# knee point voltage of a current transformer

## knee point voltage of a current transformer

Knee Point Voltage of a Current Transformer is defined as the voltage at which 10 % increase in voltage of CT secondary results in 50 % increase in secondary current

as we know CT core is made of CRGO (Cold Rolled Grain Oriented Silicon Steel). When the primary of CT is energized a workingÂ mmfÂ is produced in the core. To produce a mmf, excitation current Ie is taken.

This mmf produces a flux in the core of CT which links with the secondary winding and as per theÂ Faradayâ€™s Law of Electromagnetic Induction, an emf is generated across the terminals of CT secondary byÂ Transformer action.

The emf induced in the CT secondary terminal is given asÂ Â Â E = 4.44fNÃ˜
Where, f is frequency ,
N is number of secondary turns and
Ã˜ is flux in the core of CT.

### Knee point voltage curve

But Ã˜ is directly proportional to mmf and mmf in turn is directly proportional to current. Thus if we increase the current, flux Ã˜ generated in the core will increase till the core saturates. Thus there must be a point where from the flux do not increase in the same proportion as the increase in current.This point is called Knee Point. After discussing this much, we can at least say that Knee Point is something related with Saturation of CT core.

If there is something called saturation, then we must drawÂ saturation curve of the CTÂ core to have more insight.

In differential and restricted earth fault (REF) protection scheme, accuracy class and ALF of the CT may not ensure the reliability of the operation.

It is desired that, differential and REF relays should not be operated when fault occurs outside the protected transformer.

When any fault occurs outside the differential protection zone, the faulty current flows through the CTs of both sides of electrical power transformer.

The both LV and HV CTs have magnetizing characteristics. Beyond the knee point, for slight increase in secondary emf a large increasing in excitation current is required.

So after this knee point excitation current of both current transformers will be extremely high, which may cause mismatch between secondary current of LV & HV current transformers.

This phenomena may cause unexpected tripping of power transformer. So the magnetizing characteristics of both LV & HV sides CTs, should be same that means they have same knee point voltage Vk as well as same excitation current Ie at Vk/2.

It can be again said that, if both knee point voltage of current transformer and magnetizing characteristic of CTs of both sides of power transformer differ, there must be a mismatch in high excitation currents of the CTs during fault which ultimately causes the unbalancing between secondary current of both groups of CTs and transformer trips.

So for choosing CT for differential protection of transformer, one should consider current transformer PS class rather its convectional protection class.

PS stands for protection special which is defined by knee point voltage of current transformer Vk and excitation current Ie at Vk/2.