Power Transformers Model Used for Inverters
Simulations
Adrian Taut, Ovidiu Pop, Serban Lungu
Applied Electronics Department, Technical University of Cluj-Napoca
Cluj-Napoca, Romania
adrian.taut@ael.utcluj.ro
Abstract — This paper intends to present a model of power
transformers used in simulation of power inverters.
Electromagnetic induction refers to the phenomenon by witch
electric current is generated in a closed circuit by the fluctuation
of current in another circuit placed next to it. For modeling of
power transformers, we implemented a Matlab software, based
on mathematical equations who describe the functionality of
power transformers. Also we compare the Matlab results with a
Pspice simulations results. Matlab program that we've
implemented enables the modification of input parameters of the
transformer and the choice of a circuit to be analyzed. Also the
Matlab model permits to view the waveforms of circuits in
transient or steady state regime.
hysteresis in a proportion to the size of the hysteresis. We
know that the conductive properties have more material. From
this cause it is necessary for analyzing load characteristics for
the induction heating systems.
T1
D1
C1
Vdc
+
Cr1
load
-
L
T2
D2
C2
Cr2
Keywords-inverters; power transformers; matlab; rectifiers;
I.
INTRODUCTION
All induction heating applied systems are developed using
electromagnetic induction. The basic principle of induction
heating is that AC current flowing through a circuit affects the
magnetic movement of a secondary circuit located near it. The
fluctuation of current inside the primary circuit provided the
answer as to how the mysterious current is generated in the
neighboring secondary circuit. The fundamental theory of
induction heating, however, is similar to that of a transformer.
Transformers find wide and important applications in RF
circuits. Historically, transformers were used in power systems
for voltage step-up and step-down [1]. I made this study about
variation of load because in many steps of this application we
can’t know the influence of the load to the electronic
equipment. For each time when we want to utilize the heating
systems we have a different load. We chose this method of
implementing a transformer, because it wants find a
transformer parameters to be used in the simulation of power
inverters used in induction heating.
II.
TEORETICAL MODEL
Induction heating is a compromised of three basic factors:
electromagnetic induction, the skin effect, and heat transfer in
load. When the AC current enters a coil, a magnetic field is
formed around the coil according to Ampere’s Law. An object
put into the magnetic field causes a change in the velocity of
the magnetic movement. If an object has conductive properties
like iron, additional heat energy is generated due to magnetic
Fig. 1. The base circuit for inducion heating system
The heating coil (L) and the load can be modeled like a
transformer with a single turn. The model can be simplified by
an equivalent inductance and resistance like we see in next
equations system.
Fig. 2. The base equivalent circuit
 Z1
 R1  jX 1 

 Z 2
 R2  jX 2 

 Z m
 jX m  jL12 


U 1  Z 1 I 1  Z m I 2 ( jX m I 1 )
 

0

Z
I

(
Z

Z
)
I
(

jX
I
)

m
1
2
S
2
m
2


U 1  R1 I 1  j ( X 1  X m ) I 1  jX m ( I 1  I 2 )
 

0  jX m ( I 1  I 2 )  R2 I 2  j ( X 2  X m ) I 2
Z e11'  [ R1  122 ( R2  RS )]  j[ X 1  122 ( X 2  X S )]  
The heating coil and the load can be represented by an
equivalent series inductance Leq, and resistance Req. The
quantity of heat generated in load will be determinate by the
resistively (ρ) and permeability (μ) of the conductive object
also the distance and the position were load is placed in
electromagnetic field [2].
 Re11'  R1   122 ( R2  RS )
 

 X e11'  X 1   122 ( X 2  X S )
For
Fig. 3. The result circuit from system equation 5

Z e11'
Xm
. The model can be
L2
simplified by an equivalent inductance and resistance like we
see in figure 4 [3].
2

Zm
Zm

I2 
I1 U1  Z1 
Z2 ZS
Z2 ZS

2

L2  R L   12 

 I 1  



Req  r   122  RL
X eq  X L1   122  X L 2

2
U
Zm
Xm

 1  Z1 
 Z1 
I1
Z2 ZS
Z2 ZS

Total impedance of secondary circuit:
Z 2t  Z 2  Z S  R2t  jX 2t 


Fig. 4. The result circuit from system 15
Impedance of secondary turn reflected in primary turns:

Z2 
'
Z
X
*
*

Z 2t  122 Z 2t  122 ( R2t  jX 2t ) 
Z2  ZS Z
2
m
2
m
2
2t

Where reflection coefficient is:

 122 
X m2
2
Z 2t

X m2

R22t  X 22t


Secondary resistance reflected in primary turns:

R2'   122 R2t   122 ( R2  RS )  0 
The most of the heat, generated by eddy currents in the
heating load is concentrated in a peripheral layer of skin depth
given by δ.
1



7
r f
4 10

2

Also, resistance RL can be determined by skin depth:

RL 




1
1
2
4 10 7
  r f 

Reactance of secondary turn reflected in primary turns:
III.

