The probability density of switching on household appliances and its approximations by the Weibull, Gauss and Lorentz functions

Data on stochastic energy consumption in the residential sector and in the village for 500 households are analyzed. The analyzed energy consumption logs from two foreign databases UK DALE and REFIT contain information about the time of switching on and off of household appliances and the power they consume. The number of recorded inclusions of household appliances in the energy consumption logs was ~30,000. It is demonstrated that the schedules of electric energy consumption in the public sector are characterized by morning and evening consumption peaks. To obtain sufficiently accurate simulation results of daily electrical load schedules, it is necessary to determine the switch-on densities of electrical appliances, i.e. the number of switch-on devices per unit of time. The article analyzes which probability density function best approximates experimental data. The approximation of the moment densities of household appliances is performed using the following functions: Weibull, Gauss, Lorentz. The calculation of the distribution parameters is justified. The search for the most appropriate type of approximation is based on comparing the standard deviation between experimental points and the theoretical function. It is shown that it is preferable to use the Weibull probability density.

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