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Smart grids leverage the data collected from smart meters to make important operational decisions. However, they are vulnerable to False Data Injection (FDI) attacks in which an attacker manipulates meter data to disrupt the grid operations. Existing works on FDI are based on a simple threat model in which a single grid operator has access to all the data, and only some meters can be compromised. Our goal is to secure smart grids against FDI under a realistic threat model. To this end, we present a threat model in which there are multiple operators, each with a partial view of the grid, and each can be fully compromised. An effective defense against FDI in this setting is to share data between the operators. However, the main challenge here is to incentivize data sharing. We address this by proposing an incentive mechanism that rewards operators for uploading data, but penalizes them if the data is missing or anomalous. We derive formal conditions under which our incentive mechanism is provably secure against operators who withhold or distort measurement data for profit. We then implement the data sharing solution on a private blockchain, introducing several optimizations that overcome the inherent performance limitations of the blockchain. Finally, we conduct an experimental evaluation that demonstrates that our implementation has practical performance.