Investigation on Optimizing Cost Function to Penalize Underestimation of Load Demand through Deep Learning Modeling

Quadratic cost function such as Mean Squared Error (MSE) has been a widely used objective function for training deep neural networks to develop energy forecasting models in Smart Grids. In this work, Penalizing Underestimation Logarithmic Squared Error (PULSE), a novel objective function is proposed with the aim of reducing the tendency of deep learning models to underestimate the target variable. Stacked Long Short-Term Memory (LSTM) networks are adopted on the time series load demand data to investigate the performance of the proposed cost function against the widely used MSE cost function. The evaluation is performed using open-source real-world electricity load diagrams dataset covering a period of three years. The performance of the proposed scheme is examined with deep learning models through several experiments. The results demonstrate that the proposed scheme is able to eliminate the tendency to underestimate and provides competitively accurate load demand forecasting results. The results are additionally compared against the state-of-the-art machine learning models developed in the literature. The proposed cost function maintains the RMSE around 4*10-2 kWh which is also the RMSE for deep learning models with MSE cost function and delivers 25% improvement in MAPE while also eliminating the underestimation of load demand.