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In this dissertation we introduce a new class of pursuit-evasion games; the herding problem. Unlike regular pursuit evasion games where the pursuer aims to hunt the evader the objective of the pursuer in this game is to drive the evader to a certain location on the x-y grid. The dissertation deals with this problem using two different methodologies. In the first, the problem is introduced in the continuous-time, continuous-space domain. The continuous time model of the problem is proposed, analyzed and we came up with an optimal control law for the pursuer is obtained so that the evader is driven to the desired destination position in the x-y grid following the local shortest path in the Euler Lagrange sense. Then, a non-holonomic realization of the two agents is proposed. In this and we show that the optimal control policy is in the form of a feedback control law that enables the pursuer to achieve the same objective using the shortest path. The second methodology deals with the discrete model representation of the problem. In this formulation, the system is represented by a finite di-graph. In this di-graph, each state of the system is represented by a node in the graph. Applying dynamic programming technique and shortest path algorithms over the finite graph representing the system, we come up with the optimal control policy that the pursuer should follow to achieve the desired goal. To study the robustness, we formulate the problem in a stochastic setting also. We analyze the stochastic model and derive an optimal control law in this setting. Finally, the case with active evader is considered, the optimal control law for this case is obtained through the application of dynamic programming technique. Ph. D.

Third generation (3G) mobile communication systems will provide services supporting high-speed data network and multimedia applications in addition to voice applications. The Smart antenna technique is one of the leading technologies that helps to meet the requirement by such services to radio network capacity. Resource management schemes such as power control, handoff and channel reservation/assignment are also essential for providing the seamless services with high quality. Smart antenna techniques will help to enhance the capability of resource management through more efficient and flexible use of resources. In this thesis, adaptive array and switched beam antenna techniques are compared in terms of algorithm, performance, complexity and hardware requirements. Based on these comparisons, sub-optimal code gate algorithm are most likely the suitable algorithms for next generation code division multiple access (CDMA) systems due to its good performances, robustness, and low complexity. A multi-cell CDMA simulator is developed for investigating the gain from smart antenna techniques in both bit error rate (BER) performance improvement and enhancement to resource management schemes. Our study shows that smart antenna techniques can significantly improve the performance of the system and help to build more powerful and flexible resource management schemes. With eight array elements, the system capacity can be increased by a factor of four. Power control command rates can be reduced through the tradeoff with the interference reduction by smart antennas. Smart antennas will also reduce handover failure rates and further increase the system capacity by reducing the resources reserved for soft handover. Master of Science

Single phase switched reluctance machines (SRMs) have a special place in the emerging high-volume, low-cost and low-performance applications in appliances and also in high-speed low-power motor drives in various industrial applications. Single phase SRMs have a number of drawbacks: low power density as they have only 50% utilization of windings, lack of self-starting feature unless otherwise built in to the machine, most of the times with permanent magnets or sometimes with distinct and special machine rotor configurations or additional mechanisms. Many of these approaches are expensive or make the manufacturing process more difficult. In order to overcome such disadvantages a method involving interpoles and windings is discussed in this research. Also, a new and novel converter topology requiring only a single switch and a single diode is realized. This research tests the concepts and feasibility of this new single-phase SRM motor topology and converter in one quadrant operation. The converter electronics and a simple minimum component, minimum cost analog converter are designed and implemented. The entire system is simulated and evaluated on its advantages and disadvantages. Simple testing without load is performed. This system has a large number of possibilities for development. Due to its lightweight, compact design and efficient, variable high-speed operation, the system might find many applications in pumps, fans, and drills. Master of Science

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.

