Fig. 5: Normalized values of hertz-sec metric as a proxy for kinetic energy, as a function inertia and damping.

a 9-node, 3-generator test network, b 30-node, 6-generator test network, c 39-node, 10-generator test network, d 57-node, 7-generator test network, e 118-node, 54-generator test network, f 300-node, 69-generator test network. The results for 1000 random operating conditions on 6 different power network benchmarks are presented. The observed hertz-sec values are color-coded by the blue dots being the lower values indicating the best network dynamic response, and the red dots being the higher values reflecting the worst network dynamic response. The range of other colors should be interpreted accordingly as described by the color guide bar. The x- and y-axes represent the generators damping and inertia, respectively. In all six power networks, the trend of hertz-sec values is such that the improvement of frequency dynamics is evident, proportional to increased damping and reduced inertia (the best dynamic responses appear at the bottom of these plots and more towards right corner whereas the worst dynamic response appear in the top of these plots and more towards left corner). In addition, the impact of damping is more pronounced than that of inertia as the changes in score of hertz-sec are more directly proportional to the changes in damping value than to the changes in inertia value. The description of power networks and the source of their data is provided in Supplementary Note 9.