A highly efficient deep learning method for short-term power load forecasting has been developed recently. It is a challenge to improve forecasting accuracy, as power consumption data at the individual household level is erratic for variable weather conditions and random human behaviour. In this paper, a robust short-term power load forecasting method is developed based on a Bidirectional long short-term memory (Bi-LSTM) and long short-term memory (LSTM) neural network with stationary wavelet transform (SWT). The actual power load data is classified according to seasonal power usage behaviour. For each load classification, short-term power load forecasting is performed using the developed method. A set of lagged power load data vectors is generated from the historical power load data, and SWT decomposes the vectors into sub-components. A Bi-LSTM neural network layer extracts features from the sub-components, and an LSTM layer is used to forecast the power load from each extracted feature. A dropout layer with fixed probability is added after the Bi-LSTM and LSTM layers to bolster the forecasting accuracy. In order to evaluate the accuracy of the proposed model, it is compared against other developed short-term load forecasting models which are subjected to two seasonal load classifications.