Results Data: A Modal Contribution Metric for Quantifying Small-Signal Variability in Power Systems with Converter-Interfaced Generation

This dataset includes the results from which the analysis was performed in the paper:
L. Benedetti, A. Egea-Alvarez, P. N. Papadopoulos, "A Modal Contribution Metric for Quantifying Small-Signal Variability in Power Systems with Converter-Interfaced Generation," submitted to IEEE Transactions on Power Systems, 2024.

Paper abstract:
Power system dynamic behaviour is changing drastically with the disconnection of synchronous generation and increasing connection of converter-interfaced units, which is not necessarily captured by traditional static grid strength metrics. This paper uses the modal superposition concept to derive metrics and information with respect to locational variability, defined in terms of the maximum deviation of system variables in different network locations. Going beyond typical grid strength metrics, the analysis considers voltage magnitude and frequency variability separately, reflecting the complexities arising from the transition to power electronic control dominated power system dynamics. A further benefit of the approach is the derivation of a clear relationship between the variability of output variables and specific modal interactions via their contribution to the response. The Kundur two-area, four-generator system is utilised and investigations are performed with the integration of grid-following and grid-forming converters to compare with the standard synchronous generator case. The methodology and suggested metric reflects the independent voltage and frequency variability trends across different locations of disturbance and observation across the network. Also exhibited is the use of the proposed method to focus on the characteristics and causes of variability at different timescales.

The generation and analysis of data was completed in MATLAB R2021b as further detailed in the paper.

README file:
Results data for the paper:

L. Benedetti, A. Egea-Alvarez, P. N. Papadopoulos, "A Modal Contribution Metric for Quantifying Small-Signal Variability in Power Systems with Converter-Interfaced Generation"

Files:

SGcase = SG-only 2-area system results

GFLscase = results after replacing SGs in area 2 with GFLs

GFMscase = results after replacing SGs in area 2 with GFMs

Timescalescase = results showing analysis on different timescales (GFMs in area 1 and with an inner voltage controller included in the GFM control)

Variables:

eigs = vector of eigenvalues

R = matrix of right eigenvectors (each column represents an eigenvalue, in the same order as eigs)

L = matrix of left eigenvectors (each column represents an eigenvalue, in the same order as eigs)

pf = participation factor matrix (each row represents an eigenvalue, in the same order as eigs)

modal_conts_w = modal contribution values to frequency (each column represents an eigenvalue. Each block of 11 rows corresponds to a different value of disturbance bus, and within each block, the entries correspond to observed bus values from 1 to 11. For example, rows 1-11 are for disturbed bus=1 and observed bus=1 to 11, rows 12-22 are for disturbed bus=2 and observed bus=1 to 11, and so on.)

modal_conts_v = modal contribution values to voltage magnitude (each column represents an eigenvalue. Each block of 11 rows corresponds to a different value of disturbance bus, and within each block, the entries correspond to observed bus values from 1 to 11. For example, rows 1-11 are for disturbed bus=1 and observed bus=1 to 11, rows 12-22 are for disturbed bus=2 and observed bus=1 to 11, and so on.)

mamc_w = matrix of maximum absolute modal contribution (MAMC) values for frequency (each row is disturbance location and each column is observation location. Note, 3D plots in the paper are rearranged along the x and y axes to better represent the layout of the system under test)

i_mamc_w = indices of eigenvalues with highest modal contribution for frequency (i.e., the mode that gives the MAMC) to be cross-referenced with eigs and pf

mamc_v = matrix of maximum absolute modal contribution (MAMC) values for frequency (each row is disturbance location and each column is observation location. Note, 3D plots in the paper are rearranged along the x and y axes to better represent the layout of the system under test)

i_mamc_v = indices of eigenvalues with highest modal contribution for frequency (i.e., the mode that gives the MAMC) to be cross-referenced with eigs and pf

v_out = time domain response of voltage magnitude at each bus in response to active power impulse disturbance at each bus (first dimension=disturbance bus, second dimension=observation bus,third dimension=timeseries data)

f_out = time domain response of frequency at each bus in response to active power impulse disturbance at each bus (first dimension=disturbance bus, second dimension=observation bus,third dimension=timeseries data)

t = time vector to be cross-referenced with v_out and t_out