The high R/X ratio of typical distribution systems makes the system voltage vulnerable to active power injection from the distributed energy resources (DERs). Moreover, the intermittent and uncertain nature of the DER generation brings new challenges to voltage management. As guided by the previous IEEE standard 1547-2003, most of the existing photovoltaic (PV) systems in the real distribution networks are equipped with conventional inverters, which only allow the PV systems to operate at unity power factor to generate active power. To utilize the voltage control capability of the existing PV systems following the guideline of the revised IEEE standard 1547-2018, this dissertation proposes a two-stage stochastic optimization strategy aimed at optimally placing the PV smart inverters with Volt-VAr capability among the existing PV systems for distribution systems with high PV penetration to mitigate voltage violations. PV smart inverters are fast-response devices compared to conventional voltage control devices in the distribution system. Historically, distribution system planning and operation studies are mainly based on quasi-static simulation, which ignores system dynamic transitions between static solutions. However, as high-penetration PV systems are present in the distribution system, the fast transients of the PV smart inverters cannot be ignored. A detailed dynamic model of the PV smart inverter with Volt-VAr control capability is developed as a dynamic link library (DLL) in OpenDSS to validate the system voltage stability with autonomous control of the optimally placed PV smart inverters. Static and dynamic verification is conducted on an actual 12.47 kV, 9 km-long Arizona utility feeder that serves residential customers. To achieve fast simulation and accommodate more complex PV models with desired accuracy and efficiency, an integrative dynamic simulation framework for OpenDSS with adaptive step size control is proposed. Based on the original fixed-step size simulation framework in OpenDSS, the proposed framework adds a function in the OpenDSS main program to adjust its step size to meet the minimum step size requirement from all the PV inverters in the system. Simulations are conducted using both the original and the proposed framework to validate the proposed simulation framework.

In recent years, with the increasing penetration of solar generation, the uncertainty and variability of the power system generation also have increased. Power systems always require a balance between generation and load. The generation of the conventional generators must be scheduled to meet the total net load of the system with the variability and uncertainty of the solar resources integrated. The ability to match generation to load requires certain flexibility of the conventional generation units as well as a flexible transmission network to deliver the power. In this work, given the generation flexibility primarily reflected in the ramping rates, as well as the minimum and maximum output of the generation units, the transmission network flexibility is assessed using the metric developed in this work.

The main topic of this thesis is the examination of the transmission system flexibility using time series power flows (TSPFs). First, a TSPFs program is developed considering the economic dispatch of all the generating stations, as well as the available ramping rate of each generating unit. The time series power flow spans a period of 24 hours with 5-minute time interval and hence includes 288 power flow snapshots. Every power flow snapshot is created based on the power system topology and the previous system state. These power flow snapshots are referred to as the base case power flow below.

Sensitivity analysis is then conducted by using the TSPFs program as a primary tool, by fixing all but one of the system changes which include: solar penetration, wires to wires interconnection, expected retirements of coal units and expected participation in the energy

imbalance market. The impact of each individual change can be evaluated by the metric developed in the following chapters.