Shooting-based stability analysis of power system oscillations

This chapter shows an application of TDSM and pit for the determination of limit cycles in power systems. The main advantage of the proposed technique is the ability to determine both stable and unstable periodic orbits in a unique framework. The proposed technique can also cope with hard limits and/or discontinuities, such as switched capacitor banks, on the right hand side of differential equations. Moreover, the technique shows a lower computational burden than other techniques proposed in the literature, e.g., [21]. The chapter also discusses an unconventional formulation of the power system model to cope with the requirements of the TDSM. The main feature of the proposed model concerns the representation of the speed reference of synchronous machines. This model is basically a generalized centre of inertia and involves a recast of the variables to avoid aperiodic drifting of machine angles. The proposed generalization of the centre of inertia indicates that a proper reformulation of synchronous machine equations allows applying techniques that are well-assessed in circuit analysis. Rethinking power system models based on rigorous formalism appears as a challenging field of research.