Distance Relaying

Distance relaying is a method of using the calculated impedance to locate the fault. There are two basic types of distance relaying - phase and ground. Often, distance relaying is used in a communication assisted scheme to provide high speed tripping.

## **Phase distance relaying**

This type of relaying provides protection against any type of phase fault. (phase to phase,3 phase, and phase to phase to ground) Phase distance relays use phase quantities, VLL/ILL, to carry out their impedance calculations. This quantity provides the impedance to the fault as shown below:

ZT = The total impedance from phase A to phase C. The whole loop.

VA = VC - IC\*ZT

VC = VA - IA\*ZT

VA - VC = (VC-VA) - (IC-IA)\*ZT

2\*(VA-VC) = -(IC-IA)\*ZT

2\*(VA-VC) = (IA-IC)\*ZT

2\*(VA-VC)/(IA-IC) = ZT

VAC/IAC = ZT/2 >>>>> half the total impedance is the impedance just to the fault

Demonstration of phase relaying and phase to phase quantities being independent of zero sequence:

a = 1 <120 deg

VA = V0 + V1 + V2

IA = I0 + I1 + I2

VC = V0 + a\*V1 +a^2\*V2

IC =  I0 + a\*IC + a^2\*I2

VAC = VA - VC = V1-a\*V1 + V2 - a^2\*V2  >>>>> Line to line quanities have no zero sequence dependency

IAC = IA - IC = I1 - a\*I1 + I2 - a^2\*I2

VAC/IAC = (V1-a\*V1 + V2 - a^2\*V2)/( I1 - a\*I1 + I2 - a^2\*I2) = ZAC  >>>>  This will hold true for ZCB and ZBA as well.  This shows mathematically that phase distance and line to line quanties are void of zero sequence dependencies. A ground fault could cause the phase distance relaying to operate with its positive and negative quantities but it will be much less sensitive than a ground distance setting with the same reach.

Since the quantities used in the calculation are all phase to phase quantities, the phase distance calculation is immune to any zero sequence voltages or currents that may be present. Likewise, since positive and negative sequence quantities are not blocked by certain transformer configurations and groundings like some do with zero sequence, phase distance protection will see through transformers that have open zero sequence impedance. (delta-delta, delta-wye, ungrounded wye-ungrounded wye).

One of the main benefits that you have with phase distance relaying over overcurrent protection is that since it is operating on a calculated impedance, it is very independent of what is happening elsewhere in the system. Fault currents can change drastically depending on the system configuration and system dispatch. The pickups and set points of the overcurrent elements may need to be set more conservatively due to them needing to operating correctly for all scenarios. Aside from infeed and weak source, phase distance relaying on a line will be relatively independent of what is happening elsewhere in the system. Phase distance relaying will be will be impacted by fault current infeed from another line or any inline generation. The result of this is that the relay will calculate the fault to be further out than what it actually is.

## **Ground distance relaying**

This type of protection offers many of the same benefits that phase distance relaying provides. Since the reach is based on an impedance calculation, it is more independent of what is happening elsewhere in the system than overcurrent. The ground distance element for SEL relays is calculated as follows:

ZA = VA/(IA +3\*k\*I0)

k is an adjustable quantity that allows you to change the ground distance calculation's sensitivity to zero sequence current. Normally, the k value is set to 1<0. For situations where mutual coupling is not an issue, the reach of the ground distance element with k= (Z0-Z1)/Z1 will be the same as for phase distance elements. This makes it convenient to set and compare the reaches of the ground distance and phase distance elements. With a 10 ohm transmission line, if the phase distance and ground distance elements were set to 8 ohms, in both cases they would reach about 80% of the line. The zero sequence impedance of a transmission line will usually be about three time larger (3\*Z1 = Z0) than its positive and negative sequence impedances and is dependent on the spacing of the transmission lines.

One downside of ground distance protection in comparison to phase distance is that it is susceptible to error caused by mutual coupling. When two transmission lines run near each other, they are capable of generating zero sequence voltages and currents in each other. This is an issue with zero sequence and not positive and negative sequence components due to the fields canceling each to a large degree. Zero sequence is present in all three phases as having the same angle and magnitude so there will be no cancellation of their magnetic fields.

