Electricity load forecasting faces rising challenges due to the advent of innovating technologies such as smart grids, electric cars and renewable energy production. For distribution network managers, a good knowledge of the future electricity consumption stands as a central point for the reliability of the network and investment strategies. In this paper, we suggest a semi-parametric approach based on generalized additive models theory to model electrical load over more than 2200 substations of the French distribution network, and this at both short and middle term horizons. These generalized additive models estimate the relationship between load and the explanatory variables: temperatures, calendar variables, etc. This methodology has been applied with good results on the French grid. In addition, we highlight the fact that the estimated functions describing the relations between demand and the driving variables are easily interpretable, and that a good temperature prediction is important.