Research Article Realization of SVM Algorithm for Indirect ...Research Article Realization of SVM...
Transcript of Research Article Realization of SVM Algorithm for Indirect ...Research Article Realization of SVM...
Research ArticleRealization of SVM Algorithm for Indirect Matrix Converter andIts Application in Power Factor Control
Gang Li
College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130061, China
Correspondence should be addressed to Gang Li; [email protected]
Received 18 June 2015; Revised 14 August 2015; Accepted 26 August 2015
Academic Editor: Don Mahinda Vilathgamuwa
Copyright Β© 2015 Gang Li. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Compared with AC-DC-AC converter, matrix converter (MC) has several advantages for its bidirectional power flow, controllablepower 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 safecommutation. Space vector PWM (SVM) algorithm for indirect matrix converter is realized on DSP and CPLD platform in thispaper. The control of the rectifier and inverter in IMC can be decoupled because of the intermediate dc-link. The space vectormodulation scheme for IMC is discussed and the PWM sequences for the rectifier and inverter are generated. And a two-stepcommutation of zero current switching (ZCS) in the rectifier is achieved. Input power factor of IMC can be changed by adjustingthe angle of the reference current vector. Experimental tests have been conducted on a RB-IGBT based indirect matrix converterprototype. The results verify the performance of the SVM algorithm and the ability of power factor correction.
1. Introduction
AC/AC conversion has two main types: AC-DC-AC con-verters and direct AC/AC converters. AC-DC-AC convertersinclude the current and voltage source topologies with acapacitor or inductor in the dc-link.DirectAC/ACconvertersinclude the cycloconverter of high-power applications andmatrix converters in low power range [1]. Matrix converterhas a compact structure without capacitor or inductor, whichhas received much attention in the academic and industrialfields worldwide in recent years [2β6]. Since Alesina andVenturini proposed a control method for matrix converterusing amathematical approach to generate the desired outputvoltage [7], the PWM algorithms for matrix convertersbecome a research focus. New PWM strategies for matrixconverters have been proposed in recent years [8β13]. Someresearcher concentrated on the realization of the PWMschemes, such as dipolar modulation technique [8], SHE-PWM [9], and beatless synchronous PWM [10]. The PWMstrategies for matrix converter are also proposed to reducethe ripple in the input and output waveforms [11, 12]. In thehigh-power applications, indirect SVPWM formultimodularmatrix converters is realized [13].
The topologies of matrix converter, including directmatrix converter and indirect matrix converter [14β16], areanother research focus inAC/ACconversion. Comparedwiththe former one, IMC has several advantages. (1) With a realdc-link, the converter consists of two stages, a rectifier and aninverter. The control of the two stages can be decoupled andthe control difficulty is lowered down. (2) With appropriatemodulation method, zero-current switching commutationin the rectifier can be simply accomplished. The systemefficiency is improved. (3) The number of power switchescan be further reduced. (4) With the dc-link, multioutputIMC can be realized [17, 18]. The topology of IMC is shownin Figure 1. The bidirectional switch in the rectifier stage iscomposed by two RB-IGBTs.
The PWM strategies in [7β13] are proposed for DMC.In [19β22], the conventional PWM algorithm, based on twolarger source line voltages, is proposed. The PWM periodof the rectifier stage is divided in two segments to reducethe switching times and the harmonics of the input current.But these PWM strategies have no zero vectors. In [23β26],carrier-PWM realization and overmodulation method forIMC are discussed.
Hindawi Publishing CorporationAdvances in Power ElectronicsVolume 2015, Article ID 740470, 10 pageshttp://dx.doi.org/10.1155/2015/740470
2 Advances in Power Electronics
Input filter Rectifier stage based onRB-IGBT
Clampcircuit
Inverter stage
A
C
B
a
b
c
p
n
M
Figure 1: Topology of indirect matrix converter using RB-IGBT.
Load
a
b
c
idc
Sa Sb Sc
ia
ib
ic
ub
ua
uc
Figure 2: Control principle of the rectifier.
In the applications of indirect matrix converter, [27]proposes IMC to control doubly fed induction generation forwind power system. IMC is used to control a microturbinegenerator [28]. A multimodular indirect matrix convertertopology is proposed to be a frequency converter used inthe medium-voltage motion drive systems [29]. And threelevel neutral-point-clamped indirect matrix converters areproposed in [30].
