Simple Carrier-Based PWM Technique for a Three ... - Semantic Scholar

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 11, NOVEMBER 2011

Simple Carrier-Based PWM Technique for a Three-to-Nine-Phase Direct AC–AC Converter Sk. Moin Ahmed, Student Member, IEEE, Atif Iqbal, Senior Member, IEEE, Haitham Abu-Rub, Senior Member, IEEE, Jose Rodriguez, Fellow, IEEE, Christian A. Rojas, Student Member, IEEE, and Mohammad Saleh

Abstract—Multiphase (more than three phases) power electronic converters are required mainly for feeding variable-speed multiphase drive systems. This paper presents one such solution by using a direct ac–ac converter that can be used to supply a nine-phase drive system. The input is a fixed-voltage and fixedfrequency three-phase input, and the output is a variable-voltage and variable-frequency nine-phase output. A simple pulsewidthmodulation technique is developed for the proposed ac–ac converter named as a nonsquare three-to-nine-phase matrixconverter configuration. The developed modulation technique is based on the comparison of a high-frequency carrier signal with the duty ratios. Although the carrier-based scheme is widely employed for the control of back-to-back converters, it has recently been used for controlling a three-to-three-phase matrix converter. This concept is extended in this paper for controlling a threeto-nine-phase matrix converter. With the two techniques that are proposed, one outputs 0.75 of the input magnitude and the other outputs reach 0.762 of the input. This is the maximum value of the output voltage in the linear modulation range that can be achieved in this configuration of the matrix converter. The viability of the proposed control techniques is proved analytically through simulation and an experimental approach. Index Terms—AC–AC converter, carrier-based pulsewidth modulation (PWM), matrix converter, multiphase, nine-phase.

I. I NTRODUCTION

C

ONTROLLED bidirectional power flow using direct ac–ac conversion as well as semiconductor switches that are arranged in the form of a matrix array are popularly known as matrix converters. Matrix converters have recently attracted Manuscript received October 19, 2010; revised January 13, 2011 and March 7, 2011; accepted March 16, 2011. Date of publication March 28, 2011; date of current version September 7, 2011. This publication was made possible in part by NPRP under Grant 08-369-2-140 from the Qatar National Research Fund and in part by the Council of Scientific and Industrial Research, New Delhi, under Grant 22(0462)/09/EMRII. S. M. Ahmed is with Aligarh Muslim University, Aligarh 202002, India, and also with Texas A&M University at Qatar, Doha, Qatar (e-mail: [email protected]). A. Iqbal is with Qatar University, Doha, Qatar, on leave from Aligarh Muslim University, Aligarh, India (e-mail: [email protected]). H. Abu-Rub is with Texas A&M University at Qatar, Doha, Qatar (e-mail: [email protected]). J. Rodriguez and C. A. Rojas are with the Universidad Tecnica Federico Santa Maria, Valparaíso 110-V, Chile (e-mail: [email protected]; [email protected]). M. Saleh is with Victoria University Australia, Melbourne, Vic. 8001, Australia, and also with Qatar Petroleum, Doha, Qatar (e-mail: [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/TIE.2011.2134062

much attention among researchers. They are becoming a serious contender to their counterpart, back-to-back converters, due to some inherent attractive features. A comprehensive overview of the development in the field of matrix-converter research is presented in [1]. It should be noted here that the most common configuration of the matrix converter discussed in the literature are three-to-three-phase ones [2], [3]. Little attention has been paid to the development of matrix converters with more than three outputs. 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 back-to-back converter 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 electronic converters makes it possible to consider the number of phases as a degree of freedom, i.e., an additional design variable. Multiphase motor drives have some inherent advantages over the traditional three-phase motor drives. Among these are the reduction of the amplitude, the increase of the frequency of torque pulsations, reduction in the rotor harmonic current losses, and lower dc link current harmonics. In addition, due to their redundant structure, multiphase motor drives improve the system reliability. Detail reviews on the development in the area of multiphase drives are presented in [4]–[9]. Since multiphase drive systems have gained popularity, a need is felt to develop power electronic converters to supply such multiphase systems. The multiphase drive systems are invariably supplied from a multiphase voltage-source inverter. A multiphase voltagesource inverter utilizes two stage power conversions and suffers from the same disadvantages of a three-phase voltage-source inverter of a distorted input current and poor input power factor. Thus, this paper focuses on the development of a novel topology of matrix converters, which is a single-stage power converter that is able to produce more than three phases. The performance of power electronic converters (ac–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 output [10], [11] and multiphase output [9], [12]. Modulation methods of matrix converters are complex and are generally classified in two different groups, direct and indirect. The direct pulsewidth-modulation (PWM) method developed by Alesina and Venturini [13] limits the output to

