Predicting the future peak demand growth becomes increasingly important as more consumer loads and electric vehicles (EVs) start connecting to the grid. Accurate forecasts will enable energy suppliers to meet demand more reliably. However, this is a challenging problem since the peak demand is very nonlinear. This study addresses the research question of how deep learning methods, such as convolutional neural networks (CNNs) and long-short term memory (LSTM) can provide better support to these areas. The goal is to build a suitable forecasting model that can accurately predict the peak demand. Several data from 2004 to 2019 was collected from Panama’s power system to validate this study. Input features such as residential consumption and monthly economic index were considered for predicting peak demand. First, we introduced three different CNN architectures which were multivariate CNN, multivariate CNN-LSTM and multihead CNN. These were then benchmarked against LSTM. We found that the CNNs outperformed LSTM, with the multivariate CNN being the best performing model. To validate our initial findings, we then evaluated the robustness of the models against Gaussian noise. We demonstrated that CNNs were far more superior than LSTM and can support spatial-temporal time series data.