<p>Cloud-based smart grids play a critical role in enabling intelligent energy distribution by forecasting electricity load patterns. However, the reliance on centralized cloud platforms to process user load data introduces substantial privacy risks. To address this, a privacy-preserving multi-layer perceptron (MLP) was previously developed using homomorphic encryption, differential privacy, and two-party secure computation. Despite these safeguards, the MLP exhibited reduced forecasting accuracy under complex load variations. To overcome these limitations, this study proposes a residual multi-layer perceptron (ResMLP) framework tailored for secure load forecasting in smart grids. The architecture incorporates residual connections to improve convergence and stability under privacy constraints and employs dual mixing layers that capture token and channel-level interactions to extract rich temporal and contextual features. This enhances model learning while preserving the encrypted nature of user data, thus minimizing privacy leakage. The model is evaluated in a real-world smart grid setting to demonstrate its robustness, predictive accuracy, and privacy-preserving capability under strict data protection requirements.</p>