ECE 441 1

Introduction to Three-Phase Power

ECE 441 2

Typical Transformer Yard

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Basic Three-Phase Circuit

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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).

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Three-Phase Power

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Definitions

• 4 wires– 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

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Phasor (Vector) Form for abc

Va=Vm/0°

Vb=Vm/-120°

Vc=Vm/+120°

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Phasor (Vector) Form for abc

Va=Vm/0°

Vb=Vm/-120°

Vc=Vm/+120°

Note that KVL applies .... Va+Vb+Vc=0

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Three-Phase Generator

• 2-pole (North-South) rotor turned by a “prime mover”

• Sinusoidal voltages are induced in each stator winding

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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

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Look at a Y-Y System

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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

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Look at the Line and Load Voltages

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CN

AB AN BN

BC BN CN

CA AN

V V V

V V V

V V V

Line Voltages Phase Voltages

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-VBN

Vector addition to find VAB=VAN-VBN

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-VBN

Using the Tip-to-Tail Method

VAB = VAN – VBN = √3VΦ

VΦ = Line-to-Neutral, or Phase Voltage

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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°.

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Summary

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Look at the Delta-Connected Load

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0

120

120BC

AB

CA

I I

I I

I I

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bB

aA AB CA

BC AB

cC CA BC

I I I

I I I

I I I

Line Currents Phase Currents

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-ICA

Vector Addition to find IaA=IAB-ICA

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-ICA

Using the Tip-to-Tail Method

IaA = √3IΦ/-30°

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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°.