<p>Various engineering systems have become rapidly automated and intelligent as sensing, communication, and computing technologies have been increasingly advanced. The dynamical behaviors of such systems have also become complicated as they need to meet requirements on performance and safety in various operating conditions. Due to the heterogeneity in its behaviors for different operating modes, it is not appropriate to use a single dynamical model to describe its dynamics, which motivates the development of the stochastic hybrid system (SHS). The SHS is defined as a dynamical system which contains interacting time-evolving continuous state and event-driven discrete state (also called a mode) with uncertainties. Due to its flexibility and effectiveness, the SHS has been widely used for modeling complex engineering systems in many applications such as air traffic control, sensor networks, biological systems, and etc.</p><p>One of the key research areas related to the SHS is the inference or estimation of the states of the SHS, which is also known as the hybrid state estimation. This task is very challenging because both the continuous and discrete states need to be inferred from noisy measurements generated from mixed time-evolving and event-driven behavior of the SHS. This becomes even more difficult when the dynamical behavior or measurement contains nonlinearity, which is the case in many engineering systems that can be modeled as the SHS.</p><p>This research aims to 1) propose a stochastic nonlinear hybrid system model and develop novel nonlinear hybrid state estimation algorithms that can deal with the aforementioned challenges, and 2) apply them to safety-critical applications in air traffic control systems such as aircraft tracking and estimated time of arrival prediction, and unmanned aircraft system traffic management.</p>

The objective of this thesis is to prove the validity of a multi-area state estimator and investigate the advantages it provides over a serial state estimator. This is done utilizing the IEEE 118 Bus Test System as a sample system. This thesis investigates the benefits that stem from utilizing a multi-area state estimator instead of a serial state estimator. These benefits are largely in the form of increased accuracy and decreased processing time. First, the theory behind power system state estimation is explained for a simple serial estimator. Then the thesis shows how conventional measurements and newer, more accurate PMU measurements work within the framework of weighted least squares estimation. Next, the multi-area state estimator is examined closely and the additional measurements provided by PMUs are used to increase accuracy and computational efficiency. Finally, the multi-area state estimator is tested for accuracy, its ability to detect bad data, and computation time.

State estimation is an important tool for power system monitoring and the present study involves integrating phasor measurement units in the state estimation process. Based on measurements taken throughout the network, the role of a state estimator is to estimate the state variables of the power system while checking that these estimates are consistent with the measurement set. In the case of power system state estimation, the state variables are the voltage phasors at each network bus.\ The classical state estimator currently used is based on SCADA (Supervisory Control and Data Acquisition) measurements. Weaknesses of the SCADA measurement system are the asynchronicity of the measurements, which introduce errors in the state estimation results during dynamic events on the electrical network.\ Wide-area monitoring systems, consisting of a network of Phasor Measurement Units (PMU) provide synchronized phasor measurements, which give an accurate snapshot of the monitored part of the network at a given time. The objective of this thesis is to integrate PMU measurements in the state estimator. The proposed state estimators use PMU measurements exclusively, or both classical and PMU measurements.\ State estimation is particularly useful to filter out measurement noise, detect and eliminate bad data. A sensitivity analysis to measurement errors is carried out for a state estimator using only PMU measurements and a classical state estimator. Measurement errors considered are Gaussian noise, systematic errors and asynchronicity errors. Constraints such as zero injection buses are also integrated in the state estimator. Bad data detection and elimination can be done before the state estimation, as in pre-estimation methods, or after, as in post-estimation methods. For pre-estimation methods, consistency tests are used. Another proposed method is validation of classical measurements by PMU measurements. Post-estimation is applied to a measurement set which has asynchronicity errors. Detection of a systematic error on one measurement in the presence of Gaussian noise is also analysed. \ The state estimation problem can only be solved if the measurements are well distributed over the network and make the network observable. Observability is crucial when trying to solve the state estimation problem. A PMU placement method based on metaheuristics is proposed and compared to an integer programming method. The PMU placement depends on the chosen objective. A given PMU placement can provide full observability or redundancy. The PMU configuration can also take into account the zero injection nodes which further reduce the number of PMUs needed to observe the network. Finally, a method is proposed to determine the order of the PMU placement to gradually extend the observable island. \ State estimation errors can be caused by erroneous line parameter or bad calibration of the measurement transformers. The problem in both cases is to filter out the measurement noise when estimating the line parameters or calibration coefficients and state variables. The proposed method uses many measurement samples which are all integrated in an augmented state estimator which estimates the voltage phasors and the additional parameters or calibration coefficients.

