Rev. Roum. Sci. Techn.– Électrotechn. et Énerg. Vol. 64, 3, pp. 223–228, Bucarest, 2019

ANALYSIS OF A FULL-BRIDGE DIRECT AC-AC BOOST CONVERTER BASED DOMESTIC INDUCTION HEATER

AVIJIT CHAKRABORTY1, ARIJIT CHAKRABARTI2, PRADIP KUMAR SADHU2

Key words: , Insulated gate bipolar transistor, Switching loss, Duty cycle, Zero-voltage switching (ZVS). Induction heating is now gradually emerging as a very reliable technology for providing faster heating in domestic and various industrial applications. It finds profound acceptability in the appliances like domestic induction cookers regarding its advantages of very fast heating, efficiency, accurate power and temperature control. Any induction heating system requires three major components, a high power converter, resonant tank circuit and control circuit respectively. Recently, new research trends in the field of domestic induction heating pursue the design and implementation of new bridgeless topologies to make efficient and cost-effective domestic induction heaters. In this paper, a highly efficient direct ac-ac boost converter based induction heater is proposed employing a full-bridge series resonant inverter (FB-SRI) with insulated gate bipolar transistor (IGBT) as the power electronic switch. Power requirement of the induction heater is continuously regulated using a closed loop control system. The proposed inverter incorporates a voltage boost control technique using only two diodes for rectification of the main supply voltage. After maintaining proper sequence of firing the IGBTs, the converter can operate with zero-voltage switching (ZVS) during both switch-on and switch-off conditions. The performance of the proposed induction heating system is later compared with a conventional full-bridge (FB) series resonant inverter (SRI) based induction heater. The entire analysis is simulated using PSIM software environment.

generates heat energy inside the work-piece while it 1. INTRODUCTION penetrated by the . For low power Recently, induction-heating process has gained a lot of applications single switch resonant inverters are used, while popularity in various fields for its faster heating technique for medium and high power applications half-bridge and [1]. Domestic induction heater is regarded as one of the full-bridge resonant inverters are used. Figure 1 shows the most common appliances of induction heating system. general block diagram of different components of a Induction heating technology is gaining popularity because domestic induction heating system. In this paper, a boost of its various attracting features like fast heating, pollution converter based full-bridge direct ac-ac domestic induction free, reliable, cost-effective and efficient operation. heating system is proposed and its performance is explained Recently, new research trends in the field of induction mathematically and also finally its performance is heating is approaching towards the innovation and compared with conventional full-bridge resonant inverter developments of various types of direct ac-ac induction based induction heater. The proposed domestic induction heating systems [2, 3]. Such induction heating system uses heating system is shown in Fig. 2. This converter has the reduced number of power semiconductor switching devices ability to supply more power compared to half bridge and other circuit components compared to conventional topology. It reduces voltage stress and current stress on the induction heating system. Moreover, such induction heating switches and thereby reduces both switching and systems can operate with a wide range of operating conduction losses. between 50 and 180 kHz. In most of the cases, single switch quasi-resonant inverter topology is used for low power applications [4], for medium power applications, half-bridge inverter topology is extensively used [5], whereas, for some medium and high power applications single or multi-output full-bridge inverter topology is Fig. 1 – Block diagram of different components of a conventional induction comprehensively used [6, 7]. Recently, to achieve very heater. accurate power control in different domestic induction heating systems, different intelligent based control techniques are successfully implemented [8, 9]. Any classical conventional induction heating systems consists of two major components, a full-bridge uncontrolled system along with a resonant inverter. The full-bridge uncontrolled rectifier initially converts utility frequency ac voltage to dc voltage. A small dc link is used to make the input power factor close to unity. This high ripple dc link voltage is fed to the input of the resonant inverter producing very high frequency current passing through the working coil. This high frequency Fig. 2 – Direct ac-ac boost converter based domestic induction heater. current generates high frequency magnetic field and

1Research Scholar in Electrical Engineering Department, Indian Institute of Technology (Indian School of Mines), Dhanbad - 826004, India, E-mail: [email protected] 2Electrical Engineering Department, Indian Institute of Technology (Indian School of Mines), Dhanbad - 826004, India. 224 Full-bridge ac-ac boost converter based induction heater 2

