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It is noteworthy here that in electrical engineering, the term ‘impedance’ can be applied to resistance alone or reactance alone, or a combination of the two. In protective relaying terminology, however, an impedance relay has a characteristic that is different from that of a relay responding to any component of impedance and therefore, the “impedance relay” is very specific.

An impedance relay is a voltage restrained overcurrent relay. The relay measures impedance up to the point of fault and gives tripping command if this impedance is less than the relay setting Z. Relay setting Z is known as replica impedance and it is proportional to the set impedance i.e. impedance up to the reach of the relay. The relay monitors continuously the line current I through CT and the bus voltage V through PT and operates when the V/I ratio falls below the set value.

**Operation of an Impedance Relay: **

The principle of operation of an impedance relay is illustrated in Fig. 3.41. The voltage element of the relay is excited through a potential transformer (PT) from the line under protection and current element of the relay is excited from a current transformer (CT) in series with the line. The portion AB of the line is the protected zone. Under normal operating conditions, the impedance of the protected line is Z.

The relay is so designed that it closes its contacts whenever impedance of the protected section falls below the set value i.e., Z in this case.

Now assume that a fault occurs at point F_{1} in the protected zone. The impedance, is the ratio of the bus voltage and fault current (V/I), between the point where the relay is located and the point of fault will become less than Z and hence the relay operates. Should the fault occur beyond the protected zone (say at point F_{2}) the impedance will be more than Z and the relay contacts do not close.

**Operating Characteristic of an Impedance Relay:**

The impedance relay is a double actuating quantity relay and essentially consists of two elements—current-operated element and voltage-operated element. The current element produces a positive or pick-up torque while the voltage element develops a negative or reset torque. Taking spring control effect as – K_{3} the torque equation of the relay is –

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T = K_{1}l^{2} – K_{2} V^{2} – K_{3} …(3.19)

Where, V and I are the rms values of voltage and current respectively. At balance point, when the relay is on the verge of operating, the net torque is zero, and

It is customary to neglect the effect of control spring, since its effect is noticeable only at current magnitudes well below those normally encountered. Hence taking K_{3 }= 0, the relay torque equation becomes-

The operating characteristic in term of voltage V and current I is shown in Fig. 3.42, where the effect of control spring is shown as causing a noticeable bend in the characteristic only at the low-current end. For all practical purposes, the dash line, which represents a constant value of Z, may be considered the operating characteristic.

The relay will pick up for any combination of V and I represented by a point above the characteristic in the positive-torque region, or, in other words, for any value of impedance less than constant value represented by the operating characteristic. By adjustment, the slope of the operating characteristic can be changed so that the relay will respond to all values of impedance less than any desired upper limit.

The more convenient way of describing the operating characteristic of a distance relay is by means of ‘impedance diagram’ or R-X diagram, as illustrated in Fig. 3.43. The numerical value of the ratio of V to I is shown as the length of the radius vector, such as Z, and the phase angle θ between V and I determines the position of vector, as shown.

Since the operation of the impedance relay is practically or actually independent of the phase angle θ, the operating characteristic is a circle with its centre at the origin. Any value of impedance less than the radius of the circle will result in positive torque and any value of impedance greater that this radius will result in negative torque. The impedance relays normally used are high speed relays.

**Types of Impedance Relays:**

**1. Electromagnetic Type Impedance Relay: **

Such a relay is shown in Fig. 3.44 (a). In this relay two torques are produced by electromagnetic action of the voltage and current and these two torques are compared. The solenoid B is voltage excited from the secondary of the PT and develops a clockwise torque pulling the plunger P_{2} downward and tends to rotate the balance arm in the clockwise direction.

The spring acts as a restraining force and sets up a mechanical torque in the clockwise direction as illustrated. Another torque is developed by the solenoid A in the counter-clockwise direction which tends to pull the plunger P_{1} downwards. This solenoid is current excited from the secondary of CT which is connected to the line under protection. This torque is called the deflecting or pick-up torque.

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In normal operating conditions i.e., when there is no fault and equilibrium prevails, the balance arm is horizontal and the relay contacts are open. When a fault occurs in the protected zone the current in the CT primary goes up and so in the relay coil. Thus torque developed by solenoid A is increased. Also due to voltage drop with the occurrence of fault the magnitude of restraining torque developed by solenoid B decreases. Thus the balance arm rotates in counter-clockwise direction and the relay contacts are closed.

The pull of the solenoid A (i.e., current element) is proportional to I^{2} and that due to solenoid B (voltage element) to V^{2}. Consequently the relay will operate when-

The values of the constants K_{1} and K_{2} depend upon the ampere-turns of the two solenoids, and the ratios of the instrument transformers. By providing tappings on the coil, the setting of the relay can be changed.

The time-impedance characteristic of the relay is shown in Fig. 3.44 (b). The ordinate represents the time of operation for the relay and the abscissa represents impedance which is proportional to distance. As may be seen the operating time for almost the entire length (for which the relay is designed to operate) is constant. Towards the end of the predetermined length, the curve rises gradually because the pulls of the voltage and current elements become nearly equal, and after the point A has been passed the operating time rapidly becomes infinite.

