Table 7 Eigenvalues and minimum damping ratio (hDE-PS: FOPID; with HVDC link)

− 0.8578, − 0.9999, − 1.0, − 0.6795, − 0.6511, − 0.527, − 0.5191, − 0.2947, − 0.2443, − 0.1935, − 0.1854, − 0.1501, − 0.1478,

− 0.0839, − 0.0696, − 0.0552, − 0.0528, − 0.0427, − 0.0421, − 0.0239, − 0.0204, − 0.0158, − 0.0151, − 0.0119, − 0.0120 ± 0.0001i,

− 0.012, − 0.0068, − 0.0055 ± 0.0006i, − 0.0055 ± 0.0005i, − 0.0009 ± 0.0030i, − 0.0025 ± 0.0025i, − 0.0045, − 0.0036, − 0.0036 ± 0.0005i, − 0.0034 ± 0.0004i, − 0.005, − 0.0027, − 0.0034, − 0.0050, − 0.0020 ± 0.0001i, − 0.0020, − 0.0016 ± 0.0002i,

− 0.0015, − 0.0013, − 0.0003 ± 0.0005i, − 0.0013 ± 0.0001i, − 0.0012, − 0.0010, − 0.0009, − 0.0006, − 0.0005, − 0.0004,

− 0.0002 ± 0.0001i, − 0.0003, − 0.0002, − 0.0001

0.2840