Inverter configurations for multipleload induction cooking applications need development. Inverter configurations for induction cooking applications are used in home appliances based on single coil inverters. For multipleload configurations, multiple coils are used. They require proper inverters, which provide independent control for each load and have fewer components. This paper presents a threeleg inverter configuration for three load induction cooking applications. Each induction coil powers one induction cooking load. This configuration operates with constant switching frequency and powers individual loads. The output power of the required load is controlled with a phaseshift control technique. This configuration is simulated and experimentally tested with three induction loads. The simulation and experimental results are in good agreement. This configuration can be extended to more loads.
I. INTRODUCTION
Induction cooking is one of the applications of induction heating. Conventionally, heating of any object involves the transfer of heat from the heat source to the object heated by conduction or radiation. The method of induction heating involves the development of heat directly in the object heated. A high frequency alternating current flowing through a coil wound over the object induces eddy currents in it. These eddy currents result in I
^{2}
R losses in the object and result in heating.
Fig. 1
shows the typical arrangement of a high frequency induction heating circuit.
Typical arrangement of an induction cooking resonant inverter.
A resonant inverter is commonly used as a source of high frequency AC supply. DC input is derived by rectifying the utility AC source. High frequency AC flowing in the load coil results in eddy currents induced in the vessel at skin depth level resulting in a heating effect. The heat generated by the eddy currents in the load is concentrated in a peripheral layer at skin depth (δ)
[1]
, which is expressed as
where, ρ is electrical resistivity, μ is magnetic permeability, μ
_{r}
is the relative magnetic permeability of the load material, and f
_{s}
is the switching frequency of the inverter.
The high frequency alternating current is induced by a high frequency inverter. The frequency of the alternating current is decided by the material of the heated vessel. The vessels may be composed of either magnetic or nonmagnetic material. Based on this, the range of frequency for induction cooking is 20 kHz to 150 kHz. These are resonated with a capacitor because of the inherently low power factor of the inductionheating load. Hence, series resonant inverters are the common choice for highfrequency induction cooking systems. Commonly preferred configurations are quasiresonant, halfbridge, and fullbridge resonant inverters
[1]

[4]
,
[19]
. Halfbridge configuration is mostly preferred, whereas for high power applications, fullbridge configuration may be used. The control of the output power of these resonant inverters can be achieved through certain methods, such as pulse amplitude modulation (PAM), pulse frequency modulation (PFM), phaseshift (PS) control, asymmetric voltage cancellation (AVC), asymmetric duty cycle (ADC) control, and hybrid control technique
[5]

[11]
,
[25]
. These control techniques have their relative merits and demerits.
Multipleload induction cooking systems are in focus for suitable inverter configurations. The main function of inverters in multipleload induction cooking systems is to reduce components count, simultaneous and independent control of each load, and high conversion efficiency. An inverter with two loads is proposed and analyzed in
[12]
. This method has one master and one slave load, and uses several resonant capacitors connected in parallel with electromechanical switches. The control of load power is achieved by activating these electromechanical switches. The disadvantages of this method are a large number of capacitors and use of electromechanical switches. An inverter configuration for twoloads is presented in
[13]
, which has three legs (six switching devices). One leg of the inverter is common for both loads, and offers independent control of each load with high efficiency. It also offers a reduced component count and better device utilization. AVC control technique is adopted for power control. In
[14]
, a twooutput induction cooking system with power factor correction is proposed. Power control for each load is performed using the AVC control technique. In
[15]
, a loadadaptive control algorithm is used for variable load and large output power range. Aspects such as efficiency, acoustic noise, and flicker control are considered in the design stage. For different ranges of output power, different control techniques are adopted. Though certain objectives are met, it makes the control structure more involved. To improve lightload performance, discontinuous conduction mode control is adopted in
[16]
, and uses variable frequencies in the range 20kHz to 150kHz. It improves light load efficiency to 95%, but variable frequency operation is the limitation of this technique. The digital implementation of induction heating load is proposed in
[17]
. An ACAC power conversion technique is presented in
[18]
for a multiple induction heating system. It has higher efficiency, a reduced components count, and reduced complexity, however uses variable frequency control, which is the limitation of this method.
