## Electric Power System (Model of Dobson and Chiang)

exd15
Variables and parameters:

V: magnitude of the load voltage

: phase angle of V

: generator voltage phase angle

: rotor speed

Q1: reactive power demand (bifurcation parameter: )

Model equations:

with variables and constants

Figure 1
Bifurcation diagram V versus load (detail: , all stationary states and some periodic states; for the latter ones is depicted).

Figure 2
Bifurcation diagram V and versus load . detail: , all stationary states and some periodic states (S: stationary, P: periodic, s: stable, u: unstable, HB: Hopf bifurcation, PD: periodic doubling)

Figure 3
Phase diagram (projection). Horizontal axis: ; vertical axis: V. ( )

Figure 4
Phase diagram (projection). Horizontal axis: ; vertical axis: V. ( )

Figure 5
Phase diagram (projection). Horizontal axis: ; vertical axis: V. ( )

Figure 6
Phase diagram, periodic orbit, unstable , T=4.6376, projection: horizontal axis , vertical axis V.

Figure 7
Phase diagram, two periodic orbits for , one stable (T=3.802) and one unstable (T=1.913) projection: horizontal axis , vertical axis V.

Figure 8
Phase diagram, unstable periodic orbit, , T=7.62, projection: horizontal axis , vertical axis V.

Figure 9
Phase diagram, , . projection: horizontal axis , vertical axis V.

Figure 10
. Periodic orbit: simple'' period.

Figure 11
. Periodic orbit: double'' period.

Figure 12
. Periodic orbit: fourfold'' period.

Figure 13

Figure 14

Figure 15
V(t), with varying linearly from to . Collapse of voltage.

Figure 16
Phase diagram corresponding to previous figure. Projection to -plane, , with varying linearly from to .

This Example
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