Resistive Reach Setting of QUAD Relays

Resistive reach setting of QUAD relays

Author : Pradeep Kumar Gangadharan

Resistive reach setting of a Quadrilateral characteristics Impedance Relay This document discusses the issues concerning the resistive reach setting of the quadrilateral characteristics of a distance relay. Though quadrilateral characteristics allows the user to set the resistive reach independent of the reactance setting, the application and measurement errors does impose some limits on the highest value that can be set. The document explains each of the influencing conditions. Finally a general guideline for setting is proposed. The main criterion that influence the resistive reach setting of a quadrilateral characteristics are; 1. Maximum expected fault resistance – The fault resistance is primarily contributed by, fault arc resistance and tower footing resistance. The resistive reach setting should ideally be more than the maximum fault resistance expected. 2. Remote in-feed – The fault current feed from the remote source will cause the resistance measured by the local relay to be more than the actual resistance. So it is desirable to set the resistive reach such that the measured resistance is within the setting even for the highest remote infeed. 3. Remote in feed with different local and remote source impedance angles - If the remote source impedance angle is different from the local source angle, then the remote current infeed to the fault resistance will cause error in the reactance measurement as well. This apparent reactance can be higher or lower than the line reactance (depends on the relative angle of the remote source, leading or lagging). Thus the resistance reach setting should be limited such that a high resistance fault beyond 100% of the protected line will not cause the apparent impedance to fall within the zone 1 setting. This condition puts a limit on the maximum R/X ratio of the quadrilateral characteristics. 4. Maximum load – Resistive reach setting should be less than the maximum load to avoid load encroachment into the operating characteristics The resistive reach setting thus should be less than the maximum load impedance with an overload factor and safety margin.

©2006 Protection Engineering And Research Laboratories

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5. Error introduced by Current/Voltage transformers and relay measurement inaccuracies – Current and voltage transformers introduce ratio and phase errors. Depending on the relay design, they also have measurement errors (usually 5 to 10%) This can result in the relay measuring impedance (both R and X) different from actual. To ensure that the worst error in measurement does not cause the relay zone 1 to overreach beyond 100% of the line, we have to put a limit on the maximum R/X ratio of the quadrilateral characteristics. Of the above four conditions, 1&2 argues to increase the resistive setting whereas 3, 4 & 5 puts a limit on the maximum value we can set for the resistive reach. So the final setting of the resistive reach should be a value, which is an acceptable compromise meeting all the four conditions. One thing to be borne in mind while deciding the setting is the philosophy of the distance protection zones. That is > Zone 1 of the distance protection is intended to protect the maximum possible portion of the protected line. With a given setting (80% or 90%), it should NEVER overreach beyond the 100% of the protected line under any system conditions or errors. > Zone 2 is primarily provided to detect all faults beyond zone 1 setting and upto the 100% of the line (also know as the end zone). The Zone 2 should NEVER underreach below 100% of the protected line under any case. Now we will discuss each of the above cases bearing in mind the basic philosophy of the protection zones. 1. Maximum expected fault resistance It is very difficult to arrive at an exact value for the arc resistance during a fault. A.R. Van C Warrington derived an empirical formula for calculating the arc resistance. This can be used to calculate an approximate value of maximum the arc resistance.

RA =

28710 L I F1.4

(1)

RA – Arc resistance in primary Ω. IF – Fault current in primary Amps. L – Length of arc in meters.


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As it can be seen that the worst case (higher arc resistance) occurs for lower fault currents. The tower footing resistance is a value which can be measured or got from the design information. 2. Remote in-feed Consider a simple system shown in figure 1 with source on both sides. The distance relay Ra at station A protects the line AB. For a single phase to ground fault at location F, with an external fault resistance is marked as Rf (which is introduced due to the fault arc and tower footing resistance).

Fig. 1 : Simple system with remote in-feed

The relay Ra will measure fault current as “Iaf” and fault voltage as “Vaf”. At present we will assume that the remote infeed is in phase with the local feed. That is the phase angle of Iaf is same as Ibf {Note the direction of the currents are marked in the diagram} Let us start with, ZLa = |ZLa| ∠θ° Iaf = |Iaf| ∠0° Ibf = |Ibf| ∠0° Now we can calculate the other values as, Voltage across the fault resistance; Vrf = (Iaf+Ibf)*Rf = Rf*|Iaf| ∠0° + Rf*|Ibf| ∠0°


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Voltage across the line impedance to fault location; VLf = Iaf*ZLa = (|Iaf| ∠0°)*(|ZLa| ∠θ°) = |Iaf|*|ZLa| ∠θ° Voltage at the relay location; Vaf = VLf+Vrf = |Iaf|*|ZLa| ∠θ° + Rf*|Iaf| ∠0° + Rf*|Ibf| ∠0° The impedance measured by the relay will thus be; Zaf =

Iaf ZLa ∠θ ° + Rf Iaf ∠0° + Rf Ibf ∠0° Vaf = Iaf Iaf ∠0°

Zaf = ZLa ∠θ ° + Rf +

Ibf Iaf

Rf

(2)

From equation (2) we can see that instead of measuring an impedance of ZLa+Rf (which is the sum of line impedance upto to fault location plus the fault resistance), the relay Ra actually a value higher by (Ibf/Iaf)*Rf. This effect is shown in figure 2 below.

