Probability density function of the instantaneous amplitude

Probability density function of the instantaneous amplitude

CHARACTERIZATION AND MODELLING EMI FROME LECTRIC DISCHARGES: A LITERATURE REVIEW

Introduction:

Communications technology for smart grid applications is an area of growing interest as mentioned in many publications(Yanetal.,2013;Gungoretal.,2011,2010;GungorandLambert, 2006; Amin and Wollenberg, 2005). Indeed, its deployment can significantly improve the efficiency, reliability and safety of the electric power grid (Gungor et al., 2010). This communications technology canbe classified in to four types: power-line communications, satellite communications, wireless communications and optical fiber communications. Of these technologies, wireless communications offers potential benefits for the implementation of smart grids, such as rapid deployment, low installation cost, and mobility. However, in industrial environments, the transmitted signal quality can be degraded due to various electromagnetic interferences. As a result, it is necessary to evaluate the communication performance in such environments.
Channel models are valuable tools for characterizing interference phenomena, performing communications analyses, and designing and optimizing communication systems in harsh and hostile environments. An accurate channel model can be provided through an experimental characterization of the interference sources that are produced mainly by electromagnetic, electrostatic or non-electric sources. For conventional wireless communication systems, interferences often come from external electromagnetic sources. The deployment of wireless sensor networks has been investigated by Gungor et al. (2010) and Gungor and Lambert (2006), along with associated opportunities and challenges. While propagation channel measurements in substations are presented, high-voltage installations can generate electromagnetic radiation in instances when the spectrum can be measured above a few GHz, as is mentioned in several publications(Portuguésetal.,2003;Mooreetal.,2006;Juddetal.,1996a;Sarathietal.,2008; Moose and O’dwyer, 1986). These electromagnetic interference (EMI) sources are highly im pulsive with short durations generally caused by electric arc discharges and partial discharges sources. Under such conditions, the conventional wireless communication systems listed in Gungor et al. (2010) and Gungor and Lambert (2006) can be interfered to such an extent as to render their performances severely degraded.

Characterization and impulsive noise models:

In the literature, models for impulsive noise are widely developed and used to extend the existing knowledge regarding the nature of impulsive noise sources and communication performance analysis. In this section, characterization methods and existing impulsive models are reviewed.

A statistical characterization of impulsive noise:

In practice, measured impulsive noise consists of impulsive events and additive background noise. The latter is produced by thermal noise from the measurement setup as well as ambient noise, which is generated by many interferences below the level of impulses as depicted in Figure1.1. Sincetheseimpulsivewaveformsarecharacterizedbytheirshortdurationandhigh amplitude, they can be detected using a simple threshold. A more sophisticated technique can be used to extract impulses from overall background noise to yield an estimation of power spectral density. This will be detailed in Chapter 2.
Impulsive interferences can be characterized in one of two ways. Using first-order statistics, statisticaldistributioncanbecalculatedusingduration,theinter-arrivaltimebetweentwoconsecutive impulses, amplitude, and energy. Assuming that impulsive noise is a non-stationary random process, short-time analysis is used in the analysis of first-order statistics. Secondorder statistics utilizes power spectral densities, and a Spectrogram, a Wigner-Ville distribution, or a scalogram can be used to estimate PSD, (Mallat, 1998; Hammond and White, 1996; Priestley, 1967).

The electromagnetic interferences in substations:

In high-voltage substations, electric arc discharges can be generated in HV equipment, either along insulation surfaces or in an air gap between a pair of electrodes. Their electromagnetic radiations are man-made noise in which the amplitude is highly impulsive. Electric arc discharges have been investigated for several years to understand the physical mechanisms involved and to assess their impacton electrical insulation. These discharge are also EMI sources for radio communications systems.
Ionization process and electrical discharge in gases:

Discharges in gases are related to a partial or complete breakdown of agas phenomenon. They occur when an applied electric field is sufficiently high. In such instances, due to a strong acceleration of free electrons, other neutral molecules and atoms become excited or ionized by collisions in which kinetic energies are exchanged. An ionization process in gases can take place by avalanche effect. Depending on the nature of the gas, the ionization process can be significant when densities of electrons are high (Kuffel et al., 2000; Loeb, 1965; Bartnikas and McMahon, 1979). Townsend (1910) found that the current through a uniform field air gap, grows exponentially when the applied voltage is sufficiently high, as shown in Figure 1.5. A pair of electrodes is separated by an air gap of a length d, and the electric field E between the electrodes is generated by anapplied voltage. AtvoltageshigherthanV2,thecurrent growth is due to ionization by electron collision in the gas (Townsend, 1910).
Various ionization phenomena can be observed during an electric discharge, such as photoionization and/or thermal ionization processes. Deionization by recombination and/or diffusion can also be observed (Kuffel et al., 2000). In addition to a high field stress, an initiatory-free electron rate can affect discharge events by a random time lag which depends on the amountofpre-ionization or irradiation of the gap (Meek and Craggs, 1953).

