Fig. 1. 6/4 Switched Reluctance Motor Geometry
Key words: Switched reluctance motor, finite element method, static characteristics
ABSTRACT
In this study, performance analysis and simulation of 6/4 - switched reluctance motor (SRM) is presented. Prediction of performance analysis of SRM is quite complex, because of its highly non-linear structure and the complex influences between the motor parameters and excitation. In this paper finite element method (FEM) analysis of 6/4 SRM is presented to calculate the static characteristic. On the basis of the FEM model, flux-current-position, torque-position curves are gathered which are the fundamental characteristics of SRM and have significant influences on motor performance. In addition calculated FEM results are used as look-up table for the simulation of SRM. Accurate results are achieved with the literature, for different firing excitation SRM performance can be analysed.
I. INTRODUCTION
The reluctance variable principle is known from the first electromagnetic experiments. The researches for electrical machines producing a continues rotation with the reluctance principle started at the nineteenth century and these machines are named as electromagnetic machines. At 1840 W.H.Taylor presented a electromagnetic machine which is the basis for today’s SRM. After this study further approaches and studies are presented. Unfortunately, because of its highly inductive current, problems at designing a accumulators for power supply, high torque ripple, heat problems and commutation problem at supply current had made SRM unattractive for industrial applications and academic researches in these days.. Since 1960’s this machines has reappeared with the development of semiconductor switches. With the availability of inexpensive fast electronic power switches and high performance digital controllers, SRM performance and control strategies are improved, leading to widespread application area in the industry.
Current interest on the subject is stimulated mainly by the contributions made by Lawrenson , in which they describe the fundamental design considerations of high efficiency SR motors such as the number of stator and rotor poles, the rotor pole pitches, suitable configuration and rating of drive circuits. Davis and Miller make other noticeable contributions, on different inverter circuits and microprocessor control strategies.
Earlier analyses of SRM performance were based on a linear or an idealised non-linear model of magnetic circuit. The linearity is made generally in the magnetic material, simplified magnetic structure and idealised current waveforms. Although such idealised approximations of the non-linear field condition may be convenient and useful for qualitative analysis of drive performance and estimating the design parameters and circuit ratings. But they lacked sufficient accuracy for further refining switch control or magnetic design. Because, SRM usually operates at magnetically saturated regions where as affecting the performance of the machine. In order to overcome these problems, finite element method is the ideally suited to handle the highly non-linear magnetic structure of SRM.
This paper deals with the detailed magnetic analyses of SRM and gathering its static characteristic. In addition the FEM analysis results are used as look-up table for the simulation with numerical solution of non-linear differential equations describing SRM.
II. BASICS OF OPERATION AND STRUCTURE
The SRM is a variable reluctance step motor that is designed for converting energy efficiently. The motor is doubly salient with different number of rotor and stator poles. Torque is produced with the attraction of rotor poles to the excited stator phase according to reluctance principle. Furthermore, the torque produced by the machine is independent of the polarity of the phase current. Then the structure of the converter can be simplified and eventually the number of power semiconductor switches can be reduced per phase (Fig 1, fig 2).
The SRM has rather simple construction; the stator consists of salient poles which carries the excitation windings wounded across the poles. Each opposite pole is connected in series to generate N-S poles. Its rotor has no winding, brush or magnet. Both stator and rotor is made of laminated steel for to decrease core losses. Its simple and robust structure makes it attractive for variable speed applications. For motoring operation a stator phase is excited when a pair of rotor poles is approaching and it must be turned off before rotor and stator poles actually come into alignment. For continuous rotation a position feedback is required. The SR driver has additional advantages compared with the conventional adjustable ac or brushless dc drives (including permanent magnet motor drives). Beside these advantages, there are some important disadvantages of SRM. Torque produced in SRM is naturally pulsed, because of its operation principle and magnetic structure. These torque ripples contribute to mechanical wear and acoustic noise especially at high speeds. The ripples can be reduced, and performance of the SRM can be improved initially through modifying geometric parameters using FEM analysis. Further reduction can be accomplished by using appropriate control with the SRM.
Fig. 1. 6/4 Switched Reluctance Motor Geometry
Fig. 2. SRM Classical Inverter Circuit
When it comes modelling of the SRM, the outward simplicity of its construction is deceiving because the magnetic structure is naturally non-linear. For improved energy conversion, the motor is operated in saturated region by making airgap narrower. Furthermore static characteristics such as static torque, flux linkages, inductances are functions of both rotor position and excitation current. In a fixed voltage both current and torque are affected by switching angles. The shape of the resultant current is dependent on the conduction interval and the stator phase inductance waveform or rotor position. Also average torque is a function of iron geometry, current pulse and level.
III. FEM ANALYSIS
The early analyses of SRM performance were based on a
linear or an idealised non-linear model of the magnetic
circuit. Although these approximations are useful for
certain analyses of drive performance and estimating
parameters. But they lack of giving information in
switching control strategy or magnetic circuit design.
Because SRM usually operates at saturated region, which
increase the efficiency and torque.
The accurate characterisation of SRMs is difficult because
of the large change in inductance between unaligned and
aligned positions and the high level of magnetic
saturation. In order to characterise the machine
experimental and theoretical studies are performed in the
literature. In experimental studies basically two ways are
mostly used.
1) Applying a sinusoidal voltage of known rms
value and frequency and measuring the resulting
rms current. Knowing the winding resistance, the
flux linkage can be calculated.
2) Using U = Ldi/dt with a constant voltage applied
and measuring the rate of rise current. From this,
flux-linkage can be calculated.
In both of this measurement techniques absolute accuracy is quite good. However distortion of applied voltage and distortion of resultant current makes this methods unsuitable at saturating regions. In this study we prefer to analyse the SRM using FEM.
Finite element methods are widely used in the design and analysis of electrical machines, which saves costs and time in the design and practical application procedure. In our FEM program two-dimensional analyse is made for 6/4 1kW SRM (fig1). The magnetic flux in the SRM is determined by computing the magnetic vector potential A, using the non-linear Poisson’s equation
Where ν is the magnetic reluctivity (which is a function of both position and the magnetic flux density) and J is the current density.