A novel torque control algorithm, which adopts a two-phase excitation, is proposed to improve the performance of the Switched Reluctance Motor (SRM) drive. By exciting two adjacent phases instead of single phase, the changing rate and the magnitude of the phase currents are much reduced. Therefore the existing problems caused by the single-phase excitation such as large torque ripple during commutation, increased audible noise and fatigue of the rotor shaft are mitigated. The electromagnetic torque is efficiently distributed to each phase by the proposed Torque Distribution Function (TDF) that also compensates the effects of mutual coupling. To describe the effects of mutual coupling between phases, a set of voltage and torque equations is newly derived for the two-phase excitation. Parameters of the SRM are obtained by Finite Element Analysis (FEA) and verified by measurements. It is shown that the mutual inductance of two adjacent phases partly contributes to generate the electromagnetic torque and introduces coupling between two adjacent phases in the current or flux linkage control loop, which has been neglected in the single-phase excitation. The dynamics of the current or flux linkage loop are coupled and nonlinear due to the mutual inductance between two adjacent phases and the time varying nature of inductance. Each phase current or flux linkage needs to be controlled precisely to achieve the required performance. A feedback linearizing current controller is proposed to linearize and decouple current control loop along with a gain scheduling scheme to maintain performance of the current control loop regardless of rotor position as well as a feedback linearizing flux linkage controller. Finally, to reduce current or flux linkage ripple, a unipolar switching strategy is proposed. The unipolar switching strategy effectively doubles the switching frequency without increasing the actual switching frequency of the switches. This contributes to the mitigation of current or flux linkage ripple and hence to the reduction of the torque ripple. Ph. D.

Electromagnetic transient and dynamic modeling and simulation studies are presented for a StatCom-SMES compensator in power systems. The transient study aims to better understand the transient process and interaction between a high power/high voltage SMES coil and its power electronics interface, dc-dc chopper. The chopper is used to attach the SMES coil to a StatCom. Following the transient study, the integration of a StatCom with SMES was explored to demonstrate the effectiveness of the combined compensator in damping power oscillations. The transient simulation package PSCAD/EMTDC has been used to perform the integrated modeling and simulation studies. A state of the art review of SMES technology was conducted. Its applications in power systems were discussed chronologically. The cost effective and feasible applications of this technology were identified. Incorporation of a SMES coil into an existing StatCom controller is one of the feasible applications, which can provide improved StatCom operation, and therefore much more flexible and controllable power system operation. The SMES coil with the following unique design characteristics of 50MW (96 MW peak), 100 MJ, 24 kV interface has been used in this study. As a consequence of the high power/ high voltage interface, special care needs to be taken with overvoltages that can stress the insulation of the coil. This requires an investigation of transient overvoltages through a detailed modeling of SMES and its power electronics interface. The electrical model for the SMES coil was developed based on geometrical dimensions of the coil. The interaction between the SMES coil and its power electronics interface (dc-dc chopper for the integration to StatCom) was modeled and simulated to identify transient overvoltages. Transient suppression schemes were developed to reduce these overvoltages. Among these are MOV implementation, surge capacitors, different configurations of the dc-dc chopper. The integration of the SMES coil to a StatCom controller was developed, and its dynamic behavior in damping oscillations following a three-phase fault was investigated through a number of simulation case studies. The results showed that the addition of energy storage to a StatCom controller can improve the StatCom-alone operation and can possibly reduce the MVA rating requirement for the StatCom operating alone. The effective location selection of a StatCom-SMES controller in a generic power system is also discussed. Ph. D.

This thesis presents a new robust filtering technique that suppresses impulsive noise in speech signals. The method makes use of Projection Statistics based on medians to detect segments of speech with impulses. The autoregressive model employed to smooth out the speech signal is identified by means of a robust nonlinear estimator known as the Schweppe-type Huber GM-estimator. Simulation results are presented that demonstrate the effectiveness of the filter. Another contribution of the work is the development of a robust version of the Kalman filter based on the Huber M-estimator. The performances of this filter are evaluated for a simple autoregressive process. Master of Science

In order to meet the high demand for power transmission capacity, some power companies have installed series capacitors on power transmission lines. This allows the impedance of the line to be lowered, thus yielding increased transmission capability. The series capacitor makes sense because it's simple and could be installed for 15 to 30% of the cost of installing a new line, and it can provide the benefits of increased system stability, reduced system losses, and better voltage regulation.1 Protective distance relays, which make use of impedance measurements in order to determine the presence and location of faults, are "fooled" by installed series capacitance on the line when the presence or absence of the capacitor in the fault circuit is not known a priori. This is because the capacitance cancels or compensates some of the inductance of the line and therefore the relay may perceive a fault to be in its first zone when the fault is actually in the second or third zone of protection. Similarly, first zone faults can be perceived to be reverse faults! Clearly this can cause some costly operating errors. The general approach of interest is a method leading to the determination of the values of series L and C of the line at the time of the fault. This is done by analyzing the synchronous and subsynchronous content of the V and I signals seperately which provides adequate information to compute the series L and C of the line. 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.

