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The Tsallis q-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the q-distribution family, which is characterized by a non-additive entropy. Due to their versatility and practicality, q-Gaussians are a natural choice for modeling input quantities in measurement models. This paper presents the characteristic function of a linear combination of independent q-Gaussian random variables and proposes a numerical method for its inversion. The proposed technique makes it possible to determine the exact probability distribution of the output quantity in linear measurement models, with the input quantities modeled as independent q-Gaussian random variables. It provides an alternative computational procedure to the Monte Carlo method for uncertainty analysis through the propagation of distributions.

The Tsallis q-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It belongs to the q-distribution family, which is characterized by a non-additive entropy. Due to their versatility and practicality, q-Gaussians are a natural choice for modeling input quantities in measurement models. This paper presents the characteristic function of a linear combination of independent q-Gaussian random variables and proposes a numerical method for its inversion. The proposed technique makes it possible to determine the exact probability distribution of the output quantity in linear measurement models, with the input quantities modeled as independent q-Gaussian random variables. It provides an alternative computational procedure to the Monte Carlo method for uncertainty analysis through the propagation of distributions. [ABSTRACT FROM AUTHOR]

State estimation (SE) is one of the principal components in any energy management system for secure and reliable operation of power systems. The aim of state estimation process is to obtain the voltage magnitude and phase angles of buses which are further utilized in various real-time practice in power systems. This paper presents two new SE methods with the direct utilization of complex synchronized measurements obtained from optimally placed phasor measurements units (PMUs). Both the proposed methods use a linear measurement model to provide optimal solution avoiding iterative procedure compared to sub-optimal results provided by most of the existing iterative SE methods. The first method portrays a new static state estimation (NSSE) and the second one presents a new dynamic state estimation (NDSE) method using the more pragmatic Brown's triple exponential (BTE) smoothing method for one step ahead prediction. The proposed approaches also include a unique detection, identification and correction of bad data method. The proposed methods have been tested on various IEEE bus test systems as well on two Indian practical systems, viz. 38-bus system of Damodar Valley Corporation and 246-bus system of Northern Regional Power Grid. The accomplishments of the proposed approaches have been evaluated by comparing it with conventional static state estimation (SSE) and dynamic state estimation (DSE) as well as newly proposed unscented Kalman filter-(UKF) and cubature Kalman filter (CKF)-based DSE methods under different simulated operating conditions. Simulation results provided validates the superiority of the proposed schemes. [ABSTRACT FROM AUTHOR]

Electrical power systems are in rapid evolution, necessitating advanced monitoring, control, and protection aspects connected to an accurate knowledge of the state of the grid. State estimation is one-way such knowledge could be achieved by estimating voltage magnitudes and phase angles at all buses in electrical networks. Electric utilities are deploying advanced Phasor Measurement Units (PMUs) in grids with conventional Remote Terminal Units (RTUs). Integrating measurements from the two types of devices for state estimation is inevitable. In the past, hybrid state estimators have been based on nonlinear models associated with various challenges, such as using nonlinear state estimation algorithms with high computational time, slow convergence, and initialization problems. For this reason, there is a need to develop hybrid linear mathematical models that eliminate issues posed by nonlinearity models. This paper presents a novel mathematical formulation that gives a linear measurement model for hybrid state estimation based on the standard steady-state branch model. The developed model is then tested in MATLAB using three standard transmission test cases (IEEE 14-BUS, IEEE 30-BUS, and IEEE 57-BUS) with available measurements subjected to different errors. Notably, the performance of the developed model based on two different state estimation algorithms, Weighted Least Square (WLS) and Weighted Least Absolute Value (WLAV), are compared. The simulation results obtained for voltage magnitudes and phase angles for all buses in the three scenarios compare well with reference values. Using Normalized Cumulative Error (NCE) as a performance index, the developed linear measurement model gives less cumulative error than the conventional nonlinear model. With measurements subjected to bad data (such as negative values for measured variables), the developed model performs better using WLAV than the WLS estimation algorithm. The computational time for all three networks is notably less when using the WLAV algorithm than the WLS algorithm.