IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012
697
Space Vector PWM Technique for a Three-to-Five-Phase Matrix Converter Atif Iqbal, Senior Member, IEEE, Sk Moin Ahmed, Student Member, IEEE, and Haitham Abu-Rub, Senior Member, IEEE
Abstract—Variable-speed multiphase (more than three phases) drive systems are seen as serious contenders to the existing three-phase drives due to their distinct advantages. Supply to the multiphase drives is invariably given from a voltage source inverter. However, this paper proposes an alternative solution for supplying multiphase drive system using a direct ac–ac converter called a matrix converter. This paper proposes the pulsewidth modulation (PWM) algorithm for the matrix converter topology with three-phase grid input and five-phase variable-voltage and variable-frequency output. The PWM control technique developed and presented in this paper is based on space vector approach. This paper presents the complete space vector model of the three-to-five-phase matrix converter topology. The space vector model yield 215 total switching combinations which reduce to 243 states considering the imposed constraints, out of which 240 are active and 3 are zero vectors. However, for space vector PWM (SVPWM) implementation, only 90 active and 3 zero vectors can be used. The SVPWM algorithm is presented in this paper. The viability of the proposed solution is proved using analytical, simulation, and experimental approaches. Index Terms—Five-phase, matrix converter, pulsewidth modulation (PWM), space vector.
I. I NTRODUCTION
T
HE matrix converter is a bidirectional power flow converter that uses semiconductor switches arranged in the form of matrix array. The matrix converter has recently attracted significant attention among researchers. Matrix converters offer some distinct advantages such as operation at unity power factor for any load, controlled bidirectional power flow, sinusoidal input and output currents, etc. A comprehensive overview of the development in the field of matrix converter research is presented in [1]. It is to be noted here that the most common configuration of the matrix converter discussed in the literature is three-phase to three-phase [2], [3]. Little
Manuscript received April 28, 2011; revised August 28, 2011; accepted October 30, 2011. Date of publication December 23, 2011; date of current version March 21, 2012. Paper 2011-IPCC-151.R1, presented at the 2010 IEEE Energy Conversion Congress and Exposition, Atlanta, GA, September 12–16, and approved for publication in the IEEE T RANSACTIONS ON I NDUSTRY A P PLICATIONS by the Industrial Power Converter Committee of the IEEE Industry Applications Society. This work was supported by an NPRP grant (08-369-2140) from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the authors. A. Iqbal is with Qatar University, 2713 Doha, Qatar, on academic leave from Aligarh Muslim University, Aligarh, India (e-mail:
[email protected]). S. M. Ahmed and H. Abu-Rub are with Texas A&M University, 23874 Doha, Qatar (e-mail:
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2011.2181469
attention has been paid on the development of matrix converter with output more than three, except in [4]–[7]. The pulsewidth modulation (PWM) technique presented in [4] for a generalized three- to n-phase matrix converter topology is based on direct duty ratio control. Space vector PWM (SVPWM) is discussed in [5] for a three-to-five-phase matrix converter considering only outer large length space vectors. In contrary, this paper utilizes 93 space vectors for the implementation, offering better voltage and current waveforms. Carrier-based PWM is elaborated for a three-to-seven-phase matrix converter in [6] and for a three-to-nine-phase matrix converter in [7]. The conventional structure for variable-speed drives consists of a three-phase motor supplied by a three-phase power electronic converter. However, when the machine is connected to a modular power electronic converter, such as a voltage source inverter or a matrix converter, then the need for a specific number of phases, such as three, disappears since simply adding one leg increases the number of output phases. Nowadays, the development of modern power electronics makes it possible to consider the number of phases as a degree of freedom, i.e., an additional design variable in electrical machines. Multiphase motor drives have some inherent advantages over the traditional three-phase motor drives, such as reducing the amplitude and increasing the frequency of torque pulsations, reducing the rotor harmonic current losses, and lowering the dc link current harmonics. In addition, owing to their redundant structure, multiphase motor drives improve system reliability. A fivephase system has several salient features that are attractive for industrial applications. The fault-tolerant property of a fivephase system makes it a strong candidate for safety critical applications such as defense, hospitals, ship propulsions, traction drive and aircraft applications, etc. The reduced volume of a machine for higher phase number is another feature that can be utilized in naval ship applications and mining applications where the space requirement is stringent. Although a fivephase system is still not used in industrial applications, it has high potential of adoption by industries. A 15-phase induction machine built by Alstom is now part of an electric drive system of a British naval ship. The machine winding is reconfigurable as five three-phase induction machines or three five-phase induction machines. Detailed reviews on the development in the area of multiphase (more than three phases) drive are presented in [8]–[11]. The performance of power electronic converters (ac to ac or ac–dc-ac) is highly dependent on their control algorithms. Thus, a number of modulation schemes are developed for voltage source inverters for three-phase [12], [13] and multiphase outputs [14]–[16]. Modulation methods
0093-9994/$26.00 © 2011 IEEE
698
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012
in series. Each power switch is bidirectional in nature, with antiparallel-connected IGBTs and diodes. The input is similar to a three-to-three-phase matrix converter having LC filters, and the output is five-phase with 72◦ phase displacement between each phase. The switching function is defined as Sjk = {1 for closed switch, 0 for open switch}, with j = {a, b, c} (input) and k = {A, B, C, D, E} (output). The switching constraint is Sak + Sbk + Sck = 1. The load to the matrix converter is assumed as a starconnected five-phase ac machine. III. S PACE V ECTOR M ODULATION A LGORITHM
Fig. 1. General power circuit topology of three-to-five-phase ac–ac matrix converter.
