Trans. Tianjin Univ. 2010, 16: 011-016 DOI 10.1007/s12209-010-0003-8

Accepted date: 2009-02-12. *Supported by the Ministry of Science and Technology of China (No. NCSTE-2006-JKZX-167) and Beijing Key Laboratory (Measurement and Control of

Electro-mechanical Systems) (No. 82063005). WANG Xiaofei, born in 1965, Dr, associate Prof. Correspondence to WANG Xiaofei, E-mail: xfinbj@sohu.com.

Model of Current Threshold for Perception in Testing Electrical Safety Performance*

WANG Xiaofei (王晓飞)1,2, ZHANG Zhaohui (张朝晖)1, LI Dong (李 东)2,

LIU Guozhong (刘国忠)2, ZHAO Xu (赵 旭)3

(1. School of Information Engineering, University of Science and Technology Beijing, Beijing 100083, China; 2. School of Electro-Optical Engineering, Beijing Information Science and Technology University, Beijing 100192, China;

3. Department of Neurology, The 306th Hospital of PLA, Beijing 100101, China)

© Tianjin University and Springer-Verlag Berlin Heidelberg 2010

Abstract：A generalized mathematical model of human body current threshold for perception was established and the current flowing through human body could be arbitrary cyclical waveforms. The relationship between human bodycurrent threshold for perception and current frequency, true root mean square (RMS) value and influence factor was described. A test system was established based on electroencephalogram (EEG) to study the relationship between human body current threshold for perception and current waveform, frequency and duty cycle so that the data could be obtained objectively and reliably. At least 850 groups of current threshold for perception and 16-lead EEGs were ac-quired. The theoretical analysis are verified by experimental data, and an amendment proposal on leakage current evaluation limits specified in International Electro-Technical Commission (IEC) standards is suggested. Keywords：electrical safety performance；leakage current; current threshold for perception；current waveform；

electroencephalogram (EEG)

Leakage current is one of the important parameters in testing electrical safety performance. The founda-tion of testing leakage current is human body impedance networks and leakage current limits specified in Interna-tional Electro-Technical Commission (IEC) standards, which are based on human body current effect and threshold. Usually the leakage current should be kept within human body current threshold for perception or reaction so that comfort and safety in operating these equipments are ensured. The human body current thresh-old is not a constant, it depends on the conditions of the human body (e.g. the touch voltage, touch area, touch pressure, humidity, ambient temperature, skin type), the time period in which the current passes through the hu-man body, the current frequency, the current waveform and the current path[1]. All the factors have been stu-died[2-7] excluding current waveforms.

Although the power supply is 50 Hz or 60 Hz sinu-soidal, the leakage current has already distorted because of the equipment nonlinearity responses. The current passing through the human body is no longer a sinusoidal

signal, and the distortion degree depends on the type of equipments. In addition, some equipments provide non-sinusoidal signals, e.g., the physiotherapy instrument generates pulse signals which directly acts on specific point to perform treatment, and it also generates leakage current from metal enclosures or parts. Therefore, study-ing the threshold model of current with cyclical arbitrary waveform brings significance in theoretical and practical sense. And it is important to obtain current thresholds for perception objectively and reliably based on electroen-cephalogram (EEG). This paper focuses on the model of the human body threshold for perception current with cyclical arbitrary waveform at frequencies 50 Hz to 1 000 Hz.

1 Model of current threshold for perception

Since the human body is adaptable to continuous stimulation[8], it can be inferred that the human nervous system is easier to be palsied and the perception ability declines as the current frequency becomes higher, which

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finally causes the increase of the perception threshold. Since DC signal is continuous stimulation indeed, the DC perception threshold may approach the maximum value. The result of IEC shows that the human body DC perception threshold is I0 = 2 mA, and the sinusoidal cur-rent threshold for perception is I10 = 0.5 mA at 50 Hz[1,2]. Meanwhile, the sinusoidal current threshold for percep-tion at 1 000 Hz obtained through a conversion according to the frequency factor Ff shown in Fig.1[2] is

1 10(1 000) 2.1 0.5 mAfI F I= ⋅ = × =

1.05 mA (1) It can be seen that the above inference is consistent with the IEC result.

