Advanced methods for the assessment of time varying waveform distortions caused by wind turbine systems. Part I: Teoretical aspects

The sensitivity to Power Quality (PQ) disturbances is today increasing in micro grids due to the great economic consequences that PQ disturbances can generate. However, micro grids include several distributed energy resources (DER) interconnected to the grid with static converters that can deteriorate the Power Quality levels. Among DER, wind turbine systems (WTSs) are expected to be widely employed due to the forecasted investment cost reduction and economic incentives. WTSs can cause significant time varying voltage and current waveform distortions whose entity depends on the WTS scheme. In case of time varying distortion, standards suggest the use of a windowed Discrete Fourier Transform (DFT) that, however, can suffer of well know spectral leakage problems. Thus, advanced spectral analysis methods should be considered. In this paper, the time varying waveforms distortions caused by different WTSs schemes are analyzed and critically compared applying DFT, some parametric methods (Prony and ESPRIT) and some hybrid methods (ESPRIT-DFT and Prony-DFT) that conjointly use DFT and parametric methods. This paper, which reports the theoretical aspects of the WTS schemes and of the spectral analysis methods, is a companion paper to a paper of the same title, Part II, in which numerical experiments are performed using test waveforms and measured non-stationary voltage and current waveforms of different WTS schemes.