Let Lk= （-△）k ＋ Vk be a SchrSdinger type operator, where k ≥1 is a positive integer and V is a nonnegative polynomial. We obtain the Lp estimates for the operators △2kLk-1 and △kLk-1/2
This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression model...This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.展开更多
Phasor measurement units(PMUs)are fundamental tools in the applications of modern power systems,where synchronized phasor estimations are needed.The accuracy and dynamic performance requirements for phasor,frequency,a...Phasor measurement units(PMUs)are fundamental tools in the applications of modern power systems,where synchronized phasor estimations are needed.The accuracy and dynamic performance requirements for phasor,frequency,and rate of change of frequency(ROCOF)estimations are established in the IEEE Std.C37.118.1-2011 along with the IEEE Std.C37.118.1 a-2014,where two PMU performances are suggested:P class filters for applications requiring fast response and M class filters for applications requiring high rejection to aliased signals.In this paper,a methodology to design new phasor estimators that satisfy the P class and M class requirements in PMUs is presented.The proposed methodology is based on finite impulse response filters,brick-wall filters,and complex filter design concepts,where frequency range,time performance,harmonic rejection and out-of-band interference requirements are considered in its design.A comparative analysis using the reference model given by the IEEE Std.C37.118.1 is presented.The results show the effectiveness of the phasor estimators under steady-state and dynamic conditions according to the PMU standard,making them suitable tools for applications in power systems.展开更多
基金Supported by the National Natural Science Foundation of China(10901018,11001002)the Beijing Foundation Program(201010009009,2010D005002000002)the Fundamental Research Funds for the Central Universities
文摘Let Lk= （-△）k ＋ Vk be a SchrSdinger type operator, where k ≥1 is a positive integer and V is a nonnegative polynomial. We obtain the Lp estimates for the operators △2kLk-1 and △kLk-1/2
文摘This paper considers the approaches and methods for reducing the influence of multi-collinearity. Great attention is paid to the question of using shrinkage estimators for this purpose. Two classes of regression models are investigated, the first of which corresponds to systems with a negative feedback, while the second class presents systems without the feedback. In the first case the use of shrinkage estimators, especially the Principal Component estimator, is inappropriate but is possible in the second case with the right choice of the regularization parameter or of the number of principal components included in the regression model. This fact is substantiated by the study of the distribution of the random variable , where b is the LS estimate and β is the true coefficient, since the form of this distribution is the basic characteristic of the specified classes. For this study, a regression approximation of the distribution of the event based on the Edgeworth series was developed. Also, alternative approaches are examined to resolve the multicollinearity issue, including an application of the known Inequality Constrained Least Squares method and the Dual estimator method proposed by the author. It is shown that with a priori information the Euclidean distance between the estimates and the true coefficients can be significantly reduced.
文摘Phasor measurement units(PMUs)are fundamental tools in the applications of modern power systems,where synchronized phasor estimations are needed.The accuracy and dynamic performance requirements for phasor,frequency,and rate of change of frequency(ROCOF)estimations are established in the IEEE Std.C37.118.1-2011 along with the IEEE Std.C37.118.1 a-2014,where two PMU performances are suggested:P class filters for applications requiring fast response and M class filters for applications requiring high rejection to aliased signals.In this paper,a methodology to design new phasor estimators that satisfy the P class and M class requirements in PMUs is presented.The proposed methodology is based on finite impulse response filters,brick-wall filters,and complex filter design concepts,where frequency range,time performance,harmonic rejection and out-of-band interference requirements are considered in its design.A comparative analysis using the reference model given by the IEEE Std.C37.118.1 is presented.The results show the effectiveness of the phasor estimators under steady-state and dynamic conditions according to the PMU standard,making them suitable tools for applications in power systems.
