硬件测量电感

2196 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 57, NO. 10, OCTOBER 2008 Experimental Investigations on Computer-Based Methods for Determination of Static Electromagnetic Characteristics of Switched Reluctance Motors R. Gobbi, N. C. Sahoo, and R. Vejian Abstract—Because of the doubly salient structure of the switched reluctance motor (SRM) and its intentional operation in deep magnetic saturation for higher power density, its static electromagnetic characteristics are highly nonlinear functions of rotor position and phase current. This makes the accurate ex- perimental measurement/determination of these characteristics a difficult task. This paper presents a comprehensive discussion and analysis on the different (most practiced) computer-based methods for the determination of these characteristics for a typical SRM. A digital signal processor (DSP)-based completely auto- mated SRM drive system has been used for these studies. For all the offline computations, user-friendly MATLAB/Simulink-based models have been developed. The experimental methods, computa- tional models, measurement results, and appropriate postmortem discussions for the determination of static flux linkage, inductance, and electromagnetic torque characteristics for an 8/6 four-phase SRM are reported. Index Terms—Flux linkage, inductance, measurement, switched reluctance motor (SRM), torque, uncertainty. I. INTRODUCTION R ECENTLY, the switched reluctance motor (SRM) hasreceived great attention due to its notable features, i.e., simple construction, low cost, easy control, high efficiency over a wide range of speeds, unidirectional power converter, fault- tolerant robust structure, and ability to run in hostile conditions [1], [2]. However, owing to the doubly salient structure and operation in magnetic saturation, its modeling and analysis is difficult since its flux linkage, inductance, and torque possess highly nonlinear relationships with rotor position and phase current. Thus, to analyze and predict the motor’s performance, good knowledge of its electromagnetic characteristics is es- sential. The finite-element analysis methods have been used in [3]–[5] for the computation of electromagnetic characteris- tics. These computationally expensive methods suffer from the effects of inaccurate modeling of nonuniform iron structures, Manuscript received October 31, 2007; revised February 22, 2008. R. Gobbi is with the Faculty of Engineering, Multimedia University, Cyberjaya 63100, Malaysia. N. C. Sahoo was with the Faculty of Engineering and Technology, Multi- media University, Melaka 75450, Malaysia. He is now with the Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721302, India (e-mail: ncsahoo@ee.iitkgp.ernet.in). R. Vejian is with the Faculty of Engineering, Multimedia University, Cyberjaya 63100, Malaysia, and also with Metronic Engineering Sdn Bhd, Shah Alam 401150, Malaysia. Digital Object Identifier 10.1109/TIM.2008.922095 and they eventually need experimental verification. A number of measurement methods have been proposed for this purpose [6]–[15]. This paper has been presented from the following perspec- tive. Out of the three electromagnetic characteristics, i.e., flux linkage, inductance, and torque, standard methods for the fairly accurate measurement of flux-linkage profiles have been de- tailed in much of the literature [6]–[15]. Among these, the dc excitation method [6] has almost been universally used with good results. A more difficult task of inductance measurement may be experimentally performed, or it may be derived from the flux-linkage characteristics. In either case, accuracy is a point of concern. The static torque characteristic measurement is fairly straightforward with the use of torque transducer. Like inductance, the torque profiles can also be computed from flux-linkage characteristics. Thus, it is of great interest and importance to have a comparative/investigative study of the determination of inductance and torque profiles by direct measurement methods as well as deriving them from flux- linkage characteristics. From the point of view presented above, first, two well- known methods for the measurement of flux-linkage character- istics are briefly presented, followed by the results of one such widely used method on a typical SRM. Then, the major empha- sis of this paper is focused on comparative evaluations of in- ductance and torque profiles measured from direct experimental procedures and computationally derived from the flux-linkage characteristics using MATLAB/Simulink-based computational models. This paper is organized as follows. Section II briefly explains the basic principles of operation and the SRM dynamic model. A brief description of the digital signal processor (DSP)- based SRM drive system is presented in Section III. The experimental results of flux-linkage measurement are discussed in Section IV. Section V deals with the determination of