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.

Corrective transmission topology control schemes are an essential part of grid operations and are used to improve the reliability of the grid as well as the operational efficiency. However, topology control schemes are frequently established based on the operator's past knowledge of the system as well as other ad-hoc methods. This research presents robust corrective topology control, which is a transmission switching methodology used for system reliability as well as to facilitate renewable integration.

This research presents three topology control (corrective transmission switching) methodologies along with the detailed formulation of robust corrective switching. The robust model can be solved off-line to suggest switching actions that can be used in a dynamic security assessment tool in real-time. The proposed robust topology control algorithm can also generate multiple corrective switching actions for a particular contingency. The solution obtained from the robust topology control algorithm is guaranteed to be feasible for the entire uncertainty set, i.e., a range of system operating states.

Furthermore, this research extends the benefits of robust corrective topology control to renewable resource integration. In recent years, the penetration of renewable resources in electrical power systems has increased. These renewable resources add more complexities to power system operations, due to their intermittent nature. This research presents robust corrective topology control as a congestion management tool to manage power flows and the associated renewable uncertainty. The proposed day-ahead method determines the maximum uncertainty in renewable resources in terms of do-not-exceed limits combined with corrective topology control. The results obtained from the topology control algorithm are tested for system stability and AC feasibility.

The scalability of do-not-exceed limits problem, from a smaller test case to a realistic test case, is also addressed in this research. The do-not-exceed limit problem is simplified by proposing a zonal do-not-exceed limit formulation over a detailed nodal do-not-exceed limit formulation. The simulation results show that the zonal approach is capable of addressing scalability of the do-not-exceed limit problem for a realistic test case.

An important operating aspect of all transmission systems is power system stability

and satisfactory dynamic performance. The integration of renewable resources in general, and photovoltaic resources in particular into the grid has created new engineering issues. A particularly problematic operating scenario occurs when conventional generation is operated at a low level but photovoltaic solar generation is at a high level. Significant solar photovoltaic penetration as a renewable resource is becoming a reality in some electric power systems. In this thesis, special attention is given to photovoltaic generation in an actual electric power system: increased solar penetration has resulted in significant strides towards meeting renewable portfolio standards. The impact of solar generation integration on power system dynamics is studied and evaluated.

This thesis presents the impact of high solar penetration resulting in potentially

problematic low system damping operating conditions. This is the case because the power system damping provided by conventional generation may be insufficient due to reduced system inertia and change in power flow patterns affecting synchronizing and damping capability in the AC system. This typically occurs because conventional generators are rescheduled or shut down to allow for the increased solar production. This problematic case may occur at any time of the year but during the springtime months of March-May, when the system load is low and the ambient temperature is relatively low, there is the potential that over voltages may occur in the high voltage transmission system. Also, reduced damping in system response to disturbances may occur. An actual case study is considered in which real operating system data are used. Solutions to low damping cases are discussed and a solution based on the retuning of a conventional power system stabilizer is given in the thesis.

This thesis presents research on innovative AC transmission design concepts and focused mathematics for electric power transmission design. The focus relates to compact designs, high temperature low sag conductors, and high phase order design. The motivation of the research is to increase transmission capacity with limited right of way.

Regarding compact phase spacing, insight into the possibility of increasing the security rating of transmission lines is the primary focus through increased mutual coupling and decreased positive sequence reactance. Compact design can reduce the required corridor width to as little as 31% of traditional designs, especially with the use of inter-phase spacers. Typically transmission lines are built with conservative clearances, with difficulty obtaining right of way, more compact phase spacing may be needed. With design consideration significant compaction can produce an increase by 5-25% in the transmission line security (steady state stability) rating. In addition, other advantages and disadvantages of compact phase design are analyzed. Also, the next two topics: high temperature low sag conductors and high phase order designs include the use of compact designs.

