision surrogate models linking the design variables to the hotspot temperature rise, loss and short-circuit electromagnetic force per unit volume of the high/low voltage windings were constructed using central composite design and response surface methodology. Finally, collaborative optimization based on the MOSFOA was performed to obtain the optimal combination of structural parameters.The resultsindicate that, while maintaining the insulation safe, compared with the initial plan, the hotspot temperature rise, loss, and short-circuit electromagnetic force per unit volume of the high/low voltage windings were reduced by 22.91%, 33.37%, 9.39%, 42.82%, and 45.52% respectively after optimization. This verified the effectiveness of the proposed optimization method.The research results provide a new method for the optimization design of dry-type transformers, and have significant reference value for improving the design efficiency and operational reliability of dry-type transformers.

Key words: epoxy resin dry-type distribution transformer    structural optimization    response surface methodology    multi-objective starfish optimization algorithm    collaborative optimization
收稿日期: 2025-09-25 出版日期: 2026-04-28
CLC:  TM 741  
基金资助: 国家自然科学基金资助项目(52572459);中国南方电网有限责任公司科技项目(YNKJXM20222302)
作者简介: 项恩新(1990—),男,高级工程师,学士,从事变配电装备性能优化研究,E-mail: 419722987@qq.com, https://orcid.org/0009-0008-1845-084X
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引用本文:

项恩新,李航,聂永杰,管京荣,王东阳. 基于多目标海星优化算法的干式配电变压器结构优化设计方法[J]. 工程设计学报, 2026, 33(2): 213-222.

Enxin XIANG,Hang LI,Yongjie NIE,Jingrong GUAN,Dongyang WANG. Structural optimization design method for dry-type distribution transformer based on multi-objective starfish optimization algorithm[J]. Chinese Journal of Engineering Design, 2026, 33(2): 213-222.

链接本文:

https://www.zjujournals.com/gcsjxb/CN/10.3785/j.issn.1006-754X.2026.06.103        https://www.zjujournals.com/gcsjxb/CN/Y2026/V33/I2/213

参数高压绕组低压绕组
额定容量/kVA800
额定电压/kV100.4
额定电流/A46.21 154.7
匝数77717
层数373
频率/Hz50
空载损耗,负载损耗/W875,5 840
联结组别Dyn11
表1  干式配电变压器基本参数
图1  干式配电变压器电磁场仿真模型网格剖分
图2  铁心 B—H 曲线
图3  干式配电变压器绕组区域网格截面
材料

密度/

(kg/m3)

热导率/

[W/(m·K)]

比热容/

[J/(kg·K)]

黏度/

[kg/(m·s)]

铜导体8 933401385
环氧树脂1 2000.461 300
绝缘纸9300.191 340
复合聚酯漆0.23
空气1.2250.024 21 006.431.789 4×10-5
表2  温度场计算中所用材料的物性参数
图4  额定运行条件下干式配电变压器电场分布云图
图5  额定运行条件下绕组单位体积损耗分布云图
图6  额定运行条件下绕组温度分布云图
图7  额定运行条件下绕组单位体积短路电动力分布云图
结构参数抽样范围
Slv-30%~30%
Shv-30%~30%
W-30%~30%
R/mm100~156
表3  干式配电变压器结构参数抽样范围
组号Shv/mm2Slv/mm2WR/mmThv/KTlv/KS/W
119.68601.750.75132.6774.4073.085 718.0
220.64746.750.97117.7370.4955.755 283.0
317.76616.250.99153.2075.6254.466 361.8
419.04674.251.25112.1375.6154.255 740.2
513.28775.750.93155.07102.9146.476 677.4
612.32877.251.11138.27114.6740.416 636.9
718.08630.750.85102.8082.3278.085 508.0
819.36906.251.17127.0771.4539.915 370.3
915.84645.250.89123.3390.4265.205 996.7
1020.32688.751.19142.0070.0745.935 874.9
1115.52703.251.13128.9391.7750.146 186.0
1212.96558.250.81110.27113.2885.796 443.4
1315.20587.251.15104.6794.0767.706 256.8
1411.36732.250.83130.80129.1959.476 727.2
1518.40514.751.05121.4780.8371.966 280.2
1617.12804.750.95134.5381.6148.635 682.6
1720.00862.750.91147.6070.6744.025 406.9
1814.88790.250.73108.4097.8969.905 498.1
1913.60529.250.87143.87104.3071.587 092.9
2011.68572.751.09125.20125.0863.297 244.7
2112.00761.251.03106.53122.1257.926 330.9
2213.92819.251.29114.00103.2945.006 180.0
2318.72891.750.77119.6077.4856.385 081.7
2416.48543.751.27136.4086.7756.956 794.4
2516.80848.251.21151.3384.8336.656 072.3
2616.16717.750.71145.7390.6461.845 933.1
2717.44833.751.07100.9382.8154.195 347.5
2814.24920.750.79140.13100.8248.615 898.0
2914.56935.251.01115.8799.1146.505 700.0
3012.64659.751.23149.47114.8745.857 301.7
表4  高/低压绕组热点温升和损耗数值计算结果
源项平方和自由度均方Fp
R2=0.987 0Radj2=0.974 4
模型8 744.1414624.58169.67<0.000 1
A: Shv8 296.4718 296.472 253.72<0.000 1
B: Slv6.5816.581.790.201 2
C: W6.2716.271.700.211 7
D: R44.27144.2712.030.003 4
AB0.3610.360.100.759 9
AC1.0811.080.290.595 4
AD0.0310.030.010.932 2
BC0.7610.760.210.656 8
BD1.1611.160.310.583 0
CD3.2813.280.890.360 1
A2231.711231.7162.94<0.000 1
B20.0910.090.030.874 6
C29.1019.102.470.136 8
D21.6611.660.450.512 0
残差55.22156.68
表5  Thv 模型方差分析结果
源项平方和自由度均方Fp
R2=0.999 2Radj2=0.998 5
模型4 350.7314310.772 691.35<0.000 1
A: Shv2.9512.9525.560.000 1
B: Slv2 111.6112 111.6118 287.34<0.000 1
C: W1 259.6111 259.6110 908.72<0.000 1
D: R784.801784.806 796.67<0.000 1
AB0.0510.050.430.520 2
AC0.4010.403.500.081 0
AD0.0210.020.160.696 3
BC16.97116.97146.93<0.000 1
BD7.6817.6866.53<0.000 1
CD8.8518.8576.61<0.000 1
A20.0010.000.01<0.000 1
B249.37149.37427.520.928 7
C227.53127.53238.40<0.000 1
D210.16110.1687.99<0.000 1
残差1.73150.011 55
表6  Tlv 模型方差分析结果
源项平方和自由度均方Fp
R2=0.999 0Radj2=0.998 0
模型10 274 873.5414733 919.542 105.40<0.000 1
A: Shv4 952 479.2614 952 479.261 4207.19<0.000 1
B: Slv2 456 285.4712 456 285.477 046.35<0.000 1
C: W693 143.361693 143.361 988.42<0.000 1
D: R1 399 514.1911 399 514.194014.79<0.000 1
AB561.161561.161.610.223 9
AC4 219.3014 219.3012.100.003 4
AD25 137.49125 137.4972.11<0.000 1
BC2 551.5012 551.507.320.016 3
BD9 200.7119 200.7126.390.000 1
CD148.241148.240.430.524 2
A2108 519.991108 519.99311.31<0.000 1
B264 169.26164 169.26184.08<0.000 1
C2218.471218.470.630.440 9
D22 786.3212 786.327.990.012 7
残差5 228.8515348.59
表7  S 模型方差分析结果
组号Shv/mm2Slv/mm2WR/mm