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AHMED et al.: CARRIER-BASED PWM TECHNIQUE FOR THREE-TO-NINE-PHASE DIRECT AC–AC CONVERTER

half the input voltage. This limit was subsequently raised to 0.866 by taking advantage of third harmonic injection [14]. 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. The space-vector PWM method for the three-to-three-phase matrix converter is elaborated in [15] and [16]. Although the space-vector PWM method and singularvalue-decomposition-based algorithm [17], [18] are suited for a three-phase system, the complexity of implementation increases with the increase in the number of switches/phases. Motivated from the simple implementation, a carrier-based PWM scheme has been introduced recently for the three-tothree-phase matrix converter [19]–[24]. A generalized carrierbased PWM scheme is suggested in [25] where the analytical expression for the distribution of a zero vector is presented. The results show a marginal distortion in the input current. However, the aim of this paper is to reduce the common-mode voltage. Recently, three-to-three-phase matrix converters are considered for several specialized applications such as wind generation systems [26], [27], ground power supply units for aircraft servicing [28], utility supply [29], sensorless electric drive applications [30], [31], and direct torque control of permanentmagnet synchronous motor drives [32]. These literatures show the growing popularity of this power converter topology. A direct ac–ac converter with three input phases and five output phases has been proposed recently [33]. A similar carrierbased PWM technique is developed for the topology with five output phases. A similar concept is extended in this paper for nine output phases. An alternative power electronic converter that can convert direct ac to ac is called back-to-back converter, and it is the real competitor of the proposed matrix converter. This topology uses a controlled rectifier in conjunction with the conventional inverter, offering the bidirectional power flow capability [34], [35]. When the two topologies (proposed three-to-nine-phase direct ac–ac converter and back-to-back converter) are compared, it is evident that 24 and 27 power switching devices are needed for back-to-back converters and three-to-nine-phase converters, respectively. The major advantage of the back-toback converter is that it offers bidirectional power flow by using fewer numbers of power switching devices and also by using unidirectional insulated-gate bipolar transistors (IGBTs). However, the requirement of a bulky dc link capacitor cannot be avoided. Moreover, the back-to-back converter needs an extra feedback current control loop for controlling the rectifier d–q axis current and also a voltage control loop for controlling the dc link voltage. Additionally, the matrix-converter topology has the capability of providing active damping by injecting reactive power. The back-to-back converter has a limitation of reactive power injection due to limited component ratings. Further comparison can be done by looking at the per switch output current, and it is lower in the case of matrix converters and, thus, is better suited for high current start-up applications and for continuous low-frequency operation. In this paper, a carrier-based PWM strategy is presented based on the comparison of the modulating signals (ninephase target output voltages) with the high-frequency triangular carrier wave. The output voltage is limited to 0.75 of

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Fig. 1. Power circuit topology of three-to-nine-phase matrix converter.

the input voltage’s magnitude in the simple extension of the three-phase system. Another scheme that is suggested in this paper is utilizing the injection of common-mode voltage in the output nine-phase target voltage. This results in an enhanced output voltage equal to 0.762 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. However, this limit can be further enhanced by employing overmodulation and at the cost of introducing low-order harmonics in the output. An analytical approach is used to develop and analyze the proposed modulation techniques and is further supported by simulation and experimental results.

II. T HREE - TO -N INE -P HASE M ATRIX C ONVERTER The power circuit topology of a three-to-nine-phase matrix converter is shown in Fig. 1. There are nine legs, with each leg having three bidirectional power switches connected 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 with LC filters, and the output is nine phases with 40◦ phase displacement between each phase. The load to the matrix converter is assumed to be a starconnected nine-phase ac machine. The switching function is defined as Sjk = {1 for closed switch, 0 for open switch}, j = {a, b, c} (input), k = {A, B, C, D, E, F, G, H, I} (output). The switching constraint is Sak + Sbk + Sck = 1. As an analogy to the voltage-source inverter, matrix converters can be seen as a three-level inverter [17], where the levels are the input voltages instead of 0, half dc link, and dc link voltages. The input phases are labeled with small letters, while the output phases are denoted with capital letters. The duty ratio of the upper switch is labeled as δap , the middle switch is labeled as δbp , and the lower switch with δcp . It is emphasized that the following constraint applies to these duty ratios: δap + δbp + δcp = 1.

