Frequency domain analysis of power system forced oscillations

A frequency domain approach is used to analyse power system forced low frequency oscillations. The gain characteristics of a closed loop transfer function, Gd(s)= Δδ/ΔPd, which reflects the effect of disturbances on power angle oscillations, are shown to be crucial in identifying the frequency ranges in which amplified oscillatory disturbances can occur. It is shown that tuning power system stabilisers (PSS), based on eigenvalue analysis, lack the insight gained from the explicit evaluation of the Gd(s) gain response. The proposed approach identifies a risky situation which could not be detected on an eigenvalue pattern. For weakly connected systems, the inherent negative damping effects, along with the PSS derivative feedback action, result in a situation where a PSS, tuned to locate the eigenvalues corresponding to the natural mode ωn at well damped locations, can still cause a hazardous situation. While flattening the |Gd(jω)| peak at ωn, the derivative supplementary excitation feedback loops can create another peak which may match oscillatory tie-line disturbances, thereby causing amplified oscillations. The paper also proposes a dynamic gain reduction scheme which can overcome this situation by decoupling the negative damping effects while accentuating the stabilising effects of the PSS derivative feedback. It is shown that a considerable reduction in the tie-line mode oscillations can be achieved. Generalisation to multimachine networks is straightforward. An Appendix is included to describe a systematic derivation of a polynomial matrix that evaluates disturbance rejection/attenuation functions in a general multi-machine environment.