X 2'   122 ( X 2  X S ) 

RESULTS
We realize the simulations on two platforms. First was
realized on Spice and second was on Matlab. We implemented
a Matlab platform for simulation the power transformers used
in induction heating applied systems. The base circuit on which
we made the simulation was a half bridge inverter and it is
present in figure 1.
We start the simulation of power inverter without the load.
We was considerate the coil resistance 2.7 Ω and the
inductance 79 uH. The commutation frequency is in this case
20 kHz. To the input I considerate the voltage value 310 V
because we have ~220 in the power network.
1.0A
741mA
0A
-812mA
-1.0A
400us
425us
450us
475us
500us
-I(L2)
Time
40A
Fig. 9. Current in load with coupling factor 0.01
0A
The Matlab platform is based to the mathematical equations
who describe the functionality of power transformers. This
platform permits to change in each time the parameters of
transformers and the regime to view the waveforms. In the next
figure we presents this platform and the results obtain after a
Matlab platform simulation at 20 kHz and 40 kHz for a
coupling factor (k) to 0.01 like in Spice simulation or 0.7.
SEL>>
-40A
I(L1)
500V
0V
-500V
0s
40us
80us
120us
160us
200us
240us
V(L1:1)
Time
Fig. 5. Current and voltage across the work coil, Spice simulation.
400V
0V
-400V
400us
425us
450us
475us
500us
V(1,2)
Time
Fig. 6. Voltage in the heating coil without load
Fig. 10. Matlab Platform simulation. Curent in work coil, curent in load and
voltage to work coil at 20kHz and k=0.01
40A
32.3A
0A
-35.4A
-40A
400us
425us
450us
475us
500us
I(R3)
Time
Fig. 7. Curent in the heating coil without load
In case of load presence the circuit must modified; the
change consist in presence of the below circuit based on circuit
from figure 8.
K K1
K_Linear
COUPLING = 0.01
L2
R3
L2
L1
1
15uH
2.7R
R4
78.6uH
14.6uH
L3
0.34uH
R4
0.8m
Fig. 11. Matlab platform simulation to 40kHz and k=0.01
0.8m
R6
100meg
R5
100meg
0
0
1'
Fig. 8. The work coil and load circuit
As you can see in this figure the matlab platform is
implemented to a friendly interface for permits to change all
parameters. First panel refers to the input voltage, frequency,
and number of period for waveforms and the second panel
refers to the electrical parameters of transformers like: primary
and secondary inductance and resistance, and coupling factor.
Fig. 14. Matlab simulation on rectifiers at 100kHz
Fig. 12. Matlab platform simulation to 20kHz and k=0.7
IV.
CONCLUSION
In induction heating applications process we can observe
the multiple possibility of the load type. In the main circuit if
we make the change we obtain an RLC equivalent circuit. The
level of inductance and capacitance is a very important factor
because the heat energy is generated in the process of energy
exchange between the inductor and the capacitor in the
resonant circuit. Some factors which determine the value of
this inductance level are power consumption, AC current,
resonant frequency.
Fig.13. Matlab platform simulation to 40kHz and k=0.7
In order to prove the results obtain for power transformers
with this matlab platform, we implemented a program
developed allows the analysis of electrical circuits who using
these transformers. A study about rectifiers with and without
capacitive filter was making with this matlab platform. The
results obtained solving the mathematical equations for these
rectifiers are graphical represented.
This platform allows to introducing the transformer
parameters like inductance and resistance in the primary and
secondary terminals, voltage and frequency of primary, the
model of power transformers like in phase or anti-phase,
number of the displayed periods, etc. Also we can visualize the
waveforms in transient or steady-state regime. The advantage
of using this software is also an educational one, offering the
possibility to show to the students the equations which describe
the functioning of the power transformers or power rectifiers.
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[1]
[2]
[3]
[4]
[5]
[6]
Fig. 13. Matlab simulation on rectifier at 50 hHz
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for induction heating applications with load-adaptive PFM control
strategy", Applied Power Electronics Conference and Exposition, 1999.
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Page(s):575 - 581
Dawson, F.P. Jain, P, "Systems for induction heating and melting
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IEEE
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R Sheffer, Fundamentals of Power Electronics with Matlab, ISBN 158450-852-3
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