This work aims to quantify the relations between the electricity demand and some of its determinants in the Residential sector of Brazil. To begin with a short discussion is carried out on the Residential energy consumption in the country throughout the last four decades so as to get to know the residential consumption within a wider context. After, we adopted an econometric modeling aiming to estimate price elasticities, income and price of home appliances. As the series of the variables studied were proved non-stationary, the Cointegration approach was adopted. Vector Error Correction Models (VECM) were estimated and used to project the consumption of electric energy during the 2011-2020 period. The third point concerns, understanding the population growth and the number of households as important factors in determining the number of residential consumer units and, consequently, the demand for electricity, has been adopted the method leadership rate based on age-period-cohort model (APC) aiming to projecting the rate at the leadership rate and the number of homes that should be attended by energy concession during the period 2010-2020. Finally, in face of information obtained from these forcasts, we applied the logarithmic mean Divisia index decomposition method I (LMDI I) in order to explain the variation in energy demand on the optics of the three variables, called Average Consumption, Attendance rate and Household.