\r\n\tSolar radiation is the radiant energy that originated from the sun in the form of electromagnetic radiation at various wavelengths. Solar radiation is the source of renewable energy and can be captured and converted into various forms of energy (e.g. electricity and heat) using different technologies.
\r\n\tA very vast amount of solar energy reaches the atmosphere and surface of the earth and solar energy has been used for heating purposes for a very long-time and after solar cells’ invention in 1954, solar cells have also been used widely for electricity generation. Solar cells convert the sunlight into electricity by the creation of voltage and electric current through the so-called photovoltaic effect.
\r\n\tPhotovoltaic (PV) solar energy has attracted significant attention in the recent decade as a reliable source for power generation due to various merits such as the free source of energy, abundant materials resources, environmentally friendly and noise-free, longtime service life, requiring low maintenance, technological advancements, market potential, and very importantly, low cost. The growth of using photovoltaic (PV) solar energy as a promising renewable energy technology, is being increased more and more worldwide. Therefore, much further research is needed for possible future developments in the field of solar photovoltaic energy.
\r\n\tThe aim of this book is to provide detailed information about solar radiation as the source of photovoltaic (PV) solar energy for a broad range of readership including undergraduate and postgraduate students, young or experienced researchers and engineers.
\r\n\tThis should be accomplished by addressing the various technical and practical aspects of solar radiation fundamentals, modeling and the measurement for photovoltaic (PV) solar energy applications.
\r\n\tThe majority of this book should describe the basic, modern, and contemporary knowledge and technology of extraterrestrial and terrestrial solar irradiance for photovoltaic (PV) solar energy.
\r\n\tThe book covers the most recent developments, innovation and applications concerning the following topics:
\r\n\t• Fundamental of solar radiation and photovoltaic solar energy
\r\n\t• Solar radiation and photovoltaic solar energy potential
\r\n\t• Solar irradiance measurement: techniques, instrumentation and uncertainty analysis
\r\n\t• Solar radiation modeling for photovoltaic solar energy applications
\r\n\t• Solar monitoring and data quality assessment
\r\n\t• Solar resource assessment and photovoltaic system performance
\r\n\t• Solar energy and photovoltaic power forecasting
\r\n\tThese are accompanied with other useful research topics and material.
",isbn:"978-1-83968-859-1",printIsbn:"978-1-83968-858-4",pdfIsbn:"978-1-83968-860-7",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"4c3d1319d7286e81bfb15c1f4b20460a",bookSignature:"Dr. Mohammadreza Aghaei",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9862.jpg",keywords:"Solar Radiation Modeling, Solar Data Assessment, Solar Monitoring, Solar Radiation Forecasting, Solar Irradiance Measurements, Solar Instruments, Solar Spectral Distributions, Uncertainty Analysis, Solar Cell Technologies, Photovoltaics (PV), Solar Resource Assessment, Photovoltaics Power Forecasting",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 17th 2020",dateEndSecondStepPublish:"October 15th 2020",dateEndThirdStepPublish:"December 14th 2020",dateEndFourthStepPublish:"March 4th 2021",dateEndFifthStepPublish:"May 3rd 2021",remainingDaysToSecondStep:"3 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"A senior researcher in the field of photovoltaic solar energy, a postdoctoral scientist at Eindhoven University of Technology (TU/e), Chair of the WG2: reliability and durability of PV in EU COST PEARL PV.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"317230",title:"Dr.",name:"Mohammadreza",middleName:null,surname:"Aghaei",slug:"mohammadreza-aghaei",fullName:"Mohammadreza Aghaei",profilePictureURL:"https://mts.intechopen.com/storage/users/317230/images/system/317230.jpg",biography:"Mohammadreza Aghaei is a senior researcher in the field of photovoltaic solar energy, Eindhoven University of Technology (TU/e), The Netherlands. He is chair of the Working Group 2: reliability and durability of PV in European Cooperation in Science and Technology, COST Action PEARL PV.\nHe received the M.S. degree in electrical engineering from the Universiti Tenaga Nasional (UNITEN), Selangor, Malaysia, in 2013, and the Ph.D. degree in electrical engineering from the Politecnico di Milano, Milan, Italy, in 2016.\nHe was a Postdoctoral Scientist with Fraunhofer ISE and Helmholtz-Zentrum Berlin (HZB)-PVcomB, Germany, in 2017 and 2018, respectively. He is a Guest Scientist with the Department of Microsystems Engineering (IMTEK), Solar Energy Engineering, University of Freiburg since 2017. He is currently a Postdoctoral Scientist with the Design of Sustainable Energy Systems Group, Eindhoven University of Technology (TU/e), The Netherlands. He has authored numerous publications in international refereed journals, book chapters, and conference proceedings. The main his research interests include Solar Energy, Photovoltaic systems, PV monitoring, LSC PV, solar cells, machine learning, and UAVs.