This paper presents a data-driven control for a set of synchronous generators based on the improved swing equation model by using the Koopman operator. First, the nonlinear dynamic of the generators is represented by a linear model in lifted space using extended dynamic mode decomposition (EDMD). Then, a linear predictor is built and used for the design of a model predictive control following three strategies: decentralized, non-cooperative, and cooperative. The Koopman representation of the generator is used to carry out an analysis, determining its eigenvalues. Several interconnected generators are controlled showing the performance of the interconnected system including voltage faults.