Current Transformer MCQ Quiz - Objective Question with Answer for Current Transformer - Download Free PDF

Matching the Error Types and Causes in Current Transformers (CTs):

In a Current Transformer (CT), various sources of errors arise due to the physical and electrical characteristics of the transformer. These errors are classified into different types, and each error type has specific causes associated with it. Understanding the relationship between these errors and their causes is crucial for ensuring the accurate performance of CTs in electrical systems.

The correct matching of error types with their causes is:

Option 3: 1 → B, 2 → C, 3 → D, 4 → A

Let us analyze each error type and its corresponding cause:

1. Ratio Error (1 → B):

Explanation: Ratio error occurs when there is a discrepancy between the actual transformation ratio of the CT and its nominal or designed transformation ratio. This discrepancy primarily arises due to the magnetizing current requirement of the core. Magnetizing current is the current needed to establish the magnetic flux in the CT core, and it does not contribute to the secondary current. As a result, it causes a deviation in the actual ratio of primary to secondary currents, leading to ratio error.

Key Cause: Magnetizing current requirement (B).

2. Phase Angle Error (2 → C):

Explanation: Phase angle error is the angular displacement between the primary current and the secondary current of a CT. Ideally, the primary and secondary currents should be in phase (for a purely resistive burden). However, due to non-ideal properties of the core material (such as hysteresis and eddy current losses), there is a phase shift between the two currents. These non-ideal core properties affect the accuracy of the CT and result in phase angle error.

Key Cause: Non-ideal core material properties (C).

3. Hysteresis Error (3 → D):

Explanation: Hysteresis error is caused by the residual magnetism or remanence in the CT core. When the core is magnetized by the primary current, some residual magnetism remains in the core even after the current is removed. This residual flux affects the accuracy of the CT and leads to hysteresis error. It is particularly significant in applications where the CT is subjected to varying primary currents.

Key Cause: Residual magnetism in the core (D).

4. Leakage Reactance Error (4 → A):

Explanation: Leakage reactance error arises due to the leakage flux in the CT windings. Leakage flux is the portion of the magnetic flux that does not link both the primary and secondary windings. This flux creates reactance in the windings, which impacts the accuracy of the CT. The leakage reactance causes a voltage drop in the windings, thereby introducing errors in the secondary current.

Key Cause: Leakage flux in windings (A).

Important Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 1 → A, 2 → B, 3 → D, 4 → C

This option incorrectly associates the causes with the error types. For example, it matches ratio error with "leakage flux in windings" (A), which is incorrect because ratio error is primarily caused by the magnetizing current requirement (B). Similarly, other mismatches make this option incorrect.

Option 2: 1 → B, 2 → A, 3 → D, 4 → C

This option also contains incorrect associations. For instance, it matches phase angle error with "leakage flux in windings" (A), which is incorrect because phase angle error is caused by non-ideal core material properties (C). The other pairings are also mismatched.

Option 4: 1 → B, 2 → A, 3 → C, 4 → D

In this option, hysteresis error is incorrectly matched with "non-ideal core material properties" (C) instead of "residual magnetism in the core" (D). Leakage reactance error is also mismatched with "residual magnetism in the core" (D) instead of "leakage flux in windings" (A).

Conclusion:

Understanding the sources of errors in CTs and their respective causes is essential for ensuring the accuracy and reliability of these devices. The correct matching of error types with their causes is as follows:

• Ratio Error: Magnetizing current requirement (B).
• Phase Angle Error: Non-ideal core material properties (C).
• Hysteresis Error: Residual magnetism in the core (D).
• Leakage Reactance Error: Leakage flux in windings (A).

Option 3 correctly identifies these relationships, making it the correct choice.

The correct answer is option 2.

