SPÍNANÝ RELUKTANČNÝ MOTOR A JEHO VYUŽITIE V TRAKČNEJ APLIKÁCII SWITCHED RELUCTANCE MOTOR AND ITS UTILIZATION IN TRACTION APPLICATIONS SPÍNANÝ RELUKTANČNÝ MOTOR A JEHO VYUŽITIE V TRAKČNEJ APLIKÁCII SWITCHED RELUCTANCE MOTOR AND ITS UTILIZATION IN TRACTION APPLICATIONS

This paper deals with the performances of switched reluctance motor (SRM) and with its utilization in electric traction. The investigation of SRM equivalent circuit parameters by measurement and by finite element method is described. The calculated and measured values of parameters are used in the mathematical model of SRM, which was simulated. The simulation outputs are time profiles of the phase currents, voltages and torque and also the torque/speed characteristic, which can be used for the traction characteristic calculation. The dependencies of the losses and efficiency on the speed are shown. The comparison of performances of induction machine and SRM is shown at the end.


Introduction
The DC series machine had a unique status in electric traction drives in the past because of its natural mechanical characteristic approaches to traction demand. The development of DC choppers with new semiconductor structures has caused DC series machines to be replaced by DC separately excited ones, whose field and armature winding are fed from two independent DC choppers to improve its hard characteristic to the soft one, so it is similar with traction characteristic. However, the development of the semiconductor and control electronics has also caused the spread usage of drives with induction machines (IM). The control techniques of IM, scalar or vector, had been theoretically brought under control and from the simulations point of view many years ago, but the power stresses of inverters and control electronics used in that time did not allow use of high power drives with IM, where electric traction also takes place. Only in the recent development of microcontrollers and semiconductor structures with high reverse blocking voltage and current density has the usage of the IM drives in electric traction been enabled.
They have become a very strong competitor to the DC drives because some advantages of the IM, such as simple construction, lower production costs and price, maintenance-free operation (there is no commutator which is the key part during the DC machine maintenance), and higher power density. Therefore, IM have come to the forefront with DC machines considering the parallel that production costs of the inverter are higher as that of DC choppers. But the IM drive has to be vector controlled to achieve prirodzene dané v jednosmernom stroji, čím sa zvyšujú nároky na riadenie a riadiacu elektroniku. To isté platí aj o tom, že prirodzená charakteristika T ϭ f() IM je v oblasti prevádzkových sklzov tvrdá a preto musí byť výstupná charakteristika pohonu, podobne ako pri cudzobudenom jednosmernom motore, upravená riadením pre trakčné požiadavky. Vektorové riadenie IM má aj nevýhody ktorými sú hlavne závislosť presnosti riadenia od presnej znalosti parametrov stroja, pretože riadené veličiny -tok a moment stroja nie sú priamo merané, ale sú vypočítavané z modelu stroja na základe meraných veličín ako sú prúdy, napätia a otáčky.
Cieľom tohoto článku je poukázať na vlastnosti SRM z hľadiska trakčnej aplikácie, uviesť metódy pre identifikáciu hlavných parametrov SRM, ktoré sú použité v matematickom modeli. Tento model je aplikovaný v simulácii, ktorej výstupom sú priebehy fázo-decoupled flux and torque control of the machine as it is naturally given in DC machines. It increases claim for the controlling and control electronics. Vector control of IM drives also has drawbacks, mainly the dependence of control preciseness on the exact knowledge of the machine equivalent circuit parameters because the controlled quantities -flux and torque are not measured directly, but they are calculated from the machine model based on the measured quantities like currents, voltages and speed.
The power electronics evolution has also started the development of drives, called "modern", although the actuators used in these drives work based on the principles invented in the 19th century. Switched reluctance machine (SRM) is one of them. Its principle of operation was invented in 1838. And just the drive with this machine is becoming a very strong competitor to the drives with IM. SRM has simpler construction and, therefore, lower production costs, higher robustness and lower maintenance demands as the drives with IM. The SRM can work only if it is fed from an inverter, but the inverter of SRM is simpler and, therefore, cheaper than the one used to feed IM. The same conclusion is also valid for controlling SRM. Basically, it is also needed for the SRM operation, but it is simpler as the vector control for drives with IM, because only the values of the phase currents and the switching time, which are speed dependent, are controlled and these non-linear dependencies can be given in table form and put to the microcontroler. The next indisputable advantage of the SRM drive is that it can be controlled in the open speed loop and also sensorlessly in the closed speed loop, which is the up-to-date trend in IM drives. The profile of the SRM torque/speed characteristics (T ϭ f(n)), although it is fed from the inverter, looks similar to traction characteristics. That is why the SRM is becoming a very strong competitor to the IM. On the other hand, we should mention also that the drawbacks of the SRM is the torque ripples, which are given by the teeth construction and phase switching, magnetic noise and speed sensor necessity if the unfailing operation is desired. From the SRM performances point of view mentioned above, the detailed analyses of the SRM used in electromobiles and locomotives are given in [2], [3].
As it was mentioned earlier, the construction of SRM is very simple. It has salient poles on stator as well as on rotor. It is preferable to name these poles as teeth, because the term of pole in the SRM expresses only the physical pole, which means salience on the inner surface of stator and outer surface of rotor. Both the stator and rotor are laminated. The field windings are located only on the stator; the rotor is passive and has a low moment of inertia. Each stator tooth has a field winding on it. The windings of the teeth, which are geometrically opposite, are connected in series, and they create one phase (for example A, Fig. 1a). The cross section area of the three phase m ϭ 3 (m -number of phases), 6/4, which means that the machine has six poles on the stator N s ϭ 6 and four poles on the rotor N r ϭ 6, SRM is shown on Fig. 1a. A two-poles field is created in this machine if the individual phases are switched.
The aims of this paper are to point out the performances of SRM from the traction application point of view and to show how the parameters of the SRM used in its model can be identified. The SRM model, described below, has been used in simulation. The results are time profiles of phase currents i and voltages u; i,

