The power-flow problem has been solved using the Newton-Raphson and Gauss-Seidel methods. Recently the holomorphic embedding method (HEM), a recursive (non-iterative) method applied to solving nonlinear algebraic systems, was applied to the power-flow problem. HEM has been claimed to have superior properties when compared to the Newton-Raphson and other iterative methods in the sense that if the power-flow solution exists, it is guaranteed that a properly configured HEM can find the high voltage solution and, if no solution exists, HEM will signal that unequivocally. Provided a solution exists, convergence of HEM in the extremal domain is claimed to be theoretically guaranteed by Stahl’s convergence-in-capacity theorem, another advantage over other iterative nonlinear solver.In this work it is shown that the poles and zeros of the rational function from fitting the local PMU measurements can be used theoretically to predict the voltage-collapse point. Different numerical methods were applied to improve prediction accuracy when measurement noise is present. It is also shown in this work that the dc optimal power flow (DCOPF) problem can be formulated as a properly embedded set of algebraic equations. Consequently, HEM may also be used to advantage on the DCOPF problem. For the systems examined, the HEM-based interior-point approach can be used to solve the DCOPF problem. While the ultimate goal of this line of research is to solve the ac OPF; tackled in this work, is a precursor and well-known problem with Padé approximants: spurious poles that are generated when calculating the Padé approximant may, at times, prevent convergence within the functions domain. A new method for calculating the Padé approximant, called the Padé Matrix Pencil Method was developed to solve the spurious pole problem. The Padé Matrix Pencil Method can achieve accuracy equal to that of the so-called direct method for calculating Padé approximants of the voltage-functions tested while both using a reduced order approximant and eliminating any spurious poles within the portion of the function’s domain of interest: the real axis of the complex plane up to the saddle-node bifurcation point.

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.

Transmission line parameters play an important role in state estimation, dynamic line rating, and fault analysis. Because of this, several methods have been proposed in the literature for line parameter estimation, especially using synchrophasor data. However, success of most prior research has been demonstrated using purely synthetic data. A synthetic dataset does not have the problems encountered with real data, such as invariance of measurements and realistic field noise. Therefore, the algorithms developed using synthetic datasets may not be as effective when used in practice. On the other hand, the true values of the line parameters are unknown and therefore the algorithms cannot be directly implemented on real data. A multi-stage test procedure is developed in this work to circumvent this problem.

In this thesis, two popular algorithms, namely, moving-window total least squares (MWTLS) and recursive Kalman filter (RKF) are applied on real data in multiple stages. In the first stage, the algorithms are tested on a purely synthetic dataset. This is followed by testing done on pseudo-synthetic datasets generated using real PMU data. In the final stage, the algorithms are implemented on the real PMU data obtained from a local utility. The results show that in the context of the given problem, RKF has better performance than MWTLS. Furthermore, to improve the performance of RKF on real data, ASPEN data are used to calculate the initial estimates. The estimation results show that the RKF algorithm can reliably estimate the sequence impedances, using ASPEN data as a starting condition. The estimation procedure is repeated over different time periods and the corresponding results are presented.

Finally, the significance of data drop-outs and its impact on the use of parameter estimates for real-time power system applications, such as state estimation and dynamic line rating, is discussed. To address the problem (of data drop-outs), an auto regressive integrated moving average (ARIMA) model is implemented. The ability of this model to predict the variations in sequence impedances is demonstrated.

Recently, a novel non-iterative power flow (PF) method known as the Holomorphic Embedding Method (HEM) was applied to the power-flow problem. Its superiority over other traditional iterative methods such as Gauss-Seidel (GS), Newton-Raphson (NR), Fast Decoupled Load Flow (FDLF) and their variants is that it is theoretically guaranteed to find the operable solution, if one exists, and will unequivocally signal if no solution exists. However, while theoretical convergence is guaranteed by Stahl’s theorem, numerical convergence is not. Numerically, the HEM may require extended precision to converge, especially for heavily-loaded and ill-conditioned power system models.

In light of the advantages and disadvantages of the HEM, this report focuses on three topics:

1. Exploring the effect of double and extended precision on the performance of HEM,

2. Investigating the performance of different embedding formulations of HEM, and

3. Estimating the saddle-node bifurcation point (SNBP) from HEM-based Thévenin-like networks using pseudo-measurements.

The HEM algorithm consists of three distinct procedures that might accumulate roundoff error and cause precision loss during the calculations: the matrix equation solution calculation, the power series inversion calculation and the Padé approximant calculation. Numerical experiments have been performed to investigate which aspect of the HEM algorithm causes the most precision loss and needs extended precision. It is shown that extended precision must be used for the entire algorithm to improve numerical performance.

