^{1}

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^{2}

This paper signifies the study of modeling and simulation of a single phase matrix converter for induction heating system. The working principle and the control method, using PID are revealing in detail. The performance of the system is carried out in MATLAB/Simulink environment with pulse width modulation switching strategy by varying the duty cycle. PID control is employed to obtain the better performance for a specified input supply for various output frequencies. The proposed control strategy of AC to AC converter has been discussed with a wide range of operating frequencies and results in low Total Harmonic Distortion.

In recent days, Induction Heating (IH) systems have broad industrial coverage [

The direct AC-AC converters also termed as Matrix Converters (MC) [

Gola and Idrish experimented the SPMC with AC source V_{i }having four bidirectional switches namely S_{1a}, S_{1b}, S_{2a}, S_{2b}, S_{3a}, S_{3b}, S_{4a} and S_{4b,} with the Induction Heating load is shown in _{1a}, S_{1b}, S_{2a} and S_{2b} are connecting the input lines to output lines directly through the intersections discussed in detail in the block diagram [

The commutation of these switches is difficult than the VSI and CSI AC-DC-AC converters due to the absence of freewheeling path in bidirectional switch configuration. As a result commutation of switches has to be actively controlled at any time instant with respect to two basic rules [

The switching pattern of the Matrix Converter switches for a constant input supply frequency of 50 Hz is given in

The switches S_{1}, S_{3} and S_{2}, S_{4} can be switched ON simultaneously as they will short circuit the input lines which will destroy the converter due to over current is shown in _{1}, S_{3} and S_{2}, S_{4} should not be switched OFF state simultaneously at any instant as it will open circuit the output phase which leads to the absence of path for the flow of inductive current leading to over voltages. This leads to a

Input frequency | 50 Hz | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Output frequency | 25 Hz | 50 Hz | 100 Hz | |||||||

Time interval | 1 | 2 | 3 | 4 | 1 | 2 | 1 | 2 | 3 | 4 |

Switching mode | S_{1a}-S_{4a} | S_{3b}-S_{2b} | S_{2a}-S_{3a} | S_{4b}-S_{1b} | S_{1a}-S_{4a} | S_{4b}-S_{1b} | S_{1a}-S_{4a} | S_{2a}-S_{3a} | S_{3b}-S_{2b} | S_{4b}-S_{1b} |

conflict as semiconductor switches cannot be switched instantaneously due to their propagation delay phenomenon and switch transient timings. The four basic operating modes of the Single Phase Matrix Converter based on power flow direction along the load for positive and negative half-cycle of the input power [

There are basically four modes of operation, i.e., forward and reverse power flow for positive half cycle and forward and reverse power flow for negative half cycle as described. In mode 1 switching operation, switches S_{1a} and S_{4a} are switched ON by the Pulse Width Modulation (PWM) signal to conduct the positive half-cycle in forward direction to the load as shown in

In mode 2 switching operation, switches S_{2a} and S_{3a} are switched ON by the PWM

signal to conduct the positive half-cycle in reverse direction to the load as shown in

In mode 3 switching operation, switches S_{2b} and S_{3b} are switched ON by the PWM signal to conduct the negative half-cycle in forward direction to the load as shown in

In mode 4 switching operation, switches S_{4b} and S_{1b} are switched ON by the PWM signal to conduct the negative half-cycle in reverse direction to the load as shown in

Based on the four operating sequences the Matrix Converter output frequency can be varied by varying the combination of the operating sequence of the switches and the switches describe the switching sequence of the Matrix Converter switches for an input voltage source frequency of 50 Hz to obtain variable frequency ranges.

a) Modeling of Single Phase to Single Phase Matrix Converter for Induction Heating

The Single Phase to Single Phase Matrix Converter module shown in

The modelling of the instantaneous input voltage is given by the Equation (1)

The instantaneous input current i_{i}(t) is given by the Equation (2.2)

The instantaneous output voltage v_{o}(t) is given by the Equation (3)

The output voltage during any cycle is given by the Equation (4)

where

^{th} cycle;

^{th} cycle.

The modulation index of any switch during any switching time is given by the Equations (5)-(8)

where

^{th} cycle;

^{th} cycle; (j = 1, 2);

b) Simulink Model of Single Phase to Single Phase Matrix Converter for Induction Heating

The simulation of Single Phase Matrix Converter is builtup with four bidirectional IGBT switches connected in Common Emmitter Mode shows in

The control signal from the PID controller output is fed to the PWM signal generator which acts as modultaion index for the PWM generator to generate pulse width modulated signals for energising the Matrix Converter switches to produce Single phase output from the Matrix Converter.

The input AC supply is fed to the Matrix Converter which energizes the Induction heating system shown in

The results obtained from PID controlled Single Phase to Single Phase Matrix Converter for Induction Heating for various operating frequencies from 25 Hz to 100 kHz is presented in following figures.

Harmonic Distortion (THD) measured for the corresponding operating frequency output. A THD of 37.52 is being measured for 50 Hz output frequency. Moreover the current and voltage waveforms are in phase which shows the unity power factor.

Hence the frequency study of the described input and the corresponding output plotted and discussed.

As stated frequency and the Total Harmonic Distortion and different frequency relationship of PID Controller based Single Phase Matrix Converter for Induction Heating are compared.

The single phase matrix converter powered by single phase source is modeled in MATLAB/Simulink and performance analysis of the converter is carried out with linear proposed PID controller. The PID controller based single phase to single phase matrix converter results were explained and discussed. Simulation is carried out for specified frequencies such as 25 Hz, 50 Hz and 100 Hz. The output of the converter presented and comparison of total harmonic distortion of the PID controller based single phase matrix converter is also presented. The performance of single phase matrix converter

S. No | Frequency in Hz | THD in % |
---|---|---|

1 | 25 | 42.06 |

2 | 50 | 37.52 |

3 | 100 | 27.14 |

controlled by PID controller is analyzed and they exhibit low Total Harmonic Distortion (THD). The proposed PID controller based matrix converters demonstrate the robust operation for induction heating load.

Umasankar, Dr.P. and Senthil Kumar, Dr.S. (2016) A General Approach for Direct Conversion of Single Phase AC to AC Converter for Induction Heating System. Circuits and Systems, 7, 3896-3910. http://dx.doi.org/10.4236/cs.2016.711325

m_{1}, m_{2}: Modulation index of PWM signals

f_{S}: Switching frequency

T_{S}: Switching cycle time

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