Optimal PMU Placement for Power System Dynamic State Estimation by Using Empirical Observability Gramian

In this paper the empirical observability Gramian calculated around the operating region of a power system is used to quantify the degree of observability of the system states under specific phasor measurement unit (PMU) placement. An optimal PMU placement method for power system dynamic state estimation is further formulated as an optimization problem which maximizes the determinant of the empirical observability Gramian and is efficiently solved by the NOMAD solver, which implements the Mesh Adaptive Direct Search (MADS) algorithm. The implementation, validation, and also the robustness to load fluctuations and contingencies of the proposed method are carefully discussed. The proposed method is tested on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system by performing dynamic state estimation with square-root unscented Kalman filter. The simulation results show that the determined optimal PMU placements by the proposed method can guarantee good observability of the system states, which further leads to smaller estimation errors and larger number of convergent states for dynamic state estimation compared with random PMU placements. Under optimal PMU placements an obvious observability transition can be observed. The proposed method is also validated to be very robust to both load fluctuations and contingencies.Comment: Accepted by IEEE Transactions on Power System

An Approximate Bayesian Long Short-Term Memory Algorithm for Outlier Detection

Long Short-Term Memory networks trained with gradient descent and back-propagation have received great success in various applications. However, point estimation of the weights of the networks is prone to over-fitting problems and lacks important uncertainty information associated with the estimation. However, exact Bayesian neural network methods are intractable and non-applicable for real-world applications. In this study, we propose an approximate estimation of the weights uncertainty using Ensemble Kalman Filter, which is easily scalable to a large number of weights. Furthermore, we optimize the covariance of the noise distribution in the ensemble update step using maximum likelihood estimation. To assess the proposed algorithm, we apply it to outlier detection in five real-world events retrieved from the Twitter platform

The Unscented Kalman Filter for Nonlinear Parameter Identification of Adaptive Cruise Control Systems

This paper develops and investigates a dual unscented Kalman filter (DUKF) for the joint nonlinear state and parameter identification of commercial adaptive cruise control (ACC) systems. Although the core functionality of stock ACC systems, including their proprietary control logic and parameters, is not publicly available, this work considers a car-following scenario with a human-driven vehicle (leader) and an ACC engaged ego vehicle (follower) that employs a constant time-headway policy (CTHP). The objective of the DUKF is to determine the CTHP parameters of the ACC by using real-time observations of space-gap and relative velocity from the vehicle's onboard sensors. Real-time parameter identification of stock ACC systems is essential for assessing their string stability, large-scale deployment on motorways, and impact on traffic flow and throughput. In this regard, $L_2$ and $L_\infty$ string stability conditions are considered. The observability rank condition for nonlinear systems is adopted to evaluate the ability of the proposed estimation scheme to estimate stock ACC system parameters using empirical data. The proposed filter is evaluated using empirical data collected from the onboard sensors of two 2019 SUV vehicles, namely Hyundai Nexo and SsangYong Rexton, equipped with stock ACC systems; and is compared with batch and recursive least-squares optimization. The set of ACC model parameters obtained from the proposed filter revealed that the commercially implemented ACC system of the considered vehicle (Hyundai Nexo) is neither $L_2$ nor $L_\infty$ string stable.Comment: 11 papes, 3 Figure

Power System Dynamic State Estimation: Motivations, Definitions, Methodologies, and Future Work

This paper summarizes the technical activities of the Task Force on Power System Dynamic State and Parameter Estimation. This Task Force was established by the IEEE Working Group on State Estimation Algorithms to investigate the added benefits of dynamic state and parameter estimation for the enhancement of the reliability, security, and resilience of electric power systems. The motivations and engineering values of dynamic state estimation (DSE) are discussed in detail. Then, a set of potential applications that will rely on DSE is presented and discussed. Furthermore, a unified framework is proposed to clarify the important concepts related to DSE, forecasting-aided state estimation, tracking state estimation, and static state estimation. An overview of the current progress in DSE and dynamic parameter estimation is provided. The paper also provides future research needs and directions for the power engineering community

Particle tracking using the unscented Kalman filter in high energy physics experiments

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London.The extended Kalman lter (EKF) has a long history in the field of non-linear tracking. More recently, statistically-based estimators have emerged that avoid the need for a deterministic linearisation process. The Unscented Kalman filter (UKF) is one such technique that has been shown to perform favourably for some non-linear systems when compared to an EKF implementation, both in terms of accuracy and robustness. In this Thesis, the UKF is applied to a high energy physics particle tracking problem where currently the EKF is being implemented. The effects of measurement redundancy are investigated to determine improvements in accuracy of particle track reconstruction. The relationship between measurement redundancy and relative observability is also investigated through an experimental and theoretical analysis. Smoothing (backward filtering), in the high energy physics experiments, is implementedusing the Rauch Tung Striebel (RTS) smoother with the EKF , however, in Unscented Kalman filter algorithms, the Jacobian matrices required by the RTS method, are not available. The Unscented Rauch Tung Striebel (URTS) smoother addresses this problem by avoiding the use of Jacobian matrices but is not effi cient for large dimensional systems such as high energy physics experiments. A technique is implemented in the RTS smoother to make it suitable for the UKF. The method is given the name the Jacobian Equivalent Rauch Tung Striebel (JE-RTS) smoother. The implementation of this method is quite straight forward when the UKF is used as an estimator

Filtering in Finance.

