Key Factors for the Design of Synchronous Reluctance Machines with Concentrated Windings

Transcription

1 IEEE PEDS 27, Honolulu, USA 2 5 December 27 Key Factors for the Design of Synchronous Reluctance Machines with Concentrated Windings Tobias Lange, Claude P. Weiss, Rik W. De Doncker Institute for Power Electronics and Electrical Drives (ISEA), RWTH Aachen University, Germany. Abstract This paper presents the key factors to designing a synchronous reluctance machine with concentrated windings. For synchronous machines the stator and pole configuration is commonly chosen according to the highest winding factor and lowest air-gap leakage factor. However, this does not always lead to the best machine. Due to the discrete field distribution of concentrated tooth windings, the air-gap harmonic content increases. This results in a high leakage inductance and a high leakage factor and consequently in a low saliency ratio of the machine. In addition to the theory of winding- and air-gap leakage factors for synchronous machines this paper introduces an analytic torque factor which is valid for all stator and rotor configurations. The torque factor describes the rotor pole utilization depending on the winding configuration. The presented discussion is based on analytic equations and finite element simulations of two segmented synchronous reluctance machines. I. INTRODUCTION TO MODULAR DRIVES This work is based on a modular drive system built with a synchronous reluctance machine (SynRM). Many industrial applications require drive systems with medium speed electric machines coupled to a gear box with a certain transmission ratio to adapt the torque and speed to the demands of the overall system. In some cases it is desirable to use direct drive systems without a gear box. High torque motors fulfill these requirements if the transmission ratio can be compensated by a larger motor diameter. In this case a direct drive is very advantageous concerning the system complexity, maintenance and efficiency. A segmented direct drive is developed especially for high-torque applications, such as drum drives. A full rotor is mounted to the circumference of the drive, while the number of segmented stator modules is installed according to the required torque. In order to segment the stator modules as displayed in fig. and to reach a high motor utilization while retaining low material cost, the motor is built as a synchronous reluctance motor. The rotor material, thereby, is manufactured from low-cost Fig. : Modular segmented motor concept electrical steel and is able to sustain high temperatures and vibrations. For drum drives especially the short axial length and therefore also the short end windings of concentrated windings are of interest. The paper first presents the key aspects and factors for designing a synchronous reluctance motor with concentrated windings followed by two example machines to validate the presented theory. II. KEY FACTORS FOR A SYNRM DESIGN WITH CONCENTRATED WINDINGS Using concentrated windings in SynRMs presents a major challenge due to their low power factor as presented in previous literature. In [] concentrated windings for synchronous reluctance motors were proposed. The low power factor is undesirable regarding the amount of copper necessary in the motor and the power electronic costs. The interaction between the proper rotor and stator geometry and also the winding configuration is the key to a successful motor design. For concentrated windings, the number of slots n s per pole P per phase m, q is smaller than one. q = n s P m < () A. Winding factor The first key factor for the design of a SynRM with concentrated windings is the winding factor defined by /7/$3. 27 IEEE,3

