Transformer Eddy Current Loss MCQ Quiz - Objective Question with Answer for Transformer Eddy Current Loss - 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: \(P_h=K_hfB_m^{1.6}\)

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

The correct answer is "option 1"

Concept: 

• A transformer at no-load (meaning, when its secondary winding is open, and there is no load connected to it) primarily behaves like an inductor.
• When AC voltage is applied to the primary winding of a transformer with no load connected to the secondary, a small current, known as the no-load current flows in the primary winding.
• This current is necessary to magnetize the core and is responsible for creating the magnetic field that links the primary and secondary windings.

Additional Information

•  The key behaviors and properties of a transformer at no-load are:
  • Magnetizing Current:The no-load current has two components: the magnetizing current and the core loss (iron loss) current.
    • The magnetizing current creates the magnetic field in the transformer core.
  • Core Loss (Iron Loss):This consists of hysteresis and eddy current losses in the transformer core.
    •  which are present due to the alternating nature of the magnetic field.
    • The core loss current component of the no-load current is responsible for these losses.
• The no-load current lags the applied voltage by almost 90 degrees because it mainly behaves as an inductance.
• However, due to the core loss component, the actual phase difference is slightly less than 90 degrees.0

• Minimal Copper Loss: Since the no-load current is typically much smaller than the full-load current, the I²R losses (copper losses) in the windings are minimal at no load.
• Voltage Regulation: At no-load, the transformer's voltage regulation is at its best because there are minimal drops across the transformer's windings due to the low current

Important Points

•  This magnetizing current (no-load current) is about 2 - 5% of the full load current and it accounts for the losses in a transformer.

Concept:

The correct answer is: 1) Eddy currents convert useful energy into heat and waste it.

• Eddy currents are circulating currents induced in conductors when they are exposed to a changing magnetic field. When eddy currents flow in a conductor, they generate heat due to the resistance of the material. This heat is a form of energy loss and is generally considered a waste of useful energy.
• Eddy currents flow in closed loops in a conductor, but they do not flow in straight lines like a wire. Instead, they flow in circular paths within the conductor, and the flow of these currents creates a magnetic field that opposes the original changing magnetic field that induced the eddy currents. This is known as Lenz's Law.
• Although eddy currents are generally considered a source of energy loss, they can also be harnessed in some applications. For example, in electrical generators, the movement of a magnetic field relative to a coil induces eddy currents in the coil, which can be converted into electrical energy. However, the design of electrical machines often includes measures to minimize eddy current losses, such as using laminated cores or magnetic materials with low electrical conductivity.

Additional InformationEddy's current losses:

• 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 EMF’s circulates 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.
• The process of lamination involves dividing the core into thin layers held together by insulating materials.
• Due to lamination effective cross-section area of each layer reduces and hence the effective resistance increases.
• As effective resistance increases, the eddy current losses will get decrease.

Mathematically, the eddy current loss is given by:

Eddy current loss in the transformer is given by:

Pe = Ke Bm2. t2. f2. V Watts

Where;

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

From the above formula, we conclude that the Eddy current loss is proportional to the square of the frequency.

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:

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

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

The correct answer is option 1):(By careful selection of slot numbers, tooth/slot geometry and air gap)

Concept:

Stray losses:

• The increment in the core loss caused by the distortion of air gap flux plus the increment in ohmic loss i.e. I2R loss due to non uniform distribution of conductor current is called Stray Load Loss.
• Stray Load loss consists of two components:

1. One originating in the iron part and other in the armature conductor. Again, in iron part of machine, the Stray Load loss consists of Eddy Current Loss in the Stator Cover, End Frames etc. caused by the armature leakage flux under loaded condition
2. Increased loss in the teeth due to distortion of the flux density wave.

• These losses will vary according to the square of the load current and are caused by leakage flux induced by load currents in the laminations and account for 4 to 5 % of total losses. These losses are reduced by careful selection of slot numbers, tooth/slot geometry, and air gap.

Concept:

Eddy current losses:

• 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 EMF’s circulates 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.
• The process of lamination involves dividing the core into thin layers held together by insulating materials.
• Due to lamination effective cross-section area of each layer reduces and hence the effective resistance increases.
• As effective resistance increases, the eddy current losses will get decrease.

Mathematically, the eddy current loss is given by:

Eddy current loss in the transformer is given by:

Pe = Ke Bm2. t2. f2. V Watts

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

From the above formula, we conclude that the Eddy current loss is proportional to the square of the frequency.

Observation:

Since the Eddy current loss is proportional to the square of the thickness of the lamination.

∴ The eddy current loss in a transformer can be reduced by decreasing the thickness of the laminations.

Concept:

Eddy current loss:

• Eddy current loss is basically I2 R loss present in the core due to the production of eddy currents in the core, because of its conductivity.
• Eddy current losses are directly proportional to the conductivity of the core.
• Eddy current losses can be reduced by either by adding silica content (4% - 5 %) to steel or by using a laminated core instead of a solid core.

