## Thursday, October 11, 2012

### Synchronous Generator

INDUCED E.M.F:
e = B l v volts
where

B = flux density Wb/sqm
v = velocity (m/s) of movement
l = length of conductors in meters.

### Frequency:

The frequency of the voltage generated is given by

f = NP/120

where P is the total number of poles and N is the speed in r.p.m.

(Kb) = Voltage obtained in multi-slots winding / Voltage obtained if the windings were all concentrated in one slot

Thus breadth factor is always less than unity.
Mathematically,

Kb= (sin δ n/2 )/ (π sin δ/2)

where n is the number of slot and is the slot pitch.

### Pitch factor:

Shortening the pitch of the coil has the same effect as the distribution of the winding. When the turns of the windings do to span a complete pitch there occurs a slight loss in the induced emf. A pitch factor ( Kp ) is given by

Kp = cos θ/2

for a coil which extends over (180° - θ) instead of 180°.

### Magnitude of Induced emf in alternators / phase:

ERMS = 4.44 Kp Kb φ f.T. volts

### Synchronous Reactance:

Xs = XL + XA

where
XL = Leakage reactance;
XA = Armature reactance.

### Synchronous Impedance:

Zs = (R2 + X2s )1/2

## SYNCHRONOUS GENERATOR CHARACTERISTICS:

### (1) Open Circuit Characteristics:

(Magnetisation Curve).

### (2) Short Circuit Characteristics:

(Terminal Voltage vs Current)

## 3) Load Characteristics of Synchronous Generator:

While the exciting current and the speed remain constant, the terminal voltage changes with the load current in the armature and the relationship between the terminal voltage and load current of an alternator is known as its load characteristics.

When the armature current increases, the terminal voltage drops. This is mainly due to

(a) Resistance and reactance of armature winding, and
(b) Armature reaction.

The load characteristics of an alternator is shown in the figure.

## Simplified equivalent AC circuit (per phase) for synchronous generator:

### (A) When RA is very small:

α = torque angle
P = 3 VφE0 sin α/ Xs

Torque induced,
T ind = 3 VφE0 sin α/ Xs ωm

where ωm = speed.

### (B) General case:

P = 3 E0/Zs [ E0cosθ – V (cosθ + α) ]
where cosθ = Ra / Zs

:. Small Ra implies θ = 90.

### cosφ = E0/√ (E20 +V2φ)

α = 900

3 P max = (3 Vφ I max E0)/√ (E20 +V2 φ) = 3 Vφ E0 / Xs