Section 6 - Chapter 7 - Chapter 21Empirical Mode Decomposition - Enhancements to the Hilbert-Huang Method for Power System Applications721.1 Introduction217.2 Estimating Non-stationary Distortions721.3 Modified Hilbert Huang Technique721.45 Algorithm for appropriate masking signal to separate higher frequencies21.57.6 Amplitude demodulation of IMF21.67.7 Demonstration21.77.8 Frequency Heterodyne21.87. 9 Stationary signals21.97.10 Non-stationary signals21.107.11 Conclusions21.117.12 ReferencesS ection 6 - Chapter 7 - Chapter 21Empirical Mode Decomposition - Enhancements to the Hilbert-Huang Method for Power System ApplicationsN. Senroy, S. Suryanarayanan and P. F. Ribeiro721.1 IntroductionWith the pervading application of power electronics and other non-linear time-varyingloads and equipment in modern power systems, distortions in line voltage and current arebecoming an increasingly complex issue. In tightly coupled power systems such as theintegrated power system (IPS) onboard all-electric ships and islanded micro-grids, theestimation and visualization of time-varying waveform distortions present an interestingresearch avenue [1]. Accurately estimating time-varying distorted voltage and current signalswill help in determining innovative power quality indices and thresholds, equipment deratinglevels and adequate mitigation methods including harmonic filter design. In this context, it is nolonger appropriate to use “harmonics” to describe the higher modes of oscillations present innon-stationary and nonlinear waveform distortions. Harmonics imply stationarity and linearityamong the modes of oscillations while the focus of this chapter, is on time-varying waveformdistortions. Key issues specific to the problem of estimating time-varying modes in distorted linevoltages and currents are: (a) distortion magnitudes are small, and typically range from 1-10%(voltage) and 10-30% (current) of the fundamental, (b) the fundamental frequency may not beconstant during the observation, due to load fluctuations and system transients, (c) typicaldistortion frequencies of interest in electric power quality studies may lie within an octave –posing a challenge of separation.Estimating the modes existing in a complex distorted signal may be reposed as aninstantaneous amplitude and frequency tracking problem. What is the degree to which thetime-frequency-magnitude resolution of the participant modes, in a distorted voltage/currentsignal, may be realized? Research has already indicated the role of the uncertainty principle inlimiting the performance of time-frequency distributions [2]. This chapter approaches theproblem as follows:1. Adaptively decompose the distorted signal into mono-component forms existing atdifferent time-scales,2. Estimate instantaneous frequencies and amplitudes of each of the separatedcomponents,3. Localize the temporal variations in these amplitudes and frequencies accurately onthe time scale.The Hilbert-Huang (HH) method, including the empirical mode decomposition (EMD),has been developed as an innovative time-frequency-magnitude resolution tool for non-stationary signals [3]. EMD is an adaptive and data driven multi-resolution technique, in which amulti-component waveform is resolved into several components. These components, referredto as intrinsic mode functions (IMF), are expected to be mono-component in nature. Applicationof Hilbert transform yields their analytic forms, from which their instantaneous amplitudes andfrequencies can be extracted. However, the original EMD technique fails to separateparticipating modes whose instantaneous frequencies simultaneously lie within an octave. The use of a masking signal based EMD was initially proposed to improve the filteringcharacteristics of the EMD [4]. In this chapter, a hybrid algorithm is presented for buildingappropriate masking signals for applying EMD to distorted signals [5]. The improved algorithmemploys fast Fourier transform (FFT) to develop masking signals to apply in conjunction with theEMD. Once a masking signal is constructed, the EMD application follows the method of [4].Since the masking signal based EMD may not always guarantee mono-component IMFs, furtherdemodulation is recommended, after applying the Hilbert transform. Another alternative to themasking signal based EMD is frequency shifting, suggested in conjunction with EMD to enhanceits discriminating capability [6]. The proposed enhancements focus on signals, typically found inpower quality applications, with the following characteristics:1. Time-varying modes whose instantaneous frequencies may lie in the same octavesimultaneously,2. Weak higher frequency signals not ‘recognizable’ by conventional EMD.The rest of the chapter is divided into sections as follows. Section II discusses differentapproaches to the problem of estimating time-varying waveform distortions. Section IIIintroduces the original Hilbert-Huang method, along with its limitations. The masking signalbased EMD is presented in detail in this section, along with the demodulation techniquessuggested for narrowband IMFs. Section IV employs a synthetic signal representative of signalsin power systems, to demonstrate the masking signal based EMD. The frequency shiftingtechnique used in conjunction with EMD is presented in Section V. Section VI is the concludingsection.217.2 Estimating Non-stationary DistortionsThe fast Fourier transform (FFT) technique is adopted as a signal processing tool, whenlinearity and stationarity are satisfied by the participating modes in a distorted waveform [7].FFT serves as a computationally efficient and accurate technique to decompose such a distortedwaveform into sinusoidal components. In the event of nonlinear modal interaction, the FFTspectrum may be spread over a wider range that may lack physical significance. When thedistortions are non-stationary, FFT may be computed over a sliding window [8]. The fixedwindow width restricts the time-frequency resolution of this method. The sliding window basedESPRIT method, i.e. estimation of signal parameters via rotational invariance techniques, canseparate closely spaced harmonics/inter-harmonics [9]. However, for