Download balanced three–phase circuits

JAMES W. NILSSON
&
SUSAN A. RIEDEL
ELECTRIC
CIRCUITS
EIGHTH EDITION
CHAPTER 11
BALANCED
THREE–PHASE
CIRCUITS
© 2008 Pearson Education
CONTENTS
11.1 Balanced Three-Phase Voltages
11.2 Three-Phase Voltage Sources
11.3 Analysis of the Wye-Wye Circuit
11.4 Analysis of the Wye-Delta Circuit
11.5 Power Calculations in Balanced ThreePhase Circuits
11.6 Measuring Average Power in ThreePhase Circuits
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11.1 Balanced Three-Phase Voltages
A basic three-phase circuit
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11.1 Balanced Three-Phase Voltages
The abc (positive)
sequence
The abc (negative)
sequence
Phasor diagrams of a balanced set of three-phase voltages
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11.2 Three-Phase Voltage Sources
A sketch of a three-phase voltage source
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11.2 Three-Phase Voltage Sources
The two basic connections of an ideal
three-phase source.
A Y-connected source
A ∆-connected source
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11.2 Three-Phase Voltage Sources
A model of a three-phase source with
winding impedance:
(a) A Y-connected source
(b) A ∆-connected source
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11.3 Analysis of the Wye-Wye Circuit
A three-phase Y-Y system
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11.3 Analysis of the Wye-Wye Circuit
A single-phase equivalent circuit
A single-phase equivalent circuit is used to
calculate the line current and the phase
voltage in one phase of the Y-Y structure. The
a-phase is normally chosen for this purpose.
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11.3 Analysis of the Wye-Wye Circuit
Line-to-line and line-to-neutral voltages
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11.3 Analysis of the Wye-Wye Circuit
Phasor diagrams showing the relationship
between line-to-line and line-to-neutral
voltages in a balanced system.
The abc sequence
The acb sequence
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11.4 Analysis of the Wye-Delta Circuit
Relationship between three-phase deltaconnected and wye-connected impedance.
Z
ZY 
3
A single-phase equivalent circuit
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11.4 Analysis of the Wye-Delta Circuit
A circuit used to establish the relationship between
line currents and phase currents in a balanced ∆ load
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11.4 Analysis of the Wye-Delta Circuit
Phasor diagrams showing the relationship
between line currents and phase currents
in a ∆-connected load.
The positive sequence
The negative sequence
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11.5 Power Calculations in Balanced
Three-Phase Circuits
Average Power in a Balanced Wye Load
A balanced Y load used to introduce average
power calculations in three-phase circuits
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11.5 Power Calculations in Balanced
Three-Phase Circuits
VL
PT  3
I L cos 
3
 3VL I L cos 
Total real power in a balanced three-phase load
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11.5 Power Calculations in Balanced
Three-Phase Circuits
Complex Power in a Balanced Wye Load
Q  V I sin 
QT  3Q  3VL I L sin 
Total reactive power in a balanced three-phase load
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11.5 Power Calculations in Balanced
Three-Phase Circuits
S  P  jQ  V I
*
ST  3S  3VL I L 
Total complex power in a balanced three-phase load
11.5 Power Calculations in Balanced
Three-Phase Circuits
Power Calculations in a Balanced Delta Load
A Δ-connected load used to
discuss power calculations
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11.6 Measuring Average Power in
Three-Phase Circuits
 A wattmeter
measures the average power
delivered to a load by using a current coil
connected in series with the load and a
potential coil connected in parallel with the
load.
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11.6 Measuring Average Power in
Three-Phase Circuits
The key features of the
electrodynamometer wattmeter
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11.6 Measuring Average Power in
Three-Phase Circuits
A general circuit whose power
is supplied by n conductors
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11.6 Measuring Average Power in
Three-Phase Circuits
The total average power in a balanced
three-phase circuit can be measured by
summing the readings of two wattmeters
connected in two different phases of the
circuit.
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11.6 Measuring Average Power in
Three-Phase Circuits
A circuit used to analyze the twowattmeter method of measuring average
power delivered to a balanced load
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THE END
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