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Traditional definitions of power quantities presented in the IEEE Standard 1459-2000 are compatible only with stationary waveforms, however for non-stationary waveforms, the wavelet-based approach has been shown to be more suitable. This paper develops a new wavelet packet transform (WPT) based approach for measuring the recommended power quantities in the IEEE Standard. The reformulated quantities are then used to evaluate the performance of a wind farm connected to a utility distribution system when subject to voltage sag due to a single-line to ground fault that occurs on a remote bus. The discrete wavelet transform-based approach along with the new wavelet packet transform based approach using Daubechies mother wavelet with order 20 and 43 are used here in order to determine the most appropriate approach and mother wavelet. The results indicate that WPT with db20 can provide the most accurate values for these power quantities that are needed in order to set protection devices, figuring out the correct amount of active power delivered and the reactive power needed to maintain the bus voltage at the specified level.