IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 48, NO. 5, OCTOBER 1999 899

A New Type of GroundingResistance Measurement Method

Li Maotang and Li Jing

Abstract—This paper discusses the measuring methods ofgrounding resistance. A new measuring method, which uses ahigher order spectrum, is suggested. Compared with a powerspectrum-based method, the new method can reduce the effectat Gaussian noise, and therefore can measure the groundingresistance more accurately. Simulation and experimental resultsdemonstrate the effectiveness of the new method.

Index Terms—Grounding resistance, higher order spectra.

I. INTRODUCTION

T HE grounding resistance in electrical systems is definedas where is the electric potential of the grounding

electric pole, and is the electric current that flows into earththrough the grounding electric pole [1]. The magnitude ofthe grounding resistance is an important technical parameter,which is connected with the safety of electric power equip-ment. If the grounding resistance is too large, the people whouse the power equipment may be killed or injured, and theequipment may be damaged [2].

Electric bridge instruments and electric potential instru-ments are usually used to measure the grounding resistance.The error is large because of a lot of disturbance in themeasurement. A white noise method has been proposed tomeasure the grounding resistance. A white noise generator isused as a power source and the voltage and current signalsare analyzed by bipath frequency spectrum analyzer. Theadvantage of this method is that the disturbing voltage can berestrained partly. But it is difficult to eliminate the disturbingvoltages completely. In order to restrain the disturbance moreeffectively, we suggest a new method that is based on higher-order spectrum.

II. POWER SPECTRUM-BASED WHITE NOISE METHOD

In the measuring method based on white noise, a whitenoise generator is used as a power source and the measuredvoltage and current signals are analyzed by bipath frequencyspectrum analyzer (Fig. 1).

Suppose the measured voltage and current are and, respectively, and the disturbance does not exist, then

(1)

Where and are random signal. is the groundingresistance. According to the theory of the correlation functions

Manuscript received December 30, 1995; revised July 11, 1999.The authors are with the Center for Space Science and Applied

Research, Chinese Academy of Sciences, Beijing, China 100080 (e-mail:mr53@sun20.cssar.ac.cn).

Publisher Item Identifier S 0018-9456(99)06694-2.

Fig. 1. Measuring system based on white noise.

and spectrum estimation [3], the auto-correlation functions ofand , respectively, are

(2)

(3)

Since the power spectrum is defined as the Fourier transformof the related auto-correlation function

(4)

(5)

where, FFT is the mark of fast Fourier transform. From theabove equations, we can get

(6)

So

(7)

Therefore the magnitude of the grounding resistance can beobtained by (7) when disturbance does not exist. Actually, dis-turbing voltages and disturbing currents do exist; the measuredvoltage and measured current, respectively, are

(8)

(9)

where and are disturbing voltage and disturbingcurrent, respectively. If we still use (7) to calculate thegrounding resistance, we can get

(10)

0018–9456/99$10.00 1999 IEEE

900 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 48, NO. 5, OCTOBER 1999

Fig. 2. Magnitude frequency chart of the ground resistance.

and are independent of each other and andare also independent of each other. So

(11)

(12)

Equation (10) becomes

(13)

In Fig. 1, the input resistance of the frequency spectrumanalyzer is larger than the grounding resistanceand thesampling resistance . In fact, there is little current throughthe frequency spectrum analyzer, and the disturbing current

beneath the ground does not go through the, so in (9),the from the sampling resistance is ,and (12) becomes . Equation (13) becomes

It is evident that the is not equal to in (13)and there is an error in calculating grounding resistance bythe power spectrum method. In addition, there are harmonicdistribution elements beneath the ground, which affect themeasuring precision of the ground resistance. Fig. 2 is themagnitude frequency chart of the ground resistance. It isobvious that harmonic disturbing elements can generate aserious error. In order to decrease or eliminate the error, wepropose a new method by using higher-order spectrum.

III. H IGHER ORDER SPECTRUM-BASED METHOD

Recently, higher order spectral analysis has received inten-sive attention in signal processing. Higher order spectra aresuperior to power spectra in the following aspects:

1) to extract information due to deviations from normality;2) to estimate the phase of parametric signals;3) to detect and characterize the properties of nonlinear

mechanisms that generate time series [3]–[5].

