Improved Dynamical Analysis Tools for DFIG Wind Farms via Traditional and Koopman Linearizations

Recent efforts to reduce carbon emissions have resulted in legislation requiring the decommissioning of fossil fuel generation. In addition, technological advances and improved economic viability of Wind Energy Conversion Systems (WECS). Many grids around the world have seen a relative increase in the penetration of wind power generation [1, 2]. Though WECS are not new, many traditional bulk power system analysis tools neglected their influence. This was of no consequence when the production of energy by WECS was small compared to the transmission capacity and production of energy using fossil fuels. Recent system events have shown that neglecting WECS is not always possible [3, 4]. Research has also shown a need for increasingly sophisticated analysis and design frameworks for WECS [4, 5, 6]. Not only are more sophisticated models required [4, 6, 7], but a larger number of scenarios must be included in planning an operation studies [5], and increasingly sophisticated techniques for analysis are required in stressed grids where the inherent nonlinear behavior of the power system is revealed [8]. Studies have shown that transient stability analyses [9] and traditional participation factors used for placement of power system stabilizers [8] benefit from the inclusion of nonlinearities in the system model. The inherent nonlinear behavior of power systems is more likely to manifest in the future as economic pressures cause the power system to be operated closer to operational limits and environmental and legal pressures cause the replacement of traditional synchronous generators with variable speed WECS. Future analysis tools will enable both a wider breadth and finer detail of dynamical studies of systems with wind farms. This work presents methods to meet both requirements. A more computationally efficient approach for contingency screening is proposed to quickly rule out contingencies that do not require detailed study, thus enabling the increase of number of contingency cases considered. In addition, a small signal model composed of an arbitrary number of individual turbines is derived and analyzed, and a nonlinear wind farm model is constructed such that mature linear analysis tools and design technologies retain their applicability. Improved Dynamical Analysis Tools for DFIG Wind Farms via Traditional and Koopman Linearizations Elliott Mitchell-Colgan GENERAL AUDIENCE ABSTRACT The electric power system is designed to economically and reliably transmit electricity to homes, industry, and businesses. The economic impact of the electric grid was demonstrated by the 2003 blackout’s visible impact in the graph of the yearly gross domestic product of the Unites States. However, because the number of customers is so large and economies of scale are leveraged to keep electricity prices low, utilities are strongly interconnected. Performing comprehensive engineering analyses to ensure reliable operation is still impossible. Instead, heuristics and safety factors are incorporated into planning processes to continually meet demand in a way that complies with Federal regulations. As evidenced by the infrequency of blackouts in the United States, the sophisticated planning processes have up to date been relatively successful. However, the power system is constantly changing. Electrical generators based on renewable energies are a beneficial addition to the grid, but these and other technological changes like high-voltage power electronic converters also come with their own challenges. These systems as currently employed tend to have a different impact on the reliability of operation than traditional fossil fuel based generators. As the system changes, so do the engineering analyses required to ensure reliable operation. In particular, the wind energy conversion systems (WECS) negatively impact the response of the grid to disturbances in certain ways due to inherent challenges harnessing the wind as an energy sources. These negative impacts (and the advent of powerful personal computing) require an increase in the sophistication of power system models. Thus, there are competing challenges: the scale of the power system necessitates computationally efficient modeling, but the complexity of analysis required to maintain reliable operation is also increasing. The primary aim of this study is to develop models and methods for more detailed yet computationally manageable simulation. To this aim, higher order linearizations and the properties of linear systems (graph theory and linear algebra) are exploited. More specifically, this document contains three studies. In the short term planning and situational awareness context, a method is proposed to quickly check credible outages of important grid equipment. This methodology enables the inspection of a wider breadth of system conditions to ameliorate the negative impacts of the unpredictability of the wind. A linear model in the traditional sense is also developed to model any arbitrary number of wind turbines in a wind farm. This enables industry players to study the impacts wind turbine interaction on the dynamic stability of the grid in response to small disturbances. Finally, a wind farm is modeled as a large matrix to model even nonlinear behavior of wind farms. This helps industry players analyze the impact of large disturbances on the grid. I would like to dedicate this dissertation to my mother and father, who have always encouraged self-cultivation and supported my search for new experiences.