Neste trabalho propõe-se um método de análise de observabilidade para estimação de estados e parâmetros em sistemas elétricos de potência, baseado nas equações normais. O método fundamenta-se na fatoração triangular da matriz ganho aumentada e nos conceitos de caminhos de fatoração. O mesmo utiliza rotinas já existentes no processo de estimação, sendo simples, de fácil implementação, rápida execução e não exige a solução de equações algébricas. Para comprovar a sua eficiência vários testes foram realizados, utilizando os sistemas de 6, 14 e 30 barras do IEEE, tendo sido satisfatórios os resultados obtidos. / In this work we propose a method of observability analysis for states and parameters estimation in electric power systems, based on the Normal Equations. The method is based on triangular factoration of the augmented gain matrix and on the concepts of factoration paths. It uses routines that there exist in the estimation process. These routines are simple, of easy implementation, fast execution and it doesn\'t demand the solution of algebraic equations. To prove your efficiency several tests were accomplished, using the 6, 14 and 30-bus IEEE test systems. The obtained results were satisfactory.

Desenvolveu-se neste trabalho um método para projeto e fortalecimento de planos de medição, para efeito de estimação de estados. O método proposto permite a obtenção de planos de medição que além de isentos de medidas críticas e de conjuntos críticos de medidas, garantem a observabilidade do sistema, mesmo com a perda simultânea de 1 ou 2 medidas quaisquer, ou, até mesmo, com a perda de 1 UTR. É um método numérico simples, de fácil implantação, que se baseia na análise da estrutura da matriz resultante da decomposição LDU, que é obtida através da fatoração triangular da matriz Jacobiana. Para comprovar a sua eficiência, vários testes foram realizados, utilizando os sistemas de 14 e 30 barras do IEEE, o sistema de 121 barras da ELETROSUL e o sistema de 383 barras da CHESF. / In this work a method to design and to upgrade Measurements Placement Plan for state estimation is proposed. The proposed method allows the obtention of measurements placement plans that, besides free of both critical measurements and critical sets, maintain the system observability when 1 or 2 measurements are lost, at same time, or even when a Remote Terminal Unit (RTU) is lost. It is a simple numerical method, easy to implement and based on the analysis of the structure of the resultant matrix of the decomposition LDU, that it is obtained through a triangular factorization of the Jacobian matrix. To prove the efficiency of the proposed method, several tests were made using the IEEE 14 and 30-bus systems, a 121-bus system from ELETROSUL and a 383-bus system from CHESF.

Orientador: Janito Vaqueiro Ferreira / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-25T19:21:19Z (GMT). No. of bitstreams: 1 Miranda_ConradoSilva_M.pdf: 11847342 bytes, checksum: 96a6b7a5caa8c1b41571795cc6e8164a (MD5) Previous issue date: 2014 / Resumo: Este trabalho tem como objetivo desenvolver um controlador para um quadrirrotor cujos parâmetros são desconhecidos. Para o controle deste sistema, normalmente são utilizados controladores avançados que dependem de parâmetros do sistema ou controladores simples que necessitam de ajuste manual dos ganhos. O controlador desenvolvido possui baixa complexidade e é capaz de ajustar seus parâmetros automaticamente para minimizar uma função de custo durante o voo, sem necessitar de conhecimento de nenhum parâmetro do sistema. Entretanto, este controlador necessita dos estados do sistema, que não estão disponíveis diretamente. Portanto, uma análise da aplicação de métodos de filtragem para estimação destes estados é realizada, comparando-se diversos possíveis modelos estocásticos. Contudo, a filtragem necessita de sensores calibrados corretamente, o que levou à criação de novos algoritmos para calibração dos sensores utilizados. Os algoritmos desenvolvidos nestas três áreas representam passos na direção de criar quadrirrotores que operam em ambientes diversificados de modo robusto / Abstract: This work's objective is to develop a controller for a quadrotor with unknown parameters. For this system's control, usually advanced controllers that require knowledge of the system's parameters or simple controllers that require manual gain tunning are used. The controller developed has low complexity and is able to adjust its parameters automatically to minimize a cost function during flight, without requiring knowledge of any system's parameter. However, this controller requires the system's states, which aren't available directly. Hence an analysis of the use of filtering methods to estimate these states is conducted, comparing many possible stochastic models. Nonetheless, the filtering requires correctly calibrated sensors, which led to the creation of new algorithms for calibrating the sensors used. The algorithms developed in these three areas represent steps in the direction of creating quadrotors that operate in diverse environments in a robust way / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

