L21- Three Phase Excitation _ reprentation.pptx

1. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 1
Basic Electrical Technology
[ELE 1051]
Three Phase AC Circuits
L21 – Generation & Representation of three phase supply

2. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 2
Topics Covered
Generation of Three Phase Supply
Representation of Three Phase Excitation
Relationship between Phase and Line
Voltages

3. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 3
Generation of Three Phase
Courtesy :
www.ece.umn.edu
ERN EYN EBN

4. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 4
3 Phase Excitation (Phase
Voltages)
R
B
Y
N
ZS
ZS
ZS
ERN
EYN
EBN
Three Phase Source
𝑉𝑅𝑁 = 𝑉
𝑚 𝑆𝑖𝑛(𝜔𝑡)
VRN
VYN
VBN
𝑉𝑌𝑁 = 𝑉
𝑚 𝑆𝑖𝑛(𝜔𝑡 − 120°)
𝑉𝐵𝑁 = 𝑉
𝑚 𝑆𝑖𝑛(𝜔𝑡 − 240°)
Phase Voltages,
𝑉𝑅𝑁 + 𝑉𝑌𝑁 + 𝑉𝐵𝑁 = 0
Summing up the phase voltages,
VRN
VYN
VBN
120
120

5. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 5
3 Phase Excitation (Phase
Voltages)..
R
B
Y
N
ZS
ZS
ZS
ERN
EYN
EBN
Three Phase Source
VRN
VYN
VBN
R
B
Y
N
VRN
VYN
VBN
Three Phase Source

6. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 6
3 Phase Excitation (Line
Voltages)
𝑉𝑅𝑌 = 𝑉𝑅𝑁 − 𝑉𝑌𝑁
Line
Voltages,
VYB
VRY
VBR
-VYN
VRY
VRN
VYN
VBN
= 𝑉
𝑚 𝑆𝑖𝑛 𝜔𝑡 − 𝑉
𝑚 𝑆𝑖𝑛(𝜔𝑡 − 120°)
= √3 × 𝑉
𝑚 𝑆𝑖𝑛 𝜔𝑡 + 30
30
R
B
Y
N
VRN
VYN
VBN
Three Phase Source

7. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 7
3 Phase Excitation (Line
Voltages)…
𝑉𝑌𝐵 = 𝑉𝑌𝑁 − 𝑉𝐵𝑁
Similarly,
= 𝑉
𝑚 𝑆𝑖𝑛 𝜔𝑡 − 120 − 𝑉
𝑚 𝑆𝑖𝑛(𝜔𝑡 − 240°)
= √3 × 𝑉
𝑚 𝑆𝑖𝑛 𝜔𝑡 − 90
VRY
-VBN
VYB
VRN
VYN
VBN
-
VRN
VBR
= 𝑉𝑅𝑌 𝑆𝑖𝑛 𝜔𝑡 − 120
𝑉𝐵𝑅 = 𝑉𝐵𝑁 − 𝑉𝑅𝑁
= 𝑉𝑅𝑌 𝑆𝑖𝑛 𝜔𝑡 + 120
𝑉𝑅𝑌 + 𝑉𝑌𝐵 + 𝑉𝐵𝑅 = 0
Summing up the Line voltages,
In a Three Phase balanced Supply, the summation of Phase voltages and
summation of Line Voltages is zero.
120
120

8. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 8
Relation b/w Phase & Line
Voltages
𝑉𝑅𝑁 = 𝑉
𝑚 𝑆𝑖𝑛(𝜔𝑡)
𝑉𝑌𝑁 = 𝑉
𝑚 𝑆𝑖𝑛(𝜔𝑡 − 120°)
𝑉𝐵𝑁 = 𝑉
𝑚 𝑆𝑖𝑛(𝜔𝑡 − 240°)
Phase Voltages
Line Voltages
𝑉𝑅𝑌 = √3 × 𝑉
𝑚 𝑆𝑖𝑛 𝜔𝑡 + 30
𝑉𝑌𝐵 = √3 × 𝑉
𝑚 𝑆𝑖𝑛 𝜔𝑡 − 90
𝑉𝐵𝑅 = √3 × 𝑉
𝑚 𝑆𝑖𝑛 𝜔𝑡 + 150
|VLine|=3 |VPhase|
VRN VYN VBN
VRY VYB VBR
t

9. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 9
Phase Sequence
1. RYB 2. RBY
VRY
VYB
VRN
VYN
VBN
VBR
120
30
VRB
VBY
VRN
VBN
VYN
VYR
120
30

10. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 10
Exercise-1
Given the phase voltage VRN of a 3 phase balanced RYB
system as 240V, express the phase and line voltages
mathematically. Also sketch the phasor diagram.
Solution:
𝑉𝑅𝑁 = 240 × √2 × 𝑆𝑖𝑛(𝜔𝑡)
𝑉𝑌𝑁 = 240 × √2 × 𝑆𝑖𝑛(𝜔𝑡 − 120°)
𝑉𝐵𝑁 = 240 × √2 × 𝑆𝑖𝑛(𝜔𝑡 − 240°)
Phase Voltages:
𝑉𝑅𝑌 = √3 × 240 × √2 × 𝑆𝑖𝑛(𝜔𝑡 + 30°)
𝑉𝑌𝐵 = √3 × 240 × √2 × 𝑆𝑖𝑛(𝜔𝑡 − 90°)
𝑉𝐵𝑅 = √3 × 240 × √2 × 𝑆𝑖𝑛(𝜔𝑡 + 150°)
Line Voltages:
VRY
VYB
VRN
VYN
VBN
VBR
120
30

11. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 11
3 Phase 3 Wire & 4 Wire Supply
3 Phase 3 Wire Supply 3 Phase 4 Wire
Supply
R
B
Y
N
VRN
VYN
VBN
R
B
Y
N
VRN
VYN
VBN
N

12. Monday, March 11, 2024 Dept. of Electrical & Electronics Engg., MIT - Manipal 12
Summary
In a three phase balanced supply,
Summation of phase voltages = zero
Summation of Line voltages = zero
Line voltage is 3 x Phase Voltage
In an RYB sequence, VRY leads VRN by 30
Power transmission is generally through 3 phase 3 wire
network and distribution is through 3 phase 4 wire
network.