Different types of transformers

• Current transformer: A current transformer (CT) is used to step down current for measurement purposes. It is a specific type of instrument transformer designed to reduce high currents to a lower, more manageable level that can be safely and accurately measured by standard electrical instruments. 
• Power transformer: A power transformer is a fixed device that converts power from one circuit to another without changing the frequency.
• Auto transformer: Autotransformers are ideal for voltage adjustment for commercial and industrial machines. They provide an efficient, low cost way of serving the proper voltage to motors and compressors, lathes, CNC machines, and other industrial equipment requiring a step up or down from a building's service voltage.
• Voltage transformer: Voltage transformers (VT), also called potential transformers (PT), are a parallel-connected type of instrument transformer. They are designed to present a negligible load to the supply being measured and have an accurate voltage ratio and phase relationship to enable accurate secondary connected metering.

The correct answer is option 1.

Different types of transformers

• Current transformer: A current transformer (CT) is used to step down current for measurement purposes. It is a specific type of instrument transformer designed to reduce high currents to a lower, more manageable level that can be safely and accurately measured by standard electrical instruments. 
• Power transformer: A power transformer is a fixed device that converts power from one circuit to another without changing the frequency.
• Auto transformer: Autotransformers are ideal for voltage adjustment for commercial and industrial machines. They provide an efficient, low cost way of serving the proper voltage to motors and compressors, lathes, CNC machines, and other industrial equipment requiring a step up or down from a building's service voltage.
• Voltage transformer: Voltage transformers (VT), also called potential transformers (PT), are a parallel-connected type of instrument transformer. They are designed to present a negligible load to the supply being measured and have an accurate voltage ratio and phase relationship to enable accurate secondary connected metering.

In a current transformer (CT), the secondary winding must always remain connected to a low-impedance load or a short circuit (like a relay or meter). If the secondary is left open, several important phenomena occur:

• Current through Secondary: Since the circuit is open, there is no path for current to flow through the secondary winding. Thus, the current through the secondary becomes zero.
• High Voltage Induced in the Secondary: With no secondary current, the magnetic flux in the core becomes very high. This leads to a very high voltage being induced across the open secondary terminals. This high voltage can damage insulation and pose a serious safety hazard.
• Core Saturation: The absence of secondary current causes core saturation, which can overheat the CT.
• Primary Current Remains Unaffected: The primary current remains the same as it depends on the system load, not on the CT's secondary.

The correct answer is secondary winding circuit.

Key Points

• Current transformers (CTs) are devices used in electrical engineering to measure alternating current (AC).
• They work by producing a reduced current accurately proportional to the current in the circuit, which can then be connected to measuring instruments like ammeters, wattmeters, or relay coils.
• The secondary winding circuit of a CT must always be closed through an appropriate load (like an ammeter or a relay coil).
• If the secondary winding is left open, it can develop dangerously high voltages, which can damage the transformer and pose a safety hazard.
• This is because the CT is designed to work with a load in the secondary circuit, ensuring that the magnetic circuit operates correctly and safely.
• When the secondary circuit is closed, the CT safely steps down the current, allowing for accurate measurement and monitoring of high current levels in the primary circuit.

 Additional Information

• Primary Winding Circuit
  • The primary winding circuit is the part of the transformer where the input current flows.
  • In a current transformer, the primary winding is connected to the high current line that needs to be measured.
  • The primary winding is usually a single turn or a few turns of heavy conductor.
• Galvanometer
  • A galvanometer is an instrument for detecting and measuring electric current.
  • It is highly sensitive and typically used in laboratory settings.
  • Galvanometers are not used with current transformers because they are not designed to handle high current levels.
• Voltmeter
  • A voltmeter is an instrument used for measuring electrical potential difference between two points in an electric circuit.
  • Voltmeters are not suitable for use with current transformers since they measure voltage, not current.

Concept:

Current transformer:

• A current transformer is a device that is used to measure high alternating current in a conductor.
• In the figure shown below the conductor act as the primary winding of a single turn that passed through the circular laminated iron core.
• The secondary winding consists of a large number of turns of fine wire wrapped around the core.
• Due to transformer action, the secondary current transforms into a lower value.

​

Let, Np is a number of turn in the primary winding

Ns is the number of turns in the secondary winding.

Ip and Is are primary and secondary turns respectively.

