Electrical Power and Energy Systems 55 (2014) 760–769

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

A new method for non-unit protection of power transmission lines basedon fault resistance and fault angle reduction

0142-0615/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijepes.2013.10.027

⇑ Corresponding author. Address: College of Electrical & Information Engineeringof Hunan University, Changsha 410082, Hunan Province, China.

E-mail address: gzwcbf@sina.com (Z. Guo).

Zhenwei Guo a,b,⇑, Jiangang Yao a, Shengjie Yang a, Hong Zhang c, Tian Mao a, Thanh Long Duong a

a College of Electrical & Information Engineering of Hunan University, Changsha, Chinab Department of Electrical Engineering of Shaoyang University, Shaoyang, Chinac College of Electrical Engineering of Southeast University, Nanjing, China

a r t i c l e i n f o

Article history:Received 27 December 2012Received in revised form 11 October 2013Accepted 14 October 2013

Keywords:Non-unit transient protection methodEnergy difference of high-frequencytransient currentTransition resistanceFault angleSingle-phase faultPower transmission lines

a b s t r a c t

In the paper, a new non-unit transient protection method suitable for single-phase faults of EHV powertransmission lines was proposed based on the analysis of the propagation characteristics induced by faulttransient current, the transition resistance and the fault angle on corresponding energy values of high-frequency transient current in extra high voltage (EHV) network. In the procedure, the transient currentenergy values from both sides of the bus were primarily normalized on the basis of transition resistanceand fault angle, and then the characteristic value with functions of direction judge and value comparisonwas obtained by calculating their difference. By utilizing the characteristic value, the methodology cameinto being, by which the impacts of both transition resistance and fault angle were eliminated. The overalldesign has a high reliability level and owns twice the scope of the conventional protection. Simulationswere performed and analyzed upon a three-phase 500 kV power system by utilizing ATP/EMTP, with var-ious kinds of typical faults being taken into account. Plenty of results verify the feasibility of the algo-rithm for ultra-high speed protection of EHV power transmission lines.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Grounding faults in transmission lines result in a large numberof high-frequency transient signals. Transient protection methodsin terms of these fault signals have the property of ultra high speedmovement immuned from affections of current transformer satu-rations, electric power system oscillations, operation mode varia-tions, etc. [1], thus can satisfy the protection developmentdemands of modern power system EHV transmission lines. In re-cent years, researches towards transient protection have beenwidely performed and studied [1–26]. Theoretically, transient pro-tection can be divided into the channel transient protection andnon-channel transient protection. The latter can not only save highinvestment for the construction of communication channels butalso avoid unreliability caused by them for it only requires thetransient information from the local end of the transmission lines,such method has been extensively studied ever since it was pro-posed [2]. The most typical way is to construct protection criterionbased on different high-band energy ratios of single-end signals[2]. A new type of border protection was proposed in literatures[13–15], by which the value of fault features becomes more obvi-ous, however, the expense would hugely increase since the current

existing wave trappers in the power system need to be reformed orreplaced.

Meanwhile, most traditional non-unit transient protectionmethods put emphasis on utilizing signal processing methods intothe protection [3–8], such as wavelet analysis, artificial neural net-works, and mathematical morphology, or on exploring improvedsignal processing methods [6,15,16,19,24,25], e.g., the literature[14] came up with a method by combining the wavelet transfor-mation with neural network, Ref. [23] uses the fourth sequentialoverlapping derivative of the positive sequence quantities of bothcurrent and voltage signals extracts transient components at bothline terminals, but all these did not dissolved the impact of faultresistance and fault angle on the protection. However, among thesemethods, there are no real breakthroughs towards the basic princi-ple of transient protection. In addition, due to serious deficiency ofneglecting the impacts of the transition resistance and fault angle[1–20], the protection reliability of traditional methods is not thathigh and their performance are not stable enough, which becomesthe main reason limiting their wide usage. Studies of [16,17] havecertified that the traditional unit transient protection is not able toprotect the overall line.

Moreover, 70–90% of the line faults occurring within EHV trans-mission lines are transitional, most of which are single-phaseground faults. Therefore, correct evaluation of such fault is of greatsignificance to maintain the stability of the EHV system [22].

Z. Guo et al. / Electrical Power and Energy Systems 55 (2014) 760–769 761

This paper is organized as follows: Section 2 analyzes the prop-agation characteristics of high-frequency transient current causedby single-phase ground faults; Section 3 introduces the principleof the proposed method in detail; Section 4 presents the amountsof simulations based upon an experimental power system undervarious kinds of faults to certify the feasibility of the methodologyby utilizing ATP/EMTP, thereafter the configuration problem of theprotection is discussed in Section 5, and finally a conclusion isgiven.