Fig.1 Variation of the frequency factor of sinusoidal current

threshold for perception with the frequency ranging from 50/60 Hz to 1 000 Hz

In view that the frequency and equivalent DC mag-nitude of an AC signal are important factors for deciding the perception threshold, the effect should be the same regardless of the current direction from the left hand to the right hand or reverse. The generalized mathematical model of the threshold for perception current with cycli-cal arbitrary waveform is established according to the theoretical analysis and a large number of experimental data of human bodies, which is shown as 0( ) (50) [RMSi i iI f I C= ⋅ ⋅ ⋅

0.001 15 ( 50) 1]f⋅ − + (2) where i denotes the waveform type, i = 1, 2 or 3 corre-sponds to sinusoidal, triangular or square respectively; Ii( f ) denotes the current threshold for perception at fre-quency f ; Ii0(50) is the current threshold for perception at 50 Hz corresponding to power supply, different human bodies have different values of Ii0(50) (abbreviated as Ii0, and when the frequency of power supply is 60 Hz, 50 in Eq.(2) is substituted by 60); RMSi is the true root mean square (RMS) value of AC flowing through human body and represents the equivalent DC magnitude of AC; C is an influence factor related to many factors, such as the flow path in human body, skin type, touch area, touch

pressure, ambient temperature and humidity. The value of C is different for different human bodies. Eq.(2) is lin-ear, and the coefficient is mainly determined by the true RMS value of current. Eq.(2) shows that the current threshold for perception becomes larger as the true RMS is larger or frequency is higher.

2

0

1RMS dT

i iI tT

ω= ∫ (3)

1.1 Sinusoidal excitation The true RMS value of the sinusoidal current with

amplitude A and angular frequency ω which flows through the human body is acquired as

2 2 2

1 0

1RMS sin d2 2

AA t tω ωπ

= =π ∫

(4)

Putting Eq.(4) into Eq.(2) and A = 2 mA, the mathematical model of the sinusoidal current threshold for perception is 1 10 1( ) [RMS 0.001 15( 50) 1]I f I C f= ⋅ ⋅ − + =

102[ 0.001 15( 50) 1]2

I C f⋅ ⋅ − + (5)

The frequency factor Ff of the sinusoidal current is computed as

1 10( )fF I f I= =

2 0.001 15( 50) 12

C f⋅ ⋅ − + (6)

When 7.022 ≈=C ,

0.001 15( 50) 1fF f= − + (7)

At this time, Eq.(7) fully coincides with the curve issued by IEC as shown in Fig.1[2].

Since the horizontal axis in Fig.1 uses the logarith-mic coordinate, the linear relationship between Ff and f is not obvious (When I10 = 0.5 mA is determined, the rela-tion curve of I1( f ) and f drawn according to a linear co-ordinate is shown as Curve 6 in Fig.4, the linear relation-ship can be seen obviously). 1.2 Triangular excitation

Similarly, the true RMS value of the triangular cur-rent with the same angular frequency and amplitude is acquired as

22 0

1 2 2RMS ( ) d AA t tω ωπ

= =π π π∫ (8)

Putting Eq.(8) into Eq.(2) and A = 2 mA, the mathematical model of the triangular current threshold for perception is 2 20 2( ) [RMS 0.001 15( 50) 1]I f I C f= ⋅ ⋅ − + =

10[4 0.001 15( 50) 1]I C fπ⋅ ⋅ − + (9)

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1.3 Square excitation A square wave can be thought of a converted form of a triangular wave.

As shown in Fig.2, the amplitude of the signal is maintained constant. Curve 1 is a triangular wave with amplitude A and angular frequency ω. Curve 1 becomes the trapezoidal wave indicated by Curve 2 as the slope increases, and indicated by Curve 3 as the slope increases further, and finally becomes the square wave indicated by Curve 4.

Fig.2 Triangular wave approaching square wave

Taking the trapezoidal wave Curve 2 in Fig.2 for example, the linear equation of rising line is

1I A tx

ω= (10)

The true RMS value of the trapezoidal wave is / 22 2

4 0

2 1 2RMS ( ) d ( ) dx

xA t t A t t

xω ω ω ω

π= + =

π π∫ ∫

2 1( ) 1A x

x− +

π (11)

When 2x = π is determined, the trapezoidal wave is transformed into the triangular wave and Eq.(11) is iden-tical to Eq.(8). When 0→x , the trapezoidal wave is transformed into a square wave, and the true RMS value of the square wave with amplitude A and angular fre-quency ω is

23

1RMS ( ) dA t t Aω ωπ

0= =

π ∫ (12)

It can be seen that the true RMS value of the trape-zoidal wave is in the range of 2 /A Aπ − . Putting Eq.(12) into Eq.(2) and 2mAA = , the mathematical model of square current threshold for per-ception is

