Spread Spectrum Modulation by Using Asymmetric … Spectrum Modulation by Using Asymmetric-Carrier Random PWM ... modulation, pulsewidth modulation (PWM) power converters. ... voltage

3710 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 10, OCTOBER 2012

Spread Spectrum Modulation by UsingAsymmetric-Carrier Random PWMLaszlo Mathe, Member, IEEE, Florin Lungeanu, Dezso Sera, Member, IEEE,

Peter Omand Rasmussen, Member, IEEE, and John K. Pedersen, Senior Member, IEEE

Abstract—This paper presents a new fixed-carrier-frequencyrandom pulsewidth modulation method, where a new type ofcarrier wave is proposed for modulation. Based on simulationsand experimental measurements, it is shown that the spread effectof the discrete components from the motor current spectra andacoustic spectra is very effective and is independent from themodulation index. The flat motor current spectrum generatesan acoustical noise close to the white noise, which improves theacoustical performance of the drive. The new carrier wave is easyto implement digitally, without employing any external circuits.The modulation method can be used in both open- and closed-loopmotor control applications.

Index Terms—AC motor drives, acoustic noise, modulation,pulsewidth modulation (PWM) power converters.

NOMENCLATURE

AC-RPWM Asymmetric-carrier random pulsewidth modu-lation (PWM) (RPWM).

CR Compare register.CVx Compare value for the PWM unit.EMI Electromagnetic interference.FCF-RPWM Fixed-carrier-frequency RPWM.m.i. Modulation index.PR Period register.PWM Pulsewidth modulation.RCF-PWM Random-carrier-frequency PWM.RPP-PWM Random-pulse-position PWM.RPWM Random PWM.SPL Sound pressure level.

I. INTRODUCTION

TO REACH controllability, high efficiency, and dynamicperformance in electrical drives, power electronic convert-

ers based on on/off control of power switches are employed(Fig. 1). To control the power switches from the converter,several modulation methods were proposed from which thePWM method is the most used technique. A drawback of this

Manuscript received December 14, 2010; revised June 8, 2011 andNovember 3, 2011; accepted November 15, 2011. Date of publicationDecember 22, 2011; date of current version April 27, 2012.

L. Mathe, D. Sera, P. O. Rasmussen, and J. K. Pedersen are with AalborgUniversity, 9220 Aalborg, Denmark (e-mail: [email protected]; [email protected];[email protected]; [email protected]).

F. Lungeanu is with the R&D Office, Danfoss Power Electronics A/S,100027 Beijing, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2011.2179272

Fig. 1. Topology of a standard full-bridge voltage-source inverter.

method is that it gives rise to discrete frequency components inthe current spectrum which lead to EMI [1]–[4] and acousticnoise in the drive [5]–[7]. A cost-effective strategy to distributethe discrete components from the current spectrum of themotor is RPWM. Several concepts of RPWM strategies canbe found in the literature [8]. The RPWM strategies from aswitching frequency point of view can be classified into twomain categories:

1) RCF-PWM;2) FCF-RPWM.

The spread of the discrete components from the motor cur-rent spectrum using RCF-PWM is more effective comparedto the FCF-RPWM method [9]–[11]. In most of the practicalapplications, the control algorithm is synchronized with theswitching; therefore, the variable switching frequency affectsthe performance of closed-loop applications [12], [13]. Usually,FCF-RPWM methods are based on the fact that the redistribu-tion of zero vectors does not have an effect on the fundamentalcomponent but changes the high frequency content of the motorcurrent spectra [14]–[16]. In [17], several FCF-RPWM methodswere analyzed and compared. The authors concluded that themethods where positions of pulses were randomized (RPP-PWM) have good performance only at low fundamental am-plitude. An RCF-PWM method where the slope of the carrierwave varies randomly can be found in [18] and [19]. In [20],the authors introduce a limitation on variable-slope modulationmethod to realize a new FCF-RPWM method. In this method,the increasing and decreasing slopes of a triangular carrierwave were chosen such that the modulation period constant ismaintained.

