Realization of SVM Algorithm for Indirect Matrix Converter and Its Application in Power Factor Control

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Introduction
AC/AC conversion has two main types: AC-DC-AC converters and direct AC/AC converters.AC-DC-AC converters include the current and voltage source topologies with a capacitor or inductor in the dc-link.Direct AC/AC converters include the cycloconverter of high-power applications and matrix converters in low power range [1].Matrix converter has a compact structure without capacitor or inductor, which has received much attention in the academic and industrial fields worldwide in recent years [2][3][4][5][6].Since Alesina and Venturini proposed a control method for matrix converter using a mathematical approach to generate the desired output voltage [7], the PWM algorithms for matrix converters become a research focus.New PWM strategies for matrix converters have been proposed in recent years [8][9][10][11][12][13].Some researcher concentrated on the realization of the PWM schemes, such as dipolar modulation technique [8], SHE-PWM [9], and beatless synchronous PWM [10].The PWM strategies for matrix converter are also proposed to reduce the ripple in the input and output waveforms [11,12].In the high-power applications, indirect SVPWM for multimodular matrix converters is realized [13].
The topologies of matrix converter, including direct matrix converter and indirect matrix converter [14][15][16], are another research focus in AC/AC conversion.Compared with the former one, IMC has several advantages.(1) With a real dc-link, the converter consists of two stages, a rectifier and an inverter.The control of the two stages can be decoupled and the control difficulty is lowered down.(2) With appropriate modulation method, zero-current switching commutation in the rectifier can be simply accomplished.The system efficiency is improved.(3) The number of power switches can be further reduced.(4) With the dc-link, multioutput IMC can be realized [17,18].The topology of IMC is shown in Figure 1.The bidirectional switch in the rectifier stage is composed by two RB-IGBTs.
The PWM strategies in [7][8][9][10][11][12][13] are proposed for DMC.In [19][20][21][22], the conventional PWM algorithm, based on two larger source line voltages, is proposed.The PWM period of the rectifier stage is divided in two segments to reduce the switching times and the harmonics of the input current.But these PWM strategies have no zero vectors.In [23][24][25][26], carrier-PWM realization and overmodulation method for IMC are discussed.In the applications of indirect matrix converter, [27] proposes IMC to control doubly fed induction generation for wind power system.IMC is used to control a microturbine generator [28].A multimodular indirect matrix converter topology is proposed to be a frequency converter used in the medium-voltage motion drive systems [29].And three level neutral-point-clamped indirect matrix converters are proposed in [30].
In this paper, the rectifier is controlled as a currentsource converter and inverter is controlled as a voltage-source converter.SVM is applied for the rectifier and SVPWM is applied for the inverter.The PWM sequence for indirect matrix converter is achieved.Two-step commutation of zerocurrent switching for the rectifier is presented.The principle of the input power factor correction for IMC is discussed.The design and implementation of indirect matrix converter prototype using RB-IGBT are introduced.The experimental results are shown to verify the performance of the proposed PWM algorithm and the ability of PFC.

Space Vector Modulation of IMC
2.1.PWM Algorithm of IMC.The control of the rectifier and inverter for IMC can be decoupled because of the dc-link.The rectifier is controlled as a current-source converter, and the inverter can be seen as an inductive load in dc-link, shown in Figure 2.
Three phase input currents can be defined as follows: In (1),   is the switch function.  can be 1, 0, and −1, which are shown in Figure 3.The switching functions of the rectifier are shown in Table 1.
Current space vector can be defined as follows: From ( 1) and ( 2),  =  dc (  +   ⋅ e 2/3 +   ⋅ e −2/3 ) .Table 1: Switching functions of the rectifier.The principle of space vector modulation (SVM) is shown in Figure 4.  ref is the reference current space vector. in is the angle of  ref .
According to the principle of space vector PWM, In ( 4),  rec is modulation index for the rectifier, which can be defined as In order to ensure the sinusoidal input current, the modulation index  rec cannot be larger than 1, In order to maintain the input power factor as unity, phase angle of  ref ,  in should follow the phase angle of input space vector voltage  in , so the voltage of dc-link is as follows: In ( 9),   ,   , and   are the three phase voltages of input sides.In order to obtain the maximum voltage ratio of the rectifier,  rec should be 1.
The inverter is controlled as voltage source converter, and the rectifier can be seen as a voltage source in dc-link.The conventional SVPWM algorithm can be used in the inverter, shown in Figure 5: Figure 5: SVPWM for inverter when 0 <  ≤ /3.
In (10),   is the period of a switching cycle. inv is the modulation index of inverter. 0 ,  1 , and  2 are the duty cycles of the zero vectors, vectors  1 and  2 , respectively. ref is the reference space voltage vector and  dc is the voltage of dc-link.
From ( 8) and ( 9), when the input voltages are symmetrical, the voltage of dc-link is constant.The modulation index of inverter is determined by the reference output space voltage vector.The calculation of duty cycles  0 ,  1 , and  2 will be simple.