2 Fig. 2: Winding layout of a 9 slot 6 pole concentrated winding the slot - pole configuration. Ideally, the winding factor of the machine should be high to enable a compact and efficient machine design. It can be calculated or taken from tables [2]. In permanent magnet machines a high winding factor is mandatory to achieve a compact and efficient machine design, which defines a certain configuration. In contrast, in SynRM design it is unfortunately not the only factor having a very strong influence on the machine output characteristic. Nevertheless calculation of the winding factor is mandatory and summarized in the following [3]. As mentioned in literature a multilayer winding has beneficial properties such as lower harmonic content, shorter end-windings and lower torque ripple [4]. In the considered application a high power factor, high efficiency and low torque ripple are most important. The multilayer winding factor is calculated by repeating the Cros method for each layer separately [5]. First, a vector S is determined by the number of coils per phase, its slot position and the winding orientation. The incoming coil side is marked with a negative sign and the outgoing coil side with a positive sign. The position is marked with the slot number of the certain coil. For example, the winding configuration of a 9 slot SynRM with 6 rotor poles is shown in fig. with its respective winding layout in fig. 2. To obtain the winding vector S, each slot number and each sign of the phase is noted as shown in (2). S = [, 3, 4, 6, 7, 9]. (2) With the help of the slot positions S, it is now possible to determine the phasor of the electromotive force (EMF). It is calculated by S and the working harmonic order of p = P /2. The working harmonic is the fundamental harmonic component of the machine. E i = sign( S i ) e (jπp S i/n s ) Thereafter, the fundamental winding factor can be calculated by accumulating the EMF sections, with n l as the number of layers. (3) 2n s/3 3 E i i= k w = (4) n l n s The winding factor in the example of fig. 2 results in a value of k w =.866. Within this study all possible permutations of the winding layout were calculated, including winding configurations with lower winding factors as well as varying the magneto-motive force (MMF). Thus, for the 9 slot 6 pole motor 9 winding factors were calculated. The results are significant for the following considerations. B. Air-gap leakage factor The power factor is very important for an overall good drive system efficiency i.e. combination of motor and inverter. However, the maximum power factor is proportional to the saliency ratio ζ of the direct- L d and quadrature axis inductance L q. ζ = L d L q = L md + L σ,d L mq + L σ,q (5) From the saliency ratio (5) the maximum power factor can be defined as cosϕ = ζ (6) ζ + The inductance L d and L q are increased by their respective leakage inductance L σ,x. The leakage inductance decreases the saliency ratio and increases the apparent power consumption of the machine. Therefore, the leakage inductance of the motor is considered in detail. Machines with concentrated windings have, due to higher harmonic content, a larger leakage inductance compared to machines with distributed windings even though concentrated windings have shorter endwindings. The leakage inductance can be divided according to (7) into an end-winding, slot, tooth and air-gap leakage inductance [6]: L σ,x = L end + L slot + L tooth + L δ (7) Most of the leakage inductance components are dependent on the slot geometry with exception of the airgap leakage inductance. The slot dimensions and shape is defined by the winding factor and manufacturing requirements. The air-gap leakage inductance depends on the harmonic magneto-motive field within the air gap. This inductance is the dominating contributor to the leakage inductance, especially in concentrated windings,3

3 MMF and Ap (a) Distributed winding 8s6p (b) Concentrated winding 9s6p Fig. 3: Magnetic vector potential in a solid rotor. Distortion with high harmonic MMF content as shown in [7]. Hence, L δ is considered in detail. L δ = L m σ δ (8) L m is the magnetizing inductance and σ δ the air-gap leakage factor. The air-gap leakage factor definition is based on [6]: ( ) p 2 kw, i σ δ = (9) i= i p i k w, p The air-gap leakage factor σ δ depends on the working harmonic p, the winding factor of the i-th harmonic k w,i and its ordinal. The fundamental harmonic adds no content to the leakage factor, therefore, only i p harmonics are summarized. Due to the strong negative influence on the performance of the machine, a low leakage factor is desired to reach a high power factor. In turn, the high power factor leads to lower power electronic costs and higher efficiency of the overall drive system. Distortion MMF and Ap (a) 8s/6p motor with distributed winding (b) 9s/6p motor with concentrated winding Fig. 4: Exemplary MMF and distortion waveforms C. Torque factor The third key aspect is the calculation of the available reluctance torque by analytic equations [8]. T = m 2p (L d L q ) i d i q () The inductances L d, L q are defined by the winding factor k w, number of phases m, permeability of the iron material µ r and geometric parameters of the motor [9]. The calculated output torque of equation () assumes an equally distributed magnetic field in the air gap. As already mentioned the main drawback of concentrated windings is the resulting high harmonic content in the air-gap flux. Unfortunately, the space harmonics cause an unequal spatial distribution and formation of rotor poles. At each rotor position the spatial utilization is unequal and results in a low output torque. In fig. 3 the magnetic vector potential distribution in a solid rotor for the example machine with 9 slots and 6 poles (9s/6p) and 8s/6p is shown. Thereby, the difference between a stator with concentrated and distributed winding is clearly visible. Fig. 3 shows that with concentrated windings just 3 poles are entirely utilized. The occurring vector potential of the remaining 3 poles is much lower which results in lower produced torque. When calculating the,32

