Lineas Paralelas Cálculo

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Power Transmission and Distribution

Calculation Example

Parallel Line Protection with Distance RelayWith and without mutual compensation

Date: 20.03.13 Nuremberg PTD EA 13

Rev. 1.0 Gustav Steynberg

135409741.doc page 1/10


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Page 2 of report dated 23/02/2005 06:59:00

1. Aim of example

This example will show how to apply the distance protection on parallel lines, giving a calculationmethod for zone reach settings. The user must decide if parallel line compensation is applied or if it issufficient to modify the ground fault reach as illustrated. Other options such as switching overparameter sets for different line conditions is only mentioned in passing.

2. Line data used for the example

The data that will be used for this example, as well as the circuit used to model the fault data is shownbelow.

Figure 1: Single line diagram for this example

Parameter SourceB00041 B00611

Rated Voltage 500 kV 500 kVOperating voltage p.u. 1.05 1.037

Short circuit power 4762 MVA 16329 MVA

R/X ratio 0.0304 0.0326R0/R1 ratio 3.57 0.3006

X0/X1 ratio 0.9157 0.5708

Table 1: Source data for model system

The two parallel lines B0022 and B0049 have the following dataParameter

Rated Voltage 500 kVLine length 10 km

R1 positive sequence resistance per km 0.0389 Ohm/kmX1 positive sequence reactance per km 0.3961Ohm/km

Cb line capaciatance per km 10 nF/km

C0 zero sequence capaciatance per km 5 nF/kmR0/R1 ratio 6.05

X0/X1 ratio 3.61R0M zero sequence mutual resistance per km 0.1953 Ohm/km

X0M zero sequence mutual reactance per km 0.7454 Ohm/km

Table 2: Line data for model system


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The connection between busbar N0001 and N0006 (B00681) is simulated with the following line data

ParameterRated Voltage 500 kV

Line length 100 kmR1 positive sequence resistance per km 0.9435 Ohm/km

X1 positive sequence reactance per km 8.9642Ohm/km

Cb line capaciatance per km 5 nF/kmC0 zero sequence capaciatance per km 2 nF/km

R0/R1 ratio 20X0/X1 ratio 20

Table 3: Data for connection B00681 between the source busbars

From the line data given in Table 2, the following parameters for diatance relay setting can becalculated:

68.1

3

105.6

3

11

0

=

=

=

L

E

L

E

L

E

R

R

R

R

RR

R

R

87.0

3

161.3

3

11

0

=

=

=

L

E

L

E

L

E

X

X

X

X

XX

X

X

3. Distance settings for Zone 1 Relay at B00181

The reach setting for the first zone is set to cover as much of the protected line as possible butensuring at the same time that no overreach occurs. The parallel line does not affect the phase tophase measuring loops, so the settings for the reach is initially done without consideration of theparallel line:

X1 (zone 1 reach in X direction) = 80% of X1 times the line length:

primX

X

= = 169.31103961.08.01

In this example no special consideration is given to the arc resistance coverage, so set the resistancereach the same as the X reach.

For the phase to ground loop the parallel line will cause an over or underreach depending on thedirection of earth current flow in the parallel line. To avoid overreach of the zone 1, the setting appliedfor XE/XL may be made smaller than the value calculated from the line data in chapter 2 above. Thefollowing may be used to calculate the modified XE/XL setting parameter for Zone 1 that applies whenthe parallel line is in service:

11 0 ++= IXEMXELXER rkkk . Equation 1

whereby kXER= modified XE/XL setting for Zone1


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kXEL= XE/XL calculated with line data = 0.87

kXEM= mutual coupling factor calculated with line data (X0M/3XL)rI0= ratio of zero sequence current on parallel line to protected line (note direction)

627.0

3961.03

7454.0

3

0

=

=

=

XEM

XEM

L

MXEM

k

k

X

Xk

If the infeeds from the two busbars feeding the parallel lines is about the same, then the zero sequencecurrent in the parallel line for faults close to the set reach limit (80%) will flow in the same direction inboth the faulted and unfaulted line (viewed from the relay with the fault at 80%). This would causeunderreach of zone 1. In this example it is apparent that the right hand source has a much strongerinfeed. It must therefore be checked to see in which direction the parallel line current flows when aphase to ground fault is applied at 80% from busbar N0001. The ratio of the two earth currents mustthen also be determined.

