Effect of Excitation on Armature Current and Power Factor MCQ Quiz - Objective Question with Answer for Effect of Excitation on Armature Current and Power Factor - Download Free PDF

Explanation:

Inverted V-Curves

Definition: Inverted V-curves are graphical representations of the relationship between the armature current and excitation in a synchronous machine, such as a generator or motor. The term "inverted V-curve" arises from the characteristic shape of the graph, which resembles an inverted "V" or a downward-facing triangle.

Correct Option Analysis:

Option 2: Power factor peaks at optimal excitation (unity PF).

This is the correct explanation for why inverted V-curves have an inverted "V" shape. The power factor (PF) of a synchronous machine is dependent on its excitation level. When the machine operates at optimal excitation, the power factor reaches unity (1), meaning the voltage and current are perfectly in phase. At this point, the armature current is minimized because the machine operates efficiently without excessive reactive power. As the excitation deviates from this optimal level—either under-excited or over-excited—the power factor decreases, leading to an increase in armature current. This behavior creates the characteristic inverted "V" shape in the graph of armature current versus excitation.

Explanation of Power Factor:

Power factor is a measure of how effectively electrical power is converted into useful work output. It is the cosine of the angle between voltage and current. A synchronous machine achieves unity power factor (cosθ = 1) when the excitation is adjusted such that the reactive power is minimized, and the machine operates purely with active power. At unity power factor, the armature current is at its lowest, and the machine operates most efficiently.

How Inverted V-Curves are Formed:

• When the excitation is less than the optimal level (under-excitation), the machine requires reactive power from the system, causing the armature current to increase.
• When the excitation is greater than the optimal level (over-excitation), the machine supplies reactive power to the system, which also increases the armature current.
• The minimum armature current occurs at the optimal excitation level, where the power factor is unity.

Importance of Inverted V-Curves:

• Inverted V-curves help operators understand the relationship between excitation and armature current, enabling them to adjust the excitation for efficient operation.
• They are essential in identifying the conditions for unity power factor operation, which minimizes losses and ensures stable system performance.

Additional Information

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

Option 1: Mechanical load affects excitation linearly.

This option is incorrect. The inverted V-curve shape is not caused by the mechanical load affecting excitation linearly. While mechanical load does influence synchronous machine operation, the characteristic inverted "V" shape arises specifically from the relationship between armature current and excitation, which is driven by the reactive power and power factor behavior, not the mechanical load.

Option 3: Stator resistance varies non-linearly with excitation.

This option is incorrect. The stator resistance in a synchronous machine is generally constant and does not vary with excitation. The inverted V-curve is a result of the interplay between excitation, reactive power, and armature current, not changes in stator resistance.

Option 4: Armature current peaks at unity power factor.

This option is incorrect and is the opposite of what occurs in an inverted V-curve. At unity power factor, the armature current is minimized, not maximized. This is because the machine operates most efficiently at this point, with minimal reactive power and optimal excitation.

Option 5: (No explanation provided in the question).

Since no explanation is provided for option 5, it is impossible to evaluate its correctness. However, based on the given options, the correct reasoning for the inverted V-curve shape is provided in option 2.

Conclusion:

The inverted V-curve shape in synchronous machines arises from the relationship between armature current and excitation. At optimal excitation, the machine achieves unity power factor, resulting in minimized armature current. Deviations from this optimal level (either under-excitation or over-excitation) increase the armature current due to changes in reactive power. This behavior creates the characteristic inverted "V" shape, which is critical for understanding and optimizing the operation of synchronous machines.

The voltage drop is minimum for unity power factors.

In an alternator, armature reaction refers to the effect of the armature current on the magnetic field of the machine. This interaction results in a distortion of the magnetic field, leading to changes in the terminal voltage.

The voltage drop due to armature reaction is minimized when the power factor is unity, meaning the load is purely resistive. In such a case, the armature reaction has the least impact on the voltage, resulting in the minimum voltage drop.

There are three causes of voltage drop in the alternator.

• Armature circuit voltage drop due to resistance
• Armature reactance
• Armature reaction

​The first two factors always tend to reduce the generated voltage, and the third factor may tend to increase or decrease the generated voltage. The nature of the load affects the voltage regulation of the alternator.