A drawback of the variable-slope modulation technique isthat external circuits are needed to generate PWM pulses. Thispaper proposes a new FCF-RPWM method called AC-RPWM.The advantage of the new AC-RPWM method compared to

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MATHE et al.: SPREAD SPECTRUM MODULATION BY USING ASYMMETRIC-CARRIER RANDOM PWM 3711

Fig. 2. Modulation used for a three-phase voltage-source converter. (a) Space vector diagram in the α−β plane. (b) Switching function during one period of thecarrier wave.

other FCF-RPWM methods is that it has good performancefor both low and high m.i. values (m.i.-normalized outputvoltage amplitude [15]). A digital implementation requiring noexternal circuits is also proposed in this paper. Finally, the errorintroduced by the motor current sampling in the top and bottomof the carrier wave is analyzed.

II. FCF-RPWM

In a conventional construction of an inverter (Fig. 1), sixactive vectors and two zero sequence vectors can be generated.The six active voltage vectors represented in the α−β plane[Fig. 2(a)] form a hexagon, where each active vector points tothe corner of the hexagon. When one of the six active vectorsis generated, the load takes energy from the dc link, forminga circuit from the load impedances as shown in Fig. 2(a) and(b). The generation of the zero sequence vector is done byconnecting the three legs of the load to the plus (V111) or minus(V000) of the dc bus. The position of a voltage vector Us inthe α−β plane is defined by the ratio between the applied timelengths for the two adjoined active vectors. The zero sequencevectors are responsible for reducing the amplitude of the re-sultant voltage vector Us. During a modulation period where atriangular carrier wave is used, two resultant voltage vectors,with arbitrary amplitude and position in the α−β plane, canbe generated. The first voltage vector is generated during thefirst part of the modulation period (rising slope, noted Trising),and the second vector is generated during the second part of themodulation period (falling slope, noted Tfalling).

The fundamental requirement of FCF-RPWM is to have con-stant update frequency and to generate the same voltage vectorin the α−β plane as it was before randomization. Due to thefact that the distribution of zero vectors (V111, V000) does notinfluence the fundamental frequency component [15], the time-length distribution of the zero vectors can vary randomly. The

Fig. 3. Repositioning of the pulse in one leg. (a) (Continuous lines) Pulsesgenerated by symmetrical modulation and (broken line) changed position ofthe pulse in leg c. (b) Vector diagram of the generated voltage vectors: The topfigure represents the first part of the modulation; the bottom figure representsthe second part of the modulation.

random variation of the zero sequence vectors gives a randomposition for the active region [the shadowed area in Fig. 2(b)]during the first and the second part of the modulation period.Using symmetrical modulation (the reference voltage vectoris updated once per modulation period), the same resultantvoltage vector is generated in the first and the second part ofthe modulation period. Fig. 3 shows the effect of repositioningof the pulse for one phase of the inverter. The pulses usingsymmetrical modulation for legs named qa, qb, and qc are repre-sented by continuous lines, while the repositioning of the pulsefor leg qc is represented by the dashed line. The average phasevoltage during the modulation period in leg qc is the same,independently of the pulse position. The generated voltagevectors Us, Us1, and Us2 differ in amplitude and position in theα−β plane, which means that the fundamental component is


Fig. 4. PWM carrier waveforms: Symmetrical carrier wave in the first modu-lation period and asymmetric carrier wave in the second modulation period.

distorted by the individual randomized pulse position in one leg.The distorted fundamental component affects the stability of thedrive, introducing current and torque ripple. Usually, the threephases of the motor are in delta or star connection; therefore,the current through one phase depends on the current in theother two phases. As a consequence, the PWM pulses have tobe synchronized to have controllability of the motor current ineach individual phase of the motor. This proves that the positionof a pulse cannot be changed in an arbitrary manner for eachleg. In the case of RPP-PWM, the pulse position of each legis modified. However, the time spent for generating the activevectors is maintained the same.