(1)

It is to be further noted that the modulation technique is developed by assuming the input side as a three-phase controlled rectifier and the output is a nine-phase voltage-source inverter

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with a fictitious dc link. The input and output voltages and currents are then related as [v out ] = [δ][v in ] [iin ] = [δ][iout ] ⎡ δaA ⎢ δaB ⎢ ⎢ δaC ⎢ ⎢ δaD ⎢ [δ] = ⎢ δaE ⎢ ⎢ δaF ⎢ ⎢ δaG ⎣ δaH δaI

(2) (3) δbA δbB δbC δbD δbE δbF δbG δbH δbI

⎤

δcA δcB ⎥ ⎥ δcC ⎥ ⎥ δcD ⎥ ⎥ δcE ⎥ ⎥ δcF ⎥ ⎥ δcG ⎥ ⎦ δcH δcI

kA = m cos(ωo t) kB = m cos(ωo t − 2π/9) (4)

kE = m cos(ωo t − 8π/9)

The carrier-based PWM scheme developed in this section follows the similar concept presented in [17]. Since the input side is three phase, the analytical treatment remains the same as that of [17]. However, the output is now increased to nine, and hence, the analysis will be modified to suit the requisite output phase number. A balanced three-phase system is assumed at the input, and an unbalanced study will be reported separately

(5)

Since the matrix converter has output voltages with frequency decoupled from the input voltages, the duty ratios of the switches are to be calculated accordingly. Thus, the duty ratios for output phase p are obtained as

(6)

where p = {A, B, C, D, E, F, G, H, I}, |V | is the peak amplitude of the input voltage, and φ is the phase shift. Therefore, the phase “pth” output voltage can be synthesized as vp = δap va + δbp vb + δcp vc .

(7)

After simple trigonometric manipulations, the following relation is obtained for output pth phase: vp =

3 kp |V | cos(φ). 2

kF = m cos(ωo t − 10π/9) kG = m cos(ωo t − 12π/9) kH = m cos(ωo t − 14π/9) kI = m cos(ωo t − 16π/9).

III. C ARRIER -BASED PWM T ECHNIQUE

δap = kp cos(ωt − φ) π δbp = kp cos ωt − 2 − φ 3 π δcp = kp cos ωt + 2 − φ 3

kC = m cos(ωo t − 4π/9) kD = m cos(ωo t − 6π/9)

where [v out ] = [vA vB vC vD vE vF vG vH vI ]T , [v in ] = [va vb vc ]T , [iout ] = [iA iB iC iD iE iF iG iH iI ]T , and [iin ] = [ia ib ic ]T .

va = |V | cos(ωt) π vb = |V | cos ωt − 2 3 π . vc = |V | cos ωt − 4 3

output voltages are independent of the input frequency and only depend on the phase shift, the amplitude of the input voltage, as well as the constant kp (which is the reference output-voltage time-varying modulating signal for the output phase p with the desired output frequency ωo ). The nine-phase reference output voltages can thus be represented as

(8)

In the aforementioned equation, the cos(φ) term indicates that the output voltage is affected by the phase shift φ. Thus, the

(9)

The output voltages can then be formulated by substituting (9) in (8). A. Application of Offset Duty In the aforementioned explanation, duty ratios become negative, which are not practically realizable. For the switches connected to output phase A, at any instant, the condition 0 ≤ daA , dbA , dcA ≤ 1 should be valid. Therefore, offset duty ratios should be added to the existing duty ratios so that the net resultant duty ratios of individual switches are always positive. Furthermore, the offset duty ratios should be added equally to all the output phases to ensure that the effect of the resultant output-voltage vector produced by the offset duty ratios is null in the load. That is, the offset duty ratios can only be added to the common-mode voltages in the output. Considering the case of output phase A π daA + dbA + dcA = kA cos(ωt − ρ) + kA cos ωt − 2 − ρ 3 π +kA cos ωt − 4 − ρ = 0. (10) 3 Absolute values of the duty ratios are added to cancel the negative components from individual duty ratios. Thus, the minimum individual offset duty ratios should be Da (t) = |kA cos(ωt − ρ)|, Db (t) = |kA cos(ωt − 2π/3 − ρ)|, and Dc (t) = |kA cos(ωt − 4π/3 − ρ)|. The effective duty ratios are {daA + Da (t), dbA + Db (t), dcA + Dc (t)}. Other output phases can be written similarly. The net duty ratio, daA + Da (t), should be accommodated within a range of 0–1. Therefore, 0 ≤ daA + Da (t) ≤ 1 can be written as 0 ≤ kA cos(ωt − ρ) + |kA cos(ωt − ρ)| ≤ 1.

