Diagnóstico del estado técnico de los equipos estáticos de la

The geyser model has as input variables: ambient temperature in degrees Celsius, inlet water temperature in degrees Celsius and hot water demand in litres per second. All three variables have sampling periods of 1 or 30 minutes. The model is able to run simulations with different input variable sampling rates so that the effect on the simulated output data can be evaluated.

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3.2.1 Ambient temperature data

Ambient temperature is the stochastic input variable to the geyser model and the kernel function. Nine years of ambient temperature data for Cape Town International Airport (CTIA), was sourced from the South African Weather Bureau [44]. This data was imported into the MATLAB work space by the txt2mat function [45]. The function reads the data in a text format and places it in a matrix. This matrix has temperature values for days of the years in rows and the hours of the day in columns. A function called inpaintn was used to search for, and interpolate, missing data values [45]. The data matrix was then reshaped to an array where each data value was assigned a number based on the time it was sampled at. This was done by making use of the MATLAB function datenum. The temperature data supplied by the South African Weather Bureau has a sampling period of 60 minutes. The data array was then linearly interpolated respectively to 1 and 30 minute sampling periods by the resample function. The hhGeyserMod function converted the temperature data arrays to a time series arrays which was then ready for input into the geyser model.

Figure 3.2.1 depicts the CTIA data during 2001. In this figure the diurnal (daily) and seasonal temperature range and fluctuations can be seen.

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3.2.2 Hot water consumption data

Hot water consumption data was generated based on the average hot water consumption profiles that were recorded by the Meyer et al. study. This was done because there was a lack of readily available domestic hot water consumption data. The function HotWgenData was written to generate a hot water consumption data set. This was done by generating a set of random numbers for the summer and winter average recorded values. These two sets of random numbers had Gaussian distributions. These summer and winter random number sets’ standard deviation was set to 17 and 30 percent respectively, which was consistent with the standard deviations observed in the recorded 60 minute data of Meyer et al study [31]. The random numbers were then added to the average 60 minute values of the consumption profiles of the Meyer et al. study. The function then allocated a corresponding date-time number to each of the hot water consumption rate values and then linearly interpolated the data from 60 minute respectively to 1 minute and 30 minute periods. The hhGeyserMod function converted the hot water consumption data arrays to time series arrays which were then ready for input into the geyser model. This was done for each of the three housing density hot water consumption profiles. The generated hot water consumption for a period of one year for different housing densities is depicted in Figures 3.2.2 to 3.2.4. The difference in seasonal and daily profiles of hot water consumption can be seen.

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Figure 3.2.3: Hot water consumption generated for medium-density housing for a period of one year.

65 From the hot water consumption figures the following observations can be made: there is a definite change in consumption profile during the seasonal transition. This is as a result of the averaging of the data in the Meyer et al. study. In reality this hot water consumption profile will have a smoother seasonal data transition. It was assumed the hot water consumption data had a Gaussian distribution, which may prove to be different once such data is recorded and analysed. However, it is none the less possible to investigate the effect different hot water consumption profiles has on electrical demand by specifying different parameters to statistical distributions using the HotWgenData function. In future work, this function could easily be upgraded so that monthly statistical parameters and distribution could be specified which would then smooth out the seasonal consumption profile. The generated hot water consumption rate increased from high-density housing to low-density housing, which is consistent with the Meyer et al. findings.

3.2.3 Geyser inlet water temperature data

The inlet water temperature data was generated based on the equation described by Hille [40]. This was done because of the lack of readily available geyser inlet water temperature data. The function InWaterTemp that was written used the equation described by Hille to generate the inlet water temperature for a specified simulation period. The variables that needed to be specified for this function were:

• depth at which the water supply pipe is buried; • dampening depth of the soil;

• time period for which the data must be generated, and • ambient temperature data set for the specified time period.

The resample function linearly interpolated the generated data respectively to 30 minute and 1 minute sampling periods. The hhGeyserMod function then converted the inlet water data arrays to time series arrays which were then ready for input into the geyser model. The generated inlet water temperature data, for a water supply depth of respectively one and seven meters, is shown in Figure 3.2.5. The soil dampen depth was 2.093 meters for these sets of generated data. It can be seen in Figure 3.2.5 that for an increase supply water pipe burial depth the amplitude of the seasonal inlet water temperature fluctuations decreases. The time phase shift also increases for an increase in burial depth.

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Figure 3.2.5: Generated geyser inlet water temperature data for a water supply pipe buried at a depth of one and seven meters for the years 2001 to 2009.