MEASUREMENT AND CHARACTERIZATION OF EMI FROM PD ACTIVITYIN HIGH-VOLTAGE SUBSTATIONS

Introduction:

The phenomenon of impulsive noise is generated by PD sources in high-voltage substations. A PD generates a current impulse, acoustic noise, visible and ultraviolet (UV) light and electromagnetic radiation, and accordingly its presence can be detected via several measurement methods. In this chapter, PD measurement methods that are based on the detection of electromagnetic radiations. These PD instrument detectors have the advantage to be non-invasive measurement methods for the HV equipment as well as one can assess impulsive EMI threats to wireless communication systems.
This specific radio noise is a source of interference for the radio communication systems. In the literature, electromagnetic radiations from PD activity have been measured in several substations (Pakala and Chartier, 1971; Pakala et al., 1968; Portugués et al., 2003; Portugués and Moore, 2006; Shan et al., 2011). However, the measurement setup employed does not cover the frequency range used by conventional wireless communications, and so the impulsive noise characterization is often incomplete. Inspired by related works in PD current measurements and characterization (Brunt and Kulkarni, 1990; Brunt, 1991; Levesque et al., 2010; Hudon and Bélec, 2005), we have developed a characterization process in which the impulsive electromagnetic radiations from PD activity are fully characterized by the amplitude of the power density, inter-arrival time, occurrence and spectrum.

