Synchronous Machines

Description: The elementary 3-phase 2-pole round rotor synchronous generator has a stator equipped with 3 coils displaced 120° from each other; although shown as concentrated, they actually are distributed. When the rotor is excited with dc and rotated, the resultant field will also rotate so that sinusoidal voltages are generated in the 3 stator phases.

Description: The elementary 3-phase 2-pole synchronous generator has a stator equipped with 3 coils displaced 120° from each other; although shown as concentrated, they actually are distributed. When the rotor is excited with dc and rotated, the resultant field will also rotate so that sinusoidal voltages are generated in the 3 stator phases, displaced 120° in time and having a frequency directly related to rotor speed.

Description: Two 3-phase power systems of differing frequencies are to be connected by closing the breakers at the moment the voltages across them are minimum. The phase voltages v a, v b, v c of the abc system and the voltages v A, v B, v C of the ABC system are represented in the left figure by phasors of constant amplitude rotating at the speed associated with the corresponding system frequencies. The voltages v aA, v bB, v cC across the breakers are seen in the right figure as amplitude modulated phasors rotating at the difference frequency (slip). This arrangement forms the basis of the operation of the synchroscope.

Description: A synchronous machine connected to an infinite bus is subjected to two consecutive step loads. A slight further increase in the load leads to instability and loss of synchronism. The bus voltage V and internal machine voltage E are portrayed in a synchronously rotating frame. The corresponding speed versus angle response is also shown.

Description: The operation of a synchronous generator delivering power to a constant power-factor load is demonstrated by means of animated phasor diagrams and compounding curves. A compounding curve shows the field excitation needed to maintain rated terminal voltage as the load is varied. The basic phasor equation is E = V + j X I.

Description: The steady-state characteristics of a synchronous motor represented by phasor diagrams are shown as function of the excitation voltage E: for low values of E, the motor is said to be under excited and the current I lags the terminal voltage V whereas, for large values of E, the motor becomes over excited with the current now leading the voltage. Note that the locus of the current phasor is a vertical line meaning that I cos( φ ) is constant; similarly the locus of E is a horizontal line satisfying the condition that E sin( δ ) is constant; both constraints are the consequence of maintaining constant power P = I V cos( φ ) = E V sin( δ ) / X. The basic phasor equation is V = E + jX I. The associated V-curve (I versus E) is also plotted.

Description: The steady-state characteristics of a synchronous motor represented by phasor diagrams are shown as function of the load P with the excitation voltage E kept constant. The power expression is P = I V cos( φ ) = E V sin( δ ) / X. The basic phasor equation is V = E + jX I. The locus of E is a portion of a circle of radius E centered at the origin of the complex plane. The locus of I is also a circle of radius E/X centered on the imaginary axis at –V/X. The power P versus the torque angle δ is also plotted.

Description: Explore alternator voltage generation.

Description: Explore synchronous machine operating characteristics.

Description: Explore v-curves of a synchronous motor.

Description: Explore steady-state characteristics of a synchronous machine.

Description: Explore synchronous machine complex power.

Description: Explore synchronous motor v-curves.

Description: Explore synchronous motor: phasor diagrams and power-angle curves.

Description: Explore synchronous generator: compounding curves..

Description: Explore synchronous generator: capability curves.

Description: Explore synchronous machine phasor diagram.

Description: Explore armature short-circuit current in a synchronous machine.

Description: Explore synchronous machine transient stability.

Description: Explore dynamic stability of a synchronous motor.

Description: Explore synchronization.