Our work concerns the modeling of a typical electrical home installation which includes the electrical power supply, typical loads and also series and parallel arc faults. In this article, we present the models, developed under Matlab/Simulink, of the power supply, two different loads (vacuum cleaner and kettle) and an arc in series on the electrical line. The comparison between these models and real electric signals was done using harmonic analysis. Experiments were made to measure current and voltage signature of typical loads in different configurations (simple and combined load). The simulation results are in good agreement with the real signatures. In order to design an arc fault circuit breaker we propose then a Hardware-In-the-Loop (HIL) simulation approach. This allows us to validate the real functioning of a numerical detection algorithm by exploiting the models of the electric system to be protected. Also we show the first test results of an algorithm based on a frequential analysis for arc fault detection, using the HIL strategy.