The book aims at providing a necessary information about power system modeling and behavior to practicing power system engineers and control system engineers so that they can think coherently about power system control. Respectively, it is focused on two themes: the nonlinear dynamics of power systems and the discrete event mechanism as a dominating factor in power system operations. The interaction of discrete protection systems and control actions as load shedding with the nonlinear continuous dynamics of the system are considered as central to the behavior of power systems. New methods of modeling, analysis, and design of hybrid systems are considered and examined from the point of view of how they can be applied to improve the understanding of power system behavior and, consequently, to design better control systems.
The book consists of an introduction and seven main chapters. Basics of electricity and magnetism are recalled in Chapter 2, and nonlinear circuits including resistors, inductors, capacitors, and memristors are discussed in Chapter 3, where circuit dynamic models are constructed using generalized Euler-Lagrange equations. Basic characteristics of AC networks are discussed in Chapter 4. Power system dynamics is addressed in Chapters 5 and 6. Here, power systems are treated as ordinary differential equations, to which the stability analysis via Lyapunov techniques is applied. Modeling power systems by more complex, differential-algebraic equations, requires a bifurcation analysis and the analysis of a network as it approaches voltage instability. Chapter 7 deals with two classical problems of power systems, voltage regulation and load frequency control. Automatic generation control, intending to regulate frequency and power interchanges between multiple interconnected control areas, is also considered in the chapter. The class of control problems related to operation in highly nonlinear regimes where failure events cause abrupt changes in the controlled system behavior is addressed in Chapter 8. The required change in control strategy involves both continuous and discrete dynamics, and the applications are conceived as a hybrid automaton. In the described approach, the transition behavior of a hybrid automaton is associated with a set of inequalities involving Boolean variables.