Torque vibration model of axial-flux surface-mounted permanent magnet synchronous machine

In order that the radius and thus ununiform structure of the teeth and otherelectrical and magnetic parts of the machine may be taken into consideration the calculation of an axial flux permanent magnet machine is, conventionally, doneby means of 3D FEM-methods. This calculation procedure, however, requires a lotof time and computer recourses. This study proves that also analytical methods can be applied to perform the calculation successfully. The procedure of the analytical calculation can be summarized into following steps: first the magnet is divided into slices, which makes the calculation for each section individually, and then the parts are submitted to calculation of the final results. It is obvious that using this method can save a lot of designing and calculating time. Thecalculation program is designed to model the magnetic and electrical circuits of surface mounted axial flux permanent magnet synchronous machines in such a way, that it takes into account possible magnetic saturation of the iron parts. Theresult of the calculation is the torque of the motor including the vibrations. The motor geometry and the materials and either the torque or pole angle are defined and the motor can be fed with an arbitrary shape and amplitude of three-phase currents. There are no limits for the size and number of the pole pairs nor for many other factors. The calculation steps and the number of different sections of the magnet are selectable, but the calculation time is strongly depending on this. The results are compared to the measurements of real prototypes. The permanent magnet creates part of the flux in the magnetic circuit. The form and amplitude of the flux density in the air-gap depends on the geometry and material of the magnetic circuit, on the length of the air-gap and remanence flux density of the magnet. Slotting is taken into account by using the Carter factor in the slot opening area. The calculation is simple and fast if the shape of the magnetis a square and has no skew in relation to the stator slots. With a more complicated magnet shape the calculation has to be done in several sections. It is clear that according to the increasing number of sections also the result will become more accurate. In a radial flux motor all sections of the magnets create force with a same radius. In the case of an axial flux motor, each radial section creates force with a different radius and the torque is the sum of these. The magnetic circuit of the motor, consisting of the stator iron, rotor iron, air-gap, magnet and the slot, is modelled with a reluctance net, which considers the saturation of the iron. This means, that several iterations, in which the permeability is updated, has to be done in order to get final results. The motor torque is calculated using the instantaneous linkage flux and stator currents. Flux linkage is called the part of the flux that is created by the permanent magnets and the stator currents passing through the coils in stator teeth. The angle between this flux and the phase currents define the torque created by the magnetic circuit. Due to the winding structure of the stator and in order to limit the leakage flux the slot openings of the stator are normally not made of ferromagnetic material even though, in some cases, semimagnetic slot wedges are used. In the slot opening faces the flux enters the iron almost normally (tangentially with respect to the rotor flux) creating tangential forces in the rotor. This phenomenon iscalled cogging. The flux in the slot opening area on the different sides of theopening and in the different slot openings is not equal and so these forces do not compensate each other. In the calculation it is assumed that the flux entering the left side of the opening is the component left from the geometrical centre of the slot. This torque component together with the torque component calculated using the Lorenz force make the total torque of the motor. It is easy to assume that when all the magnet edges, where the derivative component of the magnet flux density is at its highest, enter the slot openings at the same time, this will have as a result a considerable cogging torque. To reduce the cogging torquethe magnet edges can be shaped so that they are not parallel to the stator slots, which is the common way to solve the problem. In doing so, the edge may be spread along the whole slot pitch and thus also the high derivative component willbe spread to occur equally along the rotation. Besides forming the magnets theymay also be placed somewhat asymmetric on the rotor surface. The asymmetric distribution can be made in many different ways. All the magnets may have a different deflection of the symmetrical centre point or they can be for example shiftedin pairs. There are some factors that limit the deflection. The first is that the magnets cannot overlap. The magnet shape and the relative width compared to the pole define the deflection in this case. The other factor is that a shifting of the poles limits the maximum torque of the motor. If the edges of adjacent magnets are very close to each other the leakage flux from one pole to the other increases reducing thus the air-gap magnetization. The asymmetric model needs some assumptions and simplifications in order to limit the size of the model and calculation time. The reluctance net is made for symmetric distribution. If the magnets are distributed asymmetrically the flux in the different pole pairs will not be exactly the same. Therefore, the assumption that the flux flows from the edges of the model to the next pole pairs, in the calculation model from one edgeto the other, is not correct. If it were wished for that this fact should be considered in multi-pole pair machines, this would mean that all the poles, in other words the whole machine, should be modelled in reluctance net. The error resulting from this wrong assumption is, nevertheless, irrelevant.

