Efficiency Considerations of LLC Resonant Converter for Induction Heating Application

Induction heating is an electro thermal method which involves the fields of electromagnetism and heat transfer. It is one of the most important heating methods of an electrically conductive material which can be a ferrous or non-ferrous metal without direct contact with it [1, 2].

Compared to the other heating techniques such as resistance heating; Induction heating is considered as the more efficient heating technique; Because the case of induction heating process heat is directly generated within the workpiece itself, unlike the resistance heating, the heating element will heat up first and then through the process of conduction, the heat energy will be transferred to the workpiece, which will take longer and eventually lead to more heat loss.

Induction heating process is widely used in industrial applications such as preheating furnaces, heat treatments, welding, brazing, melting, etc [3].

One of the most important reasons that contributed to the development of this complex multiphysical phenomenon is the progress of power semiconductor devices (MOSFETs and IGBTs), and control schemes in high-frequency circuits using advanced switching techniques [4, 5].

Different power switching schemes and control methods such as phase shift control (PSC) [6, 7] which is based on variation of output power by shifting the phase of the switch conduction sequences, Single-ended voltage cancellation (AVC) [8] where the control is based on voltage-cancellation for conventional fixed-frequency, The asymmetrical duty-cycle (ADC) control technique [9] which employs an unequal duty-cycle operation of the switches in the converter and DC-density modulation control Pulses (PDM) [10]; have made voltage source resonant inverters widely used in applications requiring output power control capability.

In high temperature applications, a high current must flow across the surface of the metal for a heating effect. Otherwise the main drawbacks of the series resonant inverter (SRI) that it may require a transformer to match the output power and the high current in the induction coil.

In an industrial environment, apart from the converter and the matching transformer, the design of the induction coil and its profile itself is critical to obtain the best performance. Induction coil design using ELTA that it is a systematic design procedure for the coil for proper matching of the converter with the coil [11].

Previous work has shown that an LLC configuration can provide better performance; in the study [12] the authors proposed a novel topology based on LLC and LCL-T resonant tanks to reduce the range of operating switching frequency. while [13] the proposed converter will have the ability to respond to the load changes by varying the switching frequency to the value that fulfils the requirement. In the study [14] they have found that LLC resonant structure [15] is suitable for working in low-voltage and high-current pattern whereas LCC is suitable for high voltage and low-current pattern.

This paper describes a half-bridge LLC resonant converter based on power supplies for induction heating in high temperature application. The validity and results are verified by MATLAB simulation.

3.1 Circuit description

The circuit consist five parts; the switching bridge (inverter) [18, 19], the resonant tank, a high frequency transformer, a rectifier and a load (coil+workpiece).

The half bridge LLC tank consists of two resonant inductors, a series inductor (L_r) and a magnetizing inductor (L_m), a resonant capacitor (C_r) and an induction coil that comprises a series combination of a resistor (R_eq) and an induction coil inductor (L_coil).

The main power circuit features of a half bridge LLC resonant converter are illustrated in Figure 2.

2.png

Figure 2. half bridge LLC resonant converter

The switching bridge generates a high-frequency square wave by switching and converting the DC voltage to excite the LLC resonant tank, this last then enters the resonant tank, which eliminates the square wave harmonics and gives the output as a sine wave of the fundamental frequency [20].

The sine-wave rectifier and the filter capacitor provide the DC output voltage V_o for the load Z_Load. The nonlinear model of the converter can be obtained by the following equations.

$\frac{d i_{L r}}{d t}=\frac{1}{L_r}\left(V_{i n}-V_{c r}-V_{L m}\right)$              (2)

$\frac{d V_{c r}}{d t}=\frac{i_{L r}}{C_r}$           (3)   

$\frac{d V_0}{d t}=N\left(i_{L r}-i_{L m}\right)-\frac{V_0}{R_{e q}}$         (4)

$\frac{d i_{L m}}{d t}=\frac{V_{L m}}{L_m}$               (5)

The resonant tank gain can be derived by analyzing the equivalent resonant circuit shown in Figure 3.

3.png

Figure 3. Equivalent LLC resonant tank circuit

The resonant tank gain is the magnitude of its transfer function as in Eq. (6) [21].

$k=\frac{F_x^2(m-1)}{\sqrt{\left(m \cdot F_x^2-1\right)^2+F_x^2 \cdot\left(F_x^2-1\right)^2 \cdot(m-1)^2 \cdot Q^2}}$              (6)

$Q=\frac{\sqrt{L_r / C_r}}{Z_{a c}}$           (7)  

The sine wave is transferred to the secondary of the converter through a high-frequency transformer which scales the voltage up or down according to the output requirement, lastely the diode rectifier convert the sine wave into a stable DC output.

