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High-power density miniscale power generation and energy harvesting systems
Energy Conversion and Management 52 (2011) 46–52
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
High-power density miniscale power generation and energy harvesting systems Sergey Edward Lyshevski * Department of Electrical and Microelectronics Engineering, Rochester Institute of Technology, Rochester, NY 14623-5603, United States
a r t i c l e
i n f o
Article history: Received 4 March 2009 Received in revised form 12 October 2009 Accepted 7 June 2010 Available online 13 July 2010 Keywords: Energy Energy conversion Power generation
a b s t r a c t This paper reports design, analysis, evaluations and characterization of miniscale self-sustained power generation systems. Our ultimate objective is to guarantee highly-efficient mechanical-to-electrical energy conversion, ensure premier wind- or hydro-energy harvesting capabilities, enable electric machinery and power electronics solutions, stabilize output voltage, etc. By performing the advanced scalable power generation system design, we enable miniscale energy sources and energy harvesting technologies. The proposed systems integrate: (1) turbine which rotates a radial- or axial-topology permanent-magnet synchronous generator at variable angular velocity depending on flow rate, speed and load, and, (2) power electronic module with controllable rectifier, soft-switching converter and energy storage stages. These scalable energy systems can be utilized as miniscale auxiliary and self-sustained power units in various applications, such as, aerospace, automotive, biotechnology, biomedical, and marine. The proposed systems uniquely suit various submersible and harsh environment applications. Due to operation in dynamic rapidly-changing envelopes (variable speed, load changes, etc.), sound solutions are researched, proposed and verified. We focus on enabling system organizations utilizing advanced developments for various components, such as generators, converters, and energy storage. Basic, applied and experimental findings are reported. The prototypes of integrated power generation systems were tested, characterized and evaluated. It is documented that high-power density, high efficiency, robustness and other enabling capabilities are achieved. The results and solutions are scalable from micro (100 lW) to medium (100 kW) and heavy-duty (sub-megawatt) auxiliary and power systems. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Focused developments have been performed on enabling medium- and heavy-duty energy conversion, energy generation systems and auxiliary units from kilo- to mega-watt range. Sound solutions at the device (component) and system levels have being emerged which resulted in possibility to design high-performance systems in various applications [1,2]. The energy conversion in those systems has been examined [3–5], and, the major components have being developed. Depending on power range, specifications and requirements, conventional and permanent-magnet AC and DC generators are designed, tested, characterized and deployed [6–14]. In general, synchronous generators guarantee superior performance as compared with DC generators. Rear-earth permanent-magnet synchronous generators are the key components of high-performance sub-megawatt auxiliary power systems. For those generators, the matching controllable rectifiers [15–20] and soft-switching converters [12,21–24] have been used. However, in variety of applications, scalable super-high-density, affordable and robust miniscale energy harvesting, energy genera* Tel.: +1 585 475 4370; fax: +1 585 475 5845. E-mail address: [email protected] URL: http://people.rit.edu/seleee/ 0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.06.030
tion and auxiliary power units should be designed, developed and deployed. These miniscale systems, with output power from micro- to subkilo-watt may not effectively utilize the existing deviceand system-level solutions (components, devices, topologies and organizations) used in medium- and heavy-duty energy conversion systems. In fact, radial- and axial-topology permanent-magnet synchronous generators, power electronics and energy storage solutions can be profoundly different. The aforementioned systems commonly required to operate in harsh environment and rapidlychanging operating envelope, yet guarantee achievable super-highpower density and energy storage, efficiency, robustness, etc. The solutions and technologies for the aforementioned systems under intensive developments, and, sound systems are reported in this paper. We focus the efforts on the most promising solutions, further advancing electric machines design and analysis (analysis and design of heavy-loaded radial and axial-topology synchronous generators operating within the entire BH curve, entire load and speed envelopes) as well as power electronics solutions. In automotive, avionics, biomedical, marine, robotics and other applications, energy harvesting and power systems are key components because there is a need to generate electric energy through mechanical-to-electrical energy conversion. In fact, in various applications, from biomedical implantable devices to sensors, or from aerospace to underwater systems, self-sustained (autonomous,
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alternative and renewable) sources of energy are an ideal solution. It is important to design high-performance systems utilizing emerged technologies and advancements in electronics, energy conversion and electric machinery. The power density, efficiency, robustness and other key performance measures must be maximized. One may convert various forms of energy to electric energy. This concept has been used in geothermal, hydro, nuclear, solar, wind and other medium and large power generation systems. However, new solutions needed for various micro-, mini- and conventional systems. The designed self-sustained energy systems are aimed to power various actuators, communication units and sensors embedded, implanted or installed in autonomous platforms. For example, surface and underwater vehicles (ships, submarines, submersible vehicles, etc.) have an impenetrable hull. There is a need to power actuators, sensors, servos and other devices located outside the hull. Energy systems for implantable medical devices are also considered. In various applications, it is feasible to install micro- and miniscale power generation systems which perform controlled energy conversion and storage. For example, a turbine harvests of the water flow energy and rotates a generator which induces the voltage. This voltage is controlled by a rectifier/converter, and, the generated energy can be stored. We focus on basic research to further enable engineering and technology forefronts by applying most advanced recent findings and solutions. Highly efficient energy conversion is guaranteed by designed high-performance radial- and axial-topology permanentmagnet synchronous generators, rectifiers and soft-switching converters, etc. We examine high-power and high-energy densities generators, converters and supercapacitors. Subsystems are integrated within advanced energy system organizations. Different electronic modules are designed using distinct controlled and uncontrolled rectifiers, as well as various switching converter topologies. The system design and development include various fundamental tasks such as: (i) control and optimization of energy conversion and generation; (ii) efficient energy storage; (iii) device- and system-level optimization and matching; (iv) synthesis and design of high-performance generators; (v) synthesis of rectifiers and converters; (vi) high-fidelity analysis; and, (v) verification, testing and characterization. Some of those tasks are long-standing multidisciplinary research activities. Though electric machinery, power electronics and control of power systems are well-established engineering areas, many advances can be accomplished. In this paper, we utilize contemporary findings, as well as further enable multidisciplinary engineering and science advancing energy systems. The designed proof-of-concept prototypes of subsystems and power generation systems are tested and characterized in various applications including harsh and submersible environments. Depending on the system specifications, different topological, behavioral and performance designs are accomplished synthesizing and integrating subsystems, e.g., turbine, generator and electronics. The results are analyzed in sufficient details.