In the abovementioned literature for multipleload application, either the inverters have a larger components count or variable frequency control is adopted. Enough scope exits in this area for further improvement with constant frequency control and reduced complexity. In this paper, a threeleg inverter configuration is presented for a threeload induction cooking system. It offers constant switching frequency operation, simple control, less components count, and high efficiency.
This paper is organized as follows. In Section II, principle of operation of threeleg inverter configuration is presented. Section III describes the simulation and experimental results.Section IV presents characteristics showing power control of loads. Section V presents extension of this configuration to more than three loads. Section VI concludes the paper.
II. THREELEG INVERTER CONFIGURATION AND CONTROL SCHEME
This section describes the inverter configuration and control scheme for a threeload induction cooking application.
Fig. 2
shows the circuit diagram of this configuration.
Fig. 3
shows only load resonant tank circuits, where three loads are connected in delta across inverter output voltages
v
_{AB}
,
v
_{BC}
, and
v
_{CA}
.
Threeleg inverter configuration.
Three load resonant circuit.
An induction cooking system consists of a vessel and an induction coil. The coil and vessel are similar to the primary and secondary of a transformer. Based on this, induction cooking load in referrence to the coil is modeled as a series R
_{eq}
 L
_{r}
circuit for constant switching frequency operation
[12]
,
[20]

[24]
. R
_{eq}
is the referred equivalent resistance and L
_{r}
is the referred equivalent inductance to the coil, respectively.
The concept of series resonance is used with each load. The resonant load circuits are connected in delta at the output terminals of the inverter configuration. They are marked as leg1, leg2, and leg3. Load1 consists of C
_{r1}
, L
_{r1}
, and R
_{eq1}
, which are resonant capacitor, inductance of the load1, and equivalent load resistance in series with resonant tank, respectively. For load2, C
_{r2}
, L
_{r2}
, and R
_{eq2}
are the resonant capacitor, inductance of the load2, and equivalent load resistance in series with resonant tank, respectively. Similarly for load3, C
_{r3}
, L
_{r3}
, and R
_{eq3}
are the resonant capacitor, inductance of the load3, and equivalent load resistance in series with resonant tank, respectively.
Under an equal maximum output power of all loads, the inverter is switched at 30kHz and the gate pulses of each leg are phase shifted by 120° w. r. t. other leg pulses. All threeload circuits have the same component values and all inverter legs are operated at the same switching frequency. Hence, the resonant frequencies of all load circuits have to be the same. The resonant frequency of each load circuit is
. The switching frequency of each leg is slightly higher than their resonant frequency. The inverter switching frequency (f
_{s}
) is chosen at 5% to 10% higher than the resonant frequency (f
_{r}
) for ZVS operation.
In this configuration, the dutyratio of the gate pulses is kept constant.
Fig. 4
shows the gate pulses
v
_{g1}
,
v
_{g3}
, and
v
_{g5}
for the switching devices Q
_{1}
, Q
_{3}
, and Q
_{5}
, respectively. These are 120° phase shifted with each other. The gate pulses of Q
_{2}
, Q
_{4}
, and Q
_{6}
are 180° out of phase w.r.t. Q
_{1}
, Q
_{3}
, and Q
_{5}
respectively. The inverter output voltages across loads are
v
_{AB}
,
v
_{BC}
, and
v
_{CA}
.
Inverter gate pulses and output voltage waveforms v_{AB}, v_{BC}, and v_{CA}.
An analysis of PS control of series resonant inverter is presented in
[10]
.
Fig. 5
shows the inverter voltage waveform (
v
_{AB}
) for the load1 and load1 current (
i
_{1}
) of the threeleg inverter.
v
_{AB1}
is the fundamental component of
v
_{AB}
. The current in the resonant tank is close to sine wave because of the filtering of harmonics by the LC resonant tank. Harmonics in load current waveforms are negligible. I
_{1}
, I
_{2}
, and I
_{3}
are the r.m.s values of the load currents.
Output voltage and current with control variables.
