IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008 13 Estimating Interharmonics by Using Sliding-Window ESPRIT Irene Yu-Hua Gu, Senior Member, IEEE, and Math H. J. Bollen, Fellow, IEEE Abstract—A method is proposed for estimating interharmonic frequencies in power system voltage and current signals. The method is based on a spectrum-estimation method known as “esti- mation of signal parameters via rotational invariance techniques” (ESPRIT). To allow for a more reliable spectral estimation and to cover nonstationarity in the signal, a sliding-window version of ESPRIT is introduced. This paper describes the basic ESPRIT method as well as sliding-window ESPRIT. The paper discusses the application of the method to one synthetic signal and three measurement signals. It is shown that the method allows for very accurate frequency estimation of interharmonic components. The limitations of the methods, such as line splitting and spurious components, can be overcome by using the coherent information obtained from the sliding-window method. A number of remaining issues are also discussed in this paper. Index Terms—Classification, damped sinusoidal model, esti- mation of signal parameters via rotational invariance techniques (ESPRIT), features, power quality (PQ), sliding-window ESPRIT, time-frequency analysis of disturbances. I. INTRODUCTION I N recent years, there has been fast development in data collection, storage, transmission and processing that has, among others, resulted in an increased interest in analysis of power-system measurements. The interest is probably most vis- ible in the power-quality area (e.g., through numerous publica- tions on automatic analysis and classification of power-quality disturbances [1]). However, many of the techniques can be applied more broadly, for example, in power-system protection and for automatic analysis of fault recordings in transmission systems. A subject that has received only limited interest in the past is the presence of so-called “interharmonic” components in voltage and/or current. Fortunately this trend is changing re- cently. The above-mentioned trends have certainly contributed to this. Interharmonics are frequency components with a fre- quency that is not an integer multiple of the power-system frequency (50 or 60 Hz in most systems). Interharmonics can be due to power-electronic frequency converters such as Manuscript received July 26, 2006; revised February 5, 2007. Paper no. TPWRD-00410-2006. I. Y.-H. Gu is with the Department of Signals and Systems, Chalmers Uni- versity of Technology, Gothenburg 412 96, Sweden. M. H. J. Bollen is with STRI AB, Ludvika, 771 80, Sweden and also with Luleå University of Technology, Skellefteå, 931 87, Sweden (e-mail: math.bollen@stri.se). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2007.911130 cyclo-converters of HVDC links between two large systems [2], but also due to communication signals or active converters with high switching frequency nonsynchronized to the power-system frequency. A number of methods have been proposed for estimating the frequency and magnitude of interharmonic components [3]–[10]. These methods result typically in the amplitudes (and often the phase angles) of the signal components for a number of predefined frequencies (frequency bands) or scales. Several methods allow estimating time-varying amplitudes, but none allows for simultaneously estimating both time-varying amplitudes, frequencies, and initial phases. One of the reasons for this is that multiple solutions may exist especially where both frequency and phase angle are assumed unknown. In previous studies sinusoidal models were used for analyzing power system transients [11], [12], where the ESPRIT method was applied to the entire data sequence assuming data sta- tionarity. The result can be considered as a high-resolution frequency-domain representation of the signal. In this paper, a sliding-window approach is used that circum- vents the problem of nonstationary data by assuming signal sta- tionarity within each analysis window. The sliding-window con- cept is very similar to the short-time Fourier transform (STFT) [13] as applied successfully for many years. The spectral con- tents in each analysis window is obtained by applying a para- metric (or, model-based) method known as “estimation of signal parameters via rotational invariance techniques” (ESPRIT) [14], resulting in the frequencies, amplitudes, and phases of the domi- nant components of the signal within the analysis window. Next, the window is shifted in time and the process is repeated. This results in a time-frequency representation of the signal. The proposed method is introduced in Section II, where a dis- tinction is made between the “basic method” and the “sliding- window method.” The theory behind ESPRIT is presented in the Appendix. The proposed method is applied to one synthetic signal and four measurements in Section III. Some remaining issues and conclusions are presented in Sections IV and V. II. ESPRIT AND SLIDING-WINDOW ESPRIT A. Modelling of Power System Signals The underlying signal model for the proposed method con- sists of exponentially-damped sinusoids in additive white noise. For a given block of data (size L) from the measured signal , the underlying model for the signal is (1) 0885-8977/$25.00 © 2007 IEEE