Direct torque control of permanent magnet synchronous machines - analysis and implementation

Thedirect torque control (DTC) has become an accepted vector control method besidethe current vector control. The DTC was first applied to asynchronous machines,and has later been applied also to synchronous machines. This thesis analyses the application of the DTC to permanent magnet synchronous machines (PMSM). In order to take the full advantage of the DTC, the PMSM has to be properly dimensioned. Therefore the effect of the motor parameters is analysed taking the control principle into account. Based on the analysis, a parameter selection procedure is presented. The analysis and the selection procedure utilize nonlinear optimization methods. The key element of a direct torque controlled drive is the estimation of the stator flux linkage. Different estimation methods - a combination of current and voltage models and improved integration methods - are analysed. The effect of an incorrect measured rotor angle in the current model is analysed andan error detection and compensation method is presented. The dynamic performance of an earlier presented sensorless flux estimation method is made better by improving the dynamic performance of the low-pass filter used and by adapting the correction of the flux linkage to torque changes. A method for the estimation ofthe initial angle of the rotor is presented. The method is based on measuring the inductance of the machine in several directions and fitting the measurements into a model. The model is nonlinear with respect to the rotor angle and therefore a nonlinear least squares optimization method is needed in the procedure. A commonly used current vector control scheme is the minimum current control. In the DTC the stator flux linkage reference is usually kept constant. Achieving the minimum current requires the control of the reference. An on-line method to perform the minimization of the current by controlling the stator flux linkage reference is presented. Also, the control of the reference above the base speed is considered. A new estimation flux linkage is introduced for the estimation of the parameters of the machine model. In order to utilize the flux linkage estimates in off-line parameter estimation, the integration methods are improved. An adaptive correction is used in the same way as in the estimation of the controller stator flux linkage. The presented parameter estimation methods are then used in aself-commissioning scheme. The proposed methods are tested with a laboratory drive, which consists of a commercial inverter hardware with a modified software and several prototype PMSMs.

Induction motor versus permanent magnet synchronous motor in motion control applications: a comparative study

High dynamic performance of an electric motor is a fundamental prerequisite in motion control applications, also known as servo drives. Recent developments in the field of microprocessors and power electronics have enabled faster and faster movements with an electric motor. In such a dynamically demanding application, the dimensioning of the motor differs substantially from the industrial motor design, where feasible characteristics of the motor are for example high efficiency, a high power factor, and a low price. In motion control instead, such characteristics as high overloading capability, high-speed operation, high torque density and low inertia are required. The thesis investigates how the dimensioning of a high-performance servomotor differs from the dimensioning of industrial motors. The two most common servomotor types are examined; an induction motor and apermanent magnet synchronous motor. The suitability of these two motor types indynamically demanding servo applications is assessed, and the design aspects that optimize the servo characteristics of the motors are analyzed. Operating characteristics of a high performance motor are studied, and some methods for improvements are suggested. The main focus is on the induction machine, which is frequently compared to the permanent magnet synchronous motor. A 4 kW prototype induction motor was designed and manufactured for the verification of the simulation results in the laboratory conditions. Also a dynamic simulation model for estimating the thermal behaviour of the induction motor in servo applications was constructed. The accuracy of the model was improved by coupling it with the electromagnetic motor model in order to take into account the variations in the motor electromagnetic characteristics due to the temperature rise.

