##
**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
*Q*_{1}: 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
.

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Postscript-Files for better printing results:

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