High temperature low sag (HTLS) conductors are used to increase the thermal capacity of a transmission line up to two times the capacity compared to traditional conductors. HTLS conductors can operate continuously at 150-210oC and in emergency at 180-250oC (depending on the HTLS conductor). ACSR conductors operate continuously at 50-110oC and in emergency conditions at 110-150oC depending on the utility, line, and location. HTLS conductors have decreased sag characteristics of up to 33% compared to traditional ACSR conductors at 100oC and up to 22% at 180oC. In addition to what HTLS has to offer in terms of the thermal rating improvement, the possibility of using HTLS conductors to indirectly reduce tower height and compact the phases to increase the security limit is investigated. In addition, utilizing HTLS conductors to increase span length and decrease the number of transmission towers is investigated. The phase compaction or increased span length is accomplished by utilization of the improved physical sag characteristics of HTLS conductors.

High phase order (HPO) focuses on the ability to increase the power capacity for a given right of way. For example, a six phase line would have a thermal rating of approximately 173%, a security rating of approximately 289%, and the SIL would be approximately 300% of a double circuit three phase line with equal right of way and equal voltage line to line. In addition, this research focuses on algorithm and model development of HPO systems. A study of the impedance of HPO lines is presented. The line impedance matrices for some high phase order configurations are circulant Toeplitz matrices. Properties of circulant matrices are developed for the generalized sequence impedances of HPO lines. A method to calculate the sequence impedances utilizing unique distance parameter algorithms is presented. A novel method to design the sequence impedances to specifications is presented. Utilizing impedance matrices in circulant form, a generalized form of the sequence components transformation matrix is presented. A generalized voltage unbalance factor in discussed for HPO transmission lines. Algorithms to calculate the number of fault types and number of significant fault types for an n-phase system are presented. A discussion is presented on transposition of HPO transmission lines and a generalized fault analysis of a high phase order circuit is presented along with an HPO analysis program.

The work presented has the objective of increasing the use of rights of way for bulk power transmission through the use of innovative transmission technologies. The purpose of this dissertation is to lay down some of the building blocks and to help make the three technologies discussed practical applications in the future.

An increase in the number of inverter-interfaced photovoltaic (PV) generators on existing distribution feeders affects the design, operation, and control of the distri- bution systems. Existing distribution system analysis tools are capable of supporting only snapshot and quasi-static analyses. Capturing the dynamic effects of the PV generators during the variation in the distribution system states is necessary when studying the effects of controller bandwidths, multiple voltage correction devices, and anti-islanding. This work explores the use of dynamic phasors and differential algebraic equations (DAE) for impact analysis of the PV generators on the existing distribution feeders.

The voltage unbalance induced by PV generators can aggravate the existing unbalance due to load mismatch. An increased phase unbalance significantly adds to the neutral currents, excessive neutral to ground voltages and violate the standards for unbalance factor. The objective of this study is to analyze and quantify the impacts of unbalanced PV installations on a distribution feeder. Additionally, a power electronic converter solution is proposed to mitigate the identified impacts and validate the solution's effectiveness through detailed simulations in OpenDSS.

The benefits associated with the use of energy storage systems for electric- utility-related applications are also studied. This research provides a generalized framework for strategic deployment of a lithium-ion based energy storage system to increase their benefits in a distribution feeder. A significant amount of work has been performed for a detailed characterization of the life cycle costs of an energy storage system. The objectives include - reduction of the substation transformer losses, reduction of the life cycle cost for an energy storage system, and accommodate the PV variability.

The distribution feeder laterals in the distribution feeder with relatively high PV generation as compared to the load can be operated as microgrids to achieve reliability, power quality and economic benefits. However, the renewable resources are intermittent and stochastic in nature. A novel approach for sizing and scheduling the energy storage system and microtrubine is proposed for reliable operation of microgrids. The size and schedule of the energy storage system and microturbine are determined using Benders' decomposition, considering the PV generation as a stochastic resource.

The impact of increasing penetration of converter control-based generators (CCBGs) in a large-scale power system is assessed through a model based small signal stability analysis. Three test bed cases for the years 2010, 2020, and 2022 of the Western Electricity Coordinating Council (WECC) in the United States are used for the analysis. Increasing penetration of wind-based Type 3 and wind-based Type 4 and PV Solar CCBGs is used in the tests. The participation and interaction of CCBGs and synchronous generators in traditional electromechanical interarea modes is analyzed. Two new types of modes dominated by CCBGs are identified. The characteristics of these new modes are described and compared to electromechanical modes in the frequency domain. An examination of the mechanism of the interaction between the CCBG control states and the synchronous generator control states is presented and validated through dynamic simulations. Actual system and forecast load data are used throughout.