Fhv/

(107N/m3)

Flv/

(107N/m3)

111.68616.250.91145.7310.658.64
214.88877.250.79110.2710.077.37
312.00920.750.93136.409.575.31
419.36790.250.99151.334.704.83
517.76717.750.97100.937.898.34
612.96587.250.89106.5312.7312.14
713.28848.251.07102.809.896.57
818.72659.750.77143.876.517.90
914.24645.251.23104.678.507.91
1018.08833.751.25108.405.625.07
1119.68543.751.11142.004.867.38
1216.80674.250.71114.009.6910.50
1316.48906.251.15147.605.013.80
1415.20514.750.81134.539.3211.91
1517.12688.751.29140.134.895.03
1617.44891.750.75138.276.905.78
1713.92862.751.27125.206.694.51
1816.16630.751.03123.337.438.08
1920.00558.250.87117.736.8110.48
2015.52804.750.95130.807.396.07
2115.84601.751.05153.206.156.84
2220.32819.250.83115.876.316.71
2318.40935.251.01119.605.864.84
2419.04572.751.21112.135.778.06
2513.60529.251.19132.677.898.54
2612.32761.251.17149.477.395.02
2712.64732.250.73128.9312.099.05
2820.64746.751.13127.074.635.35
2914.56775.750.85155.077.496.01
3011.36703.251.09121.4710.837.42
表8  高/低压绕组单位体积短路电动力数值计算结果
源项平方和自由度均方Fp
R2=0.998 9Radj2=0.997 7
模型145.761410.411 814.95<0.000 1
A: Shv88.20188.201 5374.79<0.000 1
B: Slv3.8213.82666.19<0.000 1
C: W33.34133.345 812.32<0.000 1
D: R21.96121.963 827.54<0.000 1
AB0.2710.2746.56<0.000 1
AC1.6211.62282.58<0.000 1
AD0.8810.88153.69<0.000 1
BC0.1110.1119.190.000 5
BD0.0610.0610.910.004 8
CD0.3010.3051.54<0.000 1
A21.7511.75304.43<0.000 1
B20.0010.000.490.495 5
C20.1610.1627.69<0.000 1
D20.0910.0915.350.001 4
残差0.086150.0057
表9  Fhv 模型方差分析结果
源项平方和自由度均方Fp
R2=0.998 2Radj2=0.996 1
模型135.85149.701 177.90<0.000 1
A: Shv4.2714.27518.63<0.000 1
B: Slv78.33178.339 508.55<0.000 1
C: W35.05135.054 255.40<0.000 1
D: R20.60120.602 500.61<0.000 1
AB0.2410.2429.10<0.000 1
AC0.1410.1417.420.000 8
AD0.0510.056.440.022 7
BC1.8011.80218.78<0.000 1
BD0.7610.7692.17<0.000 1
CD0.3310.3340.41<0.000 1
A20.0110.010.840.374 3
B21.6211.62197.02<0.000 1
C20.1810.1822.440.000 3
D20.0910.0910.550.005 4
残差0.1236150.008 2
表10  Flv 模型方差分析结果
图8  MOSFOA流程
参数数值
迭代数量/次500
种群规模/个200
平衡参数0.5
Pareto解集规模/个100
表11  MOSFOA参数设置
图9  帕累托前沿
图10  优化方案下干式配电变压器电场分布云图
性能指标数值下降幅度/%
初始方案优化方案
Thv/K89.1868.7522.91
Tlv/K55.8037.1833.37
S/W5 869.25 318.39.39
Fhv/(107N/m3)7.594.3442.82
Flv/(107N/m3)7.143.8945.52
表12  优化方案与初始方案效果对比
  
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