Working Principle, Rotating Magnetic Field, Emf Equation, Distribution Factor , Pitch Factor of Three Phase Synchronous Generator

Rotating magnetic field:

The synchronous generator has rotating magnetic system & stationary armature conductors.The advantage of rotating magnetic field is that it is easier to insulate stationary armature winding for high voltage rather than rotating armature.

Operating Principle:

The working principle of a synchronous generator is based on electromagnetic induction phenomenon.The shaft of a synchronous generator is rotated by a prime mover (turbine) at the constant speed equal to synchronous speed.

i.e.Ns=(120f /P).

Exciter builds up the voltage and supplies to the field winding.Thus, the stator conductors or armature conductors are cut by the magnetic flux produced by rotor pole and hence by Faradays’ law of electromagnetic induction, emf will be induced in the armature conductors.

As the stator has 3 phase distributed windings, this phase voltage will be induced given by:

E_R = E_m sinωt

As phases Y & B are displaced from phase R by ± 120° then the corresponding voltage may be written as;

E_Y =E_m sin (ωt – 120°)

E_B = E_m sin (ωt + 120°)

The speed governor is used to keep the speed of machine constant and the induced voltage is made constant by the automatic voltage regulator (AVR).

Emf Equation:

Let us consider

Z = No. of conductors per phase

i.e. Z = 2×T

where,

T = No. of turns in series per phase.

P = No. of magnetic pole in the rotor

f = frequency of induced emf

ø = magnetic flux per pole

N = speed of the rotor in rpm

In one revolution of the rotor (i.e., in 60/N sec) each stator conductor is cut by a flux of ø. P, webers.

Therefore, average emf induced per conductor = dø/dt = ø.P/(60/N), volts

But for synchronous generator

we have; f = (P.N)/120

or, N = 120f/P

Therefore, average emf induced per conductor = (ø.P/60)*(120f/P) = 2.f.ø, volts Then, average emf induced per phase = 2.f.ø.Z

(Where, Z=2T) = 2.f.ø.2T = 4.f.ø.T, volts

We know that form factor for sine wave = (RMS value/ Average value) = 1.11

Therefore, RMS value of emf per phase = 1.11 * 4.f.ø.T = 4.44 f.ø.T volts.

This is the emf equation of synchronous generator for full pitch coil.There are some other factors which affect the magnitude of emf induced in stator windings.

They are pitch factor & distribution factor.

After assumption of pitch factor and distribution factor,the emf equation becomes

E= 4.44 f.ø_m.k_p.k_d.T volts per phase.

Pole pitch:It is an angular distance between the centres of two adjacent poles on a machine.

Coil Pitch:It is a distance between two sides of a coil.

One pole pitch=180 electrical degrees.

Pitch factor(k_p):

Ideally, coil span or coil pitch of armature winding is equal to the pole pitch.But in the actual machine, the coil span may be less than pole pitch.If coil span is equal to pole pitch then such type of coil is called full pitch coil.If coil span is less than one pole pitch then such type of coil is called short pitch coil or fractional pitch coil.

If α is the lagging angle of coil span behind pole pitch.Then pitch factor can be expressed as,

Distribution factor:

In actual machine, the armature windings are not concentrated in a slot. The windings are uniformly distributed in many numbers of slots to form polar group under each pole.

So,distribution factor can be defined as,

In general,It can be formulated as,

Where,

K_d =distribution factor

m =no. of slots per phase per pole

β=(180º/n)

n=no. of slots per pole

Before knowing about, winding factor, we should know about pitch factor and distribution factor as a winding factor is the product of pitch factor and distribution factor. If the winding factor is denoted by K_w, pitch factor and distribution factor are denoted by K_p and K_d respectively, then, k_w= k_pk_d.

Electrical and Geometrical degree:

Electrical degree = P/2 *geometrical degree

Where, P= no. of magnetic poles in rotor structure.