New hybrid approaches in harmonic estimation

Estimation of signal parameters has an important place in many fields and applications. The estimation of harmonics and inter-harmonics occurring in power systems is also of great importance in terms of monitoring and improving power quality. However, although traditional methods such as the Fourier transform are successful in harmonic estimation because they can reveal integer multiples of the fundamental frequency of the signal, they are insufficient in inter-harmonic estimation. Due to this shortcoming, alternative methods have been developed for the detection of inter-harmonics and methods created in other fields have been adapted. In this thesis, new methods are introduced for the implementation of Prony algorithm which belongs to parametric methods and MUSIC algorithm which is one of the subspace analysis methods with discrete Haar transform. The proposed method, which is a hybrid method derived from the Prony and discrete Haar transform, reduces the number of elements of the matrices used in the application of the Prony method, as well as lowering the degree of the polynomial used to find the frequencies. The low number of matrix elements guarantees fast convergence, while the low degree of the polynomial ensures that the roots of the relevant polynomial are less affected by noise. By using discrete Haar coefficients, the Prony method is able to detect the amplitude, phase and frequency information of the signal with a low relative error rate. On the other hand, using the results of the first proposed method, it shows that the MUSIC algorithm can also be implemented with discrete Haar transform coefficients. In addition, reducing the number of elements of the frequency vector, which examines the correlation of frequency and noise, also showed a rapid convergence in this algorithm. By using the discrete Haar coefficients, the Prony method was able to detect the amplitude, phase and frequency information of the signal with a low relative error rate. Similarly, the MUSIC algorithm was able to obtain signal frequencies with a lower error rate. It is observed that the derived methods for the estimation of the signal parameters give successful results with both the approximation and difference coefficients of the discrete Haar transform.