IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 3, MARCH 2009. Multilevel Multiphase Space Vector PWM Algorithm. With Switching ...
Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Multilevel Multiphase Space Vector PWM Algorithm With Switching State Redundancy Applied to Three-Phase Four-Leg Converters ´ ´ Oscar L´opez, Jacobo Alvarez, Francisco D. Freijedo, Alejandro G. Yepes, Jano Malvar, Pablo Fern´andez-Comesa˜ na, Jes´ us Doval-Gandoy, Andr´es Nogueiras, Alfonso Lago and Carlos M. Pe˜ nalver Electronics Technology Department, Vigo University, Spain
IECON’10, 7–10 November Phoenix, AZ, USA IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Introduction General multilevel multiphase SVPWM algorithm
New multilevel multiphase SVPWM algorithm in [Lopez, 2009] 792
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 3, MARCH 2009
Multilevel Multiphase Space Vector PWM Algorithm With Switching State Redundancy Óscar López, Member, IEEE, Jacobo Álvarez, Jesús Doval-Gandoy, Member, IEEE, and Francisco D. Freijedo, Member, IEEE
Abstract—Multilevel multiphase technology combines the benefits of multilevel converters and multiphase machines. Nevertheless, new modulation techniques must be developed to take advantage of multilevel multiphase converters. In this paper, a new space vector pulsewidth modulation algorithm for multilevel multiphase voltage source converters with switching state redundancy is introduced. As in three-phase converters, the switching state redundancy permits to achieve different goals like extending the modulation index and reducing the number of switchings. This new algorithm can be applied to the most usual multilevel topologies; it has low computational complexity, and it is suitable for hardware implementations. Finally, the algorithm was implemented in a field-programmable gate array, and it was tested by using a five-level five-phase inverter feeding a motor.
Vectors and matrices have been named with bold letters and scalars with normal letters. Lowercase letters have been used for normalized variables (except for matrices P , Nmin k , and Nmax k ). Variables related with vector space have been written by using Greek letters. Phases have been denoted by using superscripts (k). The position of vectors within sequences has been denoted by means of numeric subscripts (j or m).
Any number of phases ⇒ Three-phase four-leg systems I. I NTRODUCTION
M
OST OF the variable-speed electric drives use threephase machines. Nevertheless, since variable-speed ac drives include a power electronic converter, the number of Index Terms—Field-programmable gate array (FPGA), multilevel converter, multiphase machine, space vector pulsewidth IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching Statephases Redundancy Applied to 3-Phase Converters machine can be higher than three. The major4-Leg advantages
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Introduction Previous works
“Multilevel multiphase SVPWM algorithm” (Lopez et. al) Without redundancy
With redundancy
P =3
Equivalent to “A 3-D space vector modulation generalized algorithm for multilevel converters” (M. Prats et. al.)
Extension of “A fast space-vector modulation algorithm for multilevel three-phase converters” (N. Celanovic et. al.)
P =4
New algorithm
Extension of “Threedimensional space vector modulation algorithm for four-leg multilevel converters using abc coordinates” (L. Franquelo et. al.)
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Outline
1
Multilevel Multiphase SVPWM Algorithm
2
Application to Three-Phase Four-Leg Converters
3
Comparison With Existing Algorithm
4
Experimental Results
5
Conclusions
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
P -Phase SVPWM Formulation Multilevel multiphase converter Phase 1 +2 +1 0 –1 –2
Phase 2 +2 +1 0 –1 –2
Phase k +2 +1 0 –1 –2
Phase P +2 +1 0 –1 –2
Formulation in a P -dimensional space: Reference vector: Switching state vector:
vr = [vr 1 , vr 2 , . . . , vr P ]T ∈ RP vsj = [vs 1j , vs 2j , . . . , vs Pj ]T ∈ ZP
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Block Diagram of the general SVPWM Algorithm Modulation strategy
SVPWM N levels P phases
Transformation
integ Inverse transformation
SVPWM (2 levels, P-1 phases)
Selection
Redundant switching states: Switching states that provide the same leg-to-leg voltage.
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Algorithm Features
Valid for the standard multilevel topologies. Any number of levels. Any number of phases/legs. Sorted switching vector sequence . Minimizes number of switchings. Low computational complexity . Real-time implementation. Takes advantage of switching state redundancy.
