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10.4 Real Synchronous Generator

An authentic synchronous generator has the inductor in the rotor and the armature in the stator. In a generator with a set of poles, the direct current that flows through the rotor winding establishes the poles, designating the north and south poles based on the current flow (Fig. 10.18). The rotor-air gap-stator path encloses the magnetic field force lines.

A series of circular diagrams at the top, each containing arrows pointing in various directions, likely representing rotational or directional changes. Below, two overlapping sinusoidal waveforms are depicted, illustrating periodic oscillations. The image appears to convey concepts related to wave mechanics or rotational dynamics.

Fig. 10.18 Synchronous generator induced waves. Source from wikicommons under free to use license [12]

Question What do we get if we use an external drive mechanism to rotate the poles? As we know, rotating the poles by means of an external drive, like a turbine, it appears a rotating magnetic field.

Question What does represent a rotating magnetic field in a real synchronous generator? A rotating magnetic field moves with respect the stator coils. The application of Faraday's law results in the generation of an emf in the stator coils. These conductors do not move. Faraday's law requires taking the conductor's velocity regarding the field (A−A′) into account in order to determine the polarities of the induced electromotive forces in the stator conductors.

However, in the machine, it is the field that moves relative to the conductor (v). We see that the rotor's rotation causes a polarity change of the induced electromotive forces in the windings (Fig. 10.19). Specifically, the forces enter under the North Pole and exit under the South Pole (in the rotation direction).

Diagram of a circular system with concentric rings and labeled components. The inner circle contains a magnet with north (N) and south (S) poles. Arrows indicate the direction of magnetic field lines and velocity. Two sections, labeled A-A' and B-B', show cross-sectional views with symbols representing magnetic field interactions. The outer circle has arrows labeled <span class= $B$ indicating the magnetic field direction.">

Fig. 10.19 Polarity of induced electromagnetic forces. Source: own elaboration

According to Faraday's law, we have to plot relationship between coil speed and electromagnetic forces (Fig. 10.20).

Diagram illustrating Faraday's law of electromagnetic induction. The top section shows a coil with velocity <span class= $V_{A - A^{'}}$ moving relative to a magnetic field $B$ , with direction indicated by arrows. The bottom section depicts the polarity of the induced electromotive force (emf) with an arrow labeled $N$ and $n$ , showing the direction of coil velocity relative to the field.">

Fig. 10.20 Relationship between coil speed and electromagnetic forces. Source: own elaboration

Diagram illustrating electromagnetic induction. A straight arrow points diagonally upward, labeled "Coil velocity relative to the field." A curved arrow labeled "" and "" indicates the direction of rotation, with the text "polarity of the induced emf" nearby. The sketch represents the relationship between coil movement and induced electromotive force.

The rotation of the stator will induce a total emf in them.

E = 4.44·N·Φ₀·f (10.11)

As with transformer windings, and asynchronous machines these turns have some resistance and reactance.

练习题

In a real synchronous generator, where are the inductor and armature located?

A. The inductor is in the stator and the armature is in the rotor

B. The inductor is in the rotor and the armature is in the stator

C. Both the inductor and armature are in the rotor

D. Both the inductor and armature are in the stator

According to equation $E = 4.44 \cdot N \cdot Φ_{0} \cdot f$ , what does the variable $N$ represent?

A. The rotational speed in revolutions per second

B. The number of turns in the stator winding

C. The number of magnetic poles

D. The frequency of the generated voltage

What is created when an external drive mechanism, such as a turbine, rotates the poles of a synchronous generator?

A. A stationary magnetic field in the stator

B. A rotating magnetic field that moves relative to the stator coils

C. A direct current in the stator windings

D. An alternating current in the rotor windings

Which of the following statements about a real synchronous generator are correct?

A. Direct current flows through the rotor winding to establish the magnetic poles

B. The stator conductors remain stationary during operation

C. The stator windings have only resistance with no reactance

D. The magnetic field path includes the rotor, air gap, and stator

E. The rotor winding has no electrical resistance

In a real synchronous generator, the stator conductors move with the rotating magnetic field to generate an electromotive force.

The rotation of the rotor in a synchronous generator causes the polarity of the induced electromotive forces in the stator windings to change.

In a real synchronous generator, the induced electromotive forces enter the stator conductors under the South Pole and exit under the North Pole in the direction of rotation.

The magnetic field force lines in a synchronous generator follow the ___-air gap-stator path.

The total induced emf in the stator windings is given by the equation $E =$ ___ $\cdot N \cdot Φ_{0} \cdot f$ .

Explain how a rotating magnetic field induces an electromotive force in the stator coils of a real synchronous generator.

Compare the structural configuration of a basic (elementary) synchronous generator with that of a real synchronous generator in terms of where the inductor and armature are located.

In an elementary synchronous generator (Section 10.3), the armature rotates within a stationary magnetic field, while in a real synchronous generator (Section 10.4), the field rotates while the armature remains stationary. Despite this structural difference, both configurations produce the same induced emf equation $E = 4.44 \cdot N \cdot Φ_{0} \cdot f$ . What principle explains why both configurations yield equivalent results?

A. The conductor velocity relative to the magnetic field determines the induced emf, regardless of which component moves

B. The stationary component always determines the magnitude of the induced emf

C. Only the rotating component's speed matters, not its position

D. The magnetic field strength must be identical in both configurations

In a real synchronous generator, direct current powers the rotor winding to establish magnetic poles, and when an external drive rotates these poles, the resulting rotating magnetic field induces an alternating emf in the stationary stator coils according to Faraday's law.

In an elementary synchronous generator, the armature moves through a stationary magnetic field, whereas in a real synchronous generator, the magnetic field moves relative to stationary conductors. Both configurations produce the same RMS emf value given by the equation ___ $\cdot N \cdot Φ_{0} \cdot f$ .

Which of the following statements correctly describe the relationship between elementary synchronous generators (Section 10.3) and real synchronous generators (Section 10.4)?

A. In an elementary generator, the armature is in the rotor, while in a real generator, the armature is in the stator

B. Both configurations produce sinusoidal emf with one complete cycle per rotation for a two-pole machine

C. The stator conductors in a real generator remain stationary while the magnetic field rotates

D. The linear velocity formula

v = π \cdot n \cdot D

applies only to elementary generators

E. Both configurations use the same RMS emf equation

E = 4.44 \cdot N \cdot Φ_{0} \cdot f

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10.4 Real Synchronous Generator