This document discusses delta-star and star-delta transformations of electrical networks. It provides derivations of the transformation formulas and explains that a delta network can be converted to an equivalent star network, and vice versa, using the formulas. It also discusses advantages like reduced starting current and disadvantages like reduced starting torque of star-delta connections. Additionally, it explains the relationships between line and phase voltages in star and delta networks.

1. GANDHINAGAR
INSTITUTE OF
TECHNOLOGY.

2. Branch : Electrical
Division : F
ACTIVE LEARNING
ASSIGMENT
Subject : Elements of Electrical
Engineering.

3. PREPARED BY
ENROLLMENT
NO.
Kavan Patel -140120109032
Mihir Thaker -140120109060
Pallav Shah -140120109053

4. • INTRODUCTION
• DELTA-STAR TRANSFORMATION
• STAR-DELTA TRANSFORMATION
• ADVANTAGES
• DISADVANTAGES
• Phase Voltage and Line Voltage

5. DE
NETWORK

6. INTRODUCINTRODUC
TIONTION

7. INTRODUCTION
• Three branches in an electrical network
can be connected in numbers of forms but
most common among them is either star
or delta form.
• In delta connection three branches are so
connected that they form a closed loop
that is they are mesh connected. As these
three branches are connected nose to tail
they forms an triangular closed loop, this
type of connection shown as delta
connection.

8. • On the other hand when either terminal
of three branches are connected to a
common point to form a Y like pattern is
known as star connection.
• But these star and delta connections can
be transformed from one form to other.
For simplifying complex network, it is
often required delta to star or star to delta
transformation.

9. • The replacement of delta or mesh by
equivalent star connection is known
as delta - star transformation.
• The two connections are equivalent
or identical to each other if the
impedance is measured between any
pair of lines.

10. Derivation (Δ-Y)
To convert a delta network to an equivalent star
network we need to derive a transformation
formula for equating the various resistors to each
other between the various terminals. Consider the
circuit below.

12. • Consider a delta system whose three corner points are A, B
and C as shown in the figure. Electrical resistance of the
branch between points A & B, B & C and C & A are R1, R2 and
R3 respectively. The resistance between the points A & B will
be
• Now, one star system is connected to these points A, B, and C
as shown in the figure. Three arms RA, RB and RC of the star
system are connected with A, B and C respectively. Now if we
measure the electrical resistance value between points A and
B, we will get
R = R + R

13. • Since the two systems are identical, resistance measured
between terminals A and B in both systems must be equal.
Similarly resistance between points B and C being equal in the
two system
And resistance between points C and A being equal in the two
system

14. Adding equations (I), (II) and (III) we get,
Subtracting equations (I), (II) and (III) from equation (IV) we get,

15. • The relation of delta - star transformation can be
expressed as follows
• The equivalent star resistance connected to a
given terminal is equal to the product of the two
delta resistances connected to the same terminal
divided by the sum of the delta connected
resistances.
• If the delta connected system has same resistance
R at its three sides then equivalent star resistance
r will be:

16. Star-Delta
Network

17. STAR - DELTA
TRANSFORMATION
• For star - delta transformation we just
multiply equations (v), (VI) & (VI), (VII) & (VII),
(V) that is by doing (v)X(VI) + (VI)X(VII) +
(VII)X(V) we get

18. Now dividing equation (VIII) by equations (V),
(VI) and equations (VII) separately we get,

19. •The neutral point allows both types of loads (single phase or
three phases) to be met.
•a ) Star-Delta starters are widely used due to their relatively
low price.
b ) The components require very little space.
c ) The starting current is reduced to approximately one-third.

20. Disadvantages of Star-Delta Connection
•If secondary of this transformer should be paralleled with
secondary of another transformer without phase shift, there
would be a problem
a ) The supply voltage must be the same as the rated motor
voltage for Delta connection.
b ) Because the starting current is reduced to
approximately one-third of the rated current, the starting
torque is also reduced to one-third.

21. Relation ship between
line voltage and phase
voltage in staR
connected system.

22. In that figure WhereIn that figure Where
VRY=VYB =VBR =Line voltages =VLVRY=VYB =VBR =Line voltages =VL
VRN=VYN =VBN =Phase voltages =VphVRN=VYN =VBN =Phase voltages =Vph
IRN=IYN =IBN =Iph = Phase currentsIRN=IYN =IBN =Iph = Phase currents
IR=IY=IB=IL = Line currentsIR=IY=IB=IL = Line currents
In a star connected system Iph=IL In a star connected system Iph=IL
Applying KVL between the lines R andYApplying KVL between the lines R andY
VRY –VRN +VYN = 0VRY –VRN +VYN = 0
VRY =VRN -VYNVRY =VRN -VYN
Applying KVL between the linesY and BApplying KVL between the linesY and B
VYB =VYN -VBNVYB =VYN -VBN
Similarly applying KVL between the lines B and RSimilarly applying KVL between the lines B and R
VBR –VBN +VRN = 0VBR –VBN +VRN = 0
VBR =VBN -VRNVBR =VBN -VRN

23. Similarly
VYB =√3 Vph
VBR =√3 Vph
VYB = VBR = VL
VL= √3 Vph
VL
Vph = -----------
√3

24. Relation ship betweenRelation ship between
line voltage andline voltage and
phase voltagephase voltage in “in “delta”delta”
connected system.connected system.
VRY = VR'Y'
VYB = VY'B'
V BR = VB'R'
Line voltage = phase voltage
VL= Vph
VRY= VYB= VBR = VL
VY'B'= VB'R'= VR'Y'= Vph
VL= Vph
VR'Y‘ is the voltage across the phase
VRY is the voltage between line R and Y

25. Assuming a RYB phase sequence, then three line voltages are VRY, VYB and VBR.
Applying KCL at nodes R'Y'and B'
At node R'
IR + IB'R' = IR'Y'
IR = IR'Y' - IB'R'
At node Y'
IY + IR'Y' = IY'B'
IY = IY'B' - IR'Y'
At node B'
IB + IY'B' = IB'R'
IB = IB'R' - IY'B'

26. vectoR diagRam
The three phase
voltages of delta
connected load are
VR'Y', VY'B',VB'R'.
Taking VR'Y' as the
reference voltage, and
also we know that,
VR'Y' = VRY
VY'B'= VYB
VB'R' = VBR

28. THANK
YOU