An analysis is presented on the use of a proof-mass actuator as a regenerative force actuator for the mitigation of earthquake disturbances in civil structures. A proof-mass actuator is a machine which accelerates a mass along a linear path. Such actuators can facilitate two-way power flow. In regenerative force actuation, a bi- directional power-electronic drive is used to facilitate power flow both to and from the proof-mass actuator power supply. With proper control system design, this makes it possible to suppress a disturbance on a structure using mostly energy extracted from the disturbance itself, rather than from an external power source. In this study, three main objectives are accomplished. First, a new performance measure, called the "required energy capacity," is proposed as an assessment of the minimum size of the electric power supply necessary to facilitate the power flow required of the closed-loop system for a given disturbance. The relationship between the required energy capacity and the linear control system design, which is based on positive position feedback concepts, is developed. The dependency of the required energy capacity on hybrid realizations of the control law are discussed, and hybrid designs are found which minimize this quantity for specific disturbance characteristics. As the second objective, system identification and robust estimation methods are used to develop a stochastic approach to the performance assessment of structural control systems, which evaluates the average worst-case performance for all earthquakes "similar" to an actual data record. This technique is used to evaluate the required energy capacity for a control system design. In the third objective, a way is found to design a battery capacity which takes into account the velocity rating of the proof-mass actuator. Upon sizing this battery, two nonlinear controllers are proposed which automatically regulate the power flow in the closed-loop system to accommodate a power supply with a finite energy capacity, regardless of the disturbance size. Both controllers are based on a linear control system design. One includes a nonlinearity which limits power flow out of the battery supply. The other includes a nonlinearity which limits the magnitude of the proof-mass velocity. The latter of these is shown to yield superior performance. Master of Science

Robust estimation methods have been successfully applied to the problem of power system state estimation in a real-time environment. The Schweppe-type GM-estimator with the Huber psi-function (SHGM) has been fully installed in conjunction with a topology processor in the EEF utility, headquartered in Fribourg, Switzerland. Some basic concepts of maximum likelihood estimation and robust analysis are reviewed, and applied to the development of the SHGM-estimator. The algorithms used by the topology processor and state estimator are presented, and the superior performance of the SHGM-estimator over the classic weighted least squares estimator is demonstrated on the EEF network. The measurement configuration of the EEF network has been evaluated, and suggestions for its reinforcement have been proposed. Master of Science

Many utilities implement the financial incentive plans in promoting their Demand-Side Management (DSM) programs. The plans are intended to reduce the customer investment cost for a high efficiency equipment option, so that to make the investment more attractive. Despite its potential to increase customer participation, the financial incentives could cause a considerable increase in program cost to the utility. An analysis of financial incentive impact on the utility DSM program is conducted in this thesis. The analysis uses the combination of the customer participation modeling and the cost-benefit analysis of a DSM program. A modeling of customer participation by a discrete choice model is presented. The model uses the logistic probability functions. The benefit and cost of DSM programs are explored to develop the analysis methodology. Two typical energy conservation options of DSM programs are taken for case studies to demonstrate the analysis. The analysis is also conducted to see the effect of financial incentives on the performance of DSM programs in a fluctuating marginal energy cost. The result of this research shows that the financial incentive could induce the customer participation, thus provide an increase of benefit and costs. However, this research also reveals that, in certain circumstances, the financial incentive may result in a decrease of net benefit due to significant increase of cost. These imply that utilities must carefully evaluate the financial incentive plan in their DSM programs, before the programs are implemented. Master of Science

