JNTU B.Tech III ELECTRICAL MACHINES-III Previous Question Paper (October - 2020 - R13)

The primary differences between distributed and concentrated windings in alternators are as follows:

• Concentrated Winding: In this type of winding, all the coils of a phase are wound together as a single coil and placed in a single slot. This results in a single coil group per phase per pole.
• Distributed Winding: In this type of winding, the coils of a phase are spread out or distributed across multiple slots under each pole. This means a phase winding is divided into several coil groups.
• Harmonics: Concentrated windings tend to produce higher order harmonics in the generated EMF due to the concentrated flux. Distributed windings help to reduce harmonics, particularly the third harmonic, leading to a more sinusoidal EMF waveform.
• EMF Magnitude: Distributed windings generally produce a slightly lower EMF compared to concentrated windings for the same number of conductors and flux, due to the 'breadth factor' or 'distribution factor' (Kd), which is less than 1.
• MMF Distribution: Concentrated windings produce a fundamental MMF wave with a sharp peak. Distributed windings produce an MMF wave that is closer to sinusoidal.
• Slot Utilization: Distributed windings make better use of the available slots in the stator core.
• Cooling: Distributed windings offer better cooling due to the conductors being spread out.
• Applications: Concentrated windings are typically found in smaller DC machines and some older AC machines. Distributed windings are standard in modern alternators and AC motors due to their advantages in EMF waveform and harmonic reduction.

Given:

• Type of connection: Star connected
• Line Voltage (VL): 11 KV = 11000 V
• Apparent Power (S): 10 MVA = 10 x 10^6 VA
• Power Factor (pf): 0.85 lagging
• Armature Resistance per phase (Ra): 0.1 Ω
• Synchronous Reactance per phase (Xs): 0.66 Ω

We need to calculate the generated voltage per phase (Eg).

Step 1: Calculate the phase voltage (Vph).

For a star-connected alternator, the phase voltage is related to the line voltage by:

Step 2: Calculate the phase current (Iph).

The apparent power S is given by:

Since the alternator is star-connected, the line current (IL) is equal to the phase current (Iph):

Alternatively, using phase voltage:

Step 3: Calculate the synchronous impedance per phase (Zs).

The magnitude of the synchronous impedance is:

Step 4: Calculate the generated voltage per phase (Eg).

The voltage equation for an alternator is:

Since the power factor is 0.85 lagging, the current Iph lags the phase voltage Vph by an angle θ, where:

We can represent Vph and Iph in phasor form. Let Vph be along the real axis:

The current Iph lags Vph by 31.79°:

Now, calculate the voltage drop Iph * Zs:

The angle of Zs is arctan(0.66/0.1) = arctan(6.6) ≈ 81.47°.

Convert the voltage drop to rectangular form:

Now, add this voltage drop to the phase voltage:

The magnitude of the generated voltage per phase is:

Final Answer: The generated voltage per phase is approximately 6583.0 V.