AMAZON multi-meters discounts AMAZON oscilloscope discounts
Basics: The section is devoted to Switched Reluctance Motor (SRM) drives.
Firstly nonlinear magnetizing curves of SRM are presented and their importance for motor's operation is discussed. The model presented in the section takes into account these nonlinear characteristics depending on phase current and rotor position angle, but ignores mutual magnetization of phases. The magnetization curves are regarded in a specific and original way as a product of nonlinear functions de pending on magnetic saturation and rotor position angle. This approach seems to be useful as it enables one to analyze the influence of particular construction elements on characteristics of a motor. In consequence mutual inductances of phases are disregarded, but their actual influence is presented for two typical SRMs, and proved to be marginal. Several problems of SRM operation and control are presented based on mathematical models and results of computer simulations. Among others they are: determining a pulse sequence for starting, direct start up with cur rent limitation, breaking and a comprehensive discussion of generator operation conditions. The problem of regulation parameters fitting is also presented, considered from a point of view of gaining possibly high efficiency and low torque ripple level. As far as control of SRM is concerned there is sliding mode control discussed as well as current control and DTC with an aim to minimize torque pulsation at various states of operation. Besides, there is the problem of a control with and without position/speed sensors presented and state observers application discussed that enable this kind of control.
Introduction
Switched reluctance motor (SRM) as an engineering solution to the design of the electric motor in rotational motion realizes one of the earliest ideas of operation principle for the electric motor, which originates from the first half of the 19th century. It employs the simple concept of an electromechanical system based on the attraction of a ferromagnetic element by an electromagnet. In order to make this idea viable for a rotational motor alternately energized coils are situated on Zs stator teeth, while Zr salient rotor teeth without windings are attracted by adequately energized stator windings. The art in their design as well as the fundamental technological problem is associated with adequate energizing and de-energizing stator windings in a proper phase sequence in order to ensure a smooth rotation of the rotor whose teeth are attracted by generated magnetic field. Despite simple operating principle the practical operation of SRM motor is associated with a need to apply fast and efficient electronic switches in order to realize the switching sequence. Besides, sensors of rotor position with sufficient precision are needed to secure commutation of the currents in the windings. For these reasons the development and wide application of the design started as late as 1980s when adequate power electronic components were available to realize such switching functions. In order to ensure a starting torque and possibly smooth rotational motion it’s necessary that rotor teeth are not aligned in respect to all corresponding stator teeth concurrently. For a motor with a single pole pair p = 1, this simultaneous alignment occurs only for the opposite teeth, i.e. more generally at an angular interval of p/p. For this reason the number of stator and rotor teeth is usually different. The most common solutions apply the following sequence of teeth numbers: Zs/Zr = 6/4 and Zs/Zr = 8/6. Self-evidently, other teeth number sequence is encountered, e.g. Zs/Zr = 4/2 for a two-phase motor, or Zs/Zr = 10/8 for a motor with five phase windings in the stator. The number of phases for motors with a single pole pair is equal to m = Zs/2. This results from the fact that the opposite stator teeth are energized simultaneously with an equal current during the connection of the coils in series. But parallel connection of windings on opposite stator teeth is also possible. As a result, two coils of opposite stator teeth form a single phase winding of the motor. For higher pole pair numbers, the number of pairs of stator and rotor teeth, whose axes overlap, is respectively higher and amounts to p > 1 while the stator windings belonging to the same phase are energized in the same sequence; hence, the number of phases is equal to m = Zs/(2p). This affects the respectively higher electromagnetic torque of the motor. Fig __presents a cross-section of a Zs/Zr = 6/4 SRM motor, i.e. a reluctance three-phase motor.
+-+-+- Cross-section of a Zs/Zr = 6/4 SRM motor, with the indication of rotor position angle theta_r, and switch angles a_on and a_off.