2. Analysis of propagation characteristics of transienthigh-frequency current

When a single-phase fault happens in a transmission line, bothtransition resistance and initial fault angle have big impact on theintensity of the massive emerging transient signals. The high fre-quency transient signal will decay substantially when the transientcurrent signal reaches the target bus, with reflection as well asrefraction occurring at the same time. In a real deployed powersystem, the refraction transient current of the overhead lines con-nected to a common bus are approximately equal since their waveimpedances are basically the same.

Take the 500 kV EHV bus system displayed in Fig. 1 as an exam-ple, the transmission lines Z, Z1, Z2 and Z3 are linked to the bus A,and their wave impedances are designated to be Z, Z1, Z2 and Z3

respectively. The total distributed capacitance of the bus A andits relevant electrical devices connected is equivalent to the valueC. When a ground fault occurs in one of the lines, such as the line Z,the transient high-frequency voltage u01 and the transient high-fre-quency current i01 generated will transmit along the path Z to thebus A, with both refraction and reflection coexisting. The u01 willproject onto the bus A with the same value of the voltage refractionwave u02 for all branches connected to the same node, while thecurrent refraction waves of each line, i.e., i0z1, i0z2, i0z3 and i0zc , aredifferent.

The sum of their values is expressed as (i01 þ i001), namely:

i01 þ i001 ¼ i0z1 þ i0z2 þ i0z3 þ i0zC ð1Þ

i0Zn¼ u02

Znn ¼ 1;2;3;C ð2Þ

The equally distributed capacitance C would exert a bypass ef-fect with a tiny small impedance ZC emerged for the high frequencyfault current, and massive transient high-frequency currents willpass through the capacitance into the ground with the principlethat the higher the frequency, the more into the earth. Therefore,the transient currents i0z1; i0z2, i0z3 detected at the starting ends of

Fig. 1. Demonstration of transient current propagation characteristics.

the lines Z1, Z2, Z3 are much smaller compared to (i01 þ i001). In a prac-tical EHV transmission system, the wave impedances of lines con-nected to the common bus are approximately equal since theirwire types are essentially the same (e.g., the value of the waveimpedance for commonly 4-bundled conductors utilized in500 kV overhead lines ranges from 255 X to 265 X). From the for-mula (2), it is easy to learn that i0z1, i0z2 and i0z3 are approximatelyequivalent.

Similarly, when a ground fault occurs in a bus or any other con-nected electrical devices, the detected transient high-frequencycurrents, namely, i001, i0z1, i0z2, i0z3 of the lines Z, Z1, Z2, Z3, are approx-imately equal as well.

3. Adaptive non-unit transient current protection forsingle-phase faults of transmission lines based on transitionresistance and fault angle reduction

Fig. 2 displays our experimental multi-segmented system ofEHV transmission lines. The proposed protection is installed inthe bus C-terminal with the target lines BC and CD, of which theline BC locates in the forward protected area while the line CDlocates in the reverse protected area, being protected.

3.1. Calculation of the transition resistance

To calculate the transition resistance for a single-phase (sup-pose the A phase) ground short circuit happening in the locateF1, we define the following parameters [20]:

Rf is the transition resistance; Zf is the measured impedance atthe installation site; _If is the short-circuit current of the fault point;_Ig1, _Ig2 are the phase currents of the power transmission side(B-side) and the power receiving side (C-side) of the line BCrespectively.

The total power consumed by the fault resistance in the faultpoint is equal to that of the A-phase, i.e., the relationship of follow-ing equation exists:

Pa þ jQ a ¼ Zf ð_Ig1 þ _Ig2ÞðIg1 þ Ig2Þ ð3Þ

In the formula Ig1 and Ig2 stand for the conjugate vectors of _Ig1, _Ig2,while Pa and Qa represent the active and reactive power of phaseA supplying for the transition resistance by the power sources fromboth sides.

Assume that the load is purely inductive, then the followingproportional relationship between the total power eS0 of the powertransmission side and eS00 of the power receiving side can bededuced:

eS 0 ¼ keS 00 ð4Þ

In the formula k is the power distribution coefficient of the receiv-ing side to the transmission side.

Therefore, the proportional relationship between the power ofthe short-circuit point supplied by the transmission side and thereceiving side can be obtained:

P00 þ jQ 00 ¼ kðP0 þ jQ 0Þ ð5Þ

Equally, the currents of the short-circuit point from both sideshave the following relationships:

_Ig2 ¼ k_Igl ð6Þ

Ig2 ¼ kIgl ð7Þ

Based on the formula (5), the total power of the short-circuitpoint can be written as:

Fig. 2. Schematic diagram of the self-adaptive non-unit transient current protection.