The Objective of the Remote Measurements Calibration (RMC) method is to minimize systematic errors through an appropriate scaling procedure. A new method for RMC has been developed. This method solves the problems of observability, multiplicity of solutions, and ambiguity of reference points associated with the method proposed by Adibi et. al. [6-9]. The new algorithm uses the simulated annealing technique together with the matroid method to identify and minimize the number of RTUs (Remote Terminal Units) required to observe the system. After field calibration, these RTUs provide measurements that are used to estimate the whole state of the system. These estimates are then returned as a reference for remotely calibrating the remaining RTUs. The calibration coefficients are estimated by means of highly robust estimator, namely the Least Median of Squares (LMS) estimator. The calibration method is applicable to large systems by means of network tearing and dynamic programming. The number of field calibrations can be decreased further whenever multiple voltage measurements at the same buses are available. The procedure requires that the measurement biases are estimated from recorded metered values when buses, or lines, or transformers are disconnected. It also requires the application of a robust comparative voltage calibration method. To this end, a modified Friedman test has been developed and its robustness characteristics investigated. Ph. D.

This thesis investigates and develops a direct method for transient stability analysis using the energy approach [1] and the Phasor Measurement Units (PMUs). The originality of this new method results from a combination of a prediction of the post-fault trajectory based on the PMUs and the Transient Energy Function of a multimachine system. Thanks to the PMUs, the weakness of the direct methods, which is the over-simplification of the generator model, is overcome. This new method consists of fitting a curve to the data of the post-fault path provided by PMUs and identifying the controlling unstable equilibrium point (c.u.e.p.). Two second-order linear models have been estimated and evaluated from a prediction viewpoint. These are a polynomial function and an auto-regressive model. These parameters have been estimated by means of the least-squares estimator. They have been compared to the model proposed by Y. Ohura et al. [6], which has been upgraded into an iterative algorithm. The post-fault trajectory is predicted until the exit point located on the Potential Energy Boundary Surface (p.e.b.s.) is reached. In order to detect with efficiency this exit point and to find the c.u.e.p., it is proposed a combination of the so called "Ball-Drop" method [22] and an improved version of the Shadowing method. These combined procedures give accurate results when they are compared to the step-by-step method, which directly integrates the differential equations using a fourth-order Runga-Kutta method. The simulations have been carried out on a 3-machine system and on the 10-machine New-England power system. Master of Science

The objective of this thesis is to estimate, for a distribution network, confidence intervals containing the values of nodal hourly power consumption and nodal maximum power consumption per customer where they are not measured. The values of nodal hourly power consumption are needed in operational as well as in planning stages to carry out load flow studies. As for the values of nodal maximum power consumption per customer, they are used to solve planning problems such as transformer sizing. Confidence interval estimation was preferred to point estimation because it takes into consideration the large variability of the consumption values. A computationally intensive statistical technique, namely the bootstrap method, is utilized to estimate these intervals. It allows us to replace idealized model assumptions for the load distributions by model free analyses. Two studies have been executed. The first one is based on the original nonparametric bootstrap method to calculate a 95% confidence interval for nodal hourly power consumption. This estimation is carried out for a given node and a given hour of the year. The second one makes use of the parametric bootstrap method in order to infer a 95% confidence interval for nodal maximum power consumption per customer. This estimation is realized for a given node and a given month. Simulation results carried out on a real data set are presented and discussed. Master of Science

Low frequency oscillations are detrimental to the goals of maximum power transfer and optimal power system security. A contemporary solution to this problem is the addition of power system stabilizers to the automatic voltage regulators on the generators in the power system. The damping provided by this additional stabilizer provides the means to reduce the inhibiting effects of the oscillations. This thesis is an investigation of the use of synchronized phasor measurements as input signals for power system stabilizers installed on the generators of a two-area, 4-machine test power system. A remote measurement feedback controller has been designed and placed in the test power system. Synchronized phasor measurements from optimally sited measurement units were shown to improve the damping of low-frequency inter-area oscillations present in the test system when the proposed controller was included in the generator feedback control loop. The benefit of the damping of these oscillations was evident through the ability to increase the tie-line power flowing in the test system once the proposed control scheme was implemented. Time-domain simulations were used to verify the robustness of the proposed control during severe events, such as a short- circuit or sudden large variations of load. Master of Science