2. Power generation system The power generation system consists of a turbine, generator and power electronic module. Sound solutions are researched and applied. We utilize: (1) high efficiency turbines; (2) highpower density permanent-magnet radial and axial topologies synchronous generators; (3) high efficiency controlled rectifiers and soft-switching converters, integrated with high energy density storage double-layer capacitors (supercapacitors). The designed energy generation systems are aimed for harsh environment, submersible and biocompatible applications. To ensure an optimal design, guarantee soundness and enable an expanded operational envelope, a turbine rotor houses perma-
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nent magnets forming an integrated turbine-generator module. The coated rear-earth hard magnets, encapsulated in polymers, are embedded in the turbine aperture. The generator windings and electronic module reside in a sealed package. The airgap between magnets and windings, filled with water or air, can vary to maximize the power density, efficiency and other core performance measures. The induced phase voltages are supplied to a multistage electronic module which rectifies the voltage, varies the voltage magnitude to the specified DC or AC voltage, stabilizes the output voltage, and stores the energy. We design, integrate and optimize all system components thereby guaranteeing soundness, optimality, efficiency, robustness, losses minimization, etc. The energy conversion and output voltage are effectively controlled by controlling a rectifier and switching converter. Various permanent-magnet generators were synthesized, designed and tested. The analysis is performed for commercial and newly synthesized generators. The images of some examined high-performance radial- and axial-topology generators with the outer diameter from 2 mm to 10 cm are documented in Fig. 1a. These medium- and high-speed generators (100 to 100,000 rad/s, 1 mW to 100 W) induce ac phase voltages from 1 to 100 V. The windings are placed in the stationary sealed waterproof case. In radial and axial-topology generators, the segmented permanent magnets are used to form ring- and disk-shaped magnets with various outer and inner diameters matching the integrated turbine-generator rotor housing. The Pelton turbine is utilized for submersible applications. The vanes sizing, geometry and curvature are defined performing an application-specific design to ensure maximum efficiency within the operating envelope. An integrated turbine-generator module, shown in Fig. 1b, contains permanent magnets on the turbine rotor thereby guarantying a unique utilization of the turbine structure. This solution ensures superior performance, robustness, enhanced operating envelope, harsh environment operation, etc. Controlled two- and three-phase rectifiers with filtering capacitors and inductors are used to rectify the induced ac phase voltages to a DC voltage. Controlled two- and four-quadrant buck, boost and buck-boost converter topologies [12,21–24] were synthesized and utilized to ensure high efficiency within the expanding current and voltage envelopes. The operating principle is based on the changing the duty ratio (duty cycle). We utilize the softswitching concept in order to increase efficiency, reduce losses, reduce electromagnetic loading, etc. As rectifier and converter topologies are defined, analog proportional-integral control laws are designed and implemented to stabilize the output voltage or to ensure the desired output voltage. It is found that the DC output voltage can be increased by a factor of 10 within the operating envelope. The flyback converter is used to enable the stabilization abilities maintaining the output voltage of the controlled switching converters to the desired value. The converter utilizes a transformer to reduce or increase the voltage, isolate the input from the output, and enable the desired impedance. The low-amplitude voltage ripple (±0.1 V), produced on the transformer output due to the transistors switching, charging/discharging and other effects, is eliminated by using a supercapacitor-inductor circuitry parallel with the resistive-inductive load with time-varying impedance ZL. It is found that one may effectively control the power factor which is of a great importance to guarantee high efficiency if the loads impedance ZL(t) varies. The supercapacitor stage stores the energy. Supercapacitors have high energy and power densities (100 J/g and 10 W/g). In addition, supercapacitors possess high charging capacity, enabling charging/discharging characteristics, unlimited number of cycles, high efficiency, temperature stability, robustness, etc. The power electronic module may integrate a power management system with a microcontroller to optimize the energy conversion, control and stabilize the output
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Fig. 1. (a) High-performance radial- and axial-topology permanent-magnet synchronous generators: From 2 mm to 10 cm rotor outer diameter, 1 mW–100 W, 100– 100,000 rad/s. Windings are on the stator, while permanent magnets are on the rotor; and, (b) turbines with segmented permanent magnets forming an integrated turbinegenerator module.
voltage, minimize losses, guarantee impedance matching is ZL(t) varies, etc. The use of advanced controlled rectifiers, soft-switching converters and supercapacitor storage stages ensure the maximal achievable power and energy densities.
2.1. Device and system level designs To solve a wide range of challenging problems, we perform fundamental research and focus on advanced hardware solutions. Hence, we departed from an abstract and generic systems engineering concept. Advanced system organizations, enabling device topologies, sound component synthesis, high-performance device integration and coherent analysis provide one with the abilities to optimize the overall system performance. The torque generation, energy conversion, voltage induction, energy storage and other inherent mechanisms are consistently studied allowing one to systematically design and integrate turbines, generators and electronics using the requirements, specifications, device/system capabilities and other features. The power density, efficiency, robustness, overloading, controllability, stabilization and other key performance characteristics depend on the device and system levels design and utilization. The application-specific synthesis allows us to optimize components and subsystems for different operating envelopes guaranteeing the best achievable performance. Distinct hardware solutions (turbine – generator – power electronics with energy storage stage – load) are tested for different angular velocity and loads in the full operating envelopes. The design specifications are met, and, optimal or near-optimal achievable performance is guaranteed.
3. Permanent-magnet synchronous generators: theory and experiments 3.1. Analysis and design fundamentals To design and analyze permanent-magnet synchronous generators, we apply the electromagnetic theory [3,12,25–27]. The topologic synthesis of radial and axial topologies generators is accomplished by utilizing an electromagnetic system and geometry classifier [4]. High electromagnetic loads impose challenges in design of high performance and high-energy density generators. Hard magnets have wide BH curves (high coercivity) and possess high-energy storage capacity. We use neodymium iron boron (Nd2Fe14B) and samarium cobalt (Sm1Co5 and Sm2Co17) magnets. The energy density wm is defined by the area enclosed by the BH curve, and wm = ½B H, where B and H are the field density and intensity. The energy stored in a permanent magnet of volume V Rb is W ¼ V a HdB. Using the magnetization M and permeability l, one has W = lVM H. Permanent magnets operate on the demagnetization curve of the hysteresis loop, and the second quadrant of the BH curve is studied. The operating point varies as function of loads. Furthermore, l = l0lr = B/H. The variations of the relative permeability lr, as a function of the electromagnetic load, are lr(H) = dB/dH. The demagnetization and energy production curves are in mutual correspondence. The electromagnetic interaction of permanent magnets and windings results in the induced emf ¼ H H H @B E dl ¼ ðv BÞ dl ds thereby generating l l s @t motional inductionðgenerationÞ
transformer induction
the phase induced voltages. The magnetomotive force is H H H mmf ¼ l H dl ¼ s J ds þ s @D ds. The relationship between the @t
S.E. Lyshevski / Energy Conversion and Management 52 (2011) 46–52
prime mover (turbine), electromagnetic load TeL, friction Tf and stochastic loads TnL torques is Tt = TeL + Tf + TnL. The rated achievable generator power density is found to be 1 W/cm3 for highperformance 0.01–100 W synchronous generators. The power density is significantly affected by the design, topology, magnets, operating envelope (loads, velocity, temperature, etc.) and other factors. The magnetic flux through any surface is expressed using the R magnetic field density B as w ¼ s B ds. For the magnetically coupled abc stator windings, using the Kirchhoff voltage law, one finds the following differential equations which describe the circuitry-electromagnetic dynamics of the three-phase generators
dwas ¼ r s ias ; dt
dwbs ¼ r s ibs ; dt
dwcs ¼ r s ics ; dt
ð1Þ
where ias, ibs and ics are the phase currents; was, wbs and wcs are the abc flux linkages as given by 2 3 P1 2 3 2 32 3 2n1 a sin h was Lss Lms Lms ias n r n¼1 6 P1 7 6 7 6 76 7 2n1 ðhr 23 pÞ 7 4 wbs 5 ¼ 4 Lms Lss Lms 54 ibs 5 þ wm 6 4 n¼1 an sin 5; P 2n1 1 2 wcs Lms Lms Lss ics ðhr þ 3 pÞ n¼1 an sin Lss and Lms are the self- and mutual inductances; wm is the effective R amplitude of the flux linkages established by magnets, w ¼ s B ds, B = lH, l = l0lr(H); an are the variables- and technology-specific and operating envelope-dependent coefficients; rs is the equivalent stator resistance. The torsional-mechanical dynamics is described by the following differential equations
dxr P 2Bm T t T eL xr T nL ; ¼ 2J dt P
dhr ¼ xr ; dt
ð2Þ
where xr and hr are the electrical angular velocity and displacement; TeL is the electromagnetic load torque
" 1 X Pwm 2n2 T eL ¼ ð2n 1Þan cos hr sin hr ias 2 n¼1 1 X 2 2 2n2 ð2n 1Þan cos hr p sin hr p þibs 3 3 n¼1 # 1 X 2 2 2n2 ð2n 1Þan cos hr þ p sin hr þ p ; þics 3 3 n¼1
ð3Þ
Tt is the turbine torque; Bm is the friction coefficient; J is the moment of inertia; P is the number of poles. Using differential equations for magnetically coupled circuitry (1) and torsional-mechanical dynamics (2) one obtains the nonlinear mathematical model of radial- and axial-topology permanent-magnet synchronous generators. This model is used in the generator and system analysis. The results are applied to perform various designs tasks at the device and system levels. We reported the first principles for permanent-magnet synchronous generators which are utilized in design and optimization. High-efficiency, high-power and high-energy densities synchronous generators were designed, characterized and evaluated. Example 3.1. One performs the design attempting to ensure the electromagnetic interactions with a1 = 1 and all other an = 0. This can be achieved when generator operates from 0% to 50% load (near-linear BH curve). For a = 1, Eq. (3) gives 1 T eL ¼ Pw2m ias cos hr þ ibs cos hr 23 p þ ics cos hr þ 23 p .
