Renewable energy from wind and solar resources can contribute significantly to the decarbonisation of the conventionally fossil-driven electricity grid. However, their seamless integration with the grid poses significant challenges due to their intermittent generation patterns, which is intensified by the existing uncertainties and fluctuations from the demand side. A resolution is increasing energy storage and standby power generation which results in economic losses. Alternatively, enhancing the predictability of wind and solar energy as well as demand enables replacing such expensive hardware with advanced control and optimization systems. The present research contribution establishes consistent sets of data and develops data-driven models through machine-learning techniques. The aim is to quantify the uncertainties in the electricity grid and examine the predictability of their behaviour. The predictive methods that were selected included conventional artificial neural networks (ANN), support vector regression (SVR) and Gaussian process regression (GPR). For each method, a sensitivity analysis was conducted with the aim of tuning its parameters as optimally as possible. The next step was to train and validate each method with various datasets (wind, solar, demand). Finally, a predictability analysis was performed in order to ascertain how the models would respond when the prediction time horizon increases. All models were found capable of predicting wind and solar power, but only the neural networks were successful for the electricity demand. Considering the dynamics of the electricity grid, it was observed that the prediction process for renewable wind and solar power generation, and electricity demand was fast and accurate enough to effectively replace the alternative electricity storage and standby capacity.