Complex compactly-supported orthonormal wavelets: constructions and applications in power system

Summary form only given. The essence of the wavelet transform (WT) is to measure the local similarity between two waveforms: a signal and a wavelet. The waveform of a signal or a wavelet depends not only on its magnitude spectrum (MSP) but also on its phase spectrum (PSP). How well the PSP of a wavelet matches the PSP of a signal greatly influences the WT efficiency. On the other hand, phase information which can be extracted by a complex WT is important in power systems. The ability to extract phase information is crucial for a wavelet to be used in power systems. Compactly-supported (in time-domain) orthonormal wavelets (CSOWs) have an excellent property in that their analysis and synthesis filters are the same, and are finite impulse response type. WTs and inverse WTs with CSOWs can be implemented easily and quickly. However, all the existing CSOWs are real ones. It is impossible to extract phase information of a signal under analysis by them. Another drawback of CSOWs is their poor PSPs. This makes them behave not very well when the signals have a variety of PSPs. This paper describes how to construct a large number of complex CSOWs with various PSPs from existing real CSOWs, and how to take combined information (CI) from a complex WT instead of the more usually used simple information (SI), in order to highlight slight distinctions between similar signals in more detail. A number of simulated applications in power systems demonstrate that the derived complex wavelets are more superior to the original ones and so is CI to SI.