Alternator and Synchronous Motors MCQ Quiz - Objective Question with Answer for Alternator and Synchronous Motors - 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.

Explanation:

Synchronous Reactance in Synchronous Machines

Definition: In the equivalent circuit model of a synchronous machine, the synchronous reactance (denoted by X_s) is the combined reactance that accounts for the effects of both the leakage reactance (X₁) and the magnetizing reactance (X_a). It is a crucial parameter in the analysis and operation of synchronous machines, such as synchronous generators and motors.

Formula: The synchronous reactance is expressed as:

X_s = X₁ + X_a

Here:

• X₁: Leakage reactance, which represents the reactance due to leakage flux that does not contribute to the main magnetic field.
• X_a: Magnetizing reactance, which represents the reactance due to the main magnetic flux linking the stator and rotor.

Working Principle:

The equivalent circuit of a synchronous machine includes the synchronous reactance as a single reactance to simplify the analysis. When an alternating current flows through the stator winding of the synchronous machine, part of the flux produced by the current leaks out and does not link with the rotor. This is accounted for by the leakage reactance (X₁). The remaining flux links with the rotor, and its effect is represented by the magnetizing reactance (X_a). Together, these reactances form the synchronous reactance (X_s).

Importance of Synchronous Reactance:

• Synchronous reactance plays a significant role in determining the voltage regulation and power factor of synchronous machines.
• It impacts the steady-state performance of the machine, particularly under load conditions.
• Higher synchronous reactance leads to reduced fault current levels, which is advantageous for system protection.

Correct Option Analysis:

The correct option is:

Option 1: X_s = X₁ + X_a

This option is correct because it accurately represents the synchronous reactance as the sum of the leakage reactance (X₁) and the magnetizing reactance (X_a). The addition of these two reactances provides a complete representation of the reactance in the equivalent circuit of the synchronous machine. This formula is derived from the fact that both leakage and magnetizing reactances are connected in series within the machine's equivalent circuit.

Additional Information

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

Option 2: X_s = X₁ × X_a

This option is incorrect because it implies that the synchronous reactance is the product of the leakage reactance and the magnetizing reactance. In the equivalent circuit model, the reactances are in series, and their effects are additive, not multiplicative. Therefore, this representation does not hold true for synchronous machines.

Option 3: X_s = X₁ - X_a

This option is also incorrect because it suggests that the synchronous reactance is the difference between the leakage reactance and the magnetizing reactance. However, the synchronous reactance is a sum of these two reactances, as they both contribute positively to the total reactance in the equivalent circuit.

Option 4: X_s = X₁ ÷ X_a

This option is incorrect because it implies that the synchronous reactance is the division of the leakage reactance by the magnetizing reactance. This does not represent the physical or mathematical relationship between these reactances in the equivalent circuit of the synchronous machine.

Conclusion:

Understanding the concept of synchronous reactance is vital for analyzing the performance of synchronous machines. The synchronous reactance (X_s) is the sum of the leakage reactance (X₁) and the magnetizing reactance (X_a). This additive relationship is fundamental to the equivalent circuit representation and helps in understanding the operation of synchronous machines under various load conditions. Incorrect options, such as multiplication, subtraction, or division of reactances, do not accurately describe the concept of synchronous reactance and are not applicable in this context.

Explanation:

Excitation Voltage in Salient Pole Synchronous Machine

Definition: In a salient pole synchronous machine, excitation voltage is the voltage required at the field winding to establish the necessary magnetic flux for the machine's operation. This flux interacts with the armature winding to produce the required electromagnetic torque. The excitation voltage is also influenced by the power factor, load conditions, and machine's reactance.

Expression for Excitation Voltage:

The excitation voltage for generating action in a salient pole synchronous machine is given by:

E_o = V Cos δ + I_qR_a + I_dX_d

Where:

• E_o: Excitation voltage
• V: Terminal voltage
• δ: Power angle
• I_q: Quadrature axis component of armature current
• I_d: Direct axis component of armature current
• R_a: Armature resistance
• X_d: Direct axis synchronous reactance

Derivation:

The excitation voltage in salient pole synchronous machines depends on the phasor relationship between the terminal voltage, armature current, and the synchronous reactance. The machine's synchronous reactance is divided into two components:

• Direct axis reactance (X_d): This is associated with the magnetic flux along the direct axis.
• Quadrature axis reactance (X_q): This is associated with the magnetic flux along the quadrature axis.

The armature current can be resolved into two components:

• I_d: Direct axis component, which contributes to the direct axis magnetic flux.
• I_q: Quadrature axis component, which contributes to the quadrature axis magnetic flux.

The excitation voltage is determined by considering the power angle δ and the phasor addition of the resistive and reactive components of voltage drops across the armature resistance (R_a) and reactances.

Advantages of This Expression:

• Provides a comprehensive understanding of the relationship between excitation voltage and operating parameters such as load current and power factor.
• Helps in designing and analyzing the performance of synchronous machines under different load conditions.

