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

Authors: Gang Li
Journal: Advances in Power Electronics
 (2015)

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## Abstract

Compared with AC-DC-AC converter, matrix converter (MC) has several advantages for its bidirectional power flow, controllable power factor, and the absence of large energy storage in dc-link. The topology of MC includes direct matrix converter (DMC) and indirect matrix converter (IMC). IMC has received great attention worldwide because of its easy implementation and safe commutation. Space vector PWM (SVM) algorithm for indirect matrix converter is realized on DSP and CPLD platform in this paper. The control of the rectifier and inverter in IMC can be decoupled because of the intermediate dc-link. The space vector modulation scheme for IMC is discussed and the PWM sequences for the rectifier and inverter are generated. And a two-step commutation of zero current switching (ZCS) in the rectifier is achieved. Input power factor of IMC can be changed by adjusting the angle of the reference current vector. Experimental tests have been conducted on a RB-IGBT based indirect matrix converter prototype. The results verify the performance of the SVM algorithm and the ability of power factor correction.


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## Body

## 1. 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 [2–6]. 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 [8–13]. 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 [14–16], 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.Figure 1
Topology of indirect matrix converter using RB-IGBT.The PWM strategies in [7–13] are proposed for DMC. In [19–22], 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 [23–26], 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 current-source 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 zero-current 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.


## 2. 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 Figure2.Figure 2
Control principle of the rectifier.Three phase input currents can be defined as follows:(1)ij=Sj·idcj=a,b,c.In (1), Sj is the switch function. Sj can be 1, 0, and −1, which are shown in Figure 3. The switching functions of the rectifier are shown in Table 1.Table 1
Switching functions of the rectifier.
Number
S
a
S
b
S
c
1
1
0
−1
2
0
1
−1
3
−1
1
0
4
−1
0
1
5
0
−1
1
6
1
−1
0
7
0
0
0Figure 3
The statues ofSa.
(a)
S
a
=
1
(b)
S
a
=
-
1
(c)
S
a
=
0Current space vector can be defined as follows:(2)I=ia+ib·ej2π/3+ic·e-j2π/3.From (1) and (2), (3)I=idcSa+Sb·ej2π/3+Sc·e-j2π/3.The principle of space vector modulation (SVM) is shown in Figure4. Iref is the reference current space vector. θin is the angle of Iref.Figure 4
Current space vectors of the rectifier.According to the principle of space vector PWM,(4)t1=mrecTssin⁡π/2-θinsin⁡π/3,t2=mrecTssin⁡θin-π/6sin⁡π/3,t0=Ts-t1-t2,(5)d1=t1Ts,d2=t2Ts,d0=t0Ts.In (4), mrec is modulation index for the rectifier, which can be defined as (6)mrec=IrefIdc.In order to ensure the sinusoidal input current, the modulation indexmrec cannot be larger than 1,(7)mrec⩽1.In order to maintain the input power factor as unity, phase angle ofIref, θin should follow the phase angle of input space vector voltage Uin, so the voltage of dc-link is as follows:(8)Udc=mrec·Uin,(9)Uin=ua+ub·ej2π/3+uc·e-j2π/3.In (9), ua, ub, and uc are the three phase voltages of input sides. In order to obtain the maximum voltage ratio of the rectifier, mrec 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 Figure5:(10)T1=minvTssin⁡π/3-θsin⁡π/3,T2=minvTssin⁡θsin⁡π/3,T0=Ts-T1-T2,D1=T1Ts,D2=T2Ts,D0=T0Ts,minv=UrefUdc.Figure 5
SVPWM for inverter when0<θ≤π/3.In (10), Ts is the period of a switching cycle. minv is the modulation index of inverter. D0, D1, and D2 are the duty cycles of the zero vectors, vectors V1 and V2, respectively. Uref is the reference space voltage vector and Udc 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 D0, D1, and D2 will be simple.