4 output torque of a SynRM with concentrated windings without considering the spatial harmonic content, the analytical torque calculation is incorrect. The correlation between reduced output torque and reduced utilization of the magnetic poles in the rotor seems likely. This consideration leads to the definition of a torque factor F torque to describe this effect. The MMF is defined by the current sheet distribution A(θ el ) of the stator. The current sheet distribution is calculated from the tooth width, the spatial position of the slots and the 3 phase currents applied to each tooth coil. Furthermore, the amplitude as well as the phase of the working harmonic A p (θ el ), for example p=3 in the 9s/6p machine, is calculated by the spatial fast fourier transform (FFT) of the MMF. In order to determine distortion D mmf of the stator field, which cannot produce reluctance torque, the MMF and the fundamental harmonic is subtracted. θ el is the electrical angle in degrees. D mmf = A(θ el ) A p (θ el ) () In fig. 4 the fundamental harmonic (blue), also called working harmonic, the MMF (red) and the distortion D mmf (ocher) are depicted. The waveforms are shown for the 9s/6p machine with concentrated windings in fig. 4b. In comparison the considerably lower MMF distortion is shown for the 8s/6p machine with distributed windings in fig. 4a. With the help of the distortion which describes the amount of non torque producing area, the pole utilization can be determined as the following: F torque = θ s=36 θ s= ( ) A(θel ) A p (θ el ) 2 dθ el (2) A(θ el ) For segmented machines the integral is determined over the angle θ s of the stator section. For the 9s/6p motor one circumferential integral from to 36 is calculated. The torque factor of the 9s/6p motor is F torque =.687 and of the 8s/6p distributed winding is F torque =.92. Now the output torque of the motor can be correctly predicted by analytic equations. The theoretical output torque of equation () is reduced by the torque factor F torque. D. Summary of key factors With these three factors, the maximum torque density and power factor of a SynRM with concentrated windings can be defined. The formulas are valid for all synchronous machines with and without permanent magnets, as well as with distributed or concentrated windings. For PMSM with distributed windings the impact of the introduced torque factor is very low, but it is essential for designing a SynRM with concentrated windings. Understanding these effects is fundamental for choosing the best machine configuration. A high winding factor inconclusively leads to a good torque density. The saliency ratio and thus the leakage flux also affects the machine performance. Finally, the torque factor determines the magnetic utilization of the rotor and its output torque. Thus, a winding configuration with a lower winding factor, low leakage inductance and high torque factor can give good motor performance. All three factors resulting for a 2 layer winding and various configurations are summarized in table I. TABLE I: Key factors for various configurations poles slots 6 8 k w,p σ δ F torque.687 <.3 <.3 k w,p σ δ F torque.687 <.3 k w,p σ δ.46 F torque I σ δ.2 k w,p.7235 F torque.764 III. CASE STUDYS To validate the presented theory from section II, two motors are designed and compared. The motors are designed as torque motors with high torque density and thus a high number of poles are chosen. The motor is built as a segmented motor, whereby the stator consists of quarter sections similar to the one shown in fig.. The axial length and the air-gap length are constant for both designs. The first motor is the baseline with 36 slots 24 poles, i.e. a 9s/6p quarter motor with all four stator segments present. The second motor is built with 8 slots I The listed factors are obtained for an optimized 3 layer winding.,33

5 MMF and Ap (a) 2 layer winding (b) 3 layer winding Fig. 5: Magnetic vector potential of the 8s/p motor Distortion and poles. The 8s/p has been chosen because of the promising key factor values from table I. In an analytical pre-design the machines are sized to meet the requirements of maximum power factor, maximum output torque, cooling capability, low torque ripple and geometrical as well as electrical parameters. During the design phase the machines are adapted to also meet the demands given by manufacturing processes. Furthermore, the winding dimensioning, stator and rotor geometry are determined. Thereafter, the motors are optimized with a finite element analysis (FEA) in Jmagdesigner 6. To gain accurate results in preferably few simulations a design of experiment (DOE) analysis is performed. Thus, it is possible to tune several parameters simultaneously and gain knowledge of the parameter dependences and their resulting effects. With the help of Minitab 7 an analytic equation with all relevant parameter cross-coupling is calculated, which in turn is used for the design optimization process. To determine this analytic fit equation in Minitab the DOE parameter table is calculated in FEA and the results of the transient field analysis are fed back. A detailed description of the optimization process is presented in []. The design requirements for both machines are given in table II. A. 36 slot 24 pole SynRM As baseline motor a state-of-the-art 9s/6p configuration with a promising winding- and air-gap leakage factor is chosen (table I). This configuration is used as a 9 module resulting in a 36 slot and 24 pole machine when using four modules. The stator is equipped with a double layer concentrated winding to keep the harmonic content low. The resulting torque factor amounts to.687. MMF and Ap Distortion (a) 2 layer winding (b) 3 layer winding Fig. 6: MMF and distortion of the 8s/p motor with different winding layers B. 8 slot pole SynRM The 8 slot pole motor is chosen to achieve a high torque factor with a low leakage inductance. The winding factor is also acceptable for this winding configuration. Fig. 5a depicts the magnetic vector potential in a solid rotor. The possible rotor pole utilization is clearly visible, while the respective MMF and distortion is shown in fig. 6a. The basic two layer winding can be further improved by increasing the layer number from two to three. Then the winding system is split into two different,34