In this paper, the rectifier is controlled as a current-source converter and inverter is controlled as a voltage-sourceconverter. SVM is applied for the rectifier and SVPWM isapplied for the inverter. The PWM sequence for indirectmatrix converter is achieved. Two-step commutation of zero-current switching for the rectifier is presented. The principleof the input power factor correction for IMC is discussed.The design and implementation of indirect matrix converterprototype using RB-IGBT are introduced. The experimentalresults are shown to verify the performance of the proposedPWM algorithm and the ability of PFC.
2. Space Vector Modulation of IMC
2.1. PWM Algorithm of IMC. The control of the rectifier andinverter for IMC can be decoupled because of the dc-link.Therectifier is controlled as a current-source converter, and theinverter can be seen as an inductive load in dc-link, shown inFigure 2.
Three phase input currents can be defined as follows:
ππ = ππ β πdc π = π, π, π. (1)
In (1), ππ is the switch function. ππ can be 1, 0, and β1,which are shown in Figure 3. The switching functions of therectifier are shown in Table 1.
Current space vector can be defined as follows:
πΌ = ππ + ππ β eπ2π/3
+ ππ β eβπ2π/3
. (2)
From (1) and (2),
πΌ = πdc (ππ + ππ β eπ2π/3
+ ππ β eβπ2π/3
) . (3)
Advances in Power Electronics 3
Sa
(a) ππ = 1
Sa
(b) ππ = β1
Sa Sa
(c) ππ = 0
Figure 3: The statues of ππ.
Table 1: Switching functions of the rectifier.
Number ππ ππ ππ
1 1 0 β12 0 1 β13 β1 1 04 β1 0 15 0 β1 16 1 β1 07 0 0 0
b
c
I
IIIII
IV
V VI
I3(β1 1 0)
I2(0 1 β1)
I4(β1 0 1)
I1(1 0 β1)
I5(0 β 1 1)
I6(1 β 1 0)
Iref
πin a
Figure 4: Current space vectors of the rectifier.
The principle of space vectormodulation (SVM) is shownin Figure 4. πΌref is the reference current space vector. πin is theangle of πΌref .
According to the principle of space vector PWM,
π‘1 =πrecππ sin (π/2 β πin)
sin (π/3),
π‘2 =πrecππ sin (πin β π/6)
sin (π/3),
π‘0 = ππ β π‘1 β π‘2,
(4)
π1 =π‘1
ππ
,
π2 =π‘2
πs,
π0 =π‘0
ππ
.
(5)
In (4), πrec is modulation index for the rectifier, whichcan be defined as
πrec =πΌrefπΌdc
. (6)
In order to ensure the sinusoidal input current, themodulation indexπrec cannot be larger than 1,
πrec β©½ 1. (7)
In order tomaintain the input power factor as unity, phaseangle of πΌref , πin should follow the phase angle of input spacevector voltage πin, so the voltage of dc-link is as follows:
πdc = πrec β πin, (8)
πin = π’π + π’π β eπ2π/3
+ π’π β eβπ2π/3
. (9)
In (9), π’π, π’π, and π’π are the three phase voltages of inputsides. In order to obtain the maximum voltage ratio of therectifier,πrec should be 1.
The inverter is controlled as voltage source converter, andthe rectifier can be seen as a voltage source in dc-link. Theconventional SVPWM algorithm can be used in the inverter,shown in Figure 5:
π1 =πinvππ sin (π/3 β π)
sin (π/3),
π2 =πinvππ sin (π)sin (π/3)
,
4 Advances in Power Electronics
1 1 10 0 0
I
II
III
IV
V
VI
Vref
V1 Β· T1
V2 Β· T2
π
V5(1 0 0) V6(1 0 1)
V4(1 1 0)
V3(0 1 0) V2(0 1 1)
V1(0 0 1)
Figure 5: SVPWM for inverter when 0 < π β€ π/3.
π0 = ππ β π1 β π2,
π·1 =π1
ππ
,
π·2 =π2
ππ
,
π·0 =π0
ππ
,
πinv =πrefπdc
.
(10)
In (10), ππ is the period of a switching cycle. πinv is themodulation index of inverter. π·0, π·1, and π·2 are the dutycycles of the zero vectors, vectorsπ1 andπ2, respectively.πrefis the reference space voltage vector and πdc is the voltage ofdc-link.
From (8) and (9), when the input voltages are symmetri-cal, the voltage of dc-link is constant.Themodulation index ofinverter is determined by the reference output space voltagevector. The calculation of duty cycles π·0, π·1, and π·2 will besimple.
2.2. Commutation and PWM Sequence. Generally, a bidi-rectional switch in matrix converters is constructed by twoIGBTs and two diodes or two RB-IGBTs. Commutationsbetween two bidirectional switches need four steps withvoltage/current signal. Figure 6 is the process of four-stepcommutation with voltage signal. π‘π0, π‘π1, π‘π2, and π‘π3 are thetimes for four-step commutation.
