1 Electric Rotating Stator Generator with Permanent Magnets and Fixed Rotor with Concentrated Windings: Analysis and Study on its Magnetic Circuit Gonçalo Miguéis, Student, DEEC/AC Energia and P.J. Costa Branco, LAETA/IDMEC Abstract In the past couple of years, the permanent magnet synchronous generator has been a widely used generator. In spite of its many advantages it also presents some disadvantages. This papers aims to identify them and propose a topology that nullifies this disadvantages. A single phase low voltage generator belonging to an isolated system and providing 20kW to a load modeling a residence is proposed. The presented generator is aimed to work through the kinetic energy extracted from a river current. This research will study and analyze the electromagnetic waveforms and the thermal distribution of the generator through a finite element model. The equations best suited to calculate the power losses in the low speed permanent magnet generator will be identified. Particular attention will be allocated to the identification of the main constraints in the generator sizing. Finally, the dielectric insulation lifetime will be estimated. configuration makes the magnetization in loco of the magnets difficult. The study of a new topology in which the magnets are located in the outer part of the machine, that part being the rotor, is proposed in this paper. With this approach the centrifugal force tends to compress the magnets instead of ungluing them, while making this component more easily accessible allowing for an easy maintenance. The proposed generator was designed to operate through the kinetic energy extracted from river currents. The name of the used system is RiverSails, [6], and was developed by the company Tidal Sails. The system consists in a series of extruded aluminum sails, attached to wire ropes strung across the tidal stream. It forms a geometric figure similar to that represented in Fig 1. The generator studied is aimed to be placed in the corners of that system. Index Terms PM synchronous generator, power losses, finite-element analysis (FEA), thermal analysis, electromagnetic analysis. T I. INTRODUCTION he permanent magnet synchronous generator was developed around 1950 [1], and since then, has been the main electrical machine topology in both low velocities applications, such as energy production through alternative sources [2,3], as well as high velocities applications, such as aeronautical industry and flywheels [4,5]. The permanent magnet generator has great benefits such as the absence of brushes, smaller volume and higher efficiency. In this type of generator, the permanent magnets are usually located in the inner part of the machine. However, this topology has some drawbacks, the main one being the occasional ungluing of the magnets due to centrifugal forces originated by the rotational motion of the generator. Another drawback is the fact that this Fig.1. RiverSails system Based on the river speed the generator was targeted to rotate at 100 rpm at nominal operation. II. MATERIALS THAT FORM THE GENERATOR In this section the materials that form the generator are presented. A. Permanent magnets Permanent magnets were chosen to be made of NdFeB. This choice was based on the fact that this type of magnets presents the higher value of residual magnetic flux density at satisfactory working temperatures [7]. The demagnetization curves of the selected magnets are represented in Fig. 2.
electrical machines. The methods used to calculate these losses are presented in this section. 2 A. Copper losses The copper losses in the generator windings, P cu, were calculated through equation (1). This equation is only valid for sinusoidal systems. As it is not the case, the total copper losses are the some of the equation (1) applied to all the harmonics of the generator current. The parameter r cu is the winding resistance and I In is the rms value of the generator current. 2 P cu = r cu I In (1) Fig.2. Demagnetization curves of the permanent magnets B. Soft magnetic material Due to its low cost, a non-oriented type of magnetic material was chosen. Its magnetization curve is illustrated in Fig. 3. This material is constituted by laminated and dielectrically insulated sheets. C. Shaft Fig.3. BH curve of the soft magnetic material Steel was selected to form the shaft of the generator. This material was chosen due to its strong mechanical characteristics associated with the fact that it is nonmagnetic and so does not influence the magnetic circuit of the generator. D. Conductors The conductors are made of copper. This is a common choice in the construction of electric machines due to relation between its price and electrical conductivity. III. POWER LOSSES CALCULATION In addition to reducing the efficiency, the power losses also have the adverse effect of the heating the B. Ferromagnetic materials losses Due to low velocity of the generator and consequent low electric frequency of its currents, it is sometimes difficult to estimate the Steinmetz coefficients from the manufacturer data. Therefore, the Steinmetz equation, regardless of being one of the most used in that matter, is not used in this paper to estimate losses in the ferromagnetic materials. The selected equation is (2). The symbol J F represents the rms value of the current density of the Foucault currents and σ is the electrical conductivity of the material where the losses are calculated. P F = J F 2 dv (2) V σ The ferromagnetic materials include the permanent magnets and the soft ferromagnetic material. Since the soft magnetic material is formed by a series of insulated electrical sheets, its electrical conductivity differs from that of a solid block. The equation (4) allows the estimation of the electrical conductivity of the laminated material, [8]. The symbol σ eq is the equivalent electrical conductivity of the laminated material, σ M is the electrical conductivity of the nonlaminated material, x lam is the number of laminations that the material has and can be calculated through the equation (3). In this equation D is the depth of the generator and ε lam is the thickness of one sheet. x lam = D (3) ε lam σ eq = σ M 2 (4) x lam IV. ELECTRICAL GENERATOR, POWER CONVERTER AND LOAD The electrical generator geometry as well as the power converter and load, which forms the isolated system in study, is presented in this section.