A bifurcation analysis is used to investigate the complex dynamics of two heavily loaded single-machine-infinite-busbar power systems modeling the characteristics of the BOARDMAN generator with respect to the rest of the North-Western American Power System and the CHOLLA# generator with respect to the SOWARO station. In the BOARDMAN system, we show that there are three Hopf bifurcations at practical compensation values, while in the CHOLLA#4 system, we show that there is only one Hopf bifurcation. The results show that as the compensation level increases, the operating condition loses stability with a complex conjugate pair of eigenvalues of the Jacobian matrix crossing transversely from the left- to the right-half of the complex plane, signifying a Hopf bifurcation. As a result, the power system oscillates subsynchronously with a small limit-cycle attractor. As the compensation level increases, the limit cycle grows and then loses stability via a secondary Hopf bifurcation, resulting in the creation of a two-period quasiperiodic subsynchronous oscillation, a two-torus attractor. On further increases of the compensation level, the quasiperiodic attractor collides with its basin boundary, resulting in the destruction of the attractor and its basin boundary in a bluesky catastrophe. Consequently, there are no bounded motions. When a damper winding is placed either along the q-axis, or d-axis, or both axes of the BOARDMAN system and the machine saturation is considered in the CHOLLA#4 system, the study shows that, there is only one Hopf bifurcation and it occurs at a much lower level of compensation, indicating that the damper windings and the machine saturation destabilize the system by inducing subsynchronous resonance. Finally, we investigate the effect of linear and nonlinear controllers on mitigating subsynchronous resonance in the CHOLLA#4 system . The study shows that the linear controller increases the compensation level at which subsynchronous resonance occurs and the nonlinear controller does not affect the location and type of the Hopf bifurcation, but it reduces the amplitude of the limit cycle born as a result of the Hopf bifurcation. Ph. D.

Estimation of nonlinear models finds applications in every field of engineering and the sciences. Much work has been done to build solid statistical theories for its use and interpretation. However, there has been little analysis of the tolerance of nonlinear model estimators to deviations from assumptions and normality. We focus on analyzing the robustness properties of M-estimators of nonlinear models by studying the effects of deviations from assumptions and normality on these estimators. We discuss St. Laurent and Cook's Jacobian Leverage and identify the relationship of the technique to the robustness concept of influence. We derive influence functions for M-estimators of nonlinear models and show that influence of position becomes, more generally, influence of model. The result shows that, for M-estimators, we must bound not only influence of residual but also influence of model. Several examples highlight the unique problems of nonlinear model estimation and demonstrate the utility of the influence function. Master of Science

This dissertation presents a new algorithm for optimal power flow in distribution systems. The new algorithm, Discrete Ascent Optimal Programming (DAOP), will converge to the same solution as the Lagrange multiplier approach as demonstrated by example. An intuitive discussion illustrating the path of convergence is presented along with a theorem concerning convergence. Because no partial derivatives, solutions of simultaneous equations, or matrix operations are required, the DAOP algorithm is simple to apply and program. DAOP is especially suited for programming with pointers. Advantages of the new algorithm include its simplicity, ease of incorporating inequality constraints, and the ability to predict the number of steps required to reach a solution. In addition to optimal power flow, the algorithm, heuristic in nature, can be applied to switch placement design, reconfiguration, and economic dispatch. The basic principles of the algorithm have been used to devise a phase balancing routine which has been implemented in the Distribution Engineering Workstation (DEWorkstation) software package sponsored by the Electric Power Research Institute (EPRI). The new algorithm presented in this dissertation works toward a solution by performing a series of calculations within a finite number of steps. At the start of the algorithm, the assumption is made that no power is flowing in the system. Each step adds a discrete unit of load to the system in such a fashion as to minimize loss. As progress toward the solution is made, more and more load is satisfied and the losses in the system continue to increase. The algorithm is terminated when all system load is satisfied. When the algorithm is finished, the sources which should supply each load have been identified along with the amount of power delivered by each source. Discussion will show that the method will converge to a solution that is within the discrete step size of the optimum. The algorithm can be thought of as an ascent method because the cost (losses) continually increases as more and more load is satisfied. Hence, the name Discrete Ascent Optimal Programming (DAOP) has been given to the algorithm. The new algorithm uses the topology of the power system such that the entire system is not considered at each step. Therefore, DAOP is not an exhaustive state enumeration scheme. Only those portions of the system containing loads most closely connected (via least loss paths) to the sources are first considered. As loads become supplied during the course of the solution, other loads are considered and supplied until the system is fully loaded. Ph. D.