of matrix converters are complex and are generally classified in two different groups, called direct and indirect. The direct PWM method developed by Alesina and Venturini [17] limits the output to half the input voltage. This limit was subsequently raised to 0.866 by taking advantage of third harmonic injection [18], and it was realized that this is the maximum output that can be obtained from a three-to-three-phase matrix converter in the linear modulation region. Indirect method assumes a matrix converter as a cascaded virtual three-phase rectifier and a virtual voltage source inverter with imaginary dc link. With this representation, the SVPWM method of VSI is extended to a matrix converter [19]–[21]. SVPWM applied to a multilevel matrix converter is also reported recently [22]. A carrier-based PWM scheme is introduced recently for three-to-three-phase matrix converter [23]–[25]. However, SVPWM is more suitable for digital implementation. In this paper, the SVPWM strategy is presented based on the space vector model of the three-to-five matrix converter. The complete space vector model is presented along with the SVPWM algorithm. It is seen that the output voltage is limited to 0.7886 of the input magnitude. Theoretically, this is the maximum output magnitude that can be obtained in this matrix converter configuration in the linear modulation region. Nevertheless, this limit can be further enhanced by using overmodulation strategy at the expense of higher complexity. This paper presents the simulation results which are further validated using experimental investigation. The simulation and experimental results match to a good extent. II. T HREE - TO -F IVE -P HASE M ATRIX C ONVERTER The general power circuit topology of a three-to-five-phase matrix converter is shown in Fig. 1. There are five legs, with each leg having three bidirectional power switches connected
The space vector algorithm is based on the representation of the three-phase input current and five-phase output line voltages on the space vector plane. In matrix converters, each output phase is connected to each input phase depending on the state of the switches. For a three-to-five-phase matrix converter, the total number of switches is 15. With this number of switches, the total combination of switching is 215 . For safe switching in the matrix converter, the following rules should be observed. 1) The input phases should never be short circuited. 2) The output phases should never be open circuited at any switching time. Considering the aforementioned two rules, there are 35 , i.e., 243, different switching combinations for connecting the output phases to the input phases. These switching combinations can be analyzed in five groups. The switching combinations are represented as {p, q, r}, where p, q, and r represent the number of output phases connected to input phase A, phase B, and phase C, respectively. 1) p, q, r ∈ 0, 0, 5|p = q = r: All of the output phases are connected to the same input phase. This group consists of three possible switching combinations, i.e., either all output phases connect to input phase A or input phase B or input phase C. {5, 0, 0} represents the switching conditions when all of the output phases connect to input phase A. {0, 5, 0} represents the switching conditions when all of the output phases connect to input phase B. {0, 0, 5} represents the switching conditions when all of the output phases connect to input phase C. These vectors have zero magnitude and frequency. These are called zero vectors. 2) p, q, r ∈ 0, 1, 4|p = q = r: Four of the output phases are connected to the same input phase, and the fifth output phase is connected to any of the other two input phases. Here, 4 means four different output phases are connected to input phase A. The number 1 means that one output phase other than the previous four is connected to input phase B and input phase C is not connected to any output phase. As such, there exist six different switching states ({4, 1, 0}, {1, 4, 0}, {1, 0, 4}, {0, 1, 4}, {0, 4, 1}, and {4, 0, 1}). Out of these, one switching state can have further five different combinations, i.e., every switching state has 5 C4 ×1 C1 = 5 combinations. This group hence consists of 6 × 5 = 30 switching combinations in all. These
IQBAL et al.: SPACE VECTOR PWM TECHNIQUE FOR A THREE-TO-FIVE-PHASE MATRIX CONVERTER
vectors have a variable amplitude at a constant frequency in space. It means that the amplitude of the output voltages depends on the selected input line voltages. In this case, the phase angle of the output voltage space vector does not depend on the phase angle of the input voltage space vector. The 30 combinations in this group determine ten prefixed positions of the output voltage space vectors which are not dependent on αi . A similar condition is also valid for current vectors. The 30 combinations in this group determine six prefixed positions of the input current space vectors which are not dependent on αo . 3) p, q, r ∈ 0, 2, 3|p = q = r: Three of the output phases are connected to the same input phase, and the two other output phases are connected to any of the other two input phases. As such, there exist six different switching states ({3, 2, 0}, {2, 3, 0}, {2, 0, 3}, {0, 2, 3}, {0, 3, 2}, and {3, 0, 2}). Out of these, one switching permutation can have further ten different combinations, i.e., every switching permutation has 5 C3 ×2 C2 = 10 combinations. This group hence consists of 6 × 10 = 60 switching combinations. These vectors also have a variable amplitude at a constant frequency in space. The 60 combinations in this group determine ten prefixed positions of the output voltage space vectors which are not dependent on αi . A similar condition is also valid for current vectors. The 60 combinations in this group determine six prefixed positions of the input current space vectors which are not dependent on αo . 