1 Study and Characterization of the Limiting Thermal Phenomena in Low-Speed Permanent Magnet Synchronous Generators for Wind Energy Mariana Cavique, Student, DEEC/AC Energia, João F.P. Fernandes, LAETA/IDMEC, and P.J. Costa Branco, LAETA/IDMEC Abstract The heating caused by losses in low-speed power PM generators can be harmful to the sensitive parts of electrical equipment, such as electrical insulation and permanent magnets. The prediction of the temperature of low-speed generators is important in order to estimate its lifetime. Due to the increasing requirements such as energy efficiency, cost reduction, or exploitation of new topologies and materials, a thermal model becomes necessary for improvements on generator design to reduce temperatures. This paper gives an approach of an analytical thermal model based on lumped-parameters developed for the prediction of the temperature of a low-speed 50 kw generator with radial topology. Particular attention is given to the calculation of iron losses, by Finite Element Analysis (FEA), and copper losses. In addition, the results obtained by lumped-parameter thermal analysis are compared with Finite Element Thermal Analysis. Index Terms Synchronous generator, thermal model, power losses, finite-element analysis (FEA), lumpedparameter thermal analysis the machine design, it is possible to achieve a more homogeneous distribution of temperature and avoid hot spots on the machine. The information from a thermal model can then be useful to improve the overall design of the machine in terms of efficiency and cooling requirements. It is therefore justifiable the need to obtain a thermal model that is not only appropriate to the materials and machine geometry, but also to their operating conditions in order to predict its thermal behavior and thus its limitations. In section II is presented the analytical thermal lumped-circuit model. In section III is presented the geometry of the studied machine. In section IV are estimated the losses of the machine, where FEA is used as a tool for electromagnetic analysis to estimate the iron losses. In section V the analytical thermal model is compared with a finite-element analysis. Finally, in section VI, are drawn some conclusions. G I. INTRODUCTION ENERATORS for wind turbine applications such as any electrical machine present power losses with different origins. The interest of knowing the temperature distribution in this type of generator is directly related to the reduction of the lifetime of the electrical equipment, since power losses can create particularly harmful heating conditions to sensitive parts of the machine, mostly in electrical insulation and in permanent magnets. This topic started to receive more attention due to market globalization and the requirement for smaller, cheaper, and more efficient low-speed power generators [1]. If the thermal constraints are taken into account at an early stage of the optimization of II. THERMAL MODEL BASED ON LUMPED PARAMETERS Thermal models based on lumped-parameters are described by an equivalent thermal circuit that consists of thermal resistances (represents the process of conduction or convection heat transfer), thermal capacitances (used to take into account the change in internal energy of the material with time), besides current sources (represents the different thermal power sources or heat sources). In steadystate analysis the capacitances can be neglected. The nodes of the circuit are separated by thermal resistances that represent heat transfer between components. Table I resumes the comparison of the thermal and electrical properties for this model.
2 TABLE I ANALOGY BETWEEN HEAT-TRANSFER CIRCUIT AND ELECTRICAL CIRCUIT Thermal Property Unit Electrical Property Unit Thermal resistance Thermal capacity ºC/W Electrical resistance Electrical capacity W sec/ºc Temperature ºC Electric voltage V Heat Flow W Electric current A V/A A sec/v The heat sources considered at the thermal circuit are due to the copper and iron losses. The basic assumption of the model is that the heat flows mainly at the radial direction. In this case, the geometric structure of the generator becomes a simplified equivalent structure, as shown in Fig. 1. The electrical machine is then modeled by concentric cylinders representing their different materials, with each one having a volume equivalent to the real volume of corresponding material. Fig. 1 shows a simplified model of the generator modeled by cylindrical layers. This gives a circuit with 8 nodes associated with temperatures at the interfaces of the layers considered in Fig. 1. The temperature at each node will therefore be determined from the ambient temperature for a given loss distribution. Fig. 2. Lumped parameter circuit for the generator model considered in Figure 1. In the circuit of Fig. 2, the node is located on the inner surface of permanent magnet. The temperature then decreases as a function of radius and tends naturally to the outside temperature. A. Conduction Heat Transfer The mathematical model for heat transfer by conduction is the heat equation. For a cylindrical geometry and assuming that the heat flows only in a radial direction, so that the only space coordinate needed to specify the system is r, the differential equation that governs the heat flow is equation (1).[2] (1) Fig. 1. Section of the generator modeled by cylindrical layers. Each layer can be characterized by having a thermal resistance that is to be associated with the heat flux originating outside of the respective layer. On the other hand, when the production of heat flux occurs in the layer itself (for example: iron losses, and copper losses )) must also be considered a second thermal resistance to heat flow now itself,. A simplified thermal circuit of the generator that models the main heat transfer paths is given in Fig. 2. where (in Joule per kilogram degree Celsius) is the specific heat, (in kilogram per cubic meter) is the density of the material, (in watts per cubic meter) the internal thermal power generation (iron and copper losses), k (in watt per meter degree Celsius) is the thermal conductivity of the material and T (in degree Celsius) is the temperature. Consider a cylindrical layer of inside radius, outside radius, and length L. In steady state and without internal heat generation the solution for the equation (1) (with the time dependent terms neglected as well as the term) is given by (2), taking into account the boundary conditions: at, and at. (2)
3 Conduction thermal resistance in a cylindrical layer without internal heat generation, can be calculated using equation (3). For a cylindrical layer with uniformly distributed heat sources, the term can t be neglected. The steady state solution of the equation (1) is given by (4) taking into account the boundary conditions at and at. The total power losses generated at the cylindrical layer is given by (5). Conduction thermal resistance in a cylindrical layer with internal heat generation can be calculated using (6). B. Convection Heat Transfer Convection resistances are used for heat transfer across the air gap (internal convection) and from the outside of the machine to ambient (external convection). In this model we consider only external convection because, due to the low speed of the generator, we can consider conduction as the main heat transfer process at the air gap. Convection thermal resistance can be obtained by (7) where the heat transfer surface is considered the curve surface of a cylinder. In (7), parameter L (in meters) is the machine length, h (in watt per square meter degree Celsius) is the convection-heat-transfer coefficient and R (in meters) is the machine radius. Experiments show that h is dependent of numerous factors including the type of flow (natural, forced, laminar or turbulent), on which geometry the flow is given (flat, cylindrical or spherical), and also the (3) (4) (5) (6) (7) physical fluid properties (density mass, viscosity, speed, thermal conductivity, etc.). In practice, the convection heat transfer coefficient is most often based on empirical formulations. The natural convection heat transfer coefficient for a horizontal cylinder can be approximated by (8) according to [2] and [3]. where is the difference between the outer surface of the machine and ambient temperature, and are values dependent of the geometry and flow conditions. In order to get acceptable results from the accuracy point of view and because convection is a complex thermal phenomenon that cannot be solved by pure mathematical approaches, empirical data from the generator to be studied were used to calibrate the correlation. The correlation (8) can be written in a logarithm form: Through a linear regression we can obtain the and values. The empirical data from the generator are presented at the Table II. [4] The data shows the measured temperature rise at no load and at about 32kW. TABLE II MEASURED TEMPERATURE RISE AT NO LOAD AND AT ABOUT 32KW Temperature (ºC) At no load At about 32kW Stator House - 33.8ºC Inside air 10.6ºC 40ºC Coil centre 14ºC 69.2ºC Slot bottom 15ºC 51.9ºC Tooth tip 15.7ºC 57.6ºC The temperature rise at the surface of the machine (Stator House) at about 32kW is taken directly from the table,. While at no load, the temperature rise at the surface of the machine is estimated based on the measured temperature rise at Tooth tip (15.7ºC) minus the temperature rise that occurs between the tooth tip and the surface of the machine (this temperature rise is based on estimated power losses and conduction resistances obtained in section II), giving. The definition of the convection thermal resistance is used to find the correspondent h to each temperature rise: (8) (9)
4 (10) The estimated power losses for the generator at no load is 365W, while at about 32kW is 2217W. Using the expression (10) we obtain and Using these two points we obtain the values and. III. PM SYNCHRONOUS GENERATOR WITH RADIAL GEOMETRY In order to analyze the operating losses in a lowspeed generator (iron and copper losses) and the consequent development of the respective thermal model, it has been studied a 50kW PM synchronous generator, with application to wind turbine, described in [4] and whose photo is shown in Fig. 3. (a) (b) Fig. 4. Drawings of the generator studied. (a) Global view (b) Detailed view. Picture from [4]. Fig. 5. Magnetization curve for M250-50A. Fig. 3. Photo of the 50kW PM synchronous generator studied. Picture from [4]. Due to the area of application of the generator in its project (wind power), it has a nominal low speed (51.7 r.p.m), a nominal voltage of 173V, a nominal current of 99A and presents 116 poles. As shown in Fig. 4 the design is a radial flux machine with permanent magnets placed on the rotor and with one layer of 60 concentrated coils (each one have 19 turns and consists of 36 parallel round conductors of Ø1.2mm). It has a stator outer diameter of 1777 mm and length of 100mm. The permanent magnets used in this application are NdFeB magnets with rectangular geometry ( and ). At the core was used a M250-50A material, alloy steel with non-oriented silicon and lamination 0,5mm whose magnetization curve is at Fig. 5. This is a patented construction from SmartMotor AS [4]. The generator has 116 poles and 120 slots (or teeth) displaced around its diameter. With this relation poles/slots, the relative position between each tooth and one magnet varies along the perimeter of the machine (as shown in Fig. 6) IV. POWER LOSSES In this section, the different operating losses generated in various regions of the radial generator are evaluated and thus its thermal model. A. No load losses (Iron Losses) Stator Losses Iron losses consist of hysteresis and eddy current losses,. The specific loss (W/Kg) is approximately given by relation (11). (11) To obtain the constant values and it has been used data from the manufacturer of the lamination (M250-50A) about material specific losses at different flux densities (0.1T-1.8T) and frequencies. The values obtained were and. Fig. 6(a) shows B field distribution in a generator region where stator teeth are almost aligned with the magnets. On the contrary, Fig. 6(b) shows B distribution where stator teeth are located unaligned with the magnets. These results indicate that the maximum B values are reached at the teeth of iron stator core, reaching up to 1,75T at the end of the tooth, as shown in Fig. 6(b).
5 Fig. 7. Regions considered for magnetic flux density measurements. Rotor Losses (a) The rotor consists of an iron structure where permanent magnets are located. The material assumed to this structure is the same as the ferromagnetic core of the stator (M250-50A), and therefore the losses of this structure are obtained by the equation (11) with values of and obtained in the section above. As it was done in the study of the losses in the stator, the harmonic content of the radial and tangential components of B is estimated numerically with FEM calculations in two points marked in Fig. 8. It was found that, in these two points, the variation of B is very small, and so the associated losses (less than 1W) are considered not significant compared with stator losses. (b) Fig. 6. Magnetic flux density distribution by FEA simulation.(a) stator teeth almost aligned with the magnets. (b) stator teeth unaligned with the magnets. To calculate the iron losses in each tooth, this was divided in four regions, as shown Fig. 7. Those divisions are justified because is at the end of each tooth that are achieved higher B values, causing magnetic saturation of the material and thus different harmonic content at B in that region. The harmonic content of radial and tangential B components is estimated numerically with FEM calculations in each region. Integrating the loss density over the ferromagnetic material volume, total iron losses were evaluated. These were done for the rated speed (51.7 r.p.m) and frequency of 50Hz, obtaining 321W of stator losses, 0.64% of the rated power. Fig. 8. Points considered for magnetic flux density measurements. The power losses at the permanent magnets occur due to eddy currents and can be estimated using equation (12). The equation shows the dependence of the losses with respect to its dimensions (width, and volume ), electrical conductivity ) and the frequency and amplitude of the magnetic flux density.
Phase current(a) Copper Losses(W) 6 (12) Since the magnetic flux density is approximately uniform throughout the magnet, B was measured in the total area of the magnet shown in Fig.9. When the generator is at no load, B has a 100Hz harmonic with amplitude approximately 0,025T. This variation of the magnetic flux density originates according to (12) a power loss of 43W, 0.09% of the rated power. (13) The phase resistance was obtained with the experimental data of Fig. 10 and so the value of measured resistance includes the temperature and frequency influence. Fig. 11 presents the copper losses for each power level, where it can be concluded that at nominal condition (50kW) the copper losses achieve the value of 3955W, 8% of the rated power. 4000 3500 3000 2500 2000 1500 1000 500 Resistive C=440uF C=850uF C=960uF 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Output Power(W) x 10 4 Fig. 11. Copper losses as a function of output power. Fig. 9. Surface considered for magnetic flux density measurements. B. Copper Losses The generator was loaded with three-phase resistive and increasing capacitive symmetric loads at 51.7 r.p.m. to investigate the generator load capabilities. Fig. 10 presents, for each load, the phase currents reached and respective generator power level. The results show that an output nominal power near 50kW can only be reached with a capacitance around 960μF ( ) reaching a phase current of 99A. C. Iron Losses with loaded machine The losses with loaded machine are calculated with a current of 99A, current achieved to the nominal power level 50kW. The losses now in the stator reached 472W, +47% above than the no-load iron losses (321W). The magnet losses were also recomputed, taking into account the magnetic flux density originated by an electrical current of 99A. The losses rise to 76W, 0.15% of the rated power. These results add up to the copper losses (3955W) resulting in a total power losses at the nominal condition of 4504W. 100 80 60 40 20 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Output Power(W) x 10 4 Fig. 10. Phase current as a function of output power. Resistive C=440uF C=850uF C=960uF Knowing phase current values,, and the electric phase resistance,, copper losses can easily be obtained by: V. THERMAL FINITE ELEMENT ANALYSIS The main goal of using FEA in the thermal study is to have a more accurate calculation of conduction heat transfer in complex geometric shapes and to identify the hot spots of the material that it s not possible to recognize using a lumped-parameters thermal model approach using cylindrical layers. FEA only brings advantage to model conduction heat transfer because for convection boundaries, the same convection correlations used in the lumped-circuit analysis must be adopted [1]. Fig. 12 shows the temperature distribution at the nominal condition from rotor to stator structure, including air-gap and magnets, obtained using the implemented FEM thermal model. As seen in Fig. 12,
7 the estimated surface temperature is 89.3ºC, while the estimated temperature near the magnet is 115.2ºC. Fig. 12. Generator temperature distribution by FEA simulation. Using the lumped parameters analysis described in section II that gives an average temperature value for each generator part, the estimated surface temperature was 89.3 ºC, while the estimated temperature near the magnet was 112.4 ºC. These values are similar to the FEA analysis, differing at 2.4% inside the machine, as shown in Fig.13 permanent magnets. The magnet losses represent 0.2% of the rated power. Many of the complex thermal phenomena, especially thermal convection, that occur in electric machines cannot be solved by pure analytical approaches. For that reason in our case, empirical data from the generator were used to calibrate the analytical model in order to get acceptable results from the accuracy point of view. The thermal model developed based on lumped parameters presented high accuracy results relating to finite element analysis tools. The temperature inside the machine differs between the two models in only 2.4%. The results obtained by the two models show that the estimated temperature on electrical winding is below 100ºC. This temperature allows the use of an electric insulation of any temperature class. The expected temperature for the permanent magnets (N35) is 115 C. At this temperature the operating point of the magnet is in the linear region of the magnetization curve and so demagnetization problems are not expected. REFERENCES [1] A. Boglietti, A. Cavagnino, D. Staton, M. Shanel, M. Mueller, C. Mejuto Evolution and Modern Approaches for Thermal Analysis of Electrical Machines IEEE Transactions on Industry Electronics, vol. 56, NO. 3, 2009. [2] J. Holfman, Heat Transfer, McGraw-Hill, 10ª edição, 1997. [3] L. Theodore, Heat Transfer Applications for the Practicing Engineer, Wiley, 2011. [4] Ø. Krøvel, Design of Large Permanent Magnetized Synchronous Electric Machine, Norwegian University of Science and Technology Faculty of Information Technology, Mathematics and Electrical Engineering, 2011. [5] S. N. Vukosavic, Electrical Machines, New York: Springer, 2013. Fig. 13. Comparison between the two thermal models. VI. CONCLUSIONS The dominating losses are the copper losses that were obtained with experimental results. They were obtained for different loads, achieving at the rated load 8% of the output power. The iron losses were calculated using a finite element analysis tool (COMSOL Multiphysics 4.3). The majority of the iron stator losses, that represents 0.9% of the rated power, occur at the teeth of iron core, where the maximum magnetic flux density is located. The rotor losses at the iron structure were considered not significant compared with stator losses due to the stationary magnetic field imposed by the presence of