Load 3 A. PM synchronous generator A single phase low voltage generator is proposed in this paper. This implies that the maximum value of its rms voltage has to be lower than 1kV, [9]. In Fig. 4 the directions of magnetization of the permanent magnets as well as the winding direction of the conductors are presented. Due to difficulties in representation it is only pictured a winding per pole in Fig. 4. However, the generator has N s windings in series per slot. In order to reduce copper losses there are also N P of this circuits in parallel. Fig.4. Magnetization direction of the permanent magnets and winding direction of the electrical conductors B. Power converter The use of a power converter is necessary due to the voltage amplitude and electric frequency difference between the generator and load. An AC/DC/AC converter is proposed and can be seen in Fig. 6. This converter consists of a single-phase rectifier followed by a capacitor (DC link) and a three-phase inverter. Fig. 5 illustrates a 3D image of the permanent magnet generator. Its dimensions are synthetized in Tab. I. G MP Fig. 6. Isolated electrical system with focus on power converter C. Electric load Rectifier Inverter Load Fig. 5 Electrical generator proposed geometry TABLE I GEOMETRIC CHARACTERISTICS OF THE ELECTRICAL GENERATOR Parameter Value Stator diameter [mm] 486 Air gap [mm] 1 Permanent magnets 6 height [mm] Rotor diameter [mm] 540 Depth [mm] 480 Number of pole pairs 10 Fig. 7. Isolated electrical system with focus on electrical load The electrical load is intended to model an average residence. For this reason, it is constituted by a three phase resistance in series with an inductor with a power factor of 0.86. It is also intended that the generator provides 20 kw of active power to the load. The electrical load is represented Fig. 7.
4 V. REQUIREMENTS IN SIZING PM GENERATOR The sizing of the proposed generator implies the fulfilment of certain conditions, both electromagnetic and thermal. This section lists these constraints. A. Electromagnetic constraints The first of these constraints are expressed in equations (5) and (6) and require that the magnetic flux density in soft magnetic material in the rotor, B Idt, and the stator, B Idz, of the generator are less than the value that forms a knee in the magnetization curve of this material, B J. Its conditions assure the non-saturation of the material. B Idt B J (5) B Idz B J (6) The following of these constraints are depicted in equation (7) and determines the maximum number of windings in a slot, N Max, assuring that the area of the simulated number of windings is less than the area of the slot in which they will be allocated. The variable Are a Cond is the cross section of a conductor, 2.09 μ m 2, Are a Slot is the area of the slot, and K cu is the window the utilization factor and represents the fraction of the core window area that is filled by copper, its usual values vary between 0.3 and 0.7 [10]. The selected value was 0.5. N S N P K cu Are a Slot Area Cond = N Max (7) The following constraints, eq. (8) and eq. (9), assure that the generator doesn t exceed a maximum voltage limit, eq. (8), and that the active power delivered to the load, P C, is the desired, eq. (9). V Ge rmax is the maximum value of the voltage at the generator terminals. This voltage value was imposed in order to avoid the use of dv/dt filters, [11]. V Ge rmax < 1 kv (8) P C = 20 kw (9) The last constraint is related to the ability of the permanent magnets to keep its magnetization competence. For this it is required that the flux density in the magnet, B Mag, is more than that forming the knee in Fig. 2, [12], in this case 0. 35 T. B Mag > 0.35 T (10) If the constraints (7) to (10) are not met, the parameter N S which represents the number of windings in series per slot, should be decreased. If the constraints (5) and (6) are not met the geometry of the generator should be rearranged. B. Thermal requirements Once again the first thermal requirement is related to the competence of the permanent magnets to keep its magnetization ability. For this it is required that the temperature in the magnets, T Mag, is less than his maximum operation temperature value, [12]. For the chosen permanent magnets this temperature is 150, but in order to assure a safety margin it was decided