In this article we present an introduction to various Filtering algorithms and some of their applications to the world of Quantitative Finance. We shall first mention the fundamental case of Gaussian noises where we obtain the well-known Kalman Filter. Because of common nonlinearities, we will be discussing the Extended Kalman Filter.Commodity Prices; Term Structure; Stock Prices; Kalman Filter;

Intelligent approach for processmodelling and optimization on electrical dischargemachining of polycrystalline diamond

Polycrystalline diamond (PCD) is increasingly becomes an important material used in the industry for cutting tools of difficult-to-machine materials due to its excellent characteristics such as hardness, toughness and wear resistance. However, its applications are restricted because of the PCD material is difficult to machine. Therefore, electrical discharge machining (EDM) is an ideal method suitable for PCD materials due to its non-contact process nature. The performance of EDM, however, is significantly influenced by its process parameters and type of electrode. In this study, soft computing technique was utilized to optimize the performance of the EDM in roughing condition for eroding PCD with copper tungsten or copper nickel electrode. Central composite design with five levels of three machining parameters viz. peak current, pulse interval and pulse duration has been used to design the experimental matrix. The EDM experiment was conducted based on the design experimental matrix. Subsequently, the effectiveness of EDM on shaping PCD with copper tungsten and copper nickel was evaluated in terms of material removal rate (MRR) and electrode wear rate (EWR). It was found that copper tungsten electrode gave lower EWR, in comparison with the copper nickel electrode. The predictive model of radial basis function neural network (RBFNN) was developed to predict the MRR and EWR of the EDM process. The prominent predictive ability of RBFNN was confirmed as the prediction errors in terms of mean-squared error were found within the range of 6.47E−05 to 7.29E−06. Response surface plot was drawn to study the influences of machining parameters of EDM for shaping PCD with copper tungsten and copper nickel. Subsequently, moth search algorithm (MSA) was used to determine the optimal machining parameters, such that the MRR was maximized and EWR was minimized. Based on the obtained optimal parameters, confirmation test with the absolute error within the range of 1.41E−06 to 5.10E−05 validated the optimization capability of MSA

Static and Dynamic State Estimation Applications in Power Systems Protection and Control Engineering

The developed methodologies are proposed to serve as support for control centers and fault analysis engineers. These approaches provide a dependable and effective means of pinpointing and resolving faults, which ultimately enhances power grid reliability. The algorithm uses the Least Absolute Value (LAV) method to estimate the augmented states of the PCB, enabling supervisory monitoring of the system. In addition, the application of statistical analysis based on projection statistics of the system Jacobian as a virtual sensor to detect faults on transmission lines. This approach is particularly valuable for detecting anomalies in transmission line data, such as bad data or other outliers, and leverage points. Through the integration of remote PCB status with virtual sensors, it becomes possible to accurately detect faulted transmission lines within the system. This, in turn, saves valuable troubleshooting time for line engineers, resulting in improved overall efficiency and potentially significant cost savings for the company. When there is a temporary or permanent fault, the generator dynamics will be affected by the transmission line reclosing, which could impact the system\u27s stability and reliability. To address this issue, an unscented Kalman filter (UKF) and optimal performance iterated unscented Kalman filter (IUKF) dynamic state estimation techniques are proposed. These techniques provide an estimate of the dynamic states of synchronous generators, which is crucial for monitoring generator states during transmission lines reclosing for temporary and permanent fault conditions. Several test systems were employed to evaluate reclosing following faults on transmission lines, including the IEEE 14-bus system, Kundur\u27s two-area model, and the reduced Western Electricity Coordinating Council (WECC) model of UTK electrical engineering hardware test bed (HTB). The developed methods offer a comprehensive solution to address the challenges posed by unbalanced faults on transmission lines, such as line-to-line, line-to-line-ground, and line-to-ground faults. Utilities must consider these faults when developing protective settings. The effectiveness of the solution is confirmed by monitoring the reaction of dynamic state variables following transmission lines reclosing after temporary faults and transmission line lockout from permanent faults