Three-Phase Sine AC Power Generation

The three-phase sinusoidal alternating current of a generator consists of three alternating electromotive forces with the same frequency, phase difference of 120° electrical angle, and each phase winding can generate a sinusoidally varying alternating electromotive force during operation. When the generator rotates, three-phase alternating electromotive forces are induced in the armature coils, with a phase difference of 120° between each phase. The variation curve of the three-phase sinusoidal alternating electromotive forces takes the moment when the U-phase winding's electromotive force starts to rise from zero as the initial phase; the V-phase winding's electromotive force lags behind the U-phase by 120°, and the W-phase winding's electromotive force lags behind the V-phase by another 120°.

In this way, the U, V, and W three-phase windings sequentially generate sinusoidally varying electromotive forces.

The instantaneous value of the U-phase electromotive force is:

eu= Emsinωt (V)

The instantaneous value of the V-phase electromotive force lags behind the U-phase by 120° electrical angle, which is:

ev= Emsinωt−120° (V)

The instantaneous value of the W-phase electromotive force lags behind the V-phase by 120° electrical angle, that is, lags behind the U-phase by 240° electrical angle (or leads the U-phase by 120° electrical angle), which is:

ew= Emsinωt−240° (V)

The three start ends of the three-phase windings are directly used as phase lines for output, while the other three tail ends of the three-phase windings are connected together to serve as the common loop for each phase winding. The three sets of windings of a three-phase alternator are internally connected according to the designed connection method, and the six start and tail ends of the three-phase windings are led out, then connected in star or delta connection. The two connection methods will be briefly described below.

Star Connection

When the windings are connected in star connection, the voltage measured by a voltmeter between the start end and tail end of each phase winding is called the phase voltage. From the measurement, it can be seen that under normal conditions, the three phase voltages should be equal in value. The voltage measured by a voltmeter between the start ends of each phase winding is called the line voltage. From the measurement, it is known that the three line voltages of the windings are also equal in value. Through practice and analysis, it has been proved that under the symmetrical condition of three-phase windings, the relationship between phase voltage and line voltage is:

Uuv= √3Uu

Uvw= √3Uv

Uwu= √3Uw

That is, when the three-phase symmetrical windings are connected in star connection, the line voltage is √3 times the phase voltage. If the three-phase load they are connected to is also balanced and symmetrical, the line current is equal to the phase current.

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