762 Z. Guo et al. / Electrical Power and Energy Systems 55 (2014) 760–769

Pa þ jQ a ¼ P00a þ jQ 00a þ P00a þ jQ 00a ¼ ð1þ kÞðP0a þ jQ 0aÞ ð8Þ

Based on the formulas (6) and (7), the formula (3) can be ex-pressed as:

Pa þ jQ a ¼ Zf ð1þ kÞ2I2g1 ð9Þ

By utilizing the formulas (8) and (9), the real part of the faultimpedance below can be got:

Rf ¼P0a

ð1þ kÞI2g1

ð10Þ

In the above formula P0a represents the monitored active power ofthe short circuit point supplied by the transmission side at theinstallation site of the protection.

3.2. Calculation of the fault angle

First, let us define the following parameters:Tf is the happening time of the failure; fu is the voltage fre-

quency; Tk is the nearest zero-cross moment, at which the voltagetransfers from negative to positive, to Tf, hu are the voltage phaseangle at the installation site which can be formulate as the follow-ing cosine function model.

A voltage cycle Tu = 1/fu is equivalent to 360�, and the period offaulty for the voltage changing from negative to positive zero isequivalent to Dh.

Dh ¼ 360 � ðTf � TkÞ=Tu ¼ 360 � fu � ðTf � TkÞ ð11Þ

Voltage can be formulated with cosine function model. In onefull cycle, the corresponding angle for voltage from negative to po-sitive is 270�. So, the transient angle of the voltage at protectioninstallation time can be expressed as:

hu ¼ Dhþ 270 ¼ 360 � fu � ðTf � TkÞ þ 270 ð12Þ

The phase voltages and currents can be considered as a combi-nation of three modulus components, i.e., 0, a and b, of which thelatter two waveforms transmit at the speed of light, while theformer has a lower speed (for most overhead lines, the speed isabout 70% of light) [21]. Based on the differential value between

the arrival time to the installation of waveform 0 and the wave-form a (or, b), the failure initial phase angle can be calculatedaccording to the measured voltage phase angle. Assuming thereaching moments of component phase currents a and 0 to theinstallation are Ta and T0 respectively, the fault angle hf can be de-duced by the following formulas:

T0 � Ts ¼Lv0¼ L

0:7v ð13Þ

Ta � Ts ¼Lva¼ L

v ð14Þ

Using Eqs. (13) and (14), we then arrive at

T0 � Ta ¼L

0:7v �Lv ¼

0:30:7� L

v ð15Þ

Using Eq. (15), we get

Dt ¼ Lv ¼

0:30:7� ðT0 � TaÞ ð16Þ

The fault angle hf expressed in degrees is thus given by

hf ¼ hu þDtTu� 360 ¼ hu þ

0:70:3� T0 � Ta

Tu� 360 ð17Þ

where Tu = 0.02 s, when fu = 50 Hz.

3.3. The principle of the proposed protection

In Fig. 2, the detected fault currents of CT1 and CT2 of both sidesfor the bus C are expressed as I1f and I2f; the corresponding high-frequency components are I1hf and I2hf, respectively. P_I1hf, P_I2hf

are values of active power calculated from I1hf, I2hf, on the basisof the following formula:

P I1hf ¼Xn

j¼1

I21hfj

P I2hf ¼Xn

j¼1

I22hfj

8>>>><>>>>:

; ðn is designated as 200Þ ð18Þ

Z. Guo et al. / Electrical Power and Energy Systems 55 (2014) 760–769 763

When a single-phase ground fault happens in transmissionlines, both transition resistance and fault angle have great influ-ence on the values of P_I1hf and P_I2hf. Therefore, direct utilizationof P_I1hf and P_I2hf for constructing the protection criterion willinevitably reduce the protection reliability, which may lead tounwarranted trips or failures. In our process, in order to eliminatethe impacts of different transition resistance and fault angle, P_I1hf

and P_I2hf were normalized based on the transition resistance andfault angle as CP_I1hf, CP_I2hf, which were then used to build theprotection criterions. Related formulas are:

CP I1hf ¼1c� P I1hf ð19Þ

CP I2hf ¼1c� P I2hf ð20Þ

In which c represents the conversion coefficient, defined by thefollowing formula:

c ¼ ð1þ cosða � hf þ h0ÞÞ � ðeb�Rf þ c � ed�Rf Þ ð21Þ

In the formula (21), a, b, c, d, h0 are five constants, Rf and hf stand forthe values of the transition resistance and fault angle respectively.

Based on the formula (22), we define the characteristic valuediffCP_I1hfI2hf, which were used to judge the fault area.

diffCP I1hf I2hf ¼ CP I1hf � CP I2hf ð22Þ

In Fig. 2, the protection proposed is installed in the terminal of Cbus. For the convenience of description, we define the protectionset diffCP. At the same time, we designate the line BC to be the for-ward protected area, while the line CD to be the reverse protectionarea.