\nDr. Aghaei is a member of the International Energy Agency, PVPS program-Task 13 and International Solar Energy Society, and also an MC member in EU COST Action PEARL PV.",institutionString:"Eindhoven University of Technology",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Eindhoven University of Technology",institutionURL:null,country:{name:"Netherlands"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"10",title:"Earth and Planetary Sciences",slug:"earth-and-planetary-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"247865",firstName:"Jasna",lastName:"Bozic",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/247865/images/7225_n.jpg",email:"jasna.b@intechopen.com",biography:"As an Author Service Manager, my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"61252",title:"Polymer Resonant Waveguide Gratings",doi:"10.5772/intechopen.76917",slug:"polymer-resonant-waveguide-gratings",body:'Conventional optical waveguides work on the principle to guide waves in a material surrounded by other material media, the refractive index of the material should be slightly higher than that of surrounded media such that light can bounce along the waveguide by means of total internal reflections at the boundaries between different media. The indefinite guiding progress the waves from successive boundaries which must interfere constructively to generate a continuous and stable interference pattern along the waveguide. If the interference pattern in not fully constructive, the waves cancel, owing to the self-destruction. The conventional optical waveguides are primarily the most common type of thin film optical filters used widely as narrowband filters in laser cavities, optical telecommunications, and light modulators [1]. However, the realization of sub-nanometer narrowband filters with thin film technique require hundreds of optical thin-films stack with stringent tolerances over thicknesses and refractive index variations [2]. Resonant Waveguide Gratings (RWGs) are a new class of narrowband filters and are widely used in applications such as polarizers [3], laser cavity reflectors [3, 4], light modulators [5], biosensors [6], and wavelength division multiplexing [7]. Such narrowband reflectance/transmittance spectral characteristics can be observed by sub-wavelength grating structures in terms of resonance anomalies [8, 9] with numerous potential applications. RWG operates with resonance effects with relatively simpler structure of few layers. Owing to the resonant nature of the sub-wavelength grating, the leaky modes are supported by the structure (waveguide layer and a grating layer) [10]. In the absence of the grating layer, waveguide layer supports a true bound mode. This bound mode becomes leaky when a grating layer is added with the waveguide layer. Eventually, optical energy is coupled out of the waveguide into radiation modes. On the other hand, the incident plane wave energy is coupled to the waveguide. The incident plane wave energy is coupled into leaky modes and then back to one or more radiation modes. This coupling mostly depends on the wavelength, angle of incidence and other structural parameters of the grating layer. At resonance a sharp peak in reflected/transmitted light might be observed at a specific combination of these parameters.
Large scale demands for cost-effective yet reliable and efficient photonic components have led many researchers to consider polymer materials. Polymeric materials become widely useful and increasingly attractive in the fabrication of various micro and nanostructures with the potential replacement of conventional inorganic materials such as SiO2 and LiNbO3 or semiconductors. Novel polymers have been introduced for replication of nanostructure RWG through inexpensive and mass-production process [11]. The polymeric materials offer high thermal expansion coefficient (almost an order of magnitude) in comparison to traditional inorganic materials as well as thermo-optic coefficient which enable them to use as fast rate switches. Investigations to fabricate RWG in polymeric materials have been actively pursued throughout over the past two decades [12, 13].
The capability to fabricate precise novel structures at micro to nanoscale with a wide variety of materials imposes great challenges to the advancement of nanotechnology and the nanosciences. The semiconductor industry continues pushing to lower structural size and to manufacture smaller transistors and high density integrated circuits. The demanding industrial processes through newly developed lithographic methodologies need to address some critical issues such as speed, reliability, overlay accuracy, etc. Many alternative approaches have been used to manufacture nanostructures in past two decades, despite of using expensive tools such as deep-UV projection lithography and electron beam lithography techniques. These techniques include micro-contact printing, scanning probe based techniques, dip-pen lithography, and Nanoimprint Lithography (NIL) [14]. NIL can not only fabricate nanostructures in resists but can also imprint functional devices in many polymers through ease and cost-effective processes in a number of applications such as photonics, data storage, biotechnology, and electronics [15].
In this chapter we present details of design, fabrication, and characterization of polymeric RWG employing affordable techniques and mass production processes. The fabrication of master stamp by electron beam lithography and subsequent replication in polymer materials by NIL is presented to target a number of applications in thermoplastics and UV curable polymers.
The grating structure to enhance the resonance anomalies of a periodic profile (periodic modulation of refractive index) by coupling illuminating plane wave to the leaky modes of the waveguide of the grating is known as resonant waveguide gratings. Diffraction grating splits incident plane wave to propagate in different directions so-called diffraction orders. The periodic structure undergo complete interference and resonates with no transmission at a particular wavelength and incident angle [16]. As a result, light couples out of the waveguide, propagates up to smaller distances, and appears in the form of narrower reflectance peaks whose power varies from 0 to 100% over a range of structural parameters [10, 16, 17].