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The resulting torsional-mechanical Eq. (2) are given as
dxr P2 wm 2 2 ¼ ½ias cos hr þ ibs cosðhr pÞ þ ics cosðhr þ pÞ 3 3 dt 4J Bm P P dhr xr T nL þ T t ; ¼ xr : 2J 2J J dt 3.2. Radial-topology permanent-magnet synchronous generators The design, analysis, evaluation and characterization tasks are performed for distinct radial-topology generators. For example, a 50 W (50 mm diameter) and 5 W (20 mm diameter) three-phase radial-topology generators, reported in Fig. 1a, have the following parameters: (1) P = 2, rss = 0.6 X, Lss = 0.002 H, Lls = 0.0002 H and wm = 0.05 V s/rad (N m/A); (2) P = 2, rss = 25 X, Lss = 0.002 H, Lls = 0.0002 H and wm = 0.045 V s/rad (N m/A). Using (1)–(3), in the full operating envelope we found that a1–0, a2–0 and 8an = 0, n > 2. The resulting circuitry-electromagnetic and torsionalmechanical equations are
dias 1 rs 2Lss Lm ias r s Lm ibs r s Lm ics ¼ 2 dt 2Lss Lss Lm L2m i h 2 þwm 2Lss Lm xr a1 cos hr þ 3a2 coshr sin hr 2 2 2 2 þwm Lm xr a1 cosðhr pÞ þ 3a2 cos hr p sin hr p 3 3 3 2 2 2 2 þwm Lm xr a1 cos hr þ p þ 3a2 cos hr þ p sin hr þ p ; 3 3 3
dibs 1 r s Lm ias rs 2Lss Lm ibs r s Lm ics ¼ 2 2 dt 2Lss Lss Lm Lm 2 þwm Lm xr a1 cos ðhr Þ þ 3a2 cos hr sin hr 2 þwm 2Lss Lm xr a1 cos hr p 3 2 2 2 þ3a2 cos hr p sin hr p 3 3 2 þ wm Lm xr a1 cos hr þ p 3 2 2 2 þ3a2 cos hr þ p sin hr þ p ; 3 3
dics 1 rs Lm ias r s Lm ibs rs ð2Lss Lm Þics ¼ 2 dt 2Lss Lss Lm L2m h i 2 þ wm Lm xr a1 cos hr þ 3a2 cos hr sin hr 2 þ wm Lm xr a1 cos hr p 3 2 2 2 þ 3a2 cos hr p sin hr p 3 3 2 þ wm 2Lss Lm xr a1 cos hr þ p 3 2 2 2 ; þ 3a2 cos hr þ p sin hr þ p 3 3 dxr P P2 wm Bm P xr T nL ; ¼ Tt T eL 2J 2J dt 4J J dhr ¼ xr ; dt
ð4Þ
h i 2 T eL ¼ ias a1 cos hr þ 3a2 cos hr sin hr þ ibs a1 cos hr 23 p þ 2 3a2 cos hr 23 p sin hr 23 p þ ics a1 cos hr þ 23 p þ 3a2 cos hr þ 23 p where
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Fig. 2. Induced phase voltage uas by a radial-topology generator for no electromagnetic load, rated load, and peak electromagnetic load. Variations of the angular velocities and magnitudes of uas are: (a) xr = 568, 555 and 531 rad/s, uas = 30 V, 28 V and 22.5 V; and, (b) xr = 278, 274 and 256 rad/s, uas = 14 V, 13.8 V and 10 V.
2 sin hr þ 23 p ; Lm is the magnetizing inductance, Lm ¼ 23 ðLss Lls Þ; Lls is the leakage inductance. The experimental results at no load, rated and peak loads are reported in Fig. 2 where the induced as phase voltage uas is documented. The angular velocity decreases as the load TeL increases because Tt is constrained. Coefficients an significantly vary in the operating envelope mainly due to changes of lr(H). The energy conversion, emf induction and other baseline phenomena are analyzed and examined. The reported analysis, design and optimization are verified.
3.3. Axial-topology permanent-magnet synchronous generators We design and examine two- and three-phase axial-topology synchronous generators with the segmented array of permanent magnets as documented in Figs. 1a and 3a. As was emphasized, the planar segmented permanent magnets array is placed on the turbine rotor, while the planar windings are on the stationary member. These high-power density axial-topology generators result in number of advantages as compared to radial-topology generators. The advantages of the axial-topology permanent-magnet generators are:
(a) Rotor
Stator Permanent Magnets
ωr
Permanent Magnets
(b)
Fig. 3. (a) Axial-topology permanent-magnet synchronous generator and (b) induced phase voltage uas in a generator for no electromagnetic load (TeL = 0), 0.5TeLrated, and peak electromagnetic load. At no load, generator is driven at two angular velocities: (i) xr = 150 rad/s and xr = 450 rad/s. For different TeL, (i) uas = 13.3 V, 10.5 V and 4.2 V (low speed operation), and, (ii) uas = 31.4 V, 26.3 V and 10.3 V (rated speed operation).
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(i) Affordability and simplicity to fabricate and assemble machines because permanent magnets and windings are planar. The segmented magnets and planar windings significantly simplify fabrication and enable performance. (ii) There are relaxed shape-geometry and sizing requirements imposed on the magnets and windings. However, device performance is significantly affected by the topology, geometry, spacing, etc. (iii) There is no rotor back ferromagnetic material required (silicon, polymers or plastics can be used). (iv) The airgap and magnet-winding separation can be adjusted. (v) It is easy to fabricate planar windings on the planar (flat) stator. (vi) There are no cogging torque. Depending on the magnet geometry, magnetization and separations of magnets, for three-phase generators, one yields
Bas ¼ BM
1 X
2n1
an sin
n¼1
Bcs ¼ BM
1 X n¼1
2n1
an sin
hr ;
Bbs ¼ BM
2 hr þ p ; 3
1 X
2n1
an sin
n¼1
2 hr p ; 3
where BM is the magnitude of the effective electromagnetic field density which is a function of the cross-sectional area, number turns, length, winding geometry, etc. Using (1), for a 50 V axial-topology generator, illustrated in Fig. 1a, a1–0 and a2–0 and 8an = 0, n > 2. The circuitry-electromagnetic dynamics is described by the following differential equations
h io dias 1 n 2 r s ias wm xr a1 cos hr þ 3a2 cos hr sin hr ; ¼ Lss dt
dibs 1 2 rs ibs wm xr a1 cos hr p ¼ Lss 3 dt 2 2 2 ; þ3a2 cos hr p sin hr p 3 3
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dics 1 2 r s ics wm xr a1 cos hr þ p ¼ Lss 3 dt 2 2 2 : þ3a2 cos hr þ p sin hr þ p 3 3 The generator parameters are experimentally found. We have Nm = 8, rs = 13.5 X, Lss = 0.035 H, wm = 0.03 V s/rad (N m/A), Bm = 0.0000005 N m s/rad and J = 0.00001 kg m2. For different angular velocities (150 rad/s and 450 rad/s at no load), the induced phase voltage uas is reported in Fig. 3b. As documented, the uas waveforms are functions of xr, TeL and Tt. All essential phenomena, including the hysteresis BH curve, electromagnetic loading, limited Tt, are coherently integrated into analysis, design and optimization tasks.