In IMC, the inverter is a conventional voltage sourceconverter and its commutation is traditional. When theinverter is on zero-vector state, the current of dc-link iszero. The commutation of the bidirectional switches in therectifier can be achieved during this period, and zero-currentswitching commutation can be realized. The PWM sequenceof IMC is shown in Figure 7 and ZCS commutation is shown
in Figure 8. π‘π0 and π‘π1 are the switching times for two-stepcommutation.
Compared with the conventional PWM algorithm [19β22], the proposed PWM algorithm increases one switchingaction in rectifier, which is a ZCS process. ZCS commutationis much simpler than four-step commutation and it needs novoltage or current signals. So voltage or current sensor in dc-link can be omitted.
2.3. Realization of SVMAlgorithm and CommutationMethod.In order to realize the SVM algorithm and commutationstrategy, a control platform based on DSP and CPLD isimplemented, shown in Figure 9. DSP TMS320F2812 of TIis to realize SVM algorithm and CPLD EPM9320LC84-15 ofAltera is to realize the commutation strategy for bidirectionalswitches in rectifier.
The input sectors Sci1βΌSci6 and output sectors Svo1βΌSvi6are determined with the angle of input voltage and outputvoltage with DSP. And 8 PWM signals, which are shown inFigure 10, are generated by SVM and SVPWM algorithmswith DSP.The 8 PWM signals are not the drive signals for theIGBTs. A decoder for drive signals is needed. CPLD is usedto decode drive signals from PWM sequences and realizetwo-step ZCS commutation. With the PWM signals PWM1β8, input sectors, and output sectors, the drive signals for thebidirectional switches can be shown as expression (11), whereππ+ is the upper bridge and ππβ is the lower bridge, π = π, π, π.
According to the SVM algorithm for rectifier, the com-mutation of bidirectional switches occurs between the upperbridges (ππ+, ππ+, ππ+) and lower bridges (ππβ, ππβ, ππβ). FromFigure 4, the input current vector πΌ1(1, 0, β1) will changeto πΌ2(0, 1, β1), and the commutation is ππ+ to ππ+. Thecommutation process can be described by the state of RB-IGBTs in the rectifier [ππ+ ππβ ππ+ ππβ ππ+ ππβ]. The pro-cess of commutation is [1 0 0 0 0 1]-[0 0 0 0 0 1]-[0 0 1 0 0 1]. Because the commutation is zero-currentswitching, the commutation of rectifier is the same asinverter. Only the dead time is needed:
ππ+ = Sci1 + Sci6 β (1 β PWM2) + Sci2 β PWM1
+ Sci4 β (PWM1 β PWM2) ,
ππβ = Sci4 + Sci3 β (1 β PWM2) + Sci5 β PWM1 + Sci1
β (PWM1 β PWM2) ,
ππ+ = Sci3 + Sci2 β (1 β PWM2) + Sci4 β PWM1
+ Sci6 β (PWM1 β PWM2) ,
ππβ = Sci6 + Sci5 β (1 β PWM2) + Sci1 β PWM1 + Sci3
β (PWM1 β PWM2) ,
ππ+ = Sci5 + Sci4 β (1 β PWM2) + Sci6 β PWM1
+ Sci2 β (PWM1 β PWM2) ,
ππβ = Sci2 + Sci1 β (1 β PWM2) + Sci3 β PWM1 + Sci5
β (PWM1 β PWM2) .
(11)
Advances in Power Electronics 5
Ua
Ub
Sap
Sap
tc0 tc1 tc2 tc3 tc0 tc1 tc2 tc3
Ua > Ub Ua < Ub
p
Sbp
Sbp
Spa Spa
Spb Spb
Sap
Sbp
Spa
Spb
Figure 6: Four-step commutation for bidirectional switches of RB-IGBT with voltage signal.
Inverter
Rectifier
Vector
Vector
0
0
1
d1 + d2
d1
d1
(D0/2 + D1 + D2)d1
(D0/2 + D1)d1
D0 Β· d2/2
V0 V0V0V1 V1V2 V2
d2(D0/2 + D1 + D2)d2(D0/2 + D1)d2
D0 Β· d1/2
Ts
I0I1 I2
Figure 7: PWM sequence for IMC.
Ua
Ub
SaSa
Sb
Sb
tc0 tc1
p
Sap
Sbp
Spa
Spb
Sap
Sbp
Spa
Spb
Figure 8: Two-step commutation for bidirectional switches of ZCS.
