1152 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 4, AUGUST 2006 A Tubular-Generator Drive For Wave Energy Conversion Vincenzo Delli Colli, Piergiacomo Cancelliere, Member, IEEE, Fabrizio Marignetti, Member, IEEE, Roberto Di Stefano, and Maurizio Scarano, Member, IEEE Abstract—This paper illustrates the operation of a tubularmachine drive as a linear generator for a heave-buoy wave energy conversion. Linear generators, which are adopted in marine power plants, offer the advantage of generating without introducing any conversion crank gear or hydraulic system. The use of a tubularmachine topology allows the electromagnetic thrust density to be improved. This paper briefly summarizes the principles of marine wave buoy interaction and reports the design analysis and control of a permanent-magnet (PM) synchronous tubular linear machine based on a scaled generator prototype and on a rotating simulation test bench. Index Terms—Heave buoy, linear synchronous generators, marine energy, tubular generators. I. I NTRODUCTION T HE USE of a tubular machine as a linear generator for a heave-buoy wave energy conversion in order to improve the force density N/m3 that can be attained is proposed in this paper. Linear machines are increasingly used today as generators. In fact, some energy sources and especially marine ones exhibit an alternating motion. One of the most promising renewable energy sources characterized by a reciprocating motion is represented by tide and wave marine energy [1]–[4]. Linear generators are suitable for direct-drive applications, since they permit a reduction in the number of subsequent energy transformation steps. Coupling an electrical generator directly with the reciprocating energy source also permits the reduction of moving parts and simplifies the system. The overall efficiency is thereby enhanced. Different electrical-machine topologies have been proposed in literature to be utilized as direct-drive linear generators [5]. One encouraging way to convert an alternating mechanical energy into an electrical energy by means of a direct drive is to use a linear tubular synchronous permanent-magnet (PM) generator. The force-to-weight ratio of such machines has been proved to be higher than the flat linear topology [6]. Section II summarizes the basic principles of the heavebuoy mechanics, whereas, Section III outlines the design of the proposed tubular generator and presents the results of the finite-element analysis (FEA) together with the experimental validation. Section IV presents the optimal buoy control, which Manuscript received March 29, 2005; revised June 28, 2005. Abstract published on the Internet May 18, 2006. The authors are with the Department of Automation (DAEIMI), Faculty of Engineering, University of Cassino, 03043 Cassino, Italy (email: [email protected]). Digital Object Identifier 10.1109/TIE.2006.878318 Fig. 1. Semisubmerged sphere as marine wave energy converter. allows the sea-to-buoy power transfer to be maximized, and Section V discusses the drive control used to perform the electromechanical and ac/dc conversion control. Finally, Section VI presents the test facility, and Section VII gives the results of the experiments on mechanical to dc power conversion obtained by means of a tubular prototype as well as the results of the wave conversion obtained by a rotating simulation test bench. II. H EAVE -B UOY M ECHANICS In this paper, a simple heave-buoy system is considered as a wave energy converter (WEC). There are many shapes for the buoy as a WEC: a sphere-shaped buoy is considered in the following. Generally, buoy WECs can be displaced in any direction when an incident wave occurs; in this formulation, the buoy WEC is restricted to oscillate in the heave mode only, as shown schematically in Fig. 1. The equation of motion for a simple heaving-buoy device is M d2 z = Fe + Fr + Fb + Fv + Ff + Fu dt2 (1) where M is the mass of the buoy, Fe is the excitation force due to the incident wave on the buoy, Fr is the radiated force, Fb is the hydrostatic buoyancy force, Fv and Ff represent unavoidable viscous and friction effects, respectively, and Fu is an outside force that could be externally imposed. The z heave 0278-0046/$20.00 © 2006 IEEE Authorized licensed use limited to: Université de Lorraine. Downloaded on November 20,2021 at 14:54:57 UTC from IEEE Xplore. Restrictions apply. DELLI COLLI et al.: TUBULAR-GENERATOR DRIVE FOR WAVE ENERGY CONVERSION coordinate represents the displacement of the center of gravity of the sphere in