III. DESCRIPTION OF THE PROPOSED

MODULATION METHOD

The PWM unit (used for motor control) of a commercialmicrocontroller usually consists of an up–down counter, threeCRs, and a PR. An up-down counter is used for generatingthe carrier wave for the PWM unit. In traditional modulationmethods like space vector modulation (SVM), the time requiredfor up-counting mode (Trising) is equal to the time requiredfor down-counting mode (Tfalling), as it is shown in the firstmodulation period in Fig. 4. By changing the ratio betweenTrising and Tfalling, the resultant voltage vectors generated inthe first and the second part of the modulation period will besimilar in position and amplitude, with the difference beingthat the resultant voltage vector is created with different mod-ulation frequency. Generating the same voltage vectors afterand before randomization fulfills the second requirement forFCF-RPWM described in the previous paragraph. To fulfill thefirst requirement for FCF-RPWM, the distribution of the timelength between the first and the second part of the modulation(Trising and Tfalling) is done such that the modulation periodTmod constant is maintained. The following equation has to befulfilled to maintain constant modulation period:

Tmod = Trising + Tfalling = constant =1

fsw(1)

where Tmod is the modulation period, Trising is the time lengthwhere the counter is counting up (the first part of the modulationperiod), Tfalling is the time length where the counter counts

down (the second part of the modulation period), and fsw isthe switching frequency.

The second modulation period in Fig. 4 represents the pro-posed asymmetrical carrier waveform, where the modulationperiod (Tmod) is maintained constant, but the distributionsof the time length between Trising and Tfalling are not equal.Having a constant time base (Tclk) for the PWM modulecounter, the slope of the carrier wave cannot be changed. As it isshown in Fig. 4, for digital implementation of the asymmetricalcarrier waveform, two different values are used for the PR,creating an asymmetrical carrier wave for modulation. From amathematical point of view, after the duty cycles are calculatedconformably [21], the compare values can be calculated for thefirst and second parts of the modulation period by using

PRrising =Trising

Tclk

PRfalling =Tfalling

Tclk

CV1 = dzv0 · PRrising

CV1 = dzv0 · PRfalling

CV2 =CV1 + dav1 · PRrising

CV2 =CV1 + dav1 · PRfalling

CV3 =CV2 + dav2 · PRrising

CV3 =CV2 + dav2 · PRfalling (2)

where PRrising and PRfalling are the PR values for the PWMtimer in the first and second parts of the modulation period,dx is the duty cycle for the active and zero sequence voltagevectors, and CVx represents the compare values in the CRs ofthe PWM module of the microcontroller.

By choosing a random time length for Trising or Tfalling inevery modulation period, the time length for the active vectorregions (highlighted in Fig. 4) will vary randomly. In otherwords, the voltage vector generated in the Trising period isgenerated at different switching frequency than the voltagevector generated in the Tfalling period. From this point ofview, the AC-RPWM method can be interpreted as an RCF-PWM, where the update of the new voltage vector is done withconstant frequency. The spread effect of discrete componentsfrom the motor current spectra using this method is effectiveeven at high m.i., where the time spent for generation of theactive vectors is longer than the time spent for generationof zero vectors. For low m.i., a very good spread effect ofthe discrete components can be reached by redistributing thetime length of the zero sequence vectors (using the RPP-PWMstrategy). As it was presented in the introduction, the redis-tribution of the time length between the zero voltage vectorsaffects the current ripple, without having any influence on thefundamental component [14]. Redistribution of the zero vectorsmodifies the position of the active vector regions (highlighted inFig. 5) in the rising and falling modulation periods. In the firstmodulation period in Fig. 5, redistribution of the zero vectorsmodifies the position of the active vector; both active regionsare centered (Tzv0 = Tzv1). In the second modulation period,


Fig. 5. First modulation period of SVM (Tzv0 = Tzv1). Redistribution of thezero vectors (Tzv0 �= Tzv1).