(11)

For the worst case, 0 ≤ 2|kA | ≤ 1. The maximum value of kA or, in other words, m in (9) is equal to 0.5. Hence, the


Fig. 2.

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Modified offset duty ratios for all input phases.

offset duty ratios corresponding to the three input phases are chosen as Da (t) = |0.5 cos(ωt − ρ)|π

Db (t) = 0.5 cos ωt − 2 − ρ

3

π

Dc (t) = 0.5 cos ωt − 4 − ρ . 3

(12)

The duty ratios for output phase A are daA = Da (t) + kA cos(ωt − ρ)

π dbA = Db (t) + kA cos ωt − 2 − ρ 3 π dcA = Dc (t) + kA cos ωt − 4 − ρ . 3

(13)

In any switching cycle, the output phase has to be connected to any of the input phases. The summation of the duty ratios in (13) must be equal to unity. However, the summation Da (t) + Db (t) + Dc (t) is less than or equal to unity. Hence, another offset duty ratio (1 − Da (t) − Db (t) − Dc (t))/3 is added to Da (t), Db (t), and Dc (t) in (14). The addition of this offset duty ratio in all switches will keep the output voltages and input currents unaffected. Similarly, the duty ratios are calculated for the other output phases. The final modified duty ratios are shown in Fig. 2. If kj with j = {A, B, C, D, E, F, G, H, I} are chosen to be nine-phase sinusoidal references as given in (9), the inputvoltage capability is not fully utilized for output-voltage generation. To overcome this, an additional common-mode term equal to (max(kj ) + min(kj ))/2 is added as in the carrierbased space-vector PWM principle as implemented in two-level inverters. Thus, the amplitude of kj can be enhanced from 0.5 with 0.5077. This is shown in Fig. 3 for an output phase. In the next section, the analytical expressions are given for the case of a three-to-nine-phase matrix converter.

C. With Common-Mode Voltage Addition The duty ratio for output phase A can be written as daA = Da (t) + (1 − Da (t) − Db (t) − Dc (t)) /3 + (kA − (max(kj ) + min(kj )) /2) cos(ωt − ρ) dbA = Db (t) + (1 − Da (t) − Db (t) − Dc (t)) /3 + (kA − (max(kj ) + min(kj )) /2) × cos(ωt − 2π/3 − ρ) dcA = Dc (t) + (1 − Da (t) − Db (t) − Dc (t)) /3 + (kA − (max(kj ) + min(kj )) /2) × cos(ωt − 4π/3 − ρ) (15) where j = {A, B, C, D, E, F, G, H, I} and Da (t) = |0.5 cos(ωt − ρ)| Db (t) = |0.5 cos(ωt − 2π/3 − ρ)| Dc (t) = |0.5 cos(ωt − 4π/3 − ρ)| .

B. Without Common-Mode Voltage Addition The duty ratio for output phase A can be written as daA = Da (t) + kA cos(ωt − ρ) + (1 − Da (t) − Db (t) − Dc (t)) /3 dbA = Db (t) + kA cos(ωt − 2π/3 − ρ) + (1 − Da (t) − Db (t) − Dc (t)) /3 dcA = Dc (t) + kA cos(ωt − 4π/3 − ρ) + (1 − Da (t) − Db (t) − Dc (t)) /3.

Fig. 3. Output-voltage reference: (a) With and without common mode added reference for an output phase. (b) References and ninth harmonic for phase A.