[pt] Este trabalho trata da comparação de quatro de métodos de identificação paramétrica para sistemas dinâmicos lineares, operando em ambiente estocástico. Dos métodos envolvidos, três são de correlações, enquanto um é uma derivação do método de mínimos quadrados. Inicialmente, foi apresentado o problema de identificação de sistemas, e são discutidos aspectos estruturais ligados à ele. A seguir é apresentado um resumo de cada método e efetuada a comparação entre eles, tanto sob o ponto de vista estrutural quanto computacional. Nesta última fase, foram feitas simulações, e utilizado dados reais. / [en] This work presents a comparison of effectiveness of form parametric identification methods for linear dynamical systems operating in a stochastic environment. Three of these methods are correlation ones, and the other is derived from the least squares method. First of all, the system identification problem was introduced, and then, the structural aspects related to it were discussed. Later on, it was presented a review ot the above mentioned methods as well as a comparison between them. Such a comparison was concerned both with structural and computational aspects. This last stage uses simulated and real data.

The dissertation research investigates estimating of power system static and dynamic states (e.g. rotor angle, rotor speed, mechanical power, voltage magnitude, voltage phase angle, mechanical reference point) as well as identification of synchronous generator parameters. The research has two focuses: i. Synchronous generator dynamic model states and parameters estimation using real-time PMU data. ii.Integrate PMU data and conventional measurements to carry out static state estimation. The first part of the work focuses on Phasor Measurement Unit (PMU) data-based synchronous generator states and parameters estimation. In completed work, PMU data-based synchronous generator model identification is carried out using Unscented Kalman Filter (UKF). The identification not only gives the states and parameters related to a synchronous generator swing dynamics but also gives the states and parameters related to turbine-governor and primary and secondary frequency control. PMU measurements of active power and voltage magnitude, are treated as the inputs to the system while voltage phasor angle, reactive power, and frequency measurements are treated as the outputs. UKF-based estimation can be carried out at real-time. Validation is achieved through event play back to compare the outputs of the simplified simulation model and the PMU measurements, given the same input data. Case studies are conducted not only for measurements collected from a simulation model, but also for a set of real-world PMU data. The research results have been disseminated in one published article. In the second part of the research, new state estimation algorithm is designed for static state estimation. The algorithm contains a new solving strategy together with simultaneous bad data detection. The primary challenge in state estimation solvers relates to the inherent non-linearity and non-convexity of measurement functions which requires using of Interior Point algorithm with no guarantee for a global optimum solution and higher computational time. Such inherent non-linearity and non-convexity of measurement functions come from the nature of power flow equations in power systems. The second major challenge in static state estimation relates to the bad data detection algorithm. In traditional algorithms, Largest Normalized Residue Test (LNRT) has been used to identify bad data in static state estimation. Traditional bad data detection algorithm only can be applied to state estimation. Therefore, in a case of finding any bad datum, the SE algorithm have to rerun again with eliminating found bad data. Therefore, new simultaneous and robust algorithm is designed for static state estimation and bad data identification. In the second part of the research, Second Order Cone Programming (SOCP) is used to improve solving technique for power system state estimator. However, the non-convex feasible constraints in SOCP based estimator forces the use of local solver such as IPM (interior point method) with no guarantee for quality answers. Therefore, cycle based SOCP relaxation is applied to the state estimator and a least square estimation (LSE) based method is implemented to generate positive semi-definite programming (SDP) cuts. With this approach, we are able to strengthen the state estimator (SE) with SOCP relaxation. Since SDP relaxation leads the power flow problem to the solution of higher quality, adding SDP cuts to the SOCP relaxation makes Problem’s feasible region close to the SDP feasible region while saving us from computational difficulty associated with SDP solvers. The improved solver is effective to reduce the feasible region and get rid of unwanted solutions violate cycle constraints. Different Case studies are carried out to demonstrate the effectiveness and robustness of the method. After introducing the new solving technique, a novel co-optimization algorithm for simultaneous nonlinear state estimation and bad data detection is introduced in this dissertation. ${\ell}_1$-Norm optimization of the sparse residuals is used as a constraint for the state estimation problem to make the co-optimization algorithm possible. Numerical case studies demonstrate more accurate results in SOCP relaxed state estimation, successful implementation of the algorithm for the simultaneous state estimation and bad data detection, and better state estimation recovery against single and multiple Gaussian bad data compare to the traditional LNRT algorithm.