State estimation plays an essential role in the monitoring and control of power transmission systems. In modern, highly inter-connected power systems the state estimation should be performed in a distributed fashion and requires information exchange between the control centers of directly connected systems. Motivated by recent reportson trojans targeting industrial control systems, in this paper we investigate how a single compromised control center can affect the outcome of distributed state estimation. We describe five attack strategies, and evaluate their impact on the IEEE 118 benchmark power system. We show that that even if the state estimation converges despite the attack, the estimate can have up to 30% of error, and bad data detection cannot locate theattack. We also show that if powerful enough, the attack can impede the convergence of the state estimation, and thus it can blind the system operators. Our results show that it is important to provide confidentiality for the measurement data in order to prevent the most powerful attacks. Finally, we discuss a possible way to detect and to mitigate these attacks. / <p>QC 20130522</p>

The objective of this thesis is to prove the validity of a multi-area state estimator and investigate the advantages it provides over a serial state estimator. This is done utilizing the IEEE 118 Bus Test System as a sample system. This thesis investigates the benefits that stem from utilizing a multi-area state estimator instead of a serial state estimator. These benefits are largely in the form of increased accuracy and decreased processing time. First, the theory behind power system state estimation is explained for a simple serial estimator. Then the thesis shows how conventional measurements and newer, more accurate PMU measurements work within the framework of weighted least squares estimation. Next, the multi-area state estimator is examined closely and the additional measurements provided by PMUs are used to increase accuracy and computational efficiency. Finally, the multi-area state estimator is tested for accuracy, its ability to detect bad data, and computation time.

abstract: This study focuses on state estimation of nonlinear discrete time systems with constraints. Physical processes have inherent in them, constraints on inputs, outputs, states and disturbances. These constraints can provide additional information to the estimator in estimating states from the measured output. Recursive filters such as Kalman Filters or Extended Kalman Filters are commonly used in state estimation; however, they do not allow inclusion of constraints in their formulation. On the other hand, computational complexity of full information estimation (using all measurements) grows with iteration and becomes intractable. One way of formulating the recursive state estimation problem with constraints is the Moving Horizon Estimation (MHE) approximation. Estimates of states are calculated from the solution of a constrained optimization problem of fixed size. Detailed formulation of this strategy is studied and properties of this estimation algorithm are discussed in this work. The problem with the MHE formulation is solving an optimization problem in each iteration which is computationally intensive. State estimation with constraints can be formulated as Extended Kalman Filter (EKF) with a projection applied to estimates. The states are estimated from the measurements using standard Extended Kalman Filter (EKF) algorithm and the estimated states are projected on to a constrained set. Detailed formulation of this estimation strategy is studied and the properties associated with this algorithm are discussed. Both these state estimation strategies (MHE and EKF with projection) are tested with examples from the literature. The average estimation time and the sum of square estimation error are used to compare performance of these estimators. Results of the case studies are analyzed and trade-offs are discussed. / Dissertation/Thesis / M.S. Electrical Engineering 2013

Presented is a method for estimating the planar position, velocity, and orientation states of a tagged shark. The method is designed for implementation on an Autonomous Underwater Vehicle (AUV) equipped with a stereo-hydrophone and receiver system that detects acoustic signals transmitted by a tag. The particular hydrophone system used here provides a measurement of relative bearing angle to the tag, but does not provide the sign (+ or -) of the bearing angle. A particle filter was used for fusing measurements over time to produce a state estimate of the tag location. The particle filter combined with an active control system allowed the system to overcome the ambiguity in the sign of the bearing angle. This state estimator was validated by tracking a stationary tag and moving tag with known positions. These experiments revealed state estimate errors were on par with those obtained by manually driven boat based tracking systems, the current method used for tracking fish and sharks over long distances. Final experiments involved the catching, releasing, and an autonomous AUV tracking of a 1 meter leopard shark (Triakis semifasciata) in SeaPlane Lagoon, Los Angeles, California.

Various sensors distributed across different parts of the electric power grid provide measurements to the control center operator for situational awareness of the system. Voltage transformer, current transformer, relay and phasor measurement units (PMU) are types of sensors for power system monitoring. The utilities monitor the operating condition of their system by processing the measurements received from these various sensors using a state estimator. A state estimator refines these measurements, compensates for any lost data and provides a snapshot of the power system. The operator at the control center does further analysis using energy management system tools based on the most recent data and required state of the system. The electric power grid is vulnerable to blackouts caused by physical disturbances, human errors and external disasters. These disturbances can also cause loss of data, sensor failure or communication link failure. This research work focuses on comparing state estimation algorithms with loss of measurement data. The measurements are assumed to be lost as clustered and scattered data sets. Weighted Least Square (WLS), Least Absolute Value (LAV) and Iteratively Reweighted Least Squares (IRLS) implementation of Weighted Least Absolute Value (WLAV) algorithms are compared for state estimation with clustered and scattered loss of data. These algorithms are tested on a six bus, I 30 bus and 137 bus utility test cases. The test results indicate the best possible algorithm in several considered scenarios based on an error index. Additionally, phasor measurements data are included in two of the state estimation algorithms to study their ability to mitigate the loss of measurement data.