2. PRINCIPLE OF OPEARTION OF DIRECT AC-AC FULL-BRIDGE SERIES RESONANT INVERTER (FB-SRI) The boost type ac-ac converter based induction heating system is shown in Fig. 2. It consists of four IGBTs (Q1- Q4) as main power semi-conductor switches. IGBTs are used instead of due to low on state voltage drop, less conduction loss and better power handling capability. It also consists of a dc link capacitor Cb , an input source Ls , two diodes DH and DL, a resonant capacitor Fig. 4 – Main Waveforms regarding the boost operation of the proposed AC- C and a series R-L combination as the resonant load. The AC boost converter based domestic induction heating system. converter is fed from an ac source Vs at its input. The input ac supply is initially rectified by the diode bridge rectifier voltageVs . In this mode, the output voltage Vo and current consists of two diodes DH and DL and this rectified voltage I are negative. This mode is shown in Fig. 3. is applied to the input of the full-bridge inverter. In the o Mode III: proposed system voltage boost operation is performed by This mode starts when the negative half cycle begins and input inductor Ls and dc link capacitor Cb . Rs is the the input ac voltage Vs is rectified by the diode DL and the internal resistance of the source inductor L . Figure 3 is s switches Q2 and Q3 are in the on condition. In this mode showing different modes of operations. the input inductor L receives energy from the ac source Mode I: s through the diode DL. At the same time, already charged dc This mode occurs for the positive half cycle ofV , when s link capacitor C also discharges through the induction the switches Q1 and Q4 are turned on. During this, the ac b heating RL load as shown in Fig. 3. The load current is voltage V is first rectified by the diode DH and the input s assumed to be flowing in the negative direction so that the source inductor L is energized from this rectified voltage. s output voltageVo is also considered to be negative. At the Besides, already charged dc link capacitor Cb also end of this mode Q2 and Q3 are turned off. discharges through the induction heating RL load. The load Mode IV: current is assumed to be flowing in the positive direction This mode also occurs during the negative half cycle of and as such the output voltageVo is also considered to be the ac source voltage Vs , when the switch Q4 is once again positive. At the end of this mode, Q1 and Q4 are turned off. turned on. During this mode the inductor Ls reverses its polarity immediately after Q2 and Q3 are turned off and the Mode II: energy stored in it is exchanged to the dc link capacitor C This mode also occurs during the positive half cycle of b and charges it in the same direction as before and like mode V , when the switch Q3 is turned on. During this, the s 1, the output voltage across the resonant load once again inductor L reverses its polarity immediately after Q1 and s becomes greater than the source voltageVs due to the Q4 are turned off and the energy stored in it is exchanged to voltage boost operation after addition of the voltage of the dc link capacitor C and charges it and moreover, the b Ls with the source voltage Vs . In this mode, the output output voltage across the resonant load becomes greater voltage Vo and current Io are positive as shown in Fig. 3. than the source voltageVs due to the voltage boost operation after addition of the voltage of Ls with the source 3. VOLTAGE AND CURRENT STRESSES OF THE SWITCHES The stress voltage appears across each switching device (Q1–Q4) during turning off conditions as represented by the following equations VQ1stress  2Vs (1a)

VQ2stress  2Vs (1b)

2Vs V   (1c) Q3stress 1 d

Fig. 3 – Different modes of operation of the proposed direct ac-ac induction 2Vs heater. V  (1d) Q4stress 1 d

3 Avijit Chakraborty, Arijit Chakrabarti, Pradip Kumar Sadhu 225

On the other hand, current stresses through each I s I  . (7) switching device (Q1–Q4) during turning off conditions can s 2 be represented by the following equations If the input power factor of the proposed induction i  i Q1stress Q4stress heating system is unity, then the input power Pin can be  I  V V (2a) expressed as follows   I  s   s c edTs sin dT s r s P  V I .  2  r L in s s (8) Now, for CCM, as from equation (7), the desired condition can be expressed as iQ2stress  iQ3stress Pin Vs  I  V V (2b)  dTs , (9)   I  s   s c1 edTs sin dT V 2L s 2  L r s s s   r which can be further expressed as where 2 1 Vs Pin  dTs . (10)  2  2 2L R  1 R  s   , r   ,Vc andVc1 be the resonant 2L  LC 4L2  From the above equation, it is clear that, for a given   supply voltage, there is a certain interlinks among the input capacitor voltages at t  dT and t  T respectively. s s source Ls and modulation parameters (Ts , d ).

