Spectrum Analysis Of Interharmonics In Electric Power System

Nowadays electric energy is most important secondary energy. Electric power plays an important role in industry production and human lives. The stability of power system and the quality of electric power directly affect national economy. Along with the rapid development of economy, all kinds of loads are rushing into electric power system, some of which are nonlinear or impact loads. So new problems about power quality appear which threaten not only the safe operation of power system but also normal production of users. Harmonic is a common power quality event, and the utilities and users have paid much attention to it. Besides harmonic whose frequency is integer multiples of basic frequency, there is also interharmonic whose frequency is not integer multiples. Interharmonic can cause flicker and disturb reactive power compensation devices or filters besides the same hazards of harmonic, so we should also pay attention to interharmonic.The precondition of repressing interharmonic is accurately analyzing the spectrum of interharmonic. IEC has provided two methods to evaluate interharmonic, IEC flickermeter proposed in IEC 61000-4-15 and grouping method based on Fourier transform in IEC 61000-4-7 and IEC 61000-4-30. Besides the aforementioned methods AR model, neural network, SVMs(Support Vector Machines) and wavelet analysis are also applied to analyze interharmonic. However these methods have shortcomings of narrow analyzing range, long time window, easily being influenced by the noise, spectrum leakage and aliasing. So a stepwise parametric method based on spatial spectrum analysis is presented in this paper. The main contents of this paper are shown as follows.(1) Firstly, this paper introduced the basic concepts about interharmonic, including definitions, hazards and limited values. Then main interharmonic sources were shown, such as converter devices, inductive motors, arc furnaces, rolling mills and ripple control signals. In order to investigate the relationship between interharmonic and flicker, a simulation model of IEC flickermeter was built up, and numerous simulations tested the performance that IEC flickermeter evaluated interharmonic. Furthermore the mechanism that interharmonic incured R.M.S. and peak fluctuation was discussed and the influence of interharmonic to lighting devices were also shown.(2) Actual instances showed the measuring method of interharmonic in IEC had flaws on estimating interharmonic frequency, estimating the number of interharmonics, synchronized sampling, the use of rectangular window, handling time-varying interharmonic and so on. Though the modified method of IEC padded zeroes at the end of sampling data to smooth the Fourier spectrum and Hanning window and interpolation were performed to correct the interharmonic information from DFT, it still cannot solve the problems at long sampling data and close interharmonic recognition. The methods based on AR model can break through the restriction from frequency resolution, but its performance was easily influenced by the order of AR model and the noise. It's not reliable that the number of neurons and its original value was estimated from the results of interpolation DFT of interharmonic signals before a self-adapting neural network trained weight parameters. When analyzing interharmonic, SVMs need carry out a higher dimensional linear regression, and had severe spectrum leakage. The wavelet analysis obtains interharmonic frequency by sliding the filters with different pass band on time axis, but easily influenced by wavelet aliasing. In order to solve the mention above problems, we need a method which can accurately estimate the number of sinusoidal components in interharmonic parametric model at first.(3) After the mathematic model of spatial spectrum analysis was introduced, interharmonic signals can be transformed to spatial signals received by linear sensor array through Euler's formula or Hilbert transform. The number of sinusoidal components of the interharmonic parametric model was corresponding to the source number of transformed spatial signals, and the frequencies of sinusoidal components were corresponding to that of transformed spatial signals. The transformed received data also had the same statistic character with sensor array model and the transformed spatial signals were not coherent each other, so the methods of spatial spectrum analysis can be applied to evaluate the spectrum of interharmonic signals.(4) The source number estimating methods were applied to estimate the number of sinusoidal components of the interharmonic parametric model, which were information theory, Gerschgorin's Disk and Canonical Correlation method. Based on maximum likelihood estimation AIC, MDL and HQ criterions from information theory were present to estimate the source number. The unitary transform of covariance matrix made the Gerschgorin's disks of signals and that of noise separated on complex plane, and Gerschgorin's radiis of signals are obviously greater than that of noise. Canonical Correlation method estimated source number by surveying the canonical correlation coefficients of the received data matrices form two space-separated linear sensor array. Numerous simulations proved that MDL of information theory, Gerschgorin's Disk and Canonical Correlation method had well performance on estimating the number of sinusoidal components.(5) The estimated source number made it possible to accurately separate signal subspace from noise subspace. Using the orthogonality between signal subspace and noise subspace or the invariance of rotating signal subspace the frequencies of every sinusoidal component can be figured out. Root-MUSIC and TLS-ESPRIT algorithm belonging to subspace methods were used to analyze the frequency information of interharmonic signal. Root-MUSIC can directly obtain the frequencies through calculation roots of a polynomial, while MUSIC need searching the spectrum peaks. ESPRIT avoided eigenvalve decomposition of covariavance matrix after multi-stage Wiener filters were obtained to form signal subspace through forward recursive algorithm, so the calculation load significantly cut off. Based on the signal subspace the total least square method can get frequencies. Numerous simulations tested the performance of Root-MUSIC and TLS-ESPRIT.(6) Finally, after the information of amplitudes and angle phases were obtained, we proposed an integrated method to analyze interharmonic spectrum. The number of sinusoidal components and their frequencies were obtained by the spatial spectrum analysis, and SVMs or GA can calculate amplitudes and angle phases when SNR was low. The proposed method succeeded in analyzing the simulated interharmonic signal while IEC modified method failed. Sampling data from actual interharmonic sources, inductive motor and rolling mill, were applied to test the proposed method, and the results showed that it performed better than IEC modified method, SVMs and Prony algorithm.