Accurate mid- and long-term petroleum products (PP) consumption forecasting is vital for strategic reserve management and energy planning. In order to address the issue of energy forecasting, a novel structural auto-adaptive intelligent grey model (SAIGM) is developed in this paper. To start with, a novel time response function for predictions that corrects the main weaknesses of the traditional grey model is established. Then, the optimal parameter values are calculated using SAIGM to increase adaptability and flexibility to deal with a variety of forecasting dilemmas. The viability and performance of SAIGM are examined with both ideal and real-world data. The former is constructed from algebraic series while the latter is made up Cameroon's PP consumption data. With its ingrained structural flexibility, SAIGM yields forecasts with RMSE of 3.10 and 1.54% MAPE. The proposed model performs better than competing intelligent grey systems that have been developed to date and is thus a valid forecasting tool that can be used to track the growth of Cameroon's PP demand.•The ability of SAIGM enhances the forecasting power of intelligent grey models to fully extracting the laws of a system, no matter the data specifications.•SAIGM is extended to include quasi-exponential series by addressing structural flexibility and parametrization concerns.•Input attributes determination and data preprocessing are not required for the proposed model.