Harmonic Loss Due to Operation of Induction Machines ... - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 2, FEBRUARY 2008

809

Harmonic Loss Due to Operation of Induction Machines From Matrix Converters Patrick W. Wheeler, Member, IEEE, Jon C. Clare, Senior Member, IEEE, Maurice Apap, and Keith J. Bradley, Associate Member, IEEE

Abstract—This paper quantifies the extra harmonic losses in an induction motor that are associated with the use of a matrix converter topology as a motor drive. These extra losses are compared to the harmonic losses associated with an inverter-based motor drive. The technique employed in the determination of the harmonic losses is described. For the matrix converter, the extra harmonic losses associated with two commonly used modulation techniques are calculated and compared. The impact of these extra losses on the cooling requirements and operation of the motor is considered. Index Terms—AC/AC power converters, calorimeter, harmonic losses, induction motors, matrix converters.

I. I NTRODUCTION

T

HE three-phase matrix converter, as shown in Fig. 1, could become a viable alternative to the voltage source inverter providing unity input power factor, bidirectional power flow, an improved input current harmonic content, and an overall reduction in size since large reactive components are not required [1]–[3]. This paper focuses on the extra harmonic loss resulting in an induction motor supplied for a matrix converter relative to operation from a sinusoidal supply. Where the extra harmonic loss is significant, appropriate derating must be applied for continuous operation. Knowledge of the extra harmonic loss is of particular importance for an integrated drive application where the motor cooling must be designed to remove the semiconductor device power loss in addition to the motor power loss. The harmonic loss in an induction motor supplied from an inverter is measured using a harmonic injection technique as described in [4]–[6]. This technique is applied to obtain the variation of a harmonic loss factor, which is measured in milliwatts per square volt, with the harmonic frequency for the motor under test. The extra harmonic loss for the induction motor under any operating condition can then be predicted from the harmonic loss factor curve and the harmonic content of the motor supply voltage. The technique has then been practically verified for motor operation with an inverter using calorimetric methods [6].

Manuscript received December 14, 2005; revised October 1, 2007. P. W. Wheeler, J. C. Clare, and K. J. Bradley are with the School of Electrical and Electronic Engineering, University of Nottingham, NG7 2RD Nottingham, U.K. M. Apap is with the University of Malta, Msida MSD 2080, Malta. 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.2007.910527

Fig. 1. Three-phase matrix converter.

The extra harmonic loss due to a matrix converter supply controlled by the modulation strategies described in [7] and [8] is calculated in this paper. A comparison with the loss due to an inverter with regular asymmetric pulsewidth modulation (PWM) is also presented. A. Three-Phase Matrix Converter The maximum line–line output voltage of the matrix converter must not be greater than the minimum line–line input voltage. This condition gives the maximum output voltage intrinsic limit of 0.866 [3]. The objective of any matrix converter modulation strategy is to obtain the target output voltages and sinusoidal input currents at a controlled input power factor subject to the constraints of not open circuiting any output phase and of not short circuiting any two input phases. Various modulation strategies have been formulated to meet this objective. The two modulation strategies most widely used in the implementation of practical matrix converters will be considered in this paper [3]. These are the optimum-amplitude Alesina–Venturini (AV) method [7] and the three-zero space vector modulation (SVM) method [15]. Many other strategies exist, but SVM techniques with one or two zeros [8] suffer from practical problems with short switch duty cycles at low modulation depths [9]. The often used cyclic variation of the AV method can be shown to be equivalent to the three-zero SVM method in terms of the vectors used and the switch duty cycles employed [8], and is therefore not separately considered in this paper.

0278-0046/$25.00 © 2008 IEEE

810


B. Optimum-Amplitude AV Method Defining the modulation duty cycle for switch Sjk as mjk (t) = tjk /Tseq gives the following input–output relations:  v1o (t)  v2o (t)  = v3o (t)   i1i (t)  i2i (t)  = i3i (t) 



m11 (t)  m21 (t) m31 (t)  m11 (t)  m12 (t) m13 (t)

  v1i (t) m12 (t) m13 (t) m22 (t) m23 (t)   v2i (t)  m32 (t) m33 (t) v3i (t)   i1o (t) m21 (t) m31 (t) m22 (t) m32 (t)   i2o (t)  m23 (t) m33 (t) i3o (t)