4) p, q, r ∈ 1, 1, 3|p = q = r: Three of the output phases are connected to the same input phase, and the two other output phases are connected to the other two input phases, respectively. As such, there exist three different switching states ({3, 1, 1}, {1, 3, 1}, and {1, 1, 3}). Out of these, each switching state can have further 20 different combinations, i.e., every switching permutation has 5 C3 ×2 C1 ×1 C1 = 20 combinations. This group hence consists of 3 × 20 = 60 switching combinations. These vectors have variable-amplitude variable frequency in space. It means that the amplitude of the output voltages depends on the selected input line voltages. In this case, the phase angle of the output voltage space vector depends on the phase angle of the input voltage space vector. The 60 combinations in this group do not determine any prefixed positions of the output voltage space vector. The locus of the output voltage space vectors forms ellipses in different orientations in space as αi is varied. A similar condition is also valid for current vectors. For the space vector modulation technique, these switching states are not used in the matrix converter since the phase angle of both input and output vectors cannot be controlled independently. 5) p, q, r ∈ 1, 2, 2|p = q = r: Two of the output phases are connected to the same input phase, the two other output phases are connected to another input phase, and the fifth output phase is connected to the third input phase. As such, there exist three different switching states ({1, 2, 2}, {2, 1, 2}, and {2, 2, 1}). Each switching state can have further 30 different combinations, i.e., every switching
699
permutation has 5 C2 ×3 C2 ×1 C1 = 30 combinations. This group hence consists of 3 × 30 = 90 switching combinations. These vectors also have variable-amplitude variable frequency in space. That is, the amplitude of the output voltages depends on the selected input line voltages. In this case, the phase angle of the output voltage space vector depends on the phase angle of the input voltage space vector. The 90 combinations in this group do not determine any prefixed positions of the output voltage space vector. The locus of the output voltage space vectors forms ellipses in different orientations in space as αi is varied. A similar condition is also valid for current vectors. For the space vector modulation technique, these switching states are also not used in the matrix converter since the phase angle of both input and output vectors cannot be controlled independently. The active switching vectors used for the proposed SVPWM of a three-to-five-phase matrix converter are the following. Group 1: {5, 0, 0} consists of 3 vectors. Group 2: {4, 1, 0} consists of 30 vectors. Group 3: {3, 2, 0} consists of 60 vectors. IV. S PACE V ECTOR C ONTROL S TRATEGY The general topology of a three-to-five-phase matrix converter is shown in Fig. 1. It consists of 15 bidirectional switches which allow any output phase to be connected to any input phase. Being the converter supplied by the voltage source, the input phases could never be short circuited and, owing to the presence of inductive loads, should not be interrupted. With these constraints in three-phase input and five-phase matrix converter, there are 243 permitted switching combinations. However, the active switching vectors used for the matrix converter modulation technique are 93. These active vectors are divided into four groups. Group 1: {5, 0, 0} consists of three vectors; these are called as zero vectors. Group 2: {4, 1, 0} consists of 30 vectors; these are called as medium vectors. Group 3: {3, 2, 0} consists of 30 vectors in which the two adjacent output phases are connected to the same input phase; these are called as large vectors. Group 4: {3, 2, 0} consists of 30 vectors in which the two alternate output phases are connected to the same input phase; these are called as small vectors. In the proposed SVPWM strategy for the three-to-five-phase matrix converter, only the switching states of groups 1, 2, and 3 are utilized. The switching states in groups 4 and 5 are not used since the corresponding switching space vectors (SSVs) are rotating with time. Input current SSVs and output voltage SSVs of each switching state in groups 2 and 3 are shown in Figs. 2 and 3, respectively. The large vectors and medium vectors are represented as “L” and “M,” respectively. The small vectors are not considered in this paper. The letters “L” and “M” refer to the large and medium vectors, respectively, and the numbers in front of the letters are the vector numbers.
700
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012
In the same way, the input and output line current space vectors are defined as 2π 4π → 2 − Ia + Ib · ej 3 + Ic · ej 3 = Ii · ejβi (3) Ii = 3 2π 4π 6π 8π → 2 − IA + IB · ej 5 + IC · ej 5 + ID · ej 5 + IE · ej 5 Io = 5 = Io ejβO . (4)
Fig. 2. Input current space vectors corresponding to the permitted switching combinations for group 3: {3, 2, 0} (all vectors).