3. Power Factor Control of IMC
According to the SVM algorithm, power factor of IMC canbe controlled by changing the angle of the reference inputcurrent vector, shown in Figure 11. The phase difference ofcurrent vector and voltage vector is π and power factor iscosπ.
It is assumed that, on the input side,
π’π = ππ cos (πππ‘) ,
π’π = ππ cos(πππ‘ β2π
3) ,
π’π = ππ cos(πππ‘ +2π
3) .
(12)
Table 2: Sectors of input current space vector.
Input sector Phase angle πππ‘1 [βπ/6, π/6)
2 [π/6, π/2)
3 [π/2, 5π/6)
4 [5π/6, 7π/6)
5 [7π/6, 3π/2)
6 [3π/2, 11π/6)
And the reference input currents are
ππ = πΌπ cos (πππ‘ β π) ,
ππ = πΌπ cos(πππ‘ β2π
3β π) ,
ππ = πΌπ cos(πππ‘ +2π
3β π) .
(13)
The active power on input side is
π = π’πππ + π’πππ + π’πππ =3
2πππΌπ cosπ. (14)
From (14), π is power angle. When π > 0, IMC absorbsreactive power. When π < 0, IMC generates reactive power.
From Figure 1, the inverter of IMC is voltage sourceconverter. The voltage of dc-link π’pn should be positive.Otherwise, the reverse recovery diode for IGBTwill be short-circuited and the semiconductor may be damaged.
The sectors of input current space vector can be dividedby the angle of input voltage space vector, which is shown inTable 2.
According to Table 2, the corresponding relationship ofinput sector and input voltage interval is shown in Figure 12.Input sector IβVI is corresponding with voltage interval 1β6.In order to maintain the DC-link voltage being positive, therelationship of line voltage and phase angle in each sector isshown in Table 3.
In order to maintain the dc-link voltage being positive,the regulation range of π is [βπ/6, π/6]. In the applicationsof power factor control, the parameter of input πΏπΆ filters haseffect of power factor control. The simplified circuit of inputπΏπΆ filters is shown in Figure 13.
In Figure 13, ππ is input source voltage vector. πΌπ isinput source current vector. πin and πΌin are input voltage
6 Advances in Power Electronics
DSP TMS320F2812
CPLD EPM9320LC84-15
Input sector signal
Output sector signal
8 PWM signals
Sampling and regulating
Input voltages
Output currents
Zero crossing
12 drive signals for rectifier
Protection of IPM
Drive and protection circuit of RB-IGBT IPM
Over current protection
6 drive signals for inverter
ub
ua
uc
iAiBiC
Figure 9: Control platform based on DSP and CPLD.
Inverter
Rectifier
Ts
t1 t3t2 t4 t5 t6 t7 t8 t
PWM1
PWM2
PWM3
PWM4
PWM5
PWM6
PWM7
PWM8
Figure 10: PWM segments generated by DSP.
and current vector. Because πin will be influenced by SVMalgorithm,ππ is used as the reference input voltage vector. πΌinis the reference input current vector. The parameters of inputπΏπΆ filters are πΏπ = πΏπ = πΏπ = πΏ = 0.7mH, πΆπ = πΆπ =
πΆπ = πΆ = 20 πF. Assume that input source voltage vector isππ = ππβ πΌ and input current vector is πΌin = πΌπβ (πΌ β π).πΌπ is decided by the load current and can be calculated withthe modulation index of IMC and the amplitude of outputcurrents.
a
b
c
π
Iref
U
Figure 11: The principle of power factor control.
From Figure 13, the differential equations for πΏπΆ filterscan be built as follows:
ππ β πin = πΏππΌπ
ππ‘,
πΌπ β πΌin = πΆππinππ‘
.
(15)
Then, the input source current πΌπ is as follows:
πΏπΆπ2πΌπ
ππ‘2+ πΌπ β (πΌin + πΆ
πππ
ππ‘) = 0. (16)
Advances in Power Electronics 7
1 2 3 4 5 6
ubua uc
t
U
(a) Input voltage intervals
I
IIIII
IV
V VI
I3(β1 1 0)
I2(0 1 β1)
I4(β1 0 1)
I5(0 β 1 1)
I6(1 β 1 0)
I1(1 0 β1)
b
a
c
(b) Sector of input current space vector
Figure 12: Input voltage interval and sector of input current space vector.
Table 3: Relationship of line voltage and phase angle.