The propagation constant of a leaky mode is complex quantity and expressed as,
where
where
In 1994, researchers used Effective Medium Theory (EMT) to model stratified media as a thin-film stack possessing some effective index. The attempts were made to achieve symmetric spectral response with low sidebands by varying thicknesses of thin-film stacks. This approach results in to design an effective thin-film layer to be antireflective at resonant wavelength [19, 20]. Several researchers considered thin-film model for the design of symmetric filters and suggested numerical solutions based on rigorous modeling methods [21]. To design grating layer, the effective index model was suggested for thin-film method [19]. In 1956, Rytov developed a transcendental equation based on EMT to correlate effective refractive index of a stratified medium to physical parameters and wavelength of light [22]. This equation can be applied to grating problems and written as for a TE-polarized light:
where nH, nL, neff are the high, low, and effective indices of the grating, respectively, f is the fill factor, d is the grating periodicity, and λ is the wavelength of the light. In the long wavelength limit
Eq. (3) is referred as the exact effective index model whereas (Eq. (4)) as zeroth order effective index model.
The fundamental structure of a RWG is shown in Figure 1. The waveguide grating consist of a substrate material with refractive index nt, a coupled grating layer with refractive index distribution n2(x) along x-direction and a superstrate layer (generally air) with refractive index ni. When light of wavelength λ illuminates the grating at an incident angle θi, it results in generation of various propagated diffraction orders through one-dimensional grating which can be calculated by fundamental grating equation, given as:
where λ is the wavelength, θin is the incident angle of light, d is the periodicity of the grating structure, θm is the diffraction order, m = 0, ±1, ±2, ±3,… is the index of diffraction order, ni, and n2 are the indices before and after the interface. For reflection gratings n2 is replaced by ni and for transmission gratings by nt.
Schematic representation of resonant waveguide Grating’s structure with forward and backward propagated diffraction orders.
Narrow reflection or transmission peaks can be achieved by understanding the physics of the structure which depends on the excitation of leaky waveguide modes. Consider a reflection grating with periodicity smaller than the wavelength of light used to allow only zeroth-order diffraction under plane wave illumination as shown in Figure 2. The resulted reflecting fields from the gratings may be assumed to produce from two contributions, namely: a direct reflection and a scattered field reflection [22]. The inherent direct reflection from upper interface is primary reflection so-called Fresnel reflection whereas the secondary reflection from the grating structure is due to excitation and rescattering of leaky waveguide modes whose phase vary continuously to fulfill the coupling relation given below:
where d is periodicity of the grating,
Schematic view of RWG with refractive index distributions and coated high index cover layer.
Polymeric materials have become potential candidate with versatility optical device performance and functionality. In comparison to inorganic materials, polymeric materials possess many attributable characteristics. The properties of polymer materials can be changed chemically after modifying the chemical structure of the monomers, polymer backbones, addition of functional groups or chromophores. Polymer materials can be made to manipulate easily by many conventional or unconventional fabrication methods such as reactive ion etching (dry etching), wet etching, soft lithography etc. [25]. Polymer materials offer a simple, low-cost, and reliable fabrication process irrespective to fragile silica or expensive semiconductor materials. Functional polymeric materials provide interesting properties for integrating several diversified materials with different functionalities.
Optical waveguide structures can be fabricated directly by electron beam lithography which is the most effective method to fabricate micro- and nanostructures [25]. Alternatively, soft lithography technique has been extensively developed during past 20 years and improving optical waveguide manufacturing by the use of a master stamp to generate several soft molds to reproduce its replicas [25, 26]. Figure 3 shows schematic of the originally NIL process proposed by Chao almost two decades before [27, 28]. The master stamp or mold containing nanoscale surface relief features is pressed against a polymeric material on a substrate with tightly controlled temperature and pressure to create a thickness contrast in polymer material. Furthermore, a thin residual layer is made beneath the stamp protrusions as a cushioning layer to protect nanoscale structure on mold surface from a direct impact of mold on the substrate. However, this residual layer can be removed at the end of the process by an anisotropic O2 plasma etching. Figure 3b and c shows Scanning Electron Microscopy (SEM) images of a mold with pillar array of diameter 10 nm and replicated hole array in poly (methyl methacrylate) (PMMA) [28].
(a) Schematic representation of originally proposed NIL process by Chou. (b) Scanning Electron Microscopy (SEM) image of a mold possessing pillar array diameter of 10 nm. (c) Replicated structure of mold in PMMA polymer material with hole array of size 10 nm. Reproduced with permission from [27]. Copyright 1997, American Institute of Physics.