A comparison of two common embedding formulations, a scalable formulation and a non-scalable formulation, is conducted and it is shown that these two formulations could have extremely different numerical properties on some power systems.

The application of HEM to the SNBP estimation using local-measurements is explored. The maximum power transfer theorem (MPTT) obtained for nonlinear Thévenin-like networks is validated with high precision. Different numerical methods based on MPTT are investigated. Numerical results show that the MPTT method works reasonably well for weak buses in the system. The roots method, as an alternative, is also studied. It is shown to be less effective than the MPTT method but the roots of the Padé approximant can be used as a research tool for determining the effects of noisy measurements on the accuracy of SNBP prediction.

In the recent past, due to regulatory hurdles and the inability to expand transmission systems, the bulk power system is increasingly being operated close to its limits. Among the various phenomenon encountered, static voltage stability has received increased attention among electric utilities. One approach to investigate static voltage stability is to run a set of power flow simulations and derive the voltage stability limit based on the analysis of power flow results. Power flow problems are formulated as a set of nonlinear algebraic equations usually solved by iterative methods. The most commonly used method is the Newton-Raphson method. However, at the static voltage stability limit, the Jacobian becomes singular. Hence, the power flow solution may fail to converge close to the true limit.

To carefully examine the limitations of conventional power flow software packages in determining voltage stability limits, two lines of research are pursued in this study. The first line of the research is to investigate the capability of different power flow solution techniques, such as conventional power flow and non-iterative power flow techniques to obtain the voltage collapse point. The software packages used in this study include Newton-based methods contained in PSSE, PSLF, PSAT, PowerWorld, VSAT and a non-iterative technique known as the holomorphic embedding method (HEM).

The second line is to investigate the impact of the available control options and solution parameter settings that can be utilized to obtain solutions closer to the voltage collapse point. Such as the starting point, generator reactive power limits, shunt device control modes, area interchange control, and other such parameters.

A nonlinear dynamic model for a passively cooled small modular reactor (SMR) is developed. The nuclear steam supply system (NSSS) model includes representations for reactor core, steam generator, pressurizer, hot leg riser and downcomer. The reactor core is modeled with the combination of: (1) neutronics, using point kinetics equations for reactor power and a single combined neutron group, and (2) thermal-hydraulics, describing the heat transfer from fuel to coolant by an overall heat transfer resistance and single-phase natural circulation. For the helical-coil once-through steam generator, a single tube depiction with time-varying boundaries and three regions, i.e., subcooled, boiling, and superheated, is adopted. The pressurizer model is developed based upon the conservation of fluid mass, volume, and energy. Hot leg riser and downcomer are treated as first-order lags. The NSSS model is incorporated with a turbine model which permits observing the power with given steam flow, pressure, and enthalpy as input. The overall nonlinear system is implemented in the Simulink dynamic environment. Simulations for typical perturbations, e.g., control rod withdrawal and increase in steam demand, are run. A detailed analysis of the results show that the steady-state values for full power are in good agreement with design data and the model is capable of predicting the dynamics of the SMR. Finally, steady-state control programs for reactor power and pressurizer pressure are also implemented and their effect on the important system variables are discussed.

Underground transmission cables in power systems are less likely to experience electrical faults, however, resulting outage times are much greater in the event that a failure does occur. Unlike overhead lines, underground cables are not self-healing from flashover events. The faulted section must be located and repaired before the line can be put back into service. Since this will often require excavation of the underground duct bank, the procedure to repair the faulted section is both costly and time consuming. These added complications are the prime motivators for developing accurate and reliable ratings for underground cable circuits.

This work will review the methods by which power ratings, or ampacity, for underground cables are determined and then evaluate those ratings by making comparison with measured data taken from an underground 69 kV cable, which is part of the Salt River Project (SRP) power subtransmission system. The process of acquiring, installing, and commissioning the temperature monitoring system is covered in detail as well. The collected data are also used to evaluate typical assumptions made when determining underground cable ratings such as cable hot-spot location and ambient temperatures.

Analysis results show that the commonly made assumption that the deepest portion of an underground power cable installation will be the hot-spot location does not always hold true. It is shown that distributed cable temperature measurements can be used to locate the proper line segment to be used for cable ampacity calculations.

For a (N+1)-bus power system, possibly 2N solutions exists. One of these solutions

is known as the high-voltage (HV) solution or operable solution. The rest of the solutions

are the low-voltage (LV), or large-angle, solutions.

In this report, a recently developed non-iterative algorithm for solving the power-

flow (PF) problem using the holomorphic embedding (HE) method is shown as

being capable of finding the HV solution, while avoiding converging to LV solutions

nearby which is a drawback to all other iterative solutions. The HE method provides a

novel non-iterative procedure to solve the PF problems by eliminating the

non-convergence and initial-estimate dependency issues appeared in the traditional

iterative methods. The detailed implementation of the HE method is discussed in the

report.

