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The digitalization level of the new power system driven by "dual carbon" is increasing, leading to a growth in the amount of data that need to be acquired. This has intensified the contradiction between data volume and acquisition capacity. Therefore, it is urgent to study compressed data acquisition methods for power systems based on data compression. In this regard, a novel compressed data acquisition method based on chaotic compressive measurement with the compressed sensing principle is proposed. Firstly, the advantages of applying compressed sensing are analyzed for data acquisition in power systems, and the key issues that need to be addressed are identified. Subsequently, a chaotic map is sampled based on the basic requirements of the measurement matrix in compressed sensing, and the chaotic compressive measurement matrix is constructed and optimized based on the sampling results. Next, the sparse data difference of the power system is used as the compression target for the optimized chaotic measurement matrix, and an acquisition process is designed to recover the complete power data from a small amount of compressed data. Finally, the proposed method is validated in a case study, and the results demonstrate that the method is correct and effective. [ABSTRACT FROM AUTHOR]