Correct Option Analysis:

The correct option is:

Option 3: E_o = V Cos δ + I_qR_a + I_dX_d

This expression correctly represents the excitation voltage in a salient pole synchronous machine. The positive signs indicate the additive nature of the voltage drops due to the armature resistance and direct axis reactance.

Additional Information

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

Option 1: E_o = V Cos δ + I_qR_a - I_dX_d

This option is incorrect because the sign of the term involving I_dX_d is negative. The excitation voltage expression inherently requires the addition of the direct axis reactance component, as it contributes positively to the net excitation voltage.

Option 2: E_o = V Cos δ - I_qR_a - I_dX_d

This option is incorrect as both I_qR_a and I_dX_d have negative signs. These terms represent the voltage drops due to the resistive and reactive components, which are additive in the excitation voltage equation.

Option 4: E_o = V Cos δ - I_qR_a + I_dX_d

This option is partially correct, as it correctly includes a positive sign for the I_dX_d term. However, the negative sign for I_qR_a is incorrect, as the armature resistance contributes positively to the net excitation voltage.

Conclusion:

The excitation voltage for a salient pole synchronous machine is expressed as:

E_o = V Cos δ + I_qR_a + I_dX_d

This expression accounts for the terminal voltage, power angle, and the contributions of armature resistance and direct axis reactance. Understanding this equation is crucial for analyzing the performance and operation of synchronous machines under various load conditions. Evaluating the other options highlights the importance of correctly interpreting the signs and relationships in the excitation voltage formula.

Armature reaction in an alternator

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.

Explanation

• Statement I is correct. The voltage drop due to armature resistance (IaRa) is in phase with the armature current (Ia) because resistance and current are always in phase in an AC circuit.
• Statement II is correct. At unity power factor, the voltage drop IaRa directly subtracts from the generated EMF (E) because the current and voltage are in phase, so the resistive drop subtracts directly from EMF.
• Statement III is incorrect. The terminal voltage is given by: V = E - I_aR_a. IaRa is a resistive drop and always reduces terminal voltage, regardless of the power factor.
• Statement IV is incorrect. Armature resistance does affect voltage regulation, as it causes a voltage drop under load.

The correct answer is option 1.

Salient pole rotors are not used in turbo alternators because they are not robust enough to withstand the high centrifugal forces and winding losses generated at the high speeds of turbo alternators. Instead, cylindrical rotors, which are more robust and have lower inertia, are used in turbo alternators. 

Difference between a salient pole and a cylindrical rotor

Concept:

Pitch factor for nth harmonic is given by,

Where α is short pitch angle in degrees

Calculation:

Given-

Total slots = 36,

Number of poles = 4

Coil span = 1 to 8 = 8 - 1 = 7 slots

Now, Slots per pole = 36 / 4 = 9

Number of empty slots = 9 – 7 = 2 slots

Hence pitch factor can be calculated as

K_c = cos 20°

• Normally the alternators are connected to the system to which a number of other alternators are also connected and hence the system behaves as an infinite bus.
• Due to the influence of this in finite buses, there will be a rotating magnetic field in the stator windings of all alternators, and these fields are all rotated in synchronous speed.
• The field created by the rotor windings gets locked with this rotating magnetic field of the stator and also rotates at the same speed.
• If the excitation of the generator fails, suddenly there will be no more magnetically locking between the rotor and rotating magnetic field of the stator.
• But still, the governor will supply the same mechanical power to the rotor due to this sudden magnetic unlocking; the rotor will be accelerated beyond the synchronous speed.
• Hence there will be a negative slip between the rotor and rotating magnetic field which creates large slip frequency currents in the rotor circuit to maintain the power output of the machine as an induction generator.

Concept:

Synchronous impedance method:

• The synchronous impedance method of calculating voltage regulation of an alternator is otherwise called as the EMF method.
• The synchronous impedance method or the EMF method is based on the concept of replacing the effect of armature reaction by an imaginary reactance.
• It gives a result that is higher than the original value. That's why it is called the pessimistic method.
• For calculating the regulation, the synchronous method requires the armature resistance per phase, the open-circuit characteristic, and the short circuit characteristic.

​Therefore, Synchronous impedance is basically obtained from occ and SCC characteristics of a three-phase alternator and is given by

at same field current

Where,

Z_s = Per phase Synchronous impedance

V_oc = Per phase Open circuit voltage of the alternator

I_sc = Per phase Short circuit current of the alternator

Application:

Given:

Rating of alternator = 500 KVA

Terminal voltage of alternator V_{t L-L} = 3.3 KV = 3300 V

Short circuit current I_sc = 110√3 A

Winding Resistance = 1 Ω

Per phase Open circuit voltage  

Per phase short circuit current I_sc = 110√3 A (by default we assume star connected)

Therefore,

Hence, Per Phase Z_s = 10 Ω

100 = 1 + X_s²

If field current or excitation of an alternator A is increased, then it will have the following effect on the alternator working in parallel operation.