While published work focuses mainly on finding the HV PF solution, modified

holomorphically embedded formulations are proposed in this report to find the

LV/large-angle solutions of the PF problem. It is theoretically proven that the proposed

method is guaranteed to find a total number of 2N solutions to the PF problem

and if no solution exists, the algorithm is guaranteed to indicate such by the oscillations

in the maximal analytic continuation of the coefficients of the voltage power series

obtained.

After presenting the derivation of the LV/large-angle formulations for both PQ

and PV buses, numerical tests on the five-, seven- and 14-bus systems are conducted

to find all the solutions of the system of nonlinear PF equations for those systems using

the proposed HE method.

After completing the derivation to find all the PF solutions using the HE method, it

is shown that the proposed HE method can be used to find only the of interest PF solutions

(i.e. type-1 PF solutions with one positive real-part eigenvalue in the Jacobian

matrix), with a proper algorithm developed. The closet unstable equilibrium point

(UEP), one of the type-1 UEP’s, can be obtained by the proposed HE method with

limited dynamic models included.

The numerical performance as well as the robustness of the proposed HE method is

investigated and presented by implementing the algorithm on the problematic cases and

large-scale power system.

Substation ground system insures safety of personnel, which deserves considerable attentions. Basic substation safety requirement quantities include ground grid resistance, mesh touch potential and step potential, moreover, optimal design of a substation ground system should include both safety concerns and ground grid construction cost. In the purpose of optimal designing the ground grid in the accurate and efficient way, an application package coded in MATLAB is developed and its core algorithm and main features are introduced in this work.

To ensure accuracy and personnel safety, a two-layer soil model is applied instead of the uniform soil model in this research. Some soil model parameters are needed for the two-layer soil model, namely upper-layer resistivity, lower-layer resistivity and upper-layer thickness. Since the ground grid safety requirement is considered under the earth fault, the value of fault current and fault duration time are also needed.

After all these parameters are obtained, a Resistance Matrix method is applied to calculate the mutual and self resistance between conductor segments on both the horizontal and vertical direction. By using a matrix equation of the relationship of mutual and self resistance and unit current of the conductor segments, the ground grid rise can be calculated. Green's functions are applied to calculate the earth potential at a certain point produced by horizontal or vertical line of current. Furthermore, the three basic ground grid safety requirement quantities: the mesh touch potential in the worst case point can be obtained from the earth potential and ground grid rise; the step potential can be obtained from two points' earth potential difference; the grid resistance can be obtained from ground grid rise and fault current.

Finally, in order to achieve ground grid optimization problem more accurate and efficient, which includes the number of meshes in the horizontal grid and the number of vertical rods, a novel two-step hybrid genetic algorithm-pattern search (GA-PS) optimization method is developed. The Genetic Algorithm (GA) is used first to search for an approximate starting point, which is used by the Pattern Search (PS) algorithm to find the final optimal result. This developed application provides an optimal grid design meeting all safety constraints. In the cause of the accuracy of the application, the touch potential, step potential, ground potential rise and grid resistance are compared with these produced by the industry standard application WinIGS and some theoretical ground grid model.

In summary, the developed application can solve the ground grid optimization problem with the accurate ground grid modeling method and a hybrid two-step optimization method.

A new photovoltaic (PV) array power converter circuit is presented. The salient features of this inverter are: transformerless topology, grounded PV array, and only film capacitors. The motivations are to reduce cost, eliminate leakage ground currents, and improve reliability. The use of Silicon Carbide (SiC) transistors is the key enabling technology for this particular circuit to attain good efficiency.

Traditionally, grid connected PV inverters required a transformer for isolation and safety. The disadvantage of high frequency transformer based inverters is complexity and cost. Transformerless inverters have become more popular recently, although they can be challenging to implement because of possible high frequency currents through the PV array's stay capacitance to earth ground. Conventional PV inverters also typically utilize electrolytic capacitors for bulk power buffering. However such capacitors can be prone to decreased reliability.

The solution proposed here to solve these problems is a bi directional buck boost converter combined with half bridge inverters. This configuration enables grounding of the array's negative terminal and passive power decoupling with only film capacitors.

Several aspects of the proposed converter are discussed. First a literature review is presented on the issues to be addressed. The proposed circuit is then presented and examined in detail. This includes theory of operation, component selection, and control systems. An efficiency analysis is also conducted. Simulation results are then presented that show correct functionality. A hardware prototype is built and experiment results also prove the concept. Finally some further developments are mentioned.

As a summary of the research a new topology and control technique were developed. The resultant circuit is a high performance transformerless PV inverter with upwards of 97% efficiency.