Such a relay is classified as definite distance type impedance relay, because it operates instantaneously for faults up to a predetermined distance from the relay.

The quality of protection provided by the distance impedance system is superior to that provided by overcurrent (time-graded) relays. Since the operating time is same for all relays, the number of feeders in series that can be protected is unlimited. It lacks, however, one important feature of the latter in that the back-up protection is not available except for short length AB.

**2. Induction Type Impedance Relay: **

Induction type impedance relay consists of a combination of an overcurrent element with a voltage-restraint element, the circuit being illustrated in Fig. 3.45 (a).

The induction type impedance relay consists of a metallic disc usually made of aluminium or copper which is capable of rotating between two electromagnets—upper magnet and lower magnet. The upper electromagnet has two separate windings similar to that of overcurrent relay. The primary winding is connected to the secondary of the CT connected in the line to be protected. The winding has a number of tappings so as to vary the current settings, the tappings are connected to a plug bridge.

The secondary winding on the upper electromagnet is connected in series with the windings on the lower electromagnet. The currents in the secondary are due to electromagnetic induction. By this arrangement leakage fluxes of upper and lower electromagnets are sufficiently displaced in space and phase to set up a rotational torque on the induction disc, as in the shaded pole induction disc motor. The torque is controlled by a permanent magnet (not shown in the figure). The controlling or braking torque caused by the permanent magnet varies directly as the driving torque.

The spindle which carries the induction disc is shown connected by means of spiral spring coupling to the second spindle which carries the bridging piece or the moving contact of the relay trip contacts. The bridge is normally held in the open position by an armature held against the pole face of an electromagnet energized by the voltage of the line. It is to be pointed out that in actual practice the spindle carrying the induction disc is attached to the inner end of the spiral spring through a geared counter shaft in order to obtain the required characteristic for the relay operating time.

Under normal operating conditions the pull exerted by the armature is more than that of the induction element and thus the trip circuit contacts remain open. When the fault occurs, the induction disc starts to rotate with a speed approximately proportional to the operating current, neglecting the effect of the control spring. Hence the time taken by the disc to turn through a given angle varies inversely as the current.

Also as the disc rotates the spring is wound. The disc continues rotating till the tension of the spring is sufficient to overcome pull of the voltage restraint electromagnet over its armature and as soon as this armature is released the trip contacts are closed.

Thus the angle through which the induction disc is to rotate for the operation of the relay depend upon the value of the pull on the restraint armature. The greater this pull, the greater would be the travel of the disc. However, this pull is also approximately proportional to the voltage, therefore, the angle through which the disc is to rotate for the operation of the relay is directly proportional to voltage V. Thus in this type of relay the time required is directly proportional to line voltage V and inversely proportional to current I i.e., the time of operation is proportional to V/I or impedance of the line or section.

The simple impedance relay, is instantaneous type i.e., it operates as soon as the impedance of the line or section falls below a certain value. But the time of operation in case of induction type impedance relay is proportional to the distance of fault from the relay point. A fault nearer to the relay will operate it earlier than a fault farther away from the relay. Because of such characteristic, this relay is called the time-distance relay.

The approximate time-distance characteristic of time-distance relay is shown in Fig. 3.45 (b). The exact time-distance characteristic is curved, as illustrated dotted in the figure.

The torque on the disc tends to be proportional to the square of the circuit current i.e., I^{2} while the pull of the restraint magnet tends to be proportional to the square of the voltage i.e., V^{2}. Thus the time of operation tends to be proportional to the square of the impedance i.e., Z^{2} or proportional to the square of the distance. Thus we get the time-distance characteristic as a curve.

**3. Directional Impedance Relays:**

The directional feature to the impedance relay can be provided by employing the impedance relay along with a directional unit as is done in the case of a simple overcurrent relay to operate as a directional overcurrent relay. This means the impedance unit will operate only when the directional unit has operated.

Directional feature senses the direction in which fault power flows with respect to the location of CT and PT.

**Directional impedance relays operate for the following conditions: **

1. Impedance between the fault point and relay location is less than the relay setting Z.

2. The fault power flows in a particular direction from relay.

The directional unit permits tripping only in the positive torque region the active portion of the impedance unit characteristic is shown shaded. The net result is that the relay will operate only for fault points that are both within the circle and above directional unit characteristic.

**Torque Equation for Directional Impedance Relay: **

Torque equation for directional element is given as –

T = K_{1} V I cos(θ – τ) Refer to Eq. (3.12)

Where, θ is the phase angle between V and I and τ is the impedance angle of the relay. Values of angles are taken as positive in clockwise direction.

When the relay is about to pick up,

the torque T = 0; cos (θ – τ) = 0

or (θ – τ) = ± 90° or θ = τ ± 90°

Hence for positive torque 0 should be ± 90°.