4. Power electronic module and experimental results A power electronic module is composed from the following major components: (1) controlled rectifier; (2) controlled soft-switching converter; (3) stabilizing circuit; (4) filters; (5) supercapacitor energy storage stage; (6) controller; (7) energy management system. The controlled rectifier and soft-switching converter topologies are utilized. By applying this sound solution, we guaranteed high efficiency, low-current switching, eliminate over-heating, minimize stresses and optimize switching profile of output-stage transistors. It was found that the converter efficiency for the peak, maximum and rated (75% of maximum) loads is 93.7%, 96.2% and 96.4%. The proportional-integral (PI) controller
ð5Þ u ¼ kp e þ
Z
kp e dt;
guarantees the maximum allowed error e(i) within 1%. Here, e(t) is the tracking error, e(t) = uref ut; uref is the reference (command) terminal DC voltage; ut is the terminal DC voltage.
Fig. 4. (a) Power electronic module; and, (b) experimental results: variations of the terminal DC voltage ut during the charging, discharging and loading regimes in the full operating envelope (rated, maximum and peak loads and varying angular velocity xrm). The applied torque Tt and mechanical power Ttxrm are limited (constrained).
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This PI controller with matching third-order notch filter (to filter 1 kHz to 1 MHz noise) were implemented using a single Analog Device quadrant operational amplifier. The stabilizing DC–DC voltage converter, integrated with filters and supercapacitors is synthesized and examined. The electronic module, documented in Fig. 4a integrates: (i) controlled threephase rectifier; (ii) soft-switching buck-boost converter with driving and controlling circuitry; (iii) supercapacitor–inductor storage stage. The output voltage at the load terminal with varying ZL(t) is stabilized as reported in Fig. 4b which document the experimental results for different loading and charging/discharging phases of operations. Comprehensive tests were conducted in the full operating envelope. For an axial-topology synchronous generator reported in Section 3.3, we specify the output terminal voltage to be stabilized at uref = const = 15 V. Different RLC loads, defined by ZL, are applied. At low angular velocity (xrm is 100 rad/s), the induced ac phase voltages are 5 V. Under the limited prime mover (turbine) torque Tt, the terminal voltage ut was ensured and stabilized at the timevarying rated ZLrated and ZLmax. Here, ZLrated(t) 2 [0 0.75]ZLmax. Thus, the RLC load, which typifies typical loads, is used. At maximum ZLmax and peak ZLpeak (RLoad = 1.2 X, results in a peak current, and a DC current at the terminal itpeak is 10 A), we have ut = 14.85 V and ut = 12.3 V due to the constraints on the mechanical (input) power Ttxrm. Here, xrm is the angular velocity of the turbine. The mechanical angular velocity is related to xr as xrm = 2xr/P. The input mechanical peak power Ttpeakxrmpeak is 200 W. Taking note of the efficiency of a generator (72% at the peak load and highly saturated BH curve), power electronics (91.4%) and filter (97.8%), one finds that the peak electric output power should be 128.7 W. As illustrated in Fig. 4b, the experimental results illustrate that the Pelectric peak = 123 W because the RLC load affect the power factor (pf – 1) resulting in additional losses. At the maximum load operating conditions ZLmax (RLoad max = 1.86 X), for the reference voltage uref = 15 V, the experimental results documented in Fig. 4b indicate that ut = 14.85 V and itmax = 8 A. Thus, Pelectric max = 119 W. The generator, power electronics and filter efficiencies were 75.8%, 94.1% and 98.1%, respectively. Different charging, discharging, loading and other conditions were tested. The efficiencies of the generator and power electronic module vary depending on the loading, BH saturation, duty ratio, current, load impedance, power factor, etc. The energy, stored by a supercapacitor depends on the allowed foot-print area and capacitor used. Our experimental findings and proof-of-concept prototypes provide evidence of soundness and exceptional capabilities of the concept proposed. 5. Conclusions In this paper, high-performance self-sustained power generation systems were synthesized, designed, analyzed, tested and evaluated. We accomplished designs of robust, high-power and high-energy densities systems which comprise of a turbine, radialor axial-topology permanent-magnet synchronous generator and electronic module. The results were evaluated and verified in the full operating envelopes for proof-of-concept subsystems and system prototypes. Basic fundamental, applied and experimental research was performed in multidisciplinary areas of energy systems, power, power electronics, electric machines and energy sources. The reported fundamental, applied and experimental results contribute to novel technological developments of energy harvesting and power systems. The examined scalable, high-effi-
ciency, affordable and robust systems can be used in a wide range of commercial and military applications including autonomous platforms, auxiliary power units, etc. References [1] Bansal RC, Bhatti TS, Kothari DP. On some of the design aspects of wind energy conversion systems. Energy Convers Manage 2002;43(16):2175–87. [2] Camporeale SM, Magi V. Streamtube model for analysis of vertical axis variable pitch turbine for marine currents energy conversion. Energy Convers Manage 2000;41(16):1811–27. [3] Krause PC, Wasynczuk O, Sudhoff SD. Analysis of electric machinery. New York: IEEE Press; 1995. [4] Lyshevski SE. Electromechanical systems, electric machines, and applied mechatronics. Boca Raton, FL: CRC Press; 1999. [5] Lior N. Advanced energy conversion to power. Energy Convers Manage 1997;38(10-13):941–55. [6] Chau KT, Li YB, Jiang JZ, Shuangxia N. Design and control of a PM brushless hybrid generator for wind power application. IEEE Trans Magnet 2006;42(10):3497–9. [7] Chunting M, Filippa M, Shen J, Natarajan N. Modeling and control of a variablespeed constant-frequency synchronous generator with brushless exciter. IEEE Trans Indus Appl 2004;40(2):565–73. [8] Honorati O, Caricchi F, Santini E. High speed AC generator (7200 rpm, 60 Hz) for autonomous power systems. IEEE Trans Energy Convers 1989;4(3):544–50. [9] Jokl AL. Electric generators: technology status. IEEE Aerosp Electron Syst Mag 1991;6(12):56–9. [10] Guo Z, Chang L. FEM study on permanent magnet synchronous generators for small wind turbines. In: Proc Conf Electrical and Computer Engineering; 2005. p. 641–44. [11] Lee H-W, Kim T-H, Ehsani M. Maximum power throughput in the multiphase brushless DC generator. IEE Proc Electr Power Appl 2005;152(3):501–8. [12] Lyshevski SE. Electromechanical systems and devices. Boca Raton, FL: CRC Press; 2008. [13] Tripathy SC, Kalantar M, Rao ND. Wind turbine driven self-excited induction generator. Energy Convers Manage 1993;34(8):641–8. [14] Zhang X-L, Wu J, Feng X-F, Zhang X-Y, Wang X-H. Research on matrix converter and brushless doubly-fed machine for wind power generation system. In: Proc Conf Power Electronics Systems and Applications; 2009. p. 1– 5. [15] Barcenas EB, Cardenas V, Arau J, Alvarez R. Practical considerations in the PWM rectifier with active filter function. In: Proc Power Electronics Congress; 2008. p. 56–62. [16] Barcenas EB, Cardenas V, Roffiel JA. Design tradeoffs in PWM rectifiers with active filtering function. In: Proc Applied Power Electronics Conference and Exposition; 2008. p. 1423–29. [17] Bouafia A, Krim F, Gaubert J-P. Design and implementation of high performance direct power control of three-phase PWM rectifier, via fuzzy and PI controller for output voltage regulation. Energy Convers Manage 2009;50(1):6–13. [18] Hart DW. Introduction to power electronics. Upper Saddle River, NJ: Prentice Hall; 1997. [19] Liutanakul P, Pierfederici S, Meibody-Tabar F. Nonlinear control techniques of a controllable rectifier/inverter-motor drive system with a small DC-link capacitor. Energy Convers and Manage 2008;49(12):3541–9. [20] Xinhui W, Panda SK, Jianxin X. Analysis and experimental validation of the output voltage and input current performances in three-phase PWM boost rectifiers under unbalanced and distorted supply voltage conditions. In: Proc Conf Control Applications; 2007. p. 605–10. [21] Adib E, Farzanehfard H. Soft switching bidirectional DC–DC converter for ultracapacitor–batteries interface. Energy Convers Manage 2009;50(12):2879–84. [22] Hiraki E, Yamamoto K, Mishima T. An isolated bidirectional DC–DC soft switching converter for super capacitor based energy storage systems. In: Proc Conf Power Electronics Specialists; 2007. p. 390–95. [23] Huai W, Qian S, Chung HSH, Tapuchi S, Ioinovici A. A ZCS current-fed fullbridge PWM converter with self-adaptable soft-switching snubber energy. IEEE Trans Power Electron 2009;24(8):1977–91. [24] Inaba CY, Konishi Y, Nakaoka M. High-frequency flyback-type soft-switching PWM DC–DC power converter with energy recovery transformer and auxiliary passive lossless snubbers. IEE Proc Electr Power Appl 2004;151(1): 32–7. [25] Miller TJE, Popescu M, Cossar C, McGilp MI, Olaru M, Davies A, et al. Embedded finite-element solver for computation of brushless permanent-magnet motors. IEEE Trans Indus Appl 2008;44(4):1124–33. [26] Miller TJE, Rabinovici R. Back-emf waveforms and core losses in brushless DC motors. IEE Proc Electr Power Appl 1994;141(3):144–54. [27] Slemon GR. Electric machines and drives. Reading, MA: Addison–Wesley Publishing Company; 1992.
