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These features and others such as high efficiency, fault tolerance and variable speed capabilities make the motor a serious competitor in the developing drives market. For military and aerospace applications, SRMs offer advantages where the whole failure of the drive has a severe impact on the operation of a system or on human safety for example.
In such applications, a single point fault must not lead to another fault or to the loss of any features of the system. The system must be capable of continuing its operation satisfactory i. The switched reluctance motor SRM , also called a variable reluctance motor VRM , is defined as a continuous run, singly-excited motor converting a specific pattern of electric pulses into continuous angular displacements. The motor has salient poles on both the stator and the rotor, with only one set of excitation windings, usually on the stator.
Neither rotor conductors nor permanent magnets are required because torque is produced by the tendency of the rotor to move itself into the minimum reluctance position with the excited stator phase. The earliest recorded SRM was built by Davidson in Scotland in , however only recently have these machines begun to see increasing use in engineering applications. This is primarily due to the fact that, although they are simple in construction, they are difficult to analyse, control, and design.
For example, a rotor position sensor is commonly used to switch the stator currents at the appropriate instants in time in order to produce a net average torque. The modern development in power electronics and computer-aided design however has brought the cost of sensing and control devices required to successfully operate SRM drive systems down to a level where these systems can be competitive with systems based on DC and induction motor technologies.
The first part is a review of theory and analysis of SRMs; the second part is a review of modelling and performance; the third part is a review of design and construction; and finally the last part is a review of design optimisation in SRMs. Initially the analysis was mainly focused on normal operating conditions but more recently fault analysis has also been investigated. Various relationships giving peripheral force and output power were derived and optimised to give the maximum output power.
This paper explained the ratio of rotor speed to the stator excitation speed. It also explained the constructional features that affect the direction of rotor rotation with respect to stator excitation.
The motor output coefficient was estimated and compared with that of different machine types. It concluded that the best output coefficient was intermediate between those for a DC motor and that for an induction motor. This is an important general paper. Koch  presented a theoretical treatment of a variable three-phase single-stack reluctance motor.
Optimum pole and gap dimensions were investigated on the basis of published permeance charts. But this treatment was incomplete in that, not only was it restricted through using a linear model, but also it failed to recognize the effects of negative torque developed during part of the operating cycle. Furthermore, no consideration was given to the possibility of switching on the current before the onset of the period of overlap or increasing phase inductance.
Lawrenson et al  presented the linear theory of switched reluctance motors. They explained that the absence of field excitation does not lead to any inferior performance, as might be imagined.
The basic modes of operation, analysis, and experimental results were described. This paper demonstrates that these machines are 2 Chapter 1 Introduction capable of extremely high levels of performance. They are also simple and cheap to manufacture and can offer important operational advantages in both industrial and domestic applications. However, the paper emphasised that serious design work and analysis must recognize the non-linear nature of the flux linkage, inductance, and static torque characteristics.
It also pointed out the necessity of time-stepping analysis in order to estimate the dynamic performance of the motor. Davis et al  described in detail the configuration for power converters for both 3- and 4-phase switched reluctance motors having single and bifilar windings. They explained that a variable speed drive using an SRM permits a simpler and cheaper converter than a PWM inverter for an induction motor.
Linear analysis was used to predict approximate current waveforms from which the converter device ratings can be estimated. The paper also explained some constraints on speed and current in order to achieve the rated power over a wide speed range, and to achieve constant torque. Lawrenson  highlighted the differences between switched reluctance motor drives and conventional synchronous reluctance motors.
He presented helpful notes about the motor construction; drive circuits and control, performance characteristics, and future potential.
He also presented an important comparison of the performance and the cost of different drives mentioning the advantages which make the SRM attractive for a wide range of applications. Miller  described a simple non-linear analysis and estimated the voltampere requirements of SRM drive.
It was shown that saturation has two main effects: increasing the motor size required for a given torque; and at the same time decreasing the KVA per horsepower output. The paper provided a formula for computing the required commutation angle, and provided the idea of the generalized power factor in SRMs. This paper also identifies the constant back emf that results from the variation of overlap angle and used it to determine the conditions necessary to achieve a flat-topped current waveform.
The model is essentially a static model only and if it were adopted for dynamic simulation, the resulting waveforms would have been unacceptable.
Ray et al  presented a review paper which contains an explanation of the claims that the SRM drives offer the advantages of simple and robust motor 3 Chapter 1 Introduction construction, high speeds, high overall efficiencies over a wide operating range of torque and speed, simple power converter circuits with a reduced number of switches and excellent controllability.
The difficulties of establishing a simple mathematical model for the motor and of calculating the torque accurately were explained. The equivalent circuit of an SRM was also presented. Harris et al  evaluated the capabilities of the switched reluctance motor drive, particularly in small integral-horsepower sizes.