Based on the analysis of Section 2, when a single-phase groundfault occurs within the forward protected area, take the point F1 asan example, the energy value of high frequency fault componentdetected near to the fault detect side is much greater than thatof the location faraway, due to the bypass effect of the equivalentdistributed capacitance C. That is to say, the inequality P_I1hf > P_I2h

exists and the value of diffCP_I1hfI2h is a great positive value. As forsingle-phase ground faults happening outside the forward pro-tected areas, the inequalities occurs as well, while the value of diff-CP_I1hfI2hf is small. Accordingly, we can distinguish whether thefault takes place inside or outside the forward protected area.

Likewise, when a single-phase ground fault occurs within thereverse protected area BC (such as in the point F3), the inequalitiesP_I1hf < P_I2hf and diffCP_I1hfI2hf < 0 are true and the absolute valueof diffCP_I1hfI2hf is great, whereas for the same kind of fault in the

0 2000 4000 6000 8000 10000

0

2

4

6

8x 104

samples

diffC

P__I

1hfI2

hf

(a) l1 mk1=

Fig. 3. Faults in the forward pro

area DE outside the reverse protected area, e.g., F4 point, the fol-lowing inequalities exist: P_I1hf < P_I2hf and diffCP_I1hfI2hf < 0, whilethe absolute value of diffCP_I1hfI2hf is small. Thus, we can judgefaults within or out of the reverse protected area.

Further, when a single-phase ground fault occurs in the lineCG or bus C, the traveling waves will arrive in CT1, CT2 simulta-neously at the first time, while the difference between I1hf andI2hf is small. Hence the absolute value of diffCP_I1hfI2hf is also smallat the beginning. Thereafter, the traveling wave I1hf will transmitto the B end along the line CB, and its majority portion will be by-passed by the distributed capacitance of the bus B, with refractionand reflection coexisting. The I001hf reflected will reach to CT1. Sim-ilarly, when I2hf reaches to the D end along the line CD, it will alsobe bypassed to a large extent by the distributed capacitance ofthe related bus, with the reflected proportion I002hf arriving inCT2. Due to different lengths of the lines, the arriving momentsof I001hf and I002hf to CT1 and CT2 are also different, with the valuesattenuating a lot. Thus the value of diffCP_I1hfI2hf will appear tobe a small magnitude with positive and negative values changingalternately.

As discussed in above section, based on the value of diffCP_I1hf-

I2hf, the failures happen inside the forward protected area BC, thereverse protected area CD and outside the protected area can becorrectively evaluated. Through this way, the ground fault protec-tion of both two lines BC and CD will be achieved by employingonly one installation.

3.4. Extraction of fault characteristic value

According to Section 2, the higher the frequency, the more thetransient current will be bypassed off by the distributed capaci-tance of the bus, and the more the difference of diffCP_I1hfI2hf be-tween failures inside and outside the protected area. However,the detection will become difficult if the frequency is too high sincethe high-band components will become extremely limited. There-fore, it is necessary to select the appropriate frequency band of thetransient signal in order to extract the fault characteristics value.Through intensive simulation studies, we found that it is suitableto choose the transient current signals between 50 kHz and100 kHz. Therefore, in our studies, we selected the sampling fre-quency to be 200 kHz, and designed a band-pass filter with a band-width of 50–100 kHz, to extract the high frequency component ofthe fault current. The filter transfer function is given by formula(23), and the coefficients are given by Appendix A. The fault char-acteristic variable diffCP_I1hfI2hf was finally calculated out by theformula (22).

HðzÞ ¼XN

n¼0

h½n�z�n ðN ¼ 238Þ ð23Þ

0 2000 4000 6000 8000 100000

2

4

6

8x 104

samples

diffC

P__I

1hfI2

hf

)b( l1 = 341km

tected area, Rf = 1 X, hf = 0�.

0 2000 4000 6000 8000 100000

1

2

3x 104

samples

diffC

P__I

1hfI2

hf

Fig. 4. Fault in the bus B, Rf = 1 X, hf = 0�.

Table 2The values of diffCP_I1hfI2hf for failures occurring in the bus B with different conditions.

hf (�) R (X)

1 50 150 260 300

0 24,980 21,510 16,900 11,730 14,26045 25,860 22,260 17,490 15,100 14,76085 28,530 25,060 22,410 19,350 18,92090 27,930 24,510 21,970 18,970 18,550

764 Z. Guo et al. / Electrical Power and Energy Systems 55 (2014) 760–769

4. Simulation cases studies

4.1. Introduction of research system

The model of the multi-segmented EHV transmission systemshown in Fig. 2 was taken from the 500 kV Pingwu line of the NorthChina Power Grid. The lengths of lines AB, BC, CD, DE and CG are180 km, 342 km, 360 km, 266 km and 270 km respectively. Otherparameters include: values of the apparent power: fu = 50 Hz,S1 = 35 MVA, S2 = 10 MVA, S3 = 20 MVA, S4 = 5 MVA, S5 = 12 MVA;parameters of the transmission line: X1 = 0.2783 X/km,R1 = 0.0270 X/km, X0 = 0.6494 X/km, R0 = 0.1948 X/km,C1 = 0.0127lF/km, C0 = 0.0090 lF/km; and the parallel equivalentdistributed capacitance of each end for the bus is designated tobe 0.01 lF [17]. Relevant parameters in the formula (21) are:a = 0.03472, b = �0.0184, c = 0.8953, d = �0.004568, h0 = �0.0164�.

