Abstract

1. Chapter 1. Introduction In Chapter 1 the actual context of electrified vehicles is presented. The paradigm shift in the auto industry, towards more energy efficient, more reliable and smarter vehicles led to the development of electrified vehicles such as the more electric vehicles (MEVs), hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs) and electric vehicles (EVs). Excepting the MEVs, all other classes are equipped with at least one motor/generator used for propulsion/braking. As for the energy they need to be fed with, it can be drawn from multiple sources, such as: chemical batteries, fuel cells (FCs) or ultra-capacitors. Comparative tables regarding potential electric machines to be used in the EV development are provided. Efficiency, terminal quantities (current, voltage), rated and maximum torque and speed are considered for comparison, amongst other quantities. Moreover the advantages as well as drawbacks are mentioned for three other classes of electrical machines, i.e. DC machine, induction machine, permanent magnet synchronous machine. The main advantages of the SR technology over the rest of the machines are discussed along with its main drawbacks. Finally some of the most representative work in the field performed by both Universities and industry is mentioned. Next, the main contributions of the thesis are pointed out in the second section of the chapter while in the last section the outline of the thesis is performed. 2. Chapter 2. Electromagnetic Model of an SRM In Chapter 2 a FE-based electromagnetic model is developed for accurately characterizing the (nonlinear) behavior of SRMs. Having the correct set of curves is rather decisive if one intends to perform high-grade control as the flux and ultimately the torque depends on both position and current. After an extensive review of the methods existing in the field for magnetic characterization, three important classes emerged. Therefore, such curves can be obtained either using empirical formulas, FE models, or measured. In this Chapter two different approaches are considered for determining the flux and eventually the torque dependence with current and position. In the first case, the magnetization characteristics are obtained based on FE analyses. Moreover the flux variation with position is compared using 2D and 3D FE models. The 2D model has been developed in FEMM software which was preferred due to its convenient interface with Matlab. Following another literature review where the effect of using the 2D FE model vs. the 3D ones are highlighted, a 3D FE model is developed as well. The static flux curves obtained using the 2D FE model are compared with the 3D FE obtained ones, in two cases: the 3D model is obtained through extrusion of the 2D model (end-windings are not modeled) and the 3D model is including the end-windings. As expected the difference between the 2D FE model and its extruded counterpart is insignificant. On the other hand, when the end-coils are modeled, the difference is rather important as it is the case of the unaligned position where it can be more flux up 22%. However, this difference is reducing as the rotor is getting closer to aligned position, where it drops under 1%. Finally, the flux curves are determined based on an experimental procedure after the integration of the voltage equation where the (transient) current and (transient) voltage are measured by means of the DC-step voltage test, i.e. with the rotor blocked, a DC step voltage is applied to the phase at different angular positions and the current and voltage waveforms are recorded. A procedure for obtaining the torque from the polynomial fitted surface of coenergy is provided. It is shown that using the latter, the numerical problems which appear using the raw surface of the coenergy instead of the fitted one, are significantly reduced. In the last core-section of the chapter, a generalized procedure for iron losses calculation is proposed starting from a matrix-based model (previously presented in the literature), taking into consideration the fact that different segments in the SRM are subject to different fundamental frequency of the magnetic flux density. In addition, the rotational effect of the flux is taken into consideration as well as the minor loops effect. One, rather important part is the procedure for determining the time variation of magnetic flux density Using the time series of the phase current (obtained through dynamic simulations based on the circuit model) and the FE obtained tables for magnetic flux density dependence with rotor position and current, the instantaneous variation of the magnetic flux density is obtained. 3. Chapter 3. Thermal Model of an SRM The miniaturization of electrical motors is decisive when choosing one used for HEV/EV propulsion. Due to the lack of permanent magnets, SRMs are subject to high current densities in the coils so as to overcome the drawback of a lower power density. Special attention must be paid to the cooling arrangement in order to remove the excessive heat that results in the machine due to the increased copper losses as well as core losses at higher speed values. The chapter starts with a brief review on thermal modeling of electric machines. Some representative work that is reported on patent development for cooling arrangements of salient poles electric machines in general and SRM in particular, is mentioned in the patent review section of the chapter. In this chapter starting from the earlier