This document discusses distance protection relay types and characteristics. It begins by explaining the principles of comparison-type distance relays using phase and impedance comparisons. It then describes several common relay characteristics including impedance, ohm, reactance, mho, and offset mho. The document also discusses power swings and loss of synchronism, explaining how to represent these phenomena on an R-X diagram using system and relay impedances.

1. ECNG 6503 -4
Advanced Power Systems Practice
Lecturer
Prof Chandrabhan Sharma
University of the West Indies
Trinidad and Tobago

2. Contents
1. Distance Protection : Relay Types
2. Power Swings and Loss of Synchronism
3. Out of Step Blocking and Tripping

3. DISTANCE PROTECTION
Relay Comparator Characteristics
Comparison of Mixed Signals
Phase comparison
Using the input voltage, VL as reference, and the current IL -ØL

4. ∴ Inputs, to comparator, S1 and S2 are given by:
S1= k1 VL + ƵR1 ILө1- øL
S2= k2 VL + ƵR2 IL ө2- øL
where k1 and k2 are real and ƵR1 ө1 and ƵR2 ө2 are replica
impedances
Expressing: S1= a + j b
S2 = c + j d
From which: a = k1VL+ ƵR1 IL cos (ө1-øL)
b= ƵR1 IL sin (ө1-øL)
c = k2VL+ ƵR2 IL cos (ө2-øL)
d= ƵR2 IL sin (ө2-øL)

5. Let the relay operate for the condition
-β≤≤β
∴ the condition for the tripping is true for cos  ≥ cos β
Squaring and for operation we have:
(ac + bd)2 ≥ cos 2 β [(ac + bd)2+(bc - ad)2]

6.  (ac + bd)2 (1-cos2β) ≥ cos2β (bc - ad)2
From which we have
(ac + bd)2 ≥ cot2β (bc - ad)2
But (ac + bd)= k1k2VL2+ ƵR1 ƵR2IL2cos (ө1- ө2)+ k1VLƵR2ILcos (ө2- øL)+ k2VL ƵR1ILcos (ө1- øL)
And (bc - ad) = -k1VLƵR2ILsin (ө2- øL)+ k2VL ƵR1ILsin (ө1- øL) + ƵR1 ƵR2IL2sin (ө1- ө2)

7. Operation occurs when:
k1k2ƵL2+ƵR1 ƵR2cos (ө1- ө2) +k1ƵL ƵR2cos (ө1- øL)+ k2ƵL ƵR1cos (ө1- øL)
≥ cot β [k2ƵL ƵR1sin (ө1- øL)+ ƵR1 ƵR2sin (ө1- ө2) - k1ƵL ƵR2sin (ө2 - øL)]
Letting β = /2 for comparison
 cot β = 0
From which we have the threshold of operation being:-
„A‟  * k1k2ƵL2+ ƵR1 ƵR2cos (ө1- ө2) + ƵL[k1ƵR2cos (ө2- øL)+ k2ƵR1cos(ө1- øL)] ≥ 0
Which represents the general threshold conditions for –90 ≤  ≤ 90.
By manipulation of the above condition, several special characteristics
may be obtained.

8. 1. Impedance Characteristics (Plain)
Let k = k2 = - k1
ө1 = ө2 = ө
And ƵR1= ƵR2= ƵRө
Then the „inputs‟ become:
S1= - kVL + ƵRILө- øL
S2= k VL + ƵRILө- øL
Substitute initial conditions into general equation „A‟, we have for
threshold:
-k2 ƵL2 + ƵR2 ≥ 0

9. Tripping occurs anytime the apparent impedance falls within the circle.
2. Ohm and Reactance Characteristics
Let k1= - k
k2= 0
ƵR1= ƵR2=ƵRө
∴the inputs become: S1= -k VL + ƵRILө - øL
S2 = ƵRILө - øL

10. Sub. into A we have:
ƵR2= k ƵL ƵRcos (ө - øL) ≥ 0
But ƵL cos øL = RL and ƵL sin øL=XL
∴Relationship becomes:

11. ∴The characteristic on the RL& XL diagram is a straight line:
Special Case :- Let ө= /2 we obtain the Reactance Relay

