A description was given in Chapter two of the non-parametric approach to probability density estimation by Charytoniuk et al. [27]. This method was used to forecast short-term electrical demand. This same method was adopted to statistically analyse the demand impacts of the simulated ECMs of chapter five. The first decision to be made when following this approach is to identify which independent variables are statistically influential on electrical demand for the energy consumer. These variables could be any one of the following: ambient temperature, wind speed, light intensity levels and humidity. The chosen independent variables and electrical demand would then be inserted into the kernel function. The independent input variables must be analysed for characteristic patterns. These groupings must be represented in the statistical analysis. Patterns of time of day, day of the week and season of the year were evident in the hot water consumption data variable. These patterns necessitate a similar grouping of PDFs in the statistical analysis to determine the relationship between dependent and independent variables.
Ambient temperature was the independent variable chosen for representation in the statistical analysis because it was evident from the study conducted by Meyer et al. that it has a significant
79 influence on the other input variables to the geyser model which were hot water demand and inlet water temperature. Standing losses are also significantly affected by the difference between ambient temperature and the temperature inside the geyser. From the demand and temperature data, a PDF was generated for a single 30 minute period on a specific day of the week and season of the year. In the statistical analysis the PDFs must describe each one of the chosen categories of characterization.
The PDFs can be used to conduct short-term load forecasting. Alternatively, by changing the geyser model’s parameters or adjusting a parameter of one of the generated input variables, it is possible to simulate the energy demand that would result from an implemented ECM.
Finally, a different approach may prove to be feasible in that two separate geyser models could be simulated. One model represents the pre-ECM demand profile and the other the post ECM demand profile. The kernel function of the post ECM could be subtracted from the kernel function of the pre-ECM which in theory results in a kernel function of the demand impact. The subtraction of the two bivariate kernel functions could be done by the multiplication of the Fourier transforms of the pre-ECM kernel function and the negative of the post ECM kernel function. An alternative method to this would be the multiplication of the characteristic functions of the kernel functions. The resultant function of either of these methods could then be inverse Fourier transformed to give the savings kernel function which could be used to generate the demand impact PDFs. This is suggested under future work in Chapter six of this thesis.
3.8 Conclusion
In summary this chapter on load modelling of a geyser has presented the methodology that was adopted to develop a model topology of a complex electrical load and the statistical analysis of its simulated demand. A brief description was given of the MATLAB functions that were developed to prepare the data for insertion into the geyser model and the kernel function. It was concluded that the model topology could be used to provide short-term load forecasting and the prediction of the impact of an ECM. A suggestion is finally given on how the pre- and post- ECM kernel functions could be subtracted from one another to produce an energy savings kernel density estimation function.
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4.1 Overview
The aim of this chapter is to gain insight into the statistical nature of the input data of the geyser model. To design an effective and efficient DSM intervention, a comprehensive understanding is required of how the independent variables of the electrical consumer are related to its dependent variables. In a modelled version of an electrical consumer, a prescribed DSM intervention may effectively change the model of the electrical consumer itself or just change some of the parameters of the model. The output data of various simulations of the model is modified through the manipulation of the input data, the parameters of the model and/-or the model itself. A greater understanding of the relationship between input and output data is gained through their statistical analysis. The geyser model effectively manipulates the statistical nature of the data when processed by the model. By knowing the relationship and the statistical attributes of the input/output data it is possible to engineer the desired results through the optimal design of DSM interventions. As a result of the above information it was deemed necessary to statistically analyse the input data to the geyser model.
The input data sets for the geyser model were:
• ambient temperature; • inlet water temperature, and • hot water consumption rate.
All of these input data sets must have the same sampling period before they are entered into the geyser model. If the data is obtained at a different sampling rate it can be linearly interpolated or averaged respectively to a higher or lower frequency. The effects of this input data manipulation are investigated on:
• statistical parameters of the input data (in this chapter), and
• simulated output data and its statistical parameters (in Chapter five).