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
High-power density miniscale power generation and energy harvesting systems Sergey Edward Lyshevski * Department of Electrical and Microelectronics Engineering, Rochester Institute of Technology, Rochester, NY 14623-5603, United States
a r t i c l e
i n f o
Article history: Received 4 March 2009 Received in revised form 12 October 2009 Accepted 7 June 2010 Available online 13 July 2010 Keywords: Energy Energy conversion Power generation
a b s t r a c t This paper reports design, analysis, evaluations and characterization of miniscale self-sustained power generation systems. Our ultimate objective is to guarantee highly-efficient mechanical-to-electrical energy conversion, ensure premier wind- or hydro-energy harvesting capabilities, enable electric machinery and power electronics solutions, stabilize output voltage, etc. By performing the advanced scalable power generation system design, we enable miniscale energy sources and energy harvesting technologies. The proposed systems integrate: (1) turbine which rotates a radial- or axial-topology permanent-magnet synchronous generator at variable angular velocity depending on flow rate, speed and load, and, (2) power electronic module with controllable rectifier, soft-switching converter and energy storage stages. These scalable energy systems can be utilized as miniscale auxiliary and self-sustained power units in various applications, such as, aerospace, automotive, biotechnology, biomedical, and marine. The proposed systems uniquely suit various submersible and harsh environment applications. Due to operation in dynamic rapidly-changing envelopes (variable speed, load changes, etc.), sound solutions are researched, proposed and verified. We focus on enabling system organizations utilizing advanced developments for various components, such as generators, converters, and energy storage. Basic, applied and experimental findings are reported. The prototypes of integrated power generation systems were tested, characterized and evaluated. It is documented that high-power density, high efficiency, robustness and other enabling capabilities are achieved. The results and solutions are scalable from micro (100 lW) to medium (100 kW) and heavy-duty (sub-megawatt) auxiliary and power systems. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Focused developments have been performed on enabling medium- and heavy-duty energy conversion, energy generation systems and auxiliary units from kilo- to mega-watt range. Sound solutions at the device (component) and system levels have being emerged which resulted in possibility to design high-performance systems in various applications [1,2]. The energy conversion in those systems has been examined [3–5], and, the major components have being developed. Depending on power range, specifications and requirements, conventional and permanent-magnet AC and DC generators are designed, tested, characterized and deployed [6–14]. In general, synchronous generators guarantee superior performance as compared with DC generators. Rear-earth permanent-magnet synchronous generators are the key components of high-performance sub-megawatt auxiliary power systems. For those generators, the matching controllable rectifiers [15–20] and soft-switching converters [12,21–24] have been used. However, in variety of applications, scalable super-high-density, affordable and robust miniscale energy harvesting, energy genera* Tel.: +1 585 475 4370; fax: +1 585 475 5845. E-mail address: [email protected] URL: http://people.rit.edu/seleee/ 0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.06.030
tion and auxiliary power units should be designed, developed and deployed. These miniscale systems, with output power from micro- to subkilo-watt may not effectively utilize the existing deviceand system-level solutions (components, devices, topologies and organizations) used in medium- and heavy-duty energy conversion systems. In fact, radial- and axial-topology permanent-magnet synchronous generators, power electronics and energy storage solutions can be profoundly different. The aforementioned systems commonly required to operate in harsh environment and rapidlychanging operating envelope, yet guarantee achievable super-highpower density and energy storage, efficiency, robustness, etc. The solutions and technologies for the aforementioned systems under intensive developments, and, sound systems are reported in this paper. We focus the efforts on the most promising solutions, further advancing electric machines design and analysis (analysis and design of heavy-loaded radial and axial-topology synchronous generators operating within the entire BH curve, entire load and speed envelopes) as well as power electronics solutions. In automotive, avionics, biomedical, marine, robotics and other applications, energy harvesting and power systems are key components because there is a need to generate electric energy through mechanical-to-electrical energy conversion. In fact, in various applications, from biomedical implantable devices to sensors, or from aerospace to underwater systems, self-sustained (autonomous,
S.E. Lyshevski / Energy Conversion and Management 52 (2011) 46–52
alternative and renewable) sources of energy are an ideal solution. It is important to design high-performance systems utilizing emerged technologies and advancements in electronics, energy conversion and electric machinery. The power density, efficiency, robustness and other key performance measures must be maximized. One may convert various forms of energy to electric energy. This concept has been used in geothermal, hydro, nuclear, solar, wind and other medium and large power generation systems. However, new solutions needed for various micro-, mini- and conventional systems. The designed self-sustained energy systems are aimed to power various actuators, communication units and sensors embedded, implanted or installed in autonomous platforms. For example, surface and underwater vehicles (ships, submarines, submersible vehicles, etc.) have an impenetrable hull. There is a need to power actuators, sensors, servos and other devices located outside the hull. Energy systems for implantable medical devices are also considered. In various applications, it is feasible to install micro- and miniscale power generation systems which perform controlled energy conversion and storage. For example, a turbine harvests of the water flow energy and rotates a generator which induces the voltage. This voltage is controlled by a rectifier/converter, and, the generated energy can be stored. We focus on basic research to further enable engineering and technology forefronts by applying most advanced recent findings and solutions. Highly efficient energy conversion is guaranteed by designed high-performance radial- and axial-topology permanentmagnet synchronous generators, rectifiers and soft-switching converters, etc. We examine high-power and high-energy densities generators, converters and supercapacitors. Subsystems are integrated within advanced energy system organizations. Different electronic modules are designed using distinct controlled and uncontrolled rectifiers, as well as various switching converter topologies. The system design and development include various fundamental tasks such as: (i) control and optimization of energy conversion and generation; (ii) efficient energy storage; (iii) device- and system-level optimization and matching; (iv) synthesis and design of high-performance generators; (v) synthesis of rectifiers and converters; (vi) high-fidelity analysis; and, (v) verification, testing and characterization. Some of those tasks are long-standing multidisciplinary research activities. Though electric machinery, power electronics and control of power systems are well-established engineering areas, many advances can be accomplished. In this paper, we utilize contemporary findings, as well as further enable multidisciplinary engineering and science advancing energy systems. The designed proof-of-concept prototypes of subsystems and power generation systems are tested and characterized in various applications including harsh and submersible environments. Depending on the system specifications, different topological, behavioral and performance designs are accomplished synthesizing and integrating subsystems, e.g., turbine, generator and electronics. The results are analyzed in sufficient details.
