The behavior of large and tightly interconnected power systems resembles, in certain circumstances, the behavior of a continuously distributed system. This resemblance motivated the derivation of continuum models, which were used to explain and predict disturbance propagation, un-damped power oscillations, and the stability of power systems. In this dissertation, we propose a one-dimensional continuum representation suitable for meshed power systems. Previous continuous representations of meshed power systems used two-dimensional spatial domains. Thus our approach has the potential to provide better resolution for comparable computational burden. It is important to note that, the computational burden required to obtain solutions for PDEs involved in the continuum representation varies notably with the solver implementation. The contributions of this dissertation are: a) Reviewing a previous continuum model and providing a detailed derivation for the one-dimensional version of it. b) Providing and describing in detail a parameter distribution technique adequate for the continuum approach. c) Identifying and documenting limitations on the continuum model voltage calculation. e) Providing a procedure to simulate the behavior of meshed power systems using the one dimensional continuum model. And f) Identifying and applying a numerical PDE solver for the continuum approach. / Ph. D.

Paralleling operation of DC/DC converters is widely used in today's distributed power systems. To ensure balanced output currents among paralleled power modules, current sharing control is usually necessary.Active current sharing controls with current feedback mechanism are widely used in today's power supplies. However, the dynamic performance of these current sharing control schemes are not yet clearly explored. In this work, the dynamic current sharing performance is evaluated for paralleling systems with the output impedance approach. As the representative of the terminal characteristic of a power converter, output impedance is a powerful tool to study the dynamic response under load transients. The dynamic current sharing analyses are then conducted for three different active current sharing control structures and a comprehensive comparison among them helps the designer to choose appropriate controls for different applications. On the other hand, high-frequency load transients are possible to happen for voltage regulators, which are the power supplies of microprocessors. In order to study the dynamic current sharing performance for a paralleling system when the perturbation frequency is higher than half of the switching frequency,the conventional output impedance concept needs to be extended. Due to the non-linear behavior of a switching modulator, the beat-frequency phenomenon could cause unexpected failure of a power supply when the perturbation frequency is close to the switching frequency. To address this issue, an unconventional multi-frequency model is proposed for high-frequency dynamic current sharing studies. With this model, the sideband components are possible to be included and the beat-frequency oscillations can be predicted. After that, the conventional impedance concept is expanded in the form of extended describing function, so that the terminal characteristics of paralleled converters are represented by a series of impedances. Besides the analyses, this work also proposed several solutions for the beat-frequency oscillation issue which are experimentally verified. In summary, both low-frequency and high-frequency dynamic current sharing performances are studied in this dissertation. The output impedance concept and its extension in the form of extended describing function are utilized as the tools for researches. With these powerful tools, more insights are obtained to help better design of a paralleling system. / Ph. D.

Much work has been done in applying computer solutions to the problem of power systems fault and stability studies. However, with a few notable exceptions, previous efforts have largely been confined to attempts to solve the problems in the classical manner by having the computer simply take over the tedious portion of the calculations. A few pioneers have succeeded in finding new methods of solving some of the problems by the use of the machine equations, without resorting to the simplifying assumptions necessary for the classical method of solution and their inevitable inaccuracies. These pioneers, however, have only dealt with the balanced condition type of fault, such as a three-phase-fault or a sudden change in load on a machine, and have ignored the far more common although less severe types of fault wherein the system becomes unbalanced due to a fault involving only one or two phases. In contrast, this thesis deals with the unbalanced type of fault on a system. The necessary equations are derived and simple problems are solved for three major types of faults, i.e., the single-phase-to-ground fault, the phase-to-phase fault, and the two-phase-to-ground fault. In addition, a program is written to simulate a field study in order that a comparison can be made. The programs used are written for the single-machine on an infinite bus, and are written so that initial steady conditions and machine and system constants may be entered easily, thus making the thesis method usable by practicing power systems engineers. The thesis method results in a great variety of useful data, which, since they may be transformed into symmetrical components form allows the use of classical methods of system reduction and re-expansion so that fault currents and voltages may be found at any point in the system. All that is required for a system analysis is the reduction of the system, the choice of program for the type of fault under consideration, and the re-expansion of the system. It is hoped that the results of this thesis may prove useful not only to those who wish to continue research in this area, but also to those who are practicing engineers concerned with system fault studies and who are in need of an improved method for the study of unbalanced faults. / Ph. D.

Balanced truncation model reduction for linear systems yields reduced-order models that satisfy a well-known error bound in terms of a system's Hankel singular values. This bound is known to hold with equality under certain conditions, such as when the full-order system is state-space symmetric. In this work, we derive more general conditions in which the balanced truncation error bound holds with equality. We show that this holds for single-input, single-output systems that exhibit a generalized type of state-space symmetry based on the sign parameters corresponding to a system's Hankel singular values. We prove an additional result that shows how to determine this state-space symmetry from the arrowhead realization of a system, if available. In particular, we provide a formula for the sign parameters of an arrowhead system in terms of the off-diagonal entries of its arrowhead realization. We then illustrate these results with an example of an arrowhead system arising naturally in power systems modeling that motivated our study. / Master of Science / Mathematical modeling of dynamical systems provides a powerful means for studying physical phenomena. Due the complexities of real-world problems, many mathematical models face computational difficulties due to the costs of accurate modeling. Model-order reduction of large-scale dynamical systems circumvents this by approximating the large-scale model with a ``smaller'' one that still accurately describes the problem of interest. Balanced truncation model reduction for linear systems is one such example, yielding reduced-order models that satisfy a tractable upper bound on the approximation error. This work investigates conditions in which this bound is known to hold with equality, becoming an exact formula for the error in reduction. We additionally show how to determine these conditions for a special class of linear dynamical systems known as arrowhead systems, which arise in special applications of network modeling. We provide an example of one such system from power systems modeling that motivated our study.