Fig. 2 : Difference in measured resistance due to remote infeed


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From equation (2) and figure 2, it can be seen that the amount of error in the resistance measured depends on the relative current feed from the remote source as compared to the local source. If the remote feed is absent then the error is zero, if the remote feed is 3 times the local feed, then the relay would measure 4 times Rf, instead of Rf. 3. Remote in feed with different local and remote source impedance angles Continuing the same discussion, in practice the local and remote fault currents need not be in phase. Let us see what happens to the measured impedance in this case. Now we will consider that the remote feed current is displaced by an angle ∅s. Then we have, Iaf = |Iaf| ∠0° Ibf = |Ibf| ∠∅s ° If we repeat the steps we followed in calculating the measured impedance in sl. no. 2, we will get, Zaf =

Iaf ZLa ∠θ ° + Rf Iaf ∠0° + Rf Ibf ∠φs° Vaf = Iaf Iaf ∠0°

Zaf = ZLa ∠θ ° + Rf +

Ibf Iaf

Rf∠φs°

(3)

From equation (3) we can see that the angle ∅s, is in fact introducing an additional reactance component to the measured impedance. Figure 3 below shows this in the impedance plane. From equation (3) and figure 3 it can be seen that the measured impedance has an additional resistance and reactance component. The reactance component of the error can either add to the line reactance (when the remote current leads the local current) or subtract from the line reactance (when the remote current lags the local current).


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Fig. 3 : Difference in measured resistance and reactance due to remote infeed

This means that if the remote current leads the local current, then the impedance relay will underreach. Whereas, if the remote current lags the local current then the relay will overreach.

Fig. 4 :Influence of remote infeed on resistive reach selection ©2006 Protection Engineering And Research Laboratories

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We are aware that the zone 1 should never overreach beyond 100% of the protected line. Thus for a given condition of local and remote source (that is ratio of |Ibf|/|Iaf| and ∅s remaining same), the chances of a high resistive fault beyond 100% of the protected line to fall within the zone 1 is more if the resistive setting of the zone is high. Figure 4 shows a case of a high resistive fault beyond 100% of line, with the relay overreaching. As we can see with resistive setting of R1, the relay would have not operated, whereas if the setting was R2, then the impedance relay would have operated in Zone 1 (which is not desirable). From the above discussion it is clear that the amount of overreaching (or underreaching) depends on, > the ratio of |Ibf|/|Iaf|, > the difference in the phase angle of the two currents and > the amount of fault resistance Rf. In some relays the top reactance line of the quadrilateral characteristics is given a tilt to overcome this problem. For some relays the tilt is a fixed setting, whereas some other relays tilt the characteristics dynamically based on the pre-fault load flow. In these relays the resistive reach setting will not have to be verified for this condition of remote current infeed with different phase angle. In case of relays which have a fixed horizontal line for the characteristics, necessary check has to be made to ensure that the relay does not overreach beyond 100% of the protected line. This may necessitate reducing the resistive reach setting. The actual limit can be decided only based on the information of remote infeed levels, maximum load and fault resistance values. 4. Maximum load It is necessary to ensure that the resistive reach setting does not exceed the maximum load resistance. As the load increases, the impedance decreases. Thus the least impedance will be seen for the maximum load condition. If the maximum load impedance is ZL, the considering an overload factor of 20%, we can fix the maximum limit of the outermost resistive reach element as;


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sin φ ⎞ ⎛ R max = 0.8Z L ⎜ cos φ − ⎟ tan θ ⎠ ⎝

(4)

where, - Maximum load impedance ZL ∅ - Maximum power factor angle (37° for 0.8 pf) θ - Angle at which the resistive reach line is tilted. This will equal the relay characteristic angle if the resistive line is parallel to the RCA line 5. Error introduced by Current/Voltage transformers and relay measurement inaccuracies Depending on the type of CTs and PTs used, they introduce errors in the voltage and current measured by the relay. These errors result in both magnitude and phase inaccuracies in the measurement by the relay. This translates into the impedance relay seeing a different fault impedance than actual. The amount of error in the impedance measured depends on the CT and PT errors. Table 1 & 2 below shows the permissible errors for CTs and PTs respectively as defined in IEC60044.

Accuracy Class

Current error at rated primary current (%)

Phase displacement at rated primary current (Minutes)

Composite error at rated accuracy limit primary current (%)

5P

+1

+ 60

5

10P

+3

-

10

Table 1: Accuracy Limits as per IEC 60044-1 Accuracy Class

Voltage ratio error (%)

Phase error (Minutes)

3P

+3

+ 120

6P

+6

+ 240

Table 2: Accuracy Limits as per IEC 60044-2

Errors in measurement also creep in from the relay design. Every product claims the maximum error for each zone. Let us now understand how these errors impose limitation on the resistive reach setting of a quadrilateral characteristic. Figure 5 shows zone 1 of a quadrilateral characteristic (only the section in the first and ©2006 Protection Engineering And Research Laboratories

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4th quadrant is shown). This quadrilateral characteristic is defined in the relay by; ZL - Impedance of the protected line. ZS -The zone reach setting, typically 80% of line Impedance for Zone 1 θ -The characteristic angle setting, RS – Resistive reach setting

Fig. 5 :Quadrilateral Characteristics of Impedance Relay

We will understand the effect of ratio and phase angle errors on the measured impedance separately. Ratio error: The impedance is calculated by taking the ratio of the appropriate voltage and current, Z=V/I. The effect of ratio error is easy to visualize. Ratio error causes the measured impedance Zm to be less than or greater than the actual impedance Z depending on the relative error % introduced by the CT and PT.