12. 3) MHO and Offset MHO
MHO  Angle Impedance Relay
Let: k = k2 = - k1 and ƵR2= 0
∴ Inputs S1= -kVL+ ƵR ILө- øL
S2= kVL
Sub into general relationship „A‟ we obtain:
-k2 ƵL2 + kƵRƵLcos (ө- øL) ≥ 0
Or YL cos (ө- øL) ≥ k YR  G/B plane straight line
YL (cos ө cos øL + sin ө sin øL) ≥ k YR
But YL cos øL = G  conductance
YL sin øL = B  admittance
∴ G cos ө + B sin ө ≥ k YR

13. As can be seen, the mho characteristic in the R/X plane is simply
an offset impedance characteristic and in the G/B plane, it is the
inverse of the ohm characteristic(hence MHO).
They are presently referred to as simply a subset of the
impedance relays i.e. angle impedance relay.

14. 4) Off-set Mho
In this case, let:
k2 = k = - k1 and ө1 = ө2 = ө
Then the inputs become:
S1= -kVL+ ƵR1 ILө- øL
S2= -kVL+ ƵR2 ILө- øL
Sub into „A‟
-k2ƵL2+ ƵR1 ƵR2+ k ƵL (ƵR1 - ƵR2) cos (ө- øL) ≥ 0 [where ƵL= ƵL ≠ ƵL 
øL]
[or ƵL= {XL2 + RL2}]
∴dividing across by – k2

15. This is a circle with centre (-g,-f) at

16. Comparator is now an AMPLITUDE COMPARATOR
Let the criteria for operation be  S2  ≥  S1 
then c2 + d2 ≥ a2 + b2
or a2 + b2 - c2 - d2 ≤ 0 (threshold)
Substitute for a, b, c and d as given before, we have:
k12VL2 + ƵR12 IL2 cos2 (ө1 – øL) + 2k1ƵR1VLILcos(ө1 – øL) - k22VL2
- ƵR22 IL2 cos2 (ө2 – øL) - 2k2 ƵR2 VL IL cos (ө2 – øL) + ƵR12 IL2 sin2 (ө1 – øL)
- ƵR22 IL2 sin2 (ө2 – øL) ≤ 0
Rearranging, we obtain:
(k12 - k22) VL2 + 2VLIL [k1ƵR1cos(ө1 – øL) - k2 ƵR2 cos (ө2 – øL)] + (ƵR12 - ƵR22) IL2 ≤ 0

17. Setting ƵL = VL/IL we obtain:
*B
(k12- k22) ƵL2 + 2ƵL[ƵR1 k1 cos (ө1– øL) - k2 ƵR2 cos (ө2– øL)] + ƵR12- ƵR22 ≤ 0
Again following the procedure as before, the equivalent
characteristics may be obtained.
Example: Circular Impedance Characteristics
Let: k2= 0 , k1= - k
Then the inputs become:
S1= - kVL + ƵR1ILө1– øL
S2 = ƵR2ILө2– øL

18. Sub into equation “B” we obtain:
k12 ƵL2 - 2k ƵLƵR2 cos (ө1– øL) + ƵR12 - ƵR22 ≤ 0
But ƵL= (XL2+RL2), therefore equation becomes:
k2 XL2 + k2 RL2 –2k ƵLƵR1(cos ө1 cos øL+ sin ө1 sin øL) + ƵR12- ƵR22 ≤ 0
Dividing through by k and rearranging

19. In the R/X plane, this is the equation of a circle of radius

20. a) If in equation (1) we let ƵR1= 0

21. Let ƵR2 = ƵR1= ƵRө in equation (1)  Mho Characteristic

22. The Stepped Characteristic

23. Zone 1 reach is usually limited to about 80% of ƵAB to take into
account the indeterminate nature of the fault resistance (under-
reach).
Zone 2 will look at (ƵAB + 20-30% ƵBC). This provides backup for
Zone 1.
Zone 3 will look at (ƵAB + ƵBC) and hence provides back-up for
both Zones 1 & 2.
Usually the Zone 3 relay is used as a starter for Zone 1 and Zone
2 protection.

24. Voltages and Current Supplied to Distance
Protection
In conventional 3-stage distance-protection schemes, it is usual
to use separate sets of relays for earth fault and phase-phase
fault impedance measurements.
Each phase is provided with a 3-stage earth-fault relay and each
pair of phases with a 3-stage phase-phase fault relay. This will
cater for all expected types of faults.
In practice, a single relay with two settings is often utilized for
Zone1 and Zone 2 relaying while another single relay is used for
Zone 3 and starting.
A distance relay measures p.p.s impedance of protected feeder
between the relaying point and the point of fault, irrespective of
the type of fault.