Design and Control of Permanent Magnet Synchronous Machine for Hybrid Electric Vehicle

This master’s thesis mainly focuses on the design requirements of an Electric drive for Hybrid car application and its control strategy to achieve a wide speed range. It also emphasises how the control and performance requirements are transformed into its design variables. A parallel hybrid topology is considered where an IC engine and an electric drive share a common crank shaft. A permanent magnet synchronous machine (PMSM) is used as an electric drive machine. Performance requirements are converted into Machine design variables using the vector model of PMSM. Main dimensions of the machine are arrived using analytical approach and Finite Element Analysis (FEA) is used to verify the design and performance. Vector control algorithm was used to control the machine. The control algorithm was tested in a low power PMSM using an embedded controller. A prototype of 10 kW PMSM was built according to the design values. The prototype was tested in the laboratory using a high power converter. Tests were carried out to verify different operating modes. The results were in agreement with the calculations.

Tooth-Coil Permanent Magnet Synchronous Machine Design for Special Applications

This doctoral thesis presents a study on the design of tooth-coil permanent magnet synchronous machines. The electromagnetic properties of concentrated non-overlapping winding permanent magnet synchronous machines, or simply tooth-coil permanent magnet synchronous machines (TC-PMSMs), are studied in details. It is shown that current linkage harmonics play the deterministic role in the behavior of this type of machines. Important contributions are presented as regards of calculation of parameters of TC-PMSMs,particularly the estimation of inductances. The current linkage harmonics essentially define the air-gap harmonic leakage inductance, rotor losses and localized temporal inductance variation. It is proven by FEM analysis that inductance variation caused by the local temporal harmonic saturation results in considerable torque ripple, and can influence on sensorless control capabilities. Example case studies an integrated application of TC-IPMSMs in hybrid off-highway working vehicles. A methodology for increasing the efficiency of working vehicles is introduced. It comprises several approaches – hybridization, working operations optimization, component optimization and integration. As a result of component optimization and integration, a novel integrated electro-hydraulic energy converter (IEHEC) for off-highway working vehicles is designed. The IEHEC can considerably increase the operational efficiency of a hybrid working vehicle. The energy converter consists of an axial-piston hydraulic machine and an integrated TCIPMSM being built on the same shaft. The compact assembly of the electrical and hydraulic machines enhances the ability to find applications for such a device in the mobile environment of working vehicles.Usage of hydraulic fluid, typically used in working actuators, enables direct-immersion oil cooling of designed electrical machine, and further increases the torque- and power- densities of the whole device.

Modeling and Parameter Estimation of Double-Star Permanent Magnet Synchronous Machines

The power rating of wind turbines is constantly increasing; however, keeping the voltage rating at the low-voltage level results in high kilo-ampere currents. An alternative for increasing the power levels without raising the voltage level is provided by multiphase machines. Multiphase machines are used for instance in ship propulsion systems, aerospace applications, electric vehicles, and in other high-power applications including wind energy conversion systems. A machine model in an appropriate reference frame is required in order to design an efficient control for the electric drive. Modeling of multiphase machines poses a challenge because of the mutual couplings between the phases. Mutual couplings degrade the drive performance unless they are properly considered. In certain multiphase machines there is also a problem of high current harmonics, which are easily generated because of the small current path impedance of the harmonic components. However, multiphase machines provide special characteristics compared with the three-phase counterparts: Multiphase machines have a better fault tolerance, and are thus more robust. In addition, the controlled power can be divided among more inverter legs by increasing the number of phases. Moreover, the torque pulsation can be decreased and the harmonic frequency of the torque ripple increased by an appropriate multiphase configuration. By increasing the number of phases it is also possible to obtain more torque per RMS ampere for the same volume, and thus, increase the power density. In this doctoral thesis, a decoupled d–q model of double-star permanent-magnet (PM) synchronous machines is derived based on the inductance matrix diagonalization. The double-star machine is a special type of multiphase machines. Its armature consists of two three-phase winding sets, which are commonly displaced by 30 electrical degrees. In this study, the displacement angle between the sets is considered a parameter. The diagonalization of the inductance matrix results in a simplified model structure, in which the mutual couplings between the reference frames are eliminated. Moreover, the current harmonics are mapped into a reference frame, in which they can be easily controlled. The work also presents methods to determine the machine inductances by a finite-element analysis and by voltage-source inverters on-site. The derived model is validated by experimental results obtained with an example double-star interior PM (IPM) synchronous machine having the sets displaced by 30 electrical degrees. The derived transformation, and consequently, the decoupled d–q machine model, are shown to model the behavior of an actual machine with an acceptable accuracy. Thus, the proposed model is suitable to be used for the model-based control design of electric drives consisting of double-star IPM synchronous machines.