4. MATHEMATICAL ANALYSIS OF THE BOOST 5. MATHEMATICAL ANALYSIS OF THE FULL- CONVERTER BRIDGE SERIES RESONANT INVERTER (FB-SRI) The proposed direct ac-ac converter based induction In this proposed work, the boost converter output voltage heater consists of two major circuits, a boost converter and is fed to the input of the full-bridge series resonant inverter. a full-bridge series resonant inverter (FB-SRI). From, the Fourier analysis method, the output power can It is assumed that in the boost converter circuit I s is the be expressed as average steady-state value of the input source current, d is 1 2  2  V the duty cycle, T is the switching period and f is the V o,n s s P  R on,rms  R 2 ob  2  2 switching frequency. The system is assumed to be linear n0 Zn n0 Zn and the rectified source current is assumed to be pure dc.  , (11) R V 2 All the are loss-less. The input power factor is  on unity.  2 2 n0 2  1  The main waveforms of the dc-dc boost converter circuit R  2f nL    s 2f nC  are depicted in Fig. 4. Here, continuous current mode  s  (CCM) is assumed to minimize the current ripple. In steady where n is the harmonic number, Z is total impedance of the state, the average voltage across the inductor is zero and RLC series resonant tank, Vo is the output voltage of the thus FB-SRI. Moreover, the peak output voltage can be expressed as Vs dTs  Vs  Vb 1  d Ts  0 . (3) follows For a boost converter the following equation is Vb 2 2 representing the voltage conversion ratio V  a  b . (12) on n n n Vb 1  . (4) The Fourier series coefficients are Vs 1  d a  sin2nd , b 1 cos 2nd . (13) The input source inductor current ripple can be expressed n n as follows By using the above equations, the output voltage can be expressed as follows V I  I  I  s dT , (5)  2 s s2 s1 s 1 cos2nd  RVb Ls P  . ob  n 2 n0   1  where I s1 and I s2 are the minimum and maximum source 2   (14) R  2fsnL   inductor current during each switching period.  2fsnC  The expression of I s using this inductor current ripple can be expressed as follows The output power also can be finally expressed as follows (using the boost converter voltage ratio) Pob  Is  Is i t  I   t, 0  t  dT  2 s   s  s , (6a) 1 cos2nd V  2  dTs  s .  n  2  (15) n0  1  2  2   1 d R 1 Q n    Is  Is    i t   I    t  dT ,dT  t  T   n   s s 2 1 d T s s s (6b)   s The normalized output power can be expressed as To achieve the continuous current conduction mode (CCM), I s1  0 and I s1  0 which is possible only if 226 Full-bridge ac-ac boost converter based induction heater 4

P R 6. EFFICIENCY ANALYSIS P  ob obnormal 2 Vs Mathematically the efficiency  of the proposed converter can be expressed as the ratio of the output power  1 cos2nd 1  . (16) to the input power. The major losses are contributed by the  n  2  n0  1  conduction losses P and switching losses 1 d 2 1 Q2    onloss   n    P respectively.   n   switch Conduction losses: in this proposed work, the conduction The expression for the resonant frequency and the quality losses in the power electronic devices like IGBT and the factor can be written as follows power diode is only considered because they are playing the most important role. In order to determine the conduction 1 fo  , (17) losses, both average and rms current have to be calculated 2 LC for each such element. Conduction losses in the switching devices (IGBT) can L be expressed as Q  2f . o R (18) Ponloss

For any conventional pulse width modulation (PWM) 2 2 (25)  Ron I1,4rms  I2,3rms Von I1,4avg  I2,3avg , controlled full-bridge series resonant inverter (FB-SRI), the output power can be expressed as where, Ron is the conduction resistance of each switch and Von is the ON state voltage drop across each switch. 1 2  2  V Von,rms on According to the already explained converter operation, P  R  R 2 oa  2  2 the current through each IGBT is the sum of input current n0 Zn n0 Zn , (19) is and output current (load current) io resulting  R V 2  on  2 2 2 2 I1,4rms  I2,3rms n0 2  1  R  2fsnL   dT T  2 f nC  ss   s  1 2 1 2 (26)  io t  is t dt   io t  is t dt. where Ts Ts 0 dTs Vs 2 2 V  a  b . (20) on n n n After simplification it can be expressed as The Fourier series coefficients are 2 2 I1,4rms  I2,3rms an  sin2nd , bn 1 cos 2nd . (21) Ts 1 2 From equations (19), (20) and (21), the output power of  i t  i t dt T  o s the conventional pulse width modulation (PWM) controlled s 0 (27) full-bridge series resonant inverter (FB-SRI) can be Ts 2 2 2 obtained and represented by the following equation  Iorms  Isrms  is t io t dt,  2 Ts  1 cos2nd Vs 0 Poa  .   2  n0  1  (22) but nR1 Q2      n  2 Po   n   Iorms  .   R (28) To get maximum output power considering the Now, using equations 6(a) and 6(b), the input current can fundamental component only, the following condition must be expressed as follows be satisfied 2d   , (23) Ts 2 2 1 2 2 Is so that the output power becomes maximum for the duty Isrms  is t dt  Is  . (29) Ts  12 cycle d  0.5 . Besides, unlike the conventional one, this 0 ac-ac induction heater provides increasing output power On the other hand, the third term with the integration of with the increasing duty cycle d due to boosted supply equation (27) can be neglected by assuming a small ripple voltage Vb of this inverter. in the input current such as From, equations (15) and (22), the ratio of the output Ts Ts power of the proposed converter and the conventional i t i t dt  I i t dt  0 . (30) converter can be expressed as  s o s  o 0 0 Pob 1  . 2 (24) Hence, finally equation (27) can be expressed as Poa 1  d  2 2 2 Po 2 I s For the duty cycle d  0.5 , this ratio becomes four i.e. I  I   I  . (31) 1,4rms 2,3rms R s 12 with this duty cycle; the proposed inverter output is four times greater than that of FB-SRI. The average current summation can be expressed as 5 Avijit Chakraborty, Arijit Chakrabarti, Pradip Kumar Sadhu 227

