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10.5 No-load Synchronous Generator

It is useful to distinguish between no-load and load scenarios when we analyze the voltage that the synchronous generator generates. A synchronous generator is in a no-load condition when its armature winding is disconnected. We see the functional diagram of a q-phase and no-loaded generator (Fig. 10.28).

Flow chart illustrating an electrical system. It begins with two voltage regulators, leading to an inductor labeled "Rotor." The inductor connects to an "Induced Stator," producing outputs <span class= $e_{1} (f)$ , $e_{2} (f)$ , and $e_{q} (f)$ . A frequency regulator connects to a turbine, influencing the inductor with torque and frequency. The system is controlled by RMS voltage and current $I_{e}$ , with a magnetic field $B_{0}$ between the rotor and stator.">

Fig. 10.28 Functional diagram of a q-phase no-load alternator.

Under these conditions, the magnetomotive force (Fmme) appears only because of the direct current (Ie) circulating through the inductor. This excitation generates flux circulation in the magnetic circuit of the synchronous machine and produces voltage e (t) in the stator's armature winding. Assuming the inductor generates a sinusoidal induction wave, the voltage in the armature winding is also sinusoidal. As previously mentioned, the frequency of the induced voltage is:

f=p·n60 (10.14)

The following expression provides the rms value of the induced no-load voltage e (t):

E0=4,44·N·Φ0·f (10.15)

It is important to note that, due to the absence of currents in the armature, the voltage is the same that the phase voltage (V) at the generator terminals.

练习题

A synchronous generator is considered to be in a no-load condition when:

A. The rotor is not rotating

B. The armature winding is disconnected

C. The excitation current is zero

D. The turbine is shut down

A 4-pole synchronous generator rotates at 1800 rpm. What is the frequency of the induced voltage?

A. 30 Hz

B. 60 Hz

C. 90 Hz

D. 120 Hz

A 3-phase synchronous generator has 100 turns per phase, a flux per pole of 0.05 Wb, and operates at 50 Hz. What is the RMS value of the induced no-load voltage per phase?

A. 222 V

B. 1110 V

C. 2220 V

D. 111 V

In a no-load synchronous generator, which of the following statements are true about the magnetomotive force and voltage generation?

A. The magnetomotive force appears only because of the direct current

I_{e}

circulating through the inductor

B. The armature current contributes significantly to the magnetomotive force

C. The excitation generates flux circulation in the magnetic circuit

D. The voltage produced in the stator's armature winding is sinusoidal if the induction wave is sinusoidal

In a no-load synchronous generator, the terminal phase voltage equals the induced voltage because there are no currents in the armature windings.

In a no-load synchronous generator, the magnetomotive force is produced by both the excitation current in the rotor and the armature current in the stator.

If the inductor of a synchronous generator produces a sinusoidal induction wave, the resulting voltage in the armature winding will also be sinusoidal.

The RMS value of the induced no-load voltage in a synchronous generator is given by the formula: $E_{0} =$ ___ $\cdot N \cdot Φ_{0} \cdot f$

The frequency of the induced voltage in a synchronous generator is calculated using the formula: $f =$ ___ $\cdot n /60$ , where $p$ is the number of poles and $n$ is the rotational speed in rpm.

Explain why the terminal phase voltage of a no-load synchronous generator equals the induced voltage $E_{0}$ .

Describe how the rotating magnetic field in a synchronous generator induces an EMF in the stator windings, and state the formula for the RMS value of this induced voltage.

A 4-pole synchronous generator operates at no-load condition with a rotor speed of 1800 rpm. According to the frequency equation $f = \frac{p \cdot n}{60}$ and the principle that each turn guarantees a complete emf cycle, what is the frequency of the induced voltage in the stator winding?

A. 30 Hz

B. 60 Hz

C. 90 Hz

D. 120 Hz

A synchronous generator operates under no-load conditions. Which of the following statements correctly describe the relationship between the excitation system and the induced voltage? Select all that apply.

A. The magnetomotive force under no-load is produced only by the direct current

I_{e}

flowing through the rotor winding

B. The rotating magnetic field established by the rotor DC current induces an emf in the stationary stator coils according to Faraday's law

C. The RMS value of the induced no-load voltage is given by

E_{0} = 4.44 \cdot N \cdot Φ_{0} \cdot f

D. The terminal phase voltage equals the induced voltage because there is no current in the armature winding

E. The stator conductors must rotate with the magnetic field to induce voltage

The equation $E_{0} = 4.44 \cdot N \cdot Φ_{0} \cdot f$ for the RMS no-load voltage of a synchronous generator is derived from the same fundamental principles as the RMS emf equation $E = 4.44 \cdot N \cdot Φ_{0} \cdot f$ for N turns of a rotating loop, where $Φ_{0} = B \cdot D \cdot L$ represents the maximum flux embraced by each loop.

In a synchronous generator, the inductor is located on the _ and the armature winding is located on the _. Under no-load conditions, when the armature winding is disconnected, the magnetomotive force is produced only by the direct current circulating through the inductor.

Explain why the terminal phase voltage of a synchronous generator under no-load conditions equals the induced voltage $E_{0}$ , and describe how the sinusoidal nature of the induced voltage is achieved through the interaction between the rotor and stator.

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10.5 No-load Synchronous Generator