The digitalization of production in smart grids entails challenges related to data collection, coordination, privacy protection, and anomaly detection. Machine learning techniques offer effective tools for processing Big Data, but identifying critical system states amidst vast amounts of data remains a challenge. To expedite data analysis, preprocessing through machine learning algorithms becomes essential. This paper introduces the advanced FedSVD algorithm, utilizing Singular Value Decomposition (SVD), which efficiently decomposes large datasets, establishes relationships, and identifies irrelevant data. The algorithm operates in federated machine learning systems, enabling local data processing on private devices while sharing only results with the global learning model. This approach enhances information processing confidentiality and facilitates the exchange of anomaly detection outcomes among network devices. The results of the study demonstrate that the modified FedSVD processing is 5 ms faster on average in comparison to the non-modified one. The proposed FedSVD algorithm calculates anomaly detection with higher accuracy by an average of 1–3% compared to the non-modified FedSVD and SVD ones. The advanced FedSVD algorithm proves to be a decentralized, confidential, and efficient solution for anomaly detection in smart grid systems.