Inductance Calculation of Tooth-Coil Permanent-Magnet Synchronous Machines

Analytical calculation methods for all the major components of the synchronous inductance of tooth-coil permanentmagnet synchronous machines are reevaluated in this paper. The inductance estimation is different in the tooth-coil machine compared with the one in the traditional rotating field winding machine. The accuracy of the analytical torque calculation highly depends on the estimated synchronous inductance. Despite powerful finite element method (FEM) tools, an accurate and fast analytical method is required at an early design stage to find an initialmachine design structure with the desired performance. The results of the analytical inductance calculation are verified and assessed in terms of accuracy with the FEM simulation results and with the prototype measurement results.

Unequal Teeth Widths for Torque Ripple Reduction in Permanent Magnet Synchronous Machines With Fractional-Slot Non-Overlapping Windings

Permanent magnet synchronous machines with fractional-slot non-overlapping windings (FSPMSM), also known as tooth-coil winding permanent magnet synchronous machines (TCW PMSM), have been under intensive research during the latest decade. There are many optimization routines explained and implemented in the literature in order to improve the characteristics of this machine type. This paper introduces a new technique for torque ripple minimization in TCW PMSM. The source of torque harmonics is also described. The low order torque harmonics can be harmful for a variety of applications, such as direct drive wind generators, direct drive light vehicle electrical motors, and for some high precision servo applications. The reduction of the torque ripple harmonics with the lowest orders (6th and 12th) is realized by machine geometry optimization technique using finite element analysis (FEA). The presented optimization technique includes the stator geometry adjustment in TCW PMSMs with rotor surface permanent magnets and with rotor embedded permanent magnets. Influence of the permanent magnet skewing on the torque ripple reduction and cogging torque elimination was also investigated. It was implemented separately and together with the stator optimization technique. As a result, the reduction of some torque ripple harmonics was attained.

Direct-Driven Interior Magnet Permanent Magnet Synchronous Motors for a Full Electric Sports Car

The design process of direct-driven permanent magnet synchronous machines (PMSMs) for a full electric 4 ´ 4 sports car is presented. The rotor structure of the machine consists of two permanent magnet layers embedded inside the rotor laminations thus resulting in some inverse saliency, where the q-axis inductance is larger than the d-axis one. An integer slot stator winding was selected to fully take advantage of the additional reluctance torque. The performance characteristics of the designed PMSMs were calculated by applying a twodimensional finite element method. Cross-saturation between the d- and q-axes was taken into account in the calculation of the synchronous inductances. The calculation results are validated by measurements.

Design and Drive-Cycle Based Analysis of Direct-Driven Permanent Magnet Synchronous Machine for a Small Urban Use Electric Vehicle

A direct-driven permanent magnet synchronous machine for a small urban use electric vehicle is presented. The measured performance of the machine at the test bench as well as the performance over the modified New European Drive Cycle will be given. The effect of optimal current components, maximizing the efficiency and taking into account the iron loss, is compared with the simple id=0 – control. The machine currents and losses during the drive cycle are calculated and compared with each other.