Most modem techniques for high resolution processing of closely spaced signals assume either uncorrelated noise or require knowledge of the noise covariance matrix. These assumptions are often invalid in practice. Here we propose a Pseudo-Autoregressive (PAR (M, p) model for estimation of an arbitrary number of signals M in the presence of a p-th order autoregressive (AR) noise environment. We derive the Cramer-Rao Lower Bound (CRLB) for the parameters of damped exponential signals in the colored noise case. A closed-form expression for the Cramer-Rao Lower Bound for the Pseudo-Autoregressive (PAR(M,p) model is obtained. Some special cases are investigated, for example, the PAR(M,p) model for p = 0, i.e., the white noise case, where our results agree with previous research results. We then evaluate the Cramer-Rao Lower Bound for two possibly closely spaced signals in a colored noise environment, showing that the colored noise assumption can lead to a much lower variance bound for the exponential parameters than under the white noise assumption. An algorithmic procedure is presented for the identification of the parameters of exponential signals, measured in colored noise. Previous papers on identifying sinusoids in noise have concentrated mainly on white noise disturbances. In a practical environment however, the disturbance is usually colored; sea-clutter in a radar context, is a lowpass type noise for example. When least squares type estimates are used in the colored noise environment, this usually leads to an unacceptable bias in the estimates. We propose an identification method, named Singular Value Decomposition Bias Elimination (SVDBE), in which it is assumed that the noise can be represented well by an AR process. The parameters of this noise model are then iteratively estimated along with the exponential signal parameters, via Singular Value Decomposition (SVD) based least squares. The iteration process starts with the white noise assumption, and improves on that by allowing the parameters in the noise model to vary away from the white noise case. A high order modal decomposition is found, and the best subset of the identified modes is selected. Simulations assess the merits of the introduced SVDBE algorithm, by comparison of the estimation results with the derived Cramer-Rao Lower Bound. Ph. D.

The objective of Remote Measurements Calibration (RMC) method is to minimize systematic errors through an appropriate scaling procedure. A new method for RMC has been developed. This method solves the problems of observability, multiplicity of solutions, and ambiguity of reference points associated with the already existing method proposed by Adibi et al. [6-9]. The new algorithm uses the concepts of the simulated annealing and the matroid tree to identify and minimize the number of RTUs (Remote Terminal Units) required to observe the system. After field calibration, these RTUs provide measurements that are used to estimate the whole state of the system. These estimates are then returned as a reference for remote calibrating the remaining RTUs. The calibration coefficients are estimated by means of the Least Median of Squares (LMS) estimator. The procedure results in the reduction of the cost associated with field calibration. Master of Science

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.

