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EE 221
CIRCUITSIIChapter 12
Three-Phase Circuits
1
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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
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US Electric Energy Generation Mix
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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
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A three-phase generator consists of a rotating
magnet (in the rotor) surrounded by stationary
windings (in the stator).
11
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
14
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
12.3 Balanced Three-Phase Connection
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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12.3 Balanced Three-Phase Connection
Answer:
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12.3 Balanced Three-Phase Connection
A balanced- system is a three-phase system with a
balanced-connected source and a balanced-connected
load.
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12.3 Balance Three-Phase Connection
Example 4:
Answer:
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12.3 Balanced Three-Phase Connection
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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24
12.3 Balanced Three-Phase Connection
Example 5: let Find the line currents
Answer:
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)cos(3)cos(3 IVIVP Lp
25
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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12.6 Application Residential Wiring
A typical wiring diagram of a room
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12.6 Application Residential Wiring
Single-phase three-wire residential wiring
+
7,600 V
-
12 6 A li ti R id ti l Wi i
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12.6 Application Residential Wiring
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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