Short Communication Comparison of five methods of compensation for the ground distance function and assessment of their effect on the resistive reach in quadrilateral characteristics Elmer Sorrentino ⇑ Dpto. de Conversión y Transporte de Energía, Universidad Simón Bolívar, Apdo. Postal 89.000, Caracas, Venezuela article info Article history: Received 6 February 2013 Received in revised form 22 March 2014 Accepted 24 March 2014 Keywords: Ground Distance Protection abstract This article compares five compensation methods for the ground distance function, in order to show the maximum fault resistances that the relays can see when they have quadrilateral characteristics. These five compensation methods are based on the description of real protective functions, found in manuals of commercial relays. For a power system taken as an example, the impedances seen by the relays are computed for each form of compensation and for different system conditions. The results show that: (a) the locus of the apparent impedance is very different for each compensation method; (b) the maxi- mum fault resistance seen with each compensation method can be very different, although the same quadrilateral characteristic is adjusted in the relays. Three of these compensation methods (A–C) are based on the positive-sequence impedance of the line, and two of these compensation methods (D, E) are based on the impedance of the ground-fault loop. The results also show that: (a) methods D and E tend to over-reach or under-reach, for solid faults; (b) the coverage for resistive faults tend to be greater for methods A and B than for methods C, D, and E; (c) the loci of the apparent impedance tend to be flat only for method C. In general, the knowledge of the behavior of the compensation method for the ground distance function is important because it should be considered when the relay settings are computed and/or when the faults are analyzed. Ó 2014 Elsevier Ltd. All rights reserved. Introduction The behavior of the Ground Distance Function (GDF) has been analyzed for years. Fault type, pre-fault load flow and relay polar- ization are some factors that influence the reach of GDF when there are fault resistances. Recently, some research efforts have been dri- ven towards: (a) the application of the concept of adaptive protec- tion, in order to improve the behavior of GDF according to the impedance seen by it [1,2]; (b) the proposal of new ways of com- pensation for GDF [3,4]. The most analyzed GDF is based on the traditional use of the residual compensation factor (K 0 ). Loci of the impedance seen by this traditional GDF, as a function of fault resistance, are circles [5]. In commercial relays, the available methods for the GDF are diverse. Some articles [6,7] show details related to this diversity, but an academic comparison between the methods applied by dif- ferent commercial relays was not available, and this article is a contribution about this topic. For a power system taken as an example, this article compares: (a) the loci for five methods of compensation of the GDF; (b) the resistive reaches, for each method of compensation, when the relays have been adjusted with the same quadrilateral characteris- tics in the R–X plane. This article clearly shows that these resistive reaches are very different. Description of the analyzed compensation methods This description of the analyzed compensation methods is based on information found in manuals of commercial relays. For each compensation method, the apparent impedance is described for the GDF in the phase A. Method A (‘‘relay A’’) This compensation method is one of the most known, usually it is described in classic textbooks, and it has been applied in com- mercial relays [8]. The impedance seen by the relay in this case (Z A ) is: Z A ¼ V A =ðI A þ K 0 I R Þ ð1Þ http://dx.doi.org/10.1016/j.ijepes.2014.03.049 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Tel.: +58 212 906 3720. E-mail address: [email protected]Electrical Power and Energy Systems 61 (2014) 440–445 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Transcript
Electrical Power and Energy Systems 61 (2014) 440–445
Contents lists available at ScienceDirect
Electrical Power and Energy Systems
journal homepage: www.elsevier .com/locate / i jepes
Short Communication
Comparison of five methods of compensation for the ground distancefunction and assessment of their effect on the resistive reach inquadrilateral characteristics
http://dx.doi.org/10.1016/j.ijepes.2014.03.0490142-0615/� 2014 Elsevier Ltd. All rights reserved.
Elmer Sorrentino ⇑Dpto. de Conversión y Transporte de Energía, Universidad Simón Bolívar, Apdo. Postal 89.000, Caracas, Venezuela
a r t i c l e i n f o
Article history:Received 6 February 2013Received in revised form 22 March 2014Accepted 24 March 2014
Keywords:GroundDistanceProtection
a b s t r a c t
This article compares five compensation methods for the ground distance function, in order to show themaximum fault resistances that the relays can see when they have quadrilateral characteristics. Thesefive compensation methods are based on the description of real protective functions, found in manualsof commercial relays. For a power system taken as an example, the impedances seen by the relays arecomputed for each form of compensation and for different system conditions. The results show that:(a) the locus of the apparent impedance is very different for each compensation method; (b) the maxi-mum fault resistance seen with each compensation method can be very different, although the samequadrilateral characteristic is adjusted in the relays. Three of these compensation methods (A–C) arebased on the positive-sequence impedance of the line, and two of these compensation methods (D, E)are based on the impedance of the ground-fault loop. The results also show that: (a) methods D and Etend to over-reach or under-reach, for solid faults; (b) the coverage for resistive faults tend to be greaterfor methods A and B than for methods C, D, and E; (c) the loci of the apparent impedance tend to be flatonly for method C. In general, the knowledge of the behavior of the compensation method for the grounddistance function is important because it should be considered when the relay settings are computedand/or when the faults are analyzed.
