Introduction

In this chapter the theoretical basis and a case study are used to illustrate the concepts of interactions between, and effectiveness of, PSSs and FDSs in a multi-machine power system. The theoretical relationships between the incremental modal induced torque coefficients (MITCs), the associated mode shifts, and increments in stabilizer gains are outlined. The case study will illustrate how the method developed for estimating rotor mode (eigenvalue) shifts can be used to assess the relative effectiveness of stabilizers and, thereby, gain some important insights which form a basis for the coordination of stabilizers [1], [2], [3], [4].

Techniques have been described in the literature for determining shifts in the modes of rotor oscillation due to changes in stabilizer parameters [5], [6], [7], [8]. These techniques have been used not only for determining optimal locations for PSSs and FACTS devices [6], [7], [8] but also for tuning PSS parameters [9], [10].

In this chapter the theory and analysis is used to:

1. • develop a new method, based on incremental MITCs, for estimating the mode or eigenvalue shifts;

2. • develop, for a given rotor mode, a method for estimating the contributions to damping of selected stabilizers for a selected increment in stabilizer gain, be they PSSs or FDSs;

3. • deduce the relative effectiveness of selected stabilizers in contributing to damping, say, of an inter-area mode;

4. • assess the effect of interactions between PSSs, particularly for inter-area and local modes;

5. • provide a basis for the systematic coordination of both PSSs and FDSs in multimachine systems [4].

Relationship between rotor mode shifts and stabilizer gainIncrements

Recall from Section 12.6 that the MTIC Tijh is the modal (complex) torque coefficient for the hth mode, λh, this torque coefficient being induced on the shaft of the ith generator by the jth stabilizer. It is established in (12.59) for both PSSs and FDSs that Tijh is dependent on the gain setting kj (in pu on device base) of stabilizer j. In Section 12.6.2 a relationship is developed between the incremental MITCs and increments in stabilizer gains; this is then employed in the following analysis to determine the eigenvalue shifts due to increments in any or all of the gains of the n PSSs and z FDSs.