25. A. Earth Fault Compensation
Let the voltage to the relay = Vph
Let the current to the relay = Iph
∴ Ƶ = Vph/Iph= Ƶ1+ Ƶe (for earth fault)
Where Ƶ1 = +ve sequence impedance
Ƶe = earth fault impedance
∴ relay only sees +ve sequence impedance if earth fault
impedance (Ƶe) is zero.

26. Let k = Ƶe/ Ƶ1  Ƶ = Ƶ1(1 + k)
∴ for Ƶ= Ƶ1
It is necessary to increase the current in the ratio (Ƶ = V/I) by
(1+k)/1.
In practice this involves the use of earth fault compensating
current transformers with adjustable tappings for differing „k‟
values.

27. B. Phase Fault Compensation
In this case, the phase-phase fault relays are supplied with:
V = VBC (line) ; IBC= IB – IC (difference)
For phase to phase fault on B & C
IB+ IC= 0
∴ Ƶ = VBC/(IB-IC )= (VB-VC) /(IB-IC )

28.  IB= (a2 - a)I1 , IC = (a - a2) I1

29. Also EBC = -j√3 EAN = a2EA – a EA = (a2-a) EA

30. C. For 3ø fault
VAB= IA Ƶ1- IBƵ1= Ƶ1 (IA - IB)
Or VAB= √3 VA ; IAB = √3 IA
∴Phase-phase faults always see Ƶ1

31. Connection of relays for current used for
(a) Earth fault compensation
(b) Phase fault compensation

32. Superimposing Relay and System
Characteristics
Converting the system‟s impedance to the relay reference:
s-secondary
p-primary
To convert power onto the R/X diagram:
Where V = line to line voltage in volts
P = 3ø power supplied in Watts
Q = 3ø vars supplied in VARs

33. Power Swings and Loss of
Synchronism
The characteristic of a power swing is the same as the early stages
of loss of synchronism, and hence, the loss of synchronism
characteristic can describe both phenomena.

36. For the particular case, the point P is seen to be a point on the loss of
synchronism characteristic.
The loss of synchronism characteristics lies on the ⊥ bisector of AB,
with the origin being the location of the relay.The loss of
synchronism characteristic has been expressed in terms of ratio of
phase voltages to phase currents. Under balanced conditions which
exists during loss of synchronism, this is the same ratio which
would be used to describe 3ø short-circuit on the system.
Therefore it is permissible to superimpose on the same R/X
diagram:
(1) Loss of synchronism characteristics
(2) 3ø short-circuit characteristics
(3) Distance relay characteristics

37. ∴ For a 3ø fault on B generator terminals, the relay would see
it as point X.
Similarly where the loss of synchronism characteristic intersects
ƵL, it would also represent a 3ø fault at that point.
This point is also called the „electrical center‟ or “impedance
center” of the system.
The point where the loss of synchronism characteristic
intersects AB (the total-impedance line) is reached when A
generator has advanced to 180 ̊ leading generator B
i.e.

38. The location of P, for various ө may be found graphically:
(for  EA  =  EB  i.e. n = 1 and  varies)

39. Special case: ө = 90 ̊
In this case, P lies on the circumference of a circle whose
diameter is AB.

40. General Case: n≠1 i.e. EA ≠ EB
Any characteristic may be obtained from the general formula:
By substituting the value of n and allowing ө to vary from 0 thru
360 ̊ we may be able to plot the required characteristic.
** All loss of synchronism characteristics are circles with their
centers on the total-impedance line AB or its extension.
For n=1  circle of infinite radius
Note: The loss of synchronism characteristics must pass through points
A & B and the centers lie on the ⊥ bisector of AB.

41. Loss of synchronism characteristics

42. Circle ABCDE is a special case where:
ө= and n – varies
For a particular n1 i.e. at C say we have:
From this relationship, one may easily construct the loss of
synchronism characteristic for any value of n.

43. With these two points one can draw a chord to the circle. The ⊥
bisector of these chords would intersect at the center of the
circle whose locus is for n=2.

44. For n >1 and Ƶ┬ = AB

45. Time – Distance Plot
Using three “Impedance” relays we can ensure complete protection
of our system.
The 1st zone gives instantaneous operation while the 2nd and 3rd
zones complete their trip ccts. via a time delay contact.

