KNEE POINT VOLTAGE OF A CURRENT TRANSFORMER
As we know from our previous discussions the function of a current transformer is to translate the current of its primary winding into a proportional value of current in the secondary winding. This stepping down of current from higher primary values to lower secondary values is utilized for metering and protection purposes in various meters and relays.
Table of Contents
The process of transformation of the current that happens inside the current transformer includes lining up the magnetic dia-poles in the direction of the magnetic field, thus generating magnetic flux.
The change in the magnetic flux is what induces the voltage in the secondary and this voltage is responsible for the proportional current that is produced in the secondary winding of the current transformer.
As we know the secondary of the CT is always shorted so an obvious question might arise about the voltage induction in the secondary winding. This voltage induction is because of the resistance of the connected burden, connection, and core resistance.
The knee point voltage of a current transformer is the point in the curve plotted as secondary winding voltage or excitation voltage to primary current or excitation current beyond which the linearity of the CT is lost. Till the knee point, the voltage and current are proportional, beyond the point, a little increase in the primary current results in a greater increase in the secondary voltage, which eventually leads the CT core to saturation. Note knee point voltage is not the saturation voltage.
This happens because every core material has different permeability and as the primary current increases the flux also increases. As the flux density approaches the knee point, the permeability decreases rapidly causing the core material to have higher magnetic resistance, i.e. the core becomes less attractive to the magnetic field lines, resulting in increased leakage flux.
SIGNIFICANCE OF KNEE POINT VOLTAGE
The core of the protection CT is made in such a way that its saturation level is high enough to handle the fault currents. But the high should be limited, as because it is merely impossible to make a magnetic core with an infinitely high saturation level.
Although the saturation level should be high, it must be limited so that in case of a fault, the entire primary current shall not be translated into the secondary winding. Otherwise, the high level of current in the secondary can irreversibly damage all the equipment/relays connected to it.
Therefore, by calculating the CT knee point voltage, we can know the minimum CT secondary voltage (Knee point) before the saturation of the CT core. So that the protective relay elements can function properly and correctly in the event of a fault.
PROCEDURE TO TEST THE KNEE PONT VOLTAGE OF CT
For conducting the test on the CT the equipment required are
- single phase autotransformer
- Multimeter
- Clamp meter
- Connection wires
The following should be done before the test:
- The circuit breaker should be in the open position
- Both side disconnector switches should be in the open position
- Connections from the CT secondary terminals should be open
After doing so, we shall connect the autotransformer to the secondary terminal of the protection core 3S1-3S2 or 3S1-3S3 depending on the core and ratio of the CT along with the multimeter for voltage measurement. We then connect the clamp meter to the wire connecting the autotransformer and the secondary terminal of the CT.
After the connection is made, we should turn the Knob of the autotransformer and note the applied voltage via the multimeter and current from the clamp meter. Many readings must be taken at a 10% increased voltage and the current at that voltage must be noted, to find the specific voltage after which a 10% increase in the voltage would give a 50% increase in the current.
That specific voltage is the knee point voltage of the CT.
CALCULATION OF KNEE POINT VOLTAGE
The requirement of CT hence is therefore governed by relay and as per relay requirement we calculate the knee point voltage.
The following formula is generically used to calculate the Knee Point Voltage.
๐๐๐=2โ๐ผ๐น/๐ถ๐Rโ(๐ ๐ถ๐+๐ ๐ฟ+๐ ๐ต)
- Where Vkp is the Knee Point Voltage (volts)
- IF is the fault current (amps)ย
- CTR is the CT ratioย
- RCT is the secondary winding resistance (ohms)ย
- RL is the lead resistance (ohms)
- RB is the relay burden (ohms)
CONCLUSION:
Beyond the knee point, the current transformer is said to enter saturation. In this region, the major part of the primary current is utilized to maintain the core flux, and since the shunt admittance is not linear, both the exciting and secondary currents depart from a sine wave.
IEEE/ANSI Standard C57.13 suggests that CTs for relaying be applied on the basis that the maximum symmetrical fault current does not exceed 20 times the CT current rating and that its burden voltage does not exceed the accuracy class voltage of the CT. Applying CTs for relaying is an art rather than a science because the engineer is left to choose the specific operating point on the excitation curve. However, there is a rationale for choosing a CT to produce the knee-point excitation at the maximum symmetrical fault current since the magnetizing reactance is at a maximum.
A popular rule of thumb suggests that the CT rating be twice the excitation voltage developed by the maximum fault current.
FAQโs
Why is knee voltage important?
Knee point is important because it indicates the protective coreโs burden should be within limits so that the protective elements of the circuit can function in events of the fault before the saturation of the core.
What happens in the region of saturation?
As the magnetic inductance becomes low at the saturation region, the entire primary current is utilized to provide excitation to the core and this is why there is no output in the secondary terminal when the CT is in saturation region.
