Introduction

In this chapter various models of synchronous generators, FACTS devices and of the power system are developed in forms which are employed in software for the analysis of the small-signal dynamic performance of multi-machine systems. Small-signal models for the synchronous generator are formulated in Section 4.2. An essential feature of this analysis is that the higher order coupled-circuit representation of the generator electromagnetic dynamic behaviour is formulated in Section 4.2.3. This is treated as the fundamental model from which the following two alternative but equivalent formulations of the electromagnetic model are derived. The first is the Operational Parameter formulation described in Section 4.2.12. The second, described in Section 4.2.13, is referred to as the Classical Parameter formulation and is expressed directly in terms of the classically-defined standard parameters of the generator. The Classical Parameter formulation is presented because it is employed in widely used power system simulation software packages such as Siemens PTI PSS®E [1] and GE PSLF™ [2]. The parameters for the fundamental coupled-circuit formulation are the resistances and inductances of the d- and q-axis circuits. The parameters for the Operational Parameter representation of the electromagnetic equations are the gains and time constants of the transfer-function representations of the respective axes and are collectively referred to as the ‘exactly-defined standard parameters’. The Classical Parameter formulation requires the classically-defined standard parameters. The relationship and conversion between the three parameter sets are outlined in Section 4.2.14.

Small-signal models of a range of FACTS devices are formulated in Section 4.3 and include those of the Static VAR Compensator (SVC), Voltage Sourced Converter (VSC), Static Synchronous Compensator (STATCOM), and HVDC transmission links. The general purpose VSC model formulated in Section 4.3.3 is used as a component in the simplified STATCOM model in Section 4.3.4 as well as for the rectifier and inverter in the model of the VSC HVDC transmission link in Section 4.3.7. A general model for a voltage-commutated thyristor- controlled AC/DC converter is formulated Section 4.3.8; this model is then used in a modular fashion to represent the rectifier and inverter of a line-commutated HVDC transmission link. A methodology to formulate the small-signal equations of the power system is described in Section 4.4. Finally, in Section 4.5 a general purpose small-signal representation of a static load model is described.