Fault at 80% B00181 B00451Earth Current AG 4200 A at 4.5 degrees 490A at 170 degrees

Table 4: Earth current for fault AG at 80% from B00181 along line B0022 with both lines in service

With the data from Table 4 the value of rI0 can be calculated (note that they flow in opposite direction):

117.0

4200

490

=

=

IO

IO

r

r

If all these results are substituted in equation 1:

797.0

1)117.0(627.087.01

=++=

XER

XER

k

k

As this setting is smaller than the XE/XL result calculated with line parameters, the relay will underreachwith this setting if the parallel line is out of service. The modified setting is smaller because the earthcurrents on the two parallel lines flow in opposite directions for an earth fault at the zone 1 reach limit of80%.

The further condition when the parallel line is open and earthed at both ends must be consideredseperately. This condition will generally cause overreach if no special measures are applied. As this isnot a normal operating condition, parameter set change-over is commonly applied for this condition. Tocalculate the modified XE/XL setting for this condition when the parallel line is open and earthed atboth ends with equation 1, the ratio of parallel to protected line earth current must be obtained for anearth fault at the end of the line (100%). These two earth currents will be in opposite directions:


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Fault at 100% B00181 B00451

Earth Current AG 3320 A at 2.1 degrees 1760A at 176.8 degreesTable 5: Earth current for fault AG at 100% from B00181 along line B0022 with line B0049 open andearthed at both ends

With the data from Table 5 the value of rI0 can be calculated:

530.0

3320

1760

=

=

IO

IO

r

r

If this parameter is substituted in equation 1:

538.0

1)53.0(627.087.01

=++=

XER

XER

k

k

This setting value of XE/XL will accommodate the earth fault at 100% of the line B0022 when theparallel line B0049 is open and earthed at both ends.

4. Distance settings for Zone 1 Relay at B00291

For the relay at the opposite line end the same applies. In this case the earth current will however be inthe same direction on both the faulted and parallel line as the right source is the strong infeed.

Fault at 80% B00291 B00561Earth Current AG 9800 A at 2.7 degrees 5670A at 2.7 degrees

Table 6: Earth current for fault AG at 80% from B00291 along line B0022


579.0

9800

5670

=

=

IO

IO

r

r

If all these results are substituted in equation 1:

233.1

1579.0627.087.01

=++=

XER

XER

k

k

As this setting is larger than the XE/XL result calculated with line parameters, the relay will overreachwith this setting if the parallel line is out of service.The further condition when the parallel line is open and earthed at both ends must be consideredseperately. This condition will generally cause overreach if no special measures are applied. As this isnot a normal operating condition, parameter set change-over is commonly applied for this condition. Tocalculate the modified XE/XL setting for this condition when the parallel line is open and earthed at

both ends with equation 1, the ratio of parallel to protected line earth current must be obtained for anearth fault at the end of the line (100%). These two earth currents will be in opposite directions:

Fault at 100% B00291 B00561


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Earth Current AG 14300 A at -2.6 degrees 7570A at 172.1 degrees

Table 7: Earth current for fault AG at 100% from B00291 along line B0022 with line B0049 open andearthed at both ends


529.0

14300

7570

=

=

IO

IO

r

r

If this parameter is substituted in equation 1:

538.01)529.0(627.087.01

= ++=XERXER

kk

This setting value of XE/XL will accommodate the earth fault at 100% of the line B0022 when theparallel line B0049 is open and earthed at both ends.

5. Summary of setting options and modelling results

Earth faults at 0, 25, 50, 75 and 100% of the line length are simulated. The 3 line conditions, both linesin service, parallel line open and parallel line open and earthed at both ends are used. The relay reachwith the calculated XE/XL settings is then evaluated with these results. The results are given in tabular

form below:

Faultposition fromB00181

Measured fault position with relevant XE/XL settingBoth lines in service Parallel line open Parallel line open and

earthed at both ends

0.87 0.797 0.538 0.87 0.797 0.538 0.87 0.797 0.538

0% 0% 0% 0% 0% 0% 0% 0% 0% 0%25% 21% 21% 25% 25% 27% 30% 34% 35% 42%

50% 44% 45% 53% 50% 53% 61% 62% 64% 73%

75% 71% 73% 86% 75% 78% 90% 82% 85% 97%

100% 130%

130%

150% 100% 103% 117%

86% 90% 100%

Table 8: Reach of relay at B00181


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Fault

position fromB00291

Measured fault position with relevant XE/XL setting

Both lines in service Parallel line open Parallel line open andearthed at both ends

0.87 1.233 0.538 0.87 1.233 0.538 0.87 1.233 0.5380% 0% 0% 0% 0% 0% 0% 0% 0% 0%

25% 26% 21% 31% 25% 21% 31% 25% 21% 30%50% 54% 45% 66% 50% 42% 62% 47% 39% 58%

75% 88% 74% 107% 75% 63% 92% 67% 56% 81%100% 135

%112%

163% 100% 85% 122%

83% 70% 100%

Table 9: Reach of relay at B00291

As expected, when the line configuration matches the conditions used to determine the setting ofXE/XL, the relay reach is accurate (in some cases this only applies at the set zone 1 reach of 80%).

