EE 221 Three Phase Circuits

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EE 221

CIRCUITSIIChapter 12

Three-Phase Circuits

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THREE-PHASE CIRCUITS

CHAPTER 12

12.1 What is a Three-Phase Circuit?

12.2 Balanced Three-Phase Voltages12.3 Balanced Three-Phase Connections

12.4 Power in a Balanced System

12.5 Unbalanced Three-Phase Systems

12.6 Application Residential Wiring

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1. Most of the electric power is generated

and distributed in three-phase.

2. The instantaneous power in a three-phase

system is constant (rather than pulsating)3. The amount of power generated by a

three-phase generator is more economical

than that of a single-phase generator

4. The amount of wire required for a three-

phase system is less than that required for

an equivalent single-phase system.

3

12.1 Advantages of Three-Phase Circuit?


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Schematic Diagram of a Power System
http://en.wikipedia.org/wiki/File:Three_Phase_Electric_Power_Transmission.jpg


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US Electric Energy Generation Mix
http://tonto.eia.doe.gov/energyexplained/images/charts/electric_power_industry_net_generation_fuel-large.gif


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Thermal Power Plants


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Nuclear Power Plant


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Natural Gas Power Plants


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Hydro Power Plants


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Renewable Power Plants
http://upload.wikimedia.org/wikipedia/commons/4/45/Giant_photovoltaic_array.jpg


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A three-phase generator consists of a rotating

magnet (in the rotor) surrounded by stationary

windings (in the stator).

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12.2 Balanced Three-Phase Voltages

A three-phase generator The generated voltages


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It is a system with a generator consisting ofthree

sources having the same amplitude and frequency

but out of phase with each other by 120.

12

12.1 Definition of a Three-Phase Circuit

Three sources

with 120 out

of phaseFour wired

system


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Two possible configurations:

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12.2 Balanced Three-Phase Voltages

Three-phase voltage sources: (a) Y-connected ; (b)-connected


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Balanced phase voltages are equal in magnitudeand are out of phase with each other by 120.

Thephase sequence is the time order in which the

voltages pass through their respective maximumvalues.

a-b-c (or positive sequence)

a-c-b (or negative sequence)

Abalanced load is one in which the phase

impedances are equal in magnitude and in phase

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12.2 Balance Three-Phase Voltages


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Example 1: Determine the phase sequence of the set ofvoltages, and the corresponding line voltages

)110cos(200)230cos(200

)10cos(200

tv

tv

tv

cn

bn

an

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12.2 Balance Three-Phase Voltages

Answer: The voltages can be expressed in phasor form as

Van leads Vcn by 120 and Vcn in turn leads Vbn by 120. Hence, we

have an a-c-b sequence (or negative sequence).

V110200V

V130200V

V10200V

cn

bn

an

V1403200V

V1003200VV203200V

bc

ca

ab


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Four possible connections

1. Y-Yconnection

2. Y- connection

3. - connection

4. -Yconnection

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12.3 Balanced Three-Phase Connections


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cabcabL

cnbnanp

pL

V

V

VV

VVV

VVV

where,3

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12.3 Balance Three-Phase Connection

A balanced Y-Y system is a three-phase system with abalanced Y-connected source and a balanced Y-connected

load.

0)III( cban

I


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Example 2:

Obtain the line currents

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12.3 Balanced Three-Phase Connection

Answer:


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19

CABCABp

cbaL

pL

I

I

II

III

III

where,3


A balanced Y- system is a three-phase system with a

balanced Y-connected source and a balanced-connectedload.


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Example 3:

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Answer:


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21


A balanced- system is a three-phase system with a

balanced-connected source and a balanced-connected

load.


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22

12.3 Balance Three-Phase Connection

Example 4:

Answer:


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23


A balanced-Y system is a three-phase system with a

balanced y-connected source and a balanced y-connected

load.


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Example 5: let Find the line currents

Answer:


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)cos(3)cos(3 IVIVP Lp

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12.4 Power in a Balanced System

)sin(3)sin(3 IVIVQ Lp

IVIVS Lp33


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Example 6

Determine the total complex power at the source and at the load

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12.3 Balanced Three-Phase Systems

Answer:

At the source:

Ss = (2087 + j834.6) VA

At the load:

SL = (1392 + j1113) VA


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12.3 BALANCED LOAD: EXAMPLE 7

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Answer:


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)III(I

,Z

V

I,Z

V

I,Z

V

I

cban

C

CN

c

B

BN

b

A

AN

a

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12.5 Unbalanced 4-Wire Circuit

An unbalanced system is due to unbalanced voltagesources or an unbalanced load.

The total power is not simply three times the power in one

phase, but the sum of the powers in the three phases.

To calculate power in an unbalanced three-phase system

requires that we find the power in each phase.


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12.5 UNBALANCED THREE-WIRE Y-CIRCUIT

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Verify the answer using nodal analysis.

Answer (mesh analysis):

12 5 UNBALANCED THREE WIRE CIRCUIT


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12.5 UNBALANCED THREE-WIRE-CIRCUIT

Calculate the line currents and total real and reactive power supplied by the source:

Rework the problem using a simpler method (i.e., source conversion)

Answer:


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12.4 Power in a Unbalanced System

)(3 12 PPQT

Three Watt-Meter Method: PT = P1+P2+P3

Two Watt-Meter Method: PT = P1+P2

Special case: for a balanced load, the total reactive power may be computedFrom the readings of the two wattmeters:


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2-WATTMETERMETHOD

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The unbalanced load is supplied by a balanced source such that Vab = 2080 V

with positive phase sequence. Calculate the reading of each wattmeter.

Verify the answer by computing the power consumed by each resistor


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12.6 Application: Residential Wiring(single-phase 3-wire)

A 120/240 household power system


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34


A typical wiring diagram of a room


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35


Single-phase three-wire residential wiring

+

7,600 V

-

12 6 A li ti R id ti l Wi i


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36


Answer:


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UTILITY APPLICATIONOFCAPACITORSFORVOLTAGE

REGULATIONAND POWER TRANSFER

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Capacitors are placed in series with high

Voltage transmission lines to improve voltage

Regulation and power transfer capability

Capacitor are also used in medium voltage powerdistribution lines to regulate voltage and reduce

power losses


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ENERGYMETER (KILO-WATT-HOURMETER)

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Old electro-mechanical meter records only

energy consumed over a time period using

mechanical dials.

New smart meter records average power,

reactive power, power factor, power demand,

energy over a period of time, etc

- Remote (wireless) reading- Remote turn ON and OFF

- Communicates with the utility operator in

near-continuous basis

- Able to communicate with home appliances

such as HVAC thermostat.


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POWERDEMAND:

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1 customer:

250,000 customers:

ELECTRICAL SAFETY


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ELECTRICAL SAFETY: Electricity is an integral part of today's modern world, and

sometimes it is easy to forget just how dangerous it can be. Given

the correct circumstances, it can shock you painfully or even kill

you.

According to the Bureau of Labor Statistics Census of Fatal

Occupational Injuries Research File, electrocution is the fifth

leading cause of work-related deaths.

The severity of injury from electrical shock depends on the amount

of electrical current and the length of time the current passes

through the body.

For example, 100 mA going through the body for just 2 seconds is

enough to cause death.

The amount of internal current a person can withstand and still be able

to control the muscles of the arm and hand can be less than 10 mA.

Currents above 10 mA can paralyze or freeze muscles. When this

freezing happens, a person is no longer able to release a tool, wire, or

other object. In fact, the electrified object may be held even more

tightly, resulting in longer exposure to the shocking current. 40


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