Therefore, the secondary current is given by,

\({I_s} = {I_p} × \frac{{{N_p}}}{{{N_s}}}\)

• Therefore, the current transformer changes the current into a lower value that can easily be measured by the measuring instrument.
• Along with a Potential transformer (PT), a current transformer (CT) can measure Power and energy also.
• Hence, CT used with Ammeter, Wattmeter, and Watt-hour meter.
   

​Calculation:

Given, N_p = 1, N_s = 8, I_p = 50 A

\({I_s} = {I_p} × \frac{{{N_p}}}{{{N_s}}}\)

I_s = 50 × (1 / 8)

I_s = 6.25 A

Ratio error in current transformer:

• In the current transformer, the primary current Ip should be exactly equal to the secondary current multiplied by turns ratio, i.e. KTIs.
• But there is a difference between primary current Ip should be exactly equal to the secondary current multiplied by the turns ratio.
• This difference is contributed by the core excitation or magnetizing component of no-load current.
• The error in the current transformer introduced due to this difference is called current error or ratio error.

The actual ratio of transformation varies with operating conditions and the error in secondary voltage is defined as

Percentage ratio error \( = \frac{{{K_n} - R}}{R} \times 100\)

Kn is the nominal ratio

R is the actual ratio

It can be reduced by secondary turns compensation i.e. slightly decreasing the secondary turns.

Phase angle error:

In an ideal voltage transformer, there should not be any phase difference between the primary voltage and the secondary voltage reversed. However, in an actual transformer, there exists a phase difference between Vo­ and V­s reversed.

The phase angle is taken as +ve when secondary voltage reversed leads the primary voltage.

The angle is -ve when the secondary voltage reversed lags the primary voltage.

It can be reduced by keeping the primary and secondary windings are wound as closely as possible.

Current Transformer:

The secondary side of the current transformer is always kept short-circuited in order to avoid core saturation and high voltage induction so that the current transformer can be used to measure high values of currents.

• The current transformer works on the principle of shorted secondary.
• It means that the burden on the system Zb is equal to 0.
• Thus, the current transformer produces a current in its secondary which is proportional to the current in its primary.

Important Points:

• The most important precaution in the use of a CT is that in no case should it be open-circuited (even accidentally).
• As the primary current is independent of the secondary current, all of it acts as a magnetizing current when the secondary is opened.
• This results in deep saturation of the core which cannot be returned to the normal state and so the CT is no longer usable.
• Again, due to large flux in the core, the flux linkage of secondary winding will be large which in turn will produce a large voltage across the secondary terminals of the CT.
• This large voltage across the secondary terminals will be very dangerous and will lead to insulation failure and there is a good chance that the person who is opening the CT secondary while primary is energized will get a fatal shock.

Phase angle error:

• Phase angle (δ) of the current transformer is the angle between the primary current Ip and secondary current Is when reversed.
• The primary and secondary phasor difference is to be 180° in the case of an ideal current transformer.
• But in practice, this angle having a difference of θ is called phase angle error.
• So, for practical current transformer θ + δ = 180°.
• The total primary current is not actually transformed in the current transformer. One part of the primary current is consumed for core excitation and the remaining is actually transformers with a turns ratio of the current transformer.
• Both ratio error and phase angle error are due to the excitation current Ie.
• Especially, the ratio error is due to the iron loss component Iw and phase angle error is due to magnetizing component I_m.

Calculation:

Given that,

Phase angle error θ = 5°

Phase angle between the primary current IP and secondary current IS  is given by 

 δ = 180° - θ

= 180° - 5°

= 175° 

Given that, impedance of secondary winding = 0.01 Ω

Rated current = 5 A

fault current = 20 times of rated current

= 20 × 5 = 100 A

The correct answer is option 1):\(\rm \theta=\frac{Im \ Cos \delta-Ic \ Sin \delta}{nIs} degree\)

Concept:

• The phase angle between the primary and secondary of the current transformer must be 180 degrees.
• The primary and secondary current must be out of phase.
• The deviation in the phase angle of the primary and secondary current is called the phase angle error.

