Grey correlation analysis on related factors of temperature drift in magnetic modulated DCCT
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摘要: 为进一步改善磁调制DCCT（Direct Current Current Transducer）的温度特性，将磁调制DCCT化整为零，利用灰色相关理论确定了DCCT各部分温度系数对整机的影响程度；同时，还提出了一种磁调制DCCT温度系数综合评价方法。根据磁调制DCCT的工作原理，把DCCT分为PCB（Printed Circuit Board）、线圈和取样电阻三部分，并分别测出DCCT整机、PCB、线圈和取样电阻的温度系数；然后，利用灰色相关理论对7个被测DCCT的各部分温度系数进行关联计算，获得相应的关联系数，从而确定DCCT温度特性的主要因素。根据DCCT温度特性的主、次要因素并结合工程实际，设定了概念DCCT作为参考，利用灰色相关理论计算出7个被测DCCT与参考DCCT的温度系数的灰色关联加权值，完成了被测磁调制DCCT温度性能的综合评价。最后，指出了降低DCCT整机温度敏感性的研究方向。Abstract: To further improve the temperature characteristics of magnetic modulation DCCT (Direct Current Current Transducer), the effects of various parts on the DCCT performance about temperature coefficient are found out by dividing the magnetic modulation DCCT into parts with grey correlation theory; at the same time, a comprehensive evaluation method of temperature coefficient of magnetic modulation DCCT is proposed. According to the working principle of magnetic modulation DCCT, DCCT is divided into three parts: printed circuit board (PCB), coil and sampling resistance. The temperature coefficients of them of the whole DCCT, PCB, coil and sampling resistance are measured respectively; then, temperature coefficient of each part of the 7 tested DCCT is calculated by using the grey correlation theory, and the correlation coefficients between the parts are obtained. Based on factors of the temperature characteristics and actual requirements, a concept DCCT is set as the reference. Using the grey correlation theory, the temperature comprehensive evaluation of the 7 tested magnetic modulation DCCTs is provided. The results provide a direction to reduce the temperature sensitivity of DCCT.
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Key words:
- hard X-ray /
- current sensor /
- temperature drift /
- magnetic modulation /
- grey correlation /
- DCCT /
- temperature coefficient
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表 1 实验结果
Table 1. Results of experiments
type of DCCT temperature coefficient/（μV·℃−1） DCCT PCB coil Rs Sinap-DCCT 400A 1# 0.6271 0.5361 0.1136 0.0206 Sinap-DCCT 200A 0.2416 0.4491 0.1685 0.0316 LEM IT 400-S 1# 0.5317 0.4744 0.3542 0.0491 LEM IT 400-S 2# 1.4765 0.8584 1.3309 0.0512 Sinap-DCCT 400A 2# 1.0717 0.8593 0.2831 0.0323 Sinap-DCCT 1000A 1# 1.9010 1.5298 0.7049 0.0242 Sinap-DCCT 1000A 2# 0.6864 1.1417 0.0652 0.0607 
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表 2 DCCT各部分温度系数的相关系数
Table 2. Correlation coefficients of Ct in each part of DCCT
different part TC of DCCT TC of PCB TC of coil TC of Rs TC of DCCT 1.000 000 − − − TC of PCB 0.802 208 1.000 000 − − TC of coil 0.718 670* 0.297 793 1.000 000 − TC of Rs −0.138 720** 0.031 939 0.169 575 1.000 000 *表示显著相关（P＜0.05），**表示极显著（P＜0.01）
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表 3 DCCT温度特性及构成因素灰色关联分析标准化结果
Table 3. Standardized results of grey correlation analysis between temperature characteristics and composition factors of DCCT
type of DCCT TC of DCCT（X0） TC of PCB（X1） TC of coil（X2） TC of Rs（X3） Sinap-DCCT 400A 1# −0.525 2 −0.754 0 −0.706 2 −1.182 6 Sinap-DCCT 200A −1.185 4 −0.973 1 −0.584 1 −0.456 4 LEM IT 400-S 1# −0.688 6 −0.909 4 −0.171 7 0.700 6 LEM IT 400-S 2# 0.929 7 0.057 5 1.997 8 0.834 2 Sinap-DCCT 400A 2# 0.236 4 0.060 0 −0.329 6 −0.410 0 Sinap-DCCT 1000A 1# 1.656 8 1.748 2 0.607 4 −0.948 3 Sinap-DCCT 1000A 2# −0.423 7 0.770 9 −0.813 6 1.462 5
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表 4 DCCT温度特性及构成因素灰色关联分析的Δi（k）
Table 4. Δi(k) of grey correlation analysis between temperature characteristics and components of DCCT
type of DCCT TC of PCB（X1） TC of coil（X2） TC of Rs（X3） Sinap-DCCT 400A 1# 0.228 8 0.181 0 0.657 4 Sinap-DCCT 200A 0.212 4 0.601 3 0.729 0 LEM IT 400-S 1# 0.220 8 0.516 9 1.389 2 LEM IT 400-S 2# 0.872 2 1.068 1 0.095 5 Sinap-DCCT 400A 2# 0.176 5 0.566 0 0.646 4 Sinap-DCCT 1000A 1# 0.091 4 1.049 4 2.605 1 Sinap-DCCT 1000A 2# 1.194 6 0.389 9 1.886 2
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表 5 DCCT温度特性与构成因素的
${\xi _{\rm{i}}}(k)$ Table 5.