In this chapter the RWG structures are designed and modeled using most efficient method which is based on the Fourier expansion, commonly known as Fourier Modal Method (FMM) or the coupled wave method (CWM) [29]. FMM determines eigen-solution values of Maxwell’s equations in a periodic or piecewise continuous medium by expanding the electromagnetic fields and permittivity functions to Fourier series and applying the boundary conditions to show fields inside the grating by an algebraic eigenvalue problem [30]. Employing FMM to periodic-modulated region, the modulated region sections in slabs where solution of Maxwell’s equations is determined at each slab. Such solutions appear in the form of forward and backward propagated fields consisting of modal fields. These fields are pseudoperiodic in nature and expressed in the
The properties of stamping material play a significant role in replication process to achieve a well-defined replicated features. In this section, patterns are defined on a resist material which is coated on a silicon substrate and written by electron beam lithography (EBL) without reactive ion etching (RIE) of silicon. Moreover, accurate control to pattern depth is challenging and inaccuracies in depth profiles are inherent with different width structures. Furthermore, the associated EBL proximity effect increases with the pattern depths and become more pronounced when beam size becomes comparable to the pattern size. The line edge variations occurred due to incomplete suppression of resist after development process resulted in polymer molecule agglomerate formation at pattern line edges [20]. Hydrogen silsesquioxane (HSQ) is a high resolution, inorganic, negative tone EB resist material with small linewidth variations in comparison to positive EB resists such as PMMA and ZEP. To fabricate structures with high resolutions, the molecular size of resist material need to be smaller than the nanoscale features to be replicated for which HSQ resist possesses dominating properties with slight line roughness and high etch resistance in addition [32].
In this Chapter we show replication of nanoscale structures in thermoplastic thin films and UV curable polymers by using an HSQ mold. The mold is fabricated by spin coating HSQ resist layer on silicon substrate, direct e-beam writing followed by development process without reactive ion etching. The HSQ resist thickness is adjusted to obtain structure design height h. Additionally, the formed structure is heat treated to improve mechanical properties of the resist for 180 min at 300°C temperature. Such thermal treatment improves density and hardness of HSQ resist to enable it for the use of hard stamp with high imprint pattern fidelity. The heat treated mold(s) are surface treated in nitrogen environment to deposit a silane layer to act as an antiadhesive layer for imprinting. Finally, the imprinted polymeric gratings with several periodicities are coated with high index amorphous TiO2 thin films by atomic layer deposition. Spectral characteristics of the replicated structures are investigated by a variable angle spectroscopic ellipsometer. Figure 4 depicts schematic representation of complete process flow of HSQ mold fabrication and imprinting into polymeric materials (thermoplastics and UV curable) with high index TiO2 thin layer.
Schematic representation of fabrication and replication process of HSQ mold and polymeric binary grating structures with nanoscale surface-relief features. Reproduced with permission from [11]. Copyright 2012, SPIE.
Figure 5 shows SEM images of top view of HSQ resist molds (grating structures) at different magnifications on silicon substrate with period d of 325 nm. Figure 6a and b shows cross-sectional view of SEM images of HSQ binary molds with period 425 nm and Figure 6c and d with period 325 nm [33].
SEM images of top view of HSQ resist master stamp on silicon substrate with periodicity (d = 325 nm) at different magnifications: (a) 100.00 KX, (b) 150.00 KX, (c) 200.00 KX, and (d) 250.00 KX.
SEM images of cross-sectional view of HSQ resist master stamp on silicon with periodicities: (a and b) d = 425 nm and (c and d) d = 325 nm. Reproduced with permission from [33]. Copyright 2013, NUST.
Figure 7 shows imprinted sub-wavelength grating structures in thermoplastic and UV curable plastic materials by NIL tool. Figure 8 shows various thin films of amorphous TiO2 coated on polycarbonate, cyclic olefin copolymer and UV curable Ormocomp by atomic layer deposition as a waveguide layer [30]. The details of conformal growth of amorphous TiO2 thin films by atomic layer deposition is described in Refs. [34, 35].
SEM images of cross-sectional view of imprinted structures in: (a and b) polycarbonate with period d = 368 nm, (c) cyclic olefin copolymer with period d = 325 nm and (d) UV curable material Ormocomp with period d = 325 nm. Reproduced with permission from [33]. Copyright 2013, NUST.
SEM images of amorphous TiO2 coated replicated gratings: (a) polycarbonate with period d = 368 nm and TiO2 thickness t = 80 nm, (b) polycarbonate with period d = 368 nm and TiO2 thickness t = 60 nm, (c) cyclic olefin copolymer with period d = 325 nm and TiO2 thickness t = 50 nm, and (d) UV curable material Ormocomp with period d = 325 nm and TiO2 thickness t = 50 nm. Reproduced with permission from [33]. Copyright 2013, NUST.
Figure 9 shows the ellipsometric measurement setup when a linearly polarized plane wave (electric field vector is parallel called TE or perpendicular called TM to the grating lines) incident on the sample at an incident angle Φ with respect to normal of the RWG sample. The light-matter interaction results in specular reflectance/transmittance of the resonant gratings. The polarization state (TE or TM) of the illuminated light is selected by a polarizer stage which transforms the unpolarized light beam into a linearly polarized light beam. The polarization stage composed of a polarizer mounted on a continuously rotated stepper motor with high accuracy. The rotating polarizer changes the intensity of the light. The phase and amplitude of the modulated light represents the polarization state of the beam entering the analyzer/detector. In general, ellipsometer predicts the ellipticity of the polarization state of the light, optical constants (n and k) of optical materials, and the thickness of the thin film. The ellipsometric measurement uses two parameters which are connected by Eq. (7) [36].
