Middle-term horizon (months to a year) power consumption prediction is a main challenge in the energy sector, in particular when probabilistic forecasting is considered. We propose a new modelling approach that incorporates trend, seasonality and weather conditions, as explicative variables in a shallow Neural Network with an autoregressive feature. We obtain excellent results for density forecast on the one-year test set applying it to the daily power consumption in New England U.S.A.. The quality of the achieved power consumption probabilistic forecasting has been verified, on the one hand, comparing the results to other standard models for density forecasting and, on the other hand, considering measures that are frequently used in the energy sector as pinball loss and CI backtesting.