Introduction

In this chapter the concept, the theory, and calculation of modal induced torque coefficients (MITCs) in multi-machine power systems are introduced. The concept of a modal induced torque coefficient is new [1], [2]. It forms the basis for calculation of the shifts in rotor modes when the stabilizer gains of one or more PSSs and/or FDSs are incremented by Δk (pu) on device base. Based on the concept of MITCs, the background theory of the rotor modes shifts, together with analysis of the effectiveness of, and interactions between, PSSs and FDSs in multi-machine systems are described in Chapter 13.

The theoretical development of MITCs in this chapter is fairly detailed and can be omitted if the practical applications of the analysis of rotor modes shifts are of primary interest. Where relevant, references are made in Chapter 13 to the results and equations that are developed in this chapter. A case study in the latter chapter demonstrates the significance of the MITCs and the insights that they provide into the dynamic performance of a multi-machine power system.

In essence, the concept of a modal induced torque coefficient is a further development of the concepts of damping and synchronising torque coefficients based on frequency response analysis (i.e. s = Jωf) [1]. In this chapter the torque coefficients are evaluated at the complex rotor modes (λh = α±jω). The frequency-analysis-based torque coefficients are introduced in Section 5.3 for a SMIB system and in Sections 9.5 and 10.6 for the multi-machine case. With shaft dynamics enabled, the modal induced torque coefficient, Tijh, for the complex rotor mode λh is defined as a complex torque coefficient which is induced on generator i due to a perturbation in the stabilizing signal of stabilizer j. The stabilizer in question may be a power system stabilizer (PSS) or a FACT device stabilizer (FDS) installed on a FACTS device. Such FACTS devices are static var compensators (SVCs), high voltage DC links, thyristor controlled series capacitors (TCSCs) among others. It will be shown that the effect of any such stabilizer on the damping of any mode of rotor oscillation can be quantified. The concept can be extended to other devices such as wind turbine generators, photovoltaics and any other power-converter based transmission or generation equipment.