TABLE IMEASURED SPL OF DIFFERENT MODULATION STRATEGIES

AND FUNDAMENTAL FREQUENCY

Fig. 6. Block diagram of a motor control using AC-RPWM in open and closedloops.

the active vectors are repositioned (Tzv0 �= Tzv1). From thepoint of view of the current ripple, the optimal position foractive vectors is in the middle like in the SVM. In Table I, theacoustic performances of four different modulation methods arepresented, at an average switching frequency of 4 kHz. The SPLwas measured with a Bruel and Kjaer sound level meter type2230 using A-weighting. The increased current ripple causeslouder acoustic noise in the motor (Table I) but transforms thewhistling noise into a white noise.

IV. DIGITAL IMPLEMENTATION OF AC-RPWM

In Fig. 6, a general block scheme of a typical motor controlstructure in open or closed loop is shown. The outcome of thecontrol block is always a calculated reference voltage vectorin the α−β plane. This voltage vector [Us from Fig. 2(a)] isdecomposed into two adjacent active voltage vectors, and thecompare values for the PWM module are usually calculatedusing the SVM block. The AC-RPWM block is an additionalblock which makes the randomization of the active and zero

sequence vectors’ time length within a modulation period. Inthis block, PRrising and PRfalling are also calculated, and theduty ratios are converted into compare values for the PWMmodule, based on (2). It can be seen from the block diagramin Fig. 6 that the main advantage of AC-RPWM is that it is verystraightforward to include into an existing closed- or open-loopcontrol algorithm, without the need for changing the controlstructure or adding hardware components. As a disadvantage,it can be mentioned that the PWM module has to be updatedtwice during the modulation period (double update is needed).

V. SIMULATION RESULTS

To compare the spectra of the motor current obtained byusing different modulation techniques, a number of simulationswere carried out in the power electronic simulation softwarePLECS 3.1 [22]. In order to make the comparison betweendifferent modulation methods with maximum randomizationfreedom, the nonlinearities like dead time and minimum pulsefilter have been neglected in the simulation.

Fig. 7 shows the current spectra produced by four modulationmethods: SVM, RPP-PWM, AC-RPWM, and the combinationof AC-RPWM with RPP-PWM. The simulations were madefor three different values of the m.i.: at low speed with m.i. =0.1, at medium speed with m.i. = 0.5, and at high speedwith m.i. = 0.9.

At low speed, the RPP-PWM method has good performance;the discrete frequency components disappear from the spectrumaround the switching frequency. However, the discrete com-ponents are present at double the switching frequency. In thecase of AC-RPWM, the discrete components are located aroundthe switching frequency. The combination of the two methodsnearly entirely eliminates the discrete components from thecurrent spectrum.

At medium speed, the time spent for generation of zerosequence vectors is less; the possibility for repositioning theactive vectors is reduced. This results in the appearance ofthe discrete components in the case of RPP-PWM. At doublethe switching frequency, the amplitude of the discrete compo-nents is considerably reduced when AC-RPWM is used. Thecombination of the two methods (RPP–AC-RPWM) gives againthe best performance.

At high speed, the time spent for generation of zero se-quence vectors is minimal; there is not a big difference betweenthe spectra obtained by using SVM or RPP-PWM. For highspeed, the performance of AC-RPWM is better than that ofRPP-PWM.

In conclusion, the combination of the two modulation meth-ods, RPP-PWM and AC-RPWM, has the best performance ofthe considered techniques in all speed ranges.

In Table II, the total harmonic distortion (THD) of thesimulated motor current is presented for the three different m.i.values. It should be noticed that, for high m.i., the THD of theRPP-PWM method is lower but the discrete components arestill present in the spectrum (the randomization effect is small);the THDs of RCF-PWM and AC-RPWM are almost the samein this case.


