# Differentially Private Clustered Federated Load Prediction Based on the Louvain Algorithm
## 1 Introduction  
The new power system is a complex intelligent network that primarily integrates new energy, along with components of information, physics, society, and big data [1, 2]. The continuous introduction of technologies, such as demand response, electricity retailers, load aggregators, digital twins, and virtual power plants, has led to increasingly complex and variable load characteristics [3]. Load forecasting is foundational in this new power system, essential for the planning, operation, and scheduling of future smart grids. Limited local data hinder effective load forecasting, making collaborative modeling essential. Recently, many load-forecasting schemes based on machine learning have been proposed. Reference [4] presented a short-term load-forecasting model based on linear regression. Reference [5] combined decision trees with convolutional neural networks to predict user power consumption, and the results showed that the prediction error was significantly reduced. In [6], a series of multiobjective predictive models were created utilizing a range of cutting-edge machine learning (ML) methodologies. For renewable energy, using wind power, a deep learning-driven self-conscious distributed cyber-physical system was proposed in [7]. However, retail providers often refuse to share data due to privacy concerns. Federated learning (FL) [8, 9] offers a distributed machine learning framework that keeps data local, presenting a novel approach to load forecasting whileensuring privacy [10; 11]. Reference [12] compared FedAvg, single-meter prediction, multi-meter centralized prediction, and federated stochastic gradient descent (FedSGD) methods and verified the superiority of FedAvg in load-prediction performance. Studies [13] have indicated that FedAvg can achieve smaller household load-prediction errors while protecting user privacy. In FL, users train load data locally and only upload the trained model parameters to the server. Despite maintaining local data, curious servers or attackers may still infer private information from a shared model or gradient parameters [14], highlighting the need for stronger privacy mechanisms. Differential privacy (DP) [15] is a widely used privacy protection technique. [PERSON]. [16] proposed a differentially private stochastic gradient descent algorithm to train neural networks within a moderate privacy budget, while [PERSON]. [17] introduced a differentially private federated learning algorithm and analyzed its performance. Implementing DP requires gradient clipping, but the fixed-threshold clipping method has significant limitations [18; 19]. If the clipping threshold is too small, clipped gradients may become overly distorted, losing valuable information from local updates. Conversely, a threshold set too large can introduce excessive random noise, negatively affecting the algorithm's performance. Therefore, both excessively high and excessively low clipping thresholds can reduce model accuracy and practicality. In addition to data privacy issues, other network security issues, such as data poisoning and evasion attacks, are also receiving increasing attention (see [20; 21] for detailed discussions). Moreover, data distribution inconsistency among clients, known as non-IID (Non-Independently and Identically Distributed) data, can introduce significant bias during model training, resulting in client drift and slower convergence [22]. This inconsistency poses challenges for achieving optimal model performance with a single global model. To tackle this issue, [PERSON]. [23] introduced the clustered federated learning (CFL) framework, which uses clustering algorithms to group clients with similar data distributions, allowing for the training of clustered personalized models to improve performance and specialization. [PERSON]. [24] proposed an adaptive clustering federated learning algorithm that accelerates similarity assessment.