3 30 3( ) [RMS 0.00115( 50) 1]I f I C f= ⋅ ⋅ − + =

30[2 0.001 15( 50) 1]I C f⋅ ⋅ − + (13)

Comparing Eqs.(4), (8) and (12), it can be found that the true RMS values of sinusoidal, triangular and square signals with the same frequency and amplitude are 3 1 2RMS RMS RMS> > (14)

Therefore, from Eqs.(5), (9) and (13), the current thre-sholds for perception have the relationship as )()()( 213 fIfIfI >> (15)

In addition, if only the duty cycle of a square signal is changed, there is no effect on the true RMS value. There-fore the square current threshold for perception has no relation with the duty cycle.

In short, the current threshold for perception mainly depends on the true RMS value and frequency of the cur-rent signal. As the true RMS value and frequency become higher, the human nervous system is easier to be palsied, perception ability becomes worse, and the current thresh-old for perception becomes higher. The current threshold for perception is also related to many factors, such as the current path, the skin type of human body, touch area and pressure between the body and equipments, ambient tem-perature and humidity. Under the same testing condition, different human bodies may have different current thresholds for perception.

2 Experiments on current thresholds for perception

In order to verify the above theory, a test system was established to measure human body current threshold for perception, as shown in Fig.3.

Fig.3 Test system of current thresholds for perception based

on EEG

The cylindrical brass with diameter of 80 mm and height of 100 mm was adopted as electrode. A pair of hands were fixed on the electrode elastically, and the touch pressure was monitored through pressure sensors. The entire palm contacted electrode under certain touch pressure to simulate the experiment conditions of large touch area and fixed touch pressure. The ambient tem-perature and humidity were 25 ℃ and 55% respectively. The experimental volunteers were healthy and 22—26 years old. The skin can be classified as the type of healthy young adults. A generator produced sinusoidal signal, triangular signal, square signal with adjustable

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amplitude and frequency ranging from 50 Hz to 1 000 Hz, and the duty cycles are 15%, 20%, 30%, 40% or 50% especially for the 50 Hz square signals. The voltage was controlled under a safe range and applied to the two elec-trodes. There was insulation beneath the feet of the ex-perimental volunteers so that the current flowed through the human body from hand to hand. A self-locking button and time-relay were used to control power-on time so that the power-on time of each experiment can be identical. When the above experiment conditions were satisfied, the influence factors on the current threshold for perception were only frequency and waveform. The μA meter

“MS8218” is a 5 12

digital multi-meter which can meas-

ure the true RMS value of very weak current. The current flowing through the human body is ad-

justed from low to high and the minimum value of the current causing any sensation will be considered as the current threshold for perception traditionally[1-7]. The re-sult is unstable since it depends on the sensation of the human body subjectively. Some researchers filter the effect of subjective experience by using physiological and psychological statistical algorithm in recent years[9-10]. Considering that EEG can reflect the excitabil-ity of the human nervous system[11], EEG monitor is in-troduced to identify whether the current reaches the per-ception threshold.

EEG monitor was used to detect the changes of EEG characteristics when the current flowed through the hu-man body. In the early study, EEGs were compared and analyzed before and after the current flowed through the human body, 92.41% EEGs changed obviously and hu-man bodies had sensation, 5.76% EEGs changed obvi-ously while human bodies had no any sensation, 1.83% EEGs had no obvious change but human bodies had sen-sation. Since EEG is more objective than the sensation, 7.59% data of current thresholds for perception are not reliable according to the traditional measuring method. All the current thresholds for perception in this paper are the true RMS value of the current when the current reaches the traditional current threshold for perception and at the same time the EEG changes obviously, so the data can be obtained objectively and reliably based on EEG.

Experiments were conducted on 32 volunteers and 850 groups of current thresholds for perception and 16-lead EEGs were obtained. The experimental data show the same trend basically. The poly-line charts of current

thresholds for perception are shown in Fig.4 (a), (b) and (c) when sinusoidal, triangular or square currents (50 Hz to 1 000 Hz) flow through human body from hand to hand. The poly-line charts of square current thresholds for perception with the duty cycle of 15%, 20%, 30%, 40% and 50% at 50 Hz are shown in Fig.5. The same se-quence number in Fig.4 and Fig.5 corresponds to the same volunteer. In Fig.4, Curve 6 is IEC leakage current

(a) Sinusoidal current threshold for perception

(b) Triangular current threshold for perception

(c) Square current threshold for perception

(d) The relationship among perception thresholds of sinusoidal (Curve 1A),

triangular (Curve 1B)and square current (Curve 1C)

Fig.4 Variation of current threshold for perception with frequency

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Fig.5 Variation of square current threshold for perception

with duty cycle at 50 Hz

limit curve. Taking No.1 volunteer in Fig.4 (a), (b)and (c) for example, the relationship among the perception thresholds of current with sinusoidal, triangular and square wave at different frequencies is shown as Curve 1A, Curve 1B and Curve 1C in Fig.4(d) respectively.

