Abstract ‘ Harmonics are the major issue in the conversion system either in DC-AC or AC-DC conversion. To reduce the harmonics, in this paper one randomized pulse position modulation (RPPM) technique using Indirect Matrix Converter (IMC) is proposed. And the RPPM scheme has been compared with the Traditional Carrier Based Modulation (TCBM) using the same Indirect Matrix Converter. The random scheme randomly places the pulse position with a limited degree of freedom, which will produce lower harmonic spectrum with higher commutation frequency. And also the Total Harmonic Distortion (THD) of the input and output waveforms will be lesser compared to the TCBM scheme. In the RPPM scheme the time period, frequency and duty ratio will be constant, only the delay interval varies. The implementation of the same is done with the help of MATLAB software.
Keywords — indirect matrix converter (IMC), Randomized Pulse Position Modulation(RPPM), Harmonic reduction ,Traditional carrier based modulation(TCBM).
I. INTRODUCTION
Matrix AC-AC converters have become industrially accepted technologies in three-phase systems. The features of the matrix converters are 1) Compact and packaged structure;2) The input and output are sinusoidal;3) Bidirectional power flow;4) Potential for high power density. The above mentioned ideal characteristics makes the matrix converter topology more attractive. The matrix converter is a force commutated converter. It is an array of controlled bidirectional switches. It does not have any DC link
In this paper as an alternative to the conventional 9 switch topology two stage conversion technique is used. This two stage conversion is done with a converter and inverter. There would not be any dc-link. In this paper, a Random technique is used by keeping its time period, frequency and duty ratio constant. Only the delay interval varies. The delay interval means delay from the beginning of the switching cycle to the turn-on within the cycle. Using this random technique the harmonic powers of the input current and output voltage which are concentrated on the multiples of the switching frequency will get reduced compared to the traditional carrier based modulation. Spreading of the harmonic energy may be carried out in various ways. Many randomization techniques and its synthesis have been discussed in many literatures.
The main purpose of this paper is to give a basic idea about the key aspects concerning with the matrix converter operation and to establish the state of the art of this technology. For the study of this art of technology first the matrix converter topologies, its control techniques the practical implementation of the bidirectional switches should be considered.
II. MATRIX CONVERTER FUNDAMENTALS
The matrix converter is a single stage converter. It is an alternative to the double sided PWM voltage source rectifier-inverter. It is an array of (m ?? n) controlled bidirectional switches. it connects m-phase voltage source to an n-phase load directly. That means which could transform m-phase input voltages into n-phase output voltages of various magnitudes. The input side of the matrix converter is considered to be voltage fed and the output is considered to be current fed. There is no dc-link. Hence large energy storage elements can be avoided and the cost also will get reduced. The circuit diagram of a three phase three phase matrix converter is shown in figure 1. The nine switches are arranged such that any of the three input phases could be connected to any output phase.
Fig. 1 3-phase to 3-phase matrix converter
An AC input LC filter is used to eliminate harmonic currents in the input side. The term ‘matrix’ is due to the fact that it uses exactly one switch for each of the possible connections between the input and output. The bidirectional switches should be controlled in such a way that at any time one and only one of the three switches connected to an output phase must be closed to prevent short circuiting of the supply lines or interrupting the load current flow in an inductive load. In the figure of three phase to three phase matrix converter the variables SAa , SAb , SAc , SBa ,SBb ,SBc , SCa , SCb , SCc represents the switching variables of the corresponding switches. The matrix converters are controlled by using these switching variables. The input voltages and output voltages similarly the input currents and output currents are related to each other by the switching matrix TSij is described below. Vo= (TSij) Vi and Ii= (TSij) Ii. Where the value of the switching matrix is
The major benefits of Random Pulse Width Modulation (RPWM) relate to acoustic and electromagnetic noise. Both of these noises are one of the major design criteria for electric propulsion in automotive application. Implementation of RPWM transforms the typical PWM harmonics into the continues density spectrum there by the electromagnetic emissions are being reduced. This will allow the reduction of onboard filtering for reduced cost, size and weight. As these acoustic noise is annoyance to the driver and passengers, the RPWM scheme compensate for the increased noise levels. This technique will spread the noise spectrum thus reducing the peak noise pressure levels.
III. BIDIRECTIONAL SWITCH
There are three arrangements for the realizations of the bidirectional switch cells are available. First is the ‘diode bridge bidirectional switch cell’ arrangement, second is the ‘common collector back to back’ and the third type of arrangement is ‘common emitter back to back’. Because of the disadvantages and conduction losses of the first two arrangements, the third type of switch cell arrangement is used. The common emitter configuration is shown in figure 2.