The effect that mutual coupling will have on the ground distance calculation is similar to the effect that it has on ground overcurrent protect. The increase or decrease in the amount of zero sequence current to the fault as the result of the mutual coupling will have the effect of increasing or decreasing the distance of the ground distance calculated point.  If two lines are parallel and the fault currents are in the same direction,  the magnetic fields will add together to increase the impedence the relay sees to the fault.  If two parallel lines have current in opposite directions, there will be cancelling of the magnetic fields and the impedance that the relay calculates to the fault will decrease.  The k value ,which is a complex component with magnitude and angle, can be used to increase or decrease the calculations sensitivity to zero sequence current. If the affects of mutual coupling appear to be an issue, it might make sense to reduce the calculation's dependence on zero sequence current and the effect mutual coupling has on the ground distance calculation.

Just like with ground overcurrent,  ground distance protection has immunity to loads (unbalanced loads that are not segregated from the zero sequence network by a transformer delta can cause zero sequence currents and all phase to phase connected loads only draw positive and negative sequence components) and generation and has difficulty seeing through transformers (delta-delta, delta-wye, ungrounded wye-ungrounded wye) who's configurations block zero sequence currents.  Customer connections often have a zero sequence blocking transformer connection. Without contributing zero sequence current, ground distance relaying that is segregated by a zero sequence transformer will be very insensitive to customer ground faults.

Another downside that ground distance protection has under phase distance is that it is more dependent on what is happening in the rest of the system. Specifically, how close the fault is to a zero sequence source.  If two ground distance relays are looking into a line and one side has a much stronger ground source,  that side will provide most and maybe nearly all of the I0 current.  The effect that this can have is that on a long line, it might be difficult for ground distance relaying on the weakly grounded side to see the fault due to having very little I0 current for its calculation. The weak side would have to base its ground distance calculation mostly on just its positive and negative sequence components

VA = (V0 + V1 + V2), IA = (I0 + I1 + I2)

ZA = VA/(IA + 3\*k\*I0)  =   (V0 + V1 + V2) / (I0 + I1 + I2 +3\*k\*I0) = (V0 + V1 + V2)/ (I1 + I2 + (3\*K+1)\*I0)

For small I0:

ZA = VA/(IA + k\*I0) = (V0 + V1 + V2)/(I1+I2).

The denominator is smaller due to small I0 and the calculated impedance will be larger than it should. Ground overcurrent protection would have this same issue with picking up the fault. The fault might be cleared with sequential tripping, the strongly ground side trips out and then the weakly grounded side would contribute zero sequence current and pickup.

Just like how phase distance relaying was impacted by infeed, ground distance relaying will be impacted by infeed from other lines and inline ground sources and generation. Anything that infeeds any postive, negative, or zero sequence currents during a SLG fault (all sequence current phasors at similar angles) will cause the impedance calculation to be larger than it should.

## **Zones and** **Communication Schemes**

The reach of the zones set for ground and phase distance relaying are dependent the type of communication scheme involved. In relaying, there is a balance that is made between speed, security, and dependability. There is no free lunch and prioritizing one comes at the expense of the others. The type of zone used in communication assisted schemes,overreaching or underreaching is one aspect which helps determine the security and dependability of the arrangement. Security is the relay's ability to guard against tripping for out of zone faults. Dependability is a relay's ability to consistently trip for in zone faults. Overreaching zones are biased towards dependability due to them covering the entire line with margin. However, since they overreach they may pickup for faults on the adjacent lines, hence lower security. In the case with DCB, the block signal prevents overtripping from occurring for a fault on an adjacent line but this requires communications to operate correctly. For undereaching zones, there is a bias towards security due to the relays inability to see an out of line fault. The zone's limited reach prevents overtripping without depending on communications.

Margin needs to be padded on top of both, overreaching and underreaching zones. A typical instantaneous zone 1 or POTT zone reach might be 75-80% of the line. Margin is need to prevent any form of error (instrument, modeling, untransposed line error ect) from causing the zone to pick up for faults on the adjacent line. Likewise, overreaching zones may have margin included ,20%+, to ensure that the entire line is covered by the zone.

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### Fig 1.  Overeaching Zones

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### Fig 2.  Undereaching Zones

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### **Permissive Overreaching Transfer Trip (POTT)**

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### **Directional Undereaching Transfer Trip (DUTT)**

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### **Permissive Undereaching Transfer Trip (PUTT)**

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=== **Direction Comparison Undereaching Blocking (DCUB)** ===