In this work, the stacked values of battery energy storage systems (BESSs) of various power and energy capacities are evaluated as they provide multiple services such as peak shaving, frequency regulation, and reserve support in an ‘Arizona-based test system’ - a simplified, representative model of Salt River Project’s (SRP) system developed using the resource stack information shared by SRP. This has been achieved by developing a mixed-integer linear programming (MILP) based optimization model that captures the operation of BESS in the Arizona-based test system. The model formulation does not include any BESS cost as the objective is to estimate the net savings in total system operation cost after a BESS is deployed in the system. The optimization model has been formulated in such a way that the savings due to the provision of a single service, either peak shaving or frequency regulation or spinning reserve support, by the BESS, can be determined independently. The model also allows calculation of combined savings due to all the services rendered by the BESS.

The results of this research suggest that the savings obtained with a BESS providing multiple services are significantly higher than the same capacity BESS delivering a single service in isolation. It is also observed that the marginal contribution of BESS reduces with increasing BESS energy capacity, a result consistent with the law of diminishing returns. Further, small changes in the simulation environment, such as factoring in generator forced outage rates or projection of future solar penetration, can lead to changes as high as 10% in the calculated stacked value.

The objectives of this research project were to develop a model of real power demand from a dc fast charging station both with and without an integrated battery energy storage system (BESS). An optimal deterministic control strategy was devel-oped to perform load-shaping under various scenarios with various load-shaping goals in mind to establish the value for BESS’s with various power and energy capacities.

To achieve these objectives, first a statistical model of electric vehicle drivers’ charging behaviors (home charging and dc fast charging) was constructed and simu-lated according to empirical charging data and several key findings about people’s charging habits in the literature.

Data of private vehicles’ driving records was extracted from the National Household Travel Survey (NHTS), derived 42 statistical distributions that mathe-matically modeled people’s driving behaviors. From this start, two algorithms were developed to simulate driver behavior: one using a database sampling method (DSM) and another using probability distribution sampling method (PDSM) to simulate the electric vehicles’ driving cycles. Both methods used data and statistical distributions derived from NHTS. Next, a model of the EV drivers’ charging behavior was incor-porated into the simulation of the electric vehicles’ driving cycles, and then the ve-hicles’ charging behaviors were simulated. From these simulations, one can forecast the real-power demand of a typical dc fast charging station with six dc 50 kW fast chargers serving a population of 700 EVs. (The ratio of six dc fast chargers to 700 EVs was selected based on the current value of this ratio in the US.) Next, a BESS was integrated into the dc fast charging station demand model and the size and charging behavior was optimized to account for different criteria which were based on the goals of the different potential owners: SRP or a third-party owner. It was established when a BESS would become economically feasible using a simplified economic model.

It was observed that the real-power demand shape is a function of the size of the BESS and the owner’s objective, i.e., flattening the demand curve or minimizing the cost of electricity.

In this work a comparison has been made between the predictions from the models using both the present theory for the underground cable temperature prediction and the CYMCAP application and the field measurements to determine which, if any, models are capable of predicting the temperature and hotspot locations in an installation where the power cable is not embedded with the optical fibers and, therefore, where the cable temperatures must be inferred from the temperature measurements made in nearby spare ducts. The temperature measurements were collected from the underground 69 kV cable at the Brandow-Pickrell installation, which is a part of Salt River Project’s power sub-transmission system. The model development and the results are explained in detail. Results from the model developed have been compared and the factors affecting the cable temperature are highlighted.

Once the models were developed, it was observed that the earth surface temperature above the installation, solar radiation and other external factors such as underlying water lines, drain pipes, etc. play a key role in heating up or cooling down the power cables. It was also determined that the hotspot location in the power cable in the main duct was the same as the hotspot location in the spare duct inside the same installation.

It was also observed that the CYMCAP model had its limitations when the earth surface temperature variations were modeled in the software as the software only allows the earth’s ambient temperature to be modeled as a constant; further, results from the MATLAB model were more in line with the present theory of underground power cable temperature prediction. However, simulation results from both the MATLAB and CYMCAP model showed deviation from the measured data. It was also observed that the spare duct temperatures in this particular underground installation seemed to be affected by external factors such as solar radiation, underlying water lines, gas lines etc. which cannot be modeled in CYMCAP.