Analytic evaluation of three-phase short circuit demagnetization and hysteresis loss risk in rotor-surface-magnet Permanent-Magnet Synchronous Machines

Permanent magnet synchronous machines (PMSM) have become widely used in applications because of high efficiency compared to synchronous machines with exciting winding or to induction motors. This feature of PMSM is achieved through the using the permanent magnets (PM) as the main excitation source. The magnetic properties of the PM have significant influence on all the PMSM characteristics. Recent observations of the PM material properties when used in rotating machines revealed that in all PMSMs the magnets do not necessarily operate in the second quadrant of the demagnetization curve which makes the magnets prone to hysteresis losses. Moreover, still no good analytical approach has not been derived for the magnetic flux density distribution along the PM during the different short circuits faults. The main task of this thesis is to derive simple analytical tool which can predict magnetic flux density distribution along the rotor-surface mounted PM in two cases: during normal operating mode and in the worst moment of time from the PM’s point of view of the three phase symmetrical short circuit. The surface mounted PMSMs were selected because of their prevalence and relatively simple construction. The proposed model is based on the combination of two theories: the theory of the magnetic circuit and space vector theory. The comparison of the results in case of the normal operating mode obtained from finite element software with the results calculated with the proposed model shows good accuracy of model in the parts of the PM which are most of all prone to hysteresis losses. The comparison of the results for three phase symmetrical short circuit revealed significant inaccuracy of the proposed model compared with results from finite element software. The analysis of the inaccuracy reasons was provided. The impact on the model of the Carter factor theory and assumption that air have permeability of the PM were analyzed. The propositions for the further model development are presented.

Cost Reduction of Permanent Magnet Synchronous Machines

Electrical machine drives are the most electrical energy-consuming systems worldwide. The largest proportion of drives is found in industrial applications. There are, however many other applications that are also based on the use of electrical machines, because they have a relatively high efficiency, a low noise level, and do not produce local pollution. Electrical machines can be classified into several categories. One of the most commonly used electrical machine types (especially in the industry) is induction motors, also known as asynchronous machines. They have a mature production process and a robust rotor construction. However, in the world pursuing higher energy efficiency with reasonable investments not every application receives the advantage of using this type of motor drives. The main drawback of induction motors is the fact that they need slipcaused and thus loss-generating current in the rotor, and additional stator current for magnetic field production along with the torque-producing current. This can reduce the electric motor drive efficiency, especially in low-speed, low-power applications. Often, when high torque density is required together with low losses, it is desirable to apply permanent magnet technology, because in this case there is no need to use current to produce the basic excitation of the machine. This promotes the effectiveness of copper use in the stator, and further, there is no rotor current in these machines. Again, if permanent magnets with a high remanent flux density are used, the air gap flux density can be higher than in conventional induction motors. These advantages have raised the popularity of PMSMs in some challenging applications, such as hybrid electric vehicles (HEV), wind turbines, and home appliances. Usually, a correctly designed PMSM has a higher efficiency and consequently lower losses than its induction machine counterparts. Therefore, the use of these electrical machines reduces the energy consumption of the whole system to some extent, which can provide good motivation to apply permanent magnet technology to electrical machines. However, the cost of high performance rare earth permanent magnets in these machines may not be affordable in many industrial applications, because the tight competition between the manufacturers dictates the rules of low-cost and highly robust solutions, where asynchronous machines seem to be more feasible at the moment. Two main electromagnetic components of an electrical machine are the stator and the rotor. In the case of a conventional radial flux PMSM, the stator contains magnetic circuit lamination and stator winding, and the rotor consists of rotor steel (laminated or solid) and permanent magnets. The lamination itself does not significantly influence the total cost of the machine, even though it can considerably increase the construction complexity, as it requires a special assembly arrangement. However, thin metal sheet processing methods are very effective and economically feasible. Therefore, the cost of the machine is mainly affected by the stator winding and the permanent magnets. The work proposed in this doctoral dissertation comprises a description and analysis of two approaches of PMSM cost reduction: one on the rotor side and the other on the stator side. The first approach on the rotor side includes the use of low-cost and abundant ferrite magnets together with a tooth-coil winding topology and an outer rotor construction. The second approach on the stator side exploits the use of a modular stator structure instead of a monolithic one. PMSMs with the proposed structures were thoroughly analysed by finite element method based tools (FEM). It was found out that by implementing the described principles, some favourable characteristics of the machine (mainly concerning the machine size) will inevitable be compromised. However, the main target of the proposed approaches is not to compete with conventional rare earth PMSMs, but to reduce the price at which they can be implemented in industrial applications, keeping their dimensions at the same level or lower than those of a typical electrical machine used in the industry at the moment. The measurement results of the prototypes show that the main performance characteristics of these machines are at an acceptable level. It is shown that with certain specific actions it is possible to achieve a desirable efficiency level of the machine with the proposed cost reduction methods.