(16)

D. Modified Duty Ratio by Ninth-Harmonic Injection at Output Reference

(14)

This section presents an alternative technique of enhancing the output-voltage magnitudes. This is done by injecting the ninth harmonic component of the output reference voltages

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function of duty ratios, and output currents are represented by (3). Considering the case for input phase a, the input current of phase a can be represented as ia = daA iA + daB iB + daC iC + daD iD + daE iE + daF iF + daG iG + daH iH + daI iI . (18) The duty ratios contain original duty ratios along with offset duty ratios and common-mode terms or harmonic injection terms as in (15)–(17). The offset duty ratios and common-mode terms or harmonic injection term will not produce any effect on the input current if the nine-phase output currents are balanced as these terms are similar for a particular input phase Fig. 4. Nine-phase reference voltages with different line voltage configuration.

into the output fundamental references. By doing so, the ninth harmonic does not appear at the output voltages. Consequently, the output-voltage magnitude is enhanced to the same level as that of the technique discussed in Section III-C. This technique is employed for enhancing the output fundamental magnitude in a two-level multiphase voltage-source inverter [36]. The difference between the technique of Section III-C and that of this section is that the offset of (16) contains all multiples of the ninth harmonic, i.e., 9n, where n = 1, 2, 3, . . . harmonics. The optimum level for the ninth harmonic to be injected is given as [34] π 1 . (17) m9 = −m1 sin 9 18 Here, m9 is the magnitude of the ninth harmonic to be injected and m1 is the magnitude of the fundamental output. The reference phase A voltage, the injected ninth harmonic, and the combined reference and ninth harmonic are shown in Fig. 3(b). It is observed from Fig. 3(b) that the output reference peak reduces to below the limiting value of 0.5, thus allowing room to further enhance the reference magnitude, resulting in an increase of 1.54% of the output voltage. The gating signals for the power switches are obtained by comparing the duty ratios daA (t), daA (t) + dbA (t), and daA (t) + dbA (t) + dcA (t) = 1, with the high-frequency triangular carrier wave. The intersection of the carrier with these three duty ratios generates the three gating signals for the three switches of leg A. Similarly, the gating signals can be produced for all 27 power switches. The nine-phase output-voltage references have four categories of line voltage references. These line voltage references can be described as Adjacent (Adj), Nonadjacent-1 (Adj-1), Nonadjacent-2 (Adj-2), and Nonadjacent-3 (Adj-3), as shown in Fig. 4. Adj output line voltages are 68.4% of the output phase voltages. Adj-1 output line voltages are 128.5% of the output phase voltages. Adj-2 output line voltages are 173.2% of the output phase voltages. Adj-3 output line voltages are 197% of the output phase voltages. E. Input-Power-Factor Calculation Input power factor can be derived by obtaining the input-andoutput-current relationship. The input current of a phase is a

(Of f set duty ratios along with common-mode terms or harmonic injection terms) ×(iA +iB +iC +iD +iE +iF +iG +iH +iI ) = 0. (19) Hence ia = (kA iA + kB iB + kC iC + kD iD + kE iE + kF iF + kG iG + kH iH + kI iI ) × cos(ωt − ρ).

(20)

Since the quantities (kA , kB , kC , kD , kE , kF , kG , kH , kI ) and (iA , iB , iC , iD , iE , iF , iG , iH , iI ) are the nine-phase output sinusoidal quantities, the term (kA iA + kB iB + kC iC + kD iD + kE iE + kF iF + kG iG + kH iH + kI iI ) =

9 mI0 cos φ0 2

(21)

where “m” is the amplitude of the modulation indexes kA , kB , kC , kD , kE , kF , kG , kH , kI in (9). I0 and φ0 are the amplitude of the output currents and output power factor angle, respectively. Combining (20) and (21), input currents can be written as 9 ia = mI0 cos φ0 cos(ωt − ρ) 2 9 2π −ρ ib = mI0 cos φ0 cos ωt − 2 3 9 4π ic = mI0 cos φ0 cos ωt − −ρ . 2 3

(22)

From (5), the input phase a voltage is given as va = |V | cos(ωt). Therefore, input current ia has a lagging phase of ρ with the input voltage va . For unity power factor, ρ has to be chosen as zero. IV. I NVESTIGATION R ESULTS A. Simulation Results The 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


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Fig. 5. Input-side waveforms of three-to-nine-phase matrix converter: (Upper trace) Source voltage and current. (Bottom trace) Input current and spectrum input current.