The holomorphic embedding method (HEM) applied to the power-flow problem (HEPF) has been used in the past to obtain the voltages and flows for power systems. The incentives for using this method over the traditional Newton-Raphson based nu-merical methods lie in the claim that the method is theoretically guaranteed to converge to the operable solution, if one exists.

In this report, HEPF will be used for two power system analysis purposes:

a. Estimating the saddle-node bifurcation point (SNBP) of a system

b. Developing reduced-order network equivalents for distribution systems.

Typically, the continuation power flow (CPF) is used to estimate the SNBP of a system, which involves solving multiple power-flow problems. One of the advantages of HEPF is that the solution is obtained as an analytical expression of the embedding parameter, and using this property, three of the proposed HEPF-based methods can es-timate the SNBP of a given power system without solving multiple power-flow prob-lems (if generator VAr limits are ignored). If VAr limits are considered, the mathemat-ical representation of the power-flow problem changes and thus an iterative process would have to be performed in order to estimate the SNBP of the system. This would typically still require fewer power-flow problems to be solved than CPF in order to estimate the SNBP.

Another proposed application is to develop reduced order network equivalents for radial distribution networks that retain the nonlinearities of the eliminated portion of the network and hence remain more accurate than traditional Ward-type reductions (which linearize about the given operating point) when the operating condition changes.

Different ways of accelerating the convergence of the power series obtained as a part of HEPF, are explored and it is shown that the eta method is the most efficient of all methods tested.

The local-measurement-based methods of estimating the SNBP are studied. Non-linear Thévenin-like networks as well as multi-bus networks are built using model data to estimate the SNBP and it is shown that the structure of these networks can be made arbitrary by appropriately modifying the nonlinear current injections, which can sim-plify the process of building such networks from measurements.

Power flow calculation plays a significant role in power system studies and operation. To ensure the reliable prediction of system states during planning studies and in the operating environment, a reliable power flow algorithm is desired. However, the traditional power flow methods (such as the Gauss Seidel method and the Newton-Raphson method) are not guaranteed to obtain a converged solution when the system is heavily loaded.

This thesis describes a novel non-iterative holomorphic embedding (HE) method to solve the power flow problem that eliminates the convergence issues and the uncertainty of the existence of the solution. It is guaranteed to find a converged solution if the solution exists, and will signal by an oscillation of the result if there is no solution exists. Furthermore, it does not require a guess of the initial voltage solution.

By embedding the complex-valued parameter α into the voltage function, the power balance equations become holomorphic functions. Then the embedded voltage functions are expanded as a Maclaurin power series, V(α). The diagonal Padé approximant calculated from V(α) gives the maximal analytic continuation of V(α), and produces a reliable solution of voltages. The connection between mathematical theory and its application to power flow calculation is described in detail.

With the existing bus-type-switching routine, the models of phase shifters and three-winding transformers are proposed to enable the HE algorithm to solve practical large-scale systems. Additionally, sparsity techniques are used to store the sparse bus admittance matrix. The modified HE algorithm is programmed in MATLAB. A study parameter β is introduced in the embedding formula βα + (1- β)α^2. By varying the value of β, numerical tests of different embedding formulae are conducted on the three-bus, IEEE 14-bus, 118-bus, 300-bus, and the ERCOT systems, and the numerical performance as a function of β is analyzed to determine the “best” embedding formula. The obtained power-flow solutions are validated using MATPOWER.

The development of new policies favoring integration of renewable energy into the grid has created a need to relook at our existing infrastructure resources and at the way the power system is currently operated. Also, the needs of electric energy markets and transmission/generation expansion planning has created a niche for development of new computationally efficient and yet reliable, simple and robust power flow tools for such studies. The so called dc power flow algorithm is an important power flow tool currently in use. However, the accuracy and performance of dc power flow results is highly variable due to the various formulations which are in use. This has thus intensified the interest of researchers in coming up with better equivalent dc models that can closely match the performance of ac power flow solution.

This thesis involves the development of novel hot start dc model using a power transfer distribution factors (PTDFs) approach. This document also discusses the problems of ill-conditioning / rank deficiency encountered while deriving this model. This model is then compared to several dc power flow models using the IEEE 118-bus system and ERCOT interconnection both as the base case ac solution and during single-line outage contingency analysis. The proposed model matches the base case ac solution better than contemporary dc power flow models used in the industry.

