Why analyse the small-signal dynamic performance of power systems?

We shall be concerned mainly with the analysis of the dynamic performance and control of large, interconnected electric power systems in the following chapters. The differential-algebraic equations which describe the behaviour of a power system are inherently non-linear. Among the non-linearities are functional types (e.g. sinδ), product types (e.g. voltage × current), limits on controller action, saturation in magnetic circuits, etc. The general method of assessing the performance of the system, with all its non-linearities, is through a time-domain simulation which reveals the response of the system to a specific disturbance, e.g. a fault, the loss of a generating unit, line switching. Typically, it may be necessary to conduct many such studies with disturbances applied in various locations in the system to ascertain its stability and dynamic characteristics. Even with many such studies, many of the characteristics of the dynamic behaviour may be missed and insights into system performance lost. In small-signal analysis of dynamic performance of multi-machine systems the stability and characteristics of the system are readily derived from eigenanalysis and other tools. Further-more, in such linear analysis the design of controllers and their integration into the dynamics of plant are facilitated.

Modern linear control system theory contains many powerful techniques, not only for determining the stability and dynamic characteristics of large linear systems, but also for tuning controllers that satisfy steady-state and dynamic performance specifications. Fortunately and importantly, Henri Poincaré [1] showed that if the linearized form of the non-linear system is stable, so is the non-linear system stable at the steady-state operating condition at which the system is linearized. Moreover, the dynamic characteristics of the system at the selected operating condition can be established from linear control system theory and, as long as the perturbations are small, the time-domain responses can be calculated. With such information the design of linear controllers may be undertaken and the resulting controls embedded in the non-linear system. In practice, if the modelling of the devices is adequate, small-signal tests involving generator controls, for example, have revealed close agreement between simulation and test results. Continuously-acting controllers of interest for synchronous generating units are Automatic Voltage Regulators (AVRs), Power System Stabilizers (PSSs) and speed governors.