the frame of the calm free-water surface. The radiated force term Fr represents the forces acting on the buoy, which are due to the wave that is radiated as a result of the buoy’s oscillation. Fr consists of an additional mass of the buoy plus a dissipative term [7]. Fr = −mr (ω) d2 d (z − x) − Rr (ω) (z − x). dt2 dt 1153 Fig. 2. Stainless-steel tube with the magnets and the iron pieces. (2) The coordinate x is the displacement of the free-water surface when an incident wave occurs in the frame of the calm free-water surface. The hydrostatic buoyancy force Fb takes into account the equilibrium between the weight force and the Archimedes force and is generally indicated as follows [7]: Fb = −Sb (z − x) (3) where Sb is the buoyancy stiffness, in which considering small excursions |z − x| a, is equal to [7] Sb = πρga2 (4) for a semisubmerged sphere of radius a and mass M = (2/3)πρa3 . In (4), ρ is the density of the sea water, and g is the acceleration of gravity. The last added term in (1) takes into account the viscous and friction effects and can be written as follows: Fv + Ff = −(Rv + Rf ) d d (z − x) = −Rl (z − x). dt dt (5) III. T UBULAR G ENERATOR D ESIGN AND V ALIDATION A. Design Basics Tubular linear machines (TLM) comprise a stator and a translator, the former being made out of a series of cylindrical metal discs machines in order to accommodate the coils and furnish with the necessary hole for the sliding of the translator. The magnets and the steel back iron are canned inside a stainlesssteel sleeve, as shown in Fig. 2. Generally, the stator is not laminated: A transverse lamination would reduce the eddy-current losses, but it would increase the effective air gap and the cogging force of the machine if this is a PM one. Analytical models of the tubular machines were provided by Marignetti and Scarano in [8], Bianchi et al. in [9], and Zhu et al. in [10]. All the models show that, in terms of electromagnetic thrust density, buried PM machines perform better than their surface-mounted counterparts. A general formula for achieving the thrust per pole Ti in a tubular buried-magnet machine has been is given in [8] Ti = 2πRBr nc i np 2δ τp k + k σ0 2 σm K (6) where R is the bore internal radius, Br is the remanence of the magnets, nc is the number of turns per slot, np is the number of slots per pole energized at the same time, k is the ratio between Fig. 3. Force-per-slot plot as a function of the air gap and the magnets’ length k normalized in relation to the pole pitch. the length of the magnets and the pole pitch, δ is the minimum air gap, σ0 is the air-gap surface, σm is the cross-sectional area of the magnets, and K is a coefficient derived from the finiteelement method (FEM) analysis to take the leakage fluxes into account. Supposing R to be unity, for a three-phase machine with a trapezoidal electromotive force (EMF) and one slot per pole and per phase, (6) can be used in order to yield the force-perslot plot as a function of the air gap and the magnet length normalized in relation to the pole pitch. Fig. 3 refers to a slot current of 1-A turn and three slots per pole. A design can be considered as being optimal when the length of the magnets is such that the thrust per slot yields a maximum. This happens in general when the length of the magnets is one third of the pole-pitch length for a one-slot-per-phase machine. B. Actual Construction The windings were wound on a plastic spool utilizing H thermal class enameled copper wire with a cross section of 1 mm2 . The number of turns per coil is 126. The main electrical and geometrical data of the machine are listed in Table I. The application of (6) to the machine above yields a total thrust of 208 N at a rated current, which was experimentally verified. The design of the tubular linear machines was verified by means of the FEM simulations, which were carried out in an axial symmetry mode, since the structure presents a rotational symmetry around the central axis. C. FEA In order to compute the direct- and quadrature-axis inductance of the tubular motor, several FEM simulations were Authorized licensed use limited to: Université de Lorraine. Downloaded on November 20,2021 at 14:54:57 UTC from IEEE Xplore. Restrictions apply. 