# Synchronous Generator

Synchronous generator is an electrical machine that produces constant frequency alternating emf (electromotive force or voltage). In our nation, the traditional AC supply commercial frequency is 50 Hz. The frequency is 60 Hz in the U.S.A. and a few other countries. Depending on the power supplied, the AC voltages generated may be single- or 3-phase. For low power applications single-phase generators are preferable. The basic principles involved in the production of emf and the constructional details of the Synchronous Generators are discussed below.

## Elementary Of Synchronous Generator

Generators need a prime mover which provides the conductor with linear or reciprocal motion. In commercial turbines, several of the commercial prime movers have rotary motion. Many industrial generator conductors are rotated around a shaft’s central axis. The conductors are placed in slots cut into a cylindrical (made of magnetic material) frame, known as the armature.

At both ends, the armature is supported by bearings attached to the shaft which passes through the armature center. Within the field framework, the armature is rotated by making a slight distance between those two parts. This gap is known as the air gap and is usually 1 to 1.5 cm in length. If the air gap remains constant throughout the proliferation of the pole arc, we have a fairly constant flux density under it in a plane perpendicular to the plane of the conductor’s motion.

The relative motion between the conductors and the magnetic flux lines is responsible for emf production; whether the conductors are rotated or the poles containing the magnetic flux are rotated is immaterial. It’s the field that is rotated in most alternators, rather than the conductors.

Just one single coil of N twists, shown by the two coil sides a and -a in diametrically opposite slots on the stator’s inner periphery (i.e. the armature because it is a stationary component here) in its cross-section is seen in the figure above.

The conductors that form these coil sides are parallel to the machine’s shaft and are connected by end connections in series (not shown in the figure). In reality, the spools are
Formed by continuous copper wire with a sufficient cross-section around a diamond-shaped wire Bobbin. The finished coil is shown in Fig.

Usually the copper wire is fine linen-covered, cotton-covered, or enamel-covered in order to be sufficiently isolated between the same coil conductors. The internal arrangement and interconnection of various coils to get the appropriate voltage from the synchronous (alternator) unit.

## Generation Of EMF In Synchronous Generator

Faraday discovered that because of the relative motion between a magnetic field and an electric conductor, an emf can be induced (or generated). Emf is only created by motion between the conductor and the magnetic field without any direct physical interaction between the conductors. The electromagnetic induction theory is better known, as seen in the diagram.

The magnetic field is created by the two stationary poles one is the north pole from which the magnetic flux lines arise and reach the other pole identified as the south pole. The amplitude of the voltage produced in the conductor was found to be proportional to the rate of flux-line shift connecting the conductor.

e=\frac { d\phi }{ dt } \approx \frac { \phi }{ t } \quad volts\quad

where
\phi = flux in Webers
t = time in seconds
e = average induced emf in volts

In functional rotating machinery, the flux shift connecting each individual conductor during rotation (of either the conductors or the poles) is not well described or readily observable. The representation of this rate of flux shift is more useful in terms of an average flux density (assumed constant) and the relative velocity of this field and a single conductor passing through it.

For the active duration conductor l traveling with a velocity of v in a flux density B magnetic field, as seen in the above Figure. The instantaneous emf, induced as,

e = Blv Volts

where
B= flux density in Tesla (Wb/m2)
l = active conductor length (m)
v = relative linear velocity between the conductor and the field (m/s)

Thus the instantaneous voltage e and the average value E of the induced emf are

e=E_m\sin { \omega t=E_m\sin { \theta } }

We assumed the conductor is moving in a perpendicular direction to the magnetic field. The above Equations are true for B and v only for this mutually orthogonal situation.

The other possible cases of motion of the conductor with respect to B are shown in the figure below

The induced emf will be zero when the conductor moves parallel to B because the rate of flux connection change is zero as the conductor does not link any new flux line/lines. In order to account for this operating condition, the above equation must be multiplied by a factor that takes into account the direction of the conductor’s movement in order to make ‘e’ zero for this operating condition, although B, l, and v are finite quantities. Intuitively we may infer that this factor must be a sine function as it has a zero value at { 0 }^{ 0 } and also at { 180 }^{ 0 } and a maximum value at { 90 }^{ 0 } .

The emf equation for the general case of a conductor moving in any direction with respect to the field is given by

e=Blv\sin { \delta }

where \delta is the angle formed between B and v always taking B as the reference.

## Direction of induced EMF In Synchronous Generator

The direction of the induced emf is given by Fleming’s Right Hand Rule

If the palm, first finger and second finger of the right hand are extended and held in three mutually perpendicular directions, so that the first finger is kept pointed in the direction of the magnetic field and the palm points in the direction of motion, then the second finger must point in the direction of the generated emf, such that the current flows in that direction. The induced emf is in a direction so as to circulate current in the direction shown by the middle finger.

Although the Right-Hand Rule assumes that the magnetic field is stationary, this rule can also be applied to a stationary conductor and moving magnetic field by assuming that the conductor moves in the opposite direction.