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m = Magnetizing component of exciting current,

δ = Angle between secondary induced voltage and secondary current

Ic = Core loss component of exciting current

n = turns ratio

Is = Secondary winding current  

Ip= Primary winding current 

The correct answer is option 2):(Current transformer )

Concept:

• A current transformer's primary coil is always connected in series with the main conductor giving rise to it also being referred to as a series transformer. The nominal secondary current is rated at 1A or 5A for ease of measurement
• A current transformer is also called  ‘series transformer’
• A current transformer (CT) is an instrument transformer in which the secondary current is substantially proportional to the primary current and differs in phase from it by ideally zero degrees.
• The primary current of the CT does not depend upon whether the load or burden is connected to the secondary & also not on the impedance value of the burden.

Power transformer

• A power transformer is a static machine used for transforming power from one circuit to another without changing the frequency.
• A power transformer can increase or decrease the voltage and current, hence can be used as either a step-up or step-down transformer.

Current transformer

• A current transformer is a type of transformer that is mainly designed to reduce the high currents to a lower value for measurement and protection purposes.
• Basically, a current transformer is a voltage step-up and current step-down transformer which means when it reduces the current, it increases the voltage in the same ratio.
• A power transformer and a current transformer are always connected in opposite phase connection.

If a power transformer has a star-connected primary and a delta-connected secondary, the CT connections on its primary and secondary sides should be connected in delta and star respectively.

In order to nullify the phase shift of the Power transformer (PT), The Current transformers (CT) are connected in a reverse configuration.

Concept:

Phase angle:

The angle by which the secondary current phasor, when reversed, differs in phase from the primary current, is known as the phase angle of the transformer.

This angle is taken to be +ve if the secondary current reversed leads to the primary current. The angle is taken as -ve if the secondary current reversed lags behind the primary current.

The angle between Is reversed and Ip is θ. Therefore, the phase angle is θ.

From the phasor diagram,

\(\tan \theta = \frac{{bc}}{{\partial b}} = \frac{{bc}}{{0a + ab}} = \frac{{{I_0}\cos \left( {\delta + \alpha } \right)}}{{n\;{I_s} + {I_0}\sin \left( {\delta + \alpha } \right)}}\)

As θ is very small,

\(\theta = \frac{{{I_0}\cos \left( {\delta + \alpha } \right)}}{{n{I_s} + {I_0}\sin \left( {\delta + \alpha } \right)}}rad\)

Now, I0 is very small as compared to n Is and therefore, we can neglect the term I0 sin (δ + α)

\(\theta \approx \frac{{{I_0}\cos \left( {\delta + \alpha } \right)}}{{n\;{I_s}}}rad\)

\(\theta = \frac{{180}}{\pi }\left( {\frac{{{I_m}\cos \delta - {I_c}\sin \delta }}{{n\;{I_s}}}} \right)\) degree

This phase angle is involved in the measurement of power and energy, the phase angle error is necessary to reduce in these measurements.

Calculation:

N₁ = 1, N₂ = 500, I_s = 5A, R₂ = 1Ω

Magnetizing ampere turns = 200 AT

\({I_0} = \frac{{{\rm{Magnetizing\ amphere\ turns}}}}{{{\rm{Primary\ turns}}}} = 200A\)

Transformation ratio

\(\begin{array}{l} n = \frac{{{N_2}}}{{{N_1}}} = \frac{{500}}{1} = 500\\ \theta = \frac{{180}}{\pi }\left( {\frac{{{I_o}\cos \left( {\alpha + \delta } \right)}}{{n{I_s}}}} \right)\\ = \frac{{180}}{\pi }\left[ {\frac{{200 \times cos0^\circ }}{{500 \times 5}}} \right] = 4.6^\circ \end{array}\)

Instrument transformers are of two types.

1. Potential transformer

2. Current transformer

These are used to extend the range of induction type of instruments.

Important Points The advantages of instrument transformers over ammeter shunts and voltage multiplies are the metering circuit is electrically isolated from the power circuit thereby providing safety in use to both the instruments and the operator and small power losses in comparison to those in ammeter shunt and voltmeter multiplier.