Table I shows the parameter values used for Equation 3 to
determine the overall heat transfer coefficient for the heating
and cooling states. The value of A for the heating state is given
by the inner surface area of the pipe which is exposed to the
warm water and for the cooling state it is given as the outer
surface area of the pipe, which is exposed to the environment.
The value of V for the heating state is given by the volume
of the copper tube that makes up the outlet pipe and for the
cooling state it is given by the volume of the water inside the
pipe as all the thermal energy of the system is stored in the
water as copper has a much lower heat capacity than water.
The simulated and measured pipe temperatures are shown in
Figure 5 for a small usage event (7 litres) for an EWH with
a set temperature of 65 ◦C. The EWH implemented schedule
control and was only allowed to turn the element on from
04:15 to 06:00. The event shown occurred mid morning after
two significant usage events (25 and 95 litres), resulting in a
lower tank temperature. Additionally, it was a warm day with
a maximum temperature of 28 ◦C which lead to an increased
pipe temperature. Figure 6 shows the measured and simulated
outlet pipe temperatures for a large usage event (74.5 litres)
for an EWH with a set temperature of 65 ◦C. The EWH
implemented regular thermostat control (i.e. on all day) and
the event shown occurred 8 hours after the previous event.
The simulated temperature of the pipe was calculated in
10 second intervals to clearly illustrate the overall shape of
the temperature curve. It should be noted that the initial start
of the temperature may lag or lead the measured data as
it is not possible to determine when exactly during the one
minute sampling interval the usage event started. Additionally,
since the temperature at the surface of the pipe was measured,
the temperature sensor reading reaches a maximum value
that is lower than the set temperature of the water in the
tank. The exposed temperature value for the heating state
in Equation 3 was adjusted accordingly in order to obtain
more accurate simulation results. The simulation results have a
similar shape to the EWH outlet temperatures measured in 10
second intervals by Weihl and Kempton [11] and are in good
agreement with the measured outlet temperature values. From
Figure 5, it can be seen that the minimum rise in temperature
that needs to be detected for a small usage event is 6 degrees
over 2 samples and that the pipe takes approximately 13
samples to fall by 2 ◦C. However, in order to obtain accurate
duration estimates of the events, the decay must be adjusted
for events that cause the outlet temperature to rise by a more
significant amount (i.e. closer to the set temperature), as shown
in Figure 6. Therefore an increase of 4 ◦C over 2 samples was
chosen as the characteristics of a start event. For a stop event,
a decrease in 2 ◦C was chosen and the number of samples was
varied depending on the maximum outlet temperature reached
after a start event. A value of seven samples was chosen for
events that increase the outlet temperature above 35 ◦C and a
value of 14 samples for an outlet temperature below 35 ◦C.
From these results, it can be seen that the minimum rise
in temperature that needs to be detected for a small usage
event is 6 degrees over 2 samples and that the pipe takes
approximately 13 samples to fall by 2 ◦C. However, in order
to obtain accurate duration estimates of the events, the decay
must be adjusted for events that cause the outlet temperature
to rise by a more significant amount (i.e. closer to the set
temperature). Therefore an increase of 4 ◦C over 2 samples was
chosen as the characteristics of a start event. For a stop event,
a decrease in 2 ◦C was chosen and the number of samples was
varied depending on the maximum outlet temperature reached
after a start event. A value of seven samples was chosen for
events that increase the outlet temperature above 35 ◦C and a
value of 14 samples for an outlet temperature below 35 ◦C.