In PS control, the peak value of
v
_{AB1}
is expressed as:
is the peak amplitude of the load1 current assumed sinusoidal, and ∅
_{1}
is the power factor angle.
The output power of load1 is expressed as:
P
_{o2}
and P
_{o3}
are output powers of load2 and load3, respectively. The total output power (P
_{T}
) is expressed as P
_{T}
= P
_{o1}
+ P
_{o2}
+ P
_{o3}
.
The quality factor (Q) for load1 and normalized switching frequency (ω
_{n}
) are expressed as:
where ω
_{s}
is angular switching frequency and ω
_{r}
is the angular resonant frequency.
From the above equations, the amplitude of the fundamental component of output voltage can be controlled by varying θ. Consequently, the load current and output power also can be controlled by varying θ.
From
Fig. 4
,
From Eqs. (7) and (9),
Eqs. (7) to (11) show that D
_{1}
and D
_{2}
are dependent on θ
_{1}
and θ
_{2}
, respectively. These are in turn dependent on α
_{1}
.
Fig. 6
shows the variation of dutyratios D
_{1}
and D
_{2}
w.r.t. phase angle(θ
_{1}
). As leg2 is common for load1 and load2, the variation of D
_{1}
results in the variation of D
_{2}
in a certain manner, which is justified by Eq. (9). θ
_{3}
will not be affected because load3 is not connected to leg2. Hence, D
_{3}
will not change.
Variation of dutyratios vs. phase angle(θ_{1}).
The output powers of load1 to load3 are proportional to
, respectively. As
varies from 30° to 90°,
varies from 30° to 0° and back to 30°. Hence
varies from 0.75 to 0 and
varies from 0.75 to 1 and back to 0.75. Whereas,
does not vary at all. Full range control of load1 power results in a 25% variation in load2 power and no variation in load3 power. In cooking applications, precise temperature control may not be very essential. This maximum variation of 25% in one of the loads when a particular load is controlled may not be a significant drawback.
III. RESULTS OF THREELEG INVERTER CONFIGURATION
The threeleg inverter configuration with the PSC technique is simulated and is experimentally verified using the parameters shown in
Table I
.
PARAMETERS OF THREELEG INVERTER CONFIGURATION
PARAMETERS OF THREELEG INVERTER CONFIGURATION
Fig. 7
shows the experimental setup of a threeleg inverter configuration.
Fig. 7
(a) shows the induction heating loads with a 3leg inverter circuit.
Fig. 7
(b) shows a 3leg inverter circuit with a pulse generator and a driver circuit. In the control circuit, two UC3875 ICs are used for six control pulses with phase shift control. Three IR2110 ICs are used as drivers. The implementation of the control circuit is simple without any logic gates. This configuration is designed and operated at a switching frequency of 30kHz.
Experimental setup of the threeleg inverter configuration. a Induction heating loads with inverter circuit b 3leg inverter circuit with control circuit
Fig. 8
shows the switching pulses for a 3leg inverter configuration.
Fig. 8
(a) shows the switching pulses for upper switching devices Q
_{1}
, Q
_{3}
, and Q
_{5}
of a 3leg inverter. These pulses are 120° phase shifted with each other.
Fig. 8
(b) shows the switching pulses for lower switching devices Q
_{2}
, Q
_{4}
, and Q
_{6}
. These pulses are also 120° phase shifted with each other and 180° phase shifted with their respective upper switching device pulses.
Switching pulses for a threeleg inverter. a Switching pulses for upper switching devices of each leg b Switching pulses for lower switching devices of each leg
All three loads are connected in delta. In addition, each load can be viewed as if connected to a fullbridge inverter. Each leg of the inverter is common for two loads. Under equal output power of all three loads, each output voltage is phase shifted from the other output voltage by 120°. Each load current is 120° phase shifted from one another. For the control of each load power θ
_{1}
, θ
_{2}
, and θ
_{3}
can be controlled. Simulation and experimental results are shown in
Figs. 9
to
10
for different PS combinations between leg1 and leg2. The load1 current can be controlled by varying the phase angle (θ
_{1}
). Similarly, the load2 current can be controlled by varying the phase angle (θ
_{2}
). For control of the load3 current, phase angle (θ
_{3}
) is varied.
