Multiple-Load Series Resonant Inverter for Induction

Cooking Application with Pulse Density Modulation

P. Sharath Kumar1

1Dept. of Electrical Engineering

1Rajarambapu Institute of Technology

Islampur, Maharashtra, India 1sharath.kumar@ritindia.edu

N. Vishwanathan2

2Dept. of Electrical Engineering

2National Institute of Technology Warangal

Warangal, Telangana, India

Abstract— Multiple-load induction cooking applications are

suitable using with multi output inverters or multi inverters are

needed for multiple-load operation. By using some common

approaches and modifications are needed in inverter

configuration for multiple-load application. This paper presents

an inverter configuration with two loads by using pulse density

modulation control technique. It allows the output power control

of each load independently with constant switching frequency

and constant duty-ratio. The pulse density modulation control

technique is obtained using phase on-off control between two legs

of the inverter to reduce acoustic noise. The proposed

configuration provides reducing the component count for

extension of multiple-loads. The control technique provides wide

range of output power control. In addition, it can achieve

efficient and stable ZVS operation in the whole load range. The

proposed configuration and control scheme is simulated and

experimentally verified.

Keywords— Induction cooking; Multiple-load; Series resonant

inverter; ZVS; Pulse density modulation control;

I. INTRODUCTION

Induction heating method is a far better approach than other conventional methods. In conventional methods, the heat is transferred from heat source to load by conduction or radiation. In induction heating, the heat is developed inside the load due to generation of eddy currents at skin depth level from the surface [1]. In recent times, considerable progress is made in control schemes and inverter configurations. Induction cooking is one of the several applications of induction heating. Fig. 1, shows a typical arrangement of high frequency induction heating circuit.

AC

UFAC

SourceDiode Rectifier

DC Link

HF Inverter IH Coil and Load

LS

Cdc

Fig. 1. Typical arrangement of induction cooking resonant inverter

Resonant inverter is commonly used as a source of high frequency AC supply. The DC input to it 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 heating effect.

Commonly used topologies for induction cooking

application are quasi resonant, half-bridge, and full bridge

inverter [2]. Out of these, full bridge inverter is preferred for

high power applications. In induction cooking application Variable Frequency (VF) scheme, Pulse Frequency Modulation (PFM), Pulse Amplitude Modulation (PAM), Phase Shift Modulation (PSM), and Asymmetrical Duty-cycle Control technique are used for output power control [3]-[8]. In VF scheme to control the output power for a constant load by varying the normalized switching frequency, in case of below resonance operation filter components are large for the low-frequency range [3]. PFM control has ZVS soft switching operating region is relatively narrow. In PAM control for constant load amplitude of the source voltage is varied to control the output power. PSM control gives high efficiency at higher duty-ratio [4]. ADC control gives ZVS at higher duty ratios in full-bridge inverter configuration [5]. For reducing switching losses, it is mainly used in half-bridge topology. AVC control gives ZVS at lower duty ratios also in full-bridge inverter configuration. AVC control technique is mainly used in full-bridge topology [5]-[7]. In induction cooking application, one inverter feeds power to a single load. For multiple load application, there is a need to develop inverter circuits and control techniques which can minimize component count and provide independent control of each load [8]. Certain techniques are available in the literature.

This paper proposes multiple-load series resonant inverter for induction cooking application with pulse density modulation control technique. The proposed inverter configuration powers two loads with independent output power control of each load. In this configuration, for PDM control technique [9]-[14] is used with phase on-off control between two legs of inverter for load output power control. The phase on-off control has no acoustic noise; due to inverter switching frequency is more than audible range. But in general PDM technique the duration of inverter gate pulse density is should be less than audible range. It can be overcome with phase on-off control technique. This configuration can be extended to multiple-loads also.

II. OPERATING PRINCIPLE OF IH AND LOAD

CHARACTERISTICS

A. Operating Principle of Induction Heating

Operating principle of IH is that when induction heating

coil is energized by high frequency current, it produces

magnetic flux. It causes eddy currents that occur in heating

load and this result in heating effect. The induced eddy currents

are concentrated in the vessel bottom layer at skin depth (δ)

level [2], which is explained by

𝛿 = 𝜌

𝜋𝜇 𝑓𝑠 =

1

4𝜋2×10−7 × 𝜌

𝜇𝑟𝑓𝑠 (1)

where, ρ is electrical resistivity, µ is magnetic permeability

and µr is relative magnetic permeability of load material and fs

is switching frequency of the inverter circuit.

The load surface resistance (RL) is determined by the load

skin depth and its material specific resistance is shown in

below expression,

RL = 𝜌

𝛿 = 𝑘 𝜌𝜇𝑟𝑓𝑠 (2)

where k is constant = 0.00198692

The load parameters depends on several variables including

the shape of the heating coil, the spacing between the heating

coil and cooking vessel (load), load electrical conductivity and

magnetic permeability, and the inverter switching frequency.