### 2.2. 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. Figure6 is the process of four-step commutation with voltage signal. tc0, tc1, tc2, and tc3 are the times for four-step commutation.Figure 6
Four-step commutation for bidirectional switches of RB-IGBT with voltage signal.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 Figure7 and ZCS commutation is shown in Figure 8. tc0 and tc1 are the switching times for two-step commutation.Figure 7
PWM sequence for IMC.Figure 8
Two-step commutation for bidirectional switches of ZCS.Compared with the conventional PWM algorithm [19–22], 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 dc-link can be omitted.


### 2.3. 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 Figure9. 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.Figure 9
Control platform based on DSP and CPLD.The 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 Figure10, 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 (11), where Si+ is the upper bridge and Si- is the lower bridge, i=a,b,c.Figure 10
PWM segments generated by DSP.According to the SVM algorithm for rectifier, the commutation of bidirectional switches occurs between the upper bridges (Sa+,Sb+,Sc+) and lower bridges (Sa-,Sb-,Sc-). From Figure 4, the input current vector I1(1,0,-1) will change to I2(0,1,-1), and the commutation is Sa+ to Sb+. The commutation process can be described by the state of RB-IGBTs in the rectifier Sa+Sa-Sb+Sb-Sc+Sc-. The process of commutation is 100001-000001-001001. Because the commutation is zero-current switching, the commutation of rectifier is the same as inverter. Only the dead time is needed:(11)Sa+=Sci1+Sci6·1⊕PWM2+Sci2·PWM1+Sci4·PWM1⊕PWM2,Sa-=Sci4+Sci3·1⊕PWM2+Sci5·PWM1+Sci1·PWM1⊕PWM2,Sb+=Sci3+Sci2·1⊕PWM2+Sci4·PWM1+Sci6·PWM1⊕PWM2,Sb-=Sci6+Sci5·1⊕PWM2+Sci1·PWM1+Sci3·PWM1⊕PWM2,Sc+=Sci5+Sci4·1⊕PWM2+Sci6·PWM1+Sci2·PWM1⊕PWM2,Sc-=Sci2+Sci1·1⊕PWM2+Sci3·PWM1+Sci5·PWM1⊕PWM2.


## 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 Figure2.Figure 2
Control principle of the rectifier.Three phase input currents can be defined as follows:(1)ij=Sj·idcj=a,b,c.In (1), Sj is the switch function. Sj can be 1, 0, and −1, which are shown in Figure 3. The switching functions of the rectifier are shown in Table 1.Table 1
Switching functions of the rectifier.
Number
S
a
S
b
S
c
1
1
0
−1
2
0
1
−1
3
−1
1
0
4
−1
0
1
5
0
−1
1
6
1
−1
0
7
0
0
0Figure 3
The statues ofSa.
(a)
S
a
=
1
(b)
S
a
=
-
1
(c)
S
a
=
0Current space vector can be defined as follows:(2)I=ia+ib·ej2π/3+ic·e-j2π/3.From (1) and (2), (3)I=idcSa+Sb·ej2π/3+Sc·e-j2π/3.The principle of space vector modulation (SVM) is shown in Figure4. Iref is the reference current space vector. θin is the angle of Iref.Figure 4
Current space vectors of the rectifier.According to the principle of space vector PWM,(4)t1=mrecTssin⁡π/2-θinsin⁡π/3,t2=mrecTssin⁡θin-π/6sin⁡π/3,t0=Ts-t1-t2,(5)d1=t1Ts,d2=t2Ts,d0=t0Ts.In (4), mrec is modulation index for the rectifier, which can be defined as (6)mrec=IrefIdc.In order to ensure the sinusoidal input current, the modulation indexmrec cannot be larger than 1,(7)mrec⩽1.In order to maintain the input power factor as unity, phase angle ofIref, θin should follow the phase angle of input space vector voltage Uin, so the voltage of dc-link is as follows:(8)Udc=mrec·Uin,(9)Uin=ua+ub·ej2π/3+uc·e-j2π/3.In (9), ua, ub, and uc are the three phase voltages of input sides. In order to obtain the maximum voltage ratio of the rectifier, mrec 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 Figure5:(10)T1=minvTssin⁡π/3-θsin⁡π/3,T2=minvTssin⁡θsin⁡π/3,T0=Ts-T1-T2,D1=T1Ts,D2=T2Ts,D0=T0Ts,minv=UrefUdc.Figure 5
SVPWM for inverter when0<θ≤π/3.In (10), Ts is the period of a switching cycle. minv is the modulation index of inverter. D0, D1, and D2 are the duty cycles of the zero vectors, vectors V1 and V2, respectively. Uref is the reference space voltage vector and Udc 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 D0, D1, and D2 will be simple.