Voltage waveform simulations across load1 with all load currents. a at θ_{1} = 60°; b at θ_{1} = 120°; c at θ_{1} = 160°
Experimental voltage waveforms across load1 and all load currents. a at θ_{1} = 60°; b at θ_{1} = 120°; cat θ_{1} = 160°
Fig. 9
shows the simulation waveforms.
Fig. 9
(a) shows the inverter output voltage of load1 and its load current along with other two loads at θ
_{1}
= 60°.
Fig. 9
(b) shows these waveforms at θ
_{1}
= 120°.
Fig. 9
(c) shows these waveforms at θ
_{1}
= 160°.
Fig. 10
shows the experimental waveforms.
Fig. 10
(a) shows the inverter output voltage across load1 and its load current along with other two loads at θ
_{1}
= 60°.
Fig. 10
(b) shows these waveforms at θ
_{1}
= 120°.
Fig. 9
(c) shows these waveforms at θ
_{1}
= 160°.
Both simulation and experimental results are in good agreement with each other. This configuration can power three loads simultaneously with constant switching frequency.
In addition, any oneload current can be controlled using the PS control technique, which gives an almost independent power control of that load. In
Figs. 9
(a) to (c) and
10
(a) to (c), the phase angle (θ
_{1}
) of load1 is taken as 60°, 120° and 160°. Hence, the corresponding load1 current is controlled by phase angle (θ
_{1}
). The current in load2 varies because of the variation in θ
_{1}
, as shown in
Fig. 11
. With an increase in θ
_{1}
, the current in load2 initially increases, reaching a peak, and then decreases. Hence, there is little variation in load2 current when load1 current is controlled. Load3 current remains constant because its phase angle (θ
_{3}
) remains constant at 60°.
Variation of load currents vs. phase angle (θ_{1}).
In induction cooking applications, this small variation of the load2 current may be tolerable as precise temperature control is not required. This configuration gives the advantage of power control of the required load, and reduces components count and offers one leg / load.
Switching devices of 3leg inverter configuration have ZVS at low phase angles(θ) with PS control technique; switching devices may not have ZVS at higher phase angles(θ), which is the limitation of this configuration.
IV. CONTROL OF LOAD POWER
In a 3leg inverter configuration, required load power control can be achieved using the PS control technique. Each load power is dependent on corresponding load currents. Load currents are controlled with their phase angles(θ) and are experimentally verified. Load current magnitudes w.r.t. and their phase angles(θ) are shown in
Table II
.
LOAD CURRENTS VS. ITS PHASE ANGLE (θ)
LOAD CURRENTS VS. ITS PHASE ANGLE (θ)
The above table shows that when θ
_{1}
varies, load1 current is controlled. Load2 current is slightly affected and load3 current remains constant. The small variation of load2 current may not be significant for cooking application. Similarly, the load2 current can be controlled by varying θ
_{2}
and the load3 current can be controlled by varying θ
_{3}
. All load currents are in r.m.s. values under the experimental condition.
Fig. 11
shows load currents versus θ
_{1}
. For a variation of θ
_{1}
from 60° to 180°, its load current varies from 9.673A to 0A. Under this condition, load2 current has small variation, as leg2 is common for load1 and load2. Under this variation of θ
_{1}
, θ
_{2}
varies from 60° to 0° and back to 60°. However, θ
_{3}
is remains constant at 60°. Each load current magnitude depends upon its load PS angle(θ). Simulation and experimental results are in good agreement with each other. Load1 output power w.r.t. its phase angle(θ) is shown in
Table III
.
LOAD1 OUTPUT POWER VS. ITS PHASE ANGLE (θ1)
LOAD1 OUTPUT POWER VS. ITS PHASE ANGLE (θ_{1})
Fig. 12
shows the overall efficiency versus θ
_{1}
. Overall efficiency for this configuration is >93% for the entire control range of one load. Total output power is measured by adding the individual load outputs. Each load output is computed as I
^{2}
R
_{eq}
. ‘I’ is the r.m.s. value of the respective load current. ‘R
_{eq}
’ is the equivalent load resistance of the respective load. Input power is obtained by multiplication of DC input voltage and average input current of the inverter.