2. Power generation system The power generation system consists of a turbine, generator and power electronic module. Sound solutions are researched and applied. We utilize: (1) high efficiency turbines; (2) highpower density permanent-magnet radial and axial topologies synchronous generators; (3) high efficiency controlled rectifiers and soft-switching converters, integrated with high energy density storage double-layer capacitors (supercapacitors). The designed energy generation systems are aimed for harsh environment, submersible and biocompatible applications. To ensure an optimal design, guarantee soundness and enable an expanded operational envelope, a turbine rotor houses perma-
47
nent magnets forming an integrated turbine-generator module. The coated rear-earth hard magnets, encapsulated in polymers, are embedded in the turbine aperture. The generator windings and electronic module reside in a sealed package. The airgap between magnets and windings, filled with water or air, can vary to maximize the power density, efficiency and other core performance measures. The induced phase voltages are supplied to a multistage electronic module which rectifies the voltage, varies the voltage magnitude to the specified DC or AC voltage, stabilizes the output voltage, and stores the energy. We design, integrate and optimize all system components thereby guaranteeing soundness, optimality, efficiency, robustness, losses minimization, etc. The energy conversion and output voltage are effectively controlled by controlling a rectifier and switching converter. Various permanent-magnet generators were synthesized, designed and tested. The analysis is performed for commercial and newly synthesized generators. The images of some examined high-performance radial- and axial-topology generators with the outer diameter from 2 mm to 10 cm are documented in Fig. 1a. These medium- and high-speed generators (100 to 100,000 rad/s, 1 mW to 100 W) induce ac phase voltages from 1 to 100 V. The windings are placed in the stationary sealed waterproof case. In radial and axial-topology generators, the segmented permanent magnets are used to form ring- and disk-shaped magnets with various outer and inner diameters matching the integrated turbine-generator rotor housing. The Pelton turbine is utilized for submersible applications. The vanes sizing, geometry and curvature are defined performing an application-specific design to ensure maximum efficiency within the operating envelope. An integrated turbine-generator module, shown in Fig. 1b, contains permanent magnets on the turbine rotor thereby guarantying a unique utilization of the turbine structure. This solution ensures superior performance, robustness, enhanced operating envelope, harsh environment operation, etc. Controlled two- and three-phase rectifiers with filtering capacitors and inductors are used to rectify the induced ac phase voltages to a DC voltage. Controlled two- and four-quadrant buck, boost and buck-boost converter topologies [12,21–24] were synthesized and utilized to ensure high efficiency within the expanding current and voltage envelopes. The operating principle is based on the changing the duty ratio (duty cycle). We utilize the softswitching concept in order to increase efficiency, reduce losses, reduce electromagnetic loading, etc. As rectifier and converter topologies are defined, analog proportional-integral control laws are designed and implemented to stabilize the output voltage or to ensure the desired output voltage. It is found that the DC output voltage can be increased by a factor of 10 within the operating envelope. The flyback converter is used to enable the stabilization abilities maintaining the output voltage of the controlled switching converters to the desired value. The converter utilizes a transformer to reduce or increase the voltage, isolate the input from the output, and enable the desired impedance. The low-amplitude voltage ripple (±0.1 V), produced on the transformer output due to the transistors switching, charging/discharging and other effects, is eliminated by using a supercapacitor-inductor circuitry parallel with the resistive-inductive load with time-varying impedance ZL. It is found that one may effectively control the power factor which is of a great importance to guarantee high efficiency if the loads impedance ZL(t) varies. The supercapacitor stage stores the energy. Supercapacitors have high energy and power densities (100 J/g and 10 W/g). In addition, supercapacitors possess high charging capacity, enabling charging/discharging characteristics, unlimited number of cycles, high efficiency, temperature stability, robustness, etc. The power electronic module may integrate a power management system with a microcontroller to optimize the energy conversion, control and stabilize the output
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S.E. Lyshevski / Energy Conversion and Management 52 (2011) 46–52
Fig. 1. (a) High-performance radial- and axial-topology permanent-magnet synchronous generators: From 2 mm to 10 cm rotor outer diameter, 1 mW–100 W, 100– 100,000 rad/s. Windings are on the stator, while permanent magnets are on the rotor; and, (b) turbines with segmented permanent magnets forming an integrated turbinegenerator module.
voltage, minimize losses, guarantee impedance matching is ZL(t) varies, etc. The use of advanced controlled rectifiers, soft-switching converters and supercapacitor storage stages ensure the maximal achievable power and energy densities.
2.1. Device and system level designs To solve a wide range of challenging problems, we perform fundamental research and focus on advanced hardware solutions. Hence, we departed from an abstract and generic systems engineering concept. Advanced system organizations, enabling device topologies, sound component synthesis, high-performance device integration and coherent analysis provide one with the abilities to optimize the overall system performance. The torque generation, energy conversion, voltage induction, energy storage and other inherent mechanisms are consistently studied allowing one to systematically design and integrate turbines, generators and electronics using the requirements, specifications, device/system capabilities and other features. The power density, efficiency, robustness, overloading, controllability, stabilization and other key performance characteristics depend on the device and system levels design and utilization. The application-specific synthesis allows us to optimize components and subsystems for different operating envelopes guaranteeing the best achievable performance. Distinct hardware solutions (turbine – generator – power electronics with energy storage stage – load) are tested for different angular velocity and loads in the full operating envelopes. The design specifications are met, and, optimal or near-optimal achievable performance is guaranteed.