TABLE I LIST OF ALL POSSIBLE MATRIX CONVERTER SWITCHING CONFIGURATIONS. THE SHORTHAND NOTATION FOR THE CONVERTER STATE GIVES THE INPUT PHASES CONNECTED TO OUTPUT PHASES 1, 2, AND 3 IN THE F IRST , S ECOND , AND T HIRD S UBSCRIPT , R ESPECTIVELY . αo IS THE ANGLE OF THE OUTPUT VOLTAGE VECTOR, AND βi IS THE ANGLE OF THE INPUT CURRENT VECTOR

(1)

(2)

where the switches, voltages, and currents are defined using the symbols shown in Fig. 1. To obtain a maximum modulation index of 0.866, input and output third harmonics are added to the target output fundamental voltage [7] as 

 cos(ωo t)− 16 cos(3ωo t)+ 2√1 3 cos(3ωi t)   1 1 √ [vo (t)] = qVimcos ωo t+ 2π 3 − 6 cos(3ωo t)+ 2 3 cos(3ωi t)  1 1 √ cos ωo t+ 4π 3 − 6 cos(3ωo t)+ 2 3 cos(3ωi t) (3) where Vim is the magnitude of the input voltage, and ωo and ωi are the output and input frequencies, respectively. Given that the input voltage set is  cos(ω i t)  [vi (t)] = Vim  cos ωi t + 2π 3 4π cos ωi t + 3 

(4)

the required modulation duty cycle for unity input power factor operation [3] is given by mjk

1 4q 2vKi vjo = + √ sin(ωi t + βk ) sin(3ωi t) 1+ 2 3 Vim 3 3 (5)

for k = 1, 2, 3 and j = 1, 2, 3, where βk = 0, 2π/3, 4π/3, for k = 1, 2, 3, respectively. Each output phase is connected to the input phases in the sequence 1–2–3 during any switching period. Fig. 2. Output line-to-neutral voltage vector and input line current vector directions generated by the 18 fixed-direction configurations.

C. SVM For the operation of the matrix converter within the constraints of Section I-A, at any instant, one and only one switch in each output phase must be conducting. This leads to 27 possible switching combinations for the matrix converter. By applying (6) and (7) to determine the output voltage and input current vectors, respectively, the magnitude and phase of these vectors for all the possible combinations are given in Table I [8]. We then have 2 v o = (v1o + av2o + a2 v3o ) 3 2 ii = (i1i + ai2i + a2 i3i ) 3

(6) (7)

where v1o , v2o , and v3o are the output phase voltages, and i1i , i2i , and i3i are the input line currents a ≡ ej

2π 3

.

The 27 switching combinations can be grouped as follows: • Eighteen combinations where the output voltage and input current vectors have fixed directions with magnitudes that vary with the input voltage phase angle and the output current phase angle, respectively. These combinations result when any two output phases are connected to the same input phase.

WHEELER et al.: HARMONIC LOSS DUE TO OPERATION OF INDUCTION MACHINES FROM MATRIX CONVERTERS

811

TABLE II SELECTION OF SWITCHING CONFIGURATIONS FOR EACH COMBINATION OF KV AND KI

• Three combinations that give null output voltage and input current vectors. All three output phases are connected to the same input phase in these combinations. • Six combinations in which each output phase is connected to a different input phase. Both the magnitude and the phase of the resultant rotating vectors are variable in these cases. The SVM strategy presented in [8] makes use of the 18 fixeddirection and three null vector combinations to achieve the desired output voltage vector and input current direction. The six rotating vectors are not used and therefore do not have a switching configuration assignment. From Fig. 2, it can be noted that for any combination of output voltage and input current sectors, four configurations that produce output voltage vectors and input current vectors lying adjacent to the desired vectors can be identified. The switching configurations used for any output voltage sector (KV ) and input current sector (KI ) combinations are given in Table II. It can be shown that the required modulation duty cycles for switching configurations I, II, III, and IV are given for unity input power factor by [6] 2 π cos β˜i − õ − δ I = √ q cos α 3 3 2 π δ II = √ q cos α cos β˜i + õ − 3 3 2 π δ III = √ q cos α cos β˜i − õ + 3 3 2 π δ IV = √ q cos α cos β˜i + õ + 3 3 I δ0 = 1 − δ + δ II + δ III + δ IV