αi and αo are the input and output voltage vector phase angles, respectively, whereas βi and βo are the input and output current vector phase angles, respectively. The SVM algorithm does the following: 1) it selects appropriate switching states, and 2) it calculates the duty cycle for each switching state. During one switching period Ts , the switching states whose SSVs are adjacent to the desired output voltage (input current) vector should be selected, and the zero switching states are applied to complete the switching period to provide the maximum outputto-input voltage transfer ratio. The aim of the proposed space vector control strategy is to generate the desired output voltage vector with the constraint of − → unity input power factor. For this purpose, let Vo be the desired → − output line voltage space vector and Vi be the input line voltage space vector at a given time. The input line to neutral voltage − → vector Ei is defined by π 1 − → − → Ei = √ Vi · e−j 6 . 3
(5)
In order to obtain unity input power factor, the direction of the → − − → input current space vector Ii has to be the same as that of Ei . → − − → Assume that Vo and Ii are in sector 1 (there are six sectors at the input side and ten sectors at the output side as the input side is three-phase and the output is five-phase). In Fig. 3, for − → − → large and medium vector configurations, Vo and Vo represent − → the components of Vo along the two adjacent vector directions. → − → − → − Similarly Ii is resolved into components Ii and Ii along the two adjacent vector directions. Possible switching states that can be utilized to synthesize the resolved voltage and current components (assuming that both input and output vectors are in sector 1) are
Fig. 3. Output voltage space vectors corresponding to the permitted switching combinations for group 3: {3, 2, 0} (large and medium vectors).
For each combination, the input and output line voltages can be expressed in terms of space vectors as 2π 4π → 2 − Vab + Vbc · ej 3 + Vca · ej 3 = Vi · ejαi (1) Vi = 3 2π 4π 6π − → 2 VAB + VBC · ej 5 + VCD · ej 5 + VDE · ej 5 Vo = 5 8π +VEA · ej 5 = Vo · ejαO .
(2)
− → Vo : ±10 L, ±11 L, ±12 L and ± 7 M, ±8 M, ±9 M − → Vo : ±1 L, ±2 L, ±3 L and ± 13 M, ±14 M, ±15 M → − Ii : ±3 L, ±6 L, ±9 L, ±12 L, ±15 L and ± 3 M, ±6 M, ±9 M, ±12 M, ±15 M → − Ii : ±1 L, ±4 L, ±7 L, ±10 L, ±13 L and ± 1 M, ±4 M, ±7 M, ±10 M, ±13 M. The output voltage and input current vectors can be synthesized simultaneously by selecting the common switching states of the output voltage components and input current components. The common switching states are ±10 L, ±12 L, ±7 M, ±9 M and ±1 L, ±3 L, ±13 M, ±15 M. From two switching states with the same number but opposite signs, only one should be used since the corresponding voltage or current space vectors are in opposite directions. Switching states with the positive signs are used to calculate the
IQBAL et al.: SPACE VECTOR PWM TECHNIQUE FOR A THREE-TO-FIVE-PHASE MATRIX CONVERTER
701
TABLE I S PACE V ECTOR C HOICE FOR SVPWM IN D IFFERENT S ECTORS
duty cycle of the switching state. If the duty cycle is positive, the switching state with a positive sign is selected; otherwise, the one with a negative sign is selected. The switching state selection for implementing SVPWM can also be explained as follows. Owing to the small variation of the input voltage during the − → switching cycle period, the desired Vo can be approximated by utilizing four (two medium and two large) switching configurations corresponding to four space vectors in the same direction − → of Vo and one zero voltage configuration. Among the six possible switching configurations, the two giving the higher voltage values corresponding to large vectors and the two giving the medium voltage values corresponding − → to medium vectors with the same sense of Vo are chosen. In the same way, four different switching configurations and − → one zero voltage configuration are used to define Vo . With reference to the example shown in Figs. 2 and 3, the input → − voltage Vi has a phase angle 0 ≤ αi ≤ (π/3). In this case, the line voltages VAB and −VCA assume the higher values. Then, according to the switching table of large and medium vectors, − → the configuration used to obtain Vo is +10 L and −12 L for large vectors and +7 M and −9 M for medium vectors, while − → those for Vo are +1 L, −3 L and +13 M, −15 M. These eight space vector combination can be utilized to determine the input current vector direction also as shown in Fig. 2. These configurations are associated to the vector directions adjacent to the input current vector position. There are 60 switching combinations for different sector combinations. These combinations for large and medium vectors are shown in Table I. Applying the space vector modulation technique, the ontime ratio δ of each configuration can be obtained by solving two systems of algebraic equations. In particular, utilizing the − → configurations +10 L, −12 L and +7 M, −9 M to generate Vo and to set the input current vector direction, one can write δ+10 L · |L| · Vab − δ−12 L · |L| · Vca + δ+7 M · |M | · Vab − δ−9 M · |M | · Vca π 5 −−→ (6) + αo = Vo = |Vo | · |L + M | · sin 3 10
2 δ+10 L √ iD 3 − π π → 2 − αi − = Ii = Ii √ sin 6 6 3 2 δ−12 L √ iD 3 − π π → 2 + αi − = Ii = Ii √ sin 6 6 3 2 δ+7 M √ iC 3 − π π → 2 − αi − = Ii = Ii √ sin 6 6 3 2 δ−9 M √ iC 3 − π π → 2 + αi − . = Ii = Ii √ sin 6 6 3
(7)
(8)
(9)
(10)
Considering a balanced system of sinusoidal supply voltages expressed as → − Vab = | Vi | cos(αi ) 2π → − Vbc = | Vi | cos αi − 3 4π → − Vca = | Vi | cos αi − . 3
(11)
The solution of the system of (6), (7), (8), (9), and (10) gives π π 10 + αo · sin − αi δ+10 L = q · |L| · √ sin 10 3 3 3 π 10 + αo · sin(αi ) δ−12 L = q · |L| · √ sin 10 3 3 π π 10 δ+7 M = q · |M | · √ sin + αo · sin − αi 10 3 3 3 π 10 + αo · sin(αi ) (12) δ−9 M = q · |M | · √ sin 10 3 3 −−→ − → where q = |Vo |/| Vi | is the voltage transfer ratio. L and M correspond to large and medium vectors, respectively.
