Approximating stochastic loads using the EM-Algorithm

Due to the increase in volatile power generation facilities, the need for flexible modeling options of an energy network is growing. One approach consists of a cellular architecture whose hierarchy levels are less pronounced. Such an architecture is provided by the Loop Circle Arc theory (LoCA theory). Each cell consists of essentially uniform basic building blocks, such as a storage unit, an energy converter, and a source and load, as well as an interface to the next cell. Based on this theory, a model of $N$ households connected to a Circle is created. In order to report the demand of the connected households to the next cell, the Arc, via the interface, it is necessary to know the summed power values. Since the households generally represent stochastic processes, the densities associated with the households are estimated under the assumption of measured consumption values over a 24-hour period. Using the EM-Algorithm, mixed distribution densities are estimated based on normal distribution densities for each household and superimposed accordingly. In this way, in addition to the expected total power consumption, a variance can be given at the same time. This allows not only an estimation of the energy to be made available at certain times. It is also possible to simplify the network, since the $N$ households can be approximated by the time evolution of the expected overall power consumption values.