Fig. 2 common emitter configuration
This arrangement consists of two diodes and two IGBT’s. The diode is connected across the IGBT to provide reverse blocking capability. The emitter terminal of the two IGBT’s will be connected to each other. By using this arrangement it is possible to independently control the direction of current compared to the other two arrangements. Here the conduction losses also will be less since only two devices carry current at a time.
IV. INDIRECT MATRIX CONVERTER
Fig. 3 IMC topology
The Indirect Matrix Converter (IMC) consists of two stages of conversion. It is cascade connection of separate d four quadrant current source rectifier stage and standard voltage source inverter stage. Basic topology of an IMC is shown in figure 3. The switch cell arrangement used for the converter stage is common emitter configuration. The rectifier stage represents a matrix converter. But the inverter sage uses normal switch cells not the common emitter switch cell arrangement. That is why the name indirect matrix converter. There is no dc-link connection between the rectifier and inverter; hence the large energy storage elements are eliminated.
V. RANDOM PULSE POSITION MODULATION SCHEME
The Random Pulse Position Modulation (RPPM) scheme proceeds with the calculation of modulation functions followed by the switching functions. For the calculation purpose stiff voltage sources are connected at the input side and stiff current sources are connected at the output side. The IMC representation using voltage stiff sources at the input side and current stiff sources at the output side is used for the analysis. This IMC topology consists of two bridge converters one is CSB and the other is VSB. The voltage stiff sources are represented by Va, Vb and Vc. The current stiff sources are represented by ia, ib and iw.
Fig. 4 IMC represented using SPPT’s and SPDT’s
For the easier analysis the IMC topology, the switches of the current source rectifier has been replaced by Single Pole Triple Throw (SPPT) switches and the switches of the voltage source inverter are represented by using Single Pole Double Throw (SPDT) switches. This arrangement is shown in figure 4. In this figure Sp and Sn represents the SPPT switches and Su, Sv and Sw represents SPDT switches. In order to proceed with the calculations first the modulation function and switching functions for the CSB, then the modulation and switching functions of the VSB needs to be calculated.
VI. MODULATION FUNCTIONS
In order to find the modulation functions for the CSB and VSB three sets of equations being considered. First set of equations are the input voltages.
Va=Vi cos'( 2??ft+??i0)
Vb=Vi cos'( 2??ft+??i0-2??/3)
Vc=Vi cos'( 2??ft+??i0+ 2??/3)
Where Vi is the amplitude of the source voltage and (2??ft+??i0) =??i(t) is the phase angle of the voltage source. Second set of equations are the output currents.
Iu=Io cos'( 2??ft+??o0)
Iv=Io cos'( 2??ft+??o0-2??/3)
Iw=Io cos'( 2??ft+??o0+ 2??/3)
Where Io is the amplitude of the source current and 2??ft+??o0=??o(t) is the phase angle of the current source. Third set of equations are the reference currents at the input terminal of the CSB.
Ia_ref=Ii_ref cos'( 2??ft+??i0)
Ib_ref=Ii_ref cos'( 2??ft+??i0-2??/3)
Ic_ref=Ii_ref cos'( 2??ft+??i0+ 2??/3)
Where Ii_ref is the amplitude of the reference source currents and 2??ft+??i0=??i(t) is the phase angle of the reference source currents. The power factor angle of the CSB is the difference between input voltages and input currents. The value of power factor angle ??i at the CSB terminals is (??i0-??i0).
VII. MODULATION FUNCTIONS of the CSB
Depending on which waveforms are needed the corresponding set of equations have to be divided into six sectors either the input voltages or input currents.. During each sector there will be a maximum medium
TABLE I. TABULATED VALUES OF MODULATION INDEX FOR ALL THE THROWS OF CSB
and minimum value. If the desired input current is maximum during one sector then the corresponding switch in the upper arm is closed. When the desired value is minimum the corresponding switch in the lower arm is closed. When that switch is closed the value of modulation index for the corresponding throw will be one. As an example during sector one the reference current of phase ‘a’ is maximum hence the corresponding switch in the upper arm that is the ‘Sap’ switch is closed. Hence the value of the modulation index corresponding to that throw map will be one.The dc-link current returns back through either Tbn or Tcn. When Sap is closed at that time San will be open since the zero states of CSB are not used. When the dc-link current returns through Tbn the corresponding value of modulation index mbn will be ‘(ib_ref/ia_ref). Similarly when the dc-link current returns through Tcn the corresponding value of modulation index will be ‘(ic_ref/ia_ref). Similarly the value of modulation index for all the throws has been tabulated as shown in table I.