3. Permanent-magnet synchronous generators: theory and experiments 3.1. Analysis and design fundamentals To design and analyze permanent-magnet synchronous generators, we apply the electromagnetic theory [3,12,25–27]. The topologic synthesis of radial and axial topologies generators is accomplished by utilizing an electromagnetic system and geometry classifier [4]. High electromagnetic loads impose challenges in design of high performance and high-energy density generators. Hard magnets have wide BH curves (high coercivity) and possess high-energy storage capacity. We use neodymium iron boron (Nd2Fe14B) and samarium cobalt (Sm1Co5 and Sm2Co17) magnets. The energy density wm is defined by the area enclosed by the BH curve, and wm = ½B H, where B and H are the field density and intensity. The energy stored in a permanent magnet of volume V Rb is W ¼ V a HdB. Using the magnetization M and permeability l, one has W = lVM H. Permanent magnets operate on the demagnetization curve of the hysteresis loop, and the second quadrant of the BH curve is studied. The operating point varies as function of loads. Furthermore, l = l0lr = B/H. The variations of the relative permeability lr, as a function of the electromagnetic load, are lr(H) = dB/dH. The demagnetization and energy production curves are in mutual correspondence. The electromagnetic interaction of permanent magnets and windings results in the induced emf ¼ H H H @B E dl ¼ ðv BÞ dl ds thereby generating l l s @t motional inductionðgenerationÞ
transformer induction
the phase induced voltages. The magnetomotive force is H H H mmf ¼ l H dl ¼ s J ds þ s @D ds. The relationship between the @t
S.E. Lyshevski / Energy Conversion and Management 52 (2011) 46–52
prime mover (turbine), electromagnetic load TeL, friction Tf and stochastic loads TnL torques is Tt = TeL + Tf + TnL. The rated achievable generator power density is found to be 1 W/cm3 for highperformance 0.01–100 W synchronous generators. The power density is significantly affected by the design, topology, magnets, operating envelope (loads, velocity, temperature, etc.) and other factors. The magnetic flux through any surface is expressed using the R magnetic field density B as w ¼ s B ds. For the magnetically coupled abc stator windings, using the Kirchhoff voltage law, one finds the following differential equations which describe the circuitry-electromagnetic dynamics of the three-phase generators
dwas ¼ r s ias ; dt
dwbs ¼ r s ibs ; dt
dwcs ¼ r s ics ; dt
ð1Þ
where ias, ibs and ics are the phase currents; was, wbs and wcs are the abc flux linkages as given by 2 3 P1 2 3 2 32 3 2n1 a sin h was Lss Lms Lms ias n r n¼1 6 P1 7 6 7 6 76 7 2n1 ðhr 23 pÞ 7 4 wbs 5 ¼ 4 Lms Lss Lms 54 ibs 5 þ wm 6 4 n¼1 an sin 5; P 2n1 1 2 wcs Lms Lms Lss ics ðhr þ 3 pÞ n¼1 an sin Lss and Lms are the self- and mutual inductances; wm is the effective R amplitude of the flux linkages established by magnets, w ¼ s B ds, B = lH, l = l0lr(H); an are the variables- and technology-specific and operating envelope-dependent coefficients; rs is the equivalent stator resistance. The torsional-mechanical dynamics is described by the following differential equations
dxr P 2Bm T t T eL xr T nL ; ¼ 2J dt P
dhr ¼ xr ; dt
ð2Þ
where xr and hr are the electrical angular velocity and displacement; TeL is the electromagnetic load torque
" 1 X Pwm 2n2 T eL ¼ ð2n 1Þan cos hr sin hr ias 2 n¼1 1 X 2 2 2n2 ð2n 1Þan cos hr p sin hr p þibs 3 3 n¼1 # 1 X 2 2 2n2 ð2n 1Þan cos hr þ p sin hr þ p ; þics 3 3 n¼1
ð3Þ
Tt is the turbine torque; Bm is the friction coefficient; J is the moment of inertia; P is the number of poles. Using differential equations for magnetically coupled circuitry (1) and torsional-mechanical dynamics (2) one obtains the nonlinear mathematical model of radial- and axial-topology permanent-magnet synchronous generators. This model is used in the generator and system analysis. The results are applied to perform various designs tasks at the device and system levels. We reported the first principles for permanent-magnet synchronous generators which are utilized in design and optimization. High-efficiency, high-power and high-energy densities synchronous generators were designed, characterized and evaluated. Example 3.1. One performs the design attempting to ensure the electromagnetic interactions with a1 = 1 and all other an = 0. This can be achieved when generator operates from 0% to 50% load (near-linear BH curve). For a = 1, Eq. (3) gives 1 T eL ¼ Pw2m ias cos hr þ ibs cos hr 23 p þ ics cos hr þ 23 p .
49
The resulting torsional-mechanical Eq. (2) are given as
dxr P2 wm 2 2 ¼ ½ias cos hr þ ibs cosðhr pÞ þ ics cosðhr þ pÞ 3 3 dt 4J Bm P P dhr xr T nL þ T t ; ¼ xr : 2J 2J J dt 3.2. Radial-topology permanent-magnet synchronous generators The design, analysis, evaluation and characterization tasks are performed for distinct radial-topology generators. For example, a 50 W (50 mm diameter) and 5 W (20 mm diameter) three-phase radial-topology generators, reported in Fig. 1a, have the following parameters: (1) P = 2, rss = 0.6 X, Lss = 0.002 H, Lls = 0.0002 H and wm = 0.05 V s/rad (N m/A); (2) P = 2, rss = 25 X, Lss = 0.002 H, Lls = 0.0002 H and wm = 0.045 V s/rad (N m/A). Using (1)–(3), in the full operating envelope we found that a1–0, a2–0 and 8an = 0, n > 2. The resulting circuitry-electromagnetic and torsionalmechanical equations are
dias 1 rs 2Lss Lm ias r s Lm ibs r s Lm ics ¼ 2 dt 2Lss Lss Lm L2m i h 2 þwm 2Lss Lm xr a1 cos hr þ 3a2 coshr sin hr 2 2 2 2 þwm Lm xr a1 cosðhr pÞ þ 3a2 cos hr p sin hr p 3 3 3 2 2 2 2 þwm Lm xr a1 cos hr þ p þ 3a2 cos hr þ p sin hr þ p ; 3 3 3
dibs 1 r s Lm ias rs 2Lss Lm ibs r s Lm ics ¼ 2 2 dt 2Lss Lss Lm Lm 2 þwm Lm xr a1 cos ðhr Þ þ 3a2 cos hr sin hr 2 þwm 2Lss Lm xr a1 cos hr p 3 2 2 2 þ3a2 cos hr p sin hr p 3 3 2 þ wm Lm xr a1 cos hr þ p 3 2 2 2 þ3a2 cos hr þ p sin hr þ p ; 3 3
dics 1 rs Lm ias r s Lm ibs rs ð2Lss Lm Þics ¼ 2 dt 2Lss Lss Lm L2m h i 2 þ wm Lm xr a1 cos hr þ 3a2 cos hr sin hr 2 þ wm Lm xr a1 cos hr p 3 2 2 2 þ 3a2 cos hr p sin hr p 3 3 2 þ wm 2Lss Lm xr a1 cos hr þ p 3 2 2 2 ; þ 3a2 cos hr þ p sin hr þ p 3 3 dxr P P2 wm Bm P xr T nL ; ¼ Tt T eL 2J 2J dt 4J J dhr ¼ xr ; dt
ð4Þ
h i 2 T eL ¼ ias a1 cos hr þ 3a2 cos hr sin hr þ ibs a1 cos hr 23 p þ 2 3a2 cos hr 23 p sin hr 23 p þ ics a1 cos hr þ 23 p þ 3a2 cos hr þ 23 p where
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Fig. 2. Induced phase voltage uas by a radial-topology generator for no electromagnetic load, rated load, and peak electromagnetic load. Variations of the angular velocities and magnitudes of uas are: (a) xr = 568, 555 and 531 rad/s, uas = 30 V, 28 V and 22.5 V; and, (b) xr = 278, 274 and 256 rad/s, uas = 14 V, 13.8 V and 10 V.
2 sin hr þ 23 p ; Lm is the magnetizing inductance, Lm ¼ 23 ðLss Lls Þ; Lls is the leakage inductance. The experimental results at no load, rated and peak loads are reported in Fig. 2 where the induced as phase voltage uas is documented. The angular velocity decreases as the load TeL increases because Tt is constrained. Coefficients an significantly vary in the operating envelope mainly due to changes of lr(H). The energy conversion, emf induction and other baseline phenomena are analyzed and examined. The reported analysis, design and optimization are verified.