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.

There has been a considerable growth in distributed photovoltaic (PV) genera-tion and its integration in electric power distribution systems. This has led to a change in the distribution system infrastructure. Properly planned distributed gen-eration can offer a variety of benefits for system operations and enhance opera-tional performance of the distribution system. However, high penetration of PV resources can give rise to operating conditions which do not arise in traditional systems and one of the potential issues that needs to be addressed involves impact on power quality of the system with respect to the spectral distortion in voltages and currents.

The test bed feeder model representing a real operational distribution feeder is developed in OpenDSS and the feeder modeling takes into consideration the ob-jective of analysis and frequency of interest. Extensive metering infrastructure and measurements are utilized for validation of the model at harmonic frequencies. The harmonic study performed is divided into two sections: study of impact of non-linear loads on total harmonic voltage and current distortions and study of impact of PV resources on high frequency spectral distortion in voltages and cur-rents. The research work incorporates different harmonic study methodologies such as harmonic and high frequency power flow, and frequency scan study. The general conclusions are presented based on the simulation results and in addition, scope for future work is discussed.

With the increased penetration of solar PV, it has become considerable for the system planners and operators to recognize the impact of PV plant on the power system stability and reliable operation of grid. This enforced the development of adequate PV system models for grid planning and interconnection studies. Western Electricity Coordinating Council (WECC) Renewable Energy Modeling Task Force has developed generator/converter, electrical controller and plant controller modules to represent positive sequence solar PV plant model for grid interconnection studies. This work performs the validation of these PV plant models against the field measured data. Sheer purpose of this validation effort is to authenticate model accuracy and their capability to represent dynamics of a solar PV plant. Both steady state and dynamic models of PV plant are discussed in this work. An algorithm to fine tune and determine the electrical controller and plant controller module gains is developed. Controller gains as obtained from proposed algorithm is used in PV plant dynamic simulation model. Model is simulated for a capacitor bank switching event and simulated plant response is then compared with field measured data. Validation results demonstrate that, the proposed algorithm is performing well to determine controller gains within the region of interest. Also, it concluded that developed PV plant models are adequate enough to capture PV plant dynamics.

With growing complexity of power grid interconnections, power systems may become increasingly vulnerable to low frequency oscillations (especially inter-area oscillations) and dependent on stabilizing controls using either local signals or wide-area signals to provide adequate damping. In recent years, the ability and potential to use wide-area signals for control purposes has increased since a significant investment has been made in the U. S. in deploying synchrophasor measurement technology. Fast and reliable communication systems are essential to enable the use of wide-area signals in controls. If wide-area signals find increased applicability in controls the security and reliability of power systems could be vulnerable to disruptions in communication systems. Even though numerous modern techniques have been developed to lower the probability of communication errors, communication networks cannot be designed to be always reliable. Given this background the motivation of this work is to build resiliency in the power grid controls to respond to failures in the communication network when wide-area control signals are used. In addition, this work also deals with the delay uncertainty associated with the wide-area signal transmission. In order to counteract the negative impact of communication failures on control effectiveness, two approaches are proposed and both approaches are motivated by considering the use of a robustly designed supplementary damping control (SDC) framework associated with a static VAr compensator (SVC). When there is no communication failure, the designed controller guarantees enhanced improvement in damping performance. When the wide-area signal in use is lost due to a communication failure, however, the resilient control provides the required damping of the inter-area oscillations by either utilizing another wide-area measurement through a healthy communication route or by simply utilizing an appropriate local control signal. Simulation results prove that with either of the proposed controls included, the system is stabilized regardless of communication failures, and thereby the reliability and sustainability of power systems is improved. The proposed approaches can be extended without loss of generality to the design of any resilient controller in cyber-physical engineering systems.