Master of Science / Department of Mechanical and Nuclear Engineering / Dale E. Schinstock / The core objective of this research is to develop an estimator capable of tracking the states of ground targets with observation measurements obtained from a single monocular camera mounted on a small unmanned aerial vehicle (UAV). Typical sensors on a small UAV include an inertial measurement unit (IMU) with three axes accelerometer and rate gyro sensors and a global positioning system (GPS) receiver which gives position and velocity estimates of the UAV. Camera images are combined with these measurements in state estimate filters to track ground features of opportunity and a target. The images are processed by a keypoint detection and matching algorithm that returns pixel coordinates for the features. Kinematic state equations are derived that reflect the relationships between the available input and output measurements and the states of the UAV, features, and target. These equations are used in the development of coupled state estimators for the dynamic state of the UAV, for estimation of feature positions, and for estimation of target position and velocity. The estimator developed is tested in MATLAB/SIMULINK, where GPS and IMU data are generated from the simulated states of a nonlinear model of a Navion aircraft. Images are also simulated based upon a fabricated environment consisting of features and a moving ground target. Target observability limitations are overcome by constraining the target vehicle to follow ground terrain, defined by local features, and subsequent modification of the target's observation model. An unscented Kalman filter (UKF) provides the simultaneous localization and mapping solution for the estimation of aircraft states and feature locations. Another filter, a loosely coupled Kalman filter for the target states, receives 3D measurements of target position with estimated covariance obtained by an unscented transformation (UT). The UT uses the mean and covariance from the camera measurements and from the UKF estimated aircraft states and feature locations to determine the estimated target mean and covariance. Simulation results confirm that the new loosely coupled filters are capable of estimating target states. Experimental data, collected from a research UAV, explores the effectiveness of the terrain estimation techniques required for target tracking.

The evolving complexity of electric power systems with higher levels of uncertainties is a new challenge faced by system operators. Therefore, new methods for power system prediction, monitoring and state estimation are relevant for the efficient exploitation of renewable energy sources and the secure operation of network assets. In order to estimate all possible operating conditions of power systems, this Thesis proposes the use of Gaussian mixture models to represent non-Gaussian correlated input variables, such as wind power output or aggregated load demands in the probabilistic load flow problem. The formulation, based on multiple Weighted Least Square runs, is also extended to monitor distribution radial networks where the uncertainty of these networks is aggravated by the lack of sufficient real-time measurements. This research also explores reduction techniques to limit the computational demands of the probabilistic load flow and it assesses the impact of the reductions on the resulting probability density functions of power flows and bus voltages. The development of synchronised measurement technology to support monitoring of electric power systems in real-time is also studied in this work. The Thesis presents and compares different formulations for incorporating conventional and synchronised measurements in the state estimation problem. As a result of the study, a new hybrid constrained state estimator is proposed. This constrained formulation makes it possible to take advantage of the information from synchronised phasor measurements of branch currents and bus voltages in polar form. Additionally, the study is extended to assess the advantages of PMU measurements in multi-area state estimators and it explores a new algorithm that minimises the data exchange between local area state estimators. Finally, this research work also presents the advantages of dynamic state estimators supported by Synchronised Measurement Technology. The dynamic state estimator is compared with the static approach in terms of accuracy and performance during sudden changes of states and the presence of bad data. All formulations presented in this Thesis were validated in different IEEE test systems.

