TABLE OF CONTENTS Linear algebra and circuit theory concepts are used in this chapter to describe the formulation of the state equations of linear dynamic systems. The Laplace transform, commonly used in the solution of simple circuits, is impractical in the context of a large power system. Some practical alternatives discussed here are modal analysis, numerical integration of the differential equations and the use of difference equations.
An electrical power system is basically a continuous system, with the exceptions of a few auxiliary components, such as the digital controllers. Digital simulation, on the other hand, is by nature a discrete time process and can only provide solutions for the differential and algebraic equations at discrete points in time.
The discrete representation can always be expressed as a difference equation, where the output at a new time point is calculated from the output at previous time points and the inputs at the present and previous time points. Hence the digital representation can be synthesised, tuned, stabilised and analysed in a similar way as any discrete system.
Thus, as an introduction to the subject matter of the book, this chapter also discusses, briefly, the subjects of digital simulation of continuous functions and the formulation of discrete systems.
An n th order linear dynamic system is described by an n th order linear differential equation which can be rewritten as n first-order linear differential equations, i.e.
| (2.1) |  |
Expressing equation 2.1 in matrix form, with parameter t removed...