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Outline
1
Multilevel Multiphase SVPWM Algorithm
2
Application to Three-Phase Four-Leg Converters
3
Comparison With Existing Algorithm
4
Experimental Results
5
Conclusions
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Formulation Converter Leg a +2 +1 0 –1 –2
Leg b +2 +1 0 –1 –2
Leg c +2 +1 0 –1 –2
Leg n +2 +1 0 –1 –2
If P = 4 ⇒ Particularized algorithm: Reference vector: Switching state vectors:
vr = [vr a , vr b , vr c , vr n ]T ∈ R4 vsj = [vs aj , vs bj , vs cj , vs nj ]T ∈ Z4
Example vr = [vr a , vr b , vr c , vr n ]T = [1.39, 1.15, 0.31, 1.12]T IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Transformation
Transformation
Calculate the reference space vector ω r from reference voltage vector vr : a a n ωr = vr − vr ω r = [ωr a , ωr b , ωr c ]T ωr b = vr b − vr n c ωr = vr c − vr n
Example vr = [1.39, 1.15, 0.31, 1.12]T
⇒
ω r = [0.27, −2.16, −1.43]T
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Reference Space Vector Decomposition Integer part of ω r : ω i = integ(ω r ) = [ωi a , ωi b , ωi c ]T ∈ Z3 integ
Fractional part of ω r : ω f = ω r − ω i = [ωf a , ωf b , ωf c ]T ∈ R3
Example ( T
ω r = [0.27, −2.16, −1.43]
⇒
ω i = [0, −3, −2]T ω f = [0.27, 0.74, 0.57]T
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Two-Level Multiphase SVPWM Algorithm Calculate the displaced space vectors ω dj & dwell times τj : Cab = [ωf a ≥ ωf b ] Cbc = [ωf b ≥ ωf c ] SVPWM (2 levels, P-1 phases)
Cca = [ωf c ≥ ωf a ]
ω d1 ω Table d2 ===⇒ ω d3 ω d4
→ → → →
τ1 τ2 τ3 τ3
Example ωf a = 0.27 ωf b = 0.74 c
ωf = 0.57
Cab = 0 ⇒
Cbc = 1 Cca = 1
ω d1 ω d2 ⇒ ω d3 ω d4
= [0, 0, 0]T = [0, 1, 0]T = [0, 1, 1]T = [1, 1, 1]T
→ → → →
τ1 τ2 τ3 τ3
= 0.26 = 0.17 = 0.30 = 0.27
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Redundant Switching Vector Selection Modulation strategy
Example ( 5-level inverter
Nmin = −2 Nmax = 2
n 1 Modulation n strategy 2 ======⇒ n 3 n4
= 1, j1 = 4 = 2, j2 = 1 = 2, j3 = 2 = 2, j4 = 3
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Switching Vector Sequence ω s1 = ω i + ω d1 ω s2 = ω i + ω d2 ω s3 = ω i + ω d3 ω s4 = ω i + ω d4 vs1 = Inverse transformation
vs2 = vs3 = vs4 =
[ωs aj1 [ωs aj2 [ωs aj3 [ωs aj4
+ n1 , ωs bj1 + n1 , ωs cj1 + n1 , n1 ]T + n2 , ωs bj2 + n2 , ωs cj2 + n2 , n2 ]T + n3 , ωs bj3 + n3 , ωs cj3 + n3 , n3 ]T + n4 , ωs bj4 + n4 , ωs cj4 + n4 , n4 ]T
Example n1 = 1, j1 = 4 ⇒
vs1 = [2, −1, 0, 1]T
n2 = 2, j2 = 1 ⇒
vs2 = [2, −1, 0, 2]T
n3 = 2, j3 = 2 ⇒
vs3 = [2, 0, 0, 2]T
n4 = 2, j4 = 3 ⇒
vs4 = [2, 0, 1, 2]T
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Dwell Times t1 = τj1 t2 = τj2 t3 = τj3 Selection
t4 = τj4
Example j1 = 4 ⇒
t1 = τ4 = 0.27
j2 = 1 ⇒
t2 = τ1 = 0.26
j3 = 2 ⇒
t3 = τ2 = 0.17
j3 = 3 ⇒
t4 = τ3 = 0.30
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Outline
1
Multilevel Multiphase SVPWM Algorithm
2
Application to Three-Phase Four-Leg Converters
3
Comparison With Existing Algorithm
4
Experimental Results
5
Conclusions
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Comparison With Existing Algorithm New particularized algorithm is similar to [Franquelo, 2006]: 458
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 2, APRIL 2006
Three-Dimensional Space-Vector Modulation Algorithm for Four-Leg Multilevel Converters Using abc Coordinates Leopoldo Garcia Franquelo, Fellow, IEEE, Ma. Ángeles Martín Prats, Member, IEEE, Ramón C. Portillo, Student Member, IEEE, Jose Ignacio León Galvan, Student Member, IEEE, Manuel A. Perales, Juan M. Carrasco, Member, IEEE, Eduardo Galván Díez, and Jose Luis Mora Jiménez
Most of the SVM algorithms found in the literature for voltage converters use a representation of voltage vectors in αβγ coordinates [3], [6], instead of using abc coordinates (referenced from now on this paper as natural coordinates). The αβγ representation offers an interesting information about the zero-sequence component of both currents and voltages (proportional to the γ coordinate), however the change of reference frame have to be carried out, implies complex calculations. In addition, the three-dimensional (3-D) representation of the switching vectors, in αβγ is difficult to understand. In [7], a new 3-D SVM in natural coordinates is applied to conventional four-leg voltage source converters showing the advantages of Index Terms—Multilevel converters, natural coordinates, using these coordinates. Previous works from the authors on generalized 3-D-SVM algorithms multilevel converter switching-vectors sequence, three-dimensional space-vector IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied for to the 3-Phase 4-Leg Converters Abstract—In this paper, a novel three-dimensional (3-D) space-vector algorithm for four-leg multilevel converters is presented. It can be applied to active power filters or neutral-current compensator applications for mitigating harmonics and zerosequence components using abc coordinates (referred from now on this paper as natural coordinates). This technique greatly simplifies the selection of the 3-D region where a given voltage vector is supposed to be found. Compared to a three-level modulation algorithm for three-leg multilevel converters, this algorithm does not increase its complexity and the calculations of the active vectors with the corresponding switching time that generate the reference voltage vector. In addition, the low-computational cost of the proposed algorithm is always the same and it is independent of the number of levels of the converter.