Experimental setup of an ellipsometer to measure specular reflectance or transmittance.
Where Rp and Rs are the complex-amplitude reflectance coefficients for p- and s-polarization state of light, Ψ represents elliptical state of polarization and Δ is the relative phase of the vibrations along x- and y-directions which can vary from zero to 2π.
Figure 10 shows designed and experimentally predicted spectral response (specular reflectance) of replicated grating structures in polycarbonate (PC), cyclic olefin copolymer (COC), and UV curable polymer Ormocomp [33]. The measured specular reflectance of PC, COC, and Ormocomp show reflectance peaks at 698.6 nm, 631.4 nm, and 630.4 nm with peak reflectance efficiencies 0.71, 0.94, and 0.65, respectively as shown in Figure 10d–f. The resonance peaks occur at different spectral positions with lower diffraction efficiencies than those calculated theoretically as shown in Figure 10a–c. The spectral shifts might occur due to inaccuracies in the dimensional profile of the replicated structures including rounding of grating edges rather completely rectangular as shown in ideal profile of Figures 1 and 2. The reduction of measured peak efficiencies are most likely caused by scattering of light from surface roughness, slight irregularities in the straightness of the grating lines, porosity and volume variations in polymers that cause refractive index changes in microscopic scale.
Theoretically calculated and experimentally measured specular reflectance of replicated gratings with grating height h = 120 nm and TiO2 thickness t = 50 nm: a) polycarbonate with periodicity (d = 368 nm), b) cyclic olefin copolymer with periodicity (d = 325 nm), c) Ormocomp with periodicity (d = 325 nm); measured reflectance spectra of all three designed gratings: d) polycarbonate, e) cyclic olefin copolymer, and f) ormocomp. Reproduced with permission from [37]. Copyright 2013, Elsevier.
The observed variations may also be explained by molecular orientations of the polymer chains. The stress induction during mold filling may result in a partial orientation and configuration of polymeric chain along principal stress directions. Such molecular orientations may relax in thermal environment over a certain length of time. If however, temperature environment is kept constant, for example, for a UV curable material, the molecular orientations can be frozen up in the glassy state of the polymers. Such frozen-in-stresses in the newly molecular chain orientations may lead to generate an anisotropic behavior in the refractive index and cause peak shift.
Figure 11a and b shows specular reflectance of two designed replicated gratings in polycarbonate (with periodicities d = 425 nm and d = 368 nm), illuminated with TE-polarized light (electric field is parallel to grating lines) at three different angles of incidence (18°, 19°, and 20°) with Full Width Half Maximum (FWHM) of about 11 nm. Figure 11c and d shows measured spectral reflectance of designed gratings (with periodicities d = 425 nm and d = 368 nm) with FWHM of 13.5 nm and 11 nm, respectively. The experimentally predicted spectra is in close agreement to that of calculated, however, the wavelength shifts may be attributed due to slight variations of refractive indices of materials interacted with light. Figure 11e shows the simulated reflectance efficiency variations of two gratings with TiO2 thicknesses of 60 nm and 75 nm. Figure 10f shows experimentally measured spectral efficiencies verses calculated ones with two TiO2 thicknesses. Both experimentally measured and calculated spectra are in agreement, provided few spectral shifts occur due to reasons described above.
Theoretically calculated specular reflectance at three illuminating angles of replicated gratings: (a) with d = 425 nm, (b) with d = 368 nm. Experimentally calculated specular reflectance at three illuminating angles of replicated gratings: (c) with d = 425 nm, (d) with d = 368 nm, (e) variation in simulated spectral reflectance as a function of TiO2 thickness t and wavelength of illuminating TE light, and (f) theoretically calculated and experimentally predicted specular reflectance as a function of wavelength. Blue curves show layer thickness t = 60 nm and brown curves t = 75 nm. Reproduced with permission from [11]. Copyright 2012, American Optical Society.
For replication by thermal NIL, the temperature of the polymer materials are raised above glass transition temperature (Tg) of polymers. At such a condition (T ˃ Tg), both Young’s modulus and viscosity of polymers reduce by several orders of magnitude in comparison to their values at room temperatures. Moreover, below Tg the value of Young’s modulus of glassy polymers remains constant for many polymers, approximately 3 × 109 Pa in comparison to their respective values at room temperature. In general practice, the temperature rise for thermal NIL is 60–90°C above Tg so that polymer transform into a viscous flow to fill micro and nanocavities, however, after imprinting process polymer is cooled down below Tg to preserve imprinted pattern. In fact, Tg is onset temperature for molecular motion in polymers. There are many factors which increase energy for molecular motion, such as, intermolecular forces, interchain steric hindrance (branching or cross-linking, bulky and stiff side groups). In some processes, it is desirable to use lower temperature values, which is then compensated by corresponding increase in the process pressure and time to obtain perfect imprinting. The requirement of high temperature and pressure for NIL process may restrict the production of NIL technology. Furthermore, the mismatch of thermal expansion coefficient between the mold material and substrate may impose limitations for pattern overlay for large substrates. Alternatively, liquid precursors having low Young’s modulus and viscosity can be cured by UV light at ambient temperatures. Due to low viscosity of the fluid the imprinting process is facilitated and minimize pattern density effects.
