Lesson 343 PHASE Sources & Loads

Learning Objectives Review the induced AC voltage output for a three phase AC generator

as a function of time and as phasors.

Define a three-wire Y-Y three phase circuit and a four-wire Y-Y three phase circuit.

Define the symbols for line to neutral voltages, line to line voltages, line currents, and phase impedances that will be used in three phase circuits.

Analyze Ohm’s law in a three-wire Y-Y three phase circuit and in a four-wire YY three phase circuit using a basic three phase generator that produces three balanced voltages which are connected to balanced loads.

Analyze Kirchhoff’s current law in a three-wire Y-Y three phase circuit and in a four-wire Y-Y three phase circuit using a basic three phase generator that produces three balanced voltages with a Y connected balanced purely resistive loads.

Why three-phase? http://www.youtube.com/watch?v=HqZtptHnC2I

1. Nearly all power generated and distributed is 3-phase, 60 Hz (or 50 Hz outside the U.S.). When single phase is needed, it can simply be taken

from one of the three phases.

2. The instantaneous power in 3-phase system can be constant (not pulsating). Results in less vibration in 3-phase machines.

3. Three phase systems are more economical that single. Amount of wire needed is less than single phase.

THREE-PHASE GENERATOR

(a) Three-phase generator; (b) induced voltages of a three-phase generator.

THREE-PHASE GENERATOR

Phasor diagram for the phase voltages of athree-phase generator.

Demonstrating that the vector sum of the phase voltages of a three-phase generator is zero.

Y-CONNECTED GENERATOR

If the three terminals denoted N in Fig. are connected together, the generator is referred to as a Y-connected three-phase generator.

Y-connected generator.

Delta(), Wye(Y) Connections

Wye (Y) Delta ()

Y-Y system

Lines

Y LoadGenerator

4-wire Y-Y system

3-wire Y-Y system

The neutral voltage (VnN) in a balanced Y-Y system is zero.

Phase voltages

Phase voltages are the voltages across phases. • For a Y load, phase voltage is measured from line to neutral (n)• For the generator, EAN, EBN and ECN are the phase voltages.

Example Problem 1

EAN = 7620-18 V

What are the phase voltages EBN, and ECN?

0

120

120

AN

BN

CN

E

E

E

E

E

E

Line voltages

Line voltages are the voltages between the lines A, B and C

Line and phase voltages of the Y-connected three-phase generator.

Determining a line voltage for a three-phase generator.

PHASE/LINE VOLTAGES

Line/Phase Voltages for a Wye Circuit

Relationship between line and phase voltages

For a balanced Y system, the magnitude of line-to-line voltage is 1.732 times the magnitude of the phase voltage.

Line to line voltage leads phase voltage by 30.

3 30

ab an bn

ab an

E E E

E E

Example Problem 2

EAN = 7620-18 V

What are the line voltages ?

3 30

ab an bn

ab an

E E E

E E

0

120

120

AN

BN

CN

E

E

E

E

E

E

CURRENTS

Line currents are the currents in the line conductors. Phase currents are the currents through phases.For Y loads, line current and phase current are the same.

Currents for a Wye Circuit

For Y loads, line current and phase current are the same.

anana ZVI /

Line current Phase current

10 0 10 120 10 120 0A A A A N A B CI = I + I + I

Diagram of 3-phase system

Example Problem 3

For the load depicted below, EAN = 277-30 V . Find the phase voltages and line voltages and currents. Sketch their phasor values.

-connected Load

For loads, phase voltage and line voltage are the same thing.

load definitions

Line currents are the currents in the line conductors. Phase currents are the currents through phases .

Y-Y

Line/Phase Currents for a Delta Circuit

Line current Phase current