The application of SRM motor has opened new boundaries in the practice of the design of electric motor drives. In connection with this, it would be of value to characterize its basic parameters and define the scope of its application. In terms of the rated power SRM motors are manufactured in a range from very small units with the output of several watts to enormous drives with the power of several hundred kW and can even reach MW level. The comparison of the energy efficiency, start-up torques and torque overloads between the typical SRM motors and the corresponding induction motors leads to the conclusion that the SRMs offer more advantages; however, the advantage of the SRM motor is not significant. A comparative analysis of a SRM motor with a corresponding induction motor ac counting also for noise emission level is based on the example. One of the characteristics of SRM motor includes the possibility of gaining high rotational speeds, as high as 10,000 [rev/min] without special engineering changes in the motor. At the same time, SMR motors whose special design makes them high speed can reach as high as 100,000 [rev/min]. One has to note that such machines have a smooth cylindrical rotor while the effect of variable reluctance is obtained as a result of the application of materials that vary in terms of magnetic permeability along the circumference of the rotor. Another special feature of SRM motor involves its mechanical characteristic theta_r = f(Tl) whose waveform is similar to the series wound DC motors. I.e., during an increased load this motor considerably slows down it rotation and when the load is reduced it accelerates.
The negative characteristics of SRM motors include high torque ripple and higher noise level in comparison to e.g. induction motors. The counter measures include the proper magnetic circuit construction and application of adequate control systems thus reducing torque pulses generated by the motor. As far as the applications of SRM motors is concerned, they are similar to the uses of induction motors and series wound DC motors. In particular, they find application in traction drives and car drives due to flexible mechanical characteristics, large torque overload capability, simple construction and high level of reliability.
SRM motors can be successfully applied in servomotors and actuators. SRM machines can also play the role of generators; however, due to the passive role of the rotor the magnetic excitation has to occur as a result of current passing through stator windings, which is associated with specific requirements regarding control and affects the efficiency of the machine as a generator. Bibliography devoted to this problem is numerous also in the context of the construction of wind power stations and this area is the subject. In terms of the investment a SRM motor drive is cheaper in comparison to an induction motor drive and so is converter as a result of the much more simplified construction of the stator winding, lack of rotor windings and less complicated system needed to supply the machine. At present, the lower popularity of the motor and smaller offer on the part of manufacturers result in the fact that SRM motors have not yet been able to demonstrate all the advantages they have over induction motors.
Operating Principle and Supply Systems
The most fundamental issue in the control of SRM motor drives is associated with adequate sequential voltage feeding to and disconnecting from motor's windings.
___ presents the cross-section of a motor with Zs/Zr = 8/6 teeth and angular position a_on and a_off rotor for which respective phase windings are supplied and subsequently disconnected from an external source. An intuitive understanding of the operating principle of such a motor suggests that the positive torque (Te > 0) , i.e. one in accordance with direction of rotation of the rotor is encountered when the rotor transfers from the position of highest reluctance to the position with smallest reluctance with respect to the teeth of the stator whose winding is supplied. The characteristic positions of the rotor are denoted as unaligned position and aligned position, the latter of which refers to the overlapping of the axis of stator teeth and the one on rotor's teeth. The winding of a given phase should be supplied with a current of an adequate value in the range of this rotation angle, i.e. aon < theta_r = a_off. I.e., the supply should be switched on as defined by angle aon slightly before the unaligned position, while the supply is disconnected (as described by angle aoff) slightly in advance in relation to the instant when a tooth reaches an aligned position. The difference between the angle of the switching on of a power supply to the phase winding and the angle when it’s disconnected is known as conduction angle, which is equal to:
As one can conclude, the above mentioned advance of switching on and off of the voltage for a specific phase of the motor results from the dynamic characteristics of current increase in the phase winding following an instant the supply is switched on and subsequent decay of the current after the supply is disconnected.
Moreover, it’s relative to the rotor's speed, inductance of the windings as well as the control of converter switches. For small rotational speeds the current in the winding increases relatively fast with regard to the entire conduction angle az while the value of the current is controlled as a result of using PWM method. In contrast, for high rotational speeds the increase after switching on and decay of the current after disconnecting the supply comes relatively slowly in the time period which is determined by the conduction angle az since this angular range of the rotor motion is covered in a very short period of time. Additionally, relatively large back EMF is induced in the windings and the increase of the current is enforced only by the difference in voltage between the supply voltage u for a given phase and the back EMF eb. As one can see, the control of the switch on angle aon and the conduction angle az forms the basic method applied in the control and adaptation of characteristics of SRM motor, beside the possibility of controlling supply voltage usually achieved with the aid of PWM method. As a consequence of analyzing the operation of SRM motor one can determine the theoretical conduction angle for a single phase e - denoted as stroke angle, which results from the number of phases and teeth of the rotor under the assumption of a separate conduction of the windings. In a typical SRM the difference in numbers of a stator and rotor teeth per pole pair is 2, i.e. Zs - Zr = 2p. Hence the stroke angle e, as the smallest... angular distance between closest stator and rotor teeth, in a state of alignment occurring for some other pair of teeth, is ...