Overall efficiency vs. phase angle (θ_{1}).
Fig. 13
shows the transient variation of all load currents for sudden variation in D
_{1}
at 1 msec. Load1 and load2 currents have smooth transition to new steady state condition. Load3 current is not affected.
Transient variation of all load currents for sudden variation in D_{1}.
From Eq. (7),
α
_{1}
and α
_{2}
are controlled independently and α
_{3}
is dependent on α
_{1}
and α
_{2}
.
Fig. 14
shows each load power control possibility in combination of all loads w.r.t. their α. In
Fig. 14
, X represents α
_{1}
for load1, Y represents α
_{2}
for load2, and Z represents α
_{3}
for load3. When α value is 0°, the load power is also zero. When α value changes from 0° to 180°, the load power changes from zero to maximum. Simultaneously, all loads can have equal maximum power for α
_{1}
= α
_{2}
= α
_{3}
= 120° i.e., respective θ values are 60° each. For different combinations of individual load powers, a lookup table can be made with possible values of α for wide operating flexibility.
Each load power control possibilities vs. their α.
V. EXTENSION OF THREELEG INVERTER CONFIGURATION
This configuration requires two switching devices per load or one leg per load, and is extended for multiple loads as shown in
Fig. 15
.
Extension of the threeleg inverter configuration to multiple loads. a Extension of threeleg inverter configuration to fourleg configuration; b Four load resonant circuit; c Five load resonant circuit; d Six load resonant circuit
In
Fig. 15
(a), a threeleg configuration is extended for four loads by adding an additional leg to the right of leg3. The switching frequency is same for the existing configuration. By controlling this load with the PS control technique, the load connected between leg3 and this additional leg4 can be independently controlled. Here also, the number of legs per load is one.
Fig. 15
(b) shows only load resonant circuits where three loads are connected in delta across the inverter output voltages
v
_{AB}
,
v
_{BC}
, and
v
_{CA}
, respectively, and an addition of fourth load is across the inverter output voltage
v
_{CD}
. Extension to fifth and sixth load is shown in
Figs. 15
(c) and (d) respectively. Independent control of fifth and sixth loads are possible with PS control technique. Hence, this method can be extended to six loads also with a number of legs per load equal to one.
VI. CONCLUSION
A threeleg inverter configuration with three loads for induction cooking applications has been presented. In this configuration, the required load can be controlled almost independently, and can be extended for more loads. The number of switching devices per load is two (i.e., one leg per load). Constant switching frequency is used for powering the loads. Each load is operated at a switching frequency of 30kHz. PS control technique is used for the power control of the required load. The design and output power control of this configuration is simple. This configuration can also be used for uniform surface heating with a minimum components count. The simulation and experimental results of this configuration are in good agreement.
BIO
P. Sharath Kumar received a B.Tech degree in Electrical and Electronics Engineering from Jawaharlal Nehru Technological University, Hyderabad, India in 2006 and a M.Tech degree from the National Institute of Technology, Kurukshetra, India in 2008. He is presently pursuing a Ph.D. in Electrical Engineering at the National Institute of Technology, Warangal, India. His area of interest is high frequency resonant inverters for induction cooking and LED lighting applications.
N. Vishwanathan received a B.Sc (Engg.) degree in electrical engineering from Dayalbagh Educational Institute, Agra, India, in 1990, a M.Tech. degree in electrical machines and industrial drives from REC, Warangal, India in 1992, and a Ph.D. from Indian Institute of Science, Bangalore, India, in 2004. He is currently working as a Professor in the Dept. of Electrical Engg., NIT, Warangal, India. His areas of interest are switched mode power conversion and induction heating applications.
Bhagwan K. Murthy obtained his B.E. (Electrical) and M.E. (Industrial Electronics) degrees from the M. S. University of Baroda, India in 1983 and 1987, respectively. He did his Ph.D. at IIT Madras in 1999. He is working as Professor of Electrical Engineering at the National Institute of Technology, Warangal, India. His research interests include application of power electronics to DSP controlled industrial drives and renewable energy.
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