Summary form only given. The essence of the wavelet transform (WT)nis to measure the local similarity between two waveforms: a signal and anwavelet. The waveform of a signal or a wavelet depends not only on itsnmagnitude spectrum (MSP) but also on its phase spectrum (PSP). How wellnthe PSP of a wavelet matches the PSP of a signal greatly influences thenWT efficiency. On the other hand, phase information which can benextracted by a complex WT is important in power systems. The ability tonextract phase information is crucial for a wavelet to be used in powernsystems. Compactly-supported (in time-domain) orthonormal waveletsn(CSOWs) have an excellent property in that their analysis and synthesisnfilters are the same, and are finite impulse response type. WTs andninverse WTs with CSOWs can be implemented easily and quickly. However,nall the existing CSOWs are real ones. It is impossible to extract phaseninformation of a signal under analysis by them. Another drawback ofnCSOWs is their poor PSPs. This makes them behave not very well when thensignals have a variety of PSPs. This paper describes how to construct anlarge number of complex CSOWs with various PSPs from existing realnCSOWs, and how to take combined information (CI) from a complex WTninstead of the more usually used simple information (SI), in order tonhighlight slight distinctions between similar signals in more detail. Annumber of simulated applications in power systems demonstrate that thenderived complex wavelets are more superior to the original ones and sonis CI to SI
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