The widespread adoption of smart meters has enabled accurate electricity demand forecasting for intelligent energy management; however, conventional centralized machine learning approaches require the transmission of sensitive household energy consumption data to cloud servers, creating significant privacy and security concerns. This study proposes a privacy-preserving federated learning framework based on a Long Short-Term Memory (LSTM) network and the Federated Averaging (FedAvg) algorithm, where multiple smart meter clients train local forecasting models independently while sharing only encrypted model parameters with a central aggregation server. Differential privacy and secure aggregation techniques are incorporated to enhance data confidentiality without exposing raw consumer data. The proposed framework is evaluated using publicly available smart meter datasets and compared with a centralized LSTM model using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), coefficient of determination (R²), communication overhead, convergence rate, and training time. Experimental results demonstrate that the proposed federated model achieves an MAE of 0.118 kWh, RMSE of 0.163 kWh, MAPE of 4.37%, and R² of 0.982, closely matching the centralized model while preserving user privacy. The incorporation of differential privacy introduces only a marginal reduction in forecasting accuracy (MAPE increased by 0.31%) while providing strong protection against information leakage. Furthermore, the framework reduces the risk of raw data exposure by 100%, converges within 42 communication rounds, and decreases communication bandwidth by approximately 38% through efficient parameter aggregation. These findings demonstrate that the proposed federated learning framework provides a secure, scalable, and high-performance solution for privacy-preserving smart meter energy forecasting, making it well suited for next-generation intelligent smart grid and edge computing applications.