$Z_{a c}=\frac{8}{\pi^2} \cdot \frac{N_P^2}{N_S^2} \cdot Z_{a c}$          (8)

$m=\frac{L_r+L_m}{L_r}$            (9)

According to another way of designating resonant converters, the LLC resonant half-bridge belongs to the family of multi-resonant converters. Actually, there are two resonant frequencies associated to this circuit f_r and f_m. the first is related to the series resonant elements L_r and C_r as in Eq. (10) [22, 23].

$f_r=\frac{1}{2 \pi \sqrt{L_r \times C_r}}$            (10)

And when the resonant elements Lr and Cr resonate with the parallel resonance element Lm. here, new frequency fs is provided as in Eq. (11).

$f_s=\frac{1}{2 \pi \sqrt{\left(L_r+L_m\right) \times C_r}}$                (11)

3.2 Modes of operation

As shown in next figures, four modes of operation exist within one switching cycle. The corresponding circuit topology for each mode of operation is shown in Figures 4(a), (b), (c), (d) respectively. The analysis is as follows.

Stage 1: MOSFET M1 is turned on and M2 is turned off the current flows from V_in to the switching bridge source of MOSFET (M1) to capacitor (C_r), resonant inductor (Lr), and primary coil of Lp. Then energy will be transferred to secondary coil of Ls, Figure 4(a).

4a.png

-Figure 4(a)-

Stage 2: MOSFET M1 and M2 are turned off; resonant inductor (Lr) will release an energy to primary coil of Lp, diode of (M2), and capacitor (Cr). Then primary side of Lp coil will transfer the energy to secondary coil of Ls. The mode 2 is shown in Figure 4 (b).

4b.png

-Figure 4(b)-

Stage 3: MOSFET M1 is turned off and M2 is turned on. The current flows from capacitor (C_r), MOSFETs (M2) and primary coil of L_p. Then the Lp will transfer the energy to secondary coil of L_s. The mode 3 is shown in Figure 4 (c).

4c.png

-Figure 4(c)-

Stage 4: MOSFETs M1 and M2 are turned off. The energy in resonant inductor (Lr) is released to capacitor (C_r), diode of (M1), Vin, and primary coil of L_p. The mode 4 is shown in Figure 4 (d).

4d.png

-Figure 4(d)-

Figure 4. Operation mode of half bridge resonant inverter

The Figure 7 shows the command signal (S1 and S2) to control the MOSFETs (M1 and M2) at the top and bottom of the half-bridge converter respectively. While applying the gating pulse to the MOSFET it is necessary to take care of the overlapping of ON time and OFF time of two semiconductor switches. If 2^nd MOSFET is given the pulse before the prior one is not completely OFF, it may cause short circuit and thus failure of the semiconductor device. Therefore the control of this switches must be complementary.

7.png

Figure 7. Signals generated for the control of a half-bridge inverter

The Figure 8 show the voltage and current waveforms at the M1 switch on the top of the converter. When the switch is in the blocked state, the voltage takes the value of the source DC at 400 volts; otherwise it takes the value of zero volts, and the current reaches about 9 amps. The appearance of the negative part of the current resulting from the change of the states of the switch.

8.png

Figure 8. MOSFET voltage and current on the top a half-bridge converter

Figure 9 demonstrates the envelope of the current in the resonant circuit. Figure 9(a) shows the current at the output of the half-bridge inverter and flowing through the series inductance L_r. We see that it is an alternating current and not sinusoidal, because of the existence of harmonics. It is corrugated between [-9, +9] amperes around. The current through the magnetizing inductance L_m is presented by Figure 9(b). We observe that, it is also an alternating current with less harmonics and filtered by the value of 80 µH, it is now rippled between [-6, +6] amperes around.

Moreover, the resonance frequency value is calculated as 50 kHz from the period value of the curve by Eq. (11). In this case, the switching frequency of the MOSFETs is double to the resonant frequency.

9.png

Figure 9. Output currents across the resonant tank

The Figure 10 presents the voltage and current waveforms at the diode D1 on the top corner left at the rectifier converter. When the diode is in the blocked state, the voltage is measured at the value of -60 volts; otherwise it takes the value of zero volts, and the current reaches about 23 amps.

10.png

Figure 10. Diode voltage and current on the top corner left at the rectifier converter

Figure 11 shows the voltage and current waveforms at the load terminal (R_eq and L_eq). The rectified voltage is measured at the value of 60 volts around, and the current reaches about 11.5 amps.

11.png

Figure 11. Output voltage and current Waveforms

From the results mentioned above, it was confirmed that the proposed scheme and assembly have good efficiency, especially that the system showed great response by controlling the first transformer by using a mathematical model that allowed to give the command signal (S1 and S2) to control the MOSFETs, the use of MOSFETs allowed us to operate at high frequencies and it is well suited for magnetic induction heating systems.

The authors gratefully acknowledge Mining Institute, Echahid Cheikh Larbi Tebessi University, Algeria for supporting this work.