B. Equivalent Circuit of IH Coil and Load

A linear equivalent model of the IH coil and load

represented by the effective equivalent inductance (Leq) in

series with effective equivalent resistance (Req) is referred to

the input side of IH coil.

R1

M10 M01 RL

Lr

Req

i1i0vO

L1 L0

vO

Fig. 2. Equivalent circuit of IH coil with load

Fig. 2, shows the equivalent circuits for IH coil with load

parameters. Load parameters are taken as single turn short

circuited secondary winding.

The circuit elements are represented as:

1) RL surface resistance of the load

2) L0 inductance of the load

3) R1 resistance of IH coil

4) L1 inductance of IH coil

5) i0, i1 load current and IH coil current

6) M10, M01 the mutual inductance between IH coil

and load.

The voltage equations for the above equivalent circuit:

v0 = i1R1 + L1

𝑑𝑖1

𝑑𝑡 + M10

𝑑𝑖0

𝑑𝑡 (3)

0 = i0RL + L0

𝑑𝑖0

𝑑𝑡 + M01

𝑑𝑖1

𝑑𝑡 (4)

From (3) and (4) equations,

Req = R1 + (𝜔𝑀 )2 .𝑅L

𝑅L2+(𝜔𝐿0)2 (5)

Lr = 𝐿1 −(𝜔𝑀 )2 .𝐿0

𝑅L2+(𝜔𝐿0)2 (6)

Req = R1 +𝐴2𝑅L (7)

Lr = 𝐿1 − 𝐴2𝐿0 (8)

where, M10 = M01 = M

and A= (𝜔𝑀 )

𝑅𝐿2+(𝜔𝐿0)2

= 𝑀

𝐿0 at 𝜔𝐿0 ≫ 𝑅𝐿

III. PROPOSED INVERTER CONFIGURATION AND

CONTROL SCHEME

This section describes the proposed inverter configuration

and control scheme for two load induction cooking

application. Fig. 3, shows the circuit diagram of proposed

three-leg inverter configuration. The two loads are connected

across the inverter output voltages vAB, and vAC respectively.

The concept of series resonance is used with each load.

The resonant load circuits are connected to leg-1, which is

common leg for both loads. They are marked as leg-1, leg-2

and leg-3 respectively. Load-1 consists of Cr1, Lr1, and Req1

which are resonant capacitor, inductance of the load-1 and

equivalent load resistance in series with resonant tank

respectively, which is connected between leg-1 and leg-2.

Similarly for load-2, Cr2, Lr2, and Req2 are resonant capacitor,

inductance of the load-2 and equivalent load resistance in

series with resonant tank respectively, which is connected

between leg-1 and leg-3.

Q1 Q2 Q4 Q3 Q6 Q5

Q1

Q2

Q4

Q3

VDC

Switching

Signals

D3

D4 D6

D5

Lr1Cr1Req1

Q6

Q5

D1

D2

Cr2Lr2 Req2

Leg-1 Leg-2 Leg-3

AB

C

i1

i2

Fig. 3. Proposed two load inverter configuration

A. Characteristics of resonant tank

The resonant tank circuit of each load in three-leg inverter

circuit is shown in Fig. 3. It can be described by the following

parameters:

The resonant angular frequency is

𝜔𝑟 = 1

𝐿𝑟𝐶𝑟 (9)

The normalized switching frequency is

𝜔𝑛 = 𝜔𝑠

𝜔𝑟 (10)

where 𝜔𝑠 = switching angular frequency = 2π × 𝑓𝑠

𝑓𝑠 = switching frequency

The characteristic impedance is

𝑍0 = 𝐿𝑟

𝐶𝑟 =

1

𝜔𝑟𝐶𝑟 = 𝜔𝑟𝐿𝑟 (11)

The IH load quality factor is

Q = 𝜔𝑟𝐿𝑟

𝑅𝑒𝑞 =

1

𝜔𝑟𝐶𝑟𝑅𝑒𝑞 =

𝑍0

𝑅𝑒𝑞 (12)

The resonant tank circuit impedance is given by

𝑍𝑒𝑞 = 𝑅𝑒𝑞 + j 𝜔𝑠𝐿𝑟 − 1

𝜔𝑠𝐶𝑟 (13)

= 𝑅𝑒𝑞 1 + 𝑗𝑄 𝜔𝑛 − 1

𝜔𝑛 (14)

𝑍𝑒𝑞 = 𝑅𝑒𝑞 1 − 𝑄2 𝜔𝑛 −1

𝜔𝑛

2

(15)