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The figure 6 shows a case where the measured impedance Zm (=Vm/Im), is less than the actual impedance Z. Here, Vm= V+Ve Im = I+ Ie Where Ve and Ie are the ratio errors in the voltage and current signals. The relay in this case is overreaching.

Fig. 6 :Error in measured impedance due to ratio error

From the figure we can gather that the amount of tolerance available for the error in magnitude of the measured impedance depends directly on the zone 1 setting. If we set the zone 1 to 80%, there is a margin of 20%. This means that even if the relay measures 20% less impedance, still the relay will not overreach beyond 100% of the protected line. This is one of the primary reasons for setting the zone 1 reach to 80% (or 85%). This under reach setting of the instantaneous zone


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accommodates the magnitude error of the instrument transformer and the relay. Phase angle error : As we had seen in table 1 & 2, the instrument transformers also introduce phase angle error. This phase angle error can result in the relay measuring a different fault angle from the actual.

Fig. 7 :Error in measured impedance due to phase error

In this case shown, the actual fault point on the impedance plane is represented by “h”. Due to a phase error θe in measurement, the relay sees the fault at point “b”. This is again a case of relay overreaching. What is shown in this case is a fault at 100% of the line and it being seen as a fault at 80% (zone 1 boundary). From the figure we can comprehend that if the resistive setting of the relay was less than Rs, then this relay would not have seen this fault. We can mathematically derive the limiting value for RS as a function of the phase angle error θe, Line impedance (ZL) and Zone 1 setting.(ZS)


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that will ensure that the relay will not overreach beyond 100% of the line. From figure 7 we can write down the following relationship; XS = ZS Sinθ XL = ZL Sinθ θe = θf - θm Length “ob’ = length “oh” = Z Length “ob” can be written as Z=

(Rs + ZsCosθ )2 + (ZsSinθ )2

(5)

The condition to ensure that the relay does not overreach can be written as; ZSinθ F − ZSinθ m < X L − X S Or, Sinθ F − Sinθ m <

XL − XS Z

(6)

Substituting the value of Z and θf in the above equation, we get; Sin(θ m + θ e ) − Sinθ m <

XL − XS

(Rs + ZsCosθ )2 + (ZsSinθ )2

We can further simplify this equation by substituting the value of ZSSinθ = XS, and we get;

Sin(θ m + θ e ) − Sinθ m <

XL −1 Xs 2

(7)

⎛ Rs ⎞ + Cotθ ⎟ + 1 ⎜ ⎝ Xs ⎠

For a given phase angle error θe, we can find the maximum value of Rs/Xs, that will satisfy the condition (7), this will be the maximum allowed ratio of the resistive reach setting for a given reactance setting. ©2006 Protection Engineering And Research Laboratories

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It can be seen that the value of XL/XS, which is the inverse of the per unit zone 1 setting and the characteristic angle θ also determines the maximum Rs/Xs ratio. The figure 8 below plots shows the maximum phase angle error a given Rs/Xs ratio can tolerate. This figure is shown for a zone 1 setting of 80% and angle setting of 75°. As we can see that with a Rs/Xs ratio of 8, the relay will not overreach beyond the protected line for a phase angle error upto 1.75°. When the Rs/Xs ratio is increased to 10 then the setting can accommodate only 1.4° phase error.

Fig. 8 : Maximum Phase angle error accommodated for different Rs/Xs ratio Z1=80%

Figure 9 shows the same plot for a zone 1 setting of 85%. Comparing this with figure 8, we see that the allowed phase angle errors are lesser in this case. In other words to accommodate a phase angle error of 1.75°, we could have a Rs/Xs ratio of 8 if the zone 1 setting is 80%, whereas the ratio can only be about 5 if the zone 1 setting is 85%.


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Fig. 9 : Maximum Phase angle error accommodated for different Rs/Xs ratio Z1=85%

We can summarize the above discussion as follows

> It is desirable to set the resistive reach as high as possible to cover the worst case of fault resistance and infeeds > The limit on the resistive reach is imposed by the errors in measurement due to remote infeed, CT/PT errors and relay errors. > For long lines the resistance reach limiting factor would be the load impedance > For short lines the measurement errors would be the deciding factor for the resistive reach setting. Usually every manufacturer suggests a safe R/X ratio for the quadrilateral characteristics. This value would have been proposed taking the possible combination of instrument transformer and relay errors.


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Resistive Reach Setting of QUAD Relays

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