Building a stochastic model of residential load on example of a water heater

The purpose of the article is to present the developed model implemented in the Mathcad environment enabling to generate a stream of events simulating the operation of a real water heater. The characteristics of the operation modes of power system loads modeled by random variables and processes are analyzed. An experimental study of the operation of a 2 kW domestic water heater is carried out to obtain a probabilistic and statistical model of consumption of a separate load electric energy. The data of water heater operation modes are obtained by the device developed for measuring and recording of the intake power of a single-phase electric load up to 5 kW. The device used is implemented on the basis of the ATmega328 microcontroller and allows to measure and record the obtained values on a SD-card. The functional diagram of the developed device is described in the article. The experimental study lasting 30 days has resulted in obtaining a numerical sequence of events, which served the basis for model construction. Statistical analysis suggests that the distribution laws of sequence probabilities of on-duty state and pauses duration can be attributed to the exponential distribution. Based on this premise, a model implemented in Mathcad environment was created. On the basis of two generated sequences with exponential distribution with the specified parameters the event flow simulating water heater operation is generated. Finally, the paper refines the duration of modeling intervals. In particular, if modeling intervals are 24 hours and more, the model provides reliable results. However, modeling of small intervals (20 hours and less) requires to take into account the change in the heater operation mode depending on the time of day. As an example the estimates of the exponential distribution of parameters for day and night operation modes of the water heater are given.

stochastic model, energy consumption modeling, intake power measurement, water heater operation mode