Kalman Filter Algorithm for Mitigation of Power System Harmonics

The maiden application of a variant of Kalman Filter (KF) algorithms known as Local Ensemble Transform Kalman Filter (LET-KF) are used for mitigation and estimation power system harmonics are proposed in this paper. The proposed algorithm is applied for estimating the harmonic parameters of power signal containing harmonics, sub-harmonics and inter-harmonics in presence of random noise. The KF group of algorithms are tested and applied for both stationary as well as dynamic signal containing harmonics. The proposed LET-KF algorithm is compared with conventional KF based algorithms like KF, Ensemble Kalman Filter (En-KF) algorithms for harmonic estimation with the random noise values 0.001, 0.05 and 0.1. Among these three noises, 0.01 random noise results will give better than other two noises. Because the phase deviation and amplitude deviation less in 0.01 random noise. The proposed algorithm gives the better results to improve the efficiency and accuracy in terms of simplicity and computational features. Hence there are less multiplicative operations, which reduce the rounding errors. It is also less expensive as it reduces the requirement of storing large matrices, such as the Kalman gain matrix used in other KF based methods

Phasor Estimation for Grid Power Monitoring: Least Square vs. Linear Kalman Filter

International audienc

Study to develop gradiometer techniques

The primary goal of the current gravity gradiometer research at Stanford has been to establish the feasibility of using a gravity gradiometer with 1 E accuracy, as the primary sensor in various applications. The two applications considered here in detail are geodesy missions and inertial navigation systems. Preliminary sections on gravity models and gravity gradiometer bias estimation are also included

Nonparametric Uncertainty Quantification for Stochastic Gradient Flows

This paper presents a nonparametric statistical modeling method for quantifying uncertainty in stochastic gradient systems with isotropic diffusion. The central idea is to apply the diffusion maps algorithm to a training data set to produce a stochastic matrix whose generator is a discrete approximation to the backward Kolmogorov operator of the underlying dynamics. The eigenvectors of this stochastic matrix, which we will refer to as the diffusion coordinates, are discrete approximations to the eigenfunctions of the Kolmogorov operator and form an orthonormal basis for functions defined on the data set. Using this basis, we consider the projection of three uncertainty quantification (UQ) problems (prediction, filtering, and response) into the diffusion coordinates. In these coordinates, the nonlinear prediction and response problems reduce to solving systems of infinite-dimensional linear ordinary differential equations. Similarly, the continuous-time nonlinear filtering problem reduces to solving a system of infinite-dimensional linear stochastic differential equations. Solving the UQ problems then reduces to solving the corresponding truncated linear systems in finitely many diffusion coordinates. By solving these systems we give a model-free algorithm for UQ on gradient flow systems with isotropic diffusion. We numerically verify these algorithms on a 1-dimensional linear gradient flow system where the analytic solutions of the UQ problems are known. We also apply the algorithm to a chaotically forced nonlinear gradient flow system which is known to be well approximated as a stochastically forced gradient flow.Comment: Find the associated videos at: http://personal.psu.edu/thb11

The estimate of amplitude and phase of harmonics in power system using the extended kalman filter

Nowadays, the amplitude of the harmonics in the power grid has increased unwittingly due to the increasing use of the nonlinear elements and power electronics. It has led to a significant reduction in power quality indicators. As a first step, the estimate of the amplitude, and the phase of the harmonics in the power grid are essential to resolve this problem. We use the Kalman filter to estimate the phase, and we use the minimal squared linear estimator to assess the amplitude. To test the aforementioned method, we use terminal test signals of the industrial charge consisting of the power converters and ignition coils. The results show that this algorithm has a high accuracy and estimation speed, and they confirm the proper performance in instantaneous tracking of the parameters

Regression analysis with missing data and unknown colored noise: application to the MICROSCOPE space mission

The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events or transmission losses. We assess the impact of missing data on the performance of linear regression analysis involving the fit of modeled or measured time series. We show that data gaps can significantly alter the precision of the regression parameter estimation in the presence of colored noise, due to the frequency leakage of the noise power. We present a regression method which cancels this effect and estimates the parameters of interest with a precision comparable to the complete data case, even if the noise power spectral density (PSD) is not known a priori. The method is based on an autoregressive (AR) fit of the noise, which allows us to build an approximate generalized least squares estimator approaching the minimal variance bound. The method, which can be applied to any similar data processing, is tested on simulated measurements of the MICROSCOPE space mission, whose goal is to test the Weak Equivalence Principle (WEP) with a precision of $10^{-15}$. In this particular context the signal of interest is the WEP violation signal expected to be found around a well defined frequency. We test our method with different gap patterns and noise of known PSD and find that the results agree with the mission requirements, decreasing the uncertainty by a factor 60 with respect to ordinary least squares methods. We show that it also provides a test of significance to assess the uncertainty of the measurement.Comment: 12 pages, 4 figures, to be published in Phys. Rev.