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

This thesis investigates the use of real-time phasor measurements for voltage and transient stability monitoring and control. Taking advantage of the ability of a Phasor Measurement Unit (PMU) placed at a bus to sample at a fast rate the voltage and current phasors of that bus) various schemes for placing PMU's are considered and evaluated. These schemes include coherency based methods and pilot point placement techniques for system controllability. A novel scheme is proposed which places a minimal set of PMU's so as to make the system measurement model observable, and thereby linear. This placement scheme is derived from the topological observability theory. It concerns the building of a spanning measurement sub-graph across the system with actual or pseudo-measurement assigned to each of its branches. The minimal PMU set is found through a dual search algorithm which uses both a modified bisecting search and a simulated annealing-based method. The former fixes the number of PMU's while the latter look for a placement set that leads to an observable network. In order to accelerate the procedure, an initial PMU placement is provided by a graph-theoretic procedure which builds a spanning measurement sub-graph according to a depth-first search. From computer simulation results performed on various test systems, it appears that only one fourth of the system buses need to be provided with PMU's in order to make the system observable. In an effort to reduce the computing time of transient stability assessment, a dynamic equivalent is presented, which results from the elimination of the load buses provided with voltage--dependent loads. The elimination is performed through a new version of the Ward equivalencing method. In this approach, the equivalent current injections are expressed in terms of the retained bus angles and a sensitivity matrix. The non-linearity of the load flow model is accounted for through piecewise linear approximations by updating the sensitivity matrix whenever the operating point moves beyond the validity of the linearization. The expressions of the incremental changes in the generator electric power is derived. The study also investigates the possibility of using the telemetered data provided by the PMU's during pre-fault and post-fault operating conditions in conjunction with a. new version of the Extended Equal Area Criterion (EEAC) method. The latter is able to handle complex loads through the dynamic Ward equivalencing method. The performance of the approach is illustrated on three test systems which have been reduced to the internal generator nodes. Ph. D.

Applications, converter topologies, and control schemes are examined for superconductive magnetic energy storage (SMES) systems. Diurnal load leveling for electric utilities and compensation for fluctuations in photovoltaic (PV) power generation are the primary applications discussed. It is demonstrated that a SMES system implemented with standard AC/DC converters offers energy storage capacity large enough, and dynamic response fast enough, to compensate for PV fluctuations due to changes in weather conditions. The method of control is developed so that the charging and discharging of the SMES system are changed in response to PV fluctuations, and the combined SMESIPV power output is smooth and controllable. An innovative control scheme is introduced for SMES that can simultaneously regulate real power and voltage independently without hardware modifications to the standard ACIDC bridge arrangement normally used for coordinated control of real and reactive power. The combination of SMES and PV systems could benefit from DCIDC converters that take advantage of the DC nature of both. It is established that DClDC converters can respond with sufficient speed to handle variations in PV power. A converter topology is devised where two DC/DC converters in cascade effectively maintain a PV array at its maximum power point and simultaneously control a SMES system to compensate for PV fluctuations. An alternative cascade configuration of an AC/DC converter with a DCIDC converter is proposed that could significantly reduce the reactive power requirements and improve the operational characteristics of a large scale SMES system connected to the utility grid. Master of Science

A reconfiguration algorithm for electrical distribution system to reduce system losses is presented. The algorithm determines the switching patterns as a function of time. Either seasonal or daily time studies may be performed. Both manual and automatic switches are used to reconfigure the system for seasonal studies, whereas only automatic switches are considered for daily studies. An algorithm for load estimation is developed. The load estimation algorithm provides load information for each time point to be analyzed. The load estimation algorithm can incorporate any or all of the following: spot loads, circuit measurements, and customer time-varying diversified load characteristics. Voltage dependency of loads is considered at the circuit level. It is shown that switching at the system peak can reduce losses but may cause a marginal increase in system peak. Voltage and current constraints are incorporated in the reconfiguration algorithm. Data base tables and data structures used in the algorithm are described. Example problems are provided to illustrate results. Ph. D.