I1,4avg  I2,3avg  is given as follows E  I  f V dTss T off pk sw b 1 1 (32) Psw  , (43) io t  is t dt   io t  is t dt.   I n Vn Ts Ts 0 dTs where, I n and Vn are the normalized current and voltage of

Now, if the output power depends only on the load the IGBT during the switching conditions and I pk is the current and with the presence of capacitor C assuming zero peak IGBT current. average load current, the following equations can be expressed 7. SIMULATION RESULTS T dT 1 s 1 s P  V i t dt  i t dt . (33) In this paper, PSIM simulation is carried out on the o T  b o T  o proposed direct ac-ac inverter based induction heater. s 0 s 0 Table1 shows the selected simulation parameters. Figures 5 This implies and 6 are presenting the output voltage, output current, Po  1  d I s . (34) source current and dc link capacitor voltage waveforms Vb with the duty cycles d  0.5 and d  0.8 respectively. Also, Figure 5 shows all these waveforms indicating stable results TdTss as the duty cycle d  0.5 provides stable operation but the 1 1 I  0  i t dt  0  i t dt waveforms that are presenting in Fig. 6 with duty cycle o T o T o s 00s d  0.8 that indicates unstable results and introduce (35) Ts harmonics at the input source current. The best result can be 1   io t dt  1 d Is , obtained for d  0.7 with voltage conversion Ts  dTs ratio n  3.4 to justify the results in Table 2. Table2 which results shows the variations of the output powers of the proposed

I1,4avg  I2,3avg  21d Is  2d 1 Is  Is . (36) direct ac-ac inverter based induction heater and the classical full-bridge series resonant inverter based induction heater As such, the switching loss of each IGBT can be with respect to the duty cycle d . From this table, it can be expressed as follows seen that the output power of the proposed direct ac-ac 2  P 2 I  inverter increases continuously with the increase of duty P  R  o  I  s  V I . (37) onloss on s  on s cycle but it is exceptionally different in classical FB-SRI,  R 12  where the maximum output power is obtained at the duty For high efficiency P  P and low input current o in cycle d  0.5 . Table 2 also shows the increase in the ripple I s  I s  0 , the above equation can be further voltage conversion ratio n with the increase in the duty expressed as follows, which is the final expression of the cycle d . Table 3 gives the evidence that the total harmonic IGBT conduction loss distortion (THD) of the input source current with the 2  P P  P variation of the source inductance Ls is less in the P  R  in  in  V in . onloss on 2 on (38) proposed direct ac-ac inverter in comparison to that of the  R V  Vs  s  classical FB-SRI. Moreover, the efficiency  of the On the other hand, conduction losses in each reverse proposed induction heater also varies a little with respect to conduction diode can be expressed as the variation of the output power as shown in Table 4. 2 Ponloss _ diode  Ron _ diode I srms  Von _ diode I s . (39) Table 5 is depicting the variations of efficiency η along Replacing the rms input current with the switching energy losses Eoff 1,4 and P onloss _ diode Eoff 2,3 respectively with respect to the variation of  I 2  (40) switching frequency.  R  I 2  s  V I . on _ diode  s  on _ diode s  12  Once again, neglecting the input ripple current, then the final expression of diode conduction loss can be expressed by the following equation 2  P  P  in  in Ponloss_ diode  Ron _ diode   Von _ diode . (41)  Vs  Vs Switching losses: each IGBT will undergo very fast switching operations, which causes switching losses. The switching losses Psw_loss depend on the switching frequency and the turn-off losses energy Eoff and it can be expressed by the following equation P  f E  E . (42) sw sw off1,4 off 2,3 Fig. 5 – Output voltage, output current, source current and dc link The normalized expression of IGBT total switching loss capacitor voltage waveforms for d = 0.5 using PSIM simulation. 228 Full-bridge ac-ac boost converter based induction heater 6