Both use the same 4D/3D transformation. Both use the same comparison operations. Both use the same lookup table.
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Differences
Modulation strategy
SVPWM
Switching state selection is new
N levels P phases
Transformation
integ Inverse transformation
If P = 4 then it is equivalent to [Franquelo06]
SVPWM (2 levels, P-1 phases)
Selection
Equivalent to [Franquelo06] New
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Space Vector Sequence Comparison
[Franquelo, 2006] 1 1 1 [San , Sbn , Scn ] = [0, −3, −2]T → d1 = 0.26 2 2 2 [San , Sbn , Scn ] = [0, −2, −2]T → d2 = 0.16
= [0, −3, −1]
T
→ d3 = 0.30
= [1, −2, −1]
T
→ d4 = 0.27
b c [ωs a 1 , ω s 1 , ωs 1 ]
4 2
San
Scn
Sbn
0 –2 –4
0
0.5
1
New algorithm:
New algorithm = [0, −3, −2]
T
→ τ1 = 0.26
b c T [ωs a 2 , ωs 2 , ωs 2 ] = [0, −2, −2] → τ2 = 0.16 b c T [ωs a 3 , ωs 3 , ωs 3 ] = [0, −3, −1] → τ3 = 0.30 b c T [ωs a 4 , ωs 4 , ωs 4 ] = [1, −2, −1] → τ4 = 0.27
Space vector sequence
3 3 3 [San , Sbn , Scn ] 4 4 4 [San , Sbn , Scn ]
[Franquelo, 2006]: Space vector sequence
vr = [1.39, 1.15, 0.31, 1.12]T
4 2
Wa
Wc
Wb
0 –2 –4
0
0.5
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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19
Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Outline
1
Multilevel Multiphase SVPWM Algorithm
2
Application to Three-Phase Four-Leg Converters
3
Comparison With Existing Algorithm
4
Experimental Results
5
Conclusions
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Experimental Setup
DSPACE DS1103 PPC Controller Board. XC3S200 FPGA. Five-level four-leg cascaded full bridge inverter (Vdc = 30 V). dSPACE
Control
FPGA
SVPWM
dc link
Trigger signals
Optical link
Inverter
Load
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Experimental setup Inverter Optical link
FPGA dSPACE
dc link
Load IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Experimental Measurements Leg voltage
Switching frequency: 10 kHz Phase references: 50 Hz, 1.9 p.u.
Ch1: Ch2: Ch3: Ch4:
Leg voltage Vs a Filtered leg voltage Vs a Leg voltage Vs n Filtered leg voltage Vs n
Neutral reference: 150 Hz, 1.5 p.u.
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Experimental Measurements Leg-to-leg voltage
Switching frequency: 10 kHz Phase reference: 50 Hz, 1.9 p.u.
Ch1: Vs b − Vs a Ch2: Filtered Vs b − Vs a
Neutral reference: 150 Hz, 1.5 p.u.
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
Conclusions
General multiphase SVPWM algorithm . Particularized for four-leg converters. Valid for standard multilevel topologies. Any number of levels. Easy to select the redundant switching states. Low computational complexity . Real-time implementation.
Extension of the 3D SVPWM algorithm in [Franquelo, 2006] The five-level version of the algorithm was: Implemented in FPGA. Tested by using a cascaded full-bridge inverter.
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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Multilevel Multiphase SVPWM Algorithm
Application to 3-Phase 4-Leg Converters
Comparison
Experimental
References
O. L´opez, J. Alvarez, J. Doval-Gandoy, and F. D. Freijedo, “Multilevel multiphase space vector PWM algorithm with switching state redundancy,” IEEE Trans. Ind. Electron., vol. 56, no. 3, pp. 792–804, Mar. 2009. L. G. Franquelo, M. M. Prats, R. Portillo, J. I. Leon, M. A. Perales, J. M. Carrasco, E. Galvan, and J. L. Mora, “Three-dimensional space-vector modulation algorithm for four-leg multilevel converters using abc coordinates,” IEEE Trans. Ind. Electron., vol. 53, no. 2, pp. 458–466, Apr. 2006.
IECON’10 - Multilevel Multiphase SVPWM Algorithm With Switching State Redundancy Applied to 3-Phase 4-Leg Converters
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