${\xi _{\rm{i}}}(k)$ between temperature characteristics and composition factors of DCCTtype of DCCT TC of PCB（X1） TC of coil（X2） TC of Rs（X3） Sinap-DCCT 400A 1# 0.910 3 0.939 6 0.711 2 Sinap-DCCT 200A 0.920 2 0.732 2 0.686 2 LEM IT 400-S 1# 0.915 1 0.766 1 0.517 9 LEM IT 400-S 2# 0.641 0 0.588 0 0.997 1 Sinap-DCCT 400A 2# 0.942 5 0.746 0 0.715 2 Sinap-DCCT 1000A 1# 1.000 0 0.592 7 0.356 7 Sinap-DCCT 1000A 2# 0.558 2 0.823 6 0.437 2 mean 0.841 0 0.741 2 0.631 6 rank 1.000 0 2.000 0 3.000 0
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表 6 基于灰色关联分析的DCCT综合评价的标准化结果
Table 6. Standardized results of comprehensive evaluation of DCCT based on grey correlation analysis
type of DCCT TC of DCCT TC of PCB TC of coil TC of Rs reference 1.000 0 1.000 0 1.000 0 1.000 0 Sinap-DCCT 400A 1# 0.313 5 0.335 1 0.081 1 0.206 1 Sinap-DCCT 200A 0.120 8 0.280 7 0.120 4 0.316 1 LEM IT 400-S 1# 0.265 8 0.296 5 0.253 0 0.491 4 LEM IT 400-S 2# 0.738 3 0.536 5 0.950 6 0.511 7 Sinap-DCCT 400A 2# 0.535 9 0.537 1 0.202 2 0.323 2 Sinap-DCCT 1000A 1# 0.950 5 0.956 1 0.503 5 0.241 6 Sinap-DCCT 1000A 2# 0.343 2 0.713 5 0.046 6 0.606 9
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表 7 基于灰色关联分析的DCCT综合评价的Δi（k）
Table 7. Δi(k) of DCCT’s comprehensive evaluation based on grey relational analysis
type of DCCT TC of DCCT TC of PCB TC of coil TC of Rs Sinap-DCCT 400A 1# 0.686 5 0.664 9 0.918 9 0.793 9 Sinap-DCCT 200A 0.879 2 0.719 3 0.879 6 0.683 9 LEM IT 400-S 1# 0.734 2 0.703 5 0.747 0 0.508 6 LEM IT 400-S 2# 0.261 7 0.463 5 0.049 4 0.488 3 Sinap-DCCT 400A 2# 0.464 1 0.462 9 0.797 8 0.676 8 Sinap-DCCT 1000A 1# 0.049 5 0.043 9 0.496 5 0.758 4 Sinap-DCCT 1000A 2# 0.656 8 0.286 5 0.953 4 0.393 1
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表 8 7个被测DCCT与参考DCCT的
${\xi _{\rm{i}}}(k)$ Table 8.
${\xi _{\rm{i}}}(k)$ between 7 tested DCCTs and reference DCCTtype of DCCT TC of DCCT TC of PCB TC of coil TC of Rs Sinap-DCCT 400A 1# 0.447 6 0.456 0 0.373 0 0.409 7 Sinap-DCCT 200A 0.383 9 0.435 3 0.383 8 0.448 6 LEM IT 400-S 1# 0.429 9 0.441 1 0.425 4 0.528 4 LEM IT 400-S 2# 0.705 0 0.553 7 0.989 6 0.539 5 Sinap-DCCT 400A 2# 0.553 3 0.554 0 0.408 5 0.451 3 Sinap-DCCT 1000A 1# 0.989 3 1.000 0 0.534 9 0.421 5 Sinap-DCCT 1000A 2# 0.459 3 0.682 1 0.364 0 0.598 5
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表 9 7个被测DCCT与参考DCCT的关联度及排序
Table 9. Correlation and rank between 7 tested DCCTs and reference DCCT
type of DCCT equal correlation weighted correlation coefficient rank coefficient rank Sinap-DCCT 400A 1# 0.421 6 6 0.431 4 6 Sinap-DCCT 200A 0.412 9 7 0.405 8 7 LEM IT 400-S 1# 0.456 2 5 0.442 2 5 LEM IT 400-S 2# 0.696 9 2 0.700 0 2 Sinap-DCCT 400A 2# 0.491 8 4 0.514 4 4 Sinap-DCCT 1000A 1# 0.736 4 1 0.844 9 1 Sinap-DCCT 1000A 2# 0.526 0 3 0.521 0 3
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