They presented a performance comparison between the SRM and the induction motor. The paper showed that the SRM is a serious competitor for the fully controlled induction motor in all its performance parameters.
Stephenson and Elkhazendar  stated clearly the influence of saturation on torque production and energy flow in switched reluctance motors. A comparison of a series of switched reluctance motors which were identical in all respects except for the iron used, was undertaken. The differences include the use of ideal non-saturating materials; the introduction of saturating materials in the pole faces; the use of real iron; and the introduction of a magnetic constriction in the pole faces.
Umans et al  presented some of the constructional variations of such machines together with the basic principles of linear and non-linear analysis. He also explained the basic excitation strategies required to produce average useful torque. Many drive circuits were described in general terms. Mecrow [11, 12] , introduced the concept of using fully-pitched windings in an SRM to improve the electrical utilisation of the motor.
It was shown that these winding configurations resulted in improved torque capability but at the expense of longer end-windings and hence more copper loss. In contrast to regular SRMs, the torque is produced due to the change of mutual inductance between phases which implies that the motor has no fault tolerance capability. The winding configuration is however still very useful for motors with long stack lengths and small rotor radii.
Various motor faults including phase open-circuit, phase short-circuit, coil short-circuit and double phase fault were developed and compared. The comparison examined the effect of these faults in the motor output power, the vibration, and the over-current value.
The main disadvantage of this paper is that it did not interpret the faults mathematically and did not explain how to improve the fault tolerance characteristics of the motor. Miller  identified and analysed a number of severe fault conditions that may occur in switched reluctance machines.
The analysis was performed using 2-D finite element analysis, magnetic circuit models, and experiments. The paper presented simple expressions for the total reluctance and radial force estimation under fault conditions. Various electrical configurations of motor windings and controller circuits were also discussed.
Mecrow et al [15, 16] identified the principal electromagnetic faults which can occur within the machine and its power converter. Fault tolerance requirements were presented and the inherent capability of the SRM to satisfy these was demonstrated. The authors suggested that with careful design, a similar degree of fault tolerance could be achieved with a permanent magnet machine PM. A comparative study of permanent magnet and switched reluctance motors was presented . The comparison showed that the modified fault tolerant PM machines could offer a greater torque density at the same degree of fault tolerance.
The work however slightly underestimated the thermal limits imposed by the permanent magnets. El-Wakeel et al  explained the main faults and critical operating conditions from electrical, mechanical, and thermal points of view. The fault tolerance drive requirements were explained. The authors discussed briefly how to improve the fault tolerance characteristics of the motor. However, the paper is only based on logical reasoning and approximate analytical modelling.
Hao and Chao  introduced electrical faults in the motor, the converter, and the rotor position detector. A comparison of regular three- and fourphase motors was undertaken in terms of the current requirement for constant power 5 Chapter 1 Introduction operation.
The analysis depends on simple linear analysis and neglected the effect of mutual inductance. The model presented did not take into account the complications introduced by magnetic saturation. Singh and Kuo  presented a mathematical model of a single-stack variable reluctance step motor. The model allowed for saturation of the magnetic circuit by assuming that the incremental self inductance components decrease linearly with the phase current.
This assumption may be difficult to justify. In addition, the model was rather unwieldy to implement. The model was used to design a high-performance printer system but the model accuracy was not demonstrated. Stephenson and Corda  presented a more elegant and efficient method of modelling the SRM. The authors avoided the conventional concept of using inductance and current, which were commonly used for other types of machines and instead used flux-linkage as a variable.
The magnetic information is stored in tabular form and numerical interpolation, integration and differentiation used to determine the instantaneous current, co-energy, and torque waveform. They used this model for a feedback linearizing control of an SRM.
Miller and McGilp  developed a simple but very efficient method for modelling the performance of SRMs. The model based only on the aligned and unaligned magnetisation curves. Between these two positions, the authors developed three magnetisation and torque models based on the structure of the magnetisation data.
The accurate modelling results reported by the authors reflect some degree of successful empiricism in the model form, however the model is suitable mainly for initial design and sizing stage. Arkadan and Kielgas  used a state space model to predict the dynamic performance characteristics under normal operating conditions. In addition, the 6 Chapter 1 Introduction effects of mutual coupling inductance between motor phases were evaluated and it was demonstrated that the exclusion of the mutual inductance had a slight effect on the results under normal operating conditions.
Torrey et al [25, 26] and presented a model that connects the fundamental design of a VRM to an analytical expression that predicts the terminal magnetisation characteristics. The modelling procedure used a simple piece-wise linear model, which was based on geometry and turns per phase, incorporated into a fast algorithm. The model parameters are based on physical reasoning and verified through three different existing SRMs. This model was shown to provide useful estimations of net and instantaneous machine performance.
The model is based on a set of normalized gauge curves of flux linkage versus rotor position at constant current, which can be used for the interpolation required during a dynamic simulation.
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