Geometrical view of state estimation and gross error analysis

• Grant number: 15/10117-8
• Support Opportunities: Scholarships abroad - Research
• Start date: August 01, 2016
• End date: July 31, 2017
• Field of knowledge: Engineering - Electrical Engineering - Power Systems
• Principal Investigator: Newton Geraldo Bretas
• Grantee: Newton Geraldo Bretas
• Host Investigator: Sean Meyn
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: University of Florida, Gainesville (UF), United States
• Associated research grant: 11/01035-7 - Power system control and analysis, AP.TEM

Abstract

In this research the geometrical view is proposed to detect, identify, and to correct parameter errors of a power's system transmission lines. Also the geometrical formulation of state estimation is proposed to analyze topological errors in power systems. Topological errors correspond to very large errors in the transmission lines parameters. A general approach of Geometrical Approaches for State Estimation in Electric Power Systems can be summarized as follows: 1. Geometrical approaches in measurement gross error's analysis; 2. Geometrical approaches in transmission lines parameter errors; 3. Geometrical approaches in topological errors. The geometrical view of state estimation was developed by Prof. Newton G. Bretas [1-4] showing that the measurement's errors and the residuals are quite different quantities. From the well-known property: in the linear formulation of state estimation the error has a unique decomposition of two components: one component hidden in the Jacobian's space and the other contained in the complement of that space, the residual. Since what is wished in state estimation is a higher influence, in the state estimation solution, of the measurements of better quality than the ones with larger errors, a natural conclusion is that in the formulation of the state estimation problem, one should minimize the error and not the residual. This new view for the state estimation (SE) implies in significant changes in its formulation: (i) one of them is that the error is the quantity to be minimized in the state estimation formulation; (ii) in the gross error detection test, the error is the quantity to be tested on the possibility of having gross error, and, as a consequence, with m (measurement number) degrees of freedom; (iii) other consequence is that the hidden error component needs to be estimated. Prof. Newton G. Bretas has also proposed new weights to the measurements when in the stage of gross error analysis. It is understood that since all the measurements are possible of having gross errors, in this stage, the weights cannot be function of the measurement quality; they should have the same weights if they have the same magnitude. Therefore the weights should be a percentage of the measurements magnitude, for example, one percent of that quantity. After the error has been detected, the measurement containing the error should be identified. To identify the measurement containing the gross error, the Largest Normalized Error Theorem (LNET) was developed by Prof. Newton G. Bretas [1]. Then the error should be estimated and the proposition is to correct the measurement's magnitude. After correcting all the measurements having errors, a new state estimation is performed but now using the quality of the measurements to define the weights to be attributed to them. (AU)