Approach for generation of test cases (Back to the homepage)
For natural oscillations, test cases of interest include a set of situations when a single or multiple sources of negative damping create a single undamped local or inter-area mode or a combination of undamped local and inter-area modes. The same base power flow was used for all test cases. Desired variety of oscillations properties for undamped natural modes was generated by modifying damping coefficients D of certain generators and by applying a fault at specific locations.
Forced oscillations of interest include situations when the injected signal has a harmonic or a rectangular periodic shape. Practically important for harmonic signal are the situations when the injected signal has a frequency (a) equal to a frequency of local or inter-area mode and thus creating a resonance; (b) close but above or below the frequency of a natural mode; (c) in between of two local or inter-area modes. For non-harmonic periodic signal, the situation is interesting when the injected signal has a spectrum whose harmonics contain high energies and could possibly coincide with (a) inter-area or (b) local natural modes.
All these situations were possible to generate by having a detailed modal analysis based on the system model by using SSAT software. Modal analysis includes the information on the spectrum of any natural mode (damping and frequency), mode shape (right eigenvector of the mode) and excitability of the mode (left eigenvector). For a certain mode, the magnitudes and phases of elements in its right eigenvector associated with states of rotor angles indicate the observability and the phase-grouping of generators for that mode, while the magnitude of each element in its left eigenvector indicate how large that mode will be excited when a fault is added to the location associated with that element.
SSAT software allows also calculating the sensitivity of real parts of eignevalues relative to variation of damping coefficient D of a generator. The sensitivity matrix for all generators and for all modes allow to controllably manipulate damping of modes by changed D values.