702
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012
With the same procedure, utilizing the configurations +1 L, − → −3 L and +13 M, −15 M to generate Vo and to set the input current vector direction yields π π 10 δ+1 L = q · |L| · √ sin − αo · sin − αi 10 3 3 3 π 10 − αo · sin(αi ) δ−3 L = q · |L| · √ sin 10 3 3 π π 10 − αo · sin − αi δ+13 M = q · |M | · √ sin 10 3 3 3 π 10 − αo · sin(αi ). δ−15 M = q · |M | · √ sin (13) 10 3 3
TABLE II M AXIMUM M ODULATION I NDEX F ORMULATION
The results obtained are valid for −(π/10) ≤ αo ≤ (π/10) and for 0 ≤ αi ≤ (π/3). Applying a similar procedure for the other possible pairs of angular sectors, the required switching configurations and the on-time ratio of each configuration can be determined. Note that the values of the on-time ratios (or duty cycle) should be positive. Furthermore, the sum of the ratios must be lower than or equal to unity. By adding (12) and (13), with the aforementioned constraints, one can write δ+10 L + δ−12 L + δ+1 L + δ−3 L + δ+7 M + δ−9 M +δ+13 M + δ−15 M ≤ 1.
(14)
The maximum value of the voltage transfer ratio can be determined as q = 0.7886 for a three-phase to five-phase matrix converter. This value is the same with what was achieved in [5]. A. Maximum Output in n by m Matrix Converter One can relate the maximum output voltage in an n-phase to m-phase matrix converter with the maximum output achievable in equivalent m-phase voltage source inverter and the length of the largest space vector of n-phase voltage source inverter. A general relationship is given as in the equation shown at the bottom of the page. The maximum output expression for the “n” by “m” phase matrix converter is correlated to the “n” and “m” phase inverter. In an “n” by “m” phase matrix converter, the input is n-phase, and the output is m-phase. It can be reimaged as two inverters (one has an n-phase output, and the other has an m-phase output) are connected back to back. In case of an m-phase inverter, the maximum output in the linear range can be written as [26] 1 . {2. cos (pi/(2.m))} The aforementioned term will be divided by the maximum vector length of the n-phase inverter to obtain the maximum output value for an “n” by “m” phase matrix converter in the linear modulation range. The Vdc is written in the formula of Table II to show the exact vector length equation for an inverter. In this case, Vdc is equal to unity.
V. C OMMUTATION R EQUIREMENTS Once the phase angles of the input current and output line voltage are known, the eight space vectors are required to implement the SVPWM. These eight space vectors are utilized until αi or αo will change the angular sector. One of the zero space voltage vectors should be employed in each switching cycle to obtain a symmetrical switching waveform. The sequence of switching of the resulting nine (eight active and one zero) space vectors should be defined in order to minimize the number of switch commutations. With reference to the αi and αo values considered in Figs. 2 and 3, the available space vectors and their sequence of switching are listed in Table III, assuming both input and output reference vectors in sector 1. The first column lists the different space vectors that will be used for the SVPWM. The second to sixth columns list the input and output phases that will be connected during switching period. The capital letter denotes the output phases (five-phase), and the small letter indicates the input phases (three-phase). Sequence of application of space vectors can be defined such that the number of switching in
Maximum possible output in n by m matrix converter =
maximum output in m-phase inverter in linear range length of the largest space vector of n-phase inverter
IQBAL et al.: SPACE VECTOR PWM TECHNIQUE FOR A THREE-TO-FIVE-PHASE MATRIX CONVERTER
703
TABLE III S PACE V ECTOR S WITCHING S EQUENCE
Fig. 4. Output phase voltages at 70 Hz.
are selected and sequenced, the on-time ratio of each configuration is calculated using (12) and (13) given for the appropriate sector.