For a motor with Zs/Zr = 6/4 teeth this gives an angle e = 360°/(3·4) = 30°, while for one with Zs/Zr = 8/6 teeth stroke angle is equal to e = 360°/(4·6) = 15°. The actual value of the conduction angles az is always greater than the stroke angle e as a result of the processes of current increase and decay in the phase windings and, hence, during the operation of the SRM motor there are periods when 2 or even 3 phase windings are in conducting ('ON') state. Since usually the aim is to gain high values of electromagnetic torque, the conduction period is extended within the range of strong attraction of the rotor's tooth by the electromagnet made up by a pair of stator teeth so that the switch off angle aoff only slightly precedes the aligned position. For this reason the process of current decay in a given phase is accelerated as much as possible to avoid negative torque values. This occurs after the rotor reaches the position determined by the angle aoff as a result of energizing this winding with is reverse voltage u that supplies the phase and, thus, causing the energy return to the source. Such a capability has to be secured through the commutation system of the phases of SRM motor.
The basic system of the power supply and commutation of a single phase winding of SRM involves an asymmetric transistor /diode H bridge shown.
Since SRM is a reluctance motor and the direction of the torque is not relative to ... the direction of the current flow through the phase winding, the commutator bridge does not need to facilitate current flow through the winding in both directions and it’s sufficient to apply two power transistors and two diodes to ensure energy supply and energy return to the source.
+-+-+ A typical commutation H-bridge circuit for switching current of a single phase of a SRM
Over the period when the winding is in supply state from the source both transistors T1 and T2 are in the ON state. This occurs for the angle of the rotation in the range from aon to aoff and when simultaneously there is a increase of the cur rent in the cycle of the PWM regulation of the voltage. However, in the section of PWM cycle when phase current decreases, only one transistor and one diode in H bridge are in ON state. This could be transistor T2 and diode D2 of the bridge and in this case we have to do with a decay of the current in the circuit in which these elements short a phase winding. In contrast, after the rotor reaches position aoff, both transistors are switched off and the current in the winding is closed in the circuit formed by two diodes D1 and D2 and the power source. This direction of the current flow determined by the diodes results in the return of the energy stored in the electromagnetic field into the source accompanied with a rapid decay of the current in the winding. We can also consider an option of mechanical energy con version over this period and it’s only relative to the actual sense of electromagnetic torque and its value. However, for the purposes of rough explanation of the operating principle of the motor we can assume that in the vicinity of the aligned position of the rotor the electromagnetic torque is small and, as a result, the return of the energy consists only in the return of the energy stored in the electromagnetic field. The following figures contain an illustration of the operation of the commutation system for a single phase winding, for the respective low rotational speed, i.e. for n = 600 [rev/min], for the mid speed ranges, i.e. 1600 [rev/min] and for higher speeds, e.g. for n = 3000 [rev/min]. The variable deciding on the switching sequence is the value of the current in this winding and it’s responsible for voltage switching between the values of u and 0 - i.e. performing so-called 'soft-chopping'. After the completion of the switching cycle in a given phase, i.e. after the rotor angle exceeds position aoff, both transistors are switched off and the current in the winding decays quickly and recuperation of energy, due to the supply with -u voltage, takes place.
+-+-+- Current commutation during a single conduction cycle of a phase winding with a current limitation, for a low speed range of SRM.
+-+-+- Similar commutation as presented, but for a medium speed range of SRM.
+-+-+- Current commutation, but for a high speed range. Current regulation is not possible in this case.
