1842 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 4, OCTOBER 2009 Phasor Estimation in the Presence of DC Offset and CT Saturation Soon-Ryul Nam, Member, IEEE, Jong-Young Park, Sang-Hee Kang, Member, IEEE, and Mladen Kezunovic, Fellow, IEEE Abstract—A hybrid algorithm for phasor estimation is proposed that is immune to dc offset and current transformer (CT) satura- tion problems. The algorithm utilizes partial sum (PS)-based and multistage least-squares (MLS)-based methods before and after CT saturation is detected, respectively. The MLS-based method is initiated when the third difference of the secondary current de- tects the start point of the first saturation period. The determi- nation of each saturation period is based on the sum of the sec- ondary current from the start point of the first saturation period. A least-squares (LS) technique estimates the dc offset parameters from the single-cycle difference of the secondary current in the un- saturated periods. Removal of dc offset from the secondary cur- rent yields the sinusoidal waveform portion. Finally, the LS tech- nique is used once again to estimate the phasor from the sinusoidal waveform portion. The performance of the algorithm was eval- uated for a-g faults on a 345-kV 100-km overhead transmission line. The Electromagnetic Transient Program was used to generate fault current signals for different fault angles and remanent fluxes. The performance evaluation shows that the proposed algorithm accurately estimates the phasor of a current signal regardless of dc offset and CT saturation. The paper concludes by describing the hardware implementation of the algorithm on a prototype unit based on a digital signal processor. Index Terms—Current transformer, dc offset, multistage least squares, saturation, partial sum, phasor estimation. I. INTRODUCTION M ODERN protective devices depend on knowing the pha- sors of the voltage and current signals. Any fault-in- duced dc offset must be removed from the current signal to es- timate the current phasor accurately. Since a dc offset is a non- periodic signal whose spectrum covers all frequencies, the pres- ence of such a dc offset may result in a phasor estimation error of almost 20%, depending on the algorithm used. It is well known that the saturation of a current transformer (CT) also has an ad- verse influence on the estimation of the current phasor. Since dc offset itself is one of main causes of CT saturation, dc offset, and Manuscript received September 27, 2007; revised February 08, 2008. Current version published September 23, 2009. This work was supported in part by the ERC program of MOST/KOSEF (Next-Generation Power Technology Center) and in part by MKE through the EIRC program (Research Center for Large- Scale Distributed Generation). Paper no. TPWRD-00581-2007. S. R. Nam and S. H. Kang are with the Next Generation Power Technology Center and the Department of Electrical Engineering, Myongji University, Yongin 449-728, Korea (e-mail: ptsouth@mju.ac.kr; shkang@mju.ac.kr). J. Y. Park is with the Electric Power Research Division, Korea Electrotech- nology Research Institute, Uiwang 437-808, Korea. M. Kezunovic is with the Department of Electrical and Computer Engi- neering, Texas A&M University, College Station, TX 77843 USA. 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.2008.2002972 CT saturation should be considered together when estimating the phasor of a current signal. Over the last two decades, several techniques have been pro- posed to deal with the dc offset problem [1]–[9]. One approach to eliminating the effect of a dc offset is to assume a specific time constant for it. The methods in this approach, such as a Kalman filer in [1] and a digital mimic filter in [2], can com- pletely remove the dc offset only when the time constant of the dc-offset matches the assumed one. Another approach is to esti- mate the dc-offset parameters. In [3] and [4], algorithms based on least squares (LS) were proposed to suppress the effect of the dc offset, which is linearized by a Taylor series expansion. LS-based algorithms can successfully suppress the effect of the dc offset over a certain range of time constants. When the time constant is small, however, their performance decreases due to the effects of the linearization. Several algorithms based on the discrete Fourier transform (DFT) have also been proposed to eliminate the effect of the dc offset. Algorithms in [5] and [6] were proposed to estimate the dc offset parameters using three successive outputs of the fundamental frequency DFT and two successive sums of single-cycle samples, respectively. Since these algorithms made use of more than one cycle samples, their response speeds were slower than other DFT-based algorithms. To cope with this drawback, [7], [8], and [9] used the output of the harmonic DFT, two partial sums of single-cycle sam- ples, and a modified notch filter, respectively, to estimate the dc offset parameters. Although most of algorithms in these two approaches exhibit good immunity to dc offset, they do produce errors in the case of CT saturation. Several other methods have been presented in [10]–[16] to deal with the CT saturation problem. In [10], an algorithm that estimates the magnetizing current to compensate for CT sat- uration was proposed. Although this algorithm is valid under various fault conditions, it requires the magnetization curve based on given CT parameters, and assumes that the remnant flux is zero before the fault occurs. Algorithms in [11] and [12] have been used to improve the accuracy of a CT, in which the initial flux is estimated and used in conjunction with the hysteresis curve to calculate the exciting current. These algo- rithms are based on two assumptions that the given CT has been preliminarily identified and that no dc component is present. In [13], the secondary current only in unsaturated periods is used to estimate the primary current including the dc offset, which is linearized by a Taylor series expansion. Due to this linearization, this algorithm does produce some errors, par- ticularly when the time constant is small. An artificial neural network (ANN) has also been used to correct the distortion of secondary currents. In [14] and [15], a feedforward ANN 0885-8977/$26.00 © 2009 IEEE Authorized licensed use limited to: Myongji University. Downloaded on September 30, 2009 at 00:52 from IEEE Xplore. Restrictions apply.