VI. I NVESTIGATION R ESULTS A. Simulation Results
one sampling period is minimum. The switching sequence in one sample period in sector 1 (both input and output reference vectors) is listed in Table III. To obtain a symmetrical switching, at first, a zero vector is applied, followed by eight active vectors in half sampling period. The mirror image of the switching sequence is employed in the second half of the sampling period. The time of applications of active and zero vectors is divided in two portions; hence, the total time of application is also halved. It is observed that, when applying vector +7 M after zero vector, only one state is changed; input phase “a” is now connected to output phase “C.” In the next transition from +7 M to +13 M, two states are changed. Each change in switching is shown by an elliptical shape. It should be noted that, in this way, only 12 commutations are required in each half sampling period. Once the configurations
MATLAB/Simulink model is developed for the proposed matrix converter control. The input voltage is fixed at 100 V peak to show the exact gain at the output side, and the switching frequency of the devices is kept at 6 kHz. The load connected to the matrix converter is R−L with the parameter values R = 10 Ω, L = 3 mH. The operation of the proposed topology of the matrix converter is tested for a wide range of frequencies, from as low as 6.7 Hz to higher frequencies (70 Hz) for deep flux weakening operation. The output phase to neutral voltage, adjacent and non-adjacent voltages are shown in Figs. 4–6. A balanced five-phase output is observed. The spectrum of the output voltage at 6.7-Hz output frequency is shown in Fig. 7. The sinusoidal nature of the input current is another distinct feature of the matrix converter. The input side current spectrum shown in Fig. 8 (lower trace) yields a completely sinusoidal waveform while completely eliminating the lower order harmonics. The THD in the input current waveform is obtained as 3.67%, which is well within the tolerance limit of the specified IEEE 19-1999 standard. Similar results are obtainable for all operating frequencies, showing a successful operation of the proposed matrix converter PWM. The presented results clearly show a successful phase transformation from three-phase input to five-phase output. The input current will not show a significant change for the change in the frequency for low inductive load, and thus, only one trace for the input current is shown in Fig. 8(a) at the 70-Hz output case only. The simulation results verify the effectiveness of the proposed solution. Hence, the proposed direct ac–ac converter can be employed for wide range speed control of multiphase drive systems.
704
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012
Fig. 5. Output currents at 70 Hz.
Fig. 6. Output phase, adjacent-1, and adjacent-II voltages for 6.67 Hz.
Fig. 8. (a) Input voltage with filtered and unfiltered input currents. (b) Input current spectrum.
Fig. 7. Frequency spectrum of the output phase voltage at 6.67 Hz.
Fig. 9.
Block diagram of the experimental setup.
IQBAL et al.: SPACE VECTOR PWM TECHNIQUE FOR A THREE-TO-FIVE-PHASE MATRIX CONVERTER
Fig. 10. Output side five-phase waveform for 70 Hz: output phase voltages (100 V, 5 ms/div).
705
Fig. 11. Output side five-phase waveform for 70 Hz: output phase currents (2 A, 5 ms/div).
B. Experimental Results A prototype three-phase to nine-phase matrix converter is developed, where the input is three-phase and the output can be configured from single to nine phases. The proposed spacevector-based modulation scheme is implemented for a threeto-five-phase matrix converter. The block schematic of the experimental setup is shown in Fig. 9. The power module is a bidirectional switch FIO 50-12BD from IXYS and is composed of a diagonal IGBT and fast diode bridge in ISOPLUS i4-PAC. The voltage blocking capability of the device is 1200 V, and the current capacity is 50 A. This comes in single chip with five output pins: four for the diode bridge and one for the gate drive of the IGBT. It controls bidirectional current flow by a single control signal. The advantage of this bidirectional power switch is the decreased number of IGBTs which is a major issue for multiphase operation, but the major disadvantage is the higher conduction losses and the two-step commutation. Extra line inductances are used for safe operation during the overlapping of current commutation. Dead-time compensation is done along with snubbers and clamping circuit. The matrix converter consists of 27 of such bidirectional power switches, of which only 15 are used. The control platform used is the Spartan 3-A DSP controller and Xilinx XC3SD1800A FPGA. Furthermore, the modulation code is written in C and is processed in the DSP. Logical tasks, such as A/D and D/A conversion, gate drive signal generation, etc., are accomplished by the powerful FPGA board. The FPGA board is able to handle up to 50 PWM signals. Clamping diodes are used for protection purposes. The input supply is given from an autotransformer and is fixed at 100 V, 50 Hz. The switching frequency of the bidirectional power switch of the matrix converter is fixed at 6 kHz. The value of the input LC filter used for this configuration is 200 µH, 10 A and 15 µF, 440 V, respectively. The developed matrix converter is tested for a wide range of output frequencies. A five-phase R−L load is connected at the output terminals of the matrix converter, with R = 10 Ω and L = 30 mH. The resulting output waveforms for the fundamental frequency of 70 and 6.7 Hz are shown in Figs. 10–11, and 12, respectively. The simulation and experimental results match to a good extent. The output voltage THD is 4.83%. This proves the viability of the proposed space vector modulation scheme for a three-to-five-phase matrix converter. To further show the unity power factor at the input side, one input phase voltage and one input phase current are shown in Fig. 13. It is evident that unity power factor is maintained at the input side. The five-
Fig. 12. Output side five-phase waveform for 6.7 Hz. (Upper trace) Output phase voltage (100 V, 25 ms/div) and output current (2 A, 25 ms/div). (Bottom trace) Output Adj-2 line-to-line voltage (100 V, 25 ms/div).
