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

Eddy's current loss:

• When an alternating magnetic field is applied to a magnetic material, an emf is induced in the material itself according to Faraday’s law of Electromagnetic induction.
• Since the magnetic material is a conducting material, these EMFs circulate current within the body of the material. These circulating currents are called Eddy currents. They are produced when the conductor experiences a changing magnetic field.
   

It is given by: \(P_e=K_eB_m^2t^2f^2V\)

where Ke = Eddy current loss coefficient

Hysteresis loss:

• Hysteresis loss in a transformer refers to the energy loss that occurs in the transformer's core material due to the repeated magnetization and demagnetization (cycling) when alternating current (AC) flows through it.
• Hysteresis loss in a transformer can be minimized by using soft magnetic materials for the core like permalloy or silicon iron.
   

It is given by: \(P_h=K_hfB_m^{1.6}\)

Core loss in the Transformer

The open-circuit test of a transformer is used to determine the core loss (iron loss), which consists of hysteresis and eddy current losses.

These losses are constant regardless of the load on the transformer because they depend only on the applied voltage, which remains the same in normal operation.

Explanation

• Transformer rating: 20 kVA
• Primary voltage (low-voltage side): 200 V
• Secondary voltage (high-voltage side): 400 V
• Power input during open-circuit test: 200 W

Since core loss is independent of load, it remains constant at all loading conditions, whether it is performed at no load or full load conditions.

Thus, the core loss when the transformer is fully loaded is still 200 W.

Losses in the transformer

Core Losses Or Iron Losses

• Eddy current loss and hysteresis loss depend on the magnetic properties of the material used for the construction of the core. So, these losses are also known as core losses or iron losses.
• Eddy's current loss: \(\rm W_e=kB_{max}^2f^2t^2V\)
• Hysteresis loss: \(\rm W_e=kB_{max}^{1.6}fV\)

Copper Loss

• Copper losses are due to the resistance of the wire in the primary and secondary windings and the current flowing through them.
• These losses can be reduced by using wire with a large cross-sectional area in the manufacturing of the coils.
   

Stray Loss

• The reason for the types of loss is the occurrence of the leakage field. When compared with copper and iron losses, the percentage of stray losses is less, so these losses can be neglected.
   

Dielectric Loss

• The oil of the transformer is the reason for this loss. Oil in a transformer is an insulating material. When the oil in the transformer deteriorates then the transformer’s efficiency will be affected.

Explanation:

Eddy currents, which are loops of electrical current induced within conductors by a changing magnetic field in the conductor, have various applications. One of the beneficial uses of eddy currents is in induction furnaces.

Induction Furnaces

Definition: Induction furnaces are electrical furnaces where the heat is generated by inducing eddy currents in the material to be melted. These furnaces use the principle of electromagnetic induction to heat and melt metals.

Working Principle: In an induction furnace, a high-frequency alternating current (AC) is passed through a coil, creating a rapidly changing magnetic field around the coil. When a conductive material, such as metal, is placed within this magnetic field, eddy currents are induced in the material. These eddy currents flow through the resistance of the material, generating heat due to the Joule heating effect. This heat is sufficient to melt the metal, allowing it to be used in various industrial processes.

Advantages:

• Precise Temperature Control: Induction furnaces allow for precise control of the temperature, making it possible to achieve the exact melting point required for different metals and alloys.
• High Efficiency: The generation of heat directly within the material to be melted ensures high energy efficiency, reducing energy consumption and operational costs.
• Cleaner Operation: Induction furnaces produce less environmental pollution compared to traditional fossil fuel-based furnaces, as they do not involve combustion processes.
• Uniform Heating: The induced eddy currents ensure uniform heating throughout the material, leading to consistent melting and better quality of the final product.
• Quick Start-Up: Induction furnaces have a rapid start-up time, allowing for quicker initiation of the melting process compared to conventional furnaces.

Applications: Induction furnaces are widely used in the metallurgical industry for melting and refining various metals, including steel, copper, aluminum, and precious metals. They are also used in foundries for casting operations and in the manufacturing of high-quality metal products.

The correct option is: Option 4: Induction furnaces

• In a 3-phase induction motor, the stator is laminated to reduce eddy current losses.
• Laminating the stator core minimizes the paths for eddy currents, thus reducing the circulating currents induced by the alternating magnetic field in the stator. This helps in lowering the energy lost as heat due to eddy currents.
• Although lamination also slightly reduces hysteresis losses, the primary purpose is to prevent eddy current losses.
   

