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Concrete Battery Enclosure (CBE-0001) Reflective Paint Test

Temperature Test Report (2015/12/07 – 2016/01/01)

Mathematical Model Data and Testing

Blue Hills Golf Course

Summary Further tests have been conducted to observe the effectiveness of the thermal paint when painting the battery

enclosures. The following data and results have been obtained over the period described in the heading. A

mathematical model for the temperature change characteristics of the cube is also given within this report.

The implications of having a mathematical model is immense: We can now predict battery temperatures in

different locations based on available climatic data for most locations on earth.

Introduction

The temperature within and around the concrete cube at Blue Hills has been monitored from the 7th of

December to the 1st of January 2016. Note that this period is one of hottest experienced in Johannesburg in

recent history.

The temperature data has been captured using 2 GSM temperature monitors and 2 Huato S100 Intelligent

Data Loggers. The 2 GSM probes were placed between the batteries within the cube, one near the top of the

batteries and the other near the centre of the batteries. One data logger was used to obtain the ambient

temperature around the cube. The other logger was placed on top of the batteries in the middle of the cube.

The values below shows the temperature of the battery case measured on the outside. These casings are

plastic and simple physics indicate that actual battery plate/electrolyte temperatures would show even lower

variations than measured below.

Results

Figure 1: Temperatures measured by the probes over the test period

0

5

10

15

20

25

30

35

40

15/12/02 15/12/07 15/12/12 15/12/17 15/12/22 15/12/27 16/01/01 16/01/06

Graph of Temperature versus Date and Time

Ambient Cube

Ambient Battery

Month SummaryMax Ambient:37.5°CAmbient avg: 23.9°CBattery avg: 24.0°C

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Observations

As can be seen from the corresponding lines the temperature within the cube and around the batteries

continues to follow the results of the previous tests. The curves of the temperature probes within the cube

continue to exhibit a far shallower temperature change when compared to ambient temperature and remain

closer to the average temperature throughout the entire test period.

When using excel to calculate the average temperature experienced by the ambient probe the program

calculate the average as 23.95C. Bottom temperature average is given at 24.47C. Temperature probes C/C and

C/T exhibit an average temperature of 23.38C and 23.86C respectively. This slightly lower average temperature

received by probes C/C and C/T may be a result of the measurements not having any decimal precision points.

Mathematical Model Observations

This is the model designed by modelling the characteristics of the cube temperature inside the BlueHills cube

using data obtained by tests 1 and 2.

Figure 2: Mathematical model of the cube reacting to ambient temperature shifts during test 2

The straight line that can be seen for the first day on the graph above is due to the lack of initial conditions

when testing the mathematical model. The line represents the average temperature of the ambient air

surrounding the cube.

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Figure 3: MATLAB graph of the mathematical model (blue), Actual probe data for ambient (red) and probe

data for temperature in the cube (green)

Figure 4: Matlab Results for percentage time the battery spent at and above certain temperatures as well as

the average temperature

Figure 5: Excel Results using the results obtained from Airdrive and the S100 data-loggers for the month of

December

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As can be seen from the model it accurately tracks the temperature characteristics within the cube itself and

follows the

𝒛 + 𝟏

𝒛 − 𝟎. 𝟗𝟗𝟕𝟐

Equation 1: Model filter transfer function

𝟐. 𝟎𝟎𝟑𝐞−𝟎.𝟎𝟎𝟐𝟖𝟎𝟑𝟗𝟑𝐧

Equation 2: Model transfer function in time assuming n is positive with a time constant of

29 hours 43 minutes 17 seconds

Analysis

The coated cube continues to exhibit the same characteristics as the previous tests. The paint drastically

lowers temperature fluctuations and the overall percentage of time the batteries will experience

temperatures above the 25 degree Celsius threshold.

The mathematical model designed is based on a transfer function of a first order Butterworth filter. As can be

seen from the equations 1 and 2 above, the time constant of the model shown is approximately 30 hours.

Conclusions

The reflective paint continues to show a dramatic decrease in temperature fluctuations within the cube. The

relative percentage of times that the cube stays over 25 degrees is reduced by a small amount. However the

most prominent result shows in the percentage of time that the cube remains over 28C.

The mathematical model derived can also accurately track the temperature changes that will occur within the

cube base. The model illustrates the simple principle which is one of the major advantages of the cube: The

average battery temperature will equal the average temperature of the location. This seems trivial but really

is effective since the average temperature (over a short term) at any site is determined by both the minimum

(night time) and maximum temperatures. Even in very hot conditions this day/night average is substantially

lower than the maximum temperature viewed in isolation. Inside a container the temperature is regulated

and roughly remains constant since a typical container contains equipment which generates heat and, even at

night, therefore does not cool down. Since batteries in standby mode does not generate heat the fact that

they experience both daytime highs and night time lows while their “thermal mass” ensures that they do not

heat up or cool down during daily variations, but remain within a degree or two at the average of the two

extremes.