Sector Line-line voltage Phase angle πππ‘1 π’ππ β₯ 0 π’ππ β₯ 0 [βπ/3, π/3)
2 π’ππ β₯ 0 π’ππ β₯ 0 [0, 2π/3)
3 π’ππ β₯ 0 π’ππ β₯ 0 [π/3, π)
4 π’ππ β₯ 0 π’ππ β₯ 0 [2π/3, 4π/3)
5 π’ππ β₯ 0 π’ππ β₯ 0 [π, 5π/3)
6 π’ππ β₯ 0 π’ππ β₯ 0 [4π/3, 2π)
Is Iin
Uin
La
Lb
Lc
CcCbCa
Us
Figure 13: Simplified circuit of input πΏπΆ filters.
Considering the fundamental part of input current andignoring harmonics current and dynamic process, inputsource current is expressed as πΌπ = πΌπ₯β π½. From (16),
πΌπ₯ (1 β πΏπΆπ2π ) β π½ = πΌπβ (πΌ β π)
β πΆππππβ (πΌ β1
2π) .
(17)
Figure 14: Prototype of RB-IGBT based indirect matrix converter.
The amplitude and angle of input source current can begot as follows:
πΌπ₯ =
β(πΌπ)2+ (πΆππππ)
2β 2πΆπππππΌπ sinπ
1 β πΏπΆπ2π
,
π½ = πΌ + arctan(πΆππππ β πΌπ sinπ
πΌπ cosπ) .
(18)
From (18), power angle is related to the capacitor ofπΏπΆ filters, the amplitude of load current, and the angle ofreference input current vector.
4. Experimental Results
The prototype of RB-IGBT based indirect matrix converterhas been developed, shown in Figure 14. It mainly includespower circuit, RB-IGBT gate drive circuit, signal processingcircuit, CPLD and DSP based control board, and heatsink. The rectifier is composed of the RB-IGBT module18MBI100W-060A from Fuji Electric [31].
8 Advances in Power Electronics
T
(a) Input phase voltage (25V/div) and current (5 A/div)
T
(b) Output line-to-line (25V/div) and current (5 A/div)
Figure 15: Experimental waveforms of proposed PWM algorithm.
T
Figure 16: The voltage (25V/div) across RB-IGBT and the dc-linkcurrent (5 A/div) during zero-current switching.
In order to verify the proposed PWM algorithm andsequence, experimental tests on IMC prototype have beencarried out. The parameters of the input filters are πΏ =
0.7mH,πΆ = 20 πF, andπ = 200Ξ©.The sampling frequency is10 kHz. Input voltage is 50Hz and output frequency is 25Hz.The load is an induction motor.
Figure 15 gives the experimental waveforms of SVMalgorithm. The THD of output current is 1.06%. The THDof input current is 6.39%. Figure 16 shows the voltage of thebidirectional switch πap-πsap and dc-link current πdc when thecommutation of bidirectional switches occurs. It can be seenthat 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 thepower factor angle is setting as β2π/15, zero, and 2π/15 areshown in Figures 17β19, respectively.
The power factor angle of experiment can be shown inTable 4. The theoretical value of power factor angle can becalculated by expression (18).
T
Figure 17: The experiment waveforms of input (25V/div) andcurrent (5 A/div) when power factor angle is β2π/15.
Table 4: Comparison of theoretical value and experimental resultof power factor angle.
Setting powerfactor angle Calculated by (18) Experimental result
π = β24β
β26.3β
β28.8β
π = 0 β7.7β
β14.4β
π = 24β
14β
10.8β
5. Conclusions
In this paper, a SVM algorithm for indirect matrix converterwith zero-current switching commutation for bidirectionalswitches is realized based on a control platform of DSP andCPLD. SVM for the rectifier and SVPWM for the inverterstage are described. PWM sequence of the SVM algorithmcan achieve two-step ZCS commutation for the rectifierbidirectional switches. The realization of PWM sequence byDSP and decoding process for drive signals of RB-IGBTs byCPLD are explained in detail.
Advances in Power Electronics 9
T
Figure 18: The experiment waveforms of input (25V/div) andcurrent (5 A/div) when power factor angle is zero.
T
Figure 19: The experiment waveforms of input (25V/div) andcurrent (5 A/div) when power factor angle is 2π/15.
Based on the modulation strategy, input power factorcorrection of IMC is discussed. Because the inverter ofIMC is VSI, the dc-link voltage should be positive and theregulation range of power angle is [βπ/6, π/6]. The influenceof the parameters in πΏπΆ filters is analyzed. A prototype ofRB-IGBT based indirect matrix converter is implemented.The experimental results show the performance of SVMalgorithm and validate the analysis of power factor controlof IMC.
Conflict of Interests
The author declares that there is no conflict of interestsregarding the publication of this paper.
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