Power System Modelling and Analysis Techniques

This chapter establishes the foundation for the power system modelling and analysis techniques used throughout this thesis. It develops the mathematical models of the power system elements that are employed in various studies conducted in subsequent chapters. These models encompass both the dynamic network model based on ordinary differential equations, where network dynamics are included, and the static network model based on algebraic equations, where network dynamics are neglected. The chapter further presents the power system analysis techniques adopted in this research, specifically modal analysis and bifurcation theory. To demonstrate the effectiveness of bifurcation theory in stability assessments, an example analysis of power system stability based on this theory is included. Finally, brief descriptions of the test networks used throughout the thesis are provided.