This thesis focuses on developing an integrated transmission and distribution framework that couples the two sub-systems together with due consideration to conventional demand flexibility. The proposed framework ensures accurate representation of the system resources and the network conditions when modeling the distribution system in the transmission OPF and vice-versa. It is further used to develop an accurate pricing mechanism (Distribution-based Location Marginal Pricing), which is reflective of the moment-to-moment costs of generating and delivering electrical energy, for the distribution system. By accurately modeling the two sub-systems, we can improve the economic efficiency and the system reliability, as the price sensitive resources can be controlled to behave in a way that benefits the power system as a whole.

With the power system being increasingly operated near its limits, there is an increasing need for a power-flow (PF) solution devoid of convergence issues. Traditional iterative methods are extremely initial-estimate dependent and not guaranteed to converge to the required solution. Holomorphic Embedding (HE) is a novel non-iterative procedure for solving the PF problem. While the theory behind a restricted version of the method is well rooted in complex analysis, holomorphic functions and algebraic curves, the practical implementation of the method requires going beyond the published details and involves numerical issues related to Taylor's series expansion, Padé approximants, convolution and solving linear matrix equations.

The HE power flow was developed by a non-electrical engineer with language that is foreign to most engineers. One purpose of this document to describe the approach using electric-power engineering parlance and provide an understanding rooted in electric power concepts. This understanding of the methodology is gained by applying the approach to a two-bus dc PF problem and then gradually from moving from this simple two-bus dc PF problem to the general ac PF case.

Software to implement the HE method was developed using MATLAB and numerical tests were carried out on small and medium sized systems to validate the approach. Implementation of different analytic continuation techniques is included and their relevance in applications such as evaluating the voltage solution and estimating the bifurcation point (BP) is discussed. The ability of the HE method to trace the PV curve of the system is identified.

t temperature (HST) and top-oil temperature (TOT) are reliable indicators of the insulation temperature. The objective of this project is to use thermal models to estimate the transformer's maximum dynamic loading capacity without violating the HST and TOT thermal limits set by the operator. In order to ensure the optimal loading, the temperature predictions of the thermal models need to be accurate. A number of transformer thermal models are available in the literature. In present practice, the IEEE Clause 7 model is used by the industry to make these predictions. However, a linear regression based thermal model has been observed to be more accurate than the IEEE model. These two models have been studied in this work.

This document presents the research conducted to discriminate between reliable and unreliable models with the help of certain metrics. This was done by first eyeballing the prediction performance and then evaluating a number of mathematical metrics. Efforts were made to recognize the cause behind an unreliable model. Also research was conducted to improve the accuracy of the performance of the existing models.

A new application, described in this document, has been developed to automate the process of building thermal models for multiple transformers. These thermal models can then be used for transformer dynamic loading.

Due to great challenges from aggressive environmental regulations, increased demand due to new technologies and the integration of renewable energy sources, the energy industry may radically change the way the power system is operated and designed. With the motivation of studying and planning the future power system under these new challenges, the development of the new tools is required. A network equivalent that can be used in such planning tools needs to be generated based on an accurate power flow model and an equivalencing procedure that preserves the key characteristics of the original system. Considering the pervasive use of the dc power flow models, their accuracy is of great concern. The industry seems to be sanguine about the performance of dc power flow models, but recent research has shown that the performance of different formulations is highly variable. In this thesis, several dc power-flow models are analyzed theoretically and evaluated numerically in IEEE 118-bus system and Eastern Interconnection 62,000-bus system. As shown in the numerical example, the alpha-matching dc power flow model performs best in matching the original ac power flow solution. Also, the possibility of applying these dc models in the various applications has been explored and demonstrated. Furthermore, a novel hot-start optimal dc power-flow model based on ac power transfer distribution factors (PTDFs) is proposed, implemented and tested. This optimal-reactance-only dc model not only matches the original ac PF solution well, but also preserves the congestion pattern obtain from the OPF results of the original ac model. Three improved strategies were proposed for applying the bus-aggregation technique to the large-scale systems, like EI and ERCOT, to improve the execution time, and memory requirements when building a reduced equivalent model. Speed improvements of up to a factor of 200 were observed.