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Finally, in Figure 7 we take a look at the
effects of a spread in the rate of energy
extraction. The first curve (1 value of the
rate of energy extraction) correspond to an A
of 0.48 'C/min. The second curve (5 different
values of the rate of energy extraction) is a
combination of dynamics for the values 0.32 ,
0.40, 0.48, 0.56 and 0.64 weighted respectively
at 6.057%, 24.096%, 39.694%, 24.096% and
6.057%. Finally, in the third curve (9
different values of the rate of energy
extraction) a larger parameter spread is
simulated by adding the values 0.16, 0.2, 0.76
and 0.80 'C/min. The weights are now changed to
11.84%, 8.1%, 7.89%, 14.4% ,15.54% ,14.4%,
7.89%, 8.1% and 11.84% respectively. In this
case we can observe again a slight difference
in the oscillatory period as well as a
difference in the amplitude of these
oscillations. A large spread in parameters
tends to shrink the amplitude of post-recovery
oscillatory transients and yields smoother
dynamics. It is worthwhile noting that most
available experimental observations of postinterruption
recovery dynamics of water
heaters, correspond to non homogeneous groups
with a very significant spread of parameters.
It is also non homogeneous load dynamics which
are relevant in studying the cold load pickup
problem for electric water heaters.
Electric water heaters are ubiquitous
components in power systems and an
understanding of their aggregate dynamics is
essential for analyzing the effects of
conservation measures, as well as direct device
control based load management schemes. Cold
load pickup is also an area where water heaters
tend to display, together with other energy
storage linked devices such as air conditioners
and electric space heaters, peculiar dynamic
behavior, in particular persistent transients.
We have presented a dynamic model of the
aggregate behavior of electric water heaters.
The model is physically meaningful in that
physical information about the devices and
their usage statistics can be directly
reflected in the model dynamics. The effects of
cycling controls can be easily simulated for planning adequate load management strategies.
Also the model dynamics tend to conform to
intuition. Most importantly, the model allows
an evaluation of the effects of cycling
controls as seen by the customers, under the
form of temperature distributions in the
controlled devices. In future work, we shall
report on algorithms for constructing optimal
peak load shaving strategies based on model
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