� 2014 Elsevier Ltd. All rights reserved.
Introduction For a power system taken as an example, this article compares:
The behavior of the Ground Distance Function (GDF) has beenanalyzed for years. Fault type, pre-fault load flow and relay polar-ization are some factors that influence the reach of GDF when thereare fault resistances. Recently, some research efforts have been dri-ven towards: (a) the application of the concept of adaptive protec-tion, in order to improve the behavior of GDF according to theimpedance seen by it [1,2]; (b) the proposal of new ways of com-pensation for GDF [3,4].
The most analyzed GDF is based on the traditional use of theresidual compensation factor (K0). Loci of the impedance seen bythis traditional GDF, as a function of fault resistance, are circles[5]. In commercial relays, the available methods for the GDF arediverse. Some articles [6,7] show details related to this diversity,but an academic comparison between the methods applied by dif-ferent commercial relays was not available, and this article is acontribution about this topic.
(a) the loci for five methods of compensation of the GDF; (b) theresistive reaches, for each method of compensation, when therelays have been adjusted with the same quadrilateral characteris-tics in the R–X plane. This article clearly shows that these resistivereaches are very different.
Description of the analyzed compensation methods
This description of the analyzed compensation methods isbased on information found in manuals of commercial relays. Foreach compensation method, the apparent impedance is describedfor the GDF in the phase A.
Method A (‘‘relay A’’)
This compensation method is one of the most known, usually itis described in classic textbooks, and it has been applied in com-mercial relays [8]. The impedance seen by the relay in this case(ZA) is:
E. Sorrentino / Electrical Power and Energy Systems 61 (2014) 440–445 441
VA, IA, IR are voltage of phase A, current of phase A, and residualcurrent (IR = IA + IB + IC), respectively, measured by the relay. K0 isthe residual compensation factor (a setting of the relay). In thisarticle, K0 is assumed to be exactly adjusted to the complex valuerequired to obtain the positive-sequence impedance of the line,up to the fault point:
K0 ¼ ðZL0 � ZLþÞ=ð3ZLþÞ ð2Þ
ZL+ and ZL0 are the positive-sequence impedance and zero-sequence impedance of the line, respectively.
Method B (‘‘relay B’’)
This compensation method is similar to the previous one, but ituses arithmetic of real numbers. It is based on the description ofsome commercial relays [9]. The impedance seen by the relay inthis case (ZB) is:
RB and XB are rectangular components of ZB. KR and KX are com-pensation factors for RB and XB. u is the lag angle of IA relative to VA.In this article, the compensation factors (KR, KX) are assumed to beexactly adjusted to:
RL0 and XL0 are rectangular components of ZL0. RL+ and XL+ arerectangular components of ZL+.
Method C (‘‘relay C’’)
This method uses a mathematical artifice to reduce the effect ofthe system conditions on the reactive reach, and it is based on acommercial relay [10]. The impedance seen by the relay in thiscase (ZC) is:
m is the reactance seen by the relay, in per-unit of XL+. XC is thereactance seen by the relay, in ohms. XL+ is the positive-sequencereactance of the line. Im is the imaginary part of a complex number.RG is the resistive effect of the ground-fault, seen by the relay. IA2
and IA0 are the negative-sequence current and zero-sequence cur-rent, respectively, measured by the relay. aL is an unitary complexnumber whose angle is hL+. hL+ is the angle of ZL+ (a setting of therelay). RL+ is the positive-sequence resistance of the line. The
Fig. 1. Analyzed qua
resistive component of the impedance seen by this relay is thesum of RG and mRL+.
Method D (‘‘relay D’’)
This method is based on the ground-fault loop impedance (andnot on the positive-sequence impedance of the line). It has beenapplied in commercial relays [11]. The impedance seen by the relayin this case (ZD) is:
ZD ¼ VA=IA ð10Þ
The setting of this relay is based on the total line impedance forthe ground-fault loop (ZLG):
ZLG ¼ ð2ZLþ þ ZL0Þ=3 ð11Þ
This relation is strictly valid for faults without contributionfrom the remote line end, but this is not a general case.