Fig. 13. Input voltage (25 V, 10 ms/div) and current (2.0 A, 10 ms/div).
phase matrix converter feeds a five-phase squirrel cage 1.5-hp induction motor at no load to observe the input current behavior at light load condition. The filtered input current leads the input voltage due to the capacitive nature of the input filter without any input displacement factor correction. The phase angle between the input phase current and voltage is 12◦ . The THDi ’s of the input current and input power factor are 4.74% and 0.967, respectively. A phase lag of 12◦ is introduced for the input
706
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 2, MARCH/APRIL 2012
Fig. 14. Input voltage (25 V, 2.5 ms/div) and filtered input current (0.2 A, 2.5 ms/div).
displacement correction, which results in 6.97% THDi and input power factor of 0.99. Both results are shown in Fig. 14. VII. C ONCLUSION A novel space vector control of a three-to-five-phase matrix converter has been discussed in this paper. The input to the matrix converter is a three-phase ac supply, and the output is five-phase. This converter is useful in a five-phase motor drive application. The output voltage magnitude is found to be limited to 78.8% of the input voltage magnitude in the linear modulation region. This is the limitation associated with this type of ac–ac converter. The proposed SVPWM strategy is derived from the analogy of the modulation of a voltage source inverter. There are 243 possible space vectors, but only 93 are useful in implementing the SVPWM. Symmetrical switching is obtained by utilizing zero space vectors and active vectors, and 24 commutations are noted in one sampling period. The analytical findings are confirmed using simulation and an experimental approach. R EFERENCES [1] P. W. Wheeler, J. Rodriguez, J. C. Clare, L. Empringham, and A. Weinstein, “Matrix converters: A technology review,” IEEE Trans. Ind. Electron., vol. 49, no. 2, pp. 276–288, Apr. 2002. [2] M. P. Kazmierkowaski, R. Krishnan, and F. Blaabjerg, Control in Power Electronics-Selected Problems. New York: Academic, 2002. [3] H. A. Toliyat and S. Campbell, DSP Based Electromechanical Motion Control. Boca Raton, FL: CRC Press, 2004. [4] S. M. Ahmed, A. Iqbal, and H. Abu-Rub, “Generalized duty ratio based pulse width modulation technique for a three-to-k phase matrix converter,” IEEE Trans. Ind. Electron., vol. 58, no. 9, pp. 3925–3937, Sep. 2011. [5] S. M. Ahmed, A. Iqbal, H. Abu-Rub, and M. R. Khan, “Space vector PWM technique for a novel 3 to 5 phase matrix converter,” in Proc. IEEE ECCE, Atalanta, 2010, pp. 1875–1880. [6] S. M. Ahmed, A. Iqbal, and H. Abu-Rub, “Carrier-based PWM technique of a novel three-to-seven-phase matrix converter,” presented at the Int. Conf. Electrical Machine ICEM, Rome, Italy, Sep. 3–6, 2010, Paper RF004 944. [7] S. M. Ahmed, A. Iqbal, H. Abu-Rub, J. Rodriguez, and C. Rojas, “Simple carrier-based PWM technique for a three to nine phase matrix converter,” IEEE Trans. Ind. Elect., vol. 58, no. 11, pp. 5014–5023, Nov. 2011.
[8] M. Jones and E. Levi, “A literature survey of state-of-the-art in multiphase ac drives,” in Proc. 37th Int. UPEC, Stafford, U.K., 2002, pp. 505–510. [9] R. Bojoi, F. Farina, F. Profumo, and Tenconi, “Dual three induction machine drives control—A survey,” IEEJ Trans. Ind. Appl., vol. 126, no. 4, pp. 420–429, 2006. [10] E. Levi, R. Bojoi, F. Profumo, H. A. Toliyat, and S. Williamson, “Multiphase induction motor drives—A technology status review,” IET Elect. Power Appl., vol. 1, no. 4, pp. 489–516, Jul. 2007. [11] E. Levi, “Multi-phase machines for variable speed applications,” IEEE Trans. Ind. Electron., vol. 55, no. 5, pp. 1893–1909, May 2008. [12] J. Holtz, “Pulsewidth modulation—A survey,” IEEE Trans. Ind. Electron., vol. 39, no. 5, pp. 410–420, Oct. 1992. [13] D. G. Holmes and T. A. Lipo, Pulse Width Modulation for Power Converters: Principle and Practice. Piscataway, NJ: IEEE Press, 2003. [14] D. Dujic, M. Jones, and E. Levi, “Generalized space vector PWM for sinusoidal output voltage generation with multiphase voltage source inverter,” Int. J. Ind. Electron. Drives, vol. 1, no. 1, pp. 1–13, 2009. [15] A. Iqbal and S. K. Moinuddin, “Comprehensive relationship between carrier-based PWM and space vector PWM in a five-phase VSI,” IEEE Trans. Power Electron., vol. 24, no. 