Effect of Load Power Factor on Armature Reaction

1.) Unity Power Factor Load: When the load has a unity power factor i.e. pure resistive load, then the armature reaction distorts the main field flux in the air gap of the machine and does not weaken it.

2.) Zero Lagging Power Factor Load: When the load power factor is zero lagging i.e. pure inductive load, then the armature reaction weakens the main field flux. Due to the reduction in the main field flux, the generated EMF is decreased.

3.) Zero Leading Power Factor Load: When the load power factor is zero leading i.e. pure capacitive load, then the armature reaction strengthens the main field flux. This causes an increase in the generated voltage.

Nature of armature reaction on alternator:

There are three causes of voltage drop in the alternator.

• Armature circuit voltage drop
• Armature reactance
• Armature reaction

​The first two factors always tend to reduce the generated voltage, and the third factor may tend to increase or decrease the generated voltage. The nature of the load affects the voltage regulation of the alternator.

Effect of Load Power Factor on Armature Reaction

1.) Unity Power Factor Load: When the load has a unity power factor i.e. pure resistive load, then the armature reaction distorts the main field flux in the air gap of the machine and does not weaken it.

2.) Zero Lagging Power Factor Load: When the load power factor is zero lagging i.e. pure inductive load, then the armature reaction weakens the main field flux. Due to the reduction in the main field flux, the generated EMF is decreased.

3.) Zero Leading Power Factor Load: When the load power factor is zero leading i.e. pure capacitive load, then the armature reaction strengthens the main field flux. This causes an increase in the generated voltage.

Nature of armature reaction on alternator:

Variation in dc excitation of a synchronous motor causes variation in both power factor and armature current. These both can be represented by an inverted v curve.

 V curve:

• The V curve shows the relationship between field current (If) and armature current (Ia)
• The field current is plotted on the x-axis whereas the armature current is plotted on the y-axis.

V curve for synchronous motor:

V curve for synchronous generator:

Inverted V – curve:

The excitation and power factor of synchronous motor can be summed up in the following graph. This is called an inverted V curve of the synchronous motor.

From the inverted V – curve,

• The synchronous motor operates at a lagging power factor when the excitation is under excited.
• The motor operates at a unity power factor at normal excitation.
• The motor operates at a leading power factor when the excitation is over-excited.

Important Points:

• Under excited alternator works at the leading power factor
• The normal excited alternator works at the unity power factor
• The overexcited alternator works at lagging power factor

Inverted V – curve:

The excitation and power factor of the synchronous motor can be summed up in the following graph. This is called an inverted V curve of the synchronous motor.

From the inverted V – curve,

• The synchronous motor operates at a lagging power factor when the excitation is under excited.
• The motor operates at a unity power factor at normal excitation.
• The motor operates at a leading power factor when the excitation is over-excited.

Important Points

• Under excited alternator works at the leading power factor
• The normal excited alternator works at the unity power factor
• The overexcited alternator works at lagging power factor

The correct answer is option 3): (supplies leading VARs and operates at leading power factor)

Synchronous generator:

A synchronous generator or alternator is capable of operating at all types of power factor i.e. either UPF, leading or lagging power factor.

• Leading power factor: If field excitation is such that Eb < V the alternator is said to be under excited and it has a leading power factor.
• Lagging power factor: If field excitation is such that Eb > V the alternator is said to be over-excited and it draws lagging current.
• Unity power factor: If field excitation is such that Eb = V the alternator is said to be normally excited. V -curve for synchronous generator or alternator is shown below

 V curve:

• The V curve shows the relationship between field current (If) and armature current (Ia)
• The field current is plotted on the x-axis whereas the armature current is plotted on the y-axis.

V curve for synchronous motor:

V curve for synchronous generator:

Synchronous motor:

V curves for synchronous motor give the relation between armature current and DC field current. The curves are shown below.

A synchronous motor is capable of operating at all types of power factor i.e. either UPF, leading, or lagging power factor.

• Lagging power factor: If field excitation is such that Eb < V the motor is said to be under excited and it has a lagging power factor.
• Leading power factor: If field excitation is such that Eb > V the motor is said to be over-excited and it draws leading current. So that the power factor improves.
• Unity power factor: If field excitation is such that Eb = V the motor is said to be normally excited.