Method E (‘‘relay E’’)
This method is also based on the ground-fault loop impedance,but the form of computing the impedance is different. It is based ona commercial relay [12]. The impedance seen by the relay in thiscase (ZE) is:
ZE ¼ nZLG þ RX ð12Þ
n is the line impedance seen by the relay, in per-unit of ZLG. RX is theresistive effect of the ground-fault, seen by the relay. n and RX (realnumbers) are computed by solving the equation of this relay (incomplex variable) for ground-faults:
VA ¼ ðnZLGÞIA þ RXIR ð13Þ
3. Description of the analyzed quadrilateral zones
Methods A, B and C are based on ZL+ (Fig. 1a), and methods Dand E are based on ZLG (Fig. 1b). Fig. 1 only shows the first quadrantbecause it is the region of main interest for this article.
Power system used as an example
A simplified model of a power system (Fig. 2) was used as anexample. This model could be obtained as a reduction of a larger
drilateral zones.
442 E. Sorrentino / Electrical Power and Energy Systems 61 (2014) 440–445
system, by the analysis of the matrix of impedances ([ZBUS]). Themodel has equivalent sources at both line terminals (M and N). ZI
is an impedance that represents the other interconnectionsbetween M and N. More simplified network models (without ZI)are frequent in the analysis of distance relays, but the modelshown in Fig. 2 is more realistic.
The line impedance from the relay location (M) up to the faultpoint is ZX, and from the fault point up to N is ZY. The system rep-resentation is obtained from Fig. 2; e.g., for ZX and ZY: ZX+ = d ZL+;ZY+ = (1 � d) ZL+; ZX0 = d ZL0; ZY0 = (1�d) ZL0. d is the distance from
0
10
20
30
40
50
60
0 50R
X Z
L+
ZA
0
10
20
30
40
50
60
R
X Z
L+
ZB
0
10
20
30
40
50
60
R
X Z
L+
0 50 0 50
Fig. 3. Loci, in primary ohms, when the remote breake
0
10
20
30
40
50
60
R
X
Z L+
ZA
0
10
20
30
40
50
60
R
X
Z L+
0
10
20
30
40
50
60
0 50 100 150 200R
X
Z L+
0 50 100 0 50
Fig. 4. Loci, in primary ohms, with S = 160 MW + j 120 MVAR
-60
-20
0
20
40
60
R
X
Z L+
ZA -60
-20
0
20
40
60
R
X
Z L+
-60
-20
0
20
40
60
0 50 100 150 200 250R
X
Z L+
ZC
0 50 100 150 200 250 0 50 100 1
Fig. 5. Loci, in primary ohms, with S = �160 MW �j120 MVA
terminal M up to the fault point, in per-unit of the total line length.For the sake of simplicity, all the simulations were performed with:ZM+ = ZM� = ZM0 = FM ZL+; ZN+ = ZN� = ZN0 = FN ZL+; ZI+ = ZI� = FI ZL+;ZI0 = FI ZL0.
FM, FN and FI are real numbers. EM and EN have the value to rep-resent the pre-fault load flow in the line. The system was simulatedby considering that the pre-fault voltage at the relay location is230 kV. The pre-fault load flow (S) is given at the relay location,in direction towards the line. The total line impedance is:ZL+ = (10 + j 50) X; ZL0 = (50 + j 150) X.
ZC
0
20
40
60
80
100 X Z
LG
ZD
R0
20
40
60
80
100
0 50 100 0 50 100
X Z
LG
ZE
R
r is open and ZI ?1 (RF = 0. . .50 X; d = 0.1. . .0.8).
ZB
0
20
40
60
80
100 X ZLG
ZD
R
250
ZC 0
20
40
60
80
100
100 0 50 100 150 200 250
0 50 100 150 200 250
X ZLG
ZE
R
, FI = 0.25, FM = 0.1, FN = 0.1 (RF = 0. . .50 X; d = 0.1. . .0.8).
ZB -120
-60
0
60
120
R
X
ZLG
ZD
-120
-60
0
60
120
50 200 250 0 100 200 300 400
0 100 200 300 400R
X
ZLG
ZE
R, FI = 0.25, FM = 0.1, FN = 0.1 (RF = 0. . .50 X; d = 0.1. . .0.8).
E. Sorrentino / Electrical Power and Energy Systems 61 (2014) 440–445 443
Obtained loci
Single-phase-to-ground faults through resistance (RF) were sim-ulated (RF from 0 up to 50 X). The reactive setting of the character-istic was set to 80% of the total line impedance, and the resistivesetting was set to 50 X. The results were obtained by varying thefault location from d = 0 up to d = 0.8, in steps of 0.1.