induc- tance profiles by experiments and by computations from flux- linkage profiles. The static torque characteristics (measured/ derived) are presented in Section VI. An approximate analysis on measurement uncertainties and error estimation is presented in Section VII. Section VIII concludes this paper. II. BASIC PRINCIPLES OF OPERATION AND MATHEMATICAL MODEL OF SRM The SRM has a salient pole stator with concentrated coils and a salient pole rotor without magnets or conductors. Its basic 0018-9456/$25.00 © 2008 IEEE GOBBI et al.: DETERMINATION OF STATIC ELECTROMAGNETIC CHARACTERISTICS OF SRMs 2197 Fig. 1. (a) Doubly salient structure of 8/6 SRM with power converter feeding power to one stator phase. (b) Nonlinear flux-linkage characteristics showing the magnetic field energy and coenergy. principles of operation can be found in [1]. A four-phase (8/6) motor is used here. All the phases are assumed to be identical, and interphase magnetic coupling is neglected. Fig. 1(a) shows the cross-sectional view of the doubly salient structure of a typical 8/6 SRM along with the commonly used unipolar power converter feeding power to one of the phase windings. The (reluctance) torque is produced in this machine by the tendency of the rotor poles to pull into alignment (minimum reluctance/maximum inductance position) with the stator poles of the excited phase. The number of stator poles is different from that of the rotor so that the motor can generate torque at any rotor position. The direction of current in the phase winding is immaterial, i.e., it is unipolar, since the torque is always toward the aligned position, irrespective of the direction of current. Thus, a motoring toque is produced in the direction of increasing inductance. To control an SRM means to control the stator phase excitation sequence according to rotor position. The complete behavior of SRM can be explained in terms of a set of flux-linkage/current/rotor angle characteristics and flux- current trajectory. These characteristics represent the variations of flux linkage with current for a set of rotor angles from unaligned to aligned position, and they heavily depend on the magnetic circuit. Because of the doubly salient structure, such characteristics are highly nonlinear, as shown in Fig. 1(b) for one of the phases, where θ1, θ2, and θ3 are the rotor angles at aligned, unaligned, and intermediate positions, respectively. Fig. 1(b) clearly shows how the motor enters into magnetic saturation for higher currents as the rotor moves from the unaligned to the aligned position. Because of these nonlinear characteristics, the current, flux linkage, and torque waveforms under normal operation are nonsinusoidal in space and time. This motor is intentionally operated under magnetic satura- tion for higher torque output and energy efficiency [16], [17], [19], [20]. The higher energy conversion is achieved because the deep magnetic saturation makes the stored magnetic field energy (Wf ) to be less than the coenergy (Wc) [as shown in Fig. 1(b) for the aligned position θ1]. Because of double saliency and magnetic saturation, the phase inductance Lk(k = 1, . . . , 4) varies with the rotor po- sition θ and current ik. The electrical circuit for each phase Fig. 2. Electrical circuit of each stator phase winding in SRM. is shown in Fig. 2. The dynamic equations governing the operation of SRM are dϕk dt = vk −Rik, k = 1, . . . , 4 (k = phase index) (1) dθ dt =ω (2) dω dt = Tt − TL J − B J ω; Tt = 4∑ k=1 Tk (3) where R is the phase resistance, ϕ is the flux linkage, ω is the motor angular speed, J is the moment of inertia of the motor drive system, B is the viscous friction coefficient, T is the phase electromagnetic torque, Tt is the total motor electromagnetic torque, v is the applied voltage, and TL is the load torque. The phase electromagnetic torque is computed from the spatial derivative of the coenergy (Wc) as [16] Tk(θ, Ik) = ∂Wc(θ, ik) ∂θ ∣∣∣∣ ik=Ik Wc(θ, Ik) = Ik∫ 0 ϕk(θ, ik)dik. (4) If there is no magnetic saturation, the magnetization curves would be straight lines. Under these circumstances, at any rotor position θ, the coenergy and instantaneous torque will be given by Wc(θ, Ik) = 1 2 Lk(θ)I2k Tk(θ, Ik) = 1 2 dLk(θ) dθ I2k . (5) 2198 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 57, NO. 10, OCTOBER 2008 Equation (5) also illustrates the fact that the sign of the generated torque is independent of current polarity. However, since the motor is intentionally operated under deep magnetic saturation for higher power density, resulting in highly non- linear magnetization characteristics, there is no unique closed- form mathematical expression as in the case of other electrical machines, and the solutions of the dynamic equations need thorough knowledge of ϕ and T as functions of rotor position and phase current. Thus, it is necessary to have an accurate knowledge of the motor’s electromagnetic characteristics for correct