π 3 π 3

π 3 π 3

(8) (9) (10) (11) (12)

where α ˜ o and β˜i are the angles of the output voltage and input current vectors measured from the bisecting line of the corresponding sectors, and δ0 is the total modulation duty cycle for the zero configuration(s) required to complete the switching period. The SVM method applied in this paper uses all the three-zero configurations with equal duty cycles in each switching period. The sequence of switching configurations in each switching period is arranged such that only one switch commutates at each switching configuration change. A double-sided modulation pattern is used such that the switching configuration sequence

for two successive switching periods for KI = 1 and KV = 1 is 03 , −3, +9, 01 , −7, +1, 02 , 02 , +1, −7, 01 , +9, −3, and 03 . II. H ARMONIC L OSS M EASUREMENT T ECHNIQUE The determination of the additional harmonic power loss in induction machines consequent upon their operation from a power electronic source is difficult because that loss is, or should be, a small fraction of the total motor power on load. There are many papers that deal with predicting the power loss [8], [9], but only a few detail its experimental evaluation. Experimentally, it has been shown that the harmonic power loss is a function of the load on the machine for lower harmonic orders up to about 5 kHz [4]. Large power motors, where the PWM frequency is low, and all the machines fed from inverters with appreciable dead time, need to have their harmonic power loss evaluated under load. The measurement methods fall into three categories. The first is the direct measurement of power loss using a calorimeter [6], [12]–[14]. This requires two separate conditions, where the motor is tested when fed from a sinusoidal supply, and also under identical load and fundamental voltage conditions, where the motor is fed from an inverter supply. The difference between the two power loss conditions is then deemed to be the harmonic power loss. Experimentally, it is exceptionally difficult to maintain precisely similar test conditions, and each test takes several hours. The second uses indirect loss measurement, where the power loss in the motor is determined from the measurement of the input and output powers. The process is otherwise the same as for the calorimetric approach but is much less accurate because of the error involved in subtracting two similarly large powers (input and output) to obtain the much smaller power loss. The third approach is to use harmonic injection [4]–[6] and the principal of superposition. Superposition is acceptable here, although the motor is a nonlinear device, as only very small perturbations are made in the flux with the tightly controlled operating conditions remaining unchanged. A small high-frequency sinusoidally varying flux is induced in the motor by the addition of a harmonic voltage into its normal inverter supply. Crucially, a small flux perturbation, which has a harmonic current that is large enough to accurately measure, usually requires quite a large harmonic voltage, hence the specific need for injecting a range of harmonic voltages. The harmonic power loss associated with this voltage is directly determined from the harmonic voltage and current and their relative phase angle, which are

812


Fig. 4. Fig. 3. Harmonic loss measurement system.

obtained by Fourier analysis of the applied motor voltage and the resulting current. The phase accuracy of the voltage and current channels is crucial since the power factor of individual harmonics is very low. The harmonic has negligible output power, and thus, the harmonic power is all loss. This power can be normalized to unity harmonic voltage to define a loss factor. By performing repeated tests and scanning the injected harmonic over the frequency range of the expected principal inverter harmonics and their sidebands, a curve of loss factor against frequency can be constructed for the motor. Evaluating the harmonic power loss of the motor for any given spectrum of voltages applied to it is then simply a matter of taking each harmonic of voltage at a time, squaring it, and multiplying the result by the normalized loss factor for that harmonic. The summation of the power losses across the spectrum provides the total harmonic power loss. The technique has been shown to be accurate by comparison with the calorimetric approach [6]. It is more rapid than the calorimetric approach and only requires the voltage spectrum applied to the motor to be evaluated when it is operating from any power electronic supply in order to determine the resulting harmonic loss. It is thus much easier to apply for purposes of comparing power electronic sources. It is not susceptible to errors caused by small differences in the loading conditions between tests on the motor when it is fed from different supply sources. Accordingly, harmonic injection is used here to compare the inverter and matrix converter harmonic losses induced in the motor. The system used for harmonic loss measurement is shown in Fig. 3. The motor under test is fed from a 22-kW insulatedgate bipolar transistor (IGBT) inverter that has been modified to accept PWM signals from an SAB167-based PWM generator [6]. The PWM generator is programmed to produce regular asymmetric sampled PWM for a modulating function that consisted of the sum of the desired fundamental voltage, the third harmonic, and an additional injected harmonic. Adjustment of the load torque and of the fundamental voltage frequency and magnitude permits the determination of the motor harmonic losses for operation of the motor at fundamental flux and the desired loading conditions.

Harmonic loss factor curve for the test motor at 80% rated torque.

