Addressing data privacy protection in the context of power load forecasting for distribution networks, a user-level load forecasting scheme based on federated learning is proposed, specifically tailored for data privacy safeguarding in user-level load forecasting scenarios. In this approach, multiple smart meters from different households collaboratively participate in the model training process, with each meter training its own personalized model for local, tailored predictions. Furthermore, the scheme integrates an adaptive gradient clipping and noise addition algorithm into personalized federated learning, bolstering the privacy protection capabilities of the solution while minimizing the impact on forecasting accuracy. Experimental analysis demonstrates that this scheme not only safeguards the privacy of power load data but also provides precise power load forecasting for distribution networks, thereby contributing to the stable operation and optimal management of the distribution grid.