The proliferation of massive non-linear loads, large motor loadings, renewable energy generation systems etc. creates many problems to the electrical power systems, such as harmonics, oscillations, which lead to the unnecessary economic cost. It is critical to implement satisfying continuous monitoring of the power quality (PQ) over the power systems. Previous works have proposed many PQ detection methodologies with promising accuracy and performance, but as more and more renewable energy is integrated into the power systems, a new challenge of frequency deviation has been raised. The accuracy of the conventional methodologies will be degraded under the frequency deviated environment, then the authors proposed in this study an instantaneous PQ indices (PQIs) detection methodology based on adaptive data resampling technique to improve the accuracy of PQIs detection within a frequency deviated environment. Finally, they validated the effectiveness of the proposal, which obtains better accuracy and performance under a frequency deviated environment with less readjustment, through simulation and measurement. Furthermore, the proposed methodology satisfies the definitions and recommendations of the IEEE Std 1459 and IEEE Std 519.