Single-phase transformers have two adjacent coils that are not physically connected. An alternating current in the primary coil produces a changing magnetic field that induces a voltage in the secondary coil. Transformers can be connected in various configurations including wye-wye, wye-delta, delta-wye, and delta-delta to step up or step down voltages depending on the ratio of turns in the secondary coil to the primary coil.

1. SINGLE
PHASE
TRANSFORMERS
1

2. 1. components:
-- 2 adjacent coils
-- coils not physically connected to each other
2

3. 2. operation:
a) AC in primary coil produces ∆ B
b) Secondary coil receives a ∆ in I & V
3
N
SN
SN
SN
SN
SN
S

4. N n
A
B
C
a
b
c
IA Ia
VAN
VAB
VCN
VBN Vbn
Van
Vcn
Vab
4
Wye / Wye connection

5. Load
Supply
Network
Transformer
Y-Y
Transformer LoadSupply Network
Xtr_s
Van Vload_an
VAN
Vnet_AN
Xnet
IA
Ia
N
n
A
a
5
Three-phase network supplies a
load through a transformer.
Xtr_s
Van
Vload_an
VAN
IA
IaVnet_AN
Xnet
Equivalent circuit of the wye-wye
Single-phase equivalent circuit for phase
A of the three-phase wye-wye
transformer system

6. Wye / Delta connection
6
A
B
C
N
VAN
VAB
VBN
VBC
VCN
IA
Iba
Icb
VCA
a
b
c
a
b
c
Ia
Ic
Ib
Vab
Vbc
Vca
Iac

7. Ia
Ib
Ic
Vab
Vbc
Vca
VCN
VBN
VAN
A
B
C
a
b
c
Icb
Iba
Iac
Transformer
AC
AC
AC
IC
IB
IA
VAN
VBN
VCN
Supply
Iab
Ibc
Ica
Load
VAB
VBC
VCA
Iac
Vca
Vbc
Vab
N
7
Wye-delta connected transformer

8. Xtr_s
Van Vs_an
VAN
IA Ia
Vp_AN
Xtr_p
Rtr_p
Rtr_s
Xm
Rc
Tspe
Y-∆
8
Single-phase equivalent circuit of a wye-delta transformer.

9. Delta / Wye connection
9
A
B
C
n
a
b
c
VBC
IaIA
Ib
Ic
VAB
VCA
Vca
Vab
Vbc
Van
Vbn
Vcn
IC
IB
ICA
IAB
IBC

10. Delta / Delta connection
10
A
B
C
a
b
c
VAB
Ia
Iba
Iac
IA
IAB
ICA
Vab

11.  ratio of the # of turns in the
secondary coil to the # of turns in
the primary coil
11
P
S
N
N
TR =
 numerical factor indicating relative change in
PD across a transformer
TR > 1 = V (step up)
TR < 1 = V (step down)

12.  ∆ in V is directly proportional to the ratio of
the # of turns in the secondary to the # of turns
in the primary
 Formula:
12
N
N
V
V
S
P
S
P
=
NS secondary coil turns
NP primary coil turns
VS secondary voltage
VP primary voltage
direct relationship

13.  Current in a transformer will be inversely
proportional to the TR of the transformer
 formula:
13
N
N
I
I
S
P
P
S
=
V
V
I
I
S
P
P
S
=
IP primary coil current
IS secondary coil current
 I vs. V = inverse relationship

14.  Based on TURNS RATIO
14
2. step-down
turns ratio < 1
VS < VP
IS > IP
1. step-up
turns ratio > 1
VS > VP
IS < IP

15. 1. air core
--inside area of coil is
empty
-- inefficient induction
15
2. open core
-- ferromagnetic
material inside coils
-- ↑B = ↑induction

16. 3. closed core
-- ferromagnetic ends
connected
-- ↑Β = ↑ induction
16
4. shell
-- lazy square eight
-- overlap of coils on
same ferromagnetic
core