Relay Setting Calculation

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During study of electrical protective relays, some special terms are frequently used. For proper understanding, the functions of different protective relays, the definition of such terms must be understood properly. Such terms are,

1. Pick up current.
2. Current setting.
3. Plug setting multiplier (PSM).
4. Time setting multiplier (TSM).

Pick Up Current of Relay

In all electrical relays, the moving contacts are not free to move. All the contacts remain in their respective normal position by some force applied on them continuously. This force is called controlling force of the relay. This controlling force may be gravitational force, may be spring force, may be magnetic force. The force applied on the relay’s moving parts for changing the normal position of the contacts, is called deflecting force. This deflecting force is always in opposition of controlling force and presents always in the relay. Although the deflecting force always presents in the relay directly connected to live line, but as the magnitude of this force is less than controlling force in normal condition, the relay does not operate. If the actuating current in the relay coil increases gradually, the deflecting force in electro mechanical relay, is also increased. Once, the deflecting force crosses the controlling force, the moving parts of the relay initiate to move to change the position of the contacts in the relay. The current for which the relay initiates it operation is called pick up current of relay.

Current Setting of Relay

The minimum pick up value of the deflecting force of an electrical relay is constant. Again the deflecting force of the coil is proportional to its number of turns and current flowing through the coil.

Now, if we can change the number of active turns of any coil, the required current to reach at minimum pick value of the deflecting force, in the coil also changes. That means if active turns of the relay coil is reduced, then proportionately more current is required to produce desired relay actuating force. Similarly if active turns of the relay coil is increased, then proportionately reduced current is required to produce same desired deflecting force.

Practically same model relays may be used in different systems. As per these systems requirement the pick up current of relay is adjusted. This is known as current setting of relay. This is achieved by providing required number of tapping in the coil. These taps are brought out to a plug bridge. The number of active turns in the coil can be changed by inserting plug in different points in the bridge.

The current setting of relay is expressed in percentage ratio of relay pick up current to rated secondary current of CT.

That means,

For example, suppose, you want that, an over current relay should operate when the system current just crosses 125% of rated current. If the relay is rated with 1 A, the normal pick up current of the relay is 1 A and it should be equal to secondary rated current of current transformer connected to the relay.

Then, the relay will be operated when the current of CT secondary becomes more than or equal 1.25 A.

As per definition,

The current setting is sometimes referred as current plug setting.

The current setting of over current relay is generally ranged from 50% to 200%, in steps of 25%. For earth fault relay it is from 10% to 70% in steps of 10%.

Plug Setting Multiplier of Relay

Plug setting multiplier of relay is referred as ratio of fault current in the relay to its pick up current.

Suppose we have connected on protection CT of ratio 200/1 A and current setting is 150%.

Hence, pick up current of the relay is, 1 × 150 % = 1.5 A

Now, suppose fault current in the CT primary is 1000 A. Hence, fault current in the CT secondary i.e. in the relay coil is, 1000 × 1/200 = 5 A

Therefore PSM of the relay is, 5 / 1.5 =3.33

Time Setting Multiplier of Relay

The operating time of an electrical relay mainly depends upon two factors :

1. How long distance to be traveled by the moving parts of the relay for closing relay contacts and
2. How fast the moving parts of the relay cover this distance.

So far adjusting relay operating time, both of the factors to be adjusted.

The adjustment of travelling distance of an electromechanical relay is commonly known as time setting. This adjustment is commonly known as time setting multiplier of relay. The time setting dial is calibrated from 0 to 1 in steps 0.05 sec.

But by adjusting only time setting multiplier, we can not set the actual time of operation of an electrical relay. As we already said, the time of operation also depends upon the speed of operation. The speed of moving parts of relay depends upon the force due to current in the relay coil. Hence it is clear that, speed of operation of an electrical relay depends upon the level of fault current. In other words, time of operation of relay depends upon plug setting multiplier. The relation between time of operation and plug setting multiplier is plotted on a graph paper and this is known as time / PSM graph. From this graph one can determine, the total time taken by the moving parts of an electromechanical relay, to complete its total travelling distance for different PSM. In time setting multiplier, this total travelling distance is divided and calibrated from 0 to 1 in steps of 0.05.

So when time setting is 0.1, the moving parts of the relay has to travel only 0.1 times of the total travelling distance, to close the contact of the relay. So, if we get total operating time of the relay for a particular PSM from time / PSM graph and if we multiply that time with the time setting multiplier, we will get, actual time of operation of relay for said PSM and TSM.

For getting clear idea, let us have a practical example. Say a relay has time setting 0.1 and you have to calculate actual time of operation for PSM 10.

From time / PSM graph of the relay as shown below, we can see the total operating time of the relay is 3 seconds. That means, the moving parts of the relay take total 3 seconds to travel 100% travelling distance. As the time setting multiplier is 0.1 here, actually the moving parts of the relay have to travel only 0.1 × 100% or 10% of the total travel distance, to close the relay contacts.

Hence, actual operating time of the relay is 3 × 0.1 = 0.3 sec. i.e. 10% of 3 sec.

Time vs PSM Curve of Relay

This is relation curve between operating time and plug setting multiplier of an electrical relay. The x-axis or horizontal axis of the Time / PSM graph represents, PSM and Y-axis or vertical axis represents time of operation of the relay. The time of operation represents in this graph is that, which required to operate the relay when time setting multiplier set at 1.

From the Time / PSM curve of a typical relay shown below, it is seen that, if PSM is 10, the time of operation of relay is 3 sec. That means, the relay will take 3 seconds to complete its operation, with time setting 1.

It is also seen from the curve that, for lower value of plug setting multiplier, i.e. for lower value of fault current, the time of operation of the relay is inversely proportional to the fault current.

But when PSM becomes more than 20, the operating time of relay becomes almost constant. This feature is necessary in order to ensure discrimination on very heavy fault current flowing through sound feeders.

Calculation of Relay Operation Time

For calculating actual relay operating time, we need to know these following operation.

1. Current setting.
2. Fault current level.
3. Ratio of current transformer.
4. Time / PSM curve.
5. Time setting.

Step – 1

From CT ratio, we first see the rated secondary current of CT. Say the CT ratio is 100 / 1 A, i.e. secondary current of CT is 1 A.

Step – 2 

From current setting we calculate the trick current of the relay. Say current setting of the relay is 150% therefore pick up current of the relay is 1 × 150% = 1.5 A.

Step – 3

Now we have to calculate PSM for the specified faulty current level. For that, we have to first divide primary faulty current by CT ratio to get relay faulty current. Say the faulty current level is 1500 A, in the CT primary, hence secondary equivalent of faulty current is 1500/(100/1) = 15 A

Step – 4

Now, after calculating PSM, we have to find out the total time of operation of the relay from Time / PSM curve. From the curve, say we found the time of operation of relay is 3 second for PSM = 10.

Step – 5

Finally that operating time of relay would be multiplied with time setting multiplier, in order to get actual time of operation of relay. Hence say time setting of the relay is 0.1.

Therefore actual time of operation of the relay for PSM 10, is 3 × 0.1 = 0.3 sec or 300 ms.