Three Phase Ac Circuit

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Three Phase AC

Circuits


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THREE PHASE AC CIRCUIT (1/2)

It is a common method of alternating current

electric power generation, transmission, and

distribution.

This was introduced and patented by NikolaTesla in the years from 1887 to 1888.

It is a type of polyphase system and is the

most common method used by gridsworldwide to transfer power. It is also used to

power large motors and other large loads.

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THREE PHASE AC CIRCUIT (2/2)

It is generally more economical than others

because it uses less conductor material to

transmit electric power than equivalent

single-phase or two-phase systems at thesame voltage.

In a three-phase system, three circuit

conductors carry three alternating currents (ofthe same frequency) which reach their

instantaneous peak values at different times.

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EXAMPLES OF THE THREE

PHASE AC CIRCUIT (1/2)

Three-phase transformer with four wire output for 208Y/120

volt service: one wire for neutral, others for A, B and C phases.

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EXAMPLES OF THE THREE

PHASE AC CIRCUIT (2/2)

Three-phase electric power transmission.

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Properties of three phase AC

circuits

The phase currents tend to cancel out one another,

summing to zero in the case of a linear balanced

load.

Power transfer into a linear balanced load is

constant.

Three-phase systems can produce a magnetic field

that rotates in a specified direction.

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Important Terms for the 3-Phase AC

Circuits (1/2)

Phase

describes or pertains to one element or device in aload, line, or source. It is simply a "branch" of the

circuit.

Line

refers to the "transmission line" or wires that connectthe source (supply) to the load. It may be modeled as asmall impedance (actually 3 of them), or even by just aconnecting line.

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Important Terms for the 3-Phase AC

Circuits (2/2)

Neutral

the 4th wire in the 3-phase system. It's where the

phases of a Y connection come together.

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2 TYPES OF 3-PHASE CONNECTION (1/2)

A. Wye or Star Connection

each phase is connected between a line and the neutral

Phase voltages: Line to neutral voltages (Va, Vb, and Vc)

Phase currents: Line currents (Ia,Ib, andIc)

Neutral connects the 3 phases

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2 TYPES OF 3-PHASE CONNECTION (2/2)

B. Delta Connection

each phase is connected between two lines

Phase voltages: Line voltages (Vab, Vbc, and Vac)

Phase currents: currents from line to line (Iab,Ibc, andIac)

Neutral is not present

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BALANCED THREE PHASE AC

CIRCUITS

Requirements:

All 3 sources are represented by a set of

balanced 3-phase variables.

All loads are 3-phase with equal impedances.

Line impedances are equal in all 3 phases.

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The three induced voltages across

the armature coils betweenterminals aa, bb, and cc canbe written as follows:

Positive (abc) sequence

Basic structure and principle of an AC

generator: (a) A 3-phase generator with

the armature rotating, (b) A 3-phase

generator with the magnet rotating, and(c) A 3-phase voltage waveform.

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Negative (acb) sequence

Basic structure and principle of an AC

generator: (a) A 3-phase generator with

the armature rotating, (b) A 3-phase

generator with the magnet rotating, and(c) A 3-phase voltage waveform.

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Relations between line and phase voltages/currents in a

balanced three phase (Y-connected)

(a) A Y-connected 3-phase source and (b)

its voltage phasor diagram.

From this phasor diagram, the

relationship between the

phase (or line-to-neutral)

voltages and the line (or line-

to-line) voltages can be

written as follows:

Note that for a Y-connected three-phase source, the amplitudes of line voltages

are 3 times that of phase voltages and the line current is the same as the phasecurrent:

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Relations between line and phase voltages/currents in a

balanced three phase (-connected)

(a) A -connected 3-phase source and (b)its current phasor diagram.

From this phasor diagram, the

relationship between thephase currents and the line

currents can be written as

follows:

Note that for a -connected three-phase source, the amplitudes of line currentsare 3 times that of phase currents and the line voltage is the same as the phasevoltage:

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DELTA-WYE CONVERSION (1/4)

A delta connected three-phase load can be replace by an equivalent

wye-connected load if the two loads are equivalent (draw the same

line currents from the three-phase source).

Delta and Wye Connected for balanced 3-phase load.