Fig. 7. Simulation results of the motor current spectrum. SVM with m.i. values of (a) 0.1, (e) 0.5, and (i) 0.9. RPP-PWM with m.i. values of (b) 0.1, (f) 0.5, and(j) 0.9. AC-RPWM with m.i. values of (c) 0.1, (g) 0.5, and (k) 0.9. RPP–AC-RPWM with m.i. values of (d) 0.1, (h) 0.5, and (l) 0.9.

TABLE IITHD OF THE MOTOR CURRENT

VI. EXPERIMENTAL RESULTS

To show the acoustic performance and the effect of thehardware limitations (dead time and minimum pulsewidth) ofthe proposed modulation method, an experimental setup wasbuilt, as shown in Fig. 8. The setup consists of a 2.2-kWasynchronous motor, a 2.2-kW Danfoss VLT AutomationDriveFC 302, and a motor control running on a Texas Instruments320F28335 floating-point microcontroller. The motor currentand vibrations on the motor shell were measured with a Brueland Kjaer pulse multianalyzer type 3560. In this work, vibrationmeasurements have been used to analyze the performance of theproposed modulation method. It is well known that the vibra-tion spectrum is similar to that of the radiated acoustic noise[23]. For randomization purposes, the built-in pseudorandomnumber generator function from “C” programming languagewas used. Figs. 9 and 10 show the measured spectra of the phasecurrent and the vibrations on the shell of the asynchronousmotor for m.i. values of 0.1, 0.5, and 0.9. The measured currentspectrum shows similar results as the simulation from theprevious section despite the fact that, for the experimental tests,limitations to ensure the minimum pulsewidth were introduced.

Fig. 8. Block diagram of the experimental setup.

The spectrum of the motor shell vibration (Fig. 10) showsthat the discrete components nearly disappeared when the AC-RPWM technique was used, regardless of the m.i. The smallpeaks from the spectrum were difficult to be distinguished byear, when the AC-RPWM method was used. The current rippleis minimal in the case of SVM; by using AC-RPWM, this ripplewas increased, which leads to higher SPL. By eliminating thediscrete components from the vibration spectra, the acousticnoise in the case of AC-RPWM becomes close to white noise.

VII. CURRENT SAMPLING

The current sampling error can cause torque oscillationwhich deteriorates the performance of the control in thecase of closed-loop applications [24]–[27]. Usually, the ac-quisition of the motor currents is done on the top and/or thebottom of the triangular carrier wave [25], [28]. In the caseof SVM, this means that the sampling of the motor currentsis done in the middle of the time length spent for zero sequencevector generation. To quantify the current sampling error, theideal case was simulated without nonlinearities (like dead time,minimum pulse filter, and saturation). The motor from theschematic shown in Fig. 1 was replaced with an R−L load.


Fig. 9. Measured phase currents of the motor. (a) SVM at 0.1 m.i. (b) SVM at 0.5 m.i. (c) SVM at 0.9 m.i. (d) RPP–AC-RPWM at 0.1 m.i. (e) RPP–AC-RPWMat 0.5 m.i. (f) RPP–AC-RPWM at 0.9 m.i.

Fig. 10. Measured vibrations on the motor shell. (a) SVM at 0.1 m.i. (b) SVM at 0.5 m.i. (c) SVM at 0.9 m.i. (d) RPP–AC-RPWM at 0.1 m.i. (e) RPP–AC-RPWMat 0.5 m.i. (f) RPP–AC-RPWM at 0.9 m.i.

The impedance of the simplified R−L circuit was set to besimilar with the impedance of the motor. Using a symmetricalregular sampled SVM method, a balanced three-phase sinu-soidal voltage can be generated. The R−L circuit will act asa first-order low-pass filter, creating a current with the samefundamental frequency as the motor phase voltage. To extractthe fundamental current component (purely sinusoidal withoutripple) from the measured current through the inductance, aresonant filter was used. The advantages of the resonant filterare that its phase shift is zero at its resonant frequency andthat it has high attenuation outside of the resonant frequency.Subtracting the fundamental current value from the measuredcurrent value gives the current measurement error when thesampling is made on the top and on the bottom of the carrierwave. Fig. 11 shows the simulation results of the macroscopic

and microscopic scales of the filtered current and the measure-ment error.

