Electromagnetic Protection (PART III)

LENDI INSTITUTE OF ENGINEERING AND TECHNOLOGY
Jonnada, Andhra Pradesh- 535005
UNIT -II
Electromagnetic Protection (PART III)
Presented by,
Dr. Rohit Babu, Associate Professor
Department of Electrical and Electronics Engineering

LENDI INSTITUTE OF ENGINEERING AND TECHNOLOGY
Jonnada, Andhra Pradesh- 535005
(Part 1) Relay connection – Balanced beam type attracted armature relay -
induction disc and induction cup relays–Torque equation – (Part 2) Relays
classification–Instantaneous– DMT and IDMT types– Applications of relays:
Over current and under voltage relays– Directional relays– Differential
relays and percentage differential relays– (Part 3) Universal torque
equation– Distance relays: Impedance– Reactance– Mho and offset mho
relays– Characteristics of distance relays and comparison.

Universal torque equation
• The universal torque equation explains the working of an electrical relay.
• The relay has some arrangement of electromagnetic.
• These electromagnetic consist current and voltage windings.
• The current through the winding produces magnetic flux.
• And the torque is produced by the interaction of the flux of the same winding or between the flux
of both the windings.
If both the current and voltage windings are used, the torque developed by the interaction between
the fluxes is given by the equation

where, θ is the angle between V and I and the τ is the relay maximum torque angle.
If the relay has current, voltage and the torque angle, the torque will be developed, and it will be
given as
where, K1, K2, K3 are the tap setting or constant of V and I. The K4 is the mechanical restraint due
to spring or gravity.
For example – In over current relay the K2 = K3= 0 because of the absence of the voltage windings.
The torque equation becomes

The negative sign attributes to K4 because the spring produces restraining torque.
Similarly, for directional relay K1 = K2 = 0 and the developed torque will be given as

Impedance Type Distance Relay
• The relay whose working depends on the distance between the impedance of the faulty section
and the position on which relay installed is known as the impedance relay or distance relay.
• It is a voltage controlled equipment.
• The relay measures the impedance of the faulty point, if the impedance is less than the
impedance of the relay setting, it gives the tripping command to the circuit breaker for closing
their contacts.

Principle of Operation of Impedance Relay
• In the normal operating condition, the
value of the line voltage is more than
the current.
• But when the fault occurs on the line
the magnitude of the current rises and
the voltage becomes less.
• The line current is inversely
proportional to the impedance of the
transmission line.

The torque equation of the relay is shown in the figure
The -K3 is the spring effect of the relay.
The V and I are the value of the voltage and current.
When the relay is in normal operating condition, then the net torque of the relay becomes zero.

If the spring control effect becomes neglected, the equation becomes

Operating Characteristic of an Impedance Relay
• The operating characteristic of the impedance relay is
shown in the figure.
• The positive torque region of the impedance relay is
above the operating characteristic line.
• In positive torque region, the impedance of the line is
more than the impedance of the faulty section.

Operating Characteristic of an Impedance Relay
• The impedance of the line is represented by the
radius of the circle.
• The phase angle between the X and R axis
represents the position of the vector.

Electromagnetic Type Impedance Relay
• In such type of relay, the torque is induced by the
electromagnetic action on the voltage and current.
• These torques are compared. Consider the circuit of
the electromagnetic type impedance relay.
• The solenoid B is excited by the voltage supplied of
the PT.
• This voltage develops the torque in the clockwise
direction, and it pulls the plunger P2 in the
downward direction.
• The spring connects to the plunger P2 apply the
restraining force on it.
• This spring generates the mechanical torque in the
clockwise direction.

The pull of the solenoid A, i.e., (current element) is proportional to I2 and that due to solenoid B
(voltage element) to V2. Consequently, the relay will operate when
The value of the constants k1 and k2 depend on the ampere-turns of the two solenoids, and the ratios
of the instrument transformers.

• The y-axis shows the operating time of the relay and
the X-axis represents their impedances.
• The operating time of the relay remains constants.

Induction Type Impedance Relay
• The circuit diagram of the induction type
impedance relay is shown in the figure below.
• This relay consists current and voltage
element.
• The relay has an aluminium disc, which is
rotating between the electromagnets.

Induction Type Impedance Relay
• In normal operating conditions the force exerted on the
armature is more than the induction element which
keeps the trip contacts open.
• When the fault occurs in the system, then the
aluminium disc starts rotating, and their rotation is
directly proportional to the current of the
electromagnet.
• The rotation of the disc-wound the spring.