4.2. Simulation and analysis of typical failures

In our research, we studied the A-phase ground faults occurringat the F1 point of BC within the forward protected area, the F2 pointof AB outside the forward protected area, the F3 point of CD withinthe reverse protected area, the F4 point of DE outside the reverseprotected area, the F5 point of the bus C, the F6 point within the lineCG, the F7 point of the bus B, and the F8 point of the bus D. Variouskinds of fault angle and transition resistance between 0 and 300 Xconsidered have been simulated in this study. We also simulatedother cases with hf between 180–360� (similar to situations for hf

designated to be 180–0�). To save the space, we only discuss somecases of the entire data.

(1) Failure within the forward protected area

The fault characteristic value of diffCP_I1hfI2hf, when a fault oc-curs in the F1 point of BC which is 1 km (mark as l1) away fromthe C end, is displayed in Fig. 3(a), with a transition resistance of1 X and a fault angle of 0�; while the diffCP_I1hfI2hf of which the dis-tance changes to be 341 km is presented in Fig. 3(b).

The maximum values of diffCP_I1hfI2hf for faults occurring at thepoint F1 with different fault angles and different transition resis-tances can be seen in Table 1. According to the data, the valuesof diffCP_I1hfI2hf are much greater than 60,000 for faults withinthe forward protected area.

(2) Failures in the bus B

Fig. 4 shows the value of diffCP_I1hfI2hf when an A-phase fault oc-curs in the F7 point of the bus, with a transition resistance of 1 Xand a fault angle of 0�.

Table 1The values of diffCP_I1hfI2hf for failures occurring in the forward protected area withdifferent conditions.

hf (�) R (X)

1 50 150 260 300

(a) l1 = 1 km0 65,360 64,520 63,650 63,240 64,060

45 65,830 64,990 64,110 63,700 64,52085 66,140 65,290 64,410 64,000 64,82090 66,300 65,580 64,820 64,470 65,170

(b) l1 = 341 km0 73,370 73,300 73,280 73,360 74,440

45 75,950 75,880 75,860 75,940 77,06085 86,630 86,430 86,280 86,310 87,57090 88,860 88,810 88,800 88,850 89,580

The maximum values of diffCP_I1hfI2hf for faults occurring in thebus with different fault angles and different transition resistancesare showed in Table 2. As presented, the characteristic value satis-fies 10,000 < diffCP_I1hfI2hf < 30,000.

(3) Failures outside the forward protected area

The results of diffCP_I1hfI2hf for faults occurring in the F2 point ofAB which is 1 km (mark the distance as l2) and 179 km away fromthe B end can be seen in Fig. 5(a and b), respectively.

The maximum values of diffCP_I1hfI2hf for faults occurring in thepoint F2 with different fault angles and different transition resis-tances can be seen in Table 3.

As can be seen, the fault characteristic value for failures outsidethe forward protected area satisfies 3000 < diffCP_I1hfI2hf < 10,000.

(4) Failures within the reverse protected area

The results of diffCP_I1hfI2hf for faults occurring in the F3 point ofCD which is 1 km (mark the distance as l3) and 359 km away fromthe C end can be seen in Fig. 6(a and b), respectively.

The maximum values of diffCP_I1hfI2hf for faults occurring in thepoint F3 with different fault angles and different transition resis-tances can be seen in Table 4. As can be seen, the values of diff-CP_I1hfI2hf for such failures inside the reverse protected area aremuch smaller than �60,000.

(5) Failures in the bus D

The value of diffCP_I1hfI2hf when an A-phase fault occurs in the F8

point of the bus D is demonstrated in Fig. 7, with a transition resis-tance of 1 X and a fault angle of 0�.

The maximum values of diffCP_I1hfI2hf for faults occurring in thebus D with different fault angles and different transition resis-tances are displayed in Table 5. As presented, the characteristic va-lue satisfies �60,000 < diffCP_I1hfI2hf < �10,000.

(6) Failures outside the reverse protected area

The results of diffCP_I1hfI2hf for faults occurring in the F4 point ofDE which is 1 km (mark the distance as l4) and 265 km away fromthe D end can be seen in Fig. 8(a and b), respectively.