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.

Robust estimation of statistical parameters is traditionally believed to exist in a trade space between robustness and efficiency. This thesis examines the Minimum Hellinger Distance Estimator (MHDE), which is known to have desirable robustness properties as well as desirable efficiency properties. This thesis confirms that the MHDE is simultaneously robust against outliers and asymptotically efficient in the univariate location case. Robustness results are then extended to the case of simple linear regression, where the MHDE is shown empirically to have a breakdown point of 50%. A geometric algorithm for solution of the MHDE is developed and implemented. The algorithm utilizes the Riemannian manifold properties of the statistical model to achieve an algorithmic speedup. The MHDE is then applied to an illustrative problem in power system state estimation. The power system is modeled as a structured linear regression problem via a linearized direct current model; robustness results in this context have been investigated and future research areas have been identified from both a statistical perspective as well as an algorithm design standpoint. / Master of Science

The power grid has evolved over the course of many decades with the usage of cyber systems and communications such as Supervisory Control And Data Acquisition (SCADA); however, due to their connectivity to the internet, the cyber-power system can be infiltrated by malicious attackers. Encryption is not a singular solution. Currently, there are several cyber security measures in development, including those based on artificial intelligence. However, there is a need for a varying but consistent attack algorithm to serve as a testbed for these AI or other practices to be trained and tested. This is important because in the event of a real attacker, it is not possible to know exactly where they will attack and in what order. Therefore, the proposed method in this thesis is to use criminology concepts and fuzzy logic inference to create this algorithm and determine its effectiveness in making decisions on a cyber-physical system model. The method takes various characteristics of the attacker as an input, builds their ideal target node, and then compares the nodes to the high-impact target and chooses one as the goal. Based on that target and their knowledge, the attackers will attack nodes if they have resources. The results show that the proposed method can be used to create a variety of attacks with varying damaging effects, and one other set of tests shows the possibility for multiple attacks, such as denial of service and false data injection. The proposed method has been validated using an extended cyber-physical IEEE 13-node distribution system and sensitivity tests to ensure that the ruleset created would take each of the inputs well. / Master of Science / For the last decades, information and communications technology has become more commonplace for electric power and energy systems around the world. As a result, it has attracted hackers to take advantage of the cyber vulnerabilities to attack critical systems and cause damage, e.g., the critical infrastructure for electric energy. The power grid is a wide-area, distributed infrastructure with numerous power plants, substations, transmission and distribution lines as well as customer facilities. For operation and control, the power grid needs to acquire measurements from substations and send control commands from the control center to substations. The cyber-physical system has its vulnerabilities that can be deployed by hackers to launch falsified measurements or commands. Much research is concerned with how to detect and mitigate cyber threats. These methods are used to determine if an attack is occurring, and, if so, what to do about it. However, for these techniques to work properly, there must be a way to test how the defense will understand the purpose and target of an actual attack, which is where the proposed modeling and simulation method for an attacker comes in. Using a set of values for their resources, motivation and other characteristics, the defense algorithm determines what the attacker's best target would be, and then finds the closest point on the power grid that they can attack. While there are still resources remaining based on the initial value, the attacker will keep choosing places and then execute the attack. From the results, these input characteristic values for the attacker can affect the decisions the attacker makes, and the damage to the system is reflected by the values too. This is tested by looking at the results for the high-impact nodes for each input value, and seeing what came out of it. This shows that it is possible to model an attacker for testing purposes on a simulation.

The problem of incorporating non-dispatchable energy sources such as solar energy into electric utility capacity expansion programs is as yet unsolved. This thesis develops methods to incorporate solar energy as a decision variable into capacity planning and capacity expansion planning algorithms. The model is based on variable or intermittent availability of solar energy. For capacity planning, certain convexity properties are established which lead to an efficient decomposition process using a Newton-type search method. For the capacity expansion planning problem, a modification of Benders' Decomposition is applied, which breaks up the problem into a master program containing the solar decision variable, and a subproblem which involves an expansion problem in conventional equipment types. The primal solution to the subproblem is found with existing algorithms, the dual solution can be obtained from the primal solution employing a network interpretation of the problem. This analysis leads to an efficient tangential approximation method. Illustrative examples, computational experience and further generalizations are also provided. / Master of Science

A real time generation station simulator which is to be used as an operator trainer is developed. The software developed simulates a Y-wound generator connected to an infinite bus through a Δ/Y step up transformer and two parallel lines. The operation of the generator is simulated under normal or abnormal conditions of the power system or the generator itself. The system is simulated in two microcomputers and interaction between the simulator and the operator is provided through the computer's screen and keyboard. Different screen representations show the behavior of the generator at any moment and based on these the operator can take any action through the generator controls provided in his keyboard. / Master of Science

This thesis discusses applications of phasor measurement units to power system monitoring and synchronous generator modeling. Adjustments to a previously developed PMU placement algorithm are described which observe generator and tie line flows explicitly and reduces the number of PMUs required for a system, still observing the major dynamic components of a system. This adjusted methodology leaves some buses unobserved. A method for estimating the state of the unobserved region is developed based on using constant admittance or constant current load models. These models are accurate for a small neighborhood around the operating point when they were calculated. To determine the maximum error expected for any given system estimate, an equation relating the maximum error in the voltages to the maximum change in load power is derived. Once the issue of power system monitoring has been presented, the application of PMUs to the synchronous generator modeling is explored. This thesis deals with the on-line identification of the generator transient model using a recursive version of the generalized least squares algorithm. Simulations have been performed to demonstrate the validity and difficulties with these methods. / Master of Science