The replication of nanophotonic components with sub-wavelength features in polymeric materials is demonstrated and described as the most promising technology to produce narrow band-pass filters which are efficient, reliable, cost-effective, environmentally stable and effective at bulk scale production. Nanoimprint lithography is an economic process which initially requires the manufacturing of a master stamp (mold) which is fabricated commonly by EBL and reactive ion etching (RIE) processes. These processes enhance cost, inaccuracies and a reduction in efficiency and device performance. This work presented the manufacturing of master stamp by EBL using a negative tone binary electron beam resist HSQ without RIE process. The sub-wavelength replicated structures’ profile height was adjusted by the thickness of resist layer on silicon substrate by spin coating process. A direct pattern writing on HSQ resist was performed by EBL followed by development for sufficient time. The RIE process step was replaced by HSQ pattern resist heat treatment to improve the mechanical and physical properties such as hardness and density of HSQ resist, respectively. The simple etchless process of mold formation brings fast prototyping of nano-optical devices with rapid processing time and high pattern fidelity, superior optical performance and wide applicability to mass production.
In NIL two important steps performed are mold release and pattern transfer. The imprinting process lead strong adhesive forces between the mold and the resist at large contact area. A perfect mold release keeps both resist shape integrity and a complete mold-resist separation as well as suitable plasma-etching resistance for pattern transfer into substrate. This means, nanoimprint resists which give rise both mold-release, etch-resist properties and allow fast and precise nanoimprinting are highly desirable.
The replicated grating structures in polymer materials further coat by thin dielectric films of TiO2 as waveguide layer to support optical modes. Theoretically simulated results agree with the experimentally measured for the RWG in a number of polymers such as polycarbonate, cyclic olefin copolymer and Ormocomp.
The author is thankful to all professors, researchers, engineers, technicians, and students who contributed to the continuous development of various different processes of the nanofabrication at the Department of Physics and Mathematics, University of Eastern Finland, Joensuu, Finland. We are greatly thankful to HoD Prof. Dr. Seppo Honkanen for providing the financial fundings to publish this Chapter from Department of Physics and Mathematics, University of Eastern Finland under Project code 931351, which is highly appreciated. We greatly appreciate the editorial support from InTech in preparing this chapter. The chapter is dedicated to my Father-in Law Mr. Ehsan Elahi (late).
Electromagnetics transients in electric power systems (EPS) are generally caused by lightning discharges and/or certain operating conditions, such as faults in equipment and transmission lines, switching of electric power system devices, voltage sags, capacitor switching, and transmission line energization and de-energization. Faulted EPS signals are associated with fast electromagnetic transients and are typically nonperiodic with high-frequency oscillations. These characteristics present a problem for traditional Fourier analysis because it assumes a periodic signal and a wide-band signal that require denser sampling and longer time periods to maintain good resolution in low frequencies. Wavelet transform (WT), on the other hand, is a powerful tool in the analysis of transient phenomena in power systems. It has the ability to extract information from the transient signals simultaneously in both time and frequency domains and has replaced the Fourier analysis in many applications. This ability to tailor the frequency resolution can greatly facilitate the detection of signal features that may be useful in characterizing the transient cause or the state of the postdisturbance electrical system.
\nOn the other hand, the waveforms associated with fast electromagnetic transients are typically nonperiodic and contain both high frequency oscillations and localized superimposed impulses on power frequency and its harmonics. These characteristics present problems for traditional Fourier analysis because the latter assumes a periodic signal that needs longer time periods to maintain good resolution in the low frequency. In this sense, WT has received great attention in power community in the last years because they are better suited for the analysis of certain types of transient waveforms than the other transform approaches.
\nMany books and papers have been written that explain WT of signals and can be read for further understanding of the basics of wavelet theory. The first recorded mention of what we now call a “wavelet” seems to be in 1909, in a thesis by A. Haar. The concept of wavelets in its present theoretical form was first proposed by J. Morlet, a Geophysicist, and the team at the Marseille Theoretical Physics Center working under A. Grossmann, a theoretical physicist, in France. They provided a way of thinking for wavelets based on physical intuition. In other words, the transform of a signal does not change the information content presented in the signal [1].
\nThus, in the first part, this chapter presents an overview of the main characteristic of wavelet transform for the transient signal analysis and the application on electric power system. The property of multiresolution in time and frequency provided by wavelets allows accurate time location of transient components while simultaneously retaining information about the fundamental frequency and its low-order harmonics. This property of the wavelet transform facilitates the detection of physically relevant features in transient signal to characterize the source of the transient or the state of the postdisturbance system.