With the remote breaker open
Faults with the remote breaker open, and with ZI ?1, weresimulated. These results are shown in Fig. 3. It can be analyticallydemonstrated that the impedance seen by relay A, with the remotebreaker open, is:
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
η)
Z C
Z A
Z B
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
η)
Z D
Z E
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
η)
Z C
Z A
Z B
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
η)
Z D
Z E
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
FI=0.25FM=1FN=1
FI=0.25FM=0.1FN=0.1
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
ς)
Z C
Z A
Z B
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
ς)
Z D
Z E
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
ς)
Z C
Z A
Z B
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
ς)
Z D
Z E
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
FI=0.25FM=0.1FN=1
FI=0.25FM=1FN=0.1
Fig. 6. Zone-1 resistive reach, in primary ohms, with
ZA ¼ VA=ðIA þ K0IRÞ ¼ ZXþ þ RF=ð1þ K0Þ ð14Þ
This causes the angular deformation in the corresponding locus.For this case, only the relay A sees an imaginary part due to theeffect of RF. On the other hand, only the relays A and B see a max-imum value of the fault resistance different than the adjustedvalue. The previous equation demonstrates analytically this effectfor the relay A.
With pre-fault load-flow towards the line
Fig. 4 shows the results for a specific condition of the systemimpedances, with the pre-fault load flow (S) at the relay locationequal to 160 MW + j 120 MVAR. These results indicate that the loci
0
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120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
Ξ)
Z C
Z A
Z B
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
Ξ)
Z D
Z E
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
Ξ)
Z C
Z A
Z B
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
Ξ)
Z D
Z E
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
ZI
FM=1FN=1
ZI
FM=0.1FN=0.1
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
Ξ)
Z C
Z A
Z B
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
Ξ)
Z D
Z E
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
Ξ)
Z C
Z A
Z B
0
20
40
60
80
100
120
140
160
0 0,2 0,4 0,6 0,8 1
d (p.u.)
Rfm
ax (
Ξ)
Z D
Z E
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
ZI
FM=0.1FN=1
ZI
FM=1FN=0.1
S = 160 MW +j 120 MVAR (RR = 50 X; XR = 0.8 XL).
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z C
Z A
Z B
0
20
40
60
80
100
d (p.u.)R
fmax
(≅
)
Z E
Z D
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z C
Z A
Z B
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z E
Z D
FI=0.25FM=1FN=1
FI=0.25FM=0.1FN=0.1
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z C
Z A
Z B
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z E
Z D
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z C
Z A
Z B
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z E
Z D
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
FI=0.25FM=0.1FN=1
FI=0.25FM=1FN=0.1
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z C
Z A
Z B
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z E
Z D
0
20
40
60
80
100
d (p.u.)R
fmax
(≅
)
Z C
Z A
Z B
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z E
Z D
ZI
FM=1FN=1
ZI
FM=0.1FN=0.1
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z C
Z A
Z B
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅) Z E
Z D
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z C
Z A
Z B
0
20
40
60
80
100
d (p.u.)
Rfm
ax (
≅)
Z E
Z D
0 0
0 0
0 0.2 0.4 0.6 0.8 1 0
0 0
0 0
0 0.2 0.4 0.6 0.8 1 0
0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1
0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1
0.2 0.4 0.6 0.8 1
0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1
0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1
0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
ZI
FM=0.1FN=1
ZI
FM=1FN=0.1
Fig. 7. Zone-1 resistive reach, in primary ohms, with S = �160 MW � j 120 MVAR (RR = 50 X; XR = 0.8 XL).
444 E. Sorrentino / Electrical Power and Energy Systems 61 (2014) 440–445
deformation is different for each form of compensation of therelays. The loci of the apparent impedance tend to be flat formethod C. On the other hand, for this particular condition, thereactive reach for solid faults changes substantially in the casesof the relays D and E. The relays D and E have a notorious over-reach for solid faults (in this case).
With pre-fault load-flow towards the busbar
In comparison with the previous case, only the sign of the pre-fault load flow was changed (i.e., S = �160 MW �j120 MVAR, forthis case). The results are shown in Fig. 5. The comments of SectionWith pre-fault load-flow towards the line are also applicable to thiscase. The relays D and E have a notorious under-reach for solidfaults (in this case).
