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

Explanation:

Reducing Eddy Current Loss in Armature Core

Definition: Eddy current loss is a type of power loss that occurs in the core of electrical machines such as motors, transformers, and generators. It is caused by circulating currents induced within the conductive material of the core due to the alternating magnetic flux. These currents flow in loops within the material, producing heat and resulting in energy loss.

Working Principle of Eddy Currents:

Eddy currents are induced in a conductor when it is exposed to a changing magnetic field, as per Faraday's law of electromagnetic induction. The magnitude of these currents depends on the rate of change of the magnetic flux, the material's electrical conductivity, and the geometry of the conductor. The circulating currents create their own magnetic field, which opposes the original magnetic field (as stated by Lenz's law), leading to energy dissipation in the form of heat.

Correct Option Analysis:

The correct option is:

Option 4: By laminating the core to reduce the flow of eddy currents.

This is the most effective method for minimizing eddy current loss. The lamination process involves dividing the core into thin layers or sheets of insulated material. These laminations are stacked together, and each layer is electrically insulated from the others, typically using a thin coating of varnish or oxide. The purpose of laminating the core is to restrict the flow of eddy currents by reducing the area available for their circulation. As a result, the eddy current paths are interrupted, and their magnitude is significantly decreased.

Why Laminating the Core Works:

• The induced voltage in the core due to the alternating magnetic flux is proportional to the rate of change of flux and the area of the loop (as per Faraday's law). By reducing the cross-sectional area of the loops using laminations, the induced voltage and hence the eddy current magnitude are minimized.
• The heat generated by eddy currents is directly proportional to the square of the current. Therefore, reducing the magnitude of eddy currents through lamination significantly reduces energy losses.
• Laminations are typically made of high-resistance materials like silicon steel, which further limits the flow of eddy currents.

Advantages of Lamination:

• Significant reduction in eddy current losses, improving the efficiency of electrical machines.
• Cost-effective and straightforward technique for core design.
• Improved thermal performance due to reduced heat generation.

Applications:

Laminated cores are widely used in transformers, electric motors, generators, and other electrical machines where alternating magnetic fields are present. This technique is crucial for ensuring the efficient operation of these devices.

Additional Information:

Eddy current loss is one of the two primary core losses in electrical machines, the other being hysteresis loss. While lamination is effective for reducing eddy current loss, hysteresis loss is minimized by using magnetic materials with low hysteresis, such as silicon steel.

Important Information

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

Option 1: By increasing the motor's speed.

This option is incorrect as increasing the motor's speed does not reduce eddy current loss. In fact, higher speeds result in a higher rate of change of magnetic flux, which increases the induced voltage and, consequently, the eddy currents. This leads to greater energy loss and heat generation.

Option 2: By increasing the core resistance.

While increasing the core resistance can theoretically reduce eddy current losses, it is not a practical solution. Core resistance is primarily determined by the material properties and geometry of the core. Lamination is a more effective and feasible method for increasing the core's effective resistance to eddy currents without compromising the machine's performance.

Option 3: By using a high resistance core material.

Using high-resistance materials like silicon steel can help in reducing eddy current losses. However, this alone is not sufficient to completely mitigate the problem. Lamination remains the most effective method for minimizing eddy currents, even when high-resistance materials are used.

Option 5: (No option provided in this case).

This option is not applicable in the given context.

Conclusion:

Among the given options, laminating the core to reduce the flow of eddy currents is the most effective and widely used method for minimizing eddy current losses. This technique significantly improves the efficiency and performance of electrical machines by reducing energy dissipation and heat generation. Understanding and implementing effective strategies to mitigate core losses is essential for the optimal design and operation of electrical devices.

The correct answer is option 2):(iron losses)

Concept:

Losses in a D.C. Machine: The losses in a DC machine can be divided as,

Where,

Ia is the 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 the DC machine

Armature copper losses:

Armature copper losses =I_a²R_a

These losses are about 30% 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_sh²R_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) = ηB_max^1.6fv

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.

In order to reduce 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.

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) = $\eta B_{max}^{1.6}fv$

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) = $K_e{B}_{max}^2{f}^2{t}^{2}v$

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 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 ∝ t2

• In order to reduce the eddy current losses, we use laminations
• In a DC machine, laminations are used to reduce eddy current losses and for insulation purposes. The approximate thickness of laminations is 0.5 mm.
• The stator frame consists of laminations of silicon steel, usually with a thickness of about 0.5 millimetre.​

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 W_e = KB²_m f²t²

Where,

K = π²/ 6ρ,

B_m = 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.