1154 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 4, AUGUST 2006 TABLE I TUBULAR LINEAR GENERATOR PARAMETERS Fig. 5. Magnetic flux density along a double pole pitch with the translator aligned on the stator d-axis. TABLE II DIRECT AND QUADRATURE INDUCTANCE CALCULATION Fig. 6. Fig. 4. Magnetic flux density along a double pole pitch with the translator aligned on the stator q-axis. performed, considering different values of a current density and in different positions of the translator. More simulations were carried out with active magnets and currents in order to visualize the magnetic field in the air gap when the flux sustained by the magnet is aligned with both the q-axis and the d-axis. Fig. 4 shows the magnetic field in the air gap with the translator in position d. Fig. 5 shows the magnetic field with the translator in position q. Using an integration tool [11], first, the flux was calculated, then the inductances on the d- and q-axes were computed. The results are listed in Table II. The inductance was also experimentally measured using a methodology based on the current response to a sinusoidal voltage on the d- and q-axes of the machine. This methodology is described in [12] and [13]. It can be noticed that the value Linear tubular machine prototype. calculated by means of the FEM method and the experimentally measured ones (see the values of Table I) are quite comparable. Fig. 6 shows the linear tubular-machine prototype. In all electrical machines, roughly forces grow linearly with the volume. The weight of the translator increases at the same rate. The machine used in this paper was designed and built to be cooled by a natural air convection. The force density of an air-cooled linear tubular machine is in the range of 1.6 × 105 N/m3 (for slot-less tubular SPM machines) to 2.4 × 105 N/m3 (for slotted tubular IPM machines) [9]. The amplitude of the force in a typical 100-kW wave buoy converter is in the order of 100 kN [18], which results into a generator of volume ranging from 0.4 to 0.6 m3 , which means that the generator weighs about 3 to 4 tons. However, it must be considered that the thermal exchange in submerged electrical devices is facilitated, hence, their power density can be further improved. IV. H EAVE -B UOY O PTIMAL E NERGY C ONVERSION The WEC considered is a sphere that is semisubmerged in its equilibrium position. As soon as an incident wave occurs, the sphere starts moving in the heave direction, and also a relative movement between the sphere and the free-water surface of the wave begins. Authorized licensed use limited to: Université de Lorraine. Downloaded on November 20,2021 at 14:54:57 UTC from IEEE Xplore. Restrictions apply. DELLI COLLI et al.: TUBULAR-GENERATOR DRIVE FOR WAVE ENERGY CONVERSION An incident wave of the height Hs = 2 A and the angular frequency ω produces a heave displacement of the free-water surface equal to x(t) = A sin(ωt). (7) Taking into account equations (2)÷(5), the dynamic (1) for a buoy restricted to oscillating in the heave mode only becomes d2 d (M + mr (ω)) 2 z + (Rr (ω) + Rl ) z + Sb z = Fe + Fu dt dt (8) where the excitation force includes the following terms Fe = Sb x + (Rr (ω) + Rl ) d d2 x + (M + mr (ω)) 2 x. (9) dt dt In terms of complex amplitudes, (8) may be written as 2 −ω [M + mr (ω)] + iω [Rr (ω) + Rl ] + Sb ẑ = F̂e + F̂u (10) where the superscript ∧ indicates the phasors of the quantities. The introduction of the mechanical impedance [7] Sb Żm (ω) = Rr (ω) + Rl + i ω (m(ω) + M ) − (11) ω modifies the complex (9) into Żm (ω)û = F̂e + F̂u (12) where û is the phasor of the speed of the oscillating buoy ( i.e., u(t) = d/dtz(t)). According to the theory on the converted power energy from a heave-buoy system [7], the maximum useful power is obtained when the external force Fu satisfies the following relationship: ∗ F̂u = −Żm (ω)û (13) where the symbol “∗” denotes the complex-conjugate quantity. This optimum condition is reported in the literature as a reactive control or complex-conjugate control and was experimentally tested for sinusoidal waves [14]. Condition (13) implies that the optimal load impedance is equal to the complex conjugate of the intrinsic impedance. As remarked in [7], due to the need for involving a mechanical reactive power in order to achieve the optimum condition, the load and control machinery, which supplies the load force Fu , should be capable of returning some energy to the buoy during part of the oscillation cycle. The external force Fu will be the electromagnetic thrust of the linear tubular generator. The reference signal for the linear direct drive will be represented by the optimal Fu expressed by (13). V. T UBULAR G ENERATOR C ONTROL A voltage-source converter (VSC) connects the TLM to a dc source. The dynamic electrical model of the generator in 1155 the synchronous reference frame is described by the following equations: vd = − R · id − dψd π + v.t · · ψq dt τp vq = − R · iq − dψq π − vt · · ψd dt τp ψd = Ld · id − ψP M ψq = Lq · iq F = 3 π · · [id · iq · (Ld − Lq ) − ψP M · iq ] . 