The analysis of SRM parameters
One of the most important parameters of SRM are magnetization curves of flux-linkage( versus current i and rotor position ⌰, given as ϭ f(⌰,i). The equivalent circuit of one phase is in Fig. 2, consisting of winding resistance R f , phase inductance L and induced voltage u i . The important difference between the equivalent circuit of SRM and other motors is that the inductance varies with current and rotor position L ϭ f(⌰,i), which means the inductance depends on two variables. Mutual inductance between phases is very low; consequently, it may be neglected. It is possible to obtain the magnetization curves of ϭ f(⌰,i) by many methods: by static measurement, by finite element method (FEM), or by analytical approach, only when one phase is supplied. The profile of measured values of the investigated motor flux-linkage can be seen on Fig. 3. Values of flux-linkage are presented only for current to 12 A, because it was very difficult to maintain the rotor in the stable position for such a high value of torque if the current was over 12 A. The rotor position was changed by 1 mechanical degree. For higher values of current the flux-linkage has been computed by means of FEM [4]. It is possible to calculate phase
Pretože SRM má vyjadrené zuby na statore aj rotore, počas jeho prevádzky neexistuje ustálený stav, v ktorom má priebeh inductance for a given current and rotor position from flux-linkage. The profile of phase inductance L ϭ f(⌰,i) of investigated SRM computed by means of FEM is shown on Fig. 4. The phase inductance is one of the input parameters of the SRM mathematical model.
The very important position in simulation takes the mathematical description of inductance versus phase current and rotor position. There are two common approaches: 1.