## 2.2. 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. Figure6 is the process of four-step commutation with voltage signal. tc0, tc1, tc2, and tc3 are the times for four-step commutation.Figure 6
Four-step commutation for bidirectional switches of RB-IGBT with voltage signal.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 Figure7 and ZCS commutation is shown in Figure 8. tc0 and tc1 are the switching times for two-step commutation.Figure 7
PWM sequence for IMC.Figure 8
Two-step commutation for bidirectional switches of ZCS.Compared with the conventional PWM algorithm [19–22], 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 dc-link can be omitted.


## 2.3. 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 Figure9. 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.Figure 9
Control platform based on DSP and CPLD.The 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 Figure10, 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 (11), where Si+ is the upper bridge and Si- is the lower bridge, i=a,b,c.Figure 10
PWM segments generated by DSP.According to the SVM algorithm for rectifier, the commutation of bidirectional switches occurs between the upper bridges (Sa+,Sb+,Sc+) and lower bridges (Sa-,Sb-,Sc-). From Figure 4, the input current vector I1(1,0,-1) will change to I2(0,1,-1), and the commutation is Sa+ to Sb+. The commutation process can be described by the state of RB-IGBTs in the rectifier Sa+Sa-Sb+Sb-Sc+Sc-. The process of commutation is 100001-000001-001001. Because the commutation is zero-current switching, the commutation of rectifier is the same as inverter. Only the dead time is needed:(11)Sa+=Sci1+Sci6·1⊕PWM2+Sci2·PWM1+Sci4·PWM1⊕PWM2,Sa-=Sci4+Sci3·1⊕PWM2+Sci5·PWM1+Sci1·PWM1⊕PWM2,Sb+=Sci3+Sci2·1⊕PWM2+Sci4·PWM1+Sci6·PWM1⊕PWM2,Sb-=Sci6+Sci5·1⊕PWM2+Sci1·PWM1+Sci3·PWM1⊕PWM2,Sc+=Sci5+Sci4·1⊕PWM2+Sci6·PWM1+Sci2·PWM1⊕PWM2,Sc-=Sci2+Sci1·1⊕PWM2+Sci3·PWM1+Sci5·PWM1⊕PWM2.