\nInitially, we will discuss the performance, advantages, and limitations of the WT in electric power system application, where the basic wavelet theory is presented. Additionally, the main publications carried out in this field will be analyzed and classified by the next areas: power system protection, power quality disturbances, power system transient, partial discharge, load forecasting, faults detection, and power system measurement. Finally, a comprehensive analysis related to the advantages and disadvantages of the WT in relation to other tools is performed.
\nThe wavelet transform theory is based on analysis of signal using varying scales in the time domain and frequency. Formalization was carried out in the 1980s, based on the generalization of familiar concepts. The wavelet term was introduced by French geophysicist Jean Morlet. The seismic data analyzed by Morlet exhibit frequency component that changed rapidly over time, for which the Fourier Transform (FT) is not appropriate as an analysis tool. Thus, with the help of theoretical physicist Croatian Alex Grossmann, Morlet introduced a new transform which allows the location of high-frequency events with a better temporal resolution [2].
\nFaulted EPS signals are associated with fast electromagnetic transients and are typically nonperiodic and with high-frequency oscillations. This characteristic presents a problem for traditional Fourier analysis because it assumes a periodic signal and a wide-band signal that require more dense sampling and longer time periods to maintain good resolution in the low frequencies [3]. The WT is a powerful tool in the analysis of transient phenomena in power system. It has the ability to extract information from the transient signals simultaneously in both time and frequency domains and has replaced the Fourier analysis in many applications [4].
\nThe short-time Fourier transform (STFT) of the continuous signal x(t) can be seen as the Fourier Transform (FT) of the signal with windowed x(t).g(t − τ) or also as a signal decomposition x(t) into basis functions g(t − τ).e−jwt. The functions based term refers to a complete set of functions that, when combined on the sum with specific weight can be used to then construct a certain sign [5].
\nIn the FT case, the base functions are complex sinusoid e−jwt with a windows centered on the τ time. The WT is described in terms of its basic functions, called wavelet or mother wavelet, and variable frequency w is replaced by an ever-escalating variable factor a (which represents the swelling) and, generally, to variable displacement in time τ, is represented by b.
\nThe main characteristic of the WT is that it uses a variable window to scan the frequency spectrum, increasing the temporal resolution of the analysis. The wavelets are represented by:
\nIn Eq. (1), the constant \n
where \n
Thus, it is evident that WT has a zero rating property that increases the degrees of freedom, allowing the introduction of the dilation parameter of the window [8].
\nThe continuous wavelet transform (CWT) of the continuous signal x(t) is defined as:
\nwhere the scale factor a and the translation factor b are continuous variables.
\nThe WT coefficient is an expansion and a particular shift represents how well the original signal x(t) corresponds to the translated and dilated mother wavelet. Thus, the coefficient group of CWT(a,b) associated with a particular signal is the wavelet representation of the original signal x(t) in relation to the mother wavelet [9].
\nThe redundancy of information and the enormous computational effort to calculate all possible translations and scales of CWT restricts its use. An alternative to this analysis is the discretization of the scale and translation factors, leading to the DWT. There are several ways to introduce the concept of DWT, the main are the decomposition bands and the decomposition pyramid (or Multi-Resolution Analysis -MRA), developed in the late 1970s [10]. The DWT of the continuous signal x(t) is given by:
\nwhere ψm,p form bases of wavelet functions, created from a translated and dilated of the mother wavelet using the dilation m and translation p parameters, respectively.
\nThus, ψm,p is defined as:
\nThe DWT of a discrete signal x[n] is derived from CWT and defined as [9]:
\nwhere g(*) is the mother wavelets and x[n] is the discretized signal function.
\nThe mother wavelets may be dilated and translated discretely by selecting the scaling and translation parameters a = a0m and b = nb0a0m respectively (with fixed constants \n
The problems of temporal resolution and frequency found in the analysis of signals with the STFT (best resolution in time at the expense of a lower resolution in frequency and vice-versa) can be reduced through a multi-resolution analysis (MRA) provided by WT. The temporal resolutions, Δt, and frequency, Δf, indicate the precision time and frequency in the analysis of the signal. Both parameters vary in terms of time and frequency, respectively, in signal analysis using WT. In the STFT, a higher temporal resolution could be achieved at the expense of frequency resolution. Intuitively, when the analysis is done from the point of view of filters series, the temporal resolution should increase increasing the center frequency of the filters bank. Thus, tax is that Δf is proportional to f, i.e.,
\nwhere c is constant.
\nThe main difference between DWT and STFT is the time-scaling parameter. The result is geometric scaling, i.e., 1, 1/a, 1/a2, …; and translation by 0, n, 2n, and so on. This scaling gives the DWT logarithmic frequency coverage in contrast to the uniform frequency coverage of the STFT, as compared in Figure 1.
\nComparison of (a) the STFT uniform frequency coverage to (b) the logarithmic coverage of the DWT.
