Abstract: Distributed photovoltaic (PV) stations exhibit decentralized data storage and significant non-independent and identically distributed (Non-IID) characteristics, causing conventional global federated learning methods to suffer from gradient conflicts during cross-site training. Meanwhile, newly joined stations face severe cold-start problems due to scarce historical data. To address these challenges, this paper proposes an Adaptive Granular-Ball Federated Learning (GB-FL) method that organically integrates Granular Computing (GrC) theory with a personalized federated learning framework, enabling adaptive grouping of heterogeneous sites and intra-granular collaborative modeling. First, a 45-dimensional site behavior characterization vector is constructed based on the statistical features of PV power curves to capture differences in power generation patterns across sites. Specifically, this includes 5-dimensional basic statistical features (daily average energy, peak power, peak time index, sunrise index, and sunset indices), 4-dimensional dynamic characteristics (ramp-up rate, ramp-down rate, intraday fluctuation intensity, and clipping ratio), as well as 24-dimensional daily average curve profile and 12-dimensional intraday fluctuation profile features. All features are processed via z-score standardization for subsequent granular-ball partitioning. On this basis, a three-stage adaptive granular-ball construction algorithm comprising "heterogeneity-driven splitting–proximity-based merging–micro-ball fusion" is designed. Specifically, during the heterogeneity-driven splitting stage, intra-granular average Euclidean distance is employed to measure heterogeneity, and a weighted scoring mechanism combined with a "worst-first" greedy strategy is introduced for recursive bisection. In the proximity-based merging stage, a dynamic threshold is defined by the median of inter-granular center distances to merge over-fragmented granular balls. In the micro-ball fusion stage, residual single-site granular balls are incorporated into neighboring granular balls satisfying heterogeneity constraints. The synergy of these three stages achieves adaptive partitioning without pre-specified cluster numbers, dividing 32 sites into 5 granular-ball structures with intra-granular homogeneity and inter-granular mutual exclusivity. Building upon the granular-ball partitioning results, each granular ball independently executes personalized federated learning. The model adopts a two-layer gated recurrent unit (GRU) with a hidden dimension of 64 as a shared temporal encoder to extract common dynamic patterns, while retaining a personalized linear prediction head for each site to fit local characteristics. Local training employs the smooth Huber loss function, and the server performs weighted aggregation of shared encoder parameters based on sample sizes. Model parameters across different granular balls remain mutually isolated, thereby effectively alleviating gradient conflicts induced by heterogeneous data. To address the cold-start problem for new stations, a prior initialization strategy based on the nearest granular ball is further proposed. Specifically, a new station is first assigned to the most similar granular ball according to its behavioral characterization, inherits the shared encoder parameters of that granular ball, and achieves rapid adaptation through few-shot fine-tuning. Experiments are conducted on data from 32 actual PV stations in Shandong Province (each containing 35,040 15-min sampling points) and the La Trobe UNISOLAR public dataset (32 stations, approximately 76,000 fifteen-minute sampling points). Data are partitioned into training, validation, and test sets in a 40%/20%/40% ratio, and experiments are repeated with 5 fixed random seeds to ensure result stability. The results demonstrate that, on the Shandong dataset, GB-FL achieves a 3.8% reduction in root mean square error (RMSE) compared with Personalized Federated Learning (PFL) (15.896 kW vs. 16.517 kW) and a 7.4% reduction in mean absolute error (MAE); a 6.0% reduction in RMSE compared with FedProx; and 2.2% and 4.6% reductions in RMSE and MAE, respectively, compared with ClusterFL. In the cold-start scenario, compared with local independent training (Local), RMSE is reduced by 7.2% (8.791 kW vs. 9.475 kW) and MAE by 11.7%. On the UNISOLAR dataset, GB-FL outperforms FeDaL in both MAE (2.161 kW) and the coefficient of determination (R2) (0.796), while its MAE standard deviation (0.049) is significantly lower than that of FeDaL (0.100), validating the method's cross-dataset generalization capability and robustness. Ablation experiments further indicate that removing the granular-ball grouping mechanism leads to a 3.91% increase in RMSE, demonstrating that the adaptive granularization strategy is the key factor underlying the performance improvement.

摘要： 分布式光伏站点数据呈现分散存储与显著非独立同分布（Non-IID）特性，导致传统全局联邦学习方法在跨站点训练过程中易产生梯度冲突；同时，新接入站点由于历史数据匮乏，面临明显的冷启动问题。针对上述挑战，本文提出一种自适应粒球联邦学习方法（Granular-Ball Federated Learning, GB-FL），将粒计算理论与个性化联邦学习框架有机融合，实现异构站点的自适应分组与粒内协同建模。首先，基于光伏功率曲线的统计特征构建45维站点行为表征向量，以刻画不同站点的发电模式差异。具体包括：5维基本统计特征（日均能量、峰值功率、峰值时刻索引、日出索引、日落索引），4维动态特性（爬坡上升率、爬坡下降率、日内波动强度、削顶比率），以及24维日均曲线轮廓与12维日内波动轮廓特征。所有特征经z-score标准化处理后用于后续粒球划分。在此基础上，设计“异质分裂—邻近合并—微粒球融合”三阶段自适应粒球构建算法。具体而言：在异质分裂阶段，以粒内平均欧氏距离度量异质性，引入加权评分机制与“最差优先”贪心策略进行递归二分；在邻近合并阶段，以粒球中心距离的中位数定义动态阈值，对过度碎片化的粒球进行合并；在微粒球融合阶段，将残余单站点粒球并入满足异质性约束的邻近粒球。三阶段协同作用实现无需预设簇数的自适应划分，将32个站点划分为5个粒内同质、粒间互斥的粒球结构。在粒球划分结果基础上，各粒球内部独立执行个性化联邦学习。模型采用两层门控循环单元（GRU，隐藏维度为64）作为共享时序编码器以提取共性动态模式，同时为每个站点保留个性化线性预测头以拟合局部特性。本地训练采用平滑Huber损失函数，服务器端基于样本量对共享编码器参数进行加权聚合，不同粒球间模型参数相互隔离，从而有效缓解异构数据引发的梯度冲突问题。针对新站点冷启动问题，进一步提出基于最近粒球的先验初始化策略。具体地，新站点首先根据行为表征归属至最相似粒球，并继承该粒球的共享编码器参数，通过少样本微调实现快速适配。实验在山东省32个实际光伏站点数据（各含35,040个15分钟采样点）以及La Trobe UNISOLAR公开数据集（32个站点，约76,000个15分钟采样点）上开展。数据按40%/20%/40%划分为训练集、验证集与测试集，并采用5个固定随机种子重复实验以保证结果稳定性。结果表明：在山东数据集上，GB-FL相较于个性化联邦学习方法（PFL）均方根误差（RMSE）降低3.8%（15.896 kW vs 16.517 kW），平均绝对误差（MAE）降低7.4%；相较于FedProx，RMSE降低6.0%；相较于ClusterFL，RMSE与MAE分别降低2.2%与4.6%。在冷启动场景下，相较于本地独立训练（Local），RMSE降低7.2%（8.791 kW vs 9.475 kW），MAE降低11.7%。在UNISOLAR数据集上，GB-FL在MAE（2.161 kW）与决定系数（R²）（0.796）指标上均优于FeDaL，同时其MAE标准差（0.049）显著低于FeDaL（0.100），验证了方法的跨数据集泛化能力与鲁棒性。消融实验进一步表明，当移除粒球分组机制后，模型RMSE上升3.91%，说明自适应粒化策略是性能提升的关键因素。