that the temperature in the magnets must be less than 135. T Mag < 135 (11) Another temperature limit that has to be respected concerns the conductor s insulation, T Cond. For the present machine, an insulator with a maximum operating temperature of 180 was chosen. T Cond < 180 (12) If the constraints (11) to (12) are not met, the parameter N P which represents the number of circuits in parallel per slot, should be increased. VI. ELECTROMAGNETIC WAVEFORMS IN NOMINAL OPERATION MODE The generator topology presented in chapter IV was simulated in an electromagnetic finite element model from a 2D geometry. The variables N S, N P and D were changed in order to fulfil all the constraints mentioned in the previous chapter. A. Electromagnetic waveforms in nominal operation mode Fig. 8 shows the magnetic flux density distribution. It can be seen in this figure that the constraints (5) and (6) are met. Fig. 8. magnetic flux density distribution B [T] Fig. 9 illustrates the isolated system in study. In this figure, the voltage and currents presented in the course of this paper are schematized. Fig. 10 shows the voltage at the generator terminals and Fig. 11 shows its harmonics. In Fig. 11 can be seen that the generator voltage has a 3rd harmonic of high amplitude, however it is not a requirement that the generator waveform be close to sinusoidal. Only the load voltage and current need to meet this criterion. We can see in Fig. 10 that the constraint (8) is met.
Load 5 I LoadA I In I LoadB V In I LoadC Fig. 13. Harmonic content of current in generator windings V Loa da V Loa db V Loa dc Fig. 9. Electrical system in study Fig. 14. Load voltage Fig. 10. Voltage at generator terminals Fig. 15. Load current Fig. 11. Harmonic content of voltage at generator terminals Fig. 12 shows the current in the generator conductors and Fig. 13 shows its harmonics. These results show once again that the generator current has some harmonics of considerable amplitude. Fig. 16 shows the load voltage waveform harmonics. It can be observed that this waveform it is not purely sinusoidal due to the existence of a harmonic of 7th order. However, the amplitude of this harmonic is less than 2% than the amplitude of the fundamental. Therefore, it can be considered negligible. Fig. 16. Harmonic content of load voltage Fig. 12. Current in the generator windings The Fig. 14 and Fig. 15 show us the load voltage and current respectively. Based on this results It can be concluded that these waveforms constitute a balanced alternate sinusoidal system. Fig. 17. Harmonic content of load current
6 On the other hand, we can see in Fig. 17 that the load current waveform is purely sinusoidal. Fig. 18 shows the magnetic flux density in the permanent magnets during an electrical cycle. This waveform is not purely sinusoidal due to effects of the magnetic flux density produced by the current that circulates in the generators conductors, according to Lenz law. Analyzing Fig. 18 it can be concluded that constraint (10) is also met. Based on these power losses values, the generator temperature distribution illustrated in Fig. 19 was obtained. T [ ] Fig. 18. Magnetic flux density in the permanent magnets VII. THERMAL FINITE ELEMENT ANALYSIS With the aim of checking whether the generator materials have a temperature value above its maximum operating temperature, the thermal behavior of the generator was simulated with the aid of a finite element program. A. 2D finite element thermal model The temperatures in the materials of the electrical generator are dependent on the surrounding external temperature and on the heat dissipation created by the power losses. The permanent magnet generator operates at low electric frequency, f, of 50 Hz according 3 to equation (13) where n is the velocity, 100 rpm and p is the number of pole pairs, 10. Since the electric frequency has a low value and since the power losses in the soft magnetic material are proportional to its frequency, we conclude that these losses can be considered negligible. n p f = (13) 60 On the other hand, the permanent magnet, P MP, and copper losses, P Cu, have a high impact on the generator temperature and are presented in Tab. II. The copper losses are the most significant ones, accounting for approximately 80% of the generator losses TABLE II LOSSES IN THE PERMANENT