Time-Characteristic of High-Speed Type Impedance Relay
The figure below shows that the relay does not operate for
the value more than the 100 percent pickup value.

Drawbacks of Impedance Relay
1. It gives the response on both the side of the CT and PT. Thus, it becomes difficult for the breaker
to determine whether the fault is external or internal.
2. The relay is easily affected by the arc resistance of the line.
3. It is very sensitive to the power swing. The powerful wings generate the faults on the line
because of which the impedances of the line vary.

Reactance Relay
• The reactance relay is a high-speed relay.
• This relay consists of two elements an overcurrent element and a current-voltage directional
element.
• The current element developed positive torque and a current-voltage developed directional
element which opposes the current element depending on the phase angle between current and
voltage.

Construction of Reactance Relay
• A typical reactance relay using the induction cup
structure is shown in the figure.
• The operating torque will be proportional to the square
of the current while the restraining torque will be
proportional to VI cos (Θ – 90°).
• The desired maximum torque angle is obtained with
the help of resistance-capacitance circuits, as illustrated
in the figure.
• If the control effect is indicated by –k3, the torque
equation becomes

Construction of Reactance Relay
where Θ, is defined as positive when I lag behind V. At the balance point net torque is zero, and
hence
The spring control effect is neglected in
the above equation, i.e., K3 = 0.

Operating Characteristic of Reactance Relay
The operating characteristic of a reactance relay is
shown in the figure.
X is the reactance of the protected line between the
relay location and the fault point, and R is the
resistance component of the impedance.
If the value of τ, in the general torque equation,
expressed below is made any other 90º, a straight line
characteristic will still be obtained, but it will not be
parallel to R-axis.
Such a relay is called an angle impedance relay.

Mho and Offset Mho Relays
A mho Relay is a high-speed relay and is also known as
the admittance relay.
In this relay operating torque is obtained by the volt-
amperes element and the controlling element is developed
due to the voltage element.
It means a mho relay is a voltage controlled directional
relay.
If the spring controlling effect is indicated by –K3, the
torque equation becomes,

If the spring controlled effect is neglected i.e., K3 = 0.

Generalised Mathematical Expression for Distance Relays
• A generalised mathematical expression for the
operating conditions of mho, offset mho and
impedance relays can be derived as follows.
• The derivation of this expression is based on the
operating condition of the offset mho relay having a
positive offset.
The radius of this circle is
(a) Offset mho relay with positive offset

where, Zr = Rr + jXr = Impedance of the protected line section.
and Zo = Ro + jXo = Impedance by which the mho circle is offset.
The centre of the mho circle is offset from the origin by
If Z (= R + j X) is the impedance seen by the relay, then the operating condition for the offset mho
relay, shown in Fig. (a), is given by

Rr, Ro, Xr and Xo are constants for a particular characteristic and hence the above expression can be
written in the generalise form as
where, the constants K1, K2 and K3 are given by
(1)
(2)

• Equation (1) is the generalised expression for the offset mho, mho and impedance relays.
• The values of K1, K2 and K3 in the generalised expression are constant for a particular characteristic
and different for different characteristics.
• Substituting the proper values of constants K1, K2 and K3 the desired mho, offset mho or
impedance characteristic can be realised.
• The values of K1, K2 and K3 for different characteristics are computed as follows.

i. For offset mho characteristic having negative offset as
shown in Fig. (b), the negative values of Ro and Xo are
used in computation of K1, K2 and K3 using Eq. (2).
(b) Offset mho relay with negative offset

ii. For mho characteristic as shown in Fig. (c), Ro and Xo
are reduced to zero, and consequently the values of
K1, K2 and K3 obtained from Eq. (2) are as follows.
(c) Mho relay
iii. For impedance characteristic, the displacement of the
centre of the circle from the origin is zero
or (Ro + jXo) = – (Rr + jXr)
Therefore, Ro = – Rr and Xo = – Xr.
Then from Eq. (2), the values of K1, K2 and K3 for impedance characteristic are as follows.

Consequently, the operating conditions for the impedance relay becomes
where, ‘r’ is the radius of the circle. Therefore, a offset mho, mho or impedance characteristic can
easily be realised by using the generalised Eq. (1) and substituting the appropriate values of K1, K2
and K3 for the desired characteristic.