prediction and analysis of the motor’s performance. Moreover, a good control strategy can be developed only if the motor’s accurate characteristics are available. This necessi- tates accurate experimental measurement/determination of the SRM’s electromagnetic characteristics. Several techniques for the measurement of these characteristics have been proposed in the literature. The purpose of this paper is to have comparative experimental investigations/evaluations on the most practiced computer-based methods. For this purpose, a DSP-based SRM drive system has been set up. III. DSP-BASED SRM DRIVE SYSTEM The purpose of this paper is to have a comparative evaluation of the most practiced computer-based methods for the deter- mination of the electromagnetic characteristics of an SRM. A DSP-based SRM drive system, using dSPACE ACE1103, has been set up for this objective. The dSPACE-based SRM drive system offers distinct advantages and is often a necessity for some specific test conditions required for the evaluation of these characteristics, as follows. 1) For the measurement of all the characteristics, the motor should be firmly installed on a test bed. The magnetiza- tion characteristics are determined at a set of (fixed) dis- crete rotor positions between the unaligned and aligned positions of a stator phase. This is achieved by a locked rotor mechanism with gear box arrangement and a timing belt to easily and precisely change (by fraction of a me- chanical degree) the rotor positions manually. Moreover, a high-precision 12-bit absolute encoder is installed for accurate rotor position measurement with good resolu- tion. The DSP system used here has the necessary digital I/O interface and MATLAB/Simulink interface package, which are easily used to correctly calculate the rotor angle from the 12-bit encoder digital data and display it in dSPACE ControlDesk. 2) The DSP system provides easy and fast acquisition of phase voltage and current signals. 3) As MATLAB/Simulink computational models are used for all offline computations for the determination of characteristics in this paper, the dSPACE system with its own MATLAB/Simulink interface package becomes handy for these purposes. No separate MATLAB soft- ware package is required. 4) For the measurement of static torque characteristics, the dSPACE system captures the torque signal, by its A/D converter (ADC), from a torque transducer mounted on the shaft of the SRM and easily displays its numerical value on the ControlDesk along with the corresponding rotor position and phase current (also sampled by ADC), which are stored and later used to plot the complete set of characteristics through its MATLAB graphics. This facilitates an easy measurement process. 5) As discussed in Section V, one of the methods for inductance measurement is by the chopped current method, where one phase of SRM is required to carry some desired level of current by pulsewidth modulation (PWM) chopping control. The PWM control of the bridge power converter feeding power to SRM can be easily carried out by the real-time workshop (RTW) of the dSPACE system, which has in-built provisions for the generation of PWM signals. 6) For the evaluation of measured static magnetization char- acteristics under dynamic conditions, it is necessary to run the motor under closed-loop speed control, which is again easily performed by RTW of the dSPACE system with a control program using MATLAB/Simulink. The phase voltage/current signals are sampled by the voltage and current sensors interfaced to the DSP for the calcula- tion of dynamic flux linkage. Further, for the calculation of dynamic flux linkage at higher currents under closed- loop speed control, it is necessary to apply load to the motor, and this can be easily performed by means of a loading unit connected in the DSP-based SRM drive system built for these studies. The schematic diagram of the DSP-based SRM drive sys- tem is shown in Fig. 3. The drive system mainly consists of two subsystems. The first subsystem is the mechanical system comprising the SRM (also a part of electrical system), absolute encoder, torque meter, gearbox/rotor locking system (used for measurements only), and loading unit (used to load the motor in closed-loop speed control). The second subsystem is the electri- cal and data acquisition system comprising the dSPACE kit and other electronic interface circuit boards. Brief explanations of the major components of these two subsystems are given here. 1) SRM: The SRM used in this paper has been manufac- tured by Rocky Mountain Technologies, USA. Its model number is SR165M, with the manufacturer specifications listed in Table I. 2) Absolute Encoder: The position encoder chosen for this project has been manufactured by Hengstler (model: AC58/0012EK.42PGB). It is a 12-bit single-turn encoder (resolution = 4096) and requires 10–30 V dc supply voltage. It generates gray code bits to minimize the error during transmission. The generated gray code signal is fed to a digital I/O using 12 pins (IO0 to IO11) of the CLP1103 connector in the dSPACE system. The signal is then manipulated using the MATLAB/Simulink model to obtain the rotor angular position. 