898 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 33, NO. 4, JULY/AUGUST 1997 A Comparison of Spectrum Estimation Techniques for Sensorless Speed Detection in Induction Machines Kevin D. Hurst, Member, IEEE, and Thomas G. Habetler, Senior Member, IEEE Abstract— This paper compares digital spectrum estimation techniques which can be used to extract speed information from rotor slot and eccentricity harmonics contained in the stator current. In previous work, speed-related current harmonics have been shown to improve the performance of existing back-EMF- based sensorless schemes, since these harmonics are parameter independent and exist at virtually any nonzero speed. Digital fil- tering, however, requires a minimum data sampling time in order to achieve the desired resolution. The contribution of this paper is to determine the optimal method for accurately extracting the speed-related harmonics in the least amount of time. Several digital signal processing algorithms are investigated, including the fast Fourier transform and other traditional methods, as well as parametric techniques which can provide improved spectrum estimation for short data records. Each approach is evaluated on the criteria of accuracy, robustness, and computation time given a short data record. Index Terms— Induction machine drives, sensorless control, spectrum estimation. I. INTRODUCTION S ENSORLESS speed estimation can provide robust, field- oriented torque control of an induction machine without a tachometer. Most sensorless control schemes rely on estima- tion of the back EMF from stator voltages and currents, but these methods are inherently dependent on motor parameters. Furthermore, voltage measurement is degraded at low speeds. In order to improve the robustness of sensorless speed esti- mation, parameter-independent magnetic saliency harmonics can be used to generate an accurate rotor speed signal [1]–[9] which can then be used to tune the parameters of a back- EMF-based observer [12]. Digital signal processing (DSP) techniques can effectively extract saliency harmonics from the stator current [1]–[3], [8], [9], [12], but they often require long sampling times, particularly at low speeds. Parametric spectrum estimation techniques, however, can offer improved peak-extraction ca- pability over the fast Fourier transform (FFT), particularly for short data records [13]. In this paper, several of these techniques are evaluated on the basis of theoretical and experi- mental results, in order to determine which algorithm produces Paper IPCSD 97–10, approved by the Electric Machines Committee of the IEEE Industry Applications Society for presentation at the 1995 Indusry Applications Society Annual Meeting, Lake Buena Vista, FL, October 8–12. Manuscript released for publication January 14, 1997. The authors are with the School of Electrical Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA. Publisher Item Identifier S 0093-9994(97)05463-7. the most accurate speed estimates in the least amount of sampling time. Saliency harmonics, which arise from rotor slotting and eccentricity, provide robust speed estimation because they are independent of time-varying motor parameters. Some research efforts have employed analog filtering to determine the har- monic frequencies [4]–[7]. It has been shown, however, that without special modification of the machine, analog filtering requires excessively complex circuitry to achieve the desired frequency resolution at low speeds [6]. Additionally, the speed signal output of an analog scheme can be corrupted by noise in the stator current spectrum [7]. Digital spectral analysis, however, can easily provide an arbitrary frequency resolution given sufficient sampling time. Furthermore, DSP analysis can be readily combined with a continuous back-EMF-based speed or flux observer which decouples the speed signal from any noise contained in the stator current measurement signal [12]. Finally, except for analog prefiltering, the entire DSP algorithm can be implemented on a microprocessor. Previous research in sensorless speed estimation using DSP analysis has focused primarily on the FFT for determination of the harmonic frequency [1]–[3]. There are other spectrum estimation algorithms, however, which are more effective for the detection of saliency harmonics, if properly applied. A previous effort to use non-FFT spectrum estimation for speed sensing, however, required excessively complex computations and was demonstrated with only limited experimental results [8], while the work in [9] provided little discussion of the spectrum estimation method. This paper describes in detail spectrum estimation methods which improve the accuracy, robustness, and minimum sampling time of sensorless speed detection without any increase in the computational burden compared to the interpolated FFT. It should be noted that nontraditional spectrum estimation methods have been suc- cessfully applied not only to sensorless speed estimation, but also to condition monitoring of rotating machinery [10]. This paper compares two interpolated, FFT-based spectrum estima- tion methods with three non-FFT, parametric algorithms, in order to determine which is most suitable for robust and fast harmonic detection in induction motors. II. SIGNAL FILTERING AND ALIASING Saliency harmonics which result from rotor slotting and rotor eccentricity provide an accurate means for determining rotor speed at virtually any speed or load condition [9]. 0093–9994/97$10.00  1997 IEEE