3.3. Axial-topology permanent-magnet synchronous generators We design and examine two- and three-phase axial-topology synchronous generators with the segmented array of permanent magnets as documented in Figs. 1a and 3a. As was emphasized, the planar segmented permanent magnets array is placed on the turbine rotor, while the planar windings are on the stationary member. These high-power density axial-topology generators result in number of advantages as compared to radial-topology generators. The advantages of the axial-topology permanent-magnet generators are:
(a) Rotor
Stator Permanent Magnets
ωr
Permanent Magnets
(b)
Fig. 3. (a) Axial-topology permanent-magnet synchronous generator and (b) induced phase voltage uas in a generator for no electromagnetic load (TeL = 0), 0.5TeLrated, and peak electromagnetic load. At no load, generator is driven at two angular velocities: (i) xr = 150 rad/s and xr = 450 rad/s. For different TeL, (i) uas = 13.3 V, 10.5 V and 4.2 V (low speed operation), and, (ii) uas = 31.4 V, 26.3 V and 10.3 V (rated speed operation).
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(i) Affordability and simplicity to fabricate and assemble machines because permanent magnets and windings are planar. The segmented magnets and planar windings significantly simplify fabrication and enable performance. (ii) There are relaxed shape-geometry and sizing requirements imposed on the magnets and windings. However, device performance is significantly affected by the topology, geometry, spacing, etc. (iii) There is no rotor back ferromagnetic material required (silicon, polymers or plastics can be used). (iv) The airgap and magnet-winding separation can be adjusted. (v) It is easy to fabricate planar windings on the planar (flat) stator. (vi) There are no cogging torque. Depending on the magnet geometry, magnetization and separations of magnets, for three-phase generators, one yields
Bas ¼ BM
1 X
2n1
an sin
n¼1
Bcs ¼ BM
1 X n¼1
2n1
an sin
hr ;
Bbs ¼ BM
2 hr þ p ; 3
1 X
2n1
an sin
n¼1
2 hr p ; 3
where BM is the magnitude of the effective electromagnetic field density which is a function of the cross-sectional area, number turns, length, winding geometry, etc. Using (1), for a 50 V axial-topology generator, illustrated in Fig. 1a, a1–0 and a2–0 and 8an = 0, n > 2. The circuitry-electromagnetic dynamics is described by the following differential equations
h io dias 1 n 2 r s ias wm xr a1 cos hr þ 3a2 cos hr sin hr ; ¼ Lss dt
dibs 1 2 rs ibs wm xr a1 cos hr p ¼ Lss 3 dt 2 2 2 ; þ3a2 cos hr p sin hr p 3 3
51
dics 1 2 r s ics wm xr a1 cos hr þ p ¼ Lss 3 dt 2 2 2 : þ3a2 cos hr þ p sin hr þ p 3 3 The generator parameters are experimentally found. We have Nm = 8, rs = 13.5 X, Lss = 0.035 H, wm = 0.03 V s/rad (N m/A), Bm = 0.0000005 N m s/rad and J = 0.00001 kg m2. For different angular velocities (150 rad/s and 450 rad/s at no load), the induced phase voltage uas is reported in Fig. 3b. As documented, the uas waveforms are functions of xr, TeL and Tt. All essential phenomena, including the hysteresis BH curve, electromagnetic loading, limited Tt, are coherently integrated into analysis, design and optimization tasks.
4. Power electronic module and experimental results A power electronic module is composed from the following major components: (1) controlled rectifier; (2) controlled soft-switching converter; (3) stabilizing circuit; (4) filters; (5) supercapacitor energy storage stage; (6) controller; (7) energy management system. The controlled rectifier and soft-switching converter topologies are utilized. By applying this sound solution, we guaranteed high efficiency, low-current switching, eliminate over-heating, minimize stresses and optimize switching profile of output-stage transistors. It was found that the converter efficiency for the peak, maximum and rated (75% of maximum) loads is 93.7%, 96.2% and 96.4%. The proportional-integral (PI) controller
ð5Þ u ¼ kp e þ
Z
kp e dt;
guarantees the maximum allowed error e(i) within 1%. Here, e(t) is the tracking error, e(t) = uref ut; uref is the reference (command) terminal DC voltage; ut is the terminal DC voltage.
Fig. 4. (a) Power electronic module; and, (b) experimental results: variations of the terminal DC voltage ut during the charging, discharging and loading regimes in the full operating envelope (rated, maximum and peak loads and varying angular velocity xrm). The applied torque Tt and mechanical power Ttxrm are limited (constrained).
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This PI controller with matching third-order notch filter (to filter 1 kHz to 1 MHz noise) were implemented using a single Analog Device quadrant operational amplifier. The stabilizing DC–DC voltage converter, integrated with filters and supercapacitors is synthesized and examined. The electronic module, documented in Fig. 4a integrates: (i) controlled threephase rectifier; (ii) soft-switching buck-boost converter with driving and controlling circuitry; (iii) supercapacitor–inductor storage stage. The output voltage at the load terminal with varying ZL(t) is stabilized as reported in Fig. 4b which document the experimental results for different loading and charging/discharging phases of operations. Comprehensive tests were conducted in the full operating envelope. For an axial-topology synchronous generator reported in Section 3.3, we specify the output terminal voltage to be stabilized at uref = const = 15 V. Different RLC loads, defined by ZL, are applied. At low angular velocity (xrm is 100 rad/s), the induced ac phase voltages are 5 V. Under the limited prime mover (turbine) torque Tt, the terminal voltage ut was ensured and stabilized at the timevarying rated ZLrated and ZLmax. Here, ZLrated(t) 2 [0 0.75]ZLmax. Thus, the RLC load, which typifies typical loads, is used. At maximum ZLmax and peak ZLpeak (RLoad = 1.2 X, results in a peak current, and a DC current at the terminal itpeak is 10 A), we have ut = 14.85 V and ut = 12.3 V due to the constraints on the mechanical (input) power Ttxrm. Here, xrm is the angular velocity of the turbine. The mechanical angular velocity is related to xr as xrm = 2xr/P. The input mechanical peak power Ttpeakxrmpeak is 200 W. Taking note of the efficiency of a generator (72% at the peak load and highly saturated BH curve), power electronics (91.4%) and filter (97.8%), one finds that the peak electric output power should be 128.7 W. As illustrated in Fig. 4b, the experimental results illustrate that the Pelectric peak = 123 W because the RLC load affect the power factor (pf – 1) resulting in additional losses. At the maximum load operating conditions ZLmax (RLoad max = 1.86 X), for the reference voltage uref = 15 V, the experimental results documented in Fig. 4b indicate that ut = 14.85 V and itmax = 8 A. Thus, Pelectric max = 119 W. The generator, power electronics and filter efficiencies were 75.8%, 94.1% and 98.1%, respectively. Different charging, discharging, loading and other conditions were tested. The efficiencies of the generator and power electronic module vary depending on the loading, BH saturation, duty ratio, current, load impedance, power factor, etc. The energy, stored by a supercapacitor depends on the allowed foot-print area and capacitor used. Our experimental findings and proof-of-concept prototypes provide evidence of soundness and exceptional capabilities of the concept proposed. 5. Conclusions In this paper, high-performance self-sustained power generation systems were synthesized, designed, analyzed, tested and evaluated. We accomplished designs of robust, high-power and high-energy densities systems which comprise of a turbine, radialor axial-topology permanent-magnet synchronous generator and electronic module. The results were evaluated and verified in the full operating envelopes for proof-of-concept subsystems and system prototypes. Basic fundamental, applied and experimental research was performed in multidisciplinary areas of energy systems, power, power electronics, electric machines and energy sources. The reported fundamental, applied and experimental results contribute to novel technological developments of energy harvesting and power systems. The examined scalable, high-effi-
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