Mathematical model of SRM
One-phase equivalent circuit of the SRM shown above can be described by the equation for the instantaneous value of voltage: where u -is the terminal voltage and u R is the voltage drop due to resistance.
Aby sme mohli získať priebehy prechodových dejov SRM je potrebné riešiť m napäťových rovníc. Pre jednu fázu má napäťová rovnica nasledovný tvar: Ak zanedbáme vzájomné indukčnosti, tak potom môžeme vyjadriť vyvíjaný elektromagnetický moment nasledovne: a súčasne which the current or voltage would have constant value, because the current and flux-linkage are established from zero every stroke depending on speed and on control strategy. Therefore, the fluxlinkage depends on both variables: phase current and rotor position, and its time derivation can be expressed as follows: where -is angular speed of rotor.
As it is known, the product of inductance and current gives the flux-linkage If equation (3) is included, the equation (2) can be rewritten: The first part of the equation u L presents a voltage drop due to inductance, and the second part is induced voltage, which is proportional to the current, angular speed and position variation of the inductance.
To get the profiles of SRM transients, it is necessary to solve m voltage equations. For one phase the voltage equation form is as follows: If mutual inductances are neglected, then it is possible to express a developed electromagnetic torque in this form: and also a) n ϭ 500 min Ϫ1 a) n ϭ 500 rpm b) n ϭ 3000 min Ϫ1 b) n = 3000 rpm Obr. 5 Simulované priebehy napätia, prúdu a spriahnutého toku Fig. 5 Simulated profiles of voltage, current and linkage flux kde J -je moment zotrvačnosti všetkých rotujúcich častí a T l je záťažový moment.
From the principles of SRM operation follows, that it is necessary to know an actual rotor position ⌰, which depends on the angular rotor speed : ⌰ ϭ ͵dt (8) To solve all given equations, it is necessary to know terminal voltage, winding resistance and moment of inertia, and the values of inductance, depending on the phase current and rotor position. To set the inductance values, approach No. 1, described in chapter 2., has been used. A mathematical model has been solved by means of simulation language MATLAB/SIMULINK, solving differential equations on the basis of numerical mathematical method Runge-Kutta.
In Fig. 5 simulated phase current, voltage and flux-linkage profiles for lower speed (Fig. 5a), n ϭ 500 rpm, and for higher speed n ϭ 3000 rpm (Fig. 5b), can be seen if load torque was equal to rated torque 11.8 Nm. In Fig. 6 measured voltage and current profiles for the same conditions as in simulations can be seen. On the basis of good coincidence simulated and measured values ( Fig. 5 and 6), the simulation can be used also for SRM design and parameters optimization. More detailed analysis of the current, voltage and other variables profiles for higher and lower speed is made in [7].

SRM Losses and Efficiency
As mentioned in the introduction, in the process of the traction drive choice the losses and efficiency must be taken into account. Generally, in electrical machines four kinds of losses are
Ak budeme zvyšovať rýchlosť motora otáčkovým regulátorom pri menovitom napätí a uhol vodivosti bude maximálny a konštantný, tak moment bude klesať so štvorcom rýchlosti, čomu zodpovedá tretia časť charakteristiky T ϭ f() od bodu P smerom doprava. Podobne ako v druhej časti charakteristiky aj v tejto časti considered: winding losses ⌬P j , iron losses ⌬P Fe , rotational losses and additional losses ⌬P ad . The Fig. 7 illustrates the profile of the losses of the investigated SRM, determined for various values of speed, if torque has been kept on the constant value T ϭ 11.8 Nm by means of hysteresis current controller, until technical condition allowed it. The analysis has been made by means of program PC-SRD, VERSION 4, seen in [5]. As seen in the profiles, until the torque can be kept in the constant value (Fig. 11), winding losses are not changing. The losses are given by the profiles of current, depending not only on the load, but also on the speed of rotation. In opposite, at the higher speeds the RMS value of the current decreases and, therefore, also decreases winding losses. Iron losses increase with increasing speed, because the time changing of flux-linkage also increases. Rotational losses also increase with speed. In Fig. 8 there is an efficiency/speed curve calculated on the basis of losses from Fig. 7.