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Note that the line-to-line voltages at the delta-connected load are

the load voltages. The a phase line currents for the wye and delta

loads are defined by the following:

Delta Connected Load Wye Connected Load

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The line currents are equal if

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The same results are found for the other two line currents. Thus, a

delta-connected load can be replaced by a wye-connected load

with one-third the impedance per phase for balanced system.

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UNBALANCED THREE PHASE AC

CIRCUITS

When the three load impedances are not equal toone another, the phasor sums and the neutral current

(In) are not zero, and the load is, therefore,

unbalanced.

The imbalance occurs when an open or short circuit

appears at the load.

If a three-phase system has an unbalanced load and

an unbalanced power source, the methods of fixingthe system are complex.

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Relationships of phase and line voltages withrespect to the phase angles (1/4)

The phase angles of the given line voltages are 120 out ofphase can be connected in either balanced/unbalanced wye or

delta connected loads.

Regarding the phase sequence suppose that a given phasesequence for example abc sequence where

The first letter represents 0 angle.

The second letter represents -120 angle.

The third letter represents 120 angle.

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Combinations of the phase sequences

The positive phase sequence has the combinations abc, bca,

and cab sequences.

The negative phase sequence has the combinations acb, cba,

and bac sequences.

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Phase angles of the voltages with respect to their types of

connection:

For a delta connected load, the line and phase voltages

simply follow the order of the sequence with the phase

angles 0, -120, and 120 respectively.

For a wye connected load, the line voltages follows the

sequence of 30, 150, and -90 respectively for positivephase sequence and -30, 90, and -150 respectively fornegative phase sequence. The phase voltages follow the

sequence of 0, -120, and 120 respectively.

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It is possible that for the abc sequence can be also represented

as the phase sequence ab-bc-ca for the line voltages sequence.

Suppose that you are going to reverse the subscript of the given

line voltage. For example, given the line voltage Vab = 12030V then Vba = 120-30 V.

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SAMPLE PROBLEMS (1/14)

1. Given the phase voltage of 235 V and the phase

current is 6.25 A. Find the line voltage and line

current connected in (a) Y, and (b) .

Solution:

(a) For Y-connected 3 phase system

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(b) For-connected 3 phase system

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2. A 3 phase balanced system contains a wye

load. The line-to-line voltage is 270 V, and the

resistance is 30 in each branch.

Find line current and neutral current for the

following load conditions.

(a) balanced load

(b) open circuit in phase a(c) short circuit in phase a

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Solution:

(a) For balanced load

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(b) For unbalanced 3 phase load

open circuit in phase a

Current flow in lines b and cbecomes the resultant of the loads

in b and c connected in series

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(c) For unbalanced 3 phase load

short circuit in phase a

The current in phase a is equal to the neutral line current,

Ia =IN. Therefore,INis the phasor sum ofIb andIc.

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Conclusion in problems (b) and (c):

In a fault condition, the neutral connection in a wye-

connected load will carry more current than the phase

under a balanced load.

Unbalanced three-phase circuits are indicated by

abnormally high currents in one or more phases. This may cause damage to equipment if the

imbalance is allowed to continue.

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3. A balanced 3-phase source of 230 V is connected to the

balanced 3-phase -connected load with the impedance ineach phase of 12 + j36 . Suppose that the phasesequence is abc sequence.

Find the line currentsIa,Ib, andIcin phasor form.

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Solution:

Transform the delta connected load to wyeconnected load

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The equivalent circuit is

Solving for the phase voltage

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Since the sequence is abc sequence,

the phase voltages are

Solving for the line currents

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4. A balanced 3-phase source of 270 V is connected to the

unbalanced 3-phase Y-connected load with the followingimpedances:Za = 15 +j20 , Zb = 12 j15 , and Zc =16 + j24 . Suppose that the phase sequence is bcasequence.

Find

a. The line currentsIa,Ib, andIcin phasor form.

b. The neutral currentINin phasor form.

36SAMPLE PROBLEMS (12/14)


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Solution:

Solving for the phase voltage

The given phase voltages for the

bca sequence are



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Solving for the line currents


Solving for the neutral current

Three Phase Ac Circuit

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