• The system terminal voltage will increase, as both alternators are not connected to the infinite bus
• The reactive power supplied by alternator A is increased, while the reactive power supplied by the other alternator B is decreased, as the total reactive power demand of the load is constant

Important Point:

Change in excitation directly affect the reactive power supplied by the alternator.

• Under excited alternator works at a leading power factor
• Normal excited alternator works at a unity power factor
• The overexcited alternator works at lagging power factor

For Synchronous motor, it is opposite of alternator.

Concept:

The power triangle is shown below.

P = Active power (or) Real power in kW = Vrms Irms cos ϕ

Q = Reactive power in kVAr = Vrms Irms sin ϕ

S = Apparent power in kVA = Vrms Irms

S = P + jQ

ϕ is the phase difference between the voltage and current

Power factor 

Calculation:

(a) Induction motors:

Power = 500 × 0.8 = 400 kW

Reactive Power = 500 × 0.6 = 300 kVAR

(b)Synchronous motor:

Power = 300 kW

Reactive Power = 0.0

Factory :

Power = 400 + 300 = 700 kW

Reactive Power = 300 + 0 = 300 kVAR

Complex Power =  = 762 kVA

Power factor = 700/(100√58) = 7/√58 = 0.92 lagging

Concept:

Normally for voltage regulation calculation, we use the following methods.

1. Synchronous impedance or emf method

2. Armature turn or mmf method

3. Zero PF or Potier method

Synchronous impedance method (EMF Method):

• The synchronous impedance method of calculating voltage regulation of an alternator is otherwise called the EMF method.
• The synchronous impedance method or the EMF method is based on the concept of replacing the effect of armature reaction with an imaginary reactance.
• This method is not accurate as it gives a result that is higher than the original value. That's why it is called the pessimistic method.
• For calculating the regulation, the synchronous method requires the armature resistance per phase, the open-circuit characteristic, and the short circuit characteristic.

Armature turn method:

It is also known as the MMF method. It gives a value which is lower than the original value. That's why it is called an optimistic method.

To calculate the voltage regulation by MMF Method, the following information is required. They are as follows:

• The resistance of the stator winding per phase
• Open circuit characteristics at synchronous speed
• Field current at rated short circuit current

Potier triangle method:

• This method depends on the separation of the leakage reactance of armature and its effects.
• It is used to obtain the leakage reactance and field current equivalent of armature reaction.
• It is the most accurate method of voltage regulation.
• For calculating the regulation, it requires open circuit characteristics and zero power factor characteristics.

Concept:

Distribution factor 

Where 

P = no of poles

S = no of slots

Calculation

No of slots = 18

No of poles = 2

No of phase = 3

Given the, Line current (I_L1) = 200 A

Power factor (cos ϕ₁) = 1

Power 

When the power factor changes to 0.5 leading. The power drawn will be same.

And given that line voltage is same

V_L2 = V_L1

cos ϕ₂ = 0.5

⇒ P₁ = P₂

⇒ I_L2 = 400 A

 Characteristics of synchronous motors:

• Runs at constant speed at all loads
• Used for power factor improvement
• Inherently not self-starting
• The speed of operation of is in synchronism with the supply frequency
• It has the unique characteristics of operating under any electrical power factor
• It is used where high power at low speed is required such as rolling mills, chippers, mixers, pumps, pumps, compressor etc.

Concept:
Voltage regulation: The voltage regulation of an AC alternator is,

Percentage voltage regulation 

E_g0 is the internal generated voltage per phase at no load

V_t is the terminal voltage per phase at full load

Voltage regulation indicates the drop in voltage from no load to the full load.

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, the third factor may tend to increase or decrease the generated voltage. The nature of the load affects the voltage regulation of the alternator.

Unity power factor load:

• At the unity power factor, the phase current in the armature I_a is in phase with the terminal phase voltage V_t. The voltage drop per phase across the effective resistance of the armature I_aR_a is also in phase with the armature current I_a.
• The inductive voltage drop due to armature reactance, I_aX_a is always leading with respect to the current through it, since the current lags the voltage by 90° in a circuit possessing inductive reactance only.
• At the unity power factor, the armature reaction voltage drop E_ar­ leads the armature current I_a which produced it, and is, therefore, always in phase with the armature reactance voltage drop I_aX_a.

The generator equation is

From the phasor diagram and the equation, the terminal voltage V_t is always less than the generated voltage per phase by a total impedance drop I_a(R_a + jX_a).

Where jX_a is the quadrature synchronous reactance voltage drop (or) the combined voltage drop due to the armature reactance and armature reaction.

Important Points:

• At unity and lagging power factor loads, the terminal voltage is always less than the induced EMF and the voltage regulation is positive.
• At higher leading loads, the terminal voltage is greater than the induced EMF and the voltage regulation is negative.
• The lower the leading power factor, the greater the voltage rise from no load (E_g0) to full load (V_t)
• The lower the lagging power factor, the greater the voltage decrease from no load (E_g0) to full load (V_t)