IDMT: Discrimination by Current and Time of Operation

Discrimination by Current and Time of Operation

Each of the two methods described so far has a fundamental disadvantage.  In the case of discrimination by time alone, the disadvantage is due to the fact that the more severe faults are cleared in the longest operating time (t1>t2>t3).  On the other hand, discrimination by current can be applied only where there is appreciable impedance between the two circuit breakers concerned.

To overcome above limitations imposed by the independent use of either time or current co-ordination; the inverse time overcurrent relay characteristic has evolved, where the time of operation is inversely proportional to the fault current level and the actual time of operation is a function of both ‘Time Multiplier Setting’ and 'Fault current'. So mathematically 

Where K is proportionality constant. The above expression indicates that mathematically for any value of current there would be time of operation. In actual practice for relay current less than set value relay would not operate or time of operation is infinity. Hence this relation can be modified as below.

But this simple expression has a drawback. To understand the drawback consider an example where let we are protecting an element “A” having current carrying capacity of 30 A. Obviously set value of for over current relay will be 30 A. Let fault current through the element is 40 A. Then as per above formula and for the proportionality constant K = 10 relay will operate in 1 Sec (With time multiplier Setting = 1).

Now consider other case of element B having current capacity 300 A. obviously over current relay setting will be 300 A. Now let 310 A current is flowing through the element B. Then in this case too relay will operate in 1 Sec (With K = 10 and time multiplier Setting = 1). Practically it should happen that for same amount of current exceeding set value; time of operation of relay for element B shall be more.

Hence to reflect the fact that higher set value of current means higher allowable time of operation for same amount of current exciding set value. The above expression is standardized as below. 

For most of the time damage to equipment is proportional to square of the current to reflect this fact above expression can be written as below

IEC standardized such relay operating characteristics for different type of protection needs by defining K and α and named them as shown in following table.

The relay operating characteristics can be plotted on graph by selecting time of operation as Y axis and the term If/ISet as X axis. We can call X axis as ‘Fault current as multiple of current set value’ or simply ‘Multiple of current”. Such graph is as shown here. Note that graph has log scale for X axis as well as Y axis. This is for displaying curves for wide range of operational time as well as multiple of current. Using this graph you can estimate the time of operation for known multiple of current value easily.

In most cases, use of the standard SI curve proves satisfactory, but if satisfactory grading cannot be achieved, use of the VI or EI curves may help to resolve the problem. However in transmission sector standard inverse is being used widely. Hence our further discussion shall be limited to standard inverse characteristics only

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Relay Time Grading Margin

The time interval that must be allowed between the operations of two adjacent relays in order to achieve correct discrimination between them is called the grading margin.  If a grading margin is not provided, or is insufficient, more than one relay will operate for a fault, leading to difficulties in determining the location of the fault and unnecessary loss of supply to some consumers.

The grading margin depends on a number of factors:

i. The fault current interrupting time of the circuit breaker

ii. Relay timing errors

iii. The overshoot time of the relay

iv. CT errors

v. Final margin on completion of operation

Considering all these factors a time grading margin of 200 ms may be adopted. Grading is initially carried out for the maximum fault level at the relaying point under consideration.

High-Set Instantaneous Over Current Relay.

A high-set instantaneous element can be used where there is significant change in impedance and there by fault currents. For example when we are protecting the transformer when HV side relay senses fault on HV side it may be cleared instantaneously.

For better understanding of all the terms discussed above we will go through setting calculations for same power system as discussed above.