Operating Characteristic of Mho Relay
(c) Mho relay
• The characteristic of a mho relay on the impedance (R – X)
diagram is a circle passing through the origin, as shown in Fig.
(c).
• The mho characteristic, occupying the least area on the R – X
diagram is least affected by power surges which remain for
longer periods in case of long lines.
• Therefore, a mho relay is best suited for the protection of long
transmission lines against phase faults.

Offset mho relays are shown in Fig. (a) and (b) are used for zone III in
a three-zone protective scheme employing mho relays for zones I and
II for the protection of power transmission lines against phase faults.
The scheme is shown in Fig. 12.35(a). For long
transmission lines, mho and offset mho characteristics, as
shown in Fig. 12.35(b) are used to discriminate between
loads and faults. An offset mho characteristic with
negative offset has more tolerance to arc resistance. By
offsetting the III zone mho characteristic to overlap the
origin, it can also be used for power swing blocking.

• The scheme is shown in Fig. (a.1). For long transmission
lines, mho and offset mho characteristics, as shown in
Fig. (b.1) are used to discriminate between loads and
faults.
(b.1) Mho and offset mho relays for long lines
(a.1) Mho and offset mho relays for transmission lines

The tripping area of a mho characteristic can be restricted by two overlapping mho characteristics
as shown in Fig. (a.2) and (b.2).
(b.2)(a.2)
(a.2) Restricted mho passing through origin, (b.2) Restricted offset mho relay

Eight most important distance relay characteristics
Since many traditional relays are still in service and since some numerical relays emulate the
techniques of the traditional relays, a brief review of impedance comparators is justified.
1. Amplitude and phase comparison
2. Plain impedance characteristic
3. Self-polarised Mho relay
4. Offset Mho/Lenticular characteristics
5. Fully Cross-Polarised Mho characteristic
6. Partially Cross-Polarised Mho characteristic
7. Quadrilateral characteristic
8. Protection against power swings

Since many traditional relays are still in service and since some numerical relays emulate the
techniques of the traditional relays, a brief review of impedance comparators is justified.
3. Self-polarised Mho relay
4. Offset Mho/Lenticular characteristics
5. Fully Cross-Polarised Mho characteristic
6. Partially Cross-Polarised Mho characteristic
7. Quadrilateral characteristic
8. Protection against power swings

Relay measuring elements whose functionality is based on the comparison of two independent
quantities are essentially either amplitude or phase comparators.
For the impedance elements of a distance relay, the quantities being compared are the voltage and
current measured by the relay.
This characteristic takes no account of the phase angle between the current and the voltage applied to
it.
For this reason its impedance characteristic when plotted on an R/X diagram is a circle with its centre
at the origin of the coordinates and of radius equal to its setting in ohms.
Operation occurs for all impedance values less than the setting, that is, for all points within the circle.

Figure 1 – Plain impedance relay
characteristic
A relay using this characteristic has three
important disadvantages:
i. It is non-directional.
ii. It has non-uniform fault resistance coverage
iii. It is susceptible to power swings and heavy loading of
a long line.

Figure 2 – Combined directional and
impedance relays

3. Self-Polarised Mho Relay
The mho impedance element is generally known as such because its characteristic is a straight line
on an admittance diagram.
The characteristic of a mho impedance element, when plotted on an R/X diagram, is a circle whose
circumference passes through the origin, as illustrated in Figures.
Figure 3 – Mho relay characteristic

The self-polarised mho characteristic can be obtained using a phase comparator circuit which
compares input signals S2 and S1 and operates whenever S2 lags S1 by between 90° and 270° as
shown in the voltage diagram of Figure (a).
The two input signals are:
S2 = V-IZn
S1 = V
where:
•V = fault voltage from VT secondary
•I = fault current from CT secondary
•Zn = impedance setting of the zone

The characteristic of Figure (a) can be converted to the impedance plane of Figure (b) by dividing
each voltage by I.
The impedance reach varies with fault angle.
when setting the relay, the difference between the line
angle θ and the relay characteristic angle Ø must be
known. The resulting characteristic is shown in Figure
(a), (b) and (c) where GL corresponds to the length of
the line to be protected.
With Ø set less than θ, the actual amount of line
protected, AB, would be equal to the relay setting value
AQ multiplied by cosine (θ−Ø).
Therefore the required relay setting AQ is given by:
AQ = AB / cos(θ−Ø)

Due to the physical nature of an arc, there is a non-linear relationship between arc voltage and arc
current, which results in a non-linear resistance. Using the empirical formula derived by A.R. van
C. Warrington, the approximate value of arc resistance can be assessed as:
Ra = L × 28,710 / I1.4
where:
•Ra = arc resistence (ohms)
•L = length of arc (metres)
•I = arc current (A)

4. Offset Mho / Lenticular Characteristics
If current bias is employed, the mho characteristic is shifted to embrace the origin, so that the
measuring element can operate for close-up faults in both the forward and the reverse directions.
The offset mho relay has two main applications:
4.1 Third Zone and Busbar Back-Up Zone
In this application it is used in conjunction with mho measuring units as a fault detector and/or
Zone 3 measuring unit.