The framework for satellite gravity data assimilation into land surface models

The Gravity Recovery and Climate Experiment (GRACE) mission has provided an unprecedented global, homogeneous observational dataset of the time variation in terrestrial water storage (TWS) since 2002. This product has seen widespread use in the study of processes in hydrology, oceanography, the cryosphere, and is particularly critical to inform, improve, and validate computational models of the Earth system. Assimilation of the GRACE TWS fields into current land surface models can correct model deficiencies due to errors in the model structure, atmospheric forcing datasets, parameters, etc. However, the assimilation process is complicated by spatial and temporal resolution discrepancies between the model and observational datasets, characterization of the error in each, and requires tuning to the unique characteristics of satellite gravity data. This study establishes a framework for hydrological data assimilation of terrestrial water storage data from GRACE, closes the loop between GRACE product development and its scientific use, and analyzes the assimilated results for use with current GRACE products and future satellite gravity missions. The framework fuses the strengths of the observational and land surface model datasets into an assimilated product representative of the signal strength and large scale structures of the GRACE dataset effectively downscaled to the high resolution land surface dynamics. The data assimilation framework was developed through a comprehensive analysis of the deficiencies and potential improvements of the satellite data products, the assimilation procedures and error characterization, and the assimilation effectiveness over time. This analysis motivated the development of a higher frequency GRACE dataset more representative of the hydrometeorological signal content with reduced temporal aliasing of the TWS signal. Three innovations were implemented in the product development: regularization, sliding windows, and mascon basis functions, to develop a high-fidelity daily gravity field product (RSWM). The signal and error profile of the RSWM product was comprehensively analyzed via an end-to-end simulation analysis of the GRACE mission. The simulation analysis developed an error covariance representative of the magnitude, correlation, and spatial pattern of error in the RSWM dataset available for use in the data assimilation system. The assimilation algorithms and tools were advanced to optimally incorporate the GRACE TWS data and error covariance information. Daily assimilation was performed globally at the one degree gridcell level, significantly reducing spatial and temporal smoothing of the assimilation update from previous basin-scale assimilation of the monthly mean GRACE datasets. Framework elements additionally defined the mechanisms of the assimilation process: (i) the Gaspari-Cohn localization radius to spatially smooth the coarser resolution GRACE data, (ii) the necessary assimilation update rate to balance assimilation performance and computational efficiency, and (iii) open-loop error growth after assimilation has conditioned the system to advise data latency requirements. The GRACE data assimilation framework is versatile and adaptable to other land surface models, different formulations of data from the current GRACE mission, and future satellite gravity datasets.Aerospace Engineerin

Planetary gyre, time-dependent eddies, torsional waves, and equatorial jets at the Earth's core surface

We report a calculation of time-dependent quasi-geostrophic core flows for 1940-2010. Inverting recursively for an ensemble of solutions, we evaluate the main source of uncertainties, namely the model errors arising from interactions between unresolved core surface motions and magnetic fields. Temporal correlations of these uncertainties are accounted for. The covariance matrix for the flow coefficients is also obtained recursively from the dispersion of an ensemble of solutions. Maps of the flow at the core surface show, upon a planetary-scale gyre, time-dependent large-scale eddies at mid-latitudes and vigorous azimuthal jets in the equatorial belt. The stationary part of the flow predominates on all the spatial scales that we can resolve. We retrieve torsional waves that explain the length-of-day changes at 4 to 9.5 years periods. These waves may be triggered by the nonlinear interaction between the magnetic field and sub-decadal non-zonal motions within the fluid outer core. Both the zonal and the more energetic non-zonal interannual motions were particularly intense close to the equator (below 10 degrees latitude) between 1995 and 2010. We revise down the amplitude of the decade fluctuations of the planetary scale circulation and find that electromagnetic core-mantle coupling is not the main mechanism for angular momentum exchanges on decadal time scales if mantle conductance is 3 10 8 S or lower