Fig 1.
p-δ curve to illustrate the equal-area criterion.
Fig 2.
Schematic one-line diagrams of (A) the IEEE 3-bus system and of (B) the system with three Ibuses (in red), two Kbuses (in green), and two Mbuses (in blue).
Fig 3.
Solutions to various forms of swing equation and its relaxations.
Fig 4.
(A) Errors in the constraints and (B) global error with various projections. Both figures are from Ref. [34].
Fig 5.
The red arrow and red cross represent the loss of load and the line fault, respectively.
Table 1.
Machine data for the IEEE 9-bus system illustrated in Fig 2.
Table 2.
Summary of the simulation results.
Fig 6.
The trajectories of (A) δ, of (B) E, of (C) Oi(t), and of (D) the magnitudes of the internal voltages after 10% of loss of the load at Bus 8 (red arrow in Fig 5).
Fig 7.
The trajectories of (A) δ, of (B) E, of (C) Oi(t), and of (D) the estimated magnitudes of internal voltages due to the entire loss of the load at Bus 8 at t = 1 sec (red arrow in Fig 5).
Fig 8.
The trajectories of (A) δ, of (B) E, of (C) Oi(t), and of (D) the estimated magnitudes of internal voltages due to the line fault at the line between Buses 7 and 8 near Bus 7 at t = 1 sec (red cross in Fig 5).
Fig 9.
(A) Post-fault trajectories of the rotor angles and (B) the magnitudes of the estimated internal voltages.
Fig 10.
(A) Post-fault trajectories of the rotor angles and (B) trajectories of the voltage magnitudes, (C) Oi(t), and (D) the estimated magnitudes of internal voltages after the fault is cleared at t = 1.1 seconds.