Parameter Estimation of Three-Phase Untransposed Short Transmission Lines From Synchrophasor Measurements

Abstract

We present a new approach for estimating the parameters of three-phase untransposed electrically short transmission lines using voltage/current synchrophasor measurements obtained from phasor measurement units. The parameters to be estimated are the entries of the longitudinal impedance matrix and the shunt admittance matrix at the rated system frequency. Conventional approaches relying on the admittance matrix of the line cannot accurately estimate these parameters for short lines, due to their high sensitivity to measurement noise. Our approach differs from the conventional ones in the following ways: First, we model the line by the three-phase transmittance matrix that is observed to be less sensitive to measurement noise than the admittance matrix. Second, we compute an accurate noise covariance matrix using the realistic specifications of noise introduced by instrument transformers and phasor measurement units. This noise covariance matrix is then used in least-squares-based estimation methods. Third, we derive different least-squares-based estimation methods based on a statistical model of estimation and show that the weighted leastsquares and the maximum likelihood methods, which make use of the noise covariance matrix produce the best estimates of the line parameters. Finally, we apply the proposed methods to a real dataset and show that our approach significantly outperforms existing ones. I. INTRODUCTION Fundamental functionalities used in the operation of power grids, e.g., state estimation (SE) [1], [2], [3], optimal power flow (OPF)-based control [4], [5], [6], [7], , Model Predictive Control [8], [9] and optimal relay tuning [10], [11], require the knowledge of transmission line (TL) parameters at the rated system frequency. Conventionally, TL parameters are obtained either by using the physical properties of the line (such as conductor dimensions, types of wires, tower geometries, ground electrical parameters) [12], [13] or by making measurements on the line when it is off-grid [14]. The first method is applicable only when accurate conductor characteristics are known, whereas the second method, although reliable, is time consuming and difficult to implement in practice. With the availability of highly accurate measurement devices, e.g., phasor measurement units (PMUs), instrument transformers (ITs), estimation methods based on measurements from these devices have gained significant research

Online Non-Iterative Estimation of Transmission Line and Transformer Parameters by SCADA Data

“…Another point is that similar to [21], [26] and other research works on transmission line parameter estimation, we assume that ratio error and phase-displacement error of instrument transformers are independent. This has also been verified experimentally in [36] where magnitude and angle measurements are treated as independent Gaussian random variables.…”

“…Class 0.5 instrument transformers are assumed to provide input measurements to the proposed algorithm [38]. Based on the maximum allowable error for this class in IEC standards [39], [40], a Gaussian error is attributed to each instrument transformer as in [26]. The measurement error can be a function of the measurand if the measured value is much less than the rated primary quantity of the instrument transformer.…”

“…Unfortunately, the measurement error distribution is not given in IEC 60819 standard. Therefore, we have followed the same methodology as in [26] and assumed a normal distribution for measurement errors which do not exceed their upper bound in 99.8% of cases. However, if the relationship between measurement error and the measurand is known explicitly, e.g.…”

“…One approach is taking possible synchronization errors into account, which results in nonlinear formulations developed in [11]- [16] based on least-squares estimation. Another approach is utilizing the phasor representation of voltage and currents, thanks to the synchronized measurements, thereby solving a linear system of equations [17]- [26].…”

“…Utilizing both SCADA and PMU measurements, the authors in [27] adopt an iterative approach to estimate the parameters of long transmission lines. Compared to scarce PMU measurements, SCADA measurements Nonlinear [11]- [16] [5], [6], [27], [29], [30] Linear [17]- [26] Proposed Method are abundant across the grid so that system operators can deploy this data with no need for additional hardware [28].…”