Introduction to three phase power
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Introduction to Three-Phase Power. Typical Transformer Yard. Basic Three-Phase Circuit. 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.

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What is three phase power
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



Definitions
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
Phasor (Vector) Form for abc

Vc=Vm/+120°

Va=Vm/0°

Vb=Vm/-120°

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Phasor vector form for abc1
Phasor (Vector) Form for abc

Vc=Vm/+120°

Va=Vm/0°

Vb=Vm/-120°

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

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Three phase generator
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
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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Definitions1
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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Phase Voltages

Line Voltages

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Vector addition to find v ab v an v bn
Vector addition to find VAB=VAN-VBN

-VBN

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Using the tip to tail method
Using the Tip-to-Tail Method

-VBN

VΦ = Line-to-Neutral, or Phase Voltage

VAB = VAN – VBN = √3VΦ

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Conclusions for the y connection
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
Summary

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Phase Currents

Line Currents

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Vector addition to find i aa i ab i ca
Vector Addition to find IaA=IAB-ICA

-ICA

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Using the tip to tail method1
Using the Tip-to-Tail Method

-ICA

IaA = √3IΦ/-30°

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Conclusions for the delta connection
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


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