W_e ∝ f²

Calculation:

Given that,

Eddy current loss at 40 Hz frequency (f₁) is W_e1 = 400 W

Maximum flux density B_m is constant

Let's consider eddy current loss at 50 Hz frequency (f₂) as W_e2

We know that for constant flux density We ∝ f2

$\frac{{\mathrm{W}}_{\mathrm{e}1}}{{\mathrm{W}}_{e2}}=\frac{f_1^2}{f_2^2}$

$\frac{400}{{\mathrm{W}}_{e2}}=\frac{{40}^2}{{50}^2}$

W_e2 = 625 W

Key Points

Hysteresis loss can be determined by using the Steinmetz formula given by,

W_h = η B^x_m f V

Where,

B_m = maximum flux density.

f = supply frequency

V = volume of the core 

x = hysteresis coefficient (range 1.5 to 2.5)

If maximum flux density is constant then hysteresis loss is directly proportional to frequency.

W_h ∝ f

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 ∝ t2

• In order to reduce the eddy current losses, we use laminations
• In a DC machine, laminations are used to reduce eddy current losses and for insulation purposes. The approximate thickness of laminations is 0.5 mm.
• The stator frame consists of laminations of silicon steel, usually with a thickness of about 0.5 millimetre.​

• The armature windings of both the D.C. and A.C. machines have to deal with alternating currents only.
• In DC machine also alternating current flow in armature which by mechanical rectifier (commutator) is converted into direct current with ripples.
• Eddy current losses are due to emf induced by a changing magnetic field. This emf causes the circulating current in the core which causes power loss.
• The process of lamination involves dividing the core into thin layers held together by insulating materials such as Varnish, Impregnated paper etc.
• 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.

Therefore, both Statement I and Statement II are individually true and Statement II is the correct explanation of Statement I.

The correct answer is option 2):(iron losses)

Concept:

Losses in a D.C. Machine: The losses in a DC machine can be divided as,

Where,

Ia is the 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 the DC machine

Armature copper losses:

Armature copper losses =I_a²R_a

These losses are about 30% 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_sh²R_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) = ηB_max^1.6fv

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.

In order to reduce 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.

Hysteresis losses: When the armature-iron of a dc machine rotates, it goes through the influence of the north and the south poles, thus causing cyclic variations of the linked magnetic flux and resulting in the occurrence of hysteresis loss in the armature core.

Hysteresis losses can be minimized by using material having least hysteresis loop area. The laminated armature construction limits the eddy current losses to a lower value but not hysteresis loss.

Explanation:

Reducing Eddy Current Loss in Armature Core

Definition: Eddy current loss is a type of power loss that occurs in the core of electrical machines such as motors, transformers, and generators. It is caused by circulating currents induced within the conductive material of the core due to the alternating magnetic flux. These currents flow in loops within the material, producing heat and resulting in energy loss.

Working Principle of Eddy Currents:

Eddy currents are induced in a conductor when it is exposed to a changing magnetic field, as per Faraday's law of electromagnetic induction. The magnitude of these currents depends on the rate of change of the magnetic flux, the material's electrical conductivity, and the geometry of the conductor. The circulating currents create their own magnetic field, which opposes the original magnetic field (as stated by Lenz's law), leading to energy dissipation in the form of heat.

Correct Option Analysis:

The correct option is:

Option 4: By laminating the core to reduce the flow of eddy currents.

This is the most effective method for minimizing eddy current loss. The lamination process involves dividing the core into thin layers or sheets of insulated material. These laminations are stacked together, and each layer is electrically insulated from the others, typically using a thin coating of varnish or oxide. The purpose of laminating the core is to restrict the flow of eddy currents by reducing the area available for their circulation. As a result, the eddy current paths are interrupted, and their magnitude is significantly decreased.

Why Laminating the Core Works:

• The induced voltage in the core due to the alternating magnetic flux is proportional to the rate of change of flux and the area of the loop (as per Faraday's law). By reducing the cross-sectional area of the loops using laminations, the induced voltage and hence the eddy current magnitude are minimized.
• The heat generated by eddy currents is directly proportional to the square of the current. Therefore, reducing the magnitude of eddy currents through lamination significantly reduces energy losses.
• Laminations are typically made of high-resistance materials like silicon steel, which further limits the flow of eddy currents.

