10.3 Elementary Synchronous Generator

10.3 Elementary Synchronous Generator

The basic synchronous generator includes a stationary inductor in the stator and a movable armature in the rotor. The most elementary arrangement consists of two-pole elementary generator (Fig. 10.14).

Fig. 10.14 Stator core and two-pole rotor. Original from haade. Source original from wikicommons under CC3.0 use license [11]

Examining a basic generator, we find that it consists of a cylindrical rotor with a diameter D and an axial length L, matching the depth of the poles, and a stator or inductor with two poles, north and south. It is of vital importance to understand the distance in windings (Fig. 10.15).

eAA′​ and $e_{B{B}^{\prime }}$, while a horizontal dashed line represents distance $D$. Another vertical dashed line on the right side is labeled $L$.">

Fig. 10.15 Elementary synchronous generator stator windings. Source own elaboration

In the rotor (Fig. 10.16), we have a loop comprising two conductors, AA′ and BB′ that connects to a conductor A′B′. This conductor is not within the field of influence of the magnetic field.

Fig. 10.16 Rotor wiring scheme. Source own elaboration

When the rotor rotates at n rps, the linear velocity of loops AA′ and BB′ is:

v=ω·radio=2π·n·D2=π·n·D (10.2)

According to Faraday's law, when moving coils AA′ and BB′ within a magnetic field, induced voltages are:

eAA′=v·B·L·senθ (10.3)

eBB′=v·B·L·senπ-θ (10.4)

Keep in mind that both voltages have the same magnitude and direction (Fig. 10.17). The induced emf within the loop is then:

eAB=2·eAA′=2·v·B·L·senθ=2π·n·D·B·L·senθ (10.5)

Fig. 10.17 Basic synchronous generator stator. Source own elaboration

The flux that the loop embraces is at its maximum value when it is vertical and perpendicular to the lines of the magnetic field and becomes:

Φ0=B·D·L (10.6)

D-L is the part that is inside the loop at the position of maximum flow.

Therefore, it is true that:

eAB=2π·n·Φ0·senθ (10.7)

The total emf in the N loops is:

e=N·2π·n·Φ0·senθ (10.8)

Recalling the definition of angular displacement θ, we have:

θ=w·t=2·π·n·t

Therefore, in the case of N turns, the emf is a sinusoidal function of magnitude. Substituting this equation into (Eq. 10.9) we have that:

e=N·2π·n·Φ0·sen2π·n·t (10.9)

Upon a comprehensive analysis of a rotor's complete rotation, it becomes evident that loops AA′ and BB′ change polarity, depending on whether they are under the influence of the North or South Pole.

Each turn guarantees a complete emf cycle. It is important to note that the coils have a polarity during the first half-cycle, and the opposite in the second half-cycle.

The value of this emf is then:

E=2·π·N·f·Φ02=4.44·N·Φ0·f (10.10)