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In this thesis, two separate problems are examines. First, sinusoidal signals are quite prevalent in practical applications. For example, any machine driven by a rotary shaft will exhibit periodic behaviour. For this reason, the estimation of sinusoidal parameters is studied extensively in the literature. Often in practical applications, there are unmodeled disturbances to the system, and the incoming measurements are noisy. Thus, estimation of the parameters of a sinusoidal signal in real-time for these conditions is of interest, calling for the use of a filter-based approach such as the Extended Kalman Filter. Considering the sinusoidal signal in its complex form, a novel approach is proposed resulting in a complex-valued filter. The resulting complex Extended Kalman Filter’s performance is evaluated in various test environments and is compared to standard approaches to the estimation problem using a Discrete Fourier Transform and standard Extended Kalman Filter. Results show that the complex Extended Kalman Filter outperforms the standard approaches in some cases in both accuracy and convergence rate. Second, research on hybrid systems has seen a large growth in interest in recent years. This is largely due to the increase of natural systems where discrete mode dynamics interact with continuous state dynamics. Switched systems are a subclass of hybrid systems that restrict their definition to continuous dynamic systems that interact with dis- crete switching events. Controller synthesis for such systems is no trivial task. Given the current trend in Artificial Intelligence and Machine Learning approaches, Dynamic Programming is explored as a means to approximate optimal control policies for switched systems. Discussions of discretization of the system’s state space are presented, followed by a high-level overview of an algorithm that leverages Dynamic Programming to find the approximated optimal control policies. Finally, the algorithm is applied to several examples to demonstrate its effectiveness. / Thesis / Master of Applied Science (MASc)

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24103号 / 工博第5025号 / 新制||工||1784(附属図書館) / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 藤本 健治, 教授 太田 快人, 准教授 丸田 一郎, 教授 泉田 啓 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The phasor measurement unit (PMU) is considered to be one of the most important measuring devices in the future of power systems. The distinction comes from its unique ability to provide synchronized phasor measurements of voltages and currents from widely dispersed locations in an electric power grid. The commercialization of the global positioning satellite (GPS) with accuracy of timing pulses in the order of 1 microsecond made possible the commercial production of phasor measurement units. Simulations and field experiences suggest that PMUs can revolutionize the way power systems are monitored and controlled. However, it is perceived that costs and communication links will affect the number of PMUs to be installed in any power system. Furthermore, defining the appropriate PMU system application is a utility problem that must be resolved. This thesis will address two key issues in any PMU initiative: placement and system applications. A novel method of PMU placement based on incomplete observability using graph theoretic approach is proposed. The objective is to reduce the required number of PMUs by intentionally creating widely dispersed pockets of unobserved buses in the network. Observable buses enveloped such pockets of unobserved regions thus enabling the interpolation of the unknown voltages. The concept of depth of unobservability is introduced. It is a general measure of the physical distance of unobserved buses from those known. The effects of depth of unobservability on the number of PMU placements and the errors in the estimation of unobserved buses will be shown. The extent and location of communication facilities affects the required number and optimal placement of PMUs. The pragmatic problem of restricting PMU placement only on buses with communication facilities is solved using the simulated annealing (SA) algorithm. SA energy functions are developed so as to minimize the deviation of communication-constrained placement from the ideal strategy as determined by the graph theoretic algorithm. A technique for true real time monitoring of voltage security using synchronized phasor measurements and decision trees is presented as a promising system application. The relationship of widening bus voltage angle separation with network stress is exploited and its connection to voltage security and margin to voltage collapse established. Decision trees utilizing angle difference attributes are utilized to classify the network voltage security status. It will be shown that with judicious PMU placement, the PMU angle measurement is equally a reliable indicator of voltage security class as generator var production. A method of enhancing the weighted least square state estimator (WLS-SE) with PMU measurements using a non-invasive approach is presented. Here, PMU data is not directly inputted to the WLS estimator measurement set. A separate linear state estimator model utilizing the state estimate from WLS, as well as PMU voltage and current measurement is shown to enhance the state estimate. Finally, the mathematical model for a streaming state estimation will be presented. The model is especially designed for systems that are not completely observable by PMUs. Basically, it is proposed to estimate the voltages of unobservable buses from the voltages of those observable using interpolation. The interpolation coefficients (or the linear state estimators, LSE) will be calculated from a base case operating point. Then, these coefficients will be periodically updated using their sensitivities to the unobserved bus injections. It is proposed to utilize the state from the traditional WLS estimator to calculate the injections needed to update the coefficients. The resulting hybrid estimator is capable of producing a streaming state of the power system. Test results show that with the hybrid estimator, a significant improvement in the estimation of unobserved bus voltages as well as power flows on unobserved lines is achieved. / Ph. D.