Concept:

• The stator is a stationary part of the induction motor. A stator winding is placed in the stator of the induction motor and the three-phase supply is given to it.
• It carries a 3-phase winding and is fed from a 3-phase supply
• The stator of the induction motor consists of three parts

1. Stator Frame
2. Stator core
3. Stator winding
    

Stator Frame:

• It is the outer part of the three-phase induction motor.
• Its main function is to support the stator core and the field winding.
• It acts as a covering, and it provides protection and mechanical strength to all the inner parts of the induction motor.
• The frame is either made up of die-cast or fabricated steel.
• The frame of three phase induction motor should be strong and rigid as the air gap length of three phase induction motor is very small.
• Otherwise, the rotor will not remain concentric with the stator, which will give rise to an unbalanced magnetic pull.
   

Stator core:

• The main function of the stator core is to carry the alternating flux. In order to reduce the eddy current loss, the stator core is laminated.
• These laminated types of structures are made up of stamping which is about 0.4 to 0.5 mm thick.
• All the stamping is stamped together to form a stator core, which is then housed in a stator frame.
• The stamping is made up of silicon steel, which helps to reduce the hysteresis loss occurring in the motor.
   

Stator winding

• The slots on the periphery of the stator core of the three-phase induction motor carry three-phase windings
•  The three phases of the winding are connected either in star or delta depending upon which type of starting method we use. We start the squirrel cage motor mostly with star-delta starter and hence the stator of the squirrel cage motor is delta connected.
• It is supplied with 3 phase AC supply

Additional Information

• A commutator is a rotary electrical switch in certain types of electric motors and electrical generators that periodically reverses the current direction between the rotor and the external circuit. It is used to convert AC to DC
• The air gap of a motor is the gap between the stator teeth or core and the rotor magnets. This gap is a key component in the motor design and affects the overall strength of the magnetic circuit and motor efficiency.

Eddy Current:​

• Eddy currents are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday’s law of induction.
• Eddy currents flow in closed loops within conductors, in-plane perpendicular to the magnetic field.
• By Lenz law, the current swirls in such a way as to create a magnetic field opposing the change; for this to occur in a conductor, electrons swirl in a plane perpendicular to the magnetic field.
• Because of the tendency of eddy currents to oppose, eddy currents cause a loss of energy.
• Eddy currents transform more useful forms of energy, such as kinetic energy, into heat, which isn’t generally useful.
• Thus eddy currents are a cause of energy loss in alternating current (AC) inductors, transformers, electric motors and generators, and other AC machinery, requiring special construction such as laminated magnetic cores or ferrite cores to minimize them.
• Eddy currents are also used to heat objects in induction heating furnaces and equipment, and to detect cracks and flaws in metal parts using eddy-current testing instruments.

• The magnitude of the current in a given loop is proportional to the strength of the magnetic field, the area of the loop, and the rate of change of flux, and inversely proportional to the resistivity of the material.

Concept:

Hysteresis losses: These are due to the reversal of magnetization in the transformer core whenever it is subjected to alternating nature of magnetizing force.

\({W_h} = \eta B_{max}^xfv\)

\({B_{max}} \propto \frac{V}{f}\)

Where

x is the Steinmetz constant

Bm = maximum flux density

f = frequency of magnetization or supply frequency

v = volume of the core

At a constant V/f ratio, hysteresis losses are directly proportional to the frequency.

Wh ∝ f

Eddy current losses: Eddy current loss in the transformer is I2R loss present in the core due to the production of eddy current.

\({W_e} = K{f^2}B_m^2{t^2}V\)

\({B_{max}} \propto \frac{V}{f}\)

Where,

K - coefficient of eddy current. Its value depends upon the nature of magnetic material

Bm - Maximum value of flux density in Wb/m2

t - Thickness of lamination in meters

f - Frequency of reversal of the magnetic field in Hz

V - Volume of magnetic material in m3

At a constant V/f ratio, eddy current losses are directly proportional to the square of the frequency.

We ∝ f2

Iron losses or core losses or constant losses are the sum of both hysteresis and eddy current losses.

Wi = Wh­ + We

At constant V/f ratio, Wi = Af + Bf2

Calculation:

The table below shows the given data.

The V/f ratio is constant in all the cases as shown in the above table.

