E315 Electric Power System I
Lecture 4: Three-Phase Systems
Isaiah Koldai(MPhil)
Lecturer
1.Three-phase System Overview
 Generators can generate three phase power either in Wye (Y) or Delta (Δ)
 A generator consists of three coils placed 120 apart.
 The voltage generated are equal in magnitude but out of phase by 120
2. Three-Phase Configurations
Delta (Δ) Configuration
Wye (Y) or Star Configuration
a
a
a
_
+
_
Wye Connected
Source
V0
n
V-240
+
c
_
a
_
+
_
V-120
+
b
b
Delta
Source
+
b
c
_
b
+
c
Three Phase Source Configuration
c
Three Phase Lines
Source-Load Connections
Source
Load
Connection
Wye
Wye
Y-Y
Wye
Delta
Y-
Delta
Delta
- 
Delta
Wye
-Y
3. Three Phase Waveforms
Phase 1 leads phase 2 by 120.
Phase 2 leads phase 3 by 120.
Phase 3 lags phase 1 by 240.
4. Equations for Star and Delta Connections
DELTA (Δ) CONNECTION
STAR (Y) CONNECTION
4.1 STAR (Y) Source
Line voltage VL= voltage between lines
Phase voltage Vph= voltage between a line and neutral (n)
In a BALANCED WYE
Line Voltage: VL=√3Vph
Line current: IL = Iph
4.2 Delta (Δ) Source
a
_
+
+
_
b
c
_
a
Vab = | Vab |  0°
Delta
Source
Vbc = Vab  -120°
b
Vca = Vab  -240°
In a BALANCED DELTA
+
c
Line Voltage: VL=Vph
Line current: IL = √3 Iph
Note that there is no connection for a common neutral point in Delta configuration.
5. Vector Analysis of Voltage
Students to prove this
Vab VanVbn
|Vp | 0|Vp | 120
|Vp | 1(cos120 jsin120)
|V |p |Vp | 1  j 3
2
2
 3|Vp | 30
Vbc  3|Vp | 90
Vca  3|Vp | 210
VL  3|Vp | LineVoltage
6. Instantaneous Power
7.Delta-to-Wye Transformation
8.Real and Reactive Power
Tutorial on pf and Capacitance Calculations for a Three-phase System
Per phase
Tutorial Questions
Do Examples 2.7 and 2.8 of the Textbook by Saadat.
END OF LECTURE