The diagram of the commutation system presented enables one to control the current in each of the phases separately. It’s possible to apply a more economical system, i.e. one enabling the application of a smaller number of power electronic switches in the design of the commutation system. One of such examples is found for a motor with m = 4 phases or a greater even number of phases. The control of the switching sequence of the phases is based on an assumption that during the operation of the motor we don't have to do with simultaneous conduction in more than two phase windings.
+-+-+- Branch-saving commutation system for m = 4 phase SRM machine.
In the presented example we exclude one branch of the converter per four branches in two complete H bridges, which means that the number of components decreases by 25%.
+-+-+- Switch saving commutation scheme with one general T0 switch and single switches for each of phase windings.
A system that goes even further in terms of the economical use of electronic components is presented. Each of the phases apply a single transistor and there is one transistor T0 that is common to them all. This system offers the possibility of reducing commutation losses; however, practically it does not permit recuperation of energy of the phase that is being in the switching off state, because it requires the transistor T_0 to be switched off. In this case we have to do with the decay of the current in the closed circuit of this phase winding across phase diode and transistor T_0. Considerable opportunities in terms of the improvement of the operation in the range of high rotational speed is offered by the system, in which phase windings containing coils situated in the opposite stator teeth have available clamps to supply each coil separately. It means that the phase winding can be effectively divided into two equal parts. In this case it’s possible to apply an alternative, in-series or parallel supply of the two parts of the phase winding and, as a result, considerably accelerate the increase and decay of the current in the winding and, additionally, increase the range of the speeds for which it’s possible to control the current. Such system configuration involving division of a winding and enabling series power supply for lower speeds and, concurrently, parallel connection at higher speeds is presented.
+-+-+- Commutation scheme of a divided SRM phase winding for changeable supply configuration of both parts.
This system for a single phase of the motor consists of two H bridges that sup ply the halves of the winding and an additional transistor T5 and diode D5 that connects these bridges. During the period when current increases after the rotor gains aon position and after it obtains the position aoff associated with the termination of the phase supply, transistor T5 is switched off and the two halves of the phase winding 1b and 1b are connected to full supply voltage u. This fact combined with two times lower inductance result in considerably faster current in crease after it’s fed as well as faster decay after the phase is disconnected as a result of switching off all five transistors T1...T5. At the beginning of a cycle, after the required value of the current is reached, transistor T5 connecting the two bridges is switched on and the winding halves are connected in a series to form a single phase winding. Within a single cycle of the supply the switching of the part phases to parallel and, subsequently, to series supply can be performed several times thus increasing the range in which it’s possible to control the current in the motor. For the case when after the switching from the parallel to series connection the currents in the two halves are not equal the currents in them have to be balanced and the surplus of the current in one section of the winding re turns through one of the diodes - D2 or D4. As it was indicated by computer simulations and the operation of such experimental set-up, the application of series-parallel switching of the winding halves in a two-phase motor (m = 2) has led to an increase of the rotational speed by 80% under rated loading and the rated current has not been exceeded.
+-+-+- A single cycle of energy conversion in SRM. T_ is co-energy conversed from magnetic to mechanical form, T_f is magnetic energy recuperated to a source in a diode conduction period of the current decay.Basics: The section is devoted to Switched Reluctance Motor (SRM) drives.
Firstly nonlinear magnetizing curves of SRM are presented and their importance for motor's operation is discussed. The model presented in the section takes into account these nonlinear characteristics depending on phase current and rotor position angle, but ignores mutual magnetization of phases. The magnetization curves are regarded in a specific and original way as a product of nonlinear functions de pending on magnetic saturation and rotor position angle. This approach seems to be useful as it enables one to analyze the influence of particular construction elements on characteristics of a motor. In consequence mutual inductances of phases are disregarded, but their actual influence is presented for two typical SRMs, and proved to be marginal. Several problems of SRM operation and control are presented based on mathematical models and results of computer simulations. Among others they are: determining a pulse sequence for starting, direct start up with cur rent limitation, breaking and a comprehensive discussion of generator operation conditions. The problem of regulation parameters fitting is also presented, considered from a point of view of gaining possibly high efficiency and low torque ripple level. As far as control of SRM is concerned there is sliding mode control discussed as well as current control and DTC with an aim to minimize torque pulsation at various states of operation. Besides, there is the problem of a control with and without position/speed sensors presented and state observers application discussed that enable this kind of control.