As energy demand continues to increase, smart grid systems that perform efficient energy management become increasingly important due to environmental and cost reasons. It requires faster prediction of electric energy consumption and valid explanation of the predicted results. Recently, several demand predictors based on deep learning that can deal with complex features of data are actively investigated, but most of them suffer from lack of explanation due to the black-box characteristics. In this paper, we propose a hybrid autoencoder-based deep learning model that predicts power demand in minutes and also provides the explanation for the predicted results. It consists of an information projector that uses auxiliary information to extract features for the current situation and a model that predicts future power demand. This model exploits the latent space composed of the two different modalities to account for the prediction. Experiments with household electric power demand data collected over five years show that the proposed model is the best with a mean squared error of 0.3764. In addition, by analyzing the latent variables extracted by the information projector, the correlation with various conditions including the power demand is confirmed to provide the reason of the coming power demand predicted.