High-frequency sampling of two line–line voltages and two line currents followed by discrete Fourier transform (DFT) analysis provides the magnitude and phase of the injected harmonic components and hence the input injected harmonic power. The injected harmonic is assumed to contribute zero average output torque. The harmonic power loss is therefore equal to the harmonic input power. The accuracy of this measurement is determined by the normal expected accuracy of the current and voltage transducers. The switching and sampling frequencies are chosen to be multiples of the fundamental frequency such that the voltage and current harmonic spectra can be accurately determined by DFT analysis over one fundamental period. The injected harmonic is varied over a range from the fifteenth harmonic of the fundamental up to the carrier frequency of the PWM generator. The injected harmonic magnitude is increased with increasing frequency to maintain a significant injected harmonic current magnitude in order to accurately measure the harmonic power loss. The harmonic loss factor curve is extended beyond the switching frequency by measuring the harmonic loss at harmonics resulting from the interaction between the injected harmonic and the sidebands centered at multiples of the carrier frequency. A. Harmonic Loss Factor Results The harmonic loss measurement technique was applied to determine the harmonic loss factor curve for a 30-kW induction motor rated at 400 V and 54 A. The motor was operated at a fundamental frequency of 25 Hz and rated flux at 80% full load torque. The motor was controlled using a standard closed-loop vector control scheme. A carrier frequency of 8 kHz was used for PWM generation, and a 250-kHz clock signal from the PWM generator was applied to the external clock triggering of the transient digitizer. The line–line voltage and line current waveforms were recorded using voltage dividers, Hall effect current transducers, and 12-bit Lecroy digitizers. Compensation for the transducer phase angle errors was applied after DFT analysis of the sampled waveforms. Fig. 4 shows the harmonic loss factor curve


813

Fig. 6. Predicted harmonic loss variation with switching frequency at rated speed.

Fig. 7. Predicted harmonic loss variation with switching frequency at 50% speed.

obtained for the test motor. Harmonic loss measurements were performed after the motor reached thermal stability, and it was ensured that the dc link voltage and the fundamental flux remained constant throughout the test. The interpolation between the loss factor data from experimental results is required for the determination of the harmonic losses for any PWM supply. The following function was fitted to the harmonic loss factor curve for 80% full load torque using a least square approach:

Kh = Fig. 5. (a) Matrix converter (AV method) line voltage harmonic spectrum (fsmod = 8 kHz). (b) Matrix converter (SVM method) line voltage harmonic spectrum (fsmod = 8 kHz). (c) Inverter line voltage harmonic spectrum (fsmod = 8 kHz).

25.75 37.63 + 0.79 (mW/V2ph ) f 1.5 f

(13)

where f is in kilohertz. The harmonic loss factor curve is unique for each different motor and therefore must be experimentally obtained before harmonic loss evaluation and be considered.

814


TABLE III PREDICTED HARMONIC LOSS AT 80% RATED TORQUE AND RATED FLUX

III. L OSS P REDICTIONS Given a matrix converter input voltage of 415 V, an induction motor with a voltage rating of 340 V is suitable for operation over the full speed range. It is assumed that a 340-V rated motor constructed with the same frame size and rotor as the 400-V test motor is used. The number of turns in the winding of the 340-V motor would be higher than for the 400-V motor. When both motors are operated at the same flux level, an equivalent circuit approach shows that the harmonic loss is the same for both motors at a frequency where the same per unit magnitude is applied. For the 340-V motor operated at rated fundamental flux and 80% rated torque, the harmonic loss factor curve is then represented by the function

Kh =

400 340

2

25.75 37.63 + 0.79 f 1.5 f

mW/V2ph .

(14) Fig. 8.

The output voltage harmonic spectrum of a matrix converter controlled with the AV method is shown in Fig. 5(a). The spectrum for a matrix converter using the SVM method is shown in Fig. 5(b). The differences between the two modulation methods can be found in the structure of the sidebands around the switching frequency harmonics and the fact that the symmetrical nature of the SVM method gives harmonics at half the modulation frequency. These results were combined with the harmonic loss factor curve for the conditions of 80% torque and rated flux at rated speed and 50% speed to give the predicted variation of total harmonic loss with switching frequency in Figs. 6 and 7 for the AV and SVM methods, respectively. The predicted results for the inverter-fed induction motor [harmonic spectra shown in Fig. 5(c)] were obtained for a 400-V rated motor at the same flux and load conditions and an inverter dc link voltage of 600 V. These spectra clearly show that the harmonics around the switching frequency and multiples of the switching frequency are considerably richer in content for the matrix converter than the inverter, which leads to higher harmonic losses in the motor. The total harmonic loss results at modulation frequencies of 8 and 10 kHz are listed in Table III. The predicted variation of the harmonic loss with modulation index at conditions of 80% torque and rated flux and a modulation frequency of 8 kHz is shown in Fig. 8. This result explains the harmonic loss at 50% speed for the AV method and provides the maximum predicted loss over the full operating range. For any reasonably high modulation frequency, the variation of the harmonic loss factor within the effective frequency range of any such group of sidebands is negligibly small. The same loss factor can then be applied to all harmonics within the

