**5. Conclusion**

Wavelet transform is a powerful signal processing tool used in power systems analysis. The most of applications of wavelet analysis in power systems include analysis and study of power quality, partial discharges, forecasting, measurement, protection and transients. It transforms a time-domain waveform into time-frequency domain and estimates the signal in the time and frequency domains simultaneously.

The most popular applications of WT are related to CWT, DWT and WPT techniques. CWT generates a huge amount of data in the form of wavelet coefficients with respect to change in scale and position. This leads to large computational burden. To overcome this limitation, DWT is used, as do in digital computers by applying DWT on discretized samples.

According to the done research, DWT is also extensively used to analyze the most of phenomena of power systems. However, an extensive study should be carried on applying DWT for power and RMS measurements. Because in MRA implemented by DWT filter banks, a signal is decomposed into non-uniform frequency sub-bands. However, for harmonic identification purposes, it is more useful if the signal is decomposed into uniform frequency sub-bands. This can be achieved using WPT filter banks.

Further, Although there have been a great effort in references to prove that one wavelet is more suitable than another, there have not been a comprehensive analysis involving a number of wavelets to prove the point of view suggested. Also, the method of comparison among them is not unified, such that a general conclusion is reached.

Therefore, in this chapter for each application in power systems, it was tried to introduce principles and algorithms in order to determine the optimal mother wavelet. According to the literature review, Daubechies family has been the most of applications in power systems analysis. Further, often db4 have been the satisfactory results than the other mother wavelets of Daubechies family. However, it is should be noted that the type of mother wavelet, the number of decomposition levels and etc, may be changed from one application and/or condition to another and therefore not be generalized to all the cases.