If the effect of spring control is taken into account, the torque equation becomes

T = K_{1 }V I cos(θ – τ) – K_{2}

At balance point i.e., when the relay is about to pick up

T = 0;

K_{1} V I cos(θ – τ) = K_{2} …(3.21)

Substituting I = V/Z in above equation we have –

K_{1} x V x (V/Z) . cos(θ – τ) = K_{2}

or Z = (K_{1}/K_{2}) V^{2} cos(θ – τ) …(3.22)

The above Eq. (3.22) describes an infinite number of circles and for each value of V there will be a corresponding circle. The characteristics of directional impedance relay for one value of V can be represented on the R-X diagram as shown in Fig. 3.48.

The fact that for some values of θ, impedance Z will be negative which should be ignored. Negative Z has no significance and cannot be shown on R-X diagram.

When cos (θ – τ) = 1 or θ = τ, impedance Z will have maximum value and will lie on the line of maximum torque OM. When cos (θ – τ) = 0, Z = 0 and θ = 99° ± τ. The characteristic will therefore be a circle with Z as diameter and the centre of the circle will lie on the line OM. The diameter of the circle will be proportional to the square of the voltage.

**4. Single Phase Impedance Type Distance Relay for Transmission Line Protection: **

A single phase impedance type distance relay for protection of transmission line consists of a single-phase directional unit, three high-speed impedance-relay units, and a time unit, together with the usual targets, seal-in-unit, and other auxiliaries. The three impedance units are labeled Z_{1}, Z_{2} and Z_{3} respectively. These can be adjusted for any desired value independently.

On R-X diagram shown in Fig. 3.50 the circle for Z_{1} is the smallest, the circle for Z_{3} is the largest, and the circle for Z_{2} is an intermediate. Thus we have divided the transmission line under protection in three zones. It can be seen from Fig. 3.50 that any value of impedance within the Z_{1} circle will cause all the three impedance units to operate. The operation of Z_{1} and the directional unit will trip a breaker directly in time T_{1} which is very short.

Whenever Z_{3} and the directional unit operate, the timing unit is energised. After a definite delay, the timing unit will first close its T_{2} contact, and later its T_{3} contact, both time delays being independently adjustable. Therefore, it can be seen that a fault within zone Z_{2} but outside zone Z_{1} (i.e., between the circles of Z_{1} and Z_{2}) will result in tripping in T_{2} time. And finally, a value of Z outside the Z_{1} and Z_{2} circles, but within the Z_{3} circle, will result in tripping in T_{3} time.

If tripping is somehow blocked, the relay will make as many attempts to trip as there are characteristic circles around a given impedance point. However, use may not be made of this possible feature.

Figure 3.50 shows also the relation of the directional-unit operating characteristic to the impedance- unit characteristics on the same R-X diagram. Since, the directional unit permits tripping only in its positive-torque region, the inactive portions of the impedance unit characteristics are shown dotted. Thus tripping will occur only for points that are both within the circles and above the directional unit characteristic.

Operating time-impedance characteristic for an impedance type distance relay is shown in Fig. 3.51. This characteristic is usually called a “stepped” time-impedance characteristic. It is noteworthy that the Z_{1} and Z_{2} units provide the primary protection for a given transmission line section while Z_{2} and Z_{3} provide backup protection for adjoining busses and line sections.

**5. Modified Impedance Type Distance Relay: **

The modified impedance type distance relay is like the impedance type except that the operating characteristics are shifted as illustrated in Fig. 3.52. It is shifted by introducing a current bias’ which merely consists of introducing into the voltage supply an additional voltage proportional to the square of the current. Hence the modified torque equation is given as –

T = K_{1} l^{2} – K_{2} (V + CI)^{2} …(3.23)

The term (V + CI) is the rms magnitude of the vector addition of V and CI involving angle θ between V and I as well as a constant angle in the constant C term. By such biasing, the characteristic circle can be shifted in any direction from the origin, and by any desired amount, even to the extent that the origin is outside the circle. Slight variations may occur in the biasing, due to circuit elements saturation. That is why, it is not the practice to make the circles pass through the origin, and therefore a separate directional unit is required.

**Drawbacks of Plain Impedance Relay: **

**The plain impedance relay, though very simple in theory and in construction, has several drawbacks such as given below: **

1. The plain impedance relay can operate in either direction. It responds to the faults on both sides of CT, PT location. So it cannot discriminate between internal and external faults.

2. The plain impedance relay is sensitive to power swing as a large area is covered by the circle on each side on R-X plane. During power swing which is caused by severe faults, the relay sees fictitious impedance and if this impedance is less than the relay setting, the relay may operate.

3. The plain impedance relay is affected by arc resistance of line fault and results in under-reach.

**Time-Characteristics of High Speed Type Impedance Relay: **

Although impedance relays with inherent time delay are encountered occasionally, only high-speed type impedance relays will be considered. The operating-time characteristic of a high-speed impedance relay is shown in Fig. 3.46. The curve shown in the figure is for a particular value of current magnitude.

For other current values similar characteristics are obtained. Curves for higher currents will lie below this curve, and curves for lower currents will lie above it. It is observed that for impedance values above 100% pick-up impedance, the relay does not operate. The curve I represents the actual characteristic while curve II is simplified representation of the same (right angle instead of curve).