Predicted harmonic loss variation with modulation index.

Fig. 9. Variation of ΣV 2 for the matrix converter AV method harmonic spectrum.

same group such that the harmonic loss due to each group is approximated by n2 n1

Kh (f )Vh2n ≈ Kh (f¯n )

n2

Vh2n

(15)

n1

where n1 number of the lowest harmonic in the cluster; n2 number of the highest harmonic in the cluster; f¯n mean frequency of the harmonics within the cluster.


815

harmonic loss for a matrix-converter-fed 340-V motor and an inverter-fed 400-V motor. This paper was done as part of the development of a matrix-converter-integrated drive where the requirement of a nonstandard motor does not constitute a disadvantage since the motor design still has to be modified to accommodate the semiconductor circuitry. For a 30-kW motor with a full load efficiency of 92%, the total motor losses when operated from a sinusoidal supply are 2.6 kW. From the presented results, the extra harmonic loss due to PWM supplies is significantly less than the other losses for switching frequencies above 6 kHz, and minimal derating is required. However, the results show that the extra harmonic loss and consequently the overall drive efficiency is affected by the choice of modulation technique.

Fig. 10.

Variation of ΣV 2 for the matrix converter SVM harmonic spectrum.

Fig. 11. Variation of ΣV 2 for the inverter harmonic spectrum.

The variation of the harmonic loss with the modulation index hence reflects the variation of ΣV 2 for the groups of sidebands at lower frequencies. The variation of ΣV 2 for the first four groups of sidebands in the harmonic spectrum for each converter is shown in Figs. 9–11. These results were obtained for a switching frequency of 8 kHz. In Fig. 8, the extra harmonic loss for the SVM method is slightly less than that of the AV method over most of the output voltage range. The lower ΣV 2 values for the SVM method lead to this result, although the SVM sidebands are centered at multiples of 4 kHz for this method instead of multiples of 8 kHz for the AV method. The extra harmonic loss for the inverter is significantly lower since the first group of sidebands has a low ΣV 2 value over most of the output voltage range, and the inverter sidebands are centered at multiples of 8 kHz. IV. C ONCLUSION The harmonic loss curve for a 30-kW induction motor has been experimentally determined and used to predict the