Torque/speed characteristic of SRM
As mentioned in the introduction, the inherent form of the SRM torque/speed characteristic (Fig. 9) is similar to traction characteristic. This characteristic consists of three basic parts.
In the first part a constant torque can be seen. It can be obtained by keeping the phase current on the constant value by a suitable kind of controller. This control is possible to carry out only in the limited speed range, maximum until the point B. At point B, the speed B , is the highest speed at which a maximum current can be supplied at a rated voltage, with fixed firing angles ⌰ 0 , and commutation angles ⌰ C (Fig. 6a). The conduction angle or dwell angle ⌰ D ϭ ⌰ C Ϫ ⌰ 0 has constant value.
In the second part of the torque/speed characteristic, between the point B and P, the control mode on the constant power (P ϭ T) can be seen (till the point P). This part of the torque/speed characteristic is possible to obtain by increasing of the conduction angle ⌰ D . The developed torque decreases, because the value of phase current decreases [7].
To get the torque/speed characteristic T ϭ f(n) of the investigated SRM, it was necessary to use the SRM mathematical model, shown in chapter 3 and in block diagram, in Fig. 10. The block diagram consists of: 1) the PID controller, 2) the mathematical model of the converter (the voltage drop due to semiconductor elements is not taken into account), 3) the SRM mathematical model, divided into three blocks: a) the block V.E. represents the voltage equations for each phase (5), b) the block T.E. represents torque equation (6), and c) the block represents speed equation (7), and from the block for calculation of the real rotor position. As it is seen in Fig. 10, the difference between required and real speed e enters the PID controller. The output of the PID controller is the required value of the current. In the converter the real and required values of current are compared, and on the basis of their difference and according to the rotor position the voltage is applied to the individual phases.
If the output torque/speed characteristic is required, it is necessary to take into account the firing angles and commutation angles, because the profile of the torque/speed characteristic depends also on the conduction angle ( Fig. 9), along which an internal torque is developed (Fig. 6a). In [1] an absolute torque zone is defined, in which a non-zero torque is produced by the given phase. In a symmetrical motor this zone is given by the value of the ratio /N r . In here investigated SRM it is 22.5°mechanical, because N r ϭ 8. Further it is defined an effective torque zone, which represents an angle, along which one phase produces a torque comparable with the rated one. This angle corresponds to this pole arc from the both overlapping poles, which is smaller. In this case the smaller is a stator pole, and its value is 15°mech. Therefore, the effective torque zone of here investigated SRM is 15°mech.

Záver
Článok sa zaoberá vyšetrovaním parametrov a vlastností SRM z hľadiska jeho využitia v elektrickej trakcii. Popísané sú parametre In Fig. 11 the SRM torque/speed characteristics for the conduction angles of 22.5°and 15°can be seen. These characteristics have been given as outputs of the simulation. For the comparison a measurement has been made, at which the conduction angle set in the converter by the producer was 15°, and the load torque was rated one. The converter has limited the speed of the investigated SRM, and therefore, it was not possible to increase them in the values used in simulation. As seen in Fig. 11, the profile of the SRM torque/speed characteristic is similar to the traction one and corresponds to its general characteristic shown in Fig. 9. For the certain traction application it is necessary to convert the torque on the traction effort, taking into account all traction resistances and the angular or rotating SRM speed convert to the speed of the traction vehicle.
In the end a comparison of some SRM and IM parameters are shown in the table 1., according to [9]. The motors with equal rated power and rated speed have been compared. Their catalogue data are as follows: m ϭ 3, totally closed, cooled by the fan, the insulation class F. Table 1.
It can be seen from the comparison that in spite of the higher magnetizing current and lower power density, the SRM efficiency is raised by 4 % in comparison with the IM drive.

Conclusion
The paper deals with the SRM parameters and performance investigation from the point of view of its application in electrical Obr. 11. Charakteristiky SRM T ϭ f(n) Fig. 11
traction. The methods of the important equivalent circuit parameters investigation are presented, mainly L, ϭ f(⌰,i). A mathematical model has been created, the equations of which are solved in the MATLAB/SIMULINK program. The time profiles of the current and voltage for low and higher speed have been compared with measured ones. On the basis of block diagrams and mathematical model, the torque/speed characteristics T ϭ f(n) for various conduction angles have been calculated and compared with the measured ones. The paper has shown a mutual correspondence between SRM torque/speed and traction characteristics. In the end, a comparison of some SRM and IM parameters have been given. From the results it can be said that SRM is suitable for traction application and can replace at present used IM.