46. Types of Relays Used in 3 Zones
Protection
1. The Impedance Relay:
Composed of 3 impedance elements each adjusted for a
different ohmic reach.
The directional element controls the tripping circuits for all three
zones. ie. preventing tripping in the reverse direction. (Affected
by fault resistance)

47. 2. The 3-Step Reactance Relay
This consists of a reactance element which gives 1st and 2nd
zones protection and a mho element which doubles as the
starting unit and 3rd zone protection element. The contacts of
the mho (starting) unit and 1st and 2nd zones are in series so
that tripping is confined within the boundaries of the mho
element.
This prevents relay operation for faults in the reverse direction or
on load currents.

48. 3. The 3-Step MHO Relay
The relay is composed of 3 mho elements, each adjusted for a
different reach.

49. In a practical relay the 3rd zone may be reversed as shown below

50. 4. Out of Step Blocking Relays
a) Impedance Element

51. b) Off-set Mho Element

52. Out – Of- Step Blocking
As we have noted, the apparent impedance follow, a definite curve during
swing and out of step conditions. The particular curve being dependant on
the voltage ratios.

53. It is apparent that when the system is near 180˚separation angle,
apparent impedance is the same as the impedance to a fault on
the line.
How can a relay differentiate between a fault on the line and a transient
swing condition?

54. If the system is carrying an interchange load shown at P, a fault
at F results in a change of impedance from P to F in practically
„zero‟ time.
On the other hand, during the first few swing cycles for the
out-of-step condition, apparent impedance „drifts‟ through point
M (EA/ EB=1.0) at relatively „slow‟ speed.
Therefore if we set up the off set mho blocking element to
block the 1st and 2nd zones of the mho relay, the time required
for the impedance to change from a point outside the blocking
characteristic to any point within the shaded area exceeds a
predetermined minimum time.
In other words blocking would be realised if the blocking
element picks-up before the relay tripping elements.
Blocking is non-inhibited if both blocking and tripping elements
pick-up at the same time.

55. The blocking element characteristic must:
a) Surround the largest tripping element characteristic
which it must block.
b) The margin (shaded area) must be such that it
allows blocking for the fastest swings expected.
c) The margin must also be small as possible so as to
avoid unnecessary operation.

56. Out – Of- Step Tripping
The basic distinction of an out step condition occurs when the
system‟s apparent impedance as seen from particular location
changes from
a. A point to the right of the system impedance.
b. To a point on the system impedance line.
c. To a point on the left of this line.
Also the change in impedance is long compared to the change
in impedance due to a fault.
The task is to design a relay which recognises these distinctive
characteristics.
We can use two reactance elements, each having an angle of
maximum torque ⊥ to the system impedance line.

57. The “pick-up” setting would then determine the distance between
these characteristics and the system impedance line i.e., the amount of
“offset”.

58. Each reactance relay („A‟ and „B‟) has two contacts.
Contact 1  closed when apparent impedance to left of characteristic
Contact 2  closed when apparent impedance to right of characteristic
Assume that and out-of-step swing occurs which starts from
some load point „P‟ and progresses with machine A leading
machine B.

59. N.B. Overcurrent unit ensures that tripping only occurs when the swing
currents are at least of the same magnitude as load currents.

60. Given that each Aux relay has a pick-up time = 0.005 s
And each Aux relay has a drop-out time = 0.1 s
Except for X3 and X6 which have adjustable long time delay
drop out. (0.5 ∼ 3.0 s)
For the condition indicated A2 and B2 are closed initially and X1
is energised.
When the swing crossed the “B” element, B1 closes and B2
opens
 X2 energises and seals in.

61. As swing progresses over the “A” characteristic, A2 opens and A1
closes, X4 energises  X3 energises and seals.
X3 remains energised for the remainder of the slip cycle until
either the o/c relay drops out or the “A” characteristic is crossed
again.
A contact from X3 may be used for tripping.
X6 is useful for swings from the reverse direction. Therefore
operation only occurs for separation beyond 180˚.

62. Maximum Slip

63. Since X2 has a time delay = 0.005 s then for operation, swing must
remain in area for at least 0.005 s.
Let ∆  = angle through which the system moves from X1 – M – X1
i.e. ∆  = 2(180- )= 4(90- /2)
∴the max slip to permit relay operation is

64. But ∆ = 4(90- /2)