Commutation and PWM Sequence.
Generally, a bidirectional switch in matrix converters is constructed by two IGBTs and two diodes or two RB-IGBTs.Commutations between two bidirectional switches need four steps with voltage/current signal.Figure 6 is the process of four-step commutation with voltage signal. 0 ,  1 ,  2 , and  3 are the times for four-step commutation.
In IMC, the inverter is a conventional voltage source converter and its commutation is traditional.When the inverter is on zero-vector state, the current of dc-link is zero.The commutation of the bidirectional switches in the rectifier can be achieved during this period, and zero-current switching commutation can be realized.The PWM sequence of IMC is shown in Figure 7 and ZCS commutation is shown in Figure 8.  0 and  1 are the switching times for two-step commutation.
Compared with the conventional PWM algorithm [19][20][21][22], the proposed PWM algorithm increases one switching action in rectifier, which is a ZCS process.ZCS commutation is much simpler than four-step commutation and it needs no voltage or current signals.So voltage or current sensor in dclink can be omitted.

Realization of SVM Algorithm and Commutation Method.
In order to realize the SVM algorithm and commutation strategy, a control platform based on DSP and CPLD is implemented, shown in Figure 9. DSP TMS320F2812 of TI is to realize SVM algorithm and CPLD EPM9320LC84-15 of Altera is to realize the commutation strategy for bidirectional switches in rectifier.
The  (11), where  + is the upper bridge and  − is the lower bridge,  = , , .

Power Factor Control of IMC
According to the SVM algorithm, power factor of IMC can be controlled by changing the angle of the reference input current vector, shown in Figure 11.The phase difference of current vector and voltage vector is  and power factor is cos .
It is assumed that, on the input side, And the reference input currents are The active power on input side is From ( 14),  is power angle.When  > 0, IMC absorbs reactive power.When  < 0, IMC generates reactive power.
From Figure 1, the inverter of IMC is voltage source converter.The voltage of dc-link  pn should be positive.Otherwise, the reverse recovery diode for IGBT will be shortcircuited and the semiconductor may be damaged.
The sectors of input current space vector can be divided by the angle of input voltage space vector, which is shown in Table 2.
According to Table 2, the corresponding relationship of input sector and input voltage interval is shown in Figure 12.Input sector I-VI is corresponding with voltage interval 1-6.In order to maintain the DC-link voltage being positive, the relationship of line voltage and phase angle in each sector is shown in Table 3.
In order to maintain the dc-link voltage being positive, the regulation range of  is [−/6, /6].In the applications of power factor control, the parameter of input  filters has effect of power factor control.The simplified circuit of input  filters is shown in Figure 13.
In Figure 13,   is input source voltage vector.  is input source current vector. in and  in are input voltage  From Figure 13, the differential equations for  filters can be built as follows: Then, the input source current   is as follows:   Considering the fundamental part of input current and ignoring harmonics current and dynamic process, input source current is expressed as   =   ∠.From (16), The amplitude and angle of input source current can be got as follows: From ( 18), power angle is related to the capacitor of  filters, the amplitude of load current, and the angle of reference input current vector.

Experimental Results
The prototype of RB-IGBT based indirect matrix converter has been developed, shown in Figure 14.It mainly includes power circuit, RB-IGBT gate drive circuit, signal processing circuit, CPLD and DSP based control board, and heat sink.The rectifier is composed of the RB-IGBT module 18MBI100W-060A from Fuji Electric [31]. Figure 15 gives the experimental waveforms of SVM algorithm.The THD of output current is 1.06%.The THD of input current is 6.39%.Figure 16 shows the voltage of the bidirectional switch  ap - sap and dc-link current  dc when the commutation of bidirectional switches occurs.It can be seen that dc-link current is around zero at the commutation point, which means that zero-current switching is realized.
The waveforms of input voltage and current when the power factor angle is setting as −2/15, zero, and 2/15 are shown in Figures 17-19, respectively.
The power factor angle of experiment can be shown in Table 4.The theoretical value of power factor angle can be calculated by expression (18).

Conclusions
In this paper, a SVM algorithm for indirect matrix converter with zero-current switching commutation for bidirectional switches is realized based on a control platform of DSP and CPLD.SVM for the rectifier and SVPWM for the inverter stage are described.PWM sequence of the SVM algorithm can achieve two-step ZCS commutation for the rectifier bidirectional switches.The realization of PWM sequence by DSP and decoding process for drive signals of RB-IGBTs by CPLD are explained in detail.Based on the modulation strategy, input power factor correction of IMC is discussed.Because the inverter of IMC is VSI, the dc-link voltage should be positive and the regulation range of power angle is [−/6, /6].The influence of the parameters in  filters is analyzed.A prototype of RB-IGBT based indirect matrix converter is implemented.The experimental results show the performance of SVM algorithm and validate the analysis of power factor control of IMC.

Figure 4 :
Figure 4: Current space vectors of the rectifier.
input sectors Sci1∼Sci6 and output sectors Svo1∼Svi6 are determined with the angle of input voltage and output voltage with DSP.And 8 PWM signals, which are shown in Figure 10, are generated by SVM and SVPWM algorithms with DSP.The 8 PWM signals are not the drive signals for the IGBTs.A decoder for drive signals is needed.CPLD is used to decode drive signals from PWM sequences and realize two-step ZCS commutation.With the PWM signals PWM1-8, input sectors, and output sectors, the drive signals for the bidirectional switches can be shown as expression

Figure 6 :
Figure 6: Four-step commutation for bidirectional switches of RB-IGBT with voltage signal.

Figure 12 :
Figure 12: Input voltage interval and sector of input current space vector.

Table 2 :
Sectors of input current space vector.

Table 3 :
Relationship of line voltage and phase angle.

Table 4 :
Comparison of theoretical value and experimental result of power factor angle.