0 2000 4000 6000 8000 10000

0

1000

2000

3000

4000

samples

diffC

P__I

1hfI2

hf

0 2000 4000 6000 8000 100000

2000

4000

6000

8000

samples

diffC

P__I

1hfI2

hf

(a) l2 mk1= )b( l2 = 179km

Fig. 5. Faults outside the forward protected area, Rf = 1 X, hf = 0�.

Table 3The values of diffCP_I1hfI2hf for failures occurring outside the forward protected area,with different conditions.

hf (�) R (X)

1 50 150 260 300

(a) l2 = 1 km0 3932 3952 3973 3980 4049

45 4070 4091 4111 4128 419285 4414 4435 4457 4472 454190 4510 4531 4554 4569 4639

(b) l2 = 179 km0 6342 6583 6863 7036 7182

45 6885 6834 7126 7305 745785 8641 8969 9351 9587 978690 8071 8378 8736 8956 9143

Table 4The values of diffCP_I1hfI2hf for failures occurring in the reverse protected area, withdifferent conditions.

hf (�) R ( X)

1 50 150 260 300

(a) l3 = 1 km0 �65,370 �64,550 �63,690 �63,290 �64,110

45 �65,850 �65,020 �64,160 �63,750 �64,57085 �66,190 �65,360 �64,490 �64,080 �64,91090 �62,100 �61,270 �61,200 �61,050 �62,260

(b) l3 = 359 km0 �119,000 �118,000 �117,100 �116,600 �118,200

45 �124,900 �123,900 �122,800 �122,400 �124,10085 �178,700 �177,200 �175,700 �175,100 �177,50090 �204,600 �202,900 �200,200 �200,500 �203,200

0 2000 4000 6000 8000 10000-4

-3

-2

-1

0x 10

4

samples

diffC

P__I

1hfI2

hf

Fig. 7. Fault in the bus D, Rf = 1 X, hf = 0�.

Z. Guo et al. / Electrical Power and Energy Systems 55 (2014) 760–769 765

The maximum values of diffCP_I1hfI2hf for faults occurring in thepoint F4 with different fault angles and different transition resis-tances can be seen in Table 6.

As shown, the fault characteristic values for failures outside thereverse protected area satisfy �20,000 < diffCP_I1hfI2hf < �3000.

(7) Failures in the bus C

The values of diffCP_I1hfI2hf, P_I1hf and P_I2hf when a single-phasefault occurs in the F5 point of the bus C is demonstrated inFig. 9.

According to the figure, the first peaks of P_I1hf and P_I2hf, whichare approximately the same closing to 60,0000, occur simulta-neously. Hence, the value of the first peak for diffCP_I1hfI2hf is small(less than 40). The peaks of P_I1hf and P_I2hf thereafter appear at dif-ferent moments with greatly reduced magnitude, leading to bothpositive and negative values for diffCP_I1hfI2hf with a range between�6000 and 2000.

0 2000 4000 6000 8000 10000-8

-6

-4

-2

0

x 104

samples

diffC

P__I

1hfI2

hf

(a) l3 mk1=

Fig. 6. Faults inside the reverse pr

(8) Failures in the line CG

The results of diffCP_I1hfI2hf for faults occurring in the F5 point ofCG which is 1 km (mark the distance as l5) and 269 km away fromthe D end can be seen in Fig. 10(a and b), respectively.

0 2000 4000 6000 8000 10000-15

-10

-5

0

x 104

samples

diffC

P__I

1hfI2

hf

)b( l3 = 359km

otected area, Rf = 1 X, hf = 0�.

Table 5The values of diffCP_I1hfI2hf for failures occurring in the bus D with differentconditions.

hf (�) R (X)

1 50 150 260 300

0 �39,560 �28,530 �18,090 �14,100 �13,48045 �41,530 �29,940 �18,990 �14,800 �14,15085 �49,420 �42,850 �27,180 �21,180 �20,25090 �57,930 �48,980 �31,060 �24,210 �23,140

0 2000 4000 6000 8000 10000-4000

-3000

-2000

-1000

0

samples

diffC

P__I

1hfI2

hf

(a) l4 mk1=

Fig. 8. Faults outside the reverse p

Table 6The values of diffCP_I1hfI2hf for failures occurring outside the reverse protected areawith different conditions.

hf (�) R (X)

1 50 150 260 300

(a) l4 = 1 km0 �3222 �3212 �3197 �3190 �3234

45 �3382 �3371 �3344 �3348 �339485 �4841 �4826 �4805 �4794 �486090 �5544 �5527 �5503 �5490 �5567

(b) l4 = 265 km0 �6741 �6996 �7295 �7479 �7635

45 �7128 �7398 �7713 �7908 �807385 �10,800 �11,210 �11,680 �11,980 �12,23090 �14,870 �15,430 �16,090 �16,490 �16,840

Fig. 9. Faults in the bus

766 Z. Guo et al. / Electrical Power and Energy Systems 55 (2014) 760–769

As shown, the situations for such failures are similar to the fail-ures in the bus C, while the value of the first peak of diffCP_I1hfI2hf istiny small, which is less than 40. The value of diffCP_I1hfI2hf variesfrom �600 to 300.