The advent of synchronized phasor measurements allows the problem of real time prediction of instability and control to be considered. The use of direct methods for these on-line applications is assessed. The classical representation of a power system allows the use of two reference frames: Center of angle and one machine as reference. Formulae allowing transition between the two reference frames are derived. It is shown that the transient energy in both formulations is the same, and that line resistances do not dampen system oscillations. Examples illustrating the mathematical characterization of the region of attraction, exit point, closest u.e.p. and controlling u.e.p. methods are presented. Half-dimensional systems (reduced-order systems) are discussed. The general expression for the gradient system which accounts for transfer conductances is derived without making use of the infinite bus assumption. Examples illustrating the following items are presented: a) Effect of the linear ray approximation on the potential energy (inability to accurately locate the u.e.p.’s); b) Comparison of Kakimoto’s and Athay’s approach for PEBS crossing detection; c) BCU method and; d) One·parameter transversality condition. It is illustrated that if the assumption of the one-parameter transversality condition is not satisfied, the PEBS and BCU methods may give incorrect results for multi-swing stability. A procedure to determine if the u.e.p. found by the BCU method lies on the stability boundary of the original system is given. This procedure improves the BCU method for off~line applications when there is time for a hybrid approach (direct and conventional), but it does not improve it for on-line applications due to the following: a) It is time consuming and b) If it finds that the u.e.p. does not belong to the stability boundary it provides no information concerning the stability/instability of the system. Ph. D. incomplete_metadata

In this thesis case studies have been made to study the impact ofSMES system on power system transmission with a decoupled Optimal Power Flow program. Linear Programming (LP) and Quadratic Programming (QP) storage scheduling methods including transmission security have been developed, LP method is suitable for single storage system and QP method is capable of solving multiple storage scheduling problem. Results on single storage system is compared with Load Shaving method, which indicate that three methods have approximately the same storage schedule and daily fuel cost. Results on two storage system with QP method suggest that the coordination between storage units can help to transfer more power from base units and reduce total fuel cost in peak hours. Master of Science

The formulation of an accurate data base consisting of system state variable values is an initial and critical step in the economical and secure operation of modern power systems. The Least Median of Squares (LMS) estimator is ideal in the sense that it can provide a good state estimate despite high percentages of bad data and multiple bad leverage points. The estimator is, however, computationally intensive. In this thesis, an efficient algorithm is developed and implemented to increase the overall speed of the LMS estimator. The algorithm generates measurement samples in a manner that allows use of the resampling technique i.e., they make the system observable and also ensure that each measurement has a nearly equal probability of appearing in each of the measurement samples. Master of Science

This thesis is in an attempt to realistically model a real-time digital generator which interfaces to an analog system simulator and which consists of the synchronous machine and its peripheral controllers such as the exciter and the governor-turbine subsystems. In this work, the exciter, the synchronous machine, the machine dynamics and the governor are modeled in detail while a simplified model of the turbine is used. The synchronous machine, the main component of this simulation, solves the discretized Park's machine equations which include flux derivative tenns and tenns pertaining to the two amortisseur windings. Treatment of saturation effects in the mutual inductances is also discussed. The Park's model is arranged to obtain a field voltage and machine armature cutTent input - machine tenninal voltage output structure, where the armature current and terminal voltage are rotor based quantities (i.e. in d-q domain). In order to interface the Park's machine model to the analog system model, the Park's and inverse Park's transformation are implemented by software modules. The implementation of a prototype model generator using a Motorola 68020 microprocessor and fast computer peripherals is discussed. The results of the digital computer simulation in real-time for the generator model under various operating conditions are presented. Master of Science

It is common to assume that the noise disturbing measuring devices is of a Gaussian nature. But this assumption is not always fulfilled. A few examples are the cases where the measurement device fails periodically, the data transmission from device to microprocessor fails or the A/D conversion fails. In these cases the noise will no longer be Gaussian distributed, but rather the noise will be a mixture of Gaussian noise and data not related to the physical process. This posses a problem for estimators derived under the Gaussian assumption, in the sense L that these estimators are likely to produce highly biased estimates in a non Gaussian environment. This thesis devises a way to robustify the Pseudo Linear Identification algorithm (PLID) which is a joint parameter and state estimator of a Kalman filter type. The PLID algorithm is originally derived under a Gaussian noise assumption. The PLID algorithm is made robust by filtering the measurements through a nonlinear odd symmetric function, called the mb function, and let the covariance updating depend on how far away the measurement is from the prediction. In the original PLID the measurements are used unfiltered in the covariance calculation. Master of Science