3) Torque Meter: The torque meter used here measures bidirectional static and dynamic shaft torque, speed, and shaft power. It is installed between the SRM and the loading unit. The device is manufactured by Himmelstein Technology, USA. The model suitable for this application is MCRT 49001 V (1–2) CFA. The full-scale torque rating GOBBI et al.: DETERMINATION OF STATIC ELECTROMAGNETIC CHARACTERISTICS OF SRMs 2199 Fig. 3. Schematic diagram of the DSP-based SRM drive system using dSPACE ACE1103. TABLE I NOMINAL PARAMETERS OF SRM (AS PROVIDED BY THE MANUFACTURER) for this torque meter is 11.29 N ·m with speed rating of 15 000 r/min. 4) Loading Unit: This is a compact ac-synchronized servo machine for driving, stopping, and braking of the SRM. It is coupled through the torque meter to the SRM and is capable of producing a maximum load torque of 10 N ·m. 5) Rotor Locking System/Gearbox: The rotor locking system consists of two metal plates. The first metal plate with a timing belt pulley is free to rotate. This metal plate is coupled to the motor shaft (or torque meter shaft during torque measurement), and it has four slots for 18-sized bolts at the periphery to be tightened using spring washers and nuts. The bolts are welded to the second metal plate that is made static. The pulley is coupled to a gearbox with a teeth ratio of 1:250 through a timing belt. This system is used only during the measurement process. 6) ACE1103 (dSPACE System): This is an advanced DSP control kit specially manufactured (by dSPACE, Germany) to facilitate university laboratories. ACE1103 consists of a DS1103 PowerPC 604 e/400 MHz controller board, 2-MB random access memory, 128-MB data log- ging memory, PX4 expansion box with high-speed serial host interface (consisting of DS814, PC-side PCI bus DS817, and optical cable), and CLP1103 connector/LED panel. The CLP1103 has been included for easy access to external hardware connections. The system works under the ControlDesk as the main platform. The control algo- rithms are developed using MATLAB/Simulink, and real- time hardware is accessed using the real-time interface blocksets provided by dSPACE. 7) Other Interface Circuits: There are six other electronic circuit boards that have been designed and developed. These are the current and voltage filter circuits (calibrated at 0.532 V/A and 16.667 mV/V, respectively), insulated- gate bipolar transistor driver circuits, PWM interface circuits, current and voltage sensor circuits, and a power supply card. Four asymmetrical bridge inverters are used in this drive system to provide power to the SRM. Fig. 4 shows a photograph of the DSP-based SRM drive system built at the Machines and Drives Laboratory of Multimedia University, Cyberjaya, Malaysia. The procedures for the deter- mination of static electromagnetic characteristics are discussed in the following sections. Since the various phases of SRM are identical to each other, only one phase is chosen for all the measurements, and thus, the phase index k is dropped for brevity. The characteristics for other phases are determined with appropriate phase shifts. IV. FLUX-LINKAGE MEASUREMENT Broadly, there are two main methods used for flux-linkage measurement in SRM, i.e., the dc excitation method [6], [8], [9] and the ac excitation method [7]. In the dc excitation method, the stator is energized by a dc voltage, when the rotor is mechanically locked at a desired position (θ), and the in- stantaneous phase voltage and current are measured [6]. The flux linkage is computed using (1) as ϕ(θ, I) = ϕ(0) + tI∫ 0 (v −Ri)dt; θ is fixed (6) 2200 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 57, NO. 10, OCTOBER 2008 Fig. 4. DSP-based SRM drive system. Fig. 5. Circuit for the measurement of phase resistance. where ϕ(0) is the initial flux linkage (at zero current), R is the phase resistance, and tI is the time instant when the current magnitude attains a value of I . In SRM, due to the absence of permanent magnets, ϕ(0) = 0. In the ac excitation method [7], a search coil is mounted on a stator pole, and a sinusoidal voltage is applied to the phase winding with the rotor being locked at a position. The flux linkage is calculated by measuring and integrating the induced electromotive force of the search coil, and then, the flux-linkage profile can be derived by joining the vertices of hysteresis loops obtained at various ac current amplitudes at fixed rotor position. Both methods yield reasonably accurate results; however, the ac method is time consuming. Therefore, the dc excitation method is widely used. To use (6), the resistance R should be known, and it should first be measured before going for flux-linkage measurement. A. Me