Analysis of continuous and discrete systems

With the exceptions of a few auxiliary components, the electrical power system is a continuous system, which can be represented mathematically by a system of differential and algebraic equations. A convenient form of these equations is the state variable formulation, in which a system of n first-order linear differential equations results from an n order system. The state variable formulation is not unique and depends on the choice of state variables. The following state variable realisations have been described in this chapter: successive differentiation, controller canonical, observer canonical and diagonal canonical. Digital simulation is by nature a discrete time process and can only provide solutions for the differential and algebraic equations at discrete points in time, hence this requires the formulation of discrete systems. 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.