The current COVID-19 pandemic and the preventive measures taken to contain the spread of the disease have drastically changed the patterns of our behavior. The pandemic and movement restrictions have significant influences on the behavior of the environment and energy profiles. In 2020, the reliability of the power system became critical under lockdown conditions and the chaining in the electrical consumption behavior. The COVID-19 pandemic will have a long-term effect on the patterns of our behavior. Unlike previous studies that covered only the start of the pandemic period, this paper aimed to examine and analyze electrical demand data over a longer period of time with five years of collected data up until November 2020. In this paper, the demand analysis based on the time series decomposition process is developed through the elimination of the impact of times series correlation, trends, and seasonality on the analysis. This aims to present and only show the pandemic’s impacts on the grid demand. The long-term analysis indicates stress on the grid (half-hourly and daily peaks, baseline demand and demand forecast error) and the effect of the COVID-19 pandemic on the power grid is not a simple reduction in electricity demand. In order to minimize the impact of the pandemic on the performance of the forecasting model, a rolling stochastic Auto Regressive Integrated Moving Average with Exogenous (ARIMAX) model is developed in this paper. The proposed forecast model aims to improve the forecast performance by capturing the non-smooth demand nature through creating a number of future demand scenarios based on a probabilistic model. The proposed forecast model outperformed the benchmark forecast model ARIMAX and Artificial Neural Network (ANN) and reduced the forecast error by up to 23.7%.