Resistive reach
Conditions for the simulation
The shape of the described quadrilateral characteristics was notchanged. The maximum fault resistance (Rfmax) that each relaycan see within the described zone was computed as a function ofthe distance (d). d was varied between 0 and 1. The apparentimpedance can be outside the relay characteristic for solid faultsand, for a greater fault resistance, the measured impedance canenter to the characteristic and leave again (as it can be observedin Figs. 4 and 5). In such cases, the maximum fault resistance thatcan be seen by the relay was not recorded. For a given distance,Rfmax was only recorded if the point for solid faults is within therelay characteristic.
E. Sorrentino / Electrical Power and Energy Systems 61 (2014) 440–445 445
The results were obtained by the combinatory variation of thefollowing cases: (a) Pre-fault load flow: towards the line ortowards the busbar; (b) Impedance that represents the additionalinterconnections: present (FI = 0.25) or nonexistent (ZI ?1); (c)Impedances of each source (busbars M and N): low values ormoderate values (FM = 0.1 or 1.0; FN = 0.1 or 1.0).
Results
The obtained results are shown in Figs. 6 and 7. The followingpoints can be highlighted:
(a) The maximum fault resistance that can be seen by eachrelay, within its quadrilateral zone, is not constant. Therange of the values is different for each relay.
(b) For all the analyzed cases, the maximum fault resistance thatcan be seen by each relay, within its quadrilateral zone, isalways lower while greater is the distance up to the fault.
(c) For the analyzed cases, the variation in the reactive reach forsolid faults is low for the relays A, B, and C. It means that theresults of the reactive reach for these models were near tothe respective adjusted distance (d = 0.8). The relays D andE tend to have over-reach when the pre-fault load flow istowards the line, and they tend to have under-reach whenthe pre-fault load flow is towards the busbar.
(d) Generally, the relays A and B have a greater resistive reachthan the other relays. The comparison between A and B indi-cates that the resistive reach of B is usually greater (it occursin 100% of the cases, for the analyzed examples). On theother hand, the relays A and B have a greater range of vari-ation of their resistive reaches than the other relays.
(e) The resistive reach of the relays C, D and E is usually similar.However, for the shown cases, the reactive reach of the relayC varies less than in the case of the relays D and E.
(f) For the case of relays D and E: relay D usually has a greaterresistive reach when the pre-fault load flow is in the direc-tion to the line, and the opposite occurs when the pre-faultload flow is in the direction to the busbar.
(g) If the faults are near to the relay location, with the pre-faultload flow towards the protected line, then the resistive reachof relays C, D and E is near to the value of the setting of theresistive limit in the characteristic. For the shown example,the setting value is 50 X, and the resistive reach of theserelays is between 40 X and 60 X for faults near to the relaylocation, in almost all the cases (the exception is C, for thecase of ZI ?1; FM = 1; FN = 0.1).
(h) If the faults are near to the relay location, with the pre-faultload flow towards the protected line, then the resistive reachof A and B is substantially greater than the setting of theresistive limit in the characteristic. For the example, this set-ting is 50 X, and the resistive reach of these relays isbetween 75 X and 150 X for faults near to relay location,approximately.
(i) If the faults are near to the relay location, with the pre-faultload flow towards the busbar, then the resistive reach of therelays A and B tends to be reduced, in comparison with thecase of the pre-fault load flow towards the protected line.
(j) The resistive reaches depend on the ratio of the systemimpedances to the line impedance (FM, FN, FI). The effect ofFM and FN is greater than the effect of FI, for the analyzedcases.
7. Conclusion
Five methods of compensation for the Ground Distance Func-tion (GDF) were analyzed. Three methods (A–C) are based on thepositive-sequence impedance of the line, and two methods (D, E)are based on the impedance of the ground-fault loop. The analysisincluded the loci of the impedances seen by the relays, as well asthe maximum fault resistance that each relay is able to see withinits zone when the relay has quadrilateral characteristic in the R–Xplane.
The loci of the impedance seen by the relays, by consideringthe effect of the pre-fault load-flow, are substantially differentfor each method of compensation of the GDF. The resistive settingfor the first zone of all the relays was adjusted to the same value,but this fact does not imply the same coverage for resistive faults.The coverage for resistive faults (or resistive reach) is the maxi-mum fault resistance that the relay is able to see within its zone,by considering the effect of the pre-fault load-flow. The resistivereach is substantially different for each form of compensation ofthe GDF.
The results also show that: (a) for solid faults, methods D and Etend to have over-reach or under-reach, and this fact was notobserved in methods A, B, or C; (b) the resistive reach tend to begreater for methods A and B than for methods C, D, and E; (c) thelocus of the apparent impedance tends to be flat only for method C.
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