In this paper, we use the fact that the high order spectrumof non-Gaussian signal is nonzero, however, that of Gaussiansignal is zero, therefore, higher-order spectrum can be usedto eliminate the effect of Gaussian noise [6]. The followingdefinitions are applied.

For a zero mean, stationary random process, the thirdorder cumulant is defined as

(14)

The one-dimensional (1-D) diagonal slice of the third ordercumulant is obtained by setting in (14), i.e.,

(15)

The two-dimensional (2-D) Fourier transform of third-ordercumulant is defined as dispectrum, i.e.,

(16)

Similarly, we define the Fourier transform of the 1-D diagonalslice of the third-order cumulant as 1(1/2)-D spectrum, i.e.,

(17)

The 1(1/2)-D spectrum not only has the properties ofhigher-order spectrum, but also is very simple in computation,therefore, we use the 1(1/2)-D spectrum as the signalprocessing tool in this paper.

A. Disturbing Voltage and Disturbing Current

There are a lot of disturbing sources that influence themeasuring accuracy because there is the influence of environ-mental factors and complicated electric potential distributionbeneath the ground. They are mainly electromagnetic dis-turbance above the ground and working frequency currentor direct current disturbance beneath the ground. Besidesthese, there is a lot of disturbing sources beneath the ground.Such as leakage current disturbance, natural electric fieldsdisturbances, excited pole strength disturbance, and so on.According to the analysis and experiment by other researchers,the influence of each disturbing source can be considered asGaussian distribution disturbance and harmonic distributiondisturbance [7], [8].

B. Signal Source Choice

According to the analysis of paragraph (1), we know thatthe disturbance has a Gaussian distribution and harmonicdisturbance. In order to restrain Gaussian noise and harmonicdisturbance by using higher-order spectrum, we select a non-Gaussian signal as the power source.

C. Higher Order Spectrum-Based Method

From (8) and (9), the observed voltage and current magni-tudes, respectively, are

(18)

(19)

MAOTANG AND JING: NEW TYPE OF GROUNDING RESISTANCE MEASUREMENT 901

where and are the voltage drop and the currentof the non-Gaussian signal between the grounding resis-tance , respectively, i.e., . is Gaussiandistribution voltage disturbance, is harmonic voltagedistribution. is Gaussian distribution current disturbanceand is harmonic current disturbance.

The 1-D diagonal slice of the third-order cumulant ofand , respectively, are

(20)

(21)

Because , , and are independent of eachother, , , and are also independent of each other,so

(22)

(23)

and are of Gaussian distribution, soand . If there is no any quadratic phase couplingbetween harmonics, then and . So

(24)

(25)

Because , we can get

(26)

So

(27)

We have

(28)

then

(29)

or

(30)

IV. COMPUTER SIMULATIONS

The measurement of grounding resistance by powerspectrum-based and higher order spectrum-based approachesare simulated. Independent exponentially distributed randomdata were generated for the non-Gaussian signal power sourcefrom the GGEXN subroutine in the International Mathematicaland Statistical Library (IMSL) [9].

TABLE IMAGNITUDES OF GROUNDING RESISTANCE

TABLE IIMEASURED VALUES AND RELATIVE ERRORS

TABLE IIIMEASURED VALUES AND RELATIVE ERRORS BY USING THE TWO METHODS

Example 1: Suppose the observed voltage and current are

respectively, where and are with non-Gaussiandistribution, and . andare white Gaussian noise and independent of each other.We define SNR , SNR

.In the simulations, we choose the data number

and , respectively, and SNR dB, SNR dB.Table I shows the magnitudes of grounding resistance

by using the power spectrum-based method and the higherorder spectrum-based method when , and Table IIshows the measured values and relative errors by using thetwo methods , respectively.

Example 2: and are similar to Example 1,however, and are colored Gaussian noise. Theywere generated by passing white Gaussian noise through theMA (2) filter [1, 2, 1]. We choose , and SNRdB, SNR dB. Table III shows the measured values andrelative errors by using the two methods.

From these simulations, we can conclude that the higherorder spectrum-based method is insensitive to Gaussian (whiteor colored) noise, however, that the power spectrum basedmethod is much more sensitive to Gaussian noises.

