The Kalman-filter-based algorithms as the mainstream algorithms of dynamic state estimation of power systems have been extensively used to provide accurate data for power system applications. However, few comparisons are made to show their advantages and disadvantages. In this paper, four Kalmanfilter-based algorithms (i.e., extended Kalman filter, unscented Kalman filter, cubature Kalman filter, and ensemble Kalman filter) are compared to show their differences from implementation complexity, estimation accuracy and calculation efficiency, the resistance to measurement errors, and the sensitivity to system scales. Finally, the simulation results on the 3-machine, 10-machine, and 48-machine power systems show their advantages and disadvantages. INDEX TERMS Cubature Kalman filter, dynamic state estimation, ensemble Kalman filter, extended Kalman filter, unscented Kalman filter. I. NOMENCLATURE a Admittance angle matrix C Equal weight cubature points vector D Damping coefficient e Unit column vector E EnKF sample set f (•) State transition function F Jacobian matrix of state transition function h(•) Measurement function H Jacobian matrix of measurement function I Unit matrix k Filtering gain p e Electromagnetic power of the generator p m Mechanical power of the generator P k Estimated error covariance P zz Innovation covariance matrix P xz The cross-covariance matrix Q System noise variance R Measurement noise variance The associate editor coordinating the review of this manuscript and approving it for publication was Wuhui Chen. S Weighted Sigma points vector T Inertia constant of the generator u Constant control vector v Measurement noise vector V Voltage amplitude w System noise vector W c Weight vectors of covariance W m Weight vectors of mean x State vector Y Reduced node admittance matrix z Measurement vector δ Generator power angle ω Generator speed ω s Generator reference speed ω δ System noise vector of generator power angle ω ω System noise vector of generator speed h Difference step size i, j The ith/jth generator k Current time n Number of generators n en Number of samples N Number of times α, β, η, λ, l Setting parameters of UKF
For any power system, the reliability of measurement data is essential in operation, management and also in planning. However, it is inevitable that the measurement data are prone to outliers, which may impact the results of data-based applications. In order to improve the data quality, the outliers cleaning method for measurement data in the distribution network is studied in this paper. The method is based on a set of association rules (AR) that are automatically generated form historical measurement data. First, the association rules are mining in conjunction with the density-based spatial clustering of application with noise (DBSCAN), k-means and Apriori technique to detect outliers. Then, for the outliers repairing process after outliers detection, the proposed method uses a distance-based model to calculate the repairing cost of outliers, which describes the similarity between outlier and normal data. Besides, the Mahalanobis distance is employed in the repairing cost function to reduce the errors, which could implement precise outliers cleaning of measurement data in the distribution network. The test results for the simulated datasets with artificial errors verify that the superiority of the proposed outliers cleaning method for outliers detection and repairing.
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