Table 5 Variation of efficiency (η) with respect to the variations of switching energy losses (for IGBTs Q1–Q4) along with switching frequency

Efficiency η [%] Eoff 1,4 [mJ] Eoff 2,3 [mJ] fsw [kHz] 98.8 19.23 18.46 140 98.7 19.32 18.49 141.5 98.6 19.35 18.51 142.3 98.5 19.37 18.52 143.8 98.4 19.38 18.53 144.1 98.3 19.40 18.54 145.4 98.2 19.42 18.56 146.5

8. CONCLUSIONS In this paper, performance analysis has been carried out of a direct ac-ac boost converter fitted full-bridge resonant inverter based domestic induction heater. The proposed

Fig. 6 – Output voltage, output current, source current and dc link induction heater features high voltage gain with reduced capacitor voltage waveforms for d = 0.8 using PSIM simulation. component count with accurate output power control over a wide range. The proposed induction heater is undergoing

Table 1 ZVS switching operations resulting in an efficient Simulation parameters operation. The output power is controlled with a suitable closed loop control system accompanied by precise control Parameters Values of voltage conversion ratio. This paper also includes an Vs 230 V analytical model of the proposed system and detailed R 90 Ω analysis of steady state behaviour of the boost circuit and L 155 µH C 8.56 nF the inverter circuit. This paper gives a comparison between

Cb 500 pF the proposed induction heater with the classical full-bridge fs 140 kHz series resonant inverter based induction heater regarding Ls 500 µH output power control at different duty cycles as well. The Rs 0.15 Ω proposed direct ac-ac induction heater also exhibits higher efficiency over a wider output power range. Table 2 Output power and voltage conversion ratio with respect to duty cycle Received on March 12, 2018 Output power of Output power Voltage Duty cycle the proposed ac-ac of classical FB- conversion (d) REFERENCES inverter (watts) SRI (watts) ratio (n) 0.1 73.2 68 1.2 1. O. Lucía, P. Maussion, E. J. Dede, J. M. Burdío, Induction Heating 0.2 349 277 1.4 Technology and Its Applications: Past Developments, Current 0.3 873 556 1.8 Technology,and Future Challenges, IEEE transactions on Industrial electronics, 61, 5, (2014). 0.4 1991 624 1.9 2. H. Sarnago, O. Lucia, A. Mediano, J. M. Burdio, Direct AC-AC 0.5 2794 695 2.1 Resonant Boost Converter for Efficient Domestic Induction 0.6 4126 630 2.8 Heating Applications, IEEE Transactions on Power Electronics, 0.7 4892 557 3.4 29, 3, pp. 1128–1139 (2014). 0.8 6295 281 5.1 3. T. Mishima, S. Sakamato, C. Ide, ZVS Phase Shift PWM-Controlled 0.9 6991 73 10.2 Single-Stage Boost Full-Bridge AC-AC Converter for High Frequency Induction Heating Applications, IEEE Transactions on Industrial Electronics, 64, 3, pp. 2054–2061 (2017). Table 3 4. A. Chakraborty, P. K. Sadhu, K. Bhaumik, P. Pal, N. Pal, Behaviour of Variation of the total harmonics distortion (THD) of the input current with a High Frequency Parallel Quasi Resonant Inverter Fitted respect to the input inductor Induction Heater with Different Switching Frequencies, Input inductor THD of input current of THD of input current of International Journal of Electrical and Computer Engineering, 6, 2, (Ls) [µH] the proposed inverter classical FB-SRI pp. 447–457 (2016). 100 16.62 23.76 5. Y. S. Kwon, S. B. Yoo, D. S. Hyun, Half Bridge series resonant 200 15.20 21.42 inverter for induction heating applications with load adaptive 300 13.48 18.99 PFM control strategy, Proc. IEEE Power Electronics Conference 400 12.79 17.96 Andex position (APEC), l, pp. 575–581 (1999). 500 12.28 17.28 6. A. Chakraborty, D. Roy, T. K. Nag, P. K. Sadhu, N. Pal, Open Loop Power Control of A Two-Output Induction Heater, Rev. Roum. 600 11.88 16.77 Sci. Techn. – Électrotechn. et Énerg., 62, 1, pp. 48–54 (2017).

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