VIII. MODULATION FUNCTIONS of the VSB
The modulation functions of the VSB are mu ,mv and mw. The values are
mu=Mo cos”(2??ft+??o0)’
mu=Mo cos”(2??ft+??o0-2??/3)’
mu=Mo cos”(2??ft+??o0+2??/3)’.
Where Mo is the modulation index and its value varies between zero and one. And in the above equation
TABLE II. MODULATION FUNCTION AMPLITUDES IN SIX SECTORS
(2??ft+??o0 ) represents the phase angle of the output voltage. The value of power factor angle ??o at the VSB terminals is (??o0-??o0). In order to find the value of modulation index the modulation function amplitude in each sector has to be determined. Expression for the averaged link current is
‘ip’=3/4 Mo Io cos’??o
The average link current should follow ia_ref during sector1. That means according to the modulation index table for the throws CSB the average link current must follow that corresponding reference current whose value of modulation index is unity. Thus the value of a ia_ref during sector 1 is
ia_ref=3/4 Mo Io cos’??o
The amplitude Mo of the VSB modulation function must be time varying function. And the value determined is
Mo(t)=4/3 (Ii_ref)/(Io cos’?? o) cos”??i(t)’
The above expression may also be expressed in terms of voltages through reciprocity as below
Mo(t)=4/3 (Vo_ref)/(Vi cos’?? o) cos”??i(t)’
The amplitudes of the modulation function at the VSB port during each sector is tabulated as shown in table II.
IX. SWITCHING FUNCTIONS of the CSB
When the modulation functions are compared with a linear carrier the switching functions are generated.
X. SWITCHING FUNCTIONS of the VSB
The modulation functions at the AC port of the VSB mu , mv and mw are compared with triangular carrier to generate the switching functions for the VSB. Since the converter and inverter operate in synchronism if changes occur in the inverter stage that will automatically happens in the converter stage also. Here the time values of the triangular carrier are multiplied with a variable called ‘random’. This variable is an inbuilt function in MATLAB. It will randomly generate values .This method of generating random pulse positions is known as Random Pulse Position Modulation (RPPM). This will reduce the amount of total harmonic distortion.
XI. SIMULATION VERIFICATION
A. RANDOMIZED PULSE POSITION MODULATION
Fig. 5 FFT analysis waveform of output current
The FFT analysis is done for the input current and output current. The FFT analysis diagram of the input and output current waveforms by using the Randomized Pulse Position Modulation scheme in Indirect Matrix Converter(IMC) is described here. Figure 5 shows the output current and figure 6 shows the input current. The input waveform also will get affected by the load discontinuities or by the introduction of harmonics in the load side. That is the reason why the input waveform is also analysed.
B. TRADITIONAL CARRIER BASED MODULATION SCHEME
The traditional carrier based modulation proceeds with the same method which have used for randomized scheme. But the position of the triangular carrier will be symmetrical for each of the carrier cycle.
Fig. 6 FFT analysis waveform of the input current
The FFT waveforms of the output current and input current is also shown here. Figure 7 shows the FFT analysis of the output current and figure 8 shows the FFT waveform of the input current.
Fig. 7 FFT waveform of the output current
Fig. 8 FFT waveform of the input current
XII. CONCLUSION
Output current THD in percentage Input current THD in percentage
RPPM scheme 27.19% 3.25%
TCBMscheme 30.22% 6.54%
TABLE III.COMPARISON OF TRADITIONAL AND RANDOM SCHEME
From the simulation results it is clear that the percentage of Total Harmonic Distortion(THD) is greater for TCBM scheme compared to RPPM scheme. The comparison is shown in table III.
XIII. REFERENCES
[1] Chen Qi,Xiyou Chen,and Ying Qiu’Carrier-based randomized pulse position modulation of an indirect matrix converter for attenuating the harmonic peaks’IEEE transactions on power electronics, vol. 28, no. 7, july 2013p.
[2] W.Wheeler, J. Rodriguez, J. C. Clar, L. Empringham, andA.Weinstein,’Matrix converters: A technology review,’ IEEE Trans. Ind. Electron.,vol. 49, no. 2, pp. 276’288, Apr. 2002.
[3] B. Wang and G. Venkataramanan, ‘A carrier based PWM algorithm forindirect matrix converters,’ in Proc. IEEE Power Electron. Spec. Conf.,Jeju, Korea, 2006, pp. 2780’2787
Shein.T . Thakkirical received the B.tech degree from Mar Athanasius College Of Engineering Kothamangalam Kerala in 2012 .The Oxford College Of engineering Banglore, where she is doing Mtech degree in the Department Of Electrical Electronics Engineering.
Sharath Kumar B completed his Btech and Mtech in Departement Of Electrical and Electronics Engineering.