Table des matières

INTRODUCTION
CHAPTER 1 CHARACTERIZATION AND MODELLING EMI FROM ELECTRIC DISCHARGES: A LITERATURE REVIEW
1.1 Introduction
1.2 Concept of electromagnetic interferences and classification
1.2.1 Definition of EMI sources
1.2.2 Natural noise sources
1.2.3 Man-made noise sources
1.2.4 Communication channels in presence of impulsive noise
1.3 Characterization and impulsive noise models
1.3.1 A statistical characterization of impulsive noise
1.3.2 Impulsive noise models
1.3.3 Probability models of impulsive noise
1.3.3.1 Memoryless models
1.3.3.2 Impulsive noise with memory: Burst noise
1.4 The electromagnetic interferences in substations
1.4.1 Ionization process and electrical discharge in gases
1.4.2 Partial discharges mechanism
1.4.3 Measurements and characterization of partial discharge sources
1.4.3.1 Measurement techniques
1.4.3.2 Characterization of PD impulses
1.4.4 Partial discharge modelling
1.4.4.1 Physical PD models
1.4.4.2 Statistical PD models for wireless channels
1.5 Discussion and conclusion
1.5.1 Proposed research plan
CHAPTER 2 MEASUREMENT AND CHARACTERIZATION OF EMI FROM PD ACTIVITY IN HIGH-VOLTAGE SUBSTATIONS 
2.1 Introduction
2.2 The measurement setup
2.3 An experimental characterization of the discharge sources
2.3.1 Amplitude of measured signals
2.3.2 Signal processing tools for impulsive noise measurement
2.3.2.1 The Denoising process
2.3.2.2 Short-time analysis for impulsive signals
2.3.2.3 Temporal location of an impulse
2.3.3 Characterization metrics definition
2.3.3.1 Characterization based on first-order statistics
2.3.3.2 Characterization based on second-order statistics
2.4 Measurements in substations
2.4.1 Description of the environment
2.4.2 First-order statistics
2.4.2.1 PRPD representation
2.4.2.2 Statistical distribution of PD characteristics
2.4.3 Waveforms and second-order statistics
2.4.3.1 Typical waveform and spectrogram
2.4.3.2 Power spectral density
2.5 Conclusion
CHAPTER 3 A PHYSICAL MODEL OF EMI INDUCED BY A PARTIAL DISCHARGE SOURCE 
3.1 Introduction
3.2 Partial discharge phenomenon and its mechanism
3.3 The physical model of partial discharge source
3.3.1 Electric field stress
3.3.2 Discharge process
3.3.3 Current and charge density
3.4 The electromagnetic radiation of the interference source induced by partial discharge
3.4.1 Electric dipole formulation
3.4.2 Power radiation of the interference source received at the antenna
3.4.3 Modelling impulsive waveforms and PSD
3.4.4 Brief summary of interference induced by discharge source
3.5 Experimental characterization process of the interference source
3.5.1 Definition of characterization metrics
3.5.2 Denoising process
3.5.3 Short-time analysis process
3.6 Experimental validation
3.6.1 Brief description of measurement setup
3.6.1.1 The measurement setup
3.6.1.2 PD sources from stator bar
3.6.2 Simulation setup
3.6.2.1 Calculation of the electric field along the surface
3.6.2.2 Discharge process in air cavity parameters
3.6.2.3 Stochastic property of the emitted radiations of PD sources
3.6.3 Simulation-measurement comparison
3.6.3.1 PRPD comparison
3.6.3.2 Statistical distributions comparison
3.6.3.3 PSD and waveforms of impulses
3.7 Conclusion
CHAPTER 4 ANALYSIS AND MODELLING OF WIDEBAND RFIMPULSIVE SIGNALS INDUCED BY PARTIAL DISCHARGES USING SECOND-ORDER STATISTICS
4.1 Introduction
4.1.1 Motivation and prior related work
4.1.2 Main contribution and organization
4.2 Measurement setup
4.3 Conjectures and mathematical formulation of EM waves
4.3.1 Second-order statistics
4.3.1.1 Time-frequency analysis
4.3.1.2 Autocorrelation function
4.3.1.3 Results from the measurement campaigns
4.3.2 A physical interpretation
4.4 The proposed model
4.4.1 Theory of filters and its relationship with time series models
4.4.2 Definition of the time series model
4.4.3 Tests for unit roots
4.4.4 Estimation and selection
4.5 The goodness-of-fit
4.5.1 Analysis of the residuals
4.5.1.1 Residuals of fitted ARMA(7,2)
4.5.1.2 Residuals of fitted ARMA(4,1)
4.5.2 Tests for heteroskedasticity
4.5.3 Analysis of the residuals of the improved models
4.5.4 Summary
4.6 Simulation and results
4.6.1 Simulation parameters
4.6.2 A comparison of measurement vs. simulation results
4.6.3 Analysis of simulated impulsive waveforms
4.6.4 Advantages and limitations of the proposed model
4.7 Conclusion
CHAPTER 5 A STATISTICAL ANALYSIS OF IMPULSIVE NOISE IN A POISSON FIELD OF INTERFERERS IN SUBSTATION ENVIRONMENTS 
5.1 Introduction
5.1.1 Prior and related work
5.1.1.1 EMIs in substation environments
5.1.1.2 Partial discharge diagnostics
5.1.1.3 Communication in substation environments
5.1.2 Contribution and organization
5.2 A mathematical formulation of multiple PD interference sources
5.2.1 Electromagnetic radiations of multiple PD sources
5.2.1.1 The emission of the PD impulses
5.2.1.2 Basic assumptions of spatial and temporal PD events
5.2.2 Propagation of EM waves induced by PD sources
5.2.2.1 The noise process observed by the receiver
5.2.2.2 A generic temporal impulsive waveform from PD
5.2.2.3 The attenuation factor
5.2.3 Spatial and temporal distribution of PD sources
5.3 Statistical analysis
5.3.1 Probability density function of the instantaneous amplitude
5.3.2 Amplitude probability distribution
5.3.3 Tails and moments
5.3.3.1 Moments ofα-stable distributions
5.3.3.2 Moments of shot-noise processes
5.3.4 A summary of important findings
5.4 Experimental and simulation results
5.4.1 Measurements in substations
5.4.2 A procedure for estimation
5.4.3 Measurement-simulation comparison
5.4.3.1 First-order statistics
5.4.3.2 Second-order statistics
5.5 A rapid identification of PD sources using blind source separation
5.5.1 Motivation and contribution
5.5.2 System model
5.5.3 Blind source separation via generalized eigenvalue decomposition
5.5.4 Simulation and results
5.6 Conclusion
CONCLUSION
BIBLIOGRAPHY

Télécharger le rapport complet