Three-Phase Circuits
Yasser. G. Hegazy
Three-Phase Circuit
Three-Phase Circuits
•
What is a Three-Phase Circuit?
•
Balance Three-Phase Voltages
•
Balance Three-Phase Connection
•
Power in a Balanced System
•
Unbalanced Three-Phase Systems
•
Application – Residential Wiring
Yasser. G. Hegazy
Three-Phase Circuit
•
It is a system produced by a generator consisting of
three sources having the same amplitude and
frequency but out of phase with each other by 120°.
Three sources
with 120° out
of phase
Four wired
system
Yasser. G. Hegazy
What is a Three-Phase Circuit?(2)
Advantages:
1. Most of the electric power is generated and
distributed in three-phase.
2. The instantaneous power in a three-phase system
can be constant.
3. The amount of power, the three-phase system is
more economical that the single-phase.
4. In fact, the amount of wire required for a threephase system is less than that required for an
equivalent single-phase system.
Yasser. G. Hegazy
Three-Phase Circuit
•
A three-phase generator consists of a rotating magnet
(rotor) surrounded by a stationary winding (stator).
A three-phase generator
Yasser. G. Hegazy
The generated voltages
Three - Phase Circuit
•
Two possible configurations:
Three-phase voltage sources: (a) Y-connected ; (b) Δ-connected
Yasser. G. Hegazy
Three - Phase Circuit
Terminology
•
Balanced phase voltages are equal in magnitude and
are out of phase with each other by 120°.
•
The phase sequence is the time order in which the
voltages pass through their respective maximum values.
•
A balanced load is one in which the phase impedances
are equal in magnitude and in phase
Yasser. G. Hegazy
Three - Phase Circuit
Three-Phase Connection
•
Four possible connections
1. Y-Y connection (Y-connected source with a
Y-connected load)
2. Y-Δ connection (Y-connected source with a
Δ-connected load)
3. Δ-Δ connection
4. Δ-Y connection
Yasser. G. Hegazy
Three - Phase Circuit
Y-Y connection
• A balanced Y-Y system is a three-phase system with a
balanced y-connected source and a balanced y-connected
load.
VL  3V p , where
V p  Van  Vbn  Vcn
VL  Vab  Vbc  Vca
P3 ph  3V p I p  3VL I L , where
VL  Vab  Vbc  Vca
I L  I p  I a  Ib  Ic
Yasser. G. Hegazy
Three - Phase Circuit
Example
Calculate the line currents in the three-wire Y-Y system shown
below:
Ans
I a  6.81  21.8 A
Ib  6.81  141.8 A
I c  6.8198.2 A
Yasser. G. Hegazy
Three - Phase Circuit
Y-Δ connection
• A balanced Y-Δ system is a three-phase system with a
balanced y-connected source and a balanced Δ-connected
load.
I L  3I p , where
I L  I a  Ib  Ic
I p  I AB  I BC  ICA
P3 ph  3V p I p  3VL I L
Yasser. G. Hegazy
Three - Phase Circuit
Example
A balanced abc-sequence Y-connected source with Van  10010
is connected to a Δ-connected load (8+j4) per phase.
Calculate the phase and line currents.
Solution
Using single-phase analysis,
Van
10010
Ia 

 33.54  16.57 A
Z / 3 2.98126.57
Other line currents are obtained using the abc phase
sequence
Yasser. G. Hegazy
Three - Phase Circuit
Δ -Δ connection
• A balanced Δ-Δ system is a three-phase system with a
balanced Δ -connected source and a balanced Δ -connected
load.
Yasser. G. Hegazy
Three - Phase Circuit
Example
A balanced Δ-connected load having an impedance 20j15  is connected to a Δ-connected positive-sequence
generator having ( Vab  3300 V). Calculate the phase
currents of the load and the line currents.
Ans:
The phase currents
I AB  13.236.87 A; I BC  13.2  81.13 A; I AB  13.2156.87 A
The line currents
I a  22.866.87 A; Ib  22.86  113.13 A; I c  22.86126.87 A
Yasser. G. Hegazy
Three - Phase Circuit
Δ -Y connection
• A balanced Δ-Y system is a three-phase system with a
balanced y-connected source and a balanced y-connected
load.
Yasser. G. Hegazy
Three - Phase Circuit
Example
A balanced Y-connected load with a phase impedance
40+j25  is supplied by a balanced, positive-sequence
Δ-connected source with a line voltage of 210V.
Calculate the phase currents. Use Vab as reference.
Answer
The phase currents
I AN  2.57  62 A;
I BN  2.57  178 A;
ICN  2.5758 A;
Yasser. G. Hegazy
Three - Phase Circuit
Unbalanced Three-Phase Systems
• An unbalanced system is due to unbalanced voltage sources or an
unbalanced load.
VAN
VBN
VCN
Ia 
, Ib 
, Ic 
,
ZA
ZB
ZC
I n  ( I a  I b  I c )
• To calculate power in an unbalanced three-phase system
requires that we find the power in each phase.
Yasser. G. Hegazy