The smart grid is a critical infrastructure that must function reliably in a geographically decentralized structure. However, this structure renders the smart grid vulnerable to stealthy cyberattacks, and data silos further limit the sharing of datasets needed to train an effective attack detection model. Moreover, most existing methods rely on the availability of enormous amounts of labeled data, which is scarce due to the need for domain knowledge. To address these issues, we propose FedCLD, a federated contrastive learning approach for detecting stealthy attacks using unlabeled data. FedCLD leverages Bootstrap Your Own Latent (BYOL), a contrastive learning model, to enhance its ability to learn robust representations from unlabeled data. With the federated learning paradigm, FedCLD enables local centers in different areas to collaboratively train local models without sharing raw datasets. Although the global representation is enhanced, the regional characteristics should be preserved. Therefore, a strategic local update scheme based on the exponential moving average (EMA) is proposed. Furthermore, we theoretically prove the convergence of FedCLD with this modified update strategy. Experiments are conducted in the industry-level PowerWorld simulator to evaluate the performance of FedCLD.