基于FFT和三次Hermite插值的人体触电判据初探*

doi:10.11985/2023.01.015

摘要/Abstract

摘要：

针对当前基于TT系统(电气设备的金属外壳直接接地的保护系统)的低电压配电网输电线路上的剩余电流保护设备无法保证人触电后马上动作的现状，首先搭建活体触电试验平台，通过单相电压有效值220 V、频率50 Hz的电源对猪表皮进行触电试验，并使用控制变量的方法研究触电波形和触电面积、触电湿度以及触电时漏电电流大小之间的关系，得到试验数据；其次，对试验数据进行处理，使用FFT计算触电时刻的谐波畸变率，使用三次Hermite插值算法，绘制触电波形包络线，计算包络线不同时刻的斜率；最后，选择谐波畸变率最小值和合适的斜率，搭建仿真平台，对试验数据拟合得到的人体阻抗进行触电仿真，使用谐波畸变率和波形峰值斜率变化作为剩余电流保护设备触电判断依据，验证了所提判据的可行性。

关键词: TT系统, 触电试验, 动态阻抗模型, 快速傅里叶变换, 三次Hermite插值

Abstract:

To address the current situation that residual current protection equipment on transmission lines of low-voltage distribution networks based on TT systems(protection systems where the metal enclosures of electrical equipment are directly grounded) cannot guarantee immediate action after human electrocution, firstly, the in vivo electrocution experiment platform is built, and the electrocution experiment is conducted on the pig epidermis through the power supply with single-phase voltage RMS 220 V and frequency 50 Hz, and the relationship between the electrocution waveform and the electrocution area, the electrocution humidity and the leakage current magnitude at the time of electrocution is studied using the method of control variables to obtain the experimental data; secondly, the experimental data are processed, and the harmonic distortion rate at the moment of touching is calculated using FFT, and the touching waveform envelope is plotted using the cubic Hermite interpolation algorithm to calculate the slope of the envelope at different moments. Finally, the minimum value of harmonic distortion rate and suitable slope are selected, and the simulation platform is built to simulate the human body impedance obtained by fitting the experimental data, and the changes of harmonic distortion rate and peak slope of waveform are used as the basis for judging the electrocution of residual current protection equipment. The feasibility of the proposed criterion is verified.

Key words: TT system, electric shock test, dynamic impedance model, fast Fourier transform, cubic Hermite interpolation

中图分类号:

TM561

王欣阳, 魏云冰, 徐浩. 基于FFT和三次Hermite插值的人体触电判据初探^*[J]. 电气工程学报, 2023, 18(1): 133-142.

WANG Xinyang, WEI Yunbing, XU Hao. Preliminary Study on the Human Body Electric Shock Criterion Based on FFT and Cubic Hermite Interpolation[J]. Journal of Electrical Engineering, 2023, 18(1): 133-142.

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限制电流/mA	触电面积/cm²	谐波畸变率(%)
限制电流/mA	触电面积/cm²	干燥情况	半湿润情况	湿润情况
30	0.5	5.49	25.72	83.33
100	0.5	71.52	16.49	15.48
300	0.5	18.97	41.93	49.97
500	0.5	15.07	10.16	68.93
30	5	154.52	43.46	9.81
100	5	14.65	44.26	33.83
300	5	11.25	100.01	75.15
500	5	138.52	39.60	66.10
30	10	30.28	16.66	9.81
100	10	43.67	137.77	93.29
300	10	43.60	44.78	340.09
500	10	51.63	5.75	243.47

限制电流/mA	触电面积/cm²	干燥情况		半湿润情况		湿润情况
限制电流/mA	触电面积/cm²	斜率1	斜率2	斜率1	斜率2	斜率1	斜率2
30	0.5	0.359 6	0.251 6	0.201 0	0.242 5	1.057 2	0.107 8
100	0.5	0.822 4	0.066 5	1.348 3	1.183 2	2.293 1	1.150 0
300	0.5	2.719 1	3.024 2	7.879 3	2.576 9	4.399 4	4.400 8
500	0.5	4.227 9	4.859 3	13.647 5	3.510 7	7.407 5	3.521 4
30	5	0.451 3	0.113 2	0.134 9	0.052 3	0.748 7	0.056 0
100	5	2.705 3	2.075 6	0.949 1	0.566 9	1.424 0	0.303 1
300	5	2.297 6	2.096 4	2.485 9	0.924 1	2.666 2	0.811 4
500	5	5.655 8	1.561 7	9.334 0	3.501 8	10.530 0	0.994 8
30	10	0.650 2	0.328 1	0.650 2	0.075 1	0.748 7	0.013 2
100	10	3.103 5	1.653 2	1.575 0	0.538 1	2.313 9	0.227 3
300	10	7.746 3	2.126 5	8.286 2	6.976 5	11.152 0	6.153 8
500	10	7.087 8	5.018 6	9.457 8	4.604 1	16.395 0	4.920 2

仿真模块参数	数值
三相电源线电压/V	10 000
三相电源容量/(V·A)	100 000
频率/Hz	50
变压器变比/(一次/二次)	10 000/400
变压器绕线方式	DYn11
线路电阻/(Ω/km)	0.012 73
线路电感/(H/km)	0.933 7×10^-3
线路电容/(F/km)	12.73×10^-9
负载功率/W	30 000
故障开关通断时间/s	0.08~0.22
人体阻抗并联电容/F	2.2×10^-7

判据	特点
文献[8]双重触电判据	能够实时计算THD，并通过THD和电流整定值判断人体触电，但会造成误判，导致误动
文献[20]JD6型漏电保护器判据	能够计算各半周波幅值幅度变化大小，并通过幅度大小判断人体触电，但仅通过幅值幅度变化判断，灵敏度低，容易造成拒动或误动
本文判据	能够实时计算THD，判断人体触电开始时刻，并通过计算各周波间的变化来进一步判断是否是人体触电，增加了可靠性和灵敏度