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.

As global energy demand has dramatically increased and traditional fossil fuels will be depleted in the foreseeable future, clean and unlimited renewable energies are recognized as the future global energy challenge solution. Today, the power grid in U.S. is building more and more renewable energies like wind and solar, while the electric power system faces new challenges from rapid growing percentage of wind and solar. Unlike combustion generators, intermittency and uncertainty are the inherent features of wind and solar. These features bring a big challenge to the stability of modern electric power grid, especially for a small scale power grid with wind and solar. In order to deal with the intermittency and uncertainty of wind and solar, energy storage systems are considered as one solution to mitigate the fluctuation of wind and solar by smoothing their power outputs. For many different types of energy storage systems, this thesis studied the operation of battery energy storage systems (BESS) in power systems and analyzed the benefits of the BESS. Unlike many researchers assuming fixed utilization patterns for BESS and calculating the benefits, this thesis found the BESS utilization patterns and benefits through an investment planning model. Furthermore, a cost is given for utilizing BESS and to find the best way of operating BESS rather than set an upper bound and a lower bound for BESS energy levels. Two planning models are proposed in this thesis and preliminary conclusions are derived from simulation results. This work is organized as below: chapter 1 briefly introduces the background of this research; chapter 2 gives an overview of previous related work in this area; the main work of this thesis is put in chapter 3 and chapter 4 contains the generic BESS model and the investment planning model; the following chapter 5 includes the simulation and results analysis of this research and chapter 6 provides the conclusions from chapter 5.

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.

The smart grid initiative is the impetus behind changes that are expected to culminate into an enhanced distribution system with the communication and control infrastructure to support advanced distribution system applications and resources such as distributed generation, energy storage systems, and price responsive loads. This research proposes a distribution-class analog of the transmission LMP (DLMP) as an enabler of the advanced applications of the enhanced distribution system. The DLMP is envisioned as a control signal that can incentivize distribution system resources to behave optimally in a manner that benefits economic efficiency and system reliability and that can optimally couple the transmission and the distribution systems. The DLMP is calculated from a two-stage optimization problem; a transmission system OPF and a distribution system OPF. An iterative framework that ensures accurate representation of the distribution system's price sensitive resources for the transmission system problem and vice versa is developed and its convergence problem is discussed. As part of the DLMP calculation framework, a DCOPF formulation that endogenously captures the effect of real power losses is discussed. The formulation uses piecewise linear functions to approximate losses. This thesis explores, with theoretical proofs, the breakdown of the loss approximation technique when non-positive DLMPs/LMPs occur and discusses a mixed integer linear programming formulation that corrects the breakdown. The DLMP is numerically illustrated in traditional and enhanced distribution systems and its superiority to contemporary pricing mechanisms is demonstrated using price responsive loads. Results show that the impact of the inaccuracy of contemporary pricing schemes becomes significant as flexible resources increase. At high elasticity, aggregate load consumption deviated from the optimal consumption by up to about 45 percent when using a flat or time-of-use rate. Individual load consumption deviated by up to 25 percent when using a real-time price. The superiority of the DLMP is more pronounced when important distribution network conditions are not reflected by contemporary prices. The individual load consumption incentivized by the real-time price deviated by up to 90 percent from the optimal consumption in a congested distribution network. While the DLMP internalizes congestion management, the consumption incentivized by the real-time price caused overloads.

Transmission expansion planning (TEP) is a complex decision making process that requires comprehensive analysis to determine the time, location, and number of electric power transmission facilities that are needed in the future power grid. This dissertation investigates the topic of solving TEP problems for large power systems. The dissertation can be divided into two parts. The first part of this dissertation focuses on developing a more accurate network model for TEP study. First, a mixed-integer linear programming (MILP) based TEP model is proposed for solving multi-stage TEP problems. Compared with previous work, the proposed approach reduces the number of variables and constraints needed and improves the computational efficiency significantly. Second, the AC power flow model is applied to TEP models. Relaxations and reformulations are proposed to make the AC model based TEP problem solvable. Third, a convexified AC network model is proposed for TEP studies with reactive power and off-nominal bus voltage magnitudes included in the model. A MILP-based loss model and its relaxations are also investigated. The second part of this dissertation investigates the uncertainty modeling issues in the TEP problem. A two-stage stochastic TEP model is proposed and decomposition algorithms based on the L-shaped method and progressive hedging (PH) are developed to solve the stochastic model. Results indicate that the stochastic TEP model can give a more accurate estimation of the annual operating cost as compared to the deterministic TEP model which focuses only on the peak load.