A run-of-mine ore milling circuit is primarily used to grind incoming ore containing precious metals to a particle size smaller than a specification size. A traditional run-of-mine (ROM) ore single-stage closed milling circuit comprises of the operational units: mill, sump and cyclone. These circuits are difficult to control because of significant nonlinearities, large time delays, large unmeasured disturbances, process variables that are difficult to measure and modelling uncertainties. A nonlinear model predictive controller with state estimation could yield good control of the ROM ore milling circuit despite these difficulties. Additionally, the ROM ore milling circuit is an energy intensive unit and a controller or power optimizer could bring significant cost savings. A nonlinear model predictive controller requires good state estimates and therefore a neural network for state estimation as an alternative to the particle filter has been addressed. The neural network approach requires fewer process variables that need to be measured compared to the particle filter. A neural network is trained with three disturbance parameters and used to estimate the internal states of the mill, and the results are compared with those of the particle filter implementation. The neural network approach performed better than the particle filter approach when estimating the volume of steel balls and rocks within the mill. A novel combined neural network and particle filter state estimator is presented to improve the estimation of the neural network approach for the estimation of volume of fines, solids and water within the mill. The estimation performance of the combined approach is promising when the disturbance magnitude used is smaller than that used to train the neural network. After state estimation was addressed, this work targets the implementation of a nonlinear controller combined with full state estimation for a grinding mill circuit. The nonlinear controller consists of a suboptimal nonlinear model predictive controller coupled with a dynamic inversion controller. This allows for fast control that is asymptotically stable. The nonlinear controller aims to reconcile the opposing objectives of high throughput and high product quality. The state estimator comprises of a particle filter for five mill states as well as an additional estimator for three sump states. Simulation results show that control objectives can be achieved despite the presence of noise and significant disturbances. The cost of energy has increased significantly in recent years. This increase in price greatly affects the mineral processing industry because of the large energy demands. A run-of-mine ore milling circuit provides a suitable case study where the power consumed by a mill is in the order of 2 MW. An attempt has been made to reduce the energy consumed by the mill in the two ways: firstly, within the nonlinear model predictive control in a single-stage circuit configuration and secondly, running multiple mills in parallel and attempting to save energy while still maintaining an overall high quality and good quantity. A formulation for power optimization of multiple ROM ore milling circuits has been developed. A first base case consisted not taking power into account in a single ROM ore milling circuit and a second base case split the load and throughput equally between two parallel milling circuits. In both cases, energy can be saved using the NMPC compared to the base cases presented without significant sacrifice in product quality or quantity. The work presented covers three topics that has yet to be addressed within the literature: a neural network for mill state estimation, a nonlinear controller with state estimation integrated for a ROM ore milling circuit and power optimization of a single and multiple ROM ore milling circuit configuration. / Dissertation (MEng)--University of Pretoria, 2015. / Electrical, Electronic and Computer Engineering / Unrestricted

abstract: The accurate monitoring of the bulk transmission system of the electric power grid by sensors, such as Remote Terminal Units (RTUs) and Phasor Measurement Units (PMUs), is essential for maintaining the reliability of the modern power system. One of the primary objectives of power system monitoring is the identification of the snapshots of the system at regular intervals by performing state estimation using the available measurements from the sensors. The process of state estimation corresponds to the estimation of the complex voltages at all buses of the system. PMU measurements play an important role in this regard, because of the time-synchronized nature of these measurements as well as the faster rates at which they are produced. However, a model-based linear state estimator created using PMU-only data requires complete observability of the system by PMUs for its continuous functioning. The conventional model-based techniques also make certain assumptions in the modeling of the physical system, such as the constant values of the line parameters. The measurement error models in the conventional state estimators are also assumed to follow a Gaussian distribution. In this research, a data mining technique using Deep Neural Networks (DNNs) is proposed for performing a high-speed, time-synchronized state estimation of the transmission system of the power system. The proposed technique uses historical data to identify the correlation between the measurements and the system states as opposed to directly using the physical model of the system. Therefore, the highlight of the proposed technique is its ability to provide an accurate, fast, time-synchronized estimate of the system states even in the absence of complete system observability by PMUs. The state estimator is formulated for the IEEE 118-bus system and its reliable performance is demonstrated in the presence of redundant observability, complete observability, and incomplete observability. The robustness of the state estimator is also demonstrated by performing the estimation in presence of Non-Gaussian measurement errors and varying line parameters. The consistency of the DNN state estimator is demonstrated by performing state estimation for an entire day. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2020

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