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Frequency scanning is a powerful and versatile approach for subsynchronous resonance (SSR) screening in power grids. Among different numerical and analytical frequency scanning techniques, the harmonic injection method is well suited for the scan of black-box models with active elements, such as in wind farms and solar plants. The results can be used for SSR risk assessment, in which accuracy performs a decisive role. The ideal situation for this method, which leads to the most accurate results, is to perform one simulation per single-frequency injection. However, for SSR studies with a wide range of frequencies and simulations with very small time steps (scale of μs), this comes at the expense of increased simulation time. This article proposes a technique to improve the accuracy of the harmonic injection method through the optimization of the crest factor while injecting all frequencies at one shot, therefore also reducing simulation time. The proposed technique was tested on a wind farm connected to a radial test case and on a portion of a Texas synthetic grid with multiple active elements, including two wind farms and a VSC-based STATCOM. The frequency scan results were benchmarked with both time-domain transient simulations and the ideal multiple single-frequency injection case and compared with other techniques. The results show that the proposed method is superior in accuracy when compared to the other techniques and is 11.71 times faster when compared to multiple single-frequency injections. [ABSTRACT FROM AUTHOR]