Influence of Travelling Current Linkage Harmonics on Inductance Variation, Torque Ripple and Sensorless Capability of Tooth-Coil Permanent-Magnet Synchronous Machines

This paper introduces an important source of torque ripple in PMSMs with tooth-coil windings (TC-PMSMs). It is theoretically proven that saturation and cross-saturation phenomena caused by the non-synchronous harmonics of the stator current linkage cause a synchronous inductance variation with a particular periodicity. This, in turn, determines the magnitude of the torque ripple and can also deteriorate the performance of signal-injection-based rotor position estimation algorithms. An improved dq- inductance model is proposed. It can be used in torque ripple reduction control schemes and can enhance the self-sensing capabilities of TC-PMSMs

Heat-transfer improvements in an axial-flux permanent-magnet synchronous machine

Axial-flux machines tend to have cooling difficulties since it is difficult to arrange continuous heat path between the stator stack and the frame. One important reason for this is that no shrink fitting of the stator is possible in an axial-flux machine. Using of liquid-cooled end shields does not alone solve this issue. Cooling of the rotor and the end windings may also be difficult at least in case of two-stator-single-rotor construction where air circulation in the rotor and in the end-winding areas may be difficult to arrange. If the rotor has significant losses air circulation via the rotor and behind the stator yokes should be arranged which, again, weakens the stator cooling. In this paper we study a novel way of using copper bars as extra heat transfer paths between the stator teeth and liquid cooling pools in the end shields. After this the end windings still suffer of low thermal conductivity and means for improving this by high-heat-conductance material was also studied. The design principle of each cooling system is presented in details. Thermal models based on Computational Fluid Dynamics (CFD) are used to analyse the temperature distribution in the machine. Measurement results are provided from different versions of the machine. The results show that significant improvements in the cooling can be gained by these steps.

Electromagnetic torque ripple and copper losses reduction in permanent magnet synchronous machines

This paper presents a method for electromagnetic torque ripple and copper losses reduction in (non-sinusoidal or trapezoidal) surface-mount permanent magnet synchronous machines (SM-PMSM). The method is based on an extension of classical dq transformation that makes it possible to write a vectorial model for this kind of machine (with a non-sinusoidal back-EMF waveform). This model is obtained by the application of that transformation in the classical machine per-phase model. That transformation can be applied to machines that have any type of back-EMF waveform, and not only trapezoidal or square-wave back-EMF waveforms. Implementation results are shown for an electrical converter, using the proposed vectorial model, feeding a non-sinusoidal synchronous machine (brushless DC motor). They show that the use of this vectorial mode is a way to achieve improvements in the performance of this kind of machine, considering the electromagnetic torque ripple and copper losses, if compared to a drive system that employs a classical six-step mode as a converter. Copyright (C) 2011 John Wiley & Sons, Ltd.