2 τp (14) In (14) vt represents the linear speed of the TLM generator, coinciding with the speed of the buoy; τp is the pole pitch, and ψP M is the flux due to PMs. The previous section shows how the desired force depends on the speed and other wave parameters. Here, it can be treated as an exogenous reference. Considering the speed and the PM flux to be known, the model is a system of five linear differential equations with the following unknowns Id , Iq , Ψd , Ψq , vd , and vq . In order to make the system solvable, one needs to add an additional equation, namely, the generator control algorithm. A possible choice for this equation is based on the control of the phase currents tracking the phase angles of the generated EMF profile [15] and is also termed field-oriented control (FOC). In a constant flux operation, the FOC implies that the direct axis current be zero iref d = 0. (15) The thrust output by the optimal complex-conjugate control of the wave buoy (10) represents the LTM reference force, hence, the quadrature current becomes iref q =−3 2 · Fu π τp ψP M . (16) The adopted strategy commonly uses two proportional plus integral (PI) regulators in the synchronous reference frame to control the currents. The control scheme requires the EMF as a function of the position of the translator to be known, in this case, only the angle of the magnet flux vector in a fixed frame; a linear encoder was therefore used. There are many ways to implement current regulators, and the easiest of these is to use a hysteresis band controller. These however generate an inconstant-switching frequency that causes a nonoptimal thermal exploitation of the powerswitching devices. This algorithm works very well with low EMFs, but with higher EMFs, the current controller will saturate in part of the cycle, and fundamental frequency related harmonics will appear. In this condition, the fundamental current will be less, and its phase will lag in relation to the command current [16]. Brooking et al. [17] used an approach based on the proportional regulators in a fixed frame. PI controllers can be used Authorized licensed use limited to: Université de Lorraine. Downloaded on November 20,2021 at 14:54:57 UTC from IEEE Xplore. Restrictions apply. 1156 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 4, AUGUST 2006 Fig. 7. Control algorithm block scheme. Fig. 8. Test bench A: tubular generator connected to an external PMSM drive. to track a current command, and three similar controllers can be implemented, one for each phase. This is a simple control method, but there are a number of problems: Due to the limited bandwidth of the control system, the actual current will have a phase lag and magnitude error, which will increase with frequency. The ripple affecting the generated voltage command may cause undue zero crossings in the modulation [16]. Instead, two PI regulators are used in the synchronous reference frame to control the currents. The control block scheme using the EMF phase reconstruction is reported in Fig. 7. VI. T EST F ACILITY A test facility comprising two separate test benches was set up in the “Giovanni D’Angelo” Laboratory of Industrial Electronics at Cassino University: 1) test bench A based on the tubular-generator prototype (Subsection A); 2) test bench B based on a rotating heave-buoy simulator (Subsection B). A. Test Bench A Based on the Tubular-Generator Prototype Test bench A is designed to test the generating capabilities of the tubular generator of Section III with the FOC of Section V regardless of the buoy mechanics. Test bench A is illustrated in Fig. 8. B. Test Bench B Based on a Rotating Heave-Buoy Simulator Test bench B intends to test the control laws of Sections IV and V, taking into account the buoy mechanics of Section II and some of the actual characteristics of the drive. This bench is based on a rotating unit composed of a PM synchronous generator replacing the tubular generator, and a PM synchronous motor (PMSM) drive controlled in order to track in real Fig. 9. Test bench B: Block scheme. time the dynamics of a WEC buoy. The unit operates with a tangential speed 2.6 times the linear speed of such a WEC and with a torque 1/20 000 times the force of the WEC. The test facility combines the real-time simulation, hardware-inthe-loop