Synchronous generator:

A synchronous generator or alternator is capable of operating at all types of power factor i.e. either UPF, leading or lagging power factor.

• Leading power factor: If field excitation is such that Eb < V the alternator is said to be under excited and it has a leading power factor.
• Lagging power factor: If field excitation is such that Eb > V the alternator is said to be over-excited and it draws lagging current. 
• Unity power factor: If field excitation is such that Eb = V the alternator is said to be normally excited.
• V -curve for synchronous generator or alternator is shown below

As the synchronous motor is a constant speed motor, the speed is independent of excitation while the power factor depends on excitation.

Example:

Effect of changing field excitation for constant load:

For a synchronous motor, as excitation (E) is increased :

• PF (i.e. cos ϕ) decreases and becomes more and more leading 
• Armature current, Ia increases.
   

As we move from normal excitation ( E = V) to overexcitation (E > V),  Ia increases from a minimum at normal excitation (Unity PF) 

A synchronous motor is capable of operating at all types of power factor i.e. either unity, leading or lagging power factor.

Lagging power factor: If field excitation is such that Eb < V the motor is said to be under excited and it has a lagging power factor.

Leading power factor: If field excitation is such that Eb > V the motor is said to be over-excited and it draw leading current. So that the power factor improves.

Unity power factor: If field excitation is such that Eb = V the motor is said to be normally excited.

A synchronous motor running with no load will lead the current i.e. leading power factor like a capacitor. This synchronous motor running without load i.e. over excited is synchronous condenser.

The synchronous condenser is used in power lines to improve power factor, power factor correction by connecting it along with transmission lines.

V -curve for synchronous motor is shown below

Mistake Points

For Alternator (Synchronous Generator):

Under excited alternator works at the leading power factor

The normal excited alternator works at the unity power factor

The over excited alternator works at lagging power factor

Armature reaction:

The effect of armature (stator) flux on the flux produced by the rotor field poles is called armature reaction. It depends on the power factor i.e. the phase relationship between the terminal voltage and armature current.

• The armature reaction flux is constant in magnitude and rotates at synchronous speed
• At unity power factor load, the armature reaction is cross-magnetizing (distortional)
• At lagging power factor load, the armature reaction is partly demagnetizing and partly cross-magnetizing; At zero power factor lagging load, it is purely demagnetizing and the induced emf will get decreased
• When the generator supplies a load at leading power factor the armature reaction is partly magnetizing and partly cross-magnetizing; At zero power factor leading load, it is purely magnetizing and the induced emf will get increased

Important Points

 V curve:

• The V curve shows the relationship between field current (If) and armature current (Ia)
• The field current is plotted on the x-axis whereas the armature current is plotted on the y-axis.

V curve for synchronous motor:

V curve for synchronous generator:

The voltage drop is minimum for unity power factors.

In an alternator, armature reaction refers to the effect of the armature current on the magnetic field of the machine. This interaction results in a distortion of the magnetic field, leading to changes in the terminal voltage.

The voltage drop due to armature reaction is minimized when the power factor is unity, meaning the load is purely resistive. In such a case, the armature reaction has the least impact on the voltage, resulting in the minimum voltage drop.

There are three causes of voltage drop in the alternator.

• Armature circuit voltage drop due to resistance
• Armature reactance
• Armature reaction

​The first two factors always tend to reduce the generated voltage, and the third factor may tend to increase or decrease the generated voltage. The nature of the load affects the voltage regulation of the alternator.

Effect of Load Power Factor on Armature Reaction

1.) Unity Power Factor Load: When the load has a unity power factor i.e. pure resistive load, then the armature reaction distorts the main field flux in the air gap of the machine and does not weaken it.

2.) Zero Lagging Power Factor Load: When the load power factor is zero lagging i.e. pure inductive load, then the armature reaction weakens the main field flux. Due to the reduction in the main field flux, the generated EMF is decreased.

3.) Zero Leading Power Factor Load: When the load power factor is zero leading i.e. pure capacitive load, then the armature reaction strengthens the main field flux. This causes an increase in the generated voltage.

Nature of armature reaction on alternator: