First-step sizing of high internal temperature machines

03/02/2015
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First-step sizing of high internal temperature machines

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First-step sizing of high internal temperature machines Daniel Roger, Jean-Philippe Lecointe, Stéphane Duchesne, Gabriel Vélu Univ. Lille Nord de France, F-59000 Lille, France UArtois, LSEE, Technoparc Futura F-62400 Béthune, France Email: daniel.roger@univ-artois.fr Abstract The paper proposes an analytical method for defining the main critical sizes of a high internal temperature motor in order to take advantages of high performances of Electrical Insulation Systems (EIS). A simplified thermal model, based on constant conductances, is proposed. This thermal equivalent circuit coupled to the single-phase electrical one works only for linear materials but it provides a global point of view of the influence of resistance variations on the machine behaviour. This simplified approach is a short cut that may provide quickly the starting point for the classical detailed motor sizing based on Finite Element (FE) multi-physics approach coupled to optimization procedures. Introduction The increase of the power density of electrical machines is an important challenge for aircraft industry. However, unavoidable physical limits deduced from Maxwell’s equations must be considered because the energy conversion is performed in the air gap. For AC rotating machines, the power density is limited by three physical parameters: • the flux density in the air gap; • the speed of the rotor; • the current density in the cylindrical layer made by the active conductors in the stator slots. The first limit depends mainly on the saturation flux density of the magnetic materials and on the stator design. The second one depends on the supply frequency, on the quality of the bearing system and on the stator and rotor mechanical deformations. The third limit is linked to the overall thermal balance of the machine. Apart from using superconducting materials, the current density in the active conductors is limited by the operating temperature of the stator EIS and the efficacy of the cooling system. A simplified thermal equivalent circuit is proposed and applied to the smooth air gap Permanent Magnet Synchronous Machine (PMSM). The single-phase electrical equivalent circuit of the PMSM is coupled to the thermal model; this coupling brings the wide point of view very useful for the first step of the high temperature machines sizing able to provide the input data of the second step optimization procedure. Simplified thermal model Heat transfer in electrical machine is a complex problem that is generally solved by a multi physics approach based on FE methods. Many publications are available in the scientific literature. Several papers present thermal model based on Lumped parameters equivalent circuit [1] [2], they explain the problem of parameter determination, which depends on air circulation inside several parts of the machine. A paper specially dedicated to the convection phenomena in the air gap explains that, even for a smooth air gap, the turbulences improve the heat transfer over a predetermined speed [3]. Among this abundant literature, temperature measurements performed inside rotating machines can be found [4] [5]; these data are useful for getting an estimation of actual thermal resistances inside machines. These papers point out the complexity of thermal problems in electrical machines and the need of detailed analyses with appropriate FE models applied on a known geometry. Electrical machines that operate with high internal temperatures are generally used for applications requiring high power density and therefore at high speed; consequently these machines must have a small diameter that is compensated by its length in order to provide an air gap surface large enough for performing the electromechanical conversion. These machines are generally dust-proof, the cooling is made by an air flux in fins on the outer surface. The thermal balance can be determined considering that the heat generated in the rotor and the stator windings passes through the magnetic core and the casing before being transferred to the atmosphere by the ventilation system. Let us for example consider a permanent magnet synchronous with a standard distributed winding. The rotor is built with a magnetic core and 2p surface- mounted permanent magnets as presented in Fig. 1. The aluminum casing is molded around the magnetic core, the contact surface between the stator core and the casing is large with a high mechanical pressure. The thermal contact is very good, therefore the casing and the stator core are supposed to be at the same temperature TC. The simplified thermal model for the steady state is the thermal equivalent circuit in figure 2 where the points R, W, C and A correspond to r Rotor, Winding, Case and Ambient temperatures. The heat sources PR, PW and PC are respectively the losses in the rotor, the windings and the stator core. The thermal conductances characterize the main heat exchanges. A small part of the rotor losses flows directly outside the machine by the shaft; this transfer corresponds to the thermal conductance GRA. The main thermal flux toward the atmosphere, symbolized by GCA, corresponds to the cooling fan that blows cold air on the external surface of the motor casing and its fins. This model considers also the machine internal couplings; the main heat-flow passes through the air gap is modeled by GRC but air turbulences in the stator slots openings create also a thermal coupling between the rotor and the windings (GWC). The EIS limits the thermal coupling between the active wires in slots and the magnetic core, this phenomena is taken into account by the thermal conductance GWC. The proposed simplified thermal model considers only 2D phenomena; it does not take into account the longitudinal airflow in the air gap nor the complex interactions that exist in the end-winding areas. Fig. 1: Example of motor cross section. Fig. 2: Motor steady-state thermal equivalent circuit. The thermal equivalent circuit yields a set of equations that can be written in a matrix form: with The temperatures derives from losses by: The simplified thermal model is applied to the geometry of a standard 11 kW machine whose main sizes are detailed in table 1. The thermal conductance estimations, obtained from the scientific literature, are given in table 2. Table 1: Example of motor sizes. Table 2: Thermal conductances. Application to the PMSM The simplest analytical model of the n-phase PMSM fed by a n-phase balanced voltage source can be express as the equivalent circuit of figure 3. This model works for linear operations in steady-state and only for smooth air gap machines. The magnitude of the rotating flux density results from two contributions: the first one is due to the magnet rotation and the second one to the n-phase stator currents in windings with a sine distribution. This superposition is modeled by the series connection of the voltage source E and the effect of the working current IW in the synchronous inductance. The stator core losses depend on the resulting flux density in the air gap: the corresponding resistance Rµ is connected in parallel with the previous series association. The stator windings are connected to the voltage source considering the stator resistance RS and the leakage inductance lS. For surface-mounted permanent magnet motors, the rotor losses are mainly due to eddy currents in the magnets induced by fast flux variations caused by stator slots. Several scientific papers deals with this subject [7], [8]; low losses are obtained using high resistivity magnets, it is also possible to split the magnets [9]. For constant speed operations, the permanent-magnet losses can be supposed constant. Fig. 3: Synchronous motor equivalent circuit. Equations (3-5) are derived from the equivalent circuit of figure 3. First of all, the expression of Vµ is derived from (3-5): then, the IW and IS are computed from (3) and (4). For a motor fed by a voltage source, the electromagnetic torque depends on the torque angle δ defined by the phase lag between the stator voltage phasor V and the magnetomotive force E ; the stability limit is |δ| = 90° [6]. When the machine works as a motor, δ is negative: in the complex plane, the phasor E follows the stator voltage phasor V. Results For this study, the computations are made for an 3- phase PMSM at 50Hz and for increasing absolute value of the torque angle as the main input variable, from |δ| = 0 to |δ| = 90°, with a small step of 1°. For each value, the calculus are performed in 7 steps : • The real axis of the rotating complex plane is aligned on the stator voltage phasor (V = V + j0). • The electromotive force phasor E is placed in the complex plane using the torque angle δ and the real constant kE that depends on the magnet thickness and its magnetic characteristics: E=kE V exp(jδ) • Electric variables Vµ , IW and IS are computed from (6), (3) and (4). • Copper and iron losses are derived from previous data PS = 3RS|IS| 2 , PC = 3|Vµ| 2 /Rµ and PR = C te . • The input stator electrical power PS, the output me- chanical power PM and the electromagnetic torque TE are determined from the power balance considering that V is real: P = 3V.Re(IS); Q = −3V.Im(IS); PM = P − PS − PC − PR; TE = p.PM /ω. • Temperatures derive from equation (2); • The resistance RS correction is made with copper temperature coefficient and the winding temperature TW ; this new value is uses for the next step. The computations are made for a single magnet sizing corresponding to kE = 1.2 that corresponds to the minimum average value of the reactive power for every torque angle and equivalent air gap thicknesses. The equivalent air gap thickness takes into account the real air gap one, the magnet thickness and its permeability. The curves are plotted for several equivalent air gap thicknesses from 4.5mm to 6.5mm for TA=40°C. The motor internal temperatures are plotted in figure 4. The horizontal dashed lines correspond to the EIS temperature limits. The first one is drawn at 155°C, it corresponds to a low-cost standard SIE; the second one, at 240°C, corresponds to a high performance Polyimide (PI) EIS available on the market; the third one is plotted at 300°C, it corresponds to a reasonable anticipation of SIE technologies. It can be seen that rotor and winding temperature curves are almost superimposed, which confirms that stator SIE temperature class is the main limit towards high temperature machines. The corresponding active and reactive powers are presented in figure 5. Fig. 4: Internal temperatures. Fig. 5: Active and reactive powers. The rated powers obtained with the three thermal limits are presented in table 3 are deduced from figures 4 and 5 for and equivalent air gap of 6.5mm. Table 3: Comparison of maximum characteristics. Stator resistances are plotted in figure 6 and copper losses in figure 7. Fig. 6: Stator resistance. Fig. 7: Copper losses for several air gap thicknesses. The strong increase of copper losses are explained by the increase to the stator resistance with temperature. The motor efficiency is plotted in figure 8. It can be seen that the equivalent air gap thickness is a major sizing parameter considering the efficiency of the high internal temperature motor; the significant efficiency decrease for high torque angles is linked to the strong increase of copper losses. Fig. 8: Efficiency for several air gap thicknesses. Conclusion The study shows that, for higher thermal class EIS, it is possible to increase strongly the mechanical power/mass ration of synchronous machines when the equivalent air gap thickness is adjusted to the high temperature design. The proposed thermo- electric analytical model does not consider non- linearities but its simplicity may provide a physical starting point for sophisticated optimization procedures based on multiphysical FE non-linear modules. The large increase of the copper losses is an important limitation on the way toward high temperature drives specially for distributed windings, which have long end-winding connections. This drawback can be limited by choosing concentrated windings with very short end-windings but they have higher cogging torques. With this structure, inorganic EIS that uses ceramics end fiberglass may be used with the rigid coils mounted on large stator slots [12]. References 1. P. Mellor, et al., “Lumped parameter thermal model for electrical machines of tefc design,” Electric Power Applications, IEE Proceedings B, vol. 138, no. 5, pp. 205–218. 2. B.-H. Lee, et al. “Temper- ature estimation of ipmsm using thermal equivalent circuit,” IEEE T. Mag., vol. 48, no. 11, pp. 2949–2952, Nov. 2012. 3. D. Howey, et al., “Air-gap convection in rotating electrical machines,” IEEE T. Ind. El., vol. 59, no. 3. 4. A. Bornschlegell, et al., “Thermal optimization of a high-power salient-pole electrical machine,” IEEE T. Ind. El.,, vol. 60, no. 5, pp. 1734-1746. 5. J. Le Besnerais, et al., “Multiphysics modeling: Electro-vibro-acoustics and heat transfer of pwm- fed induction ma- chines,” IEEE T. Ind. El., vol. 57, no. 4, pp. 1279–1287. 6. J. Lesenne, et al., Introduction à l’Electrotechnique approfondie, Tech. et Doc., Ed., 1981. 7. C. Deak, et al., “Calculation of eddy current losses in permanent magnets of synchronous machines,” SPEEDAM 2008, pp. 26–31. 8. F. Deng, “An improved iron loss estimation for permanent magnet brushless machines,” Energy Conversion, IEEE T. Energy Conv., vol. 14, no. 4, pp. 1391–1395. 9. W.-Y. Huang, et al., “Optimization of magnet segmentation for reduction of eddy-current losses in permanent magnet synchronous machine,” IEEE T. Energy Conv., vol. 25, no. 2, pp. 381– 387. 10. A. EL-Refaie, “Fractional-slot concentrated- windings synchronous permanent magnet machines: Opportunities and challenges,” IEEE T. Ind. El., vol. 57, no. 1, pp. 107–121. 11. B. Aslan, “Conception de machines polyphases aimants et bobinage concentré à pas fractionnaire avec large plage de vitesse,” Ph.D. dissertation, ParisTech, 2013. 12. V. Iosif, et al., “Experimental character- ization of the maximum turn- to-turn voltage for inorganic high temperature motor,” EIS 2014, Philadelphia.