works involving totally-enclosed non-ventilated (TENV) SRMs as well as totally-enclosed forced cooled (TEFC) induction machines, a lumped parameter thermal network (LPTN) is developed for a totally-enclosed water cooled (TEWC) SRM. The conductive parts are modeled based on the T-model described in earlier works for which the thermal resistances are calculated starting from the heat conduction equation (also known as Fourier’s law), to which some simplifying hypotheses are applied. Correlations are made for determining the convective heat transfer coefficients in the air-gap starting from Nusselt number calculated using the model of two rotating cylinders developed by Taylor, to which penalties (which are speed dependant) are applied in order to include the effect of the salient poles. For the end-cap air, a constant heat transfer coefficient as the air flow in the axial direction is neglected due to the lack of any fan coupled at the end of the shaft. Theoretical issues are provided regarding the thermal contact resistances, the heat transfer mechanism trough radiation and the circumstances in which it can be neglected as well as the calculation procedure for the thermal capacitances in order to include the transient evolution of temperature in the study. Moreover, the methodology for solving the equivalent circuit is given, both for steady and transient state using the matrix-based form of the method of node potentials (MNP). Next, a 2D model thermal FE model is developed for design optimization purposes. Furthermore, the temperature evolution in the thermally conductive segments of cross-section is determined based upon a 3D FE model and the temperature distribution is discussed considering different operating scenarios. The main heat transfer paths are discussed as well. Eventually, a comparison between the transient evolution of the temperature in the key conductive segments (stator and rotor iron, coils) when either using the LPTN or the 3D FE model. The main conclusion of the chapter is that the LPTN may represent a viable solution for predicting the evolution in time of the temperature in an SRM. However there are few rather sensitive parameters that have to be determined either using more complex models such as 3D FE or CFD or based of measured data. Moreover, the latter has to be used for determining the distribution of the temperature in a certain segment. 4. Chapter 4. SRM Design This chapter deals with the design procedure of an SRM used in HEV/EV propulsion. A FE-based multiphysics design optimization routine is developed. Two different approaches are considered regarding the initial design. In the first case the topology is obtained using a pre-sizing routine while taking into account the requirements of an electric motor used for HEVs/EVs (referred in text as SRMPRE-S), whereas in the second case the performance of the multiphysics optimization routine is assessed starting from an existing SRM and trying to increase its torque density without modifying the outer envelope nor the cooling circuit (referred in text as SRMPPT). Three different types of constraints are embedded in the optimization routine. The electromagnetic ones are given by the magnetic flux density value (both in the stator pole and stator back iron) whereas the heat generation (thermal constraint) is controlled either by means of the current density, or coupling the analysis with the FE thermal one. Furthermore, at each evaluation the circumferential mode frequency for the pulsating vibration mode m = 2 is calculated and lower boundaries are considered for limiting the deterioration of the NVH properties. The outer envelope of the machine is not subject to any change as both the outer diameter and stack length have been kept constant. Moreover, a state of the art on SRM design is presented along discussions on the optimal design of SRMs. A rather significant increase in the torque density is reported as output of the optimization routine (up to 25%) for slight decrease in efficiency (less than 1%). 5. Chapter 5. Torque Control of SRMs Chapter 5 starts with a review on some of the works conducted over the last decades in torque control and the methods proposed by the author for overcoming the main drawbacks of the SRM a the control level. It continues with a brief description of the torque production mechanism in SRMs followed by the description of the optimization problem as well as the minimization technique that is used. The positioning of the minimization technique that is used in the frame of the minimization techniques is briefly discussed as well. The flux and torque curves, determined based on the FE-model in Chapter 2, are used for developing the dynamic model of the SRM. In order to improve the convergence performance of the optimization routine, a smooth model has been developed, which in addition allowed for the separation of the two causes of ripple. Further the torque control is optimized over the entire speed range, by splitting up the problem in two as follows. At low speed an instantaneous torque control (ITC) technique is implemented by means of modeling the required shape of the current using the so-called torque sharing functions (TSFs), whereas at higher speed an average torque control (ATC) technique is considered to be sufficient. Regarding the ITC, starting from the basic rectangular variation, the ascending and descending flanks of the function are modeled using a cosine, exponential and a more general approach (further