V. EXPERIMENTAL RESULTS

A grounding resistance measuring instrument controlled bya microcomputer has been developed. The principle drawingof the instrument is shown in Figs. 3 and 4.

The methods for third order cumulants including the 1-Ddiagonal slices of the third order cumulants and for dispectraincluding the 1(1/2)-D spectra are used in the groundingresistance measurement. Because we do not know the exact

902 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 48, NO. 5, OCTOBER 1999

Fig. 3. Higher-order spectra measuring method.

Fig. 4. The chart of the instrument.

grounding resistance in the field, the experiment is performedin the laboratory with a resistor of . The precisionof the resistance is . The Gaussian distributioncurrent , is given by a Gaussian white noisegenerator. The harmonic current , is produced by analternating constant power source generator and its frequencyis 50 Hz.

The non-Gaussian signal is produced by thefollowing method: A group of non-Gaussian data is producedfrom the GGEXN Subroutine in the International Mathemat-ical and Statistical Library (IMSL). The non-Gaussian signalpower source is obtained by converting the group of non-Gaussian data by the high-speed D/A.

Table IV shows the measured values by third order cumu-lants and bispectra methods when . Compared withother methods [1], the two methods by third-order cumulantsand by bispectra can get more precise results.

VI. CONCLUSIONS

We propose a new method to measure the grounding re-sistance in electric power systems. The new method uses

TABLE IVRESULTS OF FOUR MEASURING METHODS (N = 2048)

higher-order spectrum as the signal-processing tool, therefore,it can eliminate the effect of Gaussian noise and harmonicdisturbance current and reduce the error.

A lot of simulation and experiment results show that thisnew method is very useful. How to use this method to designthe new equipment to be used in the field should be copedwith in the future.

REFERENCES

[1] IEEE Guide for Measuring Earth Resistivity, Ground Impedance, andEarth Surface Potentials of a Ground System, IEEE Standard 81, 1983.

[2] P. R. Pillai and E. P. Dick, “A review on testing and evaluatingsubstation grounding systems,”Trans. Power Delivery,vol. 7, no. 1,1992.

[3] C. L. Nikias and M. R. Raghuveer, “Bispectrum estimation: A digitalsignal processing framework,”Proc. IEEE,vol. 75, pp. 869–891, July1987.

[4] G. B. Giannakis, “Cumulants: A powerful tool in signal processing,”Proc. IEEE,vol. 75, pp. 1333–1334, 1987.

[5] A. Swami and J. M. Mendel, “Cumulant-based approach to harmonicretrieval and related problems,”IEEE Trans. Signal Processing,vol. 39,no. 5, pp. 1099–1109, 1991.

[6] J. M. Mendel, “Tutorial on higher-order statistics (spectra) in signalprocessing and system theory: Theoretical results and some application,”Proc. IEEE,vol. 19, pp. 278–305, Mar. 1991.

[7] IEEE Guide for Safety in Substation Grounding, IEEE Standard 80, 1976.[8] Disturbances in Supply Systems Caused by Household Appliances and

Similar Electrical Equipment, Part 2: Harmonics, IEC Standard 555-2,1982.

[9] C. L. Nikias and R. Pan, “Time delay estimation in unknown Gauss-ian spatially correlated noise,”IEEE Trans. Acoust., Speech, SignalProcessing,vol. 36, pp. 1706–1714, Nov. 1988.

Li Maotang was born in China on July 26, 1951. Hereceived the Ph.D. degree in electronic engineeringfrom the Industrial and Technical Engineering Uni-versity of Jilin, Jilin, China, in 1994.

Since 1982, he has been working on instrumentdesign, measurement method research, and data pro-cessing. His major work is in measurement methods,microwave remote sensing, and data processing. Hehas completed seven scientific research projects,applied for four patents, and published more than40 papers since 1987.

Li Jing was born in China on May 5, 1967. He received the B.S. degreein electronics from Jilin University, Jilin, China, the M.S. degree fromChangchun Institute of Geography, Chinese Academy of Sciences (CAS),and the Ph.D. degree from Electronics Institute, CAS, in 1990, 1994, 1997,respectively.

He has been with the Center for Space Science and Applied Research,CAS, since 1997. His research is on the design of microwave radiometers,electromagnetic transmission, and reflection in typical objects. He has twopatents and has published more than 20 papers since 1991.