3 Experimental analysis

3.1 Relationship between current threshold for perception and excitation frequency

As shown in Fig.4 (a), (b) and (c), the current thresh- old for perception increases linearly as the frequency in-creases regardless of the waveform of current, which is consistent with the relationship expressed by Eqs.(2), (5), (9) and (13). 3.2 Relationship between current threshold for

perception and excitation waveform From Fig.4(d), it can be seen that square, sinusoidal

and triangular current threshold for perception are in de-creasing order strictly, which is consistent with Eq.(15). As mentioned above, Fig.4(d) is for No.1 volunteer. The experimental data on other volunteers also present the same rule. In this paper, the difference in current wave-forms is attributed to the variation of the true RMS value of current. The greater the true RMS value of current, the bigger the human body current threshold for perception. 3.3 Relationship between current threshold for

perception and duty cycle of excitation As shown in Fig.5, the square current thresholds for

perception do not increase or decrease significantly while the duty cycle changes, i.e., the square current thresholds for perception are independent of duty cycles. 3.4 Influence factor C obtained in experiments

Data in Fig.4 (a), (b) and (c) are linearly fitted by least square algorithm according to Eqs.(5), (9) and(13) to obtain the value of C, which are shown in

Tab.1. Differences exist in current thresholds for percep-tion under the same test condition, which is expressed by C in Eqs. (2), (5), (9) and (13). The sequence numbers in Tab.1 are the same as those in Fig.4 (a), (b) and (c), and represent five volunteers respectively.

Tab.1 Influence factor C obtained in experiments Influence factor C Sequence

number Sinusoidal current

Triangular current

Square current Average

1 1.742 2.162 1.414 1.773

2 1.998 2.180 1.132 1.770

3 2.983 3.543 2.104 2.877

4 2.519 2.941 1.701 2.387

5 2.166 2.554 1.328 2.016

4 Further discussion

IEC60990 suggested that the safe limit of 50 Hz si-nusoidal leakage current is 0.5 mA, and multiplied by frequency factors illustrated in Fig.1, a sinusoidal current threshold for perception at corresponding frequency was obtained as Curve 6 in Fig.4.

This paper shows that current waveform is a unique influence on the current threshold for perception. As shown in Curve 1A of Fig.4(d), all test data are greater than IEC limits illustrated by Curve 6, which means that the IEC standard is safe for sinusoidal leakage current. As shown in Curve 1B of Fig.4(d), some data are smaller than IEC limits, which means that IEC evaluation principle may yield potentially unsafe result for triangu-lar leakage current. However, in practice, although the power supply is sinusoidal of 50 Hz or 60 Hz, in most cases the current waveform errs and approaches triangu-lar wave, so there are factors that may yield unsafe results in practice following the IEC leakage current evaluation principle. As shown in Curve 1C in Fig.4(d), all square current thresholds for perception are much greater than sinusoidal current thresholds for perception. Therefore, the IEC standard is somewhat strict for square leakage current, and the limit can be extended.

According to the mathematical model in this paper, it is suggested that the evaluation limit of sinusoidal leakage current is still 0.5 mA at 50 Hz, which is consis-tent with the IEC standard, the evaluation limit of trian-gular leakage current and square leakage current are 0.45 mA and 0.71 mA at 50 Hz respectively.

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5 Conclusions

The EEG monitor is used firstly to evaluate the cur-rent threshold for perception objectively and reliably. The current threshold for perception increases linearly with the excitation frequency. There is a relationship between the current threshold for perception and current wave-form, and the threshold is determined mainly by the cur-rent RMS value. The greater the true RMS value of the current, the bigger the human body current threshold for perception. The current threshold for perception has no relation with the current duty cycle. The current threshold for perception may be various for different human bodies. All the relations are illustrated by the generalized mathematical model presented in this paper. This paper also presents a suggestion for the amendment of the IEC leakage current evaluation.

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