Introduction to Three-Phase Power ECE 441

Typical Transformer Yard ECE 441

Basic Three-Phase Circuit ECE 441

What is Three-Phase Power? Three sinusoidal voltages of equal amplitude and frequency out of phase with each other by 120°. Known as “balanced”. Phases are labeled A, B, and C. Phases are sequenced as A, B, C (positive) or A, C, B (negative). ECE 441

Three-Phase Power ECE 441

Definitions 4 wires Color Code 3 “active” phases, A, B, C 1 “ground”, or “neutral” Color Code Phase A Red Phase B Black Phase C Blue Neutral White or Gray ECE 441

Phasor (Vector) Form for abc Vc=Vm/+120° Va=Vm/0° Vb=Vm/-120° ECE 441

Phasor (Vector) Form for abc Vc=Vm/+120° Va=Vm/0° Vb=Vm/-120° Note that KVL applies .... Va+Vb+Vc=0 ECE 441

Three-Phase Generator 2-pole (North-South) rotor turned by a “prime mover” Sinusoidal voltages are induced in each stator winding ECE 441

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How are the sources connected? (a) shows the sources (phases) connected in a wye (Y). Notice the fourth terminal, known as Neutral. (b) shows the sources (phases) connected in a delta (∆). Three terminals ECE 441

Look at a Y-Y System ECE 441

Definitions Zg represents the internal generator impedance per phase Zl represents the impedance of the line connecting the generator to the load ZA,B,C represents the load impedance per phase Zo represents the impedance of the neutral conductor ECE 441

Look at the Line and Load Voltages ECE 441

Phase Voltages Line Voltages ECE 441

Vector addition to find VAB=VAN-VBN ECE 441

Using the Tip-to-Tail Method -VBN VΦ = Line-to-Neutral, or Phase Voltage VAB = VAN – VBN = √3VΦ ECE 441

Conclusions for the Y connection The amplitude of the line-to-line voltage is equal to √3 times the amplitude of the phase voltage. The line-to-line voltages form a balanced set of 3-phase voltages. The set of line-to-line voltages leads the set of line-to-neutral (phase) voltages by 30°. ECE 441

Summary ECE 441

Look at the Delta-Connected Load ECE 441

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Phase Currents Line Currents ECE 441

Vector Addition to find IaA=IAB-ICA ECE 441

Using the Tip-to-Tail Method -ICA IaA = √3IΦ/-30° ECE 441

Conclusions for the Delta Connection The amplitude of the line current is equal to √3 times the phase current. The set of line currents lags the phase currents by 30°. ECE 441