Eddy current loss is given by We = KB2m f2t2

Where,

K = π2/ 6ρ,

Bm = maximum flux density,

f = supply frequency,

t = thickness of the laminations

If maximum flux density is constant, and thickness also constant,

In that case, eddy current losses are directly proportional to the square of the frequency.

We ∝ f2

Additional Information

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

\({W_h} = \eta B_m^{1.6}fv\)

Where, η = Steinmetz constant

Bm = maximum flux density

f = frequency of magnetization or supply frequency

v = volume of the core

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

B_m = 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.

W_h ∝ 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

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 - Volume of magnetic material in m³

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

W_e ∝ f²

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

W_i = W_h­ + W_e

At constant V/f ratio, W_i = 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.

Now, the equations for Case 1 and Case 2 are given below

Case 1: 450 = A (50) + B (50)²

Case 2: 320 = A (40) + B (40)²

By solving the above two equations,

A = 4, B = 0.1

Now, the required value for the Case 3 is

W₃ = 4 (25) + 0.1 (25)² = 162. 5 W

Consider example of Losses in a D.C. Machine:

The losses in a DC machine can be divided as,

Where,

Ia is armature current

If is field current (For series motor, Ia = If)

Ra is armature resistance

Rf is field resistance

N is the rotating speed of DC machine

Armature copper losses:

• Armature copper losses \(= I_a^2{R_a}\)
• These losses are about 30%-40% of the total full load losses.
• Armature copper losses in a DC generator vary significantly with the load current.
   

Field copper losses:

• Field copper losses \(= I_{sh}^2{R_{sh}}\)
• These losses are about 25% theoretically, but practically it is constant.
   

Iron Loss or Core Loss:

• These losses occur in the armature of a d.c. machine and are due to the rotation of armature in the magnetic field of the poles.
• It depends on the frequency (Speed) and voltage and does not depend on load or load current.
   

(i) Hysteresis loss:

• Hysteresis loss occurs in the armature of the DC machine since any given part of the armature is subjected to magnetic field reversals as it passes under successive poles.
   

Hysteresis loss (Ph) = \(η B_{max}^{1.6}fv\)

Where Bmax (∝ V/f) = Maximum flux density in the armature

f = Frequency of magnetic reversals

v = Volume of armature in m3

η = Steinmetz hysteresis co-efficient

• In order to reduce Hysteresis loss in a DC machine, the armature core is made of such materials which have a low value of Steinmetz hysteresis co-efficient or high permeability e.g., silicon steel.
   

(ii) Eddy current loss:

• In addition to the voltages induced in the armature conductors, there are also voltages induced in the armature core.
• These voltages produce circulating currents in the armature core which causes eddy current loss.

Eddy current loss (Pe) = \(K_eB_{max}^2f^2t^2v\)

Where Ke = Constant depending upon the electrical resistance of core and, t = Thickness of lamination in m.

• In order to reduced Eddy, the current loss lamination thickness should be kept as small as possible.
   

Mechanical losses:

These losses are due to friction and windage,

(i) friction loss e.g., bearing friction, brush friction, etc.

(ii) windage loss i.e., air friction of rotating armature.

These losses depend upon the speed of the machine. But for a given speed, they are practically constant.

Note: Iron losses and mechanical losses together are called stray losses.

Eddy current loss:

• Eddy current loss is basically I²R loss present in the core due to the production of eddy currents in the core because of its conductivity.
• Eddy current is directly proportional to the conductivity of the core.
• The resistance offered by the core is inversely proportional to the conductivity of the core.
• So, the core material which has more resistivity will offer less eddy current loss.
• The ferrite core usually offers more resistivity to the eddy currents than the iron core.
• Hence, a ferrite core has less eddy current loss than an iron core because ferrites have high resistance.
• Due to the high permeability property of the ferrite core, it should be having high reluctance.
• This reluctance is analogous to resistance in electrical circuits.

Concept:

• To reduce the eddy current losses, most  low-frequency power transformers and inductors use laminated cores , made of stacks of thin sheets of silicon steel.
• RF coils are mostly air core types, which can be described as an inductor that does not use a magnetic core made of a ferromagnetic material. The term air-core type refers to coils wound on plastic, ceramic, or other nonmagnetic forms, as well as those that have only air inside the windings.
• Air core coils have lower inductance than ferromagnetic core coils but are often used at high frequencies because they are free from energy losses called core losses that occur in ferromagnetic cores. We, therefore, conclude that the RF coil does not use a laminated core.

Important Points 

Copper loss:

The low-resistance copper cable used for the windings remains resistant and thus leads to heat loss.

Reducing method: By using thick wires with considerably low resistance.

Leakage of flux:

If the core design is not good then the flux produced by the primary coil may not all be connected to the secondary coil.

Reducing method: By considering the shell type core.

Eddy currents loss:

• The varying magnetic field not only induces secondary coil currents but also iron core currents themselves.
• In the iron core, these currents flow in small circles and are termed eddy currents. 

Reducing method: By considering the laminated core.

Hysteresis loss:

This is because of the repeated iron core magnetization and demagnetization induced by the alternating input current. 

Reducing method: By using alloys such as mumetal or silicon steel.