As it can be concluded from Fig. 11, the sampling error ishigh when the reference voltage vector is in the middle of asector, and it is low when the reference voltage vector has thesame position as an active vector. This means that, when thereference voltage vector is close to an active voltage vector,the sampling in the top and bottom of the triangular carrierhas minimal error. At zero crossing, the slope of the currentis maximum, which results in maximum error. Fig. 11(c) showsthat, when zero vectors are generated, the reference signal isalways between the values of the current sampled in the firstand second parts of the modulation period. This error is mainlycaused by the regular sampling. The maximum error for thiscase is approximately ±0.05 A. For this example, where 10 A


Fig. 11. Simulation results of the current using SVM with 0.5 m.i. (a) One fundamental period of the current. (b) Sampling error during the fundamental period.(c) Zoom of the current plot at zero crossing. (d) Zoom of the current plot around the maximum value of the fundamental term. (e) and (f) Zoom of the error plot.

is the peak nominal current, 15 A can be considered as amaximum measurable current. Considering the relatively highcurrent measurement error (1%), even a resolution as low as8 b is enough for analog-to-digital (AD) conversion.

By using the RPP-PWM method and by sampling the motorcurrent on the top and bottom of the triangular carrier, thecurrent will not be sampled in the middle of the time spent forgeneration of the zero sequence vectors, which further increasesthe sampling error.

This error can be reduced by using the same position forthe active vector region in the first and the second half ofthe modulation period (single update for the voltage vector).However, by introducing limitations on the possible position forthe active region, the spread effect of the discrete componentsfrom the motor current spectra is reduced.

Fig. 12 shows the inductor current in macroscopic time scalewhen the RPP-PWM and AC-RPWM techniques are used. Theinductor current is sampled in both cases in the middle and inthe top of the triangular carrier; the sampled value is subtracted

from the filtered current, which gives the sampling error. Asit was expected, the sampling error increases in the case ofrandom modulation.

In the case of AC-RPWM, the error was slightly smallerthan that in the case of RPP-PWM because the active vectorregion is placed in the middle of the half modulation period.Taking into consideration the error made by sampling on thetop and bottom of the carrier, for the random modulation, aresolution of 6 b is enough for AD conversion. In the caseof applications where this sampling error can cause problems,limitations like maximizing the time length Trising or Tfalling to,for example, 80% of the time length of the modulation periodcan be introduced. However, this kind of limitations reduces theeffectiveness of the randomization (the discrete components aregoing to be more dominant). The usage of a low-pass filter anda high sampling frequency for current measurement could be asolution [26]. However, low-pass filters affect the phase of thefiltered signal which can introduce even higher error. Using anotch filter (like the previously presented resonant filter) which


Fig. 12. Macroscopic time scale of (top) the inductor current and (bottom) the sampling error at 25-Hz fundamental frequency; RPP-PWM in the left columnand AC-RPWM in the right column.

does not affect the phase of the current can cause problemsby filtering out the low-frequency components in the measuredcurrent. In this case, the current regulators from the closed-loopcontrol will not be able to compensate for these unwanted low-frequency components.

VIII. CONCLUSION

A new FCF-RPWM method called AC-RPWM has beenpresented and analyzed in this paper. The modulation methodhas fixed update frequency, which has the advantage of easy im-plementation and integration into an existing open- or closed-loop motor control algorithm, without using any additionalhardware. The simulations and the experimental measurementsshow that the AC-RPWM method effectively spreads the dis-crete components of the current and vibration spectra inde-pendent of the m.i. This flat motor current spectrum is themain advantage compared to PWM methods like SVM anddiscontinuous PWM (DPWM). For those applications wherehigh demands for shaft-torque dynamics are needed, the cur-rent sampling has to be improved. However, the AC-RPWMmethod is well suited for applications like heating ventilationand air conditioning (HVAC), where the demand on shaft-torque dynamics is moderate and the acoustic noise issue ismore important. The proposed method can be used for thoseHVAC applications where the less efficient asynchronous motoris replaced by a permanent-magnet synchronous motor, whichrequires closed-loop control.

