Knee Point Voltage-Importance:

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Knee Point Voltage of Current Transformers:

Knee point voltage parameter is very important for Protection current transformers especially for Class-PS that is Special purpose current transformers.

First of all, we will see how Protection class CTs differ from Metering Class CTs.

There are two basic types of Current transformers metering and protection. The basic difference between the two is, for measurement CTs the limits are well defined whereas protection CTs have to operate over a wide range of currents. So their characteristics must be different from measuring CTs.

Measurement CTs require good accuracy up to 120%. They require low level saturation to protect meters, so they made with Nickel-Iron alloy core with low exciting current and knee point at low flux density.

Protection CTs accuracy is not important as measurement CTs. They require accuracy up to many times rated current, so they made with Grain oriented silicon steel with high saturation flux density.

Details of Knee Point Voltage:

Every Protection class CT Name plate contains details of Knee point voltage as shown in below figure. The name plate is for 3-Core CT with middle taps. For this CT the knee point voltage for PS-Class core is Vk >= 120V for 3S1-3S3 winding and Vk >=60V for 3S1-3S2 winding. Also the excitation current should less than or equal to 100mA at VK/4 for anyone of Core-3 windings.

Knee Point Voltage on CT-Name Plate

Current Transformers magnetization curve helps to understand the knee point voltage.

Magnetization curve of Current Transformers:

This curve is generally plotted in secondary volts vs exciting current measured in secondary. From this curve we can easily find the magnitude of exciting current required to produce the given amount of CT secondary voltage.

The magnetization or excitation curve divided into four regions.

1. From origin to ankle point

2. From ankle point to knee

3. Knee region

4. Saturation region

Knee point is simply defined as,

“Where a 10% increase in flux density cause 50% increase to exciting ampere-turns”.

The regions are shown in figure below.

Knee Point Voltage curve indicating different regions
Knee Point Voltage Curve
  • The measuring current transformer has the flux density in the region of ankle-point only.
  • Protection current transformer generally operates over-working flux density extending from the ankle-point to the knee-region of above.

Prior to saturation, the flux density in core is proportional to ampere-turns. On reaching saturation, magnetizing inductance becomes low and the total primary current is utilized in exciting the core alone and, therefore, the secondary output of CT disappears. (There is no secondary current at all even primary current present).

The saturation continues till the primary transient current is reduced below saturation level.  If CT operating in saturation zone, the CT behaves an open circuited.

Effect of saturation on performance of CT:

It is difficult to avoid saturation during short circuit condition. The effect of saturation is the reduced output, hence reduced speed of over-current relays. In differential relays the saturation disturbs the balance and stability of protection is affected. If CT exposed to higher primary currents for prolonged times Permanent saturation occurs and hence the CT can’t be used further.

Causes of saturation:

Short-circuit current has d.c component flowing for several tens of milliseconds. The d.c component causes saturation of the CT core resulting in error. The exciting current is consumed by core and the output of CT is reduced to almost zero.

How to avoid saturation effect?

Nowadays the measuring times of protective relays reduced to the transient state.

Also CTs with gapped cores are used to avoid saturation during prolonged short-circuit currents. Such CTs are used for high speed distance protection of lines.

Verification of Knee Point Voltage of CT:

Current transformers knee point voltage can be obtained from the Name plate details of Protection Class CTs. However, it is to be verified during commissioning of new CTs.

To verify the Vk value of a given Current Transformer, the process is as follows.

Exciting currents is measured for several secondary e.m.fs. This is accomplished by applying voltage to the secondary winding, the primary and other windings being open circuited. The connections are shown in figure.

Circuit connections to find Knee Point Voltage
Circuit to find Knee Point Voltage

Let us, consider an example CT of PS class used for Differential Protection with the following Knee point values.

VK ≥ 30 V

Ie ≤ 30mA  @ Vk/2

To verify the knee point voltage, increase CT secondary applied voltage gradually until reaching knee point.

The obtained readings are as follows.

Test results showing readings of Knee point voltage
Test Results of Knee Point Voltage

If we recall the definition of Knee point voltage, the value of voltage at which when the applied voltage is increased by 10 percent, causes the exciting current to increase by 50 percent.

At 36V applied voltage the current raises abruptly to the value of 0.015 Amps. This rise is from 32V to 36V (voltage increased by 10%) and current increased from 0.010A to 0.015 (current increased by 50%). Hence the knee point voltage VK of the given current transformer is at 32V.

Also the other condition at Vk/2 that is at 16V the current value should be less than or equal to 30mA also verified from the above test results.

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