MAGNET GENERATOR Parameter Value P Cu [W] 497 P MP [W] 132 Fig. 19. Thermal distribution of generator simulated in 2D finite element model Fig. 19 shows that the constraints (11) and (12) are met since the temperature on the magnets is 134 and the temperature on the copper conductors is 155. Since Fig. 19 was obtained through a 2D thermal finite element model the heat distribution was only considered radially due to software limitations. B. 3D finite element thermal model In spite of Fig. 19 presenting the worst possible scenario of the machines operation conditions, this is not the thermal distribution that it is obtained in nominal operation conditions. In order to accurately obtain this distribution, the same geometry with the same power losses values was simulated, on a 3D thermal finite element model. The thermal distribution obtained by this model is illustrated in Fig. 20. Fig. 20. Thermal distribution of generator simulated in 3D finite element model T [ ] It can be seen in Fig. 19 that the heat distribution now occurs radially and through the generator shaft. In this model the temperature on the magnets is 8
7 less and the temperature on the copper conductors is 12 less than the temperature present in Fig. 19. VIII. UNBALANCED OPERATION LOAD The performance of the generator in the event of loss of one phase of the three-phase load will be analyzed in this section. In this event, the load voltage and the load current have the waveforms represented in Fig. 21 and Fig. 22 respectively. It can be verified that the phase differences between currents or voltages becomes 90º instead of the 120º shown in Fig. 14 and Fig. 15. Fig. 21. Load voltage with loss of one of the load phases Fig. 22. Load current with loss of one of the load phases It can be concluded that the load current waveform is almost the same as the one in balanced load operation. On the other hand, the voltage waveform has a slight distortion, in addition to having a rms value of 221 V which corresponds to a reduction of 4% comparing with the balanced load operation. Regarding the generator s voltage waveform, it can be concluded that this waveform, Fig. 23, is similar to that verified in balanced load operation. Fig. 23. Generator s voltage with loss of one of the load phases On the other hand, due to the loss of one of the load phases the equivalent load impedance has a lower value than that in the balanced load operation, leading to a 40% lower rms generator s current, Fig. 24. Fig. 24. Generator s current with loss of one of the load phases Due to this low rms generator s current, the generator s copper losses drop 64%. The permanent magnet losses also suffer a reduction of 38% comparing to the balanced load operation. Since the generator s power losses in unbalanced load operation has lower values that the ones in balanced load operation, it can be implied that the generator material s temperatures will be also lower in these operation conditions. Therefore, it can be concluded that the generator supports the loss of one of the load phase without damaging its lifetime expectancy. IX. DIELECTRIC INSULATION LIFETIME ESTIMATION The electrical insulation material used to isolate between wires has a certain lifetime duration. This lifetime can be defined as the period of time since the completion of its fabrication until the point where its required performance can no longer be achieved [13]. To determine the insulation lifetime, L is equation (14) [14], was used. In this equation T is is the temperature in the dielectric insulation, k is is the Stefan-Boltzmann constant, θ is is the activation energy and B is is a constant associated with the material. L is = B is ek is T is (14) The material chosen to perform dielectric insulation in the copper conductors was polyester epoxy. This material has a maximum operation temperature of 180 and can withstand the 155 verified in the worst case scenario. The values of the parameters present in Eq.(14) are in Tab. III, [13,15], and the insulation lifetime in function of the temperature is illustrated in Fig.25. θ is TABLE III VALUES OF THE PARAMETERS IN EQ. (14) Parameter Value B is [h] 8.97 θ is [ev] 1.38 k is [ μ ev/k] 86.17 If the permanent magnet generator is always operating at nominal condition, the insulation lifetime is 144 340 h (approximately 16 years).