Advantages of Lamination:

• Significant reduction in eddy current losses, improving the efficiency of electrical machines.
• Cost-effective and straightforward technique for core design.
• Improved thermal performance due to reduced heat generation.

Applications:

Laminated cores are widely used in transformers, electric motors, generators, and other electrical machines where alternating magnetic fields are present. This technique is crucial for ensuring the efficient operation of these devices.

Additional Information:

Eddy current loss is one of the two primary core losses in electrical machines, the other being hysteresis loss. While lamination is effective for reducing eddy current loss, hysteresis loss is minimized by using magnetic materials with low hysteresis, such as silicon steel.

Important Information

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

Option 1: By increasing the motor's speed.

This option is incorrect as increasing the motor's speed does not reduce eddy current loss. In fact, higher speeds result in a higher rate of change of magnetic flux, which increases the induced voltage and, consequently, the eddy currents. This leads to greater energy loss and heat generation.

Option 2: By increasing the core resistance.

While increasing the core resistance can theoretically reduce eddy current losses, it is not a practical solution. Core resistance is primarily determined by the material properties and geometry of the core. Lamination is a more effective and feasible method for increasing the core's effective resistance to eddy currents without compromising the machine's performance.

Option 3: By using a high resistance core material.

Using high-resistance materials like silicon steel can help in reducing eddy current losses. However, this alone is not sufficient to completely mitigate the problem. Lamination remains the most effective method for minimizing eddy currents, even when high-resistance materials are used.

Option 5: (No option provided in this case).

This option is not applicable in the given context.

Conclusion:

Among the given options, laminating the core to reduce the flow of eddy currents is the most effective and widely used method for minimizing eddy current losses. This technique significantly improves the efficiency and performance of electrical machines by reducing energy dissipation and heat generation. Understanding and implementing effective strategies to mitigate core losses is essential for the optimal design and operation of electrical devices.

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) = $\eta B_{max}^{1.6}fv$

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) = $K_e{B}_{max}^2{f}^2{t}^{2}v$

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 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 ∝ t2

• In order to reduce the eddy current losses, we use laminations
• In a DC machine, laminations are used to reduce eddy current losses and for insulation purposes. The approximate thickness of laminations is 0.5 mm.
• The stator frame consists of laminations of silicon steel, usually with a thickness of about 0.5 millimetre.​

• The armature windings of both the D.C. and A.C. machines have to deal with alternating currents only.
• In DC machine also alternating current flow in armature which by mechanical rectifier (commutator) is converted into direct current with ripples.
• Eddy current losses are due to emf induced by a changing magnetic field. This emf causes the circulating current in the core which causes power loss.
• The process of lamination involves dividing the core into thin layers held together by insulating materials such as Varnish, Impregnated paper etc.
• 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.

Therefore, both Statement I and Statement II are individually true and Statement II is the correct explanation of Statement I.

The correct answer is option 2):(iron losses)

Concept:

Losses in a D.C. Machine: The losses in a DC machine can be divided as,

Where,

Ia is the 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 the DC machine

Armature copper losses:

Armature copper losses =I_a²R_a

These losses are about 30% 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_sh²R_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) = ηB_max^1.6fv

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.

In order to reduce 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.

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 W_e = KB²_m f²t²

Where,

K = π²/ 6ρ,

B_m = 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.

W_e ∝ f²

Calculation:

Given that,

Eddy current loss at 40 Hz frequency (f₁) is W_e1 = 400 W

Maximum flux density B_m is constant

Let's consider eddy current loss at 50 Hz frequency (f₂) as W_e2

We know that for constant flux density We ∝ f2

$\frac{{\mathrm{W}}_{\mathrm{e}1}}{{\mathrm{W}}_{e2}}=\frac{f_1^2}{f_2^2}$

$\frac{400}{{\mathrm{W}}_{e2}}=\frac{{40}^2}{{50}^2}$

W_e2 = 625 W

Key Points

Hysteresis loss can be determined by using the Steinmetz formula given by,

W_h = η B^x_m f V

Where,

B_m = maximum flux density.

f = supply frequency

V = volume of the core 

x = hysteresis coefficient (range 1.5 to 2.5)

If maximum flux density is constant then hysteresis loss is directly proportional to frequency.

W_h ∝ f