Phasor Measurement Units (PMUs) are widely acknowledged as one of the most promising developments in the field of real-time monitoring of power systems. By aligning the time stamps of voltage and current phasor measurements that are consistent with Coordinated Universal Time (UTC), a coherent picture of the power system state can be achieved through either direct measurements or simple linear calculations. With the growing number of PMUs planned for installation in the near future, both utilities and research institutions are looking for the best solutions to the placement of units as well as to the applications that make the most of phasor measurements. This dissertation explores a method for optimal PMU placement as well as two applications of synchronized phasor measurements in state estimation. The pre-processing PMU placement method prepares the system data for placement optimization and reduces the size of the optimization problem. It is adaptive to most of the optimal placement methods and can save a large amount of computational effort. Depth of un-observability is one of the criteria to allow the most benefit out of a staged placement of the units. PMUs installed in the system provide synchronized phasor measurements that are highly beneficial to power system state estimations. Two related applications are proposed in the dissertation. First, a post-processing inclusion of phasor measurements in state estimators is introduced. This method avoids the revision of the existing estimators and is able to realize similar results as mixing phasor data with traditional SCADA with a linear afterwards step. The second application is a method to calibrate instrument transformers remotely using phasor measurements. Several scans of phasor measurements are used to accomplish estimating system states in conjunction with complex instrument transformer correction factors. Numerical simulation results are provided for evaluation of the calibration performance with respect to the number of scans and load conditions. Conducting theoretical and numerical analysis, the methods and algorithms developed in this dissertation are aimed to strategically place PMUs and to incorporate phasor measurements into state estimators effectively and extensively for better system state monitoring. Simulation results show that the proposed placement method facilitates approaching the exact optimal placement while keep the computational effort low. Simulation also shows that the use of phasor measurement with the proposed instrument transformer correction factors and proposed state estimation enhancement largely improves the quality of state estimations. / Ph. D.

Wind observations that are critical for understanding meteorological processes occurring inside of the Earth's atmospheric boundary layer (ABL) are sparse due to limitations of conventional atmospheric sensors. In this dissertation, dynamic systems and estimation theory are combined with experimental methods to exploit the flight envelope of multirotor UAS for wind sensing. The parameters of three quadrotor motion models, consisting of a kinematic particle, a dynamic particle, and a dynamic rigid body models are developed to measure wind velocity in hovering flight. Wind tunnel and steady level flight tests are used to characterize kinematic and dynamic particle models. System identification stepwise regression and output error algorithms are used to determine the model structure and parameter estimates of rigid body models. The comparison of all three models demonstrates the rigid body model to have higher performance resolving slow-varying winds based on a frequency response analysis and field experiments conducted next to a 3-D sonic anemometer. The dissertation also presents an extension of the rigid body wind estimation framework to profile the horizontal components of wind velocity in vertical steady ascending flight. The extension employed system identification to characterize five rigid body models for steady-ascending flight speeds increasing from 0 to 2 m/s in intervals of 0.5~m/s. State observers for wind profiling were synthesized using all five rigid body models. Performance assessments employing wind observations from in situ and remote sensors demonstrated model-based wind profiling results to be be in close agreement with ground-truth wind observations. Finally, the rigid body wind sensing framework developed in this dissertations for multirotor UAS is employed to support science objectives for the Advanced Lagrangian Predictions for Hazards Assessment Project. Quadrotor wind measurements sampled at 10 m above sea level were used to characterize the leeway of a person in water for search and rescue scenarios. Leeway values determined from quadrotor wind measurements were found to be in close to leeway parameters previous published in the literature. This results demonstrates the utility of model-based wind sensing for multirotor UAS for providing wind velocity observations in complex environments where conventional wind observations are not readily available. / Doctor of Philosophy / Wind observations that are critical for understanding meteorological processes occurring inside of the Earth's atmospheric boundary layer (ABL) are sparse due to limitations of conventional atmospheric sensors. In this dissertation, dynamic systems and estimation theory are combined with experimental methods to exploit the flight envelope of multirotor UAS for wind sensing. The parameters of three quadrotor motion models, consisting of a kinematic particle model, a dynamic particle model, and a dynamic rigid body model, are characterized to measure wind velocity in hovering flight. Parameter characterizations are realized using data from wind tunnel, steady level flight tests and system identification experiments. Model-based wind estimations algorithms are developed using the kinematic particle model directly and by synthesizing state observers for the dynamic particle and rigid body models separately. For comparison purposes, the frequency response characteristic of the dynamic particle and rigid body models is examined to determine the range of wind fluctuations that each model can resolve. Performance comparisons demonstrate that the rigid body model to resolve higher wind fluctuations and yield more accurate wind estimates. The dissertation extends the rigid body wind estimation algorithm to estimate wind velocity profiles of the horizontal wind vector. The rigid body wind estimation algorithms is used to answer science questions about about the drift of a person in water.