8 REFERENCES Fig. 25. Insulation lifetime of dielectric insulator X. CONCLUSIONS During this paper, a permanent magnet topology that prevents the ungluing of the permanent magnets was studied. For this, a topology where the stator is located in the inner part of the machine and the rotor is located in his outer part was proposed. The permanent magnet generator was inserted in an isolated system composed by the generator, a power converter and an electrical load modeling a residential load. The generator was dimensioned, to have 10 pole pairs and deliver 20 kw of active power to the load. In this paper it was concluded that the losses in the soft magnetic material are negligible at low frequency, and that the Steinmetz equation is not a good approach to calculate power losses due to lack of data from the material manufactures regarding losses at low electric frequencies. An alternative approach to calculate these same power losses is presented, as well as an alternative approach to calculate electrical conductivity of the soft magnetic material due to its constitution of laminated sheets. In section V the electromagnetic and thermal constraints related to the sizing of the generator were presented. It was concluded in this paper, that although the voltage and current waveforms at the generator terminals have some harmonic content, with the application of the power converter and its filters, the voltage and current waveforms delivered to the load have almost no harmonic content. Regarding the thermal analysis, it was concluded that the thermal finite element 2D model is not as accurate as the thermal finite element 3D model since the first only considers heat dissipation radially. In the following section it was concluded that the generator supports the loss of one of the load phases without damaging its lifetime expectancy. Finally, in section VIII, the lifetime of the insulating material between the wires of the winding was estimated. This lifetime was estimated assuming the generator operation at nominal conditions. It was concluded that the insulation lifetime is approximately 16 years. [1] B. Marques, Virtual Prototyping of a Brushless Permanent Magnet AC Motor - Electromagnetic and Thermal Design using CAD, M.S. thesis, Dept. Elect. Eng. and Comput. Sci., IST, Lisbon, Portugal, 2012. [2] N. Madani, Design of a Permanent Magnet Synchronous Generator for a Vertical Axis Wind Turbine, M.S. thesis, Dept. Elect. Eng., KTH, Stockholm, Sweden, 2011 [3] T. Reigstad, Direct Driven Permanent Magnet Synchronous Generators with Diode Rectifiers for Use in Offshore Wind Turbines, M.S. thesis, Dept. Elect. Power. Eng., NTNU, Trondheim, Norway, 2007. [4] J. Cardoso, Análise de soluções para geradores eléctricos integrados em turbinas de aeronaves, M.S. thesis, Dept. Elect. Eng. and Comput. Sci., IST, Lisbon, Portugal, 2014. [5] M. Marques, Design and Control of an Electrical Machine for Flywheel EnergyStorage System, M.S. thesis, Dept. Elect. Eng. and Comput. Sci., IST, Lisbon, Portugal, 2008. [6] Tidal Sails. (2014, Oct. 2). Tidal Sails [online]. Available: http://tidalsails.com/about-us [May 6, 2016]. [7] Permanent Magnet Selection and Design Handbook, 1st ed., Magcraft Co, Richmond, Virgínia, USA, 2007. [8] J. Kim, A equivalent finite element of lamination for design of electromagnetic engine valve actuator, J. of Magnetics, vol. 4, no. 11, pp. 151-155, Aug., 2006. [9] J. Pyrhonen, T. Jokinen and V. Hrabovcová, Design of Rotating Electrical Machines, 2nd ed. New Delhi, India, Wiley, 2014. [10] M. Kazimierczuk and H. Sekiya, Design of AC Resonant Inductors Using Area Product Method, ECCE Energy Conversion Congress and Exposition, San Jose, CA, USA, 2009 [11] Motor Book, Grundfos Co, Bjerringbro, Denmark, 2004, pp. 174. [12] Magnet Guide & Tutorial, Alliance LLC Co, Valparaiso, Chile, 2013. [13] E. Brancato, Estimation of Lifetime Expectancies of Motors, IEEE Electr. Insul. Mag., vol. 8, no. 3, pp. 5-13, August, 2002 [14] T. Dakin, Electrical Insulation Deterioration Treated as a Chemical Rate Phenomenon, IEEE Trans. Commun., vol. 67, no. 1, pp. 113 115, June, 2009 [15] C. Han, Lifetime Evaluation of Class E Electrical Insulation for Small Induction Motors, IEEE Electr. Insul. Mag., vol. 27, no. 3, pp. 14, June, 2011.