As renewable energy becomes more prevalent in transmission and distribution systems, it is vital to understand the uncertainty and variability that accompany these resources. Microgrids have the potential to mitigate the effects of resource uncertainty. With the ability to exist in either an islanded mode or maintain connections with the main-grid, a microgrid can increase reliability, defer T&D; infrastructure and effectively utilize demand response. This study presents a co-optimization framework for a microgrid with solar photovoltaic generation, emergency generation, and transmission switching. Today unit commitment models ensure reliability with deterministic criteria, which are either insufficient to ensure reliability or can degrade economic efficiency for a microgrid that uses a large penetration of variable renewable resources. A stochastic mixed integer linear program for day-ahead unit commitment is proposed to account for uncertainty inherent in PV generation. The model incorporates the ability to trade energy and ancillary services with the main-grid, including the designation of firm and non-firm imports, which captures the ability to allow for reserve sharing between the two systems. In order to manage the computational complexities, a Benders' decomposition approach is utilized. The commitment schedule was validated with solar scenario analysis, i.e., Monte-Carlo simulations are conducted to test the proposed dispatch solution. For this test case, there were few deviations to power imports, 0.007% of solar was curtailed, no load shedding occurred in the main-grid, and 1.70% load shedding occurred in the microgrid.

Today, the electric power system faces new challenges from rapid developing technology and the growing concern about environmental problems. The future of the power system under these new challenges needs to be planned and studied. However, due to the high degree of computational complexity of the optimization problem, conducting a system planning study which takes into account the market structure and environmental constraints on a large-scale power system is computationally taxing. To improve the execution time of large system simulations, such as the system planning study, two possible strategies are proposed in this thesis. The first one is to implement a relative new factorization method, known as the multifrontal method, to speed up the solution of the sparse linear matrix equations within the large system simulations. The performance of the multifrontal method implemented by UMFAPACK is compared with traditional LU factorization on a wide range of power-system matrices. The results show that the multifrontal method is superior to traditional LU factorization on relatively denser matrices found in other specialty areas, but has poor performance on the more sparse matrices that occur in power-system applications. This result suggests that multifrontal methods may not be an effective way to improve execution time for large system simulation and power system engineers should evaluate the performance of the multifrontal method before applying it to their applications. The second strategy is to develop a small dc equivalent of the large-scale network with satisfactory accuracy for the large-scale system simulations. In this thesis, a modified Ward equivalent is generated for a large-scale power system, such as the full Electric Reliability Council of Texas (ERCOT) system. In this equivalent, all the generators in the full model are retained integrally. The accuracy of the modified Ward equivalent is validated and the equivalent is used to conduct the optimal generation investment planning study. By using the dc equivalent, the execution time for optimal generation investment planning is greatly reduced. Different scenarios are modeled to study the impact of fuel prices, environmental constraints and incentives for renewable energy on future investment and retirement in generation.

The Smart Grid initiative describes the collaborative effort to modernize the U.S. electric power infrastructure. Modernization efforts incorporate digital data and information technology to effectuate control, enhance reliability, encourage small customer sited distributed generation (DG), and better utilize assets. The Smart Grid environment is envisioned to include distributed generation, flexible and controllable loads, bidirectional communications using smart meters and other technologies. Sensory technology may be utilized as a tool that enhances operation including operation of the distribution system. Addressing this point, a distribution system state estimation algorithm is developed in this thesis. The state estimation algorithm developed here utilizes distribution system modeling techniques to calculate a vector of state variables for a given set of measurements. Measurements include active and reactive power flows, voltage and current magnitudes, phasor voltages with magnitude and angle information. The state estimator is envisioned as a tool embedded in distribution substation computers as part of distribution management systems (DMS); the estimator acts as a supervisory layer for a number of applications including automation (DA), energy management, control and switching. The distribution system state estimator is developed in full three-phase detail, and the effect of mutual coupling and single-phase laterals and loads on the solution is calculated. The network model comprises a full three-phase admittance matrix and a subset of equations that relates measurements to system states. Network equations and variables are represented in rectangular form. Thus a linear calculation procedure may be employed. When initialized to the vector of measured quantities and approximated non-metered load values, the calculation procedure is non-iterative. This dissertation presents background information used to develop the state estimation algorithm, considerations for distribution system modeling, and the formulation of the state estimator. Estimator performance for various power system test beds is investigated. Sample applications of the estimator to Smart Grid systems are presented. Applications include monitoring, enabling demand response (DR), voltage unbalance mitigation, and enhancing voltage control. Illustrations of these applications are shown. Also, examples of enhanced reliability and restoration using a sensory based automation infrastructure are shown.