6 winding systems with different turns per tooth and shifted by several teeth. Thereafter all coils of one phase are connected in series to obtain a three layer winding. The higher rotor pole utilization and lower MMF distortion is depicted in fig. 5b and fig. 6b respectively. The resulting torque factor amounts to.764. C. Comparison of performance The obtained motor performance parameters are listed in table III. The resulting designs show that the 8s/p motor with a lower winding factor, lower leakage factor and higher torque factor than the 9s/6p motor leads to overall better results. The designed 8s/p motor has a higher torque density, lower losses and thus a higher efficiency compared to the more common 36s/24p configuration. Even with a lower winding factor, the copper loss are lower compared to the 36s/24p motor. The motor mass is measured without end caps of the motor because the motor is constructed for use in segments with partly equipped stator modules. Both machines were built and validated on a test bench. The measurement results will be published in future. IV. CONCLUSIONS The paper presents the three key factors, winding factor, air-gap leakage factor and torque factor which are necessary to select the best machine configuration with highest torque density and power factor. The presented theory is derived and exemplary shown with a 2 kw and 5. kw segmented synchronous motor, however, is not restricted to only synchronous reluctance machines with concentrated windings. As is shown the key aspects to choosing a certain slot and pole combination is not only defined by the winding factor, but also by the leakage flux and rotor pole utilization. The presented segmented motor reaches a good power factor, high efficiency and TABLE II: Design requirements 9s/6p and 8s/p Rotor diameter 5 mm Stack length 5 mm Air-gap length.4 mm Current density 7 A /mm 2 DC-link voltage 4 V Torque density >6 Nm /mm 2 Slot-fill factor.56 TABLE III: Design results Motor 36s/24p 8s/p Rotor diameter 5 mm 5 mm Stator diameter 25 mm 26 mm End winding 7 mm 6 mm Total mass 6.3 kg 23.9 kg Torque 28.8 Nm 4 Nm Iron loss 69.6 W 37.7 W Copper loss 528 W 336 W Power factor Efficiency 6 rpm 76. % 87.3 % Efficiency 2 rpm 83.3 % 9.3 % high torque density. The modular motor structure enables additional integration possibilities in many applications as a direct drive. Especially, industry applications such as rotating tables and drum drives are of interest to this technology. ACKNOWLEDGMENTS The research project Torque-Drive (3EFHNW35) which is part of the EXIST-program was funded by the Bundesministerium für Wirtschaft und Energie and the Europäischen Sozialfonds. REFERENCES [] C. M. Spargo, B. C. Mecrow, J. D. Widmer, and C. Morton, Application of fractional-slot concentrated windings to synchronous reluctance motors, IEEE Transactions on Industry Applications, vol. 5, no. 2, pp , March 25. [2] C. C. Almendros, Design and analysis of a fractional-slot concentrated-wound permanent-magnet-assisted synchronous reluctance machine, Ph.D. dissertation, KTH Royal Institute of Technology, 25. [3] D. Martínez, Design of a permanent-magnet synchronous machine with nonoverlapping concentrated windings - for the shell eco marathon urban prototype, Ph.D. dissertation, Royal Institute of Technology, KTH Electrical Engineering, Stockholm, 22. [4] N. Bianchi and M. D. Pre, Use of the star of slots in designing fractional-slot single-layer synchronous motors, IEE Proceedings - Electric Power Applications, vol. 53, no. 3, pp , May 26.,35

7 [5] J. Cros and P. Viarouge, Synthesis of high performance pm motors with concentrated windings, IEEE Transactions on Energy Conversion, vol. 7, no. 2, pp , Jun 22. [6] W. Nürnberg, Die Asynchronmaschine. Springer-Verlag, 952. [7] B. Lehner and D. Gerling, Design considerations for concentrated winding synchronous reluctance machines, in IEEE Transportation Electrification Conference and Expo, Asia- Pacific (ITEC Asia-Pacific), June 26, pp [8] R. De Doncker, D. W. Pulle, and A. Veltman, Advanced Electrical Drives - Analysis, Modeling, Control, st ed. Springer Science+Business Media B.V., 2. [9] I. Boldea, Reluctance Synchronous Machine and Drives. Oxford Science Publications, 996. [] T. Lange, C. P. Weiss, and R. W. De Doncker, Design of experiments based optimization of synchronous and switched reluctance machines, in IEEE Power Electronics and Drive Systems, 27.,36