values R = 10 Ω and L = 1 mH. The operation of the proposed topology of the matrix converter is tested for a wide range of frequencies, from as low as 1 Hz to higher frequencies for deep flux weakening operation. The simulation results are shown for the modulation with common-mode voltage addition in the output target voltage, and the resulting waveforms are shown in Figs. 5–8. The resulting waveforms with common-mode voltage addition remain the same, with the exception of the enhanced output magnitude. Since the common-mode voltage addition does not change the nature of the output, only one set of results is presented. The results with 50-Hz input supply frequency and 25-, 60-, and 5-Hz output supply frequencies are analyzed in Figs. 6–8, respectively. The results of Fig. 5 (upper trace) show the input sinusoidal voltage waveform and the filtered input-side current. The waveform clearly shows unity power factor at the input side. This result matches the three-to-three-phase conventional matrix converters. Nevertheless, this is one of the distinct advantages of the matrix converter, obtaining unity power factor input contrary to the voltage-source inverter and back-to-back converter. The sinusoidal nature of the input current is another distinct feature of the matrix converter. The input-side current spectrum shown in Fig. 5 (lower trace) yields a completely sinusoidal waveform while completely eliminating the lower order harmonics. The total harmonic distortion in the inputcurrent waveform is obtained as 0.6%, which is well within the tolerance limit specified 19-1999 standard. The output Adj-3 line-to-line voltages and phase currents for the star-connected

Fig. 6. Output-side waveforms for 25-Hz output: (Upper trace) Nine-phase output Adj-3 line-to-line voltages. (Bottom trace) Output currents.

nine-phase R–L are shown in Figs. 6–9. A balanced nine-phase output is observed. Similar results are obtainable for all operating frequencies, showing successful operation of the proposed matrix converter. The presented results clearly show successful phase transformation from three-phase input to nine-phase output. The input current will not show significant change for the change in frequency for low inductive load, and thus, only one trace for input current is shown in Fig. 5 at 25-Hz case only. The simulation results verify the effectiveness of the proposed solution. Hence, the proposed direct ac–ac converter can be employed for widerange speed control of multiphase drive systems. To show the ratio between input and output voltages, fast Fourier transform is performed for the Adj-3 line voltage and shown in Fig. 9. The output Adj-3 line voltage is shown as 149.5 V, which is about 197% of the output phase voltage. B. Experimental Results A prototype three-to-nine-phase matrix converter is developed where the input is three phase and the output can be configured from a single phase to nine phases. The proposed carrier-based modulation scheme is implemented for a threeto-nine-phase matrix converter. The block schematic of the experimental setup is shown in Fig. 10. The power module is a bidirectional switch FIO 50-12 BD from IXYS and is composed of a diagonal IGBT and fast diode bridge in ISOPLUS i4-PAC.

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The voltage-blocking capability of the device is 1200 V, and the current capacity is 50 A. This comes in a 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 [37]. 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 such bidirectional power switches. 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. Input supply is given from an autotransformer and is fixed at 100 V and 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 100 μH, 10 A and 15 μF, 440 V, respectively. The developed matrix converter is tested for a wide range of output frequencies. A nine-phase R−L load is connected at the output terminals of the matrix


Fig. 9.

Spectrum of output Adj-3 line-to-line voltage.

converter with R = 10 Ω and L = 10 mH. The modulation code uses common-mode injection method. The resulting output waveforms for the fundamental frequency of 25, 60, and 5 Hz are shown in Figs. 11–13, respectively. The output Adj-3 line voltage for all the output fundamental frequencies have an amplitude of about 150 V. The simulation and experimental results match to a good extent. This proves the viability of the proposed modulation scheme for a three-to-nine-phase matrix converter. To further


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Fig. 10. Block diagram of experimental setup.

Fig. 12. Output-side nine-phase waveform for 60 Hz: (Upper trace) Output Adj-3 line-to-line voltage (100 V, 10 ms/div). (Bottom trace) Output phase currents (4 A, 5 ms/div).


show the unity power factor at the input side, one input phase voltage and current is shown in Fig. 14. It is evident that unity power factor is maintained at the input side. The proposed PWM scheme in this paper is equally applicable to nonsinusoidal output-voltage generation. Nonsinusoidal output voltages are particularly needed for multiphase drive applications to enhance the torque production. In addition, nonsinusoidal output is required to control two or more series/parallel-connected multiphase machines. The converter output voltages are nonsinusoidal in this case with the combination of different frequencies and amplitudes. The nine-phase matrix converter is capable of generating these nonsinusoidal voltages with controllable input displacement power factor. For the verification of generating nonsinusoidal output voltages,


two different commanding frequencies (60 and 30 Hz) are applied with the amplitude ratio of 2:1. The experimental results are shown in Figs. 15 and 16.