P_h ∝ f

\( \Rightarrow {P_{h2}} = \frac{{{f_2}}}{{{f_1}}} \times {p_h} = \frac{{40}}{{50}}{p_h} = 0.8{P_h}\)

Percentage decrease in P_h = 20%

P_e ∝ f²

\( \Rightarrow {P_{e2}} = {\left( {\frac{{{f_2}}}{{{f_1}}}} \right)^2} \times {p_h} = {\left( {\frac{{40}}{{50}}} \right)^2}{p_e} = 0.64{P_e}\)

Percentage decrease in P_e = 36%​

Concept:

In a transformer iron loss or core loss can be calculated as

Iron losses = Eddy current loss + hysteresis loss

Eddy current loss, \({P_e} = K{f^2}B_m^2{t^2}V\) 

Hysteresis loss = Kh B^η f

Where,

K = co-efficient of eddy current. Its value depends upon the nature of magnetic material

Bm = Maximum value of flux density in Wb/m2

t = Thickness of lamination in meters

f = Frequency of reversal of magnetic field in Hz

V = Volume of magnetic material in m3

K_h = Hysteresis constant

Hence

\({P_e} \propto B_m^2{f^2}{t^2}\)

\(P_e \propto {\left( {\frac{v}{f}} \right)^2} \times {f^2}{t^2}\left(\because {{B_m}\alpha \frac{V}{f}} \right)\)

When flux density (B_m) is constant, then eddy current losses are

P_e ∝ V2 t2  

and hysteresis losses are

\({P_h} \propto B_m^{1.6}f \propto \frac{{{V^{1.6}}}}{{{f^{0.6}}}}\)

Calculation:

Given-

f = 50 Hz

P_e1 = 50 W

V₁ = 220 V

V₂ = 330 V

In the given question

V / f is not same in both cases

Hence flux density is not constant

∴ \({\frac{P_e1}{P_e2}} \propto {\left( {\frac{(V_1)f}{fV_2}} \right)^2} \times {f^2}{t^2}\left(\because {{B_m}\alpha \frac{V}{f}} \right)\)

∴ P_e2 = \( {\left( {\frac{330}{220}} \right)^2} \times 50\)

P_e2 = 112.5 W

Concept:

Iron losses (P_i) = Hysteresis loss(P_h) + Eddy current loss(P_e)

Hysteresis loss ∝ Bⁿ f ∝  f

Bⁿ is flux density

with flux density being kept constant → Hysteresis loss ∝ k₁ f

Eddy current loss ∝ B² f² ∝ f²

 with flux density being kept constant → Eddy current loss ∝ K² f² 

Where, K₁ and K2 are constant for a particular transformer.

Hence total iron losses

P_i = k₁f + k₂f²

Calculation:

Given:

For 40 Hz frequency 

Core (iron) loss (Pi) = 800 watts

P_h = 600 = k₁f 

⇒ k₁ = 600/40 = 15

P_e = (800 - 600) = 200 = k₂f²

⇒ k₂ = (200/ 40²) =0.125

For 60 Hz frequency

P_i = (15 × 60) + (0.125)(60²)= 1350 watts

Concept:

Losses in a transformer

Iron loss: Losses that are generated in the conducting core laminations by the alternating magnetic field due to hysteresis and eddy currents.         

These losses are constant at all load variations.

Hysteresis loss: When the core of the transformer is applied to an alternating magnetizing force and for each cycle of emf a hysteresis loop is traced out. Power is dissipated in the form of heat known as hysteresis loss.

P_h = K_η B_mⁿf V

Where, P_h = Hysteresis loss (W)

η  = Steinmetz hysteresis coefficient, depending on material (J/m³)

B_m = Maximum flux density (Wb/m²)

n = Steinmetz exponent, ranges from 1.5 to 2.5, depending on material

f = Frequency (Hz)

V = Volume of magnetic material (m³)

Eddy current losses: When an alternating magnetic flux links with a conducting surface, it induces electric currents in this surface as currents can’t go anywhere, but as the potential across the surface is continuously changing, the currents tend to circulate through the surface these are known as eddy currents and heat generated by it is known as eddy current losses.

P_e = K_eB_m² f² t² V

Where, P_e = Eddy current loss (W)

K_e = Coefficient of eddy current.

B_m = Maximum value of flux density (wb/m²)

t = Thickness of lamination  (m)

f = Frequency (Hz)

V = Volume of magnetic material (m³)

Copper losses: Losses that are caused by currents flowing in the primary and secondary windings.

 These losses changes with change in loads.

Hysteresis losses can be minimized by

• Choosing a material with less hysteresis loop area.
• Core stamping

Eddy current losses can be minimized by

• Cores are cut into thin laminated sheets.
• The resistance of the core should be increased, Therefore by adding 3% silicon to the iron core its resistance is increased.
• The laminations are thin with relatively high resistance.