## 3. 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 Figure11. The phase difference of current vector and voltage vector is φ and power factor is cos⁡φ.Figure 11
The principle of power factor control.It is assumed that, on the input side,(12)ua=Umcos⁡ωit,ub=Umcos⁡ωit-2π3,uc=Umcos⁡ωit+2π3.And the reference input currents are(13)ia=Imcos⁡ωit-φ,ib=Imcos⁡ωit-2π3-φ,ic=Imcos⁡ωit+2π3-φ.The active power on input side is(14)P=uaia+ubib+ucic=32UmImcos⁡φ.From (14), φ is power angle. When φ>0, IMC absorbs reactive power. When φ<0, IMC generates reactive power.From Figure1, the inverter of IMC is voltage source converter. The voltage of dc-link upn should be positive. Otherwise, the reverse recovery diode for IGBT will be short-circuited 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 Table2.Table 2
Sectors of input current space vector.
Input sector
Phase angleωit
1
[
-
π
/
6
,
π
/
6
)
2
[
π
/
6
,
π
/
2
)
3
[
π
/
2,5
π
/
6
)
4
[
5
π
/
6,7
π
/
6
)
5
[
7
π
/
6,3
π
/
2
)
6
[
3
π
/
2,11
π
/
6
)According to Table2, 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.Table 3
Relationship of line voltage and phase angle.
Sector
Line-line voltage
Phase angleωit
1
u
a
b
≥
0
u
a
c
≥
0
[
-
π
/
3
,
π
/
3
)
2
u
a
c
≥
0
u
b
c
≥
0
[
0,2
π
/
3
)
3
u
b
c
≥
0
u
b
a
≥
0
[
π
/
3
,
π
)
4
u
b
a
≥
0
u
c
a
≥
0
[
2
π
/
3,4
π
/
3
)
5
u
c
a
≥
0
u
c
b
≥
0
[
π
,
5
π
/
3
)
6
u
c
b
≥
0
u
a
b
≥
0
[
4
π
/
3,2
π
)Figure 12
Input voltage interval and sector of input current space vector.
(a)
Input voltage intervals
(b)
Sector of input current space vectorIn order to maintain the dc-link voltage being positive, the regulation range ofφ is -π/6,π/6. In the applications of power factor control, the parameter of input LC filters has effect of power factor control. The simplified circuit of input LC filters is shown in Figure 13.Figure 13
Simplified circuit of inputLC filters.In Figure13, Us is input source voltage vector. Is is input source current vector. Uin and Iin are input voltage and current vector. Because Uin will be influenced by SVM algorithm, Us is used as the reference input voltage vector. Iin is the reference input current vector. The parameters of input LC filters are La=Lb=Lc=L=0.7 mH, Ca=Cb=Cc=C=20 μF. Assume that input source voltage vector is Us=Um∠α and input current vector is Iin=Im∠α-φ. Im is decided by the load current and can be calculated with the modulation index of IMC and the amplitude of output currents.From Figure13, the differential equations for LC filters can be built as follows:(15)Us-Uin=LdIsdt,Is-Iin=CdUindt.Then, the input source currentIs is as follows:(16)LCd2Isdt2+Is-Iin+CdUsdt=0.Considering the fundamental part of input current and ignoring harmonics current and dynamic process, input source current is expressed asIs=Ix∠β. From (16), (17)Ix1-LCωi2∠β=Im∠α-φ-CωiUm∠α-12π.The amplitude and angle of input source current can be got as follows:(18)Ix=Im2+CωiUm2-2CωiUmImsin⁡φ1-LCωi2,β=α+arctan⁡CωiUm-Imsin⁡φImcos⁡φ.From (18), power angle is related to the capacitor of LC filters, the amplitude of load current, and the angle of reference input current vector.


## 4. Experimental Results

The prototype of RB-IGBT based indirect matrix converter has been developed, shown in Figure14. 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 14
Prototype of RB-IGBT based indirect matrix converter.In order to verify the proposed PWM algorithm and sequence, experimental tests on IMC prototype have been carried out. The parameters of the input filters areL=0.7 mH, C=20 μF, and R=200 Ω. The sampling frequency is 10 kHz. Input voltage is 50 Hz and output frequency is 25 Hz. The load is an induction motor.Figure15 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 Sap-Usap and dc-link current idc 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.Figure 15
Experimental waveforms of proposed PWM algorithm.
(a)
Input phase voltage (25 V/div) and current (5 A/div)
(b)
Output line-to-line (25 V/div) and current (5 A/div)Figure 16
The voltage (25 V/div) across RB-IGBT and the dc-link current (5 A/div) during zero-current switching.The waveforms of input voltage and current when the power factor angle is setting as −2π/15, zero, and 2π/15 are shown in Figures 17–19, respectively.Figure 17
The experiment waveforms of input (25 V/div) and current (5 A/div) when power factor angle is −2π/15.Figure 18
The experiment waveforms of input (25 V/div) and current (5 A/div) when power factor angle is zero.Figure 19
The experiment waveforms of input (25 V/div) and current (5 A/div) when power factor angle is 2π/15.The power factor angle of experiment can be shown in Table4. The theoretical value of power factor angle can be calculated by expression (18).Table 4
Comparison of theoretical value and experimental result of power factor angle.
Setting power factor angle
Calculated by (18)
Experimental result
φ
=
-
24
°
-
26.3
°
-
28.8
°
φ
=
0
-
7.7
°
-
14.4
°
φ
=
24
°
14
°
10.8
°


## 5. 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[-π/6,π/6]. The influence of the parameters in LC 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.



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