R EFERENCES [1] A. Arias, L. Empringham, G. M. Asher, P. W. Wheeler, M. Bland, M. Apap, M. Sumner, and J. C. Clare, “Elimination of waveform distortions in matrix converters using a new dual compensation method,” IEEE Trans. Ind. Electron., vol. 54, no. 4, pp. 2079–2087, Aug. 2007. [2] K.-B. Lee and F. Blaabjerg, “Reduced-order extended Luenberger observer based sensorless vector control driven by matrix converter with nonlinearity compensation,” IEEE Trans. Ind. Electron., vol. 53, no. 1, pp. 66–75, Feb. 2006. [3] 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. [4] V. Kinnares, J. C. Clare, and K. J. Bradley, “A new technique for determining and predicting harmonic power loss in PWM fed induction machines,” in Proc. ICEM, Vigo, Spain, 1996, pp. 327–331. [5] J. C. Clare, K. J. Bradley, R. Magill, V. Kinnares, P. Wheeler, A. Ferrah, and P. Sewell, “Additional loss due to operation of machines from inverters,” in Proc. IEE Half Day Colloq. Testing Elect. Mach., London, U.K., Jun. 1999, pp. 5/1–5/8. [6] K. J. Bradley, J. C. Clare, R. Magill, A. Ferrah, P. Wheeler, P. Sewell, and W. Cao, “Enhanced harmonic injection for determination of harmonic loss in induction machines,” in Proc. IEE Power Electron. Variable Speed Drives (Conf. Publication), Sep. 2000, pp. 212–217. [7] A. Alesina and M. Venturini, “Analysis and design of optimum-amplitude nine-switch direct AC–AC converters,” IEEE Trans. Power Electron., vol. 4, no. 1, pp. 101–112, Jan. 1989. [8] D. Casadei, G. Serra, A. Tani, and L. Zarri, “Matrix converter modulation strategies: A new general approach based on space vector representation of the switch states,” IEEE Trans. Ind. Electron., vol. 49, no. 2, pp. 370– 381, Apr. 2002. [9] M. Apap, P. W. Wheeler, J. C. Clare, and K. J. Bradley, “Analysis and comparison of AC–AC matrix converter control strategies,” in Proc. IEEE Power Electron. Spec. Conf., Acapulco, Mexico, 2003, pp. 1287–1292. [10] J.-J. Lee, Y.-K. Kim, H. Nam, K.-H. Ha, J.-P. Hong, and D.-H. Hwang, “Loss distribution of three-phase induction motor fed by pulsewidthmodulated inverter,” IEEE Trans. Magn., vol. 40, no. 2, Pt. 2, pp. 762– 765, Mar. 2004. [11] T. C. Green, C. A. Hernandez-Aramburo, and A. C. Smith, “Losses in grid and inverter supplied induction machine drives,” Proc. Inst. Electr. Eng.—Electric Power Applications, vol. 150, no. 6, pp. 712–724, Nov. 7, 2003. [12] D. R. Turner, K. J. Binns, B. N. Shansadeen, and D. F. Warne, “Accurate measurement of induction motor losses using a balanced calorimeter,” Proc. Inst. Electr. Eng. B, vol. 138, no. 5, pp. 233–242, Sep. 1991. [13] P. D. Maliband, “Wide speed range three-phase induction motors for domestic applications,” Ph.D. dissertation, Cambridge Univ., Cambridge, U.K., 2006. [14] A. Julilian, V. J. Gosbell, B. S. P. Perera, and P. Cooper, “Double chamber calorimeter (DCC): A new approach to measure induction motor harmonic losses,” IEEE Trans. Energy Convers., vol. 14, no. 3, pp. 680–685, Sep. 1999. [15] D. Casadei, J. C. Clare, L. Empringham, G. Serra, A. Tani, A. Trentin, P. W. Wheeler, and L. Zarri, “Large-signal model for the stability analysis of matrix converters,” IEEE Trans. Ind. Electron., vol. 54, no. 2, pp. 939– 950, Apr. 2007.

816


Patrick W. Wheeler (M’00) received the Ph.D. degree in electrical engineering from the University of Bristol, Bristol, U.K., in 1993. In 1993, he was a Research Assistant with the Department of Electrical and Electronic Engineering, University of Nottingham, Nottingham, U.K., where he has been a Lecturer since 1996 and a Senior Lecturer in power electronic systems since 2003 in the Power Electronics, Machines and Control Group. His research interests are variable-speed ac motor drives, in particular different circuit topologies, power converters for power systems, and semiconductor switch use.

Jon C. Clare (M’90–SM’04) was born in Bristol, U.K., in 1957. He received the B.Sc. and Ph.D. degrees in electrical engineering from the University of Bristol, Bristol. From 1984 to 1990, he was a Research Assistant and a Lecturer with the University of Bristol, where he was involved in teaching and research in power electronic systems. Since 1990, he has been with the Power Electronics, Machines and Control Group, School of Electrical and Electronic Engineering, University of Nottingham, Nottingham, U.K., where he is currently a Professor of power electronics. His research interests are power electronic converters and modulation strategies, variable-speed systems, and electromagnetic compatibility. Dr. Clare is a member of the Institution of Electrical Engineers, U.K.

Maurice Apap received the B.Eng. (Hons.) and M.Sc. degrees from the University of Malta, Msida, Malta, in 1996 and 2001, respectively, and the Ph.D. degree from the University of Nottingham, Nottingham, U.K., for his work on matrix converters. He is currently a Lecturer with the University of Malta. His research interests include power electronic converters and the control of electrical drives.

Keith J. Bradley (A’93) received the Ph.D. degree in shaded pole motors from the University of Sheffield, Sheffield, U.K., in 1974. Following a period of research in low-vibration induction motors for nuclear submarines with YARD Ltd., he is currently with the School of Electrical and Electronic Engineering, University of Nottingham, Nottingham, U.K. His current research interests are concerned with tailoring machine design to optimize variable-speed drive performance and efficiency.