[ieee 2010 ieee 16th international symposium for design and technology in electronic packaging...

2010 IEEE 16th International Symposium for Design and Technology in Electronic Packaging (SIITME)

978-1-4244-8124-8/10/$26.00 ©2010 IEEE 249 23-26 Sep 2010, Pitesti, Romania

Power Transformers Model Used for Inverters Simulations

Adrian Taut, Ovidiu Pop, Serban Lungu Applied Electronics Department, Technical University of Cluj-Napoca

Cluj-Napoca, Romania [email protected]

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.

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. THEORETICAL 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

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.

Figure 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.

Figure 2. The base equivalent circuit.

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�� 222 jXRZ ��

�� 12LjjXZ mm ��

+

-

C1

C2

T1

T2 L

loadVdc

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Cr1

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)()(0)(

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mSm

mm��

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)()(0)()(

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mm

mm� ��

Figure 3. The result circuit from system equation 5.

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Total impedance of secondary circuit:

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Impedance of secondary turn reflected in primary turns:

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*2

212

*22

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2

2'2 tttt

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Where reflection coefficient is:

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Secondary resistance reflected in primary turns:

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Reactance of secondary turn reflected in primary turns:

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'2 SXXX ��

)]([)]([ 221212

2121'11 SSe XXXjRRRZ ��

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].

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��

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)()(

22121'11

22121'11

Se

Se

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For2

122 LXmRL L !"## � . The model can be

simplified by an equivalent inductance and resistance like we see in figure 4 [3].

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Leq

XXX

RrR

$��

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Figure 4. The result circuit from system 15.

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.

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&'

( $� �721041

� ��

Also, resistance RL can be determined by skin depth:

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'(& $��

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III. 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.

Figure 5. Current and voltage across the work coil, Spice simulation.

Figure 6. Voltage in the heating coil without load.

Figure 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.

Figure 8. The work coil and load circuit.

Figure 9. Current in load with coupling factor 0.01.

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.

Figure 10. Matlab Platform simulation. Curent in work coil, curent in load and voltage to work coil at 20kHz and k=0.01.

Figure 11. Matlab platform simulation to 40kHz and k=0.01.

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

L2

15uH

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0

R4

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COUPLING = 0.01K_Linear

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L1

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R3

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R40.8m

1



refers to the electrical parameters of transformers like: primary and secondary inductance and resistance, and coupling factor.



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.

Figure 14. Matlab simulation on rectifier at 50 hHz.

Figure 15. Matlab simulation on rectifiers at 100kHz.

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.

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.

REFERENCES

[1] Ali M Niknejad, Electromagnetics for High-Speed Analog and digital Comunications Circuits, Cambridge University Press 2007, ISBN 978-0-521-85350-7

[2] R Y.S. Kwon, S.B. Yoo, D.S.Hyun, "Half-bridge series resonant inverter for induction heating applications with load-adaptive PFM control strategy", Applied Power Electronics Conference and Exposition, 1999. APEC apos;99. Fourteenth Annual Volume 1, Issue, 14-18 Mar 1999 Page(s):575 - 581

[3] Dawson, F.P. Jain, P, "Systems for induction heating and melting applications: a comparison of load commutated inverter", Power Electronics Specialists Conference, 1990. PESC '90 Record, 21st Annual IEEE

[4] O. Pop, “Influence of power consumption over the input current harmonics pollution for a half-bridge power inverters”,ISSE 2008, pp.312, 2008

[5] R Sheffer, Fundamentals of Power Electronics with Matlab, ISBN 1-58450-852-3

[6] “Induction Heating Systems Topology Review”, AN9012 Fairchield Semiconductors.

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