So, with the reverse reach arranged to extend into the busbar zone, as shown in Figure 4, it will
provide back-up protection for busbar faults.
Figure 4 – Typical applications for the offset mho relay

4.2 Carrier Starting Unit in Distance Schemes With Carrier Blocking
If the offset mho unit is used for starting carrier signaling, it is arranged as shown in Figure 4 above.
The carrier is transmitted if the fault is external to the protected line but inside the reach of the offset
mho relay, to prevent accelerated tripping of the second or third zone relay at the remote station.
4.3 Application of Lenticular Characteristic
There is a danger that the offset mho relay shown in Figure 4 may operate under maximum load
transfer conditions if Zone 3 of the relay has a large reach setting. A large Zone 3 reach may be
required to provide remote back-up protection for faults on the adjacent feeder.

Figure 5 shows how the lenticular characteristic
can tolerate much higher degrees of line
loading than offset mho and plain impedance
characteristics.
Modern numerical relays typically do not use
lenticular characteristic shaping, but instead
use load encroachment (load
blinder) detection.
This allows a full mho characteristic to be used,
but with tripping prevented in the region of the
impedance plane known to be frequented by
load (ZA-ZB-ZC-ZD).

5. Fully Cross-Polarised Mho Characteristic
• By the use of a phase voltage memory system, that provides several cycles of pre-fault voltage
reference during a fault, the cross-polarisation technique is also effective for close-up three-
phase faults.
• For this type of fault, no healthy phase voltage reference is available.
• Modern digital or numerical systems can offer a synchronous phase reference for variations in
power system frequency before or even during a fault.
• The amount of the resistive coverage offered by the mho circle is directly related to the
forward reach setting.

This effect is illustrated in Figure 6, for the case
where a mho element has 100% cross-
polarisation. With cross-polarisation from the
healthy phase(s) or from a memory system, the
mho resistive expansion will occur during
a balanced three-phase fault as well as for
unbalanced faults.
Figure 6 – Fully cross-polarised mho relay characteristic
with variations of ZS/ZL ratio
The degree of resistive reach
enhancement depends on the ratio of source
impedance to relay reach (impedance)
setting as can be deduced by reference to
Figure 6.

• It must be emphasised that the apparent extension of a
fully cross-polarised impedance characteristic into the
negative reactance quadrants of Figure 7 does not
imply that there would be operation for reverse faults.
• With cross-polarisation, the relay characteristic
expands to encompass the origin of the impedance
diagram for forward faults only.
Figure 7 – Illustration of improvement in relay resistive coverage
for fully cross-polarised characteristic

6. Partially Cross-Polarised Mho Characteristic
Figure 8 – Partially cross-polarised characteristic with
‘shield’ shape
Where a reliable, independent method of faulted phase selection is not provided, a modern non-
switched distance relay may only employ a relatively small percentage of cross polarisation.

7. Quadrilateral Characteristic
• This form of polygonal impedance characteristic is
shown in Figure 9. The characteristic is provided
with forward reach and resistive reach settings that
are independently adjustable. It therefore provides
better resistive coverage than any mho-type
characteristic for short lines.
• This is especially true for earth fault impedance
measurement, where the arc resistances and fault
resistance to earth contribute to the highest values of
fault resistance. Figure 9 – Quadrilateral characteristic

8. Protection against Power Swings – Use of the Ohm Characteristic
During severe power swing conditions from which a system is unlikely to recover, stability might
only be regained if the swinging sources are separated.
Figure 10 – Application of out-of-step tripping
relay characteristic
Ohm impedance characteristics are applied along the
forward and reverse resistance axes of the R/X diagram
and their operating boundaries are set to be parallel to the
protected line impedance vector, as shown in Figure 10.

Thank you

Electromagnetic Protection (PART III)

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