4.3. Establishment of the criterions

Base on the above simulation results, the fault characteristic va-lue diffCP_I1hfI2hf has the following features: diffCP_I1hfI2hf > 60,000when failures occur inside the forward protected area; 3000 < diff-CP_I1hfI2hf < 10,000 when failures occur outside the forward pro-tected area; diffCP_I1hfI2hf < �60,000 when failures occur insidethe reverse protected area; �20,000 < diffCP_I1hfI2hf < �3000 whenfailures occur outside the reverse protected area. It is obvious thatthe differences among all these kinds of faults vary greatlydifferent.

Hence, the criterions for the protection installation can be set tobe:

(1) When diffCP_I1hfI2hf > 60,000, the faults happen in the for-ward protected area.

(2) When diffCP_I1hfI2hf < -60,000, the faults happen in thereverse protected area.

(3) Under other cases, there are no faults within the protectedarea.

0 2000 4000 6000 8000 10000-8000

-6000

-4000

-2000

0

samples

diffC

P__I

1hfI2

hf

)b( l4 = 265km

rotected area, Rf = 1 X, hf = 0�.

C, Rf = 1 X, hf = 0�.

Fig. 10. Faults in the line CG, Rf = 1 X, hf = 0�.

Z. Guo et al. / Electrical Power and Energy Systems 55 (2014) 760–769 767

5. Discussions of the protection configuration

Through the analysis above, it is clear that one diffCP set is capa-ble of protecting two outlines connecting to a certain bus reliably,hereby, only [n/2 + 1] sets are required for n outlines of a specifiedbus, which could substantially reduce the cost on installations ofthe transmission protection.

On the other hand, if all branches are equipped with the pro-posed protection and the combination of the protected circuit linesfor each set is reasonably arranged, then every single line will beunder the protection of two devices with different input signals.In this way, the dual protection that can greatly enhance the reli-ability will be achieved under the premise of no additional funds.For instance, if all the three outlets BC, CD and CG of the bus C inFig. 2 were deployed with our proposed protection installation,and their input signals were obtained separately from I1hf/I2hf of

CT1/CT2, I2hf/I3hf of CT2/CT3, and I3hf/I1hf of CT3/CT1, then all the threelines will be dual protected under normal conditions. Further,when a failure occurs in any of the three protection installations,every single line is still under normal and effective protection ofat least one set; or when any one of the three lines withdraws fromits service, the other two lines are still effectively protected by atleast one protection set.

6. Conclusion

Depending on the transient current energy values normalizedon the basis of transition resistance and fault angle, a new non-unittransient protection scheme appropriate for EHV transmissionlines has been proposed, with a large amount of simulations beingperformed to certify its validity. Theory analysis together withplentiful results shows that, the solution overcomes the deficiency

768 Z. Guo et al. / Electrical Power and Energy Systems 55 (2014) 760–769

induced by transition resistance and fault angle effectively. Spe-cially, One set of such protection equipment is capable to protecttwo outlines of a single specified bus, hereby, n outlines of a certainbus only require [n/2 + 1] sets to meet the demand of protection.Besides, if the methodology is employed similar to traditionaldeployments, the dual protection can be achieved under the pre-mise of no additional investment, while the protected area is twicethat of the conventional means, and from this point of view, thereliability can be largely promoted. What is more, since the charac-teristic values of faults happen inside and outside the protectedarea vary apparently different, the mechanism can effectivelyavoid any miscarriage of judge and make the protection easy tun-ing with high protect sensitivity. The new method has solved theshortcoming of traditional non-unit transient protection methodsthat they are unable to protect the entire line, which is the mostunique advantage of this scheme. The high feasibility, reliabilityand accuracy of the new protection principle have been verifiedby utilizing ATP/EMTP software.

Although the method was proposed for single-phase fault, theproposed protection principle also has implications for other faulttypes of transmission lines.

