A novel smart metering technique capable of anomaly detection is proposed for real-time home power management system. Smart meter (SM) data generated in real-time is collected from 900 households of single apartments. To find outliers and missing values of SM data, a deep learning model, the autoencoder consisting of a graph convolutional network (GCN) and bidirectional long short-term memory (LSTM) network, is applied to the smart metering technique. Power management based on the smart metering technique is performed by multi-objective optimization in the presence of battery storage system and electric vehicle. Results of the power management employing the proposed smart metering technique exhibit the reduction of electricity cost and amount of power supplied by the grid, as compared to the results of power management without anomaly detection.