Introduction

In Section 5.8 the P-Vr method for the tuning of the PSS for a generator in a single-machine infinite-bus (SMIB) system is described. Several other methods, which will be shown to be somewhat related to the P-Vr method, are described in the literature. Two other methods will be discussed here, the first is based on Transfer-Function Residues, the second on the so-called GEP Method. The P-Vr method, the Method of Residues and the GEP Method are reconciled for a practical, multi-machine system in [1]. However, for illustrative purposes in this chapter we will examine only the application of the Residues and GEP Methods to a generator in a SMIB system.

The background to the Method of Residues is provided in [2] and its application to PSSs is illustrated in Appendix A of [3]. The method is also used in practice for the design of Power Oscillation Dampers (PODs) which are fitted to FACTS devices such as SVCs, typically to enhance the damping of inter-area modes. The design of PODs using the Method of Residues is described in [4], however, this topic is considered in more detail in Chapter 11.

Method of Residues

Theoretical basis for the Method

The theoretical basis, calculation and significance of the residues of a transfer function are discussed earlier in Section 2.5. In essence, for a set of distinct poles ri is the residue of the pole at s = pi. A transfer function G(s) is described by its partial fraction expansion equation (2.14), or by

The derivation of residues from the state equations is outlined in Section 3.7.

Consider a SMIB system for which a PSS is to be designed and installed. The transfer function from the reference voltage input to the speed output signal of the generator is GS(s)= Δ ω/ ΔVref. The PSS, with transfer function F(s), is a speed-input PSS (although other stabilizing signals can be employed). When operating in closed-loop the PSS output is connected to the AVR summing junction, as shown in Figure 6.1.

It is emphasized that the following simple approach to the determination of the compensation transfer function of the PSS is based on the change of the rotor mode of oscillation when the PSS feedback path is switched from open to closed loop.