The phase-angle between output voltage and current is

∅ = 𝑡𝑎𝑛−1 𝑄 𝜔𝑛 − 1

𝜔𝑛 (16)

B. Pulse density modulation control technique

Pulse density modulation control is obtained using phase

on-off control technique. By making phase-in and phase-out

sequence of switching pulses between two legs of full-bridge

inverter circuit, we get phase on-off control technique. Fig. 4

shows the switching pulses of an inverter circuit and inverter

output voltage with its respective load current for a full-bridge

circuit. Q3 switching pulses are phase-in and phase-out

sequence with Q1 switching pulses. Similarly, Q4 switching

pulses are w.r.t. Q2 switching pulses. When switching pulses

are in phase-in sequence, inverter output voltage VAB applied

across load and switching pulses are in phase-out sequence,

inverter output voltage VAB becomes zero. The similar

phase-in and phase-out sequence of switching pulses is

applied for load-2 to obtain inverter output voltage VAC.

Ton

T

VAB

i1

0

0

Q1

Q2

Q3

Q4

Fig. 4. Inverter output voltage and load current with PDM control

The time constant of the envelope of load current is given

by

𝜏 = 2𝐿

𝑅𝑒𝑞=

2𝑄

𝜔 (17)

The envelope ie of resonant tank current is given by

𝑖𝑒(t) = 𝐼𝑚 1 − 𝑒−𝑡

𝜏 +I𝑒−𝑡

𝜏 for 0≤t≤Ton (18)

𝑖𝑒(t) = I(Ton) 𝑒− 𝑡−Ton

𝜏 for Ton≤t≤T (19)

where, I = 𝐼𝑚1−𝑒

−𝑇𝑜𝑛𝜏

1−𝑒−𝑇𝜏

Im: max. current in full-power operation

I : initial value of the envelope ie

The average power is obtained by multiplying VDC and ie,

as follows

P = 1

𝑇

2

𝜋𝑉𝐷𝐶 𝑖𝑒 𝑡 𝑑𝑡

𝑇𝑜𝑛0

(20)

= 2

𝜋𝑉𝐷𝐶 𝐼𝑚

𝑇𝑜𝑛 +𝜏𝑒−𝑇𝑜𝑛𝜏 −𝜏

𝑇 +

2

𝜋𝑉𝐷𝐶𝐼𝑚

𝜏𝑒𝑇𝑜𝑛𝜏 −1

𝑇𝑒𝑇𝜏−1

1 − 𝑒−𝑇𝑜𝑛𝜏

If the periodic time T of the PDM control operation is

much smaller than the time constant 𝜏, no fluctuation occurs in

the amplitude of the resonant tank current and becomes

continuous waveform.

If the periodic time T is much greater than the time

constant 𝜏, the output power is in proportion to the pulse

density because the resonant tank current becomes a

discontinuous waveform. Thus, the input power is in

proportion to the pulse density is given by

lim𝜏→0 𝑃 = 2

𝜋𝑉𝐷𝐶𝐼𝑚

𝑇𝑜𝑛

𝑇 (21)

Assuming, the inverter circuit losses are constant. Because

of the inverter circuit operates with constant switching

frequency and constant duty-ratio. Thus, the output power is

also in proportion to the pulse density is given by

𝑃𝑜𝑢𝑡 = 𝐼2𝑅𝑒𝑞𝑇𝑜𝑛

𝑇= 𝑃𝑚𝑎𝑥 𝐷𝑦 (22)

where, „I‟ is the r.m.s. value of load current

„Req‟ is the equivalent load resistance.

„Dy‟ is the pulse density ratio.

„Pmax‟ is the full output power under continuous

condition

In this paper, both loads have same component values and

their resonant frequencies are same. Hence, their power rating

is also same and operated at a switching frequency of 30 kHz.

Resonant frequency of each load circuit is, fr = 1

2𝜋 𝐿𝑟𝐶𝑟 .

Switching frequency of each leg is slightly higher than their

resonant frequency. Hence, inverter switching frequency (fs)

can be chosen 5 to 10% higher than the resonant frequency (fr)

for ZVS operation.

IV. RESULTS OF PROPOSED CONFIGURATION

Proposed configuration of full-bridge series resonant

inverter for two load induction cooking application with 3-leg

is designed and operated at constant switching frequency of

30 kHz. Proposed inverter configuration with PDM of phase

on-off control technique is simulated and experimentally

verified using the parameters shown in table I.

TABLE I. PARAMETERS OF PROPOSED CONFIGURATION

Item Symbol Value

Source voltage VDC 30V

Equivalent resistance of each load Req 1.95Ω

Equivalent inductance of each load Lr 68μH

Resonant capacitance of each load Cr 0.45μF

Dead time in each leg td 450 nsec

Time period for one PDM cycle T 0.01sec

Resonant frequency of load circuit fr 28.77kHz

Switching frequency of each leg fs 30kHz

Pmax 226 W

MOSFETs used IRFP4110PbF 100V, 180A

Experimental setup of proposed inverter configuration is

shown in Fig. 5.