Losses in the transformer:

1.) Core loss:

• It is a loss that happens in the core of a transformer when it is subjected to the change in magnetic flux \((\phi = {V \over f})\)
• Hence, core loss depends upon supply voltage and frequency.
• Core losses remain constant with an increase or decrease in the load.
• Core loss is the sum of eddy current loss and the hysteresis loss.
• The induced emf produces a current known as eddy current. The losses due to this current are known as eddy current losses.
• The losses in a transformer that are due to magnetization saturation in the core are known as hysteresis losses.

2.) Copper loss:

•  The losses produced due to heat produced by electrical currents in the transformer windings are known as the copper losses.
• These losses increase with an increase in loading conditions.

3.) Stray magnetic losses:

• The losses occurring in the transformer due to the presence of external magnetic field nearby transformer are known as stray magnetic losses.

Concept:

A transformer has mainly two types of losses

• core losses
• copper losses.

Core loss, which is also referred to as iron loss, consists of hysteresis loss and eddy current loss.

These two losses are constant when the transformer is charged. That means the amount of these losses does not depend upon the condition of a secondary load of the transformer. In all loading conditions, these are fixed.

Copper losses are directly proportional to the square of the load on the transformer.

\({W_{cu}} = {x^2}{W_{cufl}}\)

Here, x is the percentage of the full load of the transformer.

Wcufl­ is the copper losses at the full load.

As there is no change in the load, load current current will ramain same hence copper loss will be same as previous

We have,

Eddy current and hysteresis losses vary as the square of flux density.

⇒ Iron Loss (Eddy Current loss + Hysteresis loss) ∝ (flux density)²

⇒ P_i ∝ B² .... (1)

Using the concept of the EMF equation,

V ∝ f B

⇒ B ∝ V/f .... (2)

Here B is the flux density

Using equation (1) & (2),

Pi ∝ \(\frac{V^2}{f^2}\)

Since the rated voltage is constant,

∴ P_i ∝ \(\frac{1}{f^2}\)

Case 1:

P_i = 10 W and,

f = 400 Hz

⇒ 10 ∝ \(\frac{1}{400^2}\) .... (3)

Case 2:

P_i = ?

f = 50 Hz

⇒ P_i ∝ \(\frac{1}{50^2}\) .... (3)

From equation (2) & (3),

\(\frac{P_i}{10}=\frac{400^2}{50^2}=64\)

Hence, Pi = 64 × 10 = 640 W

Losses in the transformer:

1.) Core loss: 

• It is a loss that happens in the core of a transformer when it is subjected to the change in magnetic flux \((\phi = {V \over f})\)
• Hence, core loss depends upon supply voltage and frequency.
• Core losses remain constant with an increase or decrease in the load.
• Core loss is the sum of eddy current loss and the hysteresis loss.
• The induced emf produces a current known as eddy current. The losses due to this current are known as eddy current losses.
• The eddy current loss is given by: P_e = k(Bmax)2 f2vt2
• The losses in a transformer due to magnetization saturation in the core are known as hysteresis losses.
• The hysteresis loss is given by: P_h = η(Bmax)1.6 fv

2.) Copper loss:

• The losses due to the heat produced (I²R) by electrical currents in the transformer windings are known as the copper losses.
• These losses increase with an increase in loading conditions.

3.) Windage loss:

• Windage losses are caused by friction in the bearings or in the rotating parts of the motor or generator.
• These losses are proportional to the winding factor (αN²).

Eddy Current Loss:

• When an alternating magnetic field is applied to a magnetic material, an emf is induced in the material itself according to Faraday’s Law of Electromagnetic induction.
• Since the magnetic material is a conducting material, this EMF circulates current within the body of the material.
• These circulating currents are called Eddy Currents. They will occur when the conductor experiences a changing magnetic field.
• As these currents are not responsible for doing any useful work, and it produces a loss (I²R loss) in the magnetic material known as an Eddy Current Loss.

Mathematical Expression for Eddy Current Loss:

The eddy current power loss in a magnetic material is given by the equation shown below:
 \({P_e} = {K_e}B_m^2{t^2}{f^2}V\)watts
where,
K_e – co-efficient of eddy current. Its value depends upon the nature of magnetic material
B_m – maximum value of flux density in Wb/m²
t – thickness of lamination in meters
f – frequency of reversal of the magnetic field in Hz
V – The volume of magnetic material in m³

From eddy current loss equation we can write

P_e ∝\(B_m^2{f^2}\)

B_m ∝ (V / f)

P_e ∝ V²

The eddy current loss at constant voltage is independent of transformer frequency

\(\frac{{{P_{e60}}}}{{{P_{e50}}}} = \frac{{V_{60}^2}}{{V_{50}^2}} = \frac{1}{1}\)

The ratio of eddy current loss at 60 Hz to 50 Hz at constant voltage is 1:1