Because of a move from Independent System Operators (ISOs) to Regional Transmission Operators (RTOs), a need for real-time wide-area system monitoring has arisen. The state estimator (SE) is the tool currently used in power systems for real-time monitoring. Because current SE techniques become operationally expensive on such large systems, it is beneficial to consider alternate methods for wide-area state estimation (WASE). In particular, hierarchal methods for WASE become beneficial for large systems because of their speed of operation and relatively low data volume. This study tests four hierarchal WASE methods - two taken from literature, and two developed by the author — and compares them with the use of an integrated wide-area estimator. Additionally, because of their accurate and readily available measurement capability, the inclusion of phasor measurement unit (PMU) data in the WASE methods is examined. For the purpose of realistically integrating an RTO WASE with current ISOs, the methods are constrained so that they do not require sensitive data, nor do they alter the operation of the ISOs SE in any way. The methods are tested for speed of operation, global and local accuracy, and robustness under bad data and data loss. / Master of Science

There is a growing interest in robust and nonparametric methods with engineering applications, due to the nature of the data. Here, we study two power systems engineering applications that employ or recommend robust and nonparametric methods; topology error identification and voltage calibration. Topology errors are a well-known, well-documented problem for utility companies. A topology error occurs when a line's status in a power network, whether active or deactive, is misclassified. This will lead to an incorrect Jacobian matrix used to estimate the unknown parameters of a network in a nonlinear regression model. We propose a solution using nonlinear regression techniques to identify the correct status of every line in the network by deriving a statistical model of the power flows and injections while employing Kirchhoff's Current Law. Simulation results on the IEEE-118 bus system showed that the methodology was able to detect where topology errors occurred as well as identify gross measurement errors. The Friedman Two-Way Analysis of Variance by Ranks test is advocated to calibrate voltage measurements at a bus in a power network. However, it was found that the Friedman test was only slightly more robust or resistant in the presence of discordant measurements than the classical F-test. The resistance of a statistical test is defined as the fraction of bad data necessary to switch a statistical conclusion. We mathematically derive the maximum resistance to rejection and to acceptance of the Friedman test, as well as the Brown-Mood test, and show that the Brown-Mood test has a higher maximum resistance to rejection and to acceptance than the Friedman test. In addition, we simulate the expected resistance to rejection and to acceptance of both tests and show that on average the Brown-Mood test is slightly more robust to rejection while on average the Friedman test is more robust to acceptance. / Ph. D.

This dissertation presents a new, highly robust algorithm for electric power system state estimation. A graph theory-based system decomposition scheme is coupled with a high breakdown point estimator to allow reliable identification of multiple interacting bad data even in cases of conforming errors. The algorithm is inherently resistant to bad measurements in positions of leverage, makes no a priori measurement error probability distribution assumptions, and is applicable in a real-time environment. In addition to presenting a new state estimation algorithm, the weaknesses of two prominent state determination methods are explored. The comparative advantages of high breakdown point estimators are then summarized. New theorems quantifying the previously unexamined effect system sparsity has on the exact fit point of some members of this estimator family are presented. These results serve as the catalyst for the overall state estimation algorithm presented. Numerous practical implementation issues are addressed with efficient implementation techniques described at each step. / Ph. D.

The ability to analyze a power system is essential to power system engineers and planners. The Bus program, a Microsoft Windows-based program, helps users make these analyses. Unlike other power system analysis programs, the Bus program performs three different types of analyses (short circuit, load flow, and state estimation) and offers users a graphical interface on which to enter their system and data. This thesis presents the Bus program and discusses various aspects of it, focusing on the load flow and state estimation routines, which were the main thrust of the project. Each of these routines was written by setting up a flowchart and defining the calculations to be carried out. Vehicles were then developed so that users can enter system data and view the results of the calculations. The ability to do this graphically is one of the main features of the program. Several test cases are presented to demonstrate the program's operation, and a User's Manual is included to show users how to operate the program. / Master of Science

A new network model has been developed which allows the calculation of state estimates for unbalanced electric power systems. This model incorporates the effects of mutually coupled conductors, earth return paths, unbalanced device configurations, and multiple voltage references. Development of the new model appeals to multiport network theory and graph theoretic principles. Model equations are employed directly to obtain least squares estimators in the phase-voltage reference frame. The concept of power system segments is introduced and segment multiport equations are developed. The concept of power system modified primitive networks is introduced and system multiport equations are developed. Segment and system multiport equations are used to obtain a state estimator formulation in variables suitable for practical systems analysis. / Ph. D.