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ACKNOWLEDGMENT The statements made herein are solely the responsibility of the authors. R EFERENCES

Fig. 14. Input-side voltage (40 V, 10 ms/div) and current (20 A, 10 ms/div).

Fig. 15. Output filtered phase voltages for 60- and 30-Hz combination: (20 V/div and 10 ms/div).

Fig. 16. Input-side voltage (40 V/div, 10 ms/div) and current (10 A/div, 10 ms/div).

V. C ONCLUSION A novel topology of a matrix converter has been discussed in this paper. The input to the matrix converter is a threephase ac supply and the output is nine phase. This converter is useful in a nine-phase motor drive application. It possesses all the advantages offered by a conventional matrix converter such as a sinusoidal input current and unity power-factor operation at input irrespective of the load power factor. However, the output-voltage magnitude is found to be limited to 76.2% of the input-voltage magnitude in the linear modulation region. This is the limitation associated with this type of ac–ac converter. The proposed PWM strategy is derived from the analogy of the modulation of a voltage-source inverter. The analytical findings are confirmed using simulation and an experimental approach.

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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 working toward a research assignment with 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 is a recipient of a Toronto Fellowship funded by AMU.

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 with the Department of Electrical Engineering, AMU, since 1991, where he is currently an Associate. He is on academic assignment and is currently with Qatar University, Doha, Qatar. His principal areas of research are power electronics and multiphase machine drives. Dr. Iqbal is a recipient of a Maulana Tufail Ahmad Gold Medal for ranking first in the B.Sc. Engineering Exams in 1991 and an AMU research fellowship from the Engineering and Physical Sciences Research Council, U.K., for working toward the Ph.D. degree.

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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. Currently, he is a Senior Associate Professor with Texas A&M University, Doha, Qatar. Dr. Abu-Rub is the recipient of 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.

Jose Rodriguez (M’81–SM’94–F’10) received the Engineer degree in electrical engineering from the Universidad Tecnica Federico Santa Maria (UTFSM), Valparaiso, Chile, in 1977 and the Dr.-Ing. degree in electrical engineering from the University of Erlangen, Erlangen, Germany, in 1985. Since 1977, he has been with the Department of Electronics Engineering, Universidad Tecnica Federico Santa Maria, where he was the Director from 2001 to 2004 and is currently a Professor. From 2004 to 2005, he was the Vice Rector of Academic Affairs, and since 2005, he has been the Rector of the same university. His research interests include multilevel inverters, new converter topologies, control of power converters, and adjustable-speed drives. Dr. Rodriguez has been an active Associate Editor for the IEEE T RANS ACTIONS ON P OWER E LECTRONICS and the IEEE T RANSACTIONS ON I NDUSTRIAL E LECTRONICS since 2002. He has served as Guest Editor for the IEEE T RANSACTIONS ON I NDUSTRIAL E LECTRONICS in six instances [Special Sections on Matrix Converters (2002), Multilevel Inverters (2002), Modern Rectifiers (2005), High Power Drives (2007), Predictive Control of Power Converters and Drives (2008), and Multilevel Inverters (2009)]. He was the recipient of the Best Paper Award from the IEEE T RANSACTIONS ON I NDUSTRIAL E LECTRONICS in 2007 and from the IEEE I NDUSTRIAL E LECTRONICS M AGAZINE in 2008.

Christian A. Rojas (S’10) received the Engineer degree in electronic engineering from the Universidad de Concepcion, Concepcion, Chile, in 2009. He is currently working toward the Ph.D. degree at the Universidad Tecnica Federico Santa Maria, Valparaiso, Chile. He was awarded a scholarship from the Chilean Research Foundation CONICYT in 2010 to pursue his Ph.D. studies in power electronics. His research interests include matrix converters, digital control, and model predictive control of power converters and drives.

Mohammad Saleh received the B.S. degree in electrical engineering from the University of North Carolina, Charlotte, in 1989 and the M.S. degree in telecommunication and the Postgraduate Diploma in Education and Training from Victoria University, Melbourne, Australia, where he is currently working toward the Ph.D. degree. He is currently with Qatar Petroleum, Doha, Qatar.