10, pp. 2379–2390, Oct. 2009. [16] O. Lopez, D. Dujic, M. Jones, F. D. Freijedo, J. Doval-Gandoy, and E. Levi, “Multidimensional two-level multiphase space vector PWM algorithm and its comparison with multi-frequency space vector PWM method,” IEEE Trans. Ind. Electron., vol. 58, no. 2, pp. 465–475, Feb. 2011. [17] A. Alesina and M. Venturini, “Solid state power conversion: A Fourier analysis approach to generalised transformer synthesis,” IEEE Trans. Circuits Syst., vol. CAS-28, no. 4, pp. 319–330, Apr. 1981. [18] A. Alesina and M. Venturini, “Analysis and design of optimum amplitude nine-switch direct ac–ac converters,” IEEE Trans. Power Electron., vol. PEL-4, no. 1, pp. 101–112, Jan. 1989. [19] D. Casadei, G. Grandi, G. Serra, and A. Tani, “Space vector control of matrix converters with unity power factor and sinusoidal input/output waveforms,” in Proc. EPE Conf., 1993, vol. 7, pp. 170–175. [20] L. Huber and D. Borojevic, “Space vector modulated three-phase to threephase matrix converter with input power factor correction,” IEEE Trans. Ind. Appl., vol. 31, no. 6, pp. 1234–1246, Nov./Dec. 1995. [21] H. She, H. Lin, B. He, X. Wang, L. Yue, and X. An, “Implementation of voltage-based commutation in space vector modulated matrix converter,” IEEE Trans. Ind. Electron., vol. 59, no. 1, pp. 154–166, Jan. 2012. DOI:10.1109/TIE.2011.2130497. [22] L. M. Y. Lee, P. Wheeler, and C. Klumpner, “Space vector modulated multi-level matrix converter,” IEEE Trans. Ind. Electron., vol. 57, no. 10, pp. 3385–3394, Oct. 2010. [23] B. Wang and G. Venkataramanan, “A carrier-based PWM algorithm for indirect matrix converters,” in Proc. IEEE PESC, 2006, pp. 1–8. [24] Y.-D. Yoon and S.-K. Sul, “Carrier-based modulation technique for matrix converter,” IEEE Trans. Power Electron., vol. 21, no. 6, pp. 1691–1703, Nov. 2006. [25] P. C. Loh, R. Rong, F. Blaabjerg, and P. Wang, “Digital carrier modulation and sampling issues of matrix converter,” IEEE Trans. Power Electron., vol. 24, no. 7, pp. 1690–1700, Jul. 2009. [26] A. Iqbal, E. Levi, M. Jones, and S. N. Vukosavic, “Generalised sinusoidal PWM with harmonic injection for multi-phase VSIs,” in Proc. IEEEPESC, 2006, pp. 1–7.
Atif Iqbal (M’09–SM’10) received the B.Sc. and M.Sc. degrees in electrical engineering from Aligarh Muslim University (AMU), Aligarh, India, in 1991 and 1996, respectively, and the Ph.D. degree from Liverpool John Moores University, Liverpool, U.K., in 2006. He has been a Lecturer in the Department of Electrical Engineering, AMU, since 1991, where he is currently working as an Associate. He is on academic assignment and is working at Qatar University, Doha, Qatar. His principal areas of research interest is power electronics and multiphase machine drives. Dr. Iqbal was a recipient of the Maulana Tufail Ahmad Gold Medal for standing first at the B.Sc. Engg. Exams in 1991 from AMU and a research fellowship from EPSRC, U.K., for working toward the Ph.D. degree.
IQBAL et al.: SPACE VECTOR PWM TECHNIQUE FOR A THREE-TO-FIVE-PHASE MATRIX CONVERTER
Sk Moin Ahmed (S’10) was born in Hooghly, West Bengal, India, in 1983. He received the B.Tech. and M.Tech. degrees from Aligarh Muslim University (AMU), Aligarh, India, in 2006 and 2008, respectively, where he is currently working toward the Ph.D. degree. He is also pursuing a research assignment at Texas A&M University, Doha, Qatar. His principal areas of research are modeling, simulation, and control of multiphase power electronic converters and fault diagnosis using artificial intelligence. Mr. Ahmed was a gold medalist in earning the M.Tech. degree. He was a recipient of a Toronto fellowship funded by AMU. He also received the Best Research Fellow Excellence Award from Texas A&M University, Qatar, for the year 2010–2011.
707
Haitham Abu-Rub (M’99–SM’07) received the Ph.D. degree from the Electrical Engineering Department, Technical University of Gdansk, Gdansk, Poland. His main research focuses on electrical drive control, power electronics, and electrical machines. He is currently a Senior Associate Professor at Texas A&M University, Doha, Qatar. Dr. Abu-Rub has earned many prestigious international awards including the American Fulbright Scholarship, the German Alexander von Humboldt Fellowship, the German DAAD Scholarship, and the British Royal Society Scholarship.