Fig. 5. Experimental setup of proposed inverter configuration

A. Simulation and experimental results

The simulation and experimental results of proposed

configuration with PDM of phase on-off control technique are

shown in Figs. 6 to 9 for different % Dy combinations of

load-1 and load-2.

(a)

(b)

Fig. 6. Two loads are operating at 100% Dy

(a)

(b)

Fig. 7. First load is operating at 11% Dy

Time 2.0ms 2.2ms 2.4ms 2.6ms 2.8ms 3.0ms 3.2ms 3.4ms 3.6ms 3.8ms 4.0ms

0A

20A

SEL>>

0V

50V

0A

20A

0V

50V

-20A

-50V

-50V

-20A

Time

1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0ms 2.2ms 2.4ms 2.6ms 2.8ms

0A

20A

0V

50V

0A

20A

0V

3.0ms

SEL>>

50V

-50V

-20A

-50V

-20A

(a)

(b)

Fig. 8. First load is operating at 2% Dy

(a)

(b)

Fig. 9. Both loads are operating at 50% Dy

Simulation waveforms of inverter output voltage and load currents are shown in Figs. 6(a) to 9(a) at different % Dy combinations. These waveforms are shown under experimental condition in Figs. 6(b) to 9(b). Simulation and experimental waveforms are in good agreement.

B. Control of output power

In proposed configuration, both loads are similar and each

load output power (Pout) can be controlled independently with

the phase on-off control technique. In proposed phase on-off

control technique, the time constant „τ‟ is 0.7% only of one

PDM cycle periodic time „T‟. So, the load current will be in

discontinuous mode. The output power (Pout) can be derived

from eqs. (21) and (22). The output power (Pout) with

percentage of pulse density (%Dy) is shown in table II.

TABLE II. Output POWER CONTROL WITH PDM

S. No % Dy Pout

1 100 225.76 W

2 80 180.61 W

3 60 135.45 W

4 50 112.88 W

5 40 90.3 W

6 30 67.73 W

7 20 45.15 W

8 2 4.515 W

PDM is used with phase on-off control between two legs

of inverter for load output power control. At zero inverter

output voltage, inverter operates in freewheeling mode and the

total stored energy in load will be discharged. PDM control

technique offers smooth variation of power control from

minimum to maximum value. From eq. (22), the prototype

Pmax is 226 W. The periodic time for one PDM cycle is taken

0.01sec. i.e., 100 Hz is chosen and the switching pulses are

generating without any discontinuous mode to reduce acoustic

noise.

C. ZVS opearation

In wide range of power control, the inverter operates with

maximum and constant duty-ratio with PDM control

Time

2.4ms 2.6ms 2.8ms 3.0ms 3.2ms 3.4ms 3.6ms 3.8ms 4.0ms 4.2ms

0A

20A

SEL>>

0V

50V

-20A

0A

20A

0V

50V

-50V

-50V

-20A

Time

2.0ms 2.2ms 2.4ms 2.6ms 2.8ms 3.0ms 3.2ms 3.4ms 3.6ms 3.8ms 4.0ms

0A

20A

SEL>>

0V

50V

0A

20A

0V

50V

-50V

-20A

-50V

-20A

technique. For getting ZVS, at turn-on of inverter output

voltage the load current should be negative.

Fig. 10. Both loads are operating with ZVS

Fig. 10 shows that both loads operating with constant and

maximum duty-ratio and load currents are in negative at

inverter output voltage turn-on position. In whole wide range,

the inverter is operated with ZVS and the inverter efficiency is

also at 96%.

V. CONCLUSION

Two load three leg series resonant inverter configuration

with PDM control technique for induction cooking application

was proposed. PDM is used with phase on-off control between

two legs of inverter for load output power control. With the

phase on-off control technique the acoustic noise is reduced in

the audible range of PDM frequency also. At zero inverter

output voltage, inverter operates in freewheeling mode and the

total stored energy in load is to be discharged. In this

configuration, each load output power controlled

independently. The two load inverter configuration is

generalized into n-output series resonant inverter configuration

with saving of switching devices. i.e., 2n+2 switching devices

are required instant of 4n switching devices for a full-bridge

configuration. In whole wide range of inverter operation,

ensures ZVS with constant and maximum duty-ratio and

constant switching frequency of 30 kHz. Simulation and

experimental results of the proposed configuration are in good

agreement. Overall efficiency of this configuration is 96%. The

proposed configuration can be extended to multiple loads.

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