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Laszlo Mathe (S’07–M’10) received the B.Sc. de-gree in electrical engineering and the M.Sc. degreefrom the Technical University of Cluj-Napoca, Cluj-Napoca, Romania, in 2000 and 2002, respectively,and the Ph.D. degree in electrical engineering fromthe Department of Energy Technology, Aalborg Uni-versity, Aalborg, Denmark, in 2010.

Between 2002 and 2007, he was working forindustry as a Control Development Engineer. He iscurrently an Assistant Professor with Aalborg Uni-versity. His current research activities are in power

electronics, specifically in modulation and motor control.

Florin Lungeanu received the M.Sc. degree in elec-trical engineering from the Lower Danube Universityof Galati, Galati, Romania, in 1996.

He was an Assistant Professor with the LowerDanube University of Galati until 2000. He was aGuest Researcher with the Department of EnergyTechnology, Aalborg University, Aalborg, Denmark,until 2001. He moved to industry and worked asa Control Engineer for Danfoss Drives A/S and asa Power System Engineer for Vestas Wind PowerSystems A/S. He is currently a Motor and Applica-

tion Control Specialist with the R&D Office, Danfoss Power Electronics A/S,Beijing, China. His main research interests are in control for power electronics,motor and application control, and new pulsewidth modulation techniquesapplied to various state-of-the-art and novel power electronic topologies.

Dezso Sera (S’05–M’08) received the B.Sc. andM.Sc. degrees in electrical engineering from theTechnical University of Cluj-Napoca, Cluj-Napoca,Romania, in 2001 and 2002, respectively, and theM.Sc. and Ph.D. degrees from the Departmentof Energy Technology (DET), Aalborg University,Aalborg, Denmark, in 2005 and 2008, respectively.

Since 2009, he has been the Coordinator of thePhotovoltaic Systems and Microgrids Research Pro-gram at DET, Aalborg University, where he is cur-rently an Associate Professor. His current research

activities are in photovoltaic (PV) power systems in general, specifically in themodeling, characterization, diagnostics, and maximum power point tracking ofPV systems, and in the grid integration of PV power.

Peter Omand Rasmussen (M’98) was born inAarhus, Denmark, in 1971. He received the M.Sc.degree in electrical engineering and the Ph.D. degreefrom Aalborg University, Aalborg, Denmark, in 1995and 2001, respectively.

In 1998, he joined Aalborg University as an As-sistant Professor, where he has been an AssociateProfessor since 2002. His research areas are withinmagnetic gears and design and control of switchedreluctance and permanent-magnet machines.

John K. Pedersen (M’91–SM’00) was born inHolstebro, Denmark, on September 2, 1959. He re-ceived the B.Sc.E.E. degree from Aalborg Univer-sity, Aalborg, Denmark.

He was with the Department of Energy Tech-nology (DET), Aalborg University, as a TeachingAssistant from 1983 to 1984 and as an AssistantProfessor from 1984 to 1989, where he has been anAssociate Professor since 1989. He is currently theHead of DET, Aalborg University. He is the authoror coauthor of more than 170 publications, and he is

involved in a number of research projects in collaboration with industry. Hisresearch areas are in power electronics, power converters, and electrical drivesystems, including modeling, simulation, and design with focus on optimizedefficiency.

Mr. Pedersen was the recipient of the 1992 Angelos Award for his contri-bution in the control of induction machines. In 1998, he was the recipient ofan IEEE TRANSACTIONS ON POWER ELECTRONICS Prize Paper Award forbest paper published in 1997. He was also the recipient of the ABB Prize PaperAward at the Optimization of Electrical and Electronic Equipment (OPTIM)2002 Conference.

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