Participation Analysis in Impedance Models: The Grey-Box Approach for Power System Stability.

This paper develops a grey-box approach to stability analysis of complex power systems that facilitates root-cause tracing without requiring disclosure of the full details of the internal control structure of apparatus connected to the system. The grey-box enhances the impedance transfer function approach popular in power electronic systems and favoured by manufacturers of wind and solar systems for the limited disclosure required. Impedance participation factors are proposed and defined in terms of the residues of the whole-system admittance matrix. It is proved that, so defined, these impedance participation factors equal the sensitivity of whole-system eigenvalues to apparatus impedances. The classic state participation factors are related to the impedance participation factors via a chain-rule. Based on the chain-rule, a three-layer grey-box approach, with three degrees of transparency, is proposed for root-cause tracing to different depths, i.e. apparatus, states, and parameters, according to the information available. The association of impedance participation factors with eigenvalue sensitivity points to the re-tuning that would stabilize the system. The impedance participation factors can be measured in the field or calculated from black-box impedance spectra with little prior-knowledge required.