simulation, and actual motor drive to achieve the computation and actuation of the wheel dynamic in real time. Test bench B consists of the following items as shown also in the block scheme of Fig. 9. Items under test (on the left of Fig. 9): 1) control hardware; 2) dc/ac power converter; 3) PM generator. Buoy real-time simulator (on the right of Fig. 9): 1) control hardware for the real-time computation of the buoy dynamic; 2) power inverter; 3) PMSM. This facility can impose, in reduced force scale and slightly augmented speed scale, arbitrary dynamic buoy parameters and can modify the “sea conditions” when running. The simulator imposes on the PMSM the speed foreseen by the buoy equations. Because of its torque and bandwidth performances, the simulator is capable of imposing the axle speed in any type of operating conditions considered. Authorized licensed use limited to: Université de Lorraine. Downloaded on November 20,2021 at 14:54:57 UTC from IEEE Xplore. Restrictions apply. DELLI COLLI et al.: TUBULAR-GENERATOR DRIVE FOR WAVE ENERGY CONVERSION 1157 Fig. 13. TLM power transferred to the dc link. Fig. 10. TLM EMF. TABLE III MEASURED POWERS (SIMULATED SCALE) Fig. 11. TLM generated currents. Fig. 12. TLM active power generated (line above, W) and reactive (line below, VA) power generated. VII. E XPERIMENTAL R ESULTS A. Experimental Results for the Tubular-Generator Prototype of Section III Test bench A allows both the electromechanical and ac/dc conversion capabilities of the tubular prototype to be verified. Experiments were carried out including the actual control of the VSC and considering a reciprocating energy source that imposes an alternating movement of the translator with a maximum speed of 1 m/s. The latest test condition approximates the actual buoy motion. The control algorithm sketched in Fig. 7 reads the machine EMFs phase tabled as a function of the position of the translator, i.e., a linear encoder senses the position. The quadrature reference current was imposed at the constant level of 2 A. The modulation frequency of the VSC is 20 kHz. The rated dc-link voltage is 70 V. Figs. 10 and 11 show the EMFs and the generator currents, respectively. Fig. 12 shows the active and reactive power through the terminals of the generator; the power transferred to the dc link is shown in Fig. 13. The current of Fig. 11 has a good shape and a correct phase relationship with the EMFs of Fig. 12, notwithstanding the Fig. 14. Current in the first phase of the generator (actual scale). trapezoidal shape of the latter ones. This fact leads to a correct power transfer as shown in Figs. 12 and 13. The data reveal that the system ceases to transfer the power when the translator speed is lower than a given threshold. B. Experimental Results of the Control System Test of Sections II, IV, V The results obtained on the Test Bench B validate the control system test of Sections II, IV, V. The generator is controlled by the FOC algorithm of Fig. 7, which reads the magnets position by means of an incremental encoder, and it chooses consequently the current phase, while its magnitude is dictated by (16), rewritten for the rotating case. The motor of Fig. 9 emulates the action of the buoy on the generator by means of a real-time simulation of (1). The parameters of the simulated buoy are reported in Table III. The modulation frequency of the VSC is 20 kHz as well as the control update rate. The data collected cover a wave period in steady-state conditions. The dc-link voltage is 48 V. Fig. 14 reports one of the generator phase currents in the actual scale. Fig. 15 shows the force Authorized licensed use limited to: Université de Lorraine. Downloaded on November 20,2021 at 14:54:57 UTC from IEEE Xplore. Restrictions apply. 1158 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 4, AUGUST 2006 Fig. 15. Force developed by the generator on the buoy (simulated scale). Fig. 18. Position of free water (dotted) and buoy in relation to the calm free water (simulated scale). TABLE IV SECTION EFFICIENCIES Fig. 16. Speed of the buoy in relation to the seabed u (simulated scale). Fig. 17. Force developed by the wave on the buoy (simulated scale). developed by the generator on the buoy in a simulated scale. Fig. 16 shows the speed of the buoy in relation to the seabed in the simulated scale. Fig. 17 reports the force developed by the wave on the buoy in the simulated scale. The phase relationship between the last two quantities reveals whether the optimum power transfer has been attained [7]. Fig. 18 reports the positions of the free water (dotted) and of the buoy in relation to the calm free water in the simulated scale, proving that the small excursions hypothesis of Section II has been respected. TABLE V REAL-TIME-SIMULATED BUOY AND WAVE PARAMETERS (TEST BENCH B) Table III reports the measured powers of the different energyconversion sections. The first value reported is the sea power PSea , then the mechanical power transferred from the buoy to the electrical machine PBuoy . Pac represents the power converted by the electrical machine, while Pdc is the power rectified by the converter into the dc side. Table IV lists the evaluated efficiencies of the energy-conversion sections ηSea/Buoy , ηBuoy/ac , and ηac/dc , adding together the overall conversion efficiency ηT ot . Finally, Table V summarizes the real-timesimulated buoy and wave parameters of the test bench B. VIII. C ONCLUSION A first scaled PM linear generator for the marine wave energy direct-drive conversion was designed and built. This paper presents the principle of the power transmission from the wave to the buoy and outlines a control approach intended to maximize both the wave-buoy and ac/dc power transfer Authorized licensed use limited to: Université de Lorraine. Downloaded on November 20,2021 at 14:54:57 UTC from IEEE Xplore. Restrictions apply. DELLI COLLI et al.: TUBULAR-GENERATOR DRIVE FOR WAVE ENERGY CONVERSION resulting in an optimal overall conversion performance. The experimental results obtained in the laboratory environment show that both the generator and the control algorithm follow the predicted performances. Since the test bench B takes into account the sea condition, further investigations will involve the analysis of the complex-conjugate control under real sea-wave conditions. R EFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] Ocean Power Delivery. [Online]. Available: http://www.oceanpd.com Engineering Business. [Online]. Available: http://www.engb.com Wavegen. [Online]. Available: http://www/wavegen.co.uk Marine Current Turbines. [Online]. Available: http://www. marineturbines.com M. A. Mueller, “Electrical generators for direct drive wave energy converters,” Proc. IEE—Generation, Transmiss. Distrib., vol. 149, no. 4, pp. 446–456, Jul. 2002. A. W. Van Zyl, C. G. Jeans, R. J. Cruise, and C. F. Landy, “Comparison of force to weight ratios between a single-sided linear synchronous motor and a tubular linear synchronous motor,” in Proc. IEMD, May 9–12, 1999, pp. 571–573. J. Falnes, Ocean Waves and Oscillating Systems, Linear Interaction Including Wave-Energy Extraction. Cambridge, U.K.: Cambridge Univ. Press, 2002. F. Marignetti and M. Scarano, “Comparative analysis and design criteria of PM tubular actuators,” Arch. Electrotech., vol. 84, no. 5, pp. 255–264, Dec. 2002. N. Bianchi, S. Bolognani, D. D. Corte, and F. Tonel, “Tubular linear permanent magnet motors: an overall comparison,” IEEE Trans. Ind. Appl., vol. 39, no. 2, pp. 466–475, Mar.–Apr. 2003. Z. Q. Zhu, P. J. Hor, D. Howe, and J. Rees-Jones, “Novel linear tubular brushless permanent magnet motor,” in Proc. 8th Int. Conf. Electr. Mach. Drives (Conf. Publ. No. 444), Sep. 1–3, 1997, pp. 91–95. FEMLAB 3.0 Reference Manual, COMSOL, Stockholm, Sweden, 2003. G. Stumberger, B. Stumberger, and D. Dolinar, “Identification of linear synchronous reluctance motor parameters,” in Conf. Rec. IEEE-IAS Annu. Meeting, Oct. 8–12, 2000, vol. 1, pp. 7–14. B. A. Abdessattar, “Experimental identification of a linear tubular four phase stepping motor,” in Proc. IEEE Int. Conf. Syst., Man and Cybern., Oct. 6–9, 2002, vol. 5, p. 4. P. Nebel, “Maximizing the efficiency of wave-energy plants using complex-conjugate control,” J. Syst. Control Eng., vol. 206, no. 4, pp. 225–236, 1992. M. A. Mueller, N. J. Baker, P. R. M. Brooking, and J. Xiang, “Low speed linear electrical generators for renewable energy applications,” in Proc. 4th Int. Symp. LDIA, Birmingham, U.K., Sep. 8–10, 2003, pp. 29–32. B. K. Bose, Modern Power Electronics ad AC Drives. Upper Saddle River, NJ: Prentice-Hall, 2002, pp. 237–238. P. R. M. Brooking, M. A. Mueller, N. J. Baker, L. Haydock, and N. L. Brown, “Power conversion in a low speed reciprocating electrical generator,” in Proc. ICEM, Brugge, Belgium, Aug. 2002, CD-ROM. M. Leijon, H. Bernhoff, O. Agren, J. Isberg, J. Sundberg, M. Berg, K. E. Karlsson, and A. Wolfbrandt, “Multiphysics simulation of wave energy to electric energy conversion by permanent magnet linear generator,” IEEE Trans. Energy Convers., vol. 20, no. 1, pp. 219–224, Mar. 2005. Vincenzo Delli Colli was born in Cassino, Italy, in 1970. He received the Laurea degree in electrical engineering from the University of Cassino, Cassino, Italy, in 1996, and the Ph.D. degree in conversion of electrical energy from the Second University of Naples, Naples, Italy, in 2000. Since 2001, he has been a Research Assistant with the Electrical Machine Group of the University of Cassino. His main research interests are currentsource and resonant converters. 