Alternator and Synchronous Motors MCQ Quiz - Objective Question with Answer for Alternator and Synchronous Motors - Download Free PDF

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

EMF method versus MMF method of voltage regulation of the alternator

• The EMF method (also known as the synchronous impedance method) simplifies the analysis by assuming a constant synchronous impedance Z_S.
• This assumption does not account for saturation and changes in armature reaction, making it less accurate than the MMF method, which considers the actual magnetizing force required for both the air gap and core under load.
• The MMF method more accurately reflects non-linearities like magnetic saturation and is generally preferred for precise voltage regulation calculations.
   

Methods for determining the voltage regulation of the alternator

Ampere turn method (MMF method):

• The voltage regulation calculated using the MMF method will always be lower than the actual voltage regulation of an alternator; that's why it is known as the optimistic method.
• The MMF method replaces the effect of armature leakage reactance with an equivalent additional armature reaction MMF so that this MMF may be combined with the armature reaction MMF.
   

Synchronous impedance method (EMF method):

• The voltage regulation calculated using the EMF method will always be higher than the actual voltage regulation of an alternator; that's why it is known as the pessimistic method.
• The synchronous impedance method is based on the concept of replacing the effect of an armature reaction with an imaginary reactance.
   

Potier triangle method (Zero Power Factor Method):

The following assumptions are made in the Potier triangle method:

• The armature reaction MMF is constant.
• The open-circuit characteristic (O.C.C.) taken on no-load accurately represents the relation between MMF and voltage under loaded conditions.
• The voltage drop due to the armature leakage reactance (la XaL) is independent of the excitation.

Method of power factor correction

• A synchronous motor is used for power factor correction.
• Synchronous motors can be used for power factor correction by adjusting their excitation to operate at a leading power factor.
• This allows them to compensate for the lagging power factor typically associated with inductive loads like induction motors.
• By drawing leading current, synchronous motors can neutralize the reactive power consumed by inductive loads, improving the overall system power factor. 
• This leads to low heat generation and prevents excess thermal stress. With less heat, the risk of breakdown and component degradation decreases and increases the lifespan of the system.

Effect of the change of excitation of a synchronous motor 

When changing the excitation of a synchronous motor under constant mechanical load, only power factor and armature current magnitude are affected; the speed of the motor and real power output remain constant. 

• Power factor: Excitation directly influences the power factor. Increased excitation leads to a more leading power factor, while decreased excitation results in a more lagging power factor. 
• Armature current magnitude: As power factor changes due to excitation adjustments, the armature current magnitude also changes. Higher excitation generally leads to a lower armature current when the motor is over-excited, and vice versa. 
• Speed: The speed of a synchronous motor is determined by the frequency of the power supply and the number of poles. It is independent of the excitation level. 
• Real power output: Real power output is related to the load and the motor efficiency. Since the load is constant, real power output remains constant regardless of excitation changes. 

Concept:

Pitch factor for nth harmonic is given by,

\({k_c} = \cos \frac{{n\alpha }}{2}\)

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

\(\therefore \alpha = 180^\circ \times \frac{2}{{9}} = 40^\circ\)

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

\(Z_s=\frac{V_{oc}}{I_{sc}}\) 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 \(V_{oc}=\frac{3300}{√3}\ V\) 

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

Therefore,

 \(Z_s=\frac{\frac{3300}{√3}}{110√3}=\ 10\ \Omega\)

Hence, Per Phase Z_s = 10 Ω

\(Z_s=\sqrt{{R^2+X_s^2}}\)

\(10=\sqrt{{1^2+X_s^2}}\)

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

\(S = √ {{P^2} + {Q^2}} \)

ϕ is the phase difference between the voltage and current

Power factor \(\cos \phi = \frac{P}{S}\)

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 = \(\sqrt{700^2+300^2}=100\sqrt{49+9} \) = 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 \({k_d} = \frac{{sin\frac{{m\gamma }}{2}}}{{m\sin \frac{\gamma }{2}}}\)

Where \(m = \frac{{slots}}{{pole \times phase}}\)

\(\gamma = \frac{{\pi \times p}}{s}\)

P = no of poles

S = no of slots

Calculation

No of slots = 18

No of poles = 2

No of phase = 3

\(m = \frac{{18}}{{2 \times 3}} = 3\)

\(\gamma = \frac{{\pi \times 2}}{{18}} = 20^\circ\)

\({k_d} = \frac{{sin\frac{{3 \times 20}}{2}}}{{3\;sin\frac{{20}}{2}}} = \frac{{sin30^\circ }}{{3\;sin10^\circ }}\)

Given the, Line current (I_L1) = 200 A

Power factor (cos ϕ₁) = 1

Power \(\left( {{P_1}} \right) = \sqrt 3 {V_{L1}}{I_{{L_1}}}cos{\phi _1}\)

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

\({P_2} = \sqrt 3 {V_{L2}}{I_{L2}}cos{\phi _2}\) 

⇒ P₁ = P₂

\(\Rightarrow \sqrt 3 {V_{L1}}{I_{L1}}\cos {\phi _1} = \sqrt 3 {V_{L2}}{I_{L2}}\cos {\phi _2}\)

\(\Rightarrow \sqrt 3 {V_{L1}} \times 200 \times 1 = \sqrt 3 \times {V_{L2}} \times {I_{L2}} \times 0.5\)

 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 \(= \frac{{{E_{g0}} - {V_t}}}{{{V_t}}} \times 100\)

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

\({E_{g0}} = \left( {{V_p} + {I_a}{R_a}} \right) + j\left( {{I_a}{X_a} + {E_{ar}}} \right)\;V\)

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)