ECE 4300/5950 ELECTRIC POWER SYSTEMS SPRING 09 PROJECT #3
DUE: 03/09/09
The Fig. 1(a) shows the equivalent circuit of three separate two-winding transformers connected as a 3-phase
transformer bank with the prime denoting referred quantities of winding 2 to winding 1.
Eq. (4) Eq. (1)
Eq. (3)
Eq. (5) Eq. (2) i’2
λ
’
2
λ
m
L
l1
L
’l2
v
1
R
1
v
2
R
’2
v’2
N
N
n
N
L
m1 i1 + i’2
i1 i’2 i2
Fig. 1(a)
L
’l2
R
’2
A
N
L
m1
N
2
R
1
N
l
L
m1
L
l1
R
’2
L
’l2 C B
n
N
R
1
L
l1
v1
v’2
i1
Fig. 1(b)
λ
1
Each Two-winding Transformer has the Following Specifications and Equations:
The rating is 120/240 V, 1.5 KVA, 60 Hz and the circuit parameters are as follows:
R1 = 0.25 Ω; xl1 = 0.056 Ω; xm1 = 708.8 Ω; R’2 = 0.134 Ω; x’l2 = 0.056 Ω
The currents i1 and i’2 in terms of the flux linkages
λ
1,
λ
’2, and
λ
m, and inductances xl1 and x’l2 are:
1
1
1
l
m
x
i
λ
λ
−
= (1) '
2
'
2
'
2
l
m
x
i
λλ
−
= (2)
The mutual flux linkage is given
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛+= '
2
'
2
1
1
ll
Mm xx
x
λλ
λ
(3)
where xM is the mutual inductance. The flux linkages
λ
1 and
λ
’2 can be expressed by the integral equations (with
base frequency
ω
b).
∫⎭
⎬
⎫
⎩
⎨
⎧
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛−
−= dt
x
Rv
l
m
bb
1
1
111
λλ
ωωλ
(4)
∫⎭
⎬
⎫
⎩
⎨
⎧
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛−
−= dt
x
Rv
l
m
bb '
2
'
2
'
2
'
2
'
2
λλ
ωωλ
(5)
The Fig 1(b) shows a model flow diagram for the variables of the two-winding transformer.
1) Set up SIMULINK simulation file transformer_model.mdl for the model flow diagram given in Fig. 1(b)
using equations (1), (2), (3), (4), and (5). The inputs of the simulation of the two-winding transformer are
voltages and produces the winding currents as outputs. Save the file as a subsystem.
2) Set up a SIMULINK simulation file three_phase_transformer.mdl for the three-phase transformer shown in
Fig. 1(a). Note that each phase in Fig. 1(a) is a separate two-winding transformer. Therefore, the two-