1159 Piergiacomo Cancelliere (M’03) received the Laurea degree in electrical engineering from the Faculty of Engineering, University of Cassino, Cassino, Italy, in 1998. From May 1998 to January 1999, he was with REEL S.r.l. Power Electronic Devices, Vicenza, Italy, where he was engaged in research and development of power electronic drives and electrical motors. In January 1999, he joined ABB SACE, Frosinone, Italy, where he worked in the Automation Department as a Designer of automated production lines. He is currently a Research Assistant in Electrical Machines and Drives with the University of Cassino. His research interests are in design, control, and applications of special electrical machines and in power electronic converters. Mr. Cancelliere is a Registered Engineer in Italy. Fabrizio Marignetti (M’01) received the Laurea and Ph.D. degrees in electrical engineering from the Faculty of Engineering of the University of Naples “Federico II,” Naples, Italy, in 1993 and 1998, respectively. Since December 1998, he has been with the Department of Automation of the University of Cassino, Cassino, Italy, as an Assistant Professor of electrical machines and electrical drives. His research interests are in the field of electromechanical design and control of special electrical machines, especially brushless axial-flux machines, tubular actuators, linear motors, transverse-flux machines, millimachines, and micromachines and induction motors with a particular interest in drives applications. Roberto Di Stefano received the Laurea degree in electrotechnical engineering from the University of Naples, Naples, Italy. From 1993 to 1997, he was with the research group of electrical machines and converters at the University of Naples. In 1996, he joined the research group of electrical machine and drives at the University of Cassino, Cassino, Italy. Since 1996, he has been the Director of the Industrial Electronics Laboratory at the University of Cassino. Since December 2004, he has been an Associate Professor of Power Electronics and Drives. His research interests are in the fields of power electronics inverters and electrical machines. Maurizio Scarano (M’00) graduated in electrotechnical engineering from the University of Naples “Federico II,” Naples, Italy, in 1979. From 1983 to 1992, he was a University Researcher of electrotechnics with the University of Naples “Federico II,” mainly involved in research about mathematical modeling of electromagnetic actuators, and was also an Assistant Professor of electrical machines at the University of Cassino, Cassino, Italy. From 1992 to 1999, he was an Associate Professor of electrical machines with the University of Cassino. Since November 1999, he has been a Full Professor of electrical machines. From 1992 to 1999, he was a Scientific Coordinator with the Industrial Electronic Laboratory of the University of Cassino. He has been a Scientific Coordinator of several research contracts with public associations and industrial enterprises in the field of electrical drives. Since 2001, he has been a Director with the Department of Automation, Electromagnetism, Computer Science and Mathematics, University of Cassino. In the last several years, he has specialized his scientific production in the field of nontraditional actuators (linear machines, transverse-flux machines, micromachines) both by developing novel machine configurations and proposing original mathematical analysis algorithms. His experimental activity is often devoted to the design and construction of these actuators. The feeding and control of the machines built were performed carrying out proper electronic technologies. He has authored about 160 papers and notes in the field of electrical machines and drives. Prof. Scarano has been a member of the Scientific Committee of the Research Consortium of Energy and Technologic Application of Electromagnetism (CREATE) since 1996. Authorized licensed use limited to: Université de Lorraine. 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