Appendix A

h[n] = [0.00000000007340, 0.00000000030078,�0.00000000099383, �0.00000000249390, 0.00000000416421,0.00000000530162, �0.00000000460092, �0.00000000063332,�0.00000000481609, �0.00000000976980, 0.00000001119742,0.00000000577796, 0.00000000284924, 0.00000001065039,�0.00000001200053, �0.00000000073448, �0.00000001690257,�0.00000003398339, 0.00000004135334, 0.00000002897439,�0.00000000658363, 0.00000001501841, �0.00000002206094,0.00000000055161, �0.00000003860571, �0.00000007631805,0.00000009403695, 0.00000007018246, �0.00000002439353,0.00000002161281, �0.00000004140694, �0.00000000625811,�0.00000005595954, �0.00000011336725, 0.00000012574761,0.00000004435279, 0.00000011835304, 0.00000038520384,�0.00000093531195, �0.00000359538743, �0.00000335240589,0.00000735933409, 0.00002916414169, 0.00004406715803,0.00002603037860, �0.00003450512468, �0.00010957463521,�0.00013827541937, �0.00007059032905, 0.00008561161625,0.00024758306777, 0.00029195610894, 0.00014116104504,�0.00016270797653, �0.00045151686601, �0.00051348315480,�0.00024029387631, 0.00026968685234, 0.00072903646688,0.00081080530065, 0.00037201309107, �0.00040987480358,�0.00108978915830, �0.00119388122260, �0.00054023397097,0.00058782792960, 0.00154459507653, 0.00167407734489,0.00075019796938, �0.00080865329065, �0.00210724788580,�0.00226592249695, �0.00100835380162, 0.00107901396025,0.00279544468147, 0.00298796346127, 0.00132403443028,�0.00140725060793, �0.00363089652658, �0.00385505860762,�0.00174188331962, 0.00173159819748, 0.00479669191923,0.00517400134013, 0.00182636129670, �0.00278909883430,�0.00525902108332, �0.00542762744782, �0.00380811605332,0.00161271614498, 0.00906475585541, 0.00983968871345,0.00121855009896, �0.00636647455821, �0.00638458085559,�0.00649523161574, �0.00858029628069, 0.00000905677615,0.01757797983615, 0.01913175756961, �0.00113366197163,�0.01398172150549, �0.00728259180758, �0.00743370723901,�0.01886346996428, �0.00408561425565, 0.03626601656411,0.04025094626589, �0.00694642794859, �0.03301103961124,�0.00996121863789, �0.01084493453209, �0.05091712704336,�0.01719267104168, 0.11336396843626, 0.14676685278102,�0.04057748722701, �0.23068468974908, �0.13811577410459,0.13811577410459, 0.23068468974908, 0.04057748722701,

�0.14676685278102, �0.11336396843626, 0.01719267104168,0.05091712704336, 0.01084493453209, 0.00996121863789,0.03301103961124, 0.00694642794859, �0.04025094626589,�0.03626601656411, 0.00408561425565, 0.01886346996428,0.00743370723901, 0.00728259180758, 0.01398172150549,0.00113366197163, �0.01913175756961, �0.01757797983615,�0.00000905677615, 0.00858029628069, 0.00649523161574,0.00638458085559, 0.00636647455821, �0.00121855009896,�0.00983968871345, �0.00906475585541, �0.00161271614498,0.00380811605332, 0.00542762744782, 0.00525902108332,0.00278909883430, �0.00182636129670, �0.00517400134013,�0.00479669191923, �0.00173159819748, 0.00174188331962,0.00385505860762, 0.00363089652658, 0.00140725060793,�0.00132403443028, �0.00298796346127, �0.00279544468147,�0.00107901396025, 0.00100835380162, 0.00226592249695,0.00210724788580, 0.00080865329065, �0.00075019796938,�0.00167407734489, �0.00154459507653, �0.00058782792960,0.00054023397097, 0.00119388122260, 0.00108978915830,0.00040987480358, �0.00037201309107, �0.00081080530065,�0.00072903646688, �0.00026968685234, 0.00024029387631,0.00051348315480, 0.00045151686601, 0.00016270797653,�0.00014116104504, �0.00029195610894, �0.00024758306777,�0.00008561161625, 0.00007059032905, 0.00013827541937,0.00010957463521, 0.00003450512468, �0.00002603037860,�0.00004406715803, �0.00002916414169, �0.00000735933409,0.00000335240589, 0.00000359538743, 0.00000093531195,�0.00000038520384, �0.00000011835304, �0.00000004435279,�0.00000012574761, 0.00000011336725, 0.00000005595954,0.00000000625811, 0.00000004140694, �0.00000002161281,0.00000002439353, �0.00000007018246, �0.00000009403695,0.00000007631805, 0.00000003860571, �0.00000000055161,0.00000002206094, �0.00000001501841, 0.00000000658363,�0.00000002897439, �0.00000004135334, 0.00000003398339,0.00000001690257, 0.00000000073448, 0.00000001200053,�0.00000001065039, �0.00000000284924, �0.00000000577796,�0.00000001119742, 0.00000000976980, 0.00000000481609,0.00000000063332, 0.00000000460092, �0.00000000530162,�0.00000000416421, 0.00000000249390, 0.00000000099383,�0.00000000030078, �0.00000000007340, 0].

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