From Table 8 it is clear that only the condition parallel line open and earthed at both ends can result inan overreach condition by Zone1. With the XE/XL setting that applies to this condition (0.538) thisoverreach is avoided. This setting also provides more than 50% coverage of the line under all otherconditions.

In Table 9, for the right hand side, the reach modifications due to the parallel line are more severe.Here also the parallel line open condition comes close to overreach with the setting for both lines inservice (1.233). The setting for parallel line open and earthed (0.538) however again avoids overreach

under all conditions and safely covers more than 50% of the line with zone 1.

6. Conclusion

If the zero sequence parallel line compensation can not be done by measurement connection of theparallel feeder earth current to the I4 current measuring input, adaption of the settings is necessary toensure selective tripping with the Zone 1 of the distance protection.

If possible, the condition when the parallel line is open and earthed at both ends should be signalled tothe relay so that a parameter set switch over can be applied for this special condition. For this conditionactivate a parameter set with the XE/XL setting equal to 0.538 in this example. For other (normal)system conditions the XE/XL setting for parallel line open (0.87) can be applied in this example. This

setting does not overreach and ensures more than 50% coverage under all conditions.

If the parallel open and earthed condition cannot be signalled to the relay, use a fixed setting forXE/XL. In this example apply the value 0.538 which never causes overreach and still obtains more then50% coverage under all conditions.

7. Fault Resistance

When at the one line end there is a very strong infeed in comparison to the other end, the faultresistance coverage at the weak infeed end may present a problem for the distance protection. Toanalyze this, the fault resistance (ohmic) and arc resistance must be considered separately. The arc

resistance is characterized by a fixed arc voltage, independent of the magnitude of current flowingthrough it. The fault resistance however has a current dependant voltage (Ohms Law) across it. It istherefore apparent that the fault resistance presents the most difficult conditions.


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The above diagram (Figure 2-28) from the 7SA6 relay manual can be used to calculate the requiredresistance reach for Zone 1. The relay at B00181 has the weaker infeed and will be analyzed as thiswill require the largest R setting. The following equations from the 7SA6 relay manual will be used:


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In this example, for a fault at 80% along the line B0022 measured by relay at B00181:

I1 4600 AI2 17600 A

I1/I2 0.261

For the arc voltage a value of 20 kV is assumed, this corresponds to an arc length of approximately 8m.

The corresponding arc resistance is given by the following:

OhmR

R

II

UR

arc

arc

arcarc

9.0

176004600

20000

21

=+

=

+=

As no information regarding the tower footing resistance is available a value of 3 Ohm is assumed(typical values where overhead ground wires are present are less).

The required reach setting for Zone 1 earth fault reach therefore is:

OhmR

R

E

E

41.8

68.11

39.0

4870

1860012.1

1

1

=

+

+

+=

As the calculated primary Zone 1 reach in X direction (80%) was calculated to be 3.169 Ohm, thisresults in a large ratio between R and X reach (R1E / X1 = 2.65). The zone reduction angle will have tobe set accordingly. (Refer to relay manual).

Simulation of an AG fault at 80%, with the parallel line open and 3.9 Ohm fault resistance produces thefollowing relay reach measurement:


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RE/RL XE/XL Measured R Measured X Zone 1 R coverage with

Line angel = 84 degrees[8.41 + X/tan(84)]1.68 0.87 8.45 2.75 8.70

1.68 1.233 8.45 2.35 8.651.68 0.538 8.45 3.25 8.74 (max X impedance

is outside Zone 1 settingof 3.169)

Table 10: Impedance measured by relay at B00181 during AG fault at 80% along line B0022 with 3.9 Ohmfault resistance.

As shown in Table 10, the fault at the reach limit of Zone 1 with the worst case fault resistance willalways be covered by the calculated RE1 setting. Similar calculation can be applied for the relay at the

remote end. When the parallel line is in service, the weak infeed end will have stronger infeed currentso that the influence of the resistor will be less pronounced.

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