referred to as piecewise cubic sharing function). The degrees of freedom (DOFs) varying between two and an arbitrary number (for the general approach) are determined so as to minimize losses, when operating in smooth torque conditions. Based upon an optimization procedure with both linear and nonlinear constraints, the total (copper and iron) losses are minimized considering a limited available DC bus voltage. Extensive studies have been conducted for determining the optimal number of degrees of freedom (DoFs) for the piecewise cubic function. At speed values exceeding 1000rpm the average values of the torque is controlled and the optimal values for the firing angles are obtained based on a minimization routine for different objective functions. Starting from the one variable functions step by step, penalties are added for improving the ripple content and eventually the efficiency. Moreover, the drawback of the minimization routines to converge to local minima is overcome by including special routines for initial conditions generation. Finally, for the optimal sets of angles (for both control schemes), losses (iron and copper) are evaluated both in motoring and generating mode. After conducting the optimizations over the entire considered torque-speed range it was found that the generalized version of the cubic variation provides the lowest copper losses as well as an extension of the torque-speed region in which the peak torque can be produced, ripple-free (around 30%). Extensive studies have been conducted for assessing the performance of the generalized TSF. Knowing the voltage dips are not an uncommon phenomenon in EV applications, tests have been executed for determining which is the allowed dip value so as to the torque ripple is not increasing significantly. The method was proven to be robust, as significant ripple occurred only when the voltage dropped to 0.25. A value equal to one corresponded to the rated DC bus value. Moreover, the influence of different switching strategies on the phase current tracking its reference was shown and a hybrid chopping technique was implemented in order to reduce the switching frequency, thus the losses in the converter. An extension of the piecewise cubic function to SRMs with more than two phases conducting in the same time is discussed theoretically but no results are provided as most of the work in this thesis is dedicated to the 8/6 topology. In the last section a series of measured results are provided for both torque control schemes starting from the low speed (250rpm) operation, continuing with base speed (1500rpm), then double the base speed (3000rpm) and eventually at the maximum speed specified for the load in its datasheet (4000rpm). Regarding the load torque, measurements were conducted up to 30Nm, limitation given by the load (7.5kW DC machine). Using the measured phase currents, the torque is estimated based on the FE calculated torque vs. current and position table, and eventually compared with that obtained by simulations. A good agreement between measured/estimated instantaneous torque and its simulated counterpart was obtained, when on the simulations the same sampling was imposed as it was for the test bench (10kHz). 6. Chapter 6. Assessing the Performance of an SRM in Various Driving Cycles In this chapter, starting from the losses (iron and copper) evaluated using the optimal sets of angles (for both control schemes) and for both motoring and generating mode the performances of the SRM and the proposed controller are assessed by applying different driving cycles. The considered cycles fall into one of the following categories: modal (characterized by long distances traveled at constant speed), transient (characterized by constantly varying speed). Also different driving areas as simulated when considering the MOL cycle in its three forms - city, highway and rural). A simplified model of an EV has been developed in order to determine the torque and speed command that have to be given to the SRM controller. Regarding the controller, it has been shown in previous chapter that there are two torque control technique embedded in it. Tests have been made to determine the optimal speed value at which the control schemes are swapped. It is shown that for the proposed configuration the current profiling technique can be used up to 1000rpm after this point an average torque control technique being sufficient. The LPTN developed in Chapter 3 has been used for thermal characterization of the SRM under different driving conditions (considered by means of driving cycles - both standard and real-life). Moreover, for the present configuration of the drive, after testing 5 driving cycles one may observe the rather safe operation, as the maximum allowable temperature is not reached. For driving cycles of city type the average efficiency obtained was around 80% whereas for the highway type efficiencies over 90% have been obtained. Considering a vehicle of 1950kg powered by a battery with a capacity of 30kWh, the estimated range is about 200km in the city type driving cycles, whereas when cruising on the highway it can drop to 120km. 7. Chapter 7. Conclusions and Future Work In Chapter 7 the main conclusions are drawn and some suggestions for future work are made. Moreover, each chapter has its own Appendix (from A to E) in which additional data is provided, in order to ensure the reproducibility of the work/results. Doctorat en Sciences de l'ingénieur info:eu-repo/semantics/published