ECE 4300/5300 ELECTRIC POWER SYSTEMS SPRING 2016 PROJECT #2
DUE: 02/22/2016
The Fig. 1 shows the equivalent circuit of a two-winding transformer with the prime denoting referred
quantities of winding 2 to winding 1.
i’2 N :N
i2
R’2
Ll1
L’l2
R1
i1
1
2
i1 + i’2
v1
e1
em
Lm1
e’2
v’2
v2
Fig. 1
The currents i1 and i’2 in terms of the flux linkages λ1, λ’2, and λm, and inductances xl1 and x’l2 are:
i1 =
λ1 − λm
(1)
i =
'
2
λ'2 − λm
(2)
xl' 2
 λ1 λ'2 
The mutual flux linkage is given λm = xM 
+ ' 
x
 l1 xl 2 
xl1
(3) where xM is the mutual inductance. The λ1
and λ’2 can be expressed by the integral equations (with base frequency ωb)

 λ1 − λm 
dt
x


l1


λ −λ
λ = ω v − ω R 

 x
λ1 = ωb v1 − ωb R1 
'
2
'
b 2
b
'
2
'
2
'
l2
m
(4)

dt

(5)
The rating of the transformer 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 Fig. 2 shows a step-up autotransformer winding connection, where the voltage on the high-voltage side is
the sum of the winding voltages, v1 and v2, and voltage on the low-voltage side of the step-up autotransformer is
iout
v1 .
v2
iin
vout
vin
v1
Fig. 2
1. The Fig. 1 is to be reconfigured to achieve the equivalent circuit of the step-up autotransformer shown in
Fig. 2. Obtained, show, and labeled the equivalent circuit of the step-up autotransformer similar to Fig. 1.
Modify and show new equations for (1) – (5).
2. Set up SIMULINK file transformer_model.mdl to conduct the following runs on the step-up
autotransformer using a sinusoidal input voltage of vin = V1m√2 sin(120πt + θ) V and vout = (V1m + V2m)√2
sin(120πt + θ) V:
(a) With the high voltage side terminals short-circuited, that is v’out = 0, and no initial core flux, energized
the step-up autotransformer at the following point of the wave of the voltage vin:
(i) The peak of the sinusoidal supply voltage, using a θ of π/2.
(ii) The zero of the sinusoidal supply voltage, using a θ of zero.
(iii)Plot the values of vin, i1n, λm, v’0ut, and i’out for 1(a) and 1(b): both SIMULINK scope and MATLAB
plots.
(b) Replace the short-circuit termination on the secondary terminal with a fixed impedance representing 1.5
KVA, 0.8 lagging power factor of loading at rated voltage and repeat (a)(i), (a)(ii), and (a)(iii).
Use MATLAB script file transformer_parameters.m to set up the parameters of the SIMULINK and plots.
Begin by trying the ode15s or the Adams/Gear numerical method with a minimum step size of 0.1 ms, a
maximum step size of 1 ms, and an error tolerance of 10-7.
Present all m-files, mdl-files, and output plots from both MATLAB and SIMULINK scope. Also include a snap
shot of the Configuration Parameters.