The CWT follows exactly these concepts and adds the simplification of the scale, where all the impulse responses of the filter bank are defined as dilated versions of a mother wavelet [10]. The CWT is a correlation between a wavelet at different scales and the signal with the scale (or the frequency) being used as a measure of similarity. The CWT is computed by changing the scale of the analysis window, shifting the window in time, multiplying by the signal, and integrating over all times. In the discrete case, filters of different cut-off frequencies are used to analyze the signal at different scales. The signal is passed through a series of high-pass filters to analyze the high frequencies, and it is passed through a series of low-pass filters to analyze the low frequencies. Thus, the DWT can be implemented by multistage filter bank named MRA [11], as illustrated on Figure 2. The Mallat algorithm consists of series of high-pass and the low-pass filters that decompose the original signal x[n] into approximation a(n) and detail d(n) coefficient, each one corresponding to a frequency bandwidth.
\nDWT filter bank framework.
The resolution of the signal, which is a measure of the amount of detail information in the signal, is changed by the filtering operations, and the scale is changed by up-sampling and down-sampling (sub-sampling) operations. Sub-sampling a signal corresponds to reducing the sampling rate or removing some of the samples of the signal. For other hand, up-sampling a signal corresponds to increasing the sampling rate of a signal by adding new samples to the signal.
\nThe procedure starts with passing this signal x[n] through a half band digital low-pass filter with impulse response h[n]. Filtering a signal corresponds to the mathematical operation of convolution of the signal with the impulse response of the filter. The convolution operation in discrete time is defined as follows [2]:
\nA half band low-pass filter removes all frequencies that are above half of the highest frequency in the signal. For example, if a signal has a maximum of 1000 Hz component, then half band low-pass filtering removes all the frequencies above 500 Hz. However, it should always be remembered that the unit of frequency for discrete time signals is radians.
\nAfter passing the signal through a half band low-pass filter, half of the samples can be eliminated according to the Nyquist’s rule. Simply discarding every other sample will subsample the signal by two, and the signal will then have half the number of points. The scale of the signal is now doubled. Note that the low-pass filtering removes the high frequency information but leaves the scale unchanged. Only the sub-sampling process changes the scale. Resolution, on the other hand, is related to the amount of information in the signal, and therefore, it is affected by the filtering operations. Half band low-pass filtering removes half of the frequencies, which can be interpreted as losing half of the information. Therefore, the resolution is halved after the filtering operation. Note, however, the sub-sampling operation after filtering does not affect the resolution, since removing half of the spectral components from the signal makes half the number of samples redundant anyway. Half of the samples can be discarded without any loss of information.
\nThis procedure can mathematically be expressed as [2]:
\nThe decomposition of the signal into different frequency bands is simply obtained by successive high-pass and low-pass filtering of the time domain signal. The original signal x[n] is first passed through a half band high-pass filter g[n] and a low-pass filter h[n]. After the filtering, half of the samples can be eliminated according to the Nyquist’s rule, since the signal now has a highest frequency of p/2 radians instead of p. The signal can therefore be sub-sampled by 2, simply by discarding every other sample. This constitutes one level of decomposition and can mathematically be expressed as follows [2]:
\nwhere yhigh[k] and ylow[k] are the outputs of the high-pass and low-pass filters, respectively, after sub-sampling by 2.
\nIn [12], an application of WT and its advantages compared to Fourier transform is presented. One of the main advantages of wavelets is that they offer a simultaneous localization in time and frequency domain. The second main advantage of wavelets is that, using fast wavelet transform, it is computationally very fast. Wavelets have the great advantage of being able to separate the fine details in a signal. Very small wavelets can be used to isolate very fine details in a signal, while very large wavelets can identify coarse details. A wavelet transform can be used to decompose a signal into component wavelets. In wavelet theory, it is often possible to obtain a good approximation of the given function f by using only a few coefficients, which is a great achievement when compared to Fourier transform. Wavelet theory is capable of revealing aspects of data that other signal analysis techniques miss like trends, breakdown points, and discontinuities in higher derivatives and self-similarity. It can often compress or de-noise a signal without appreciable degradation [12].
\nThe Fourier transform shows up in a remarkable number of areas outside classic signal processing. Even taking this into account, we think that it is safe to say that the mathematics of wavelets is much larger than that of the Fourier transform. In fact, the mathematics of wavelets encompasses the Fourier transform. The size of wavelet theory is matched by the size of the application area. Initial wavelet applications involved signal processing and filtering. However, wavelets have been applied in many other areas including nonlinear regression and compression. An offshoot of wavelet compression allows the amount of determinism in a time series to be estimated [12].
\nRefs. [1, 13, 14] conducted studies related to this chapter. These authors also present a literature review on the application of WT in power electrical systems.
\nBy means of the bibliographic review, it is possible to highlight certain topics of interest for researchers:
Power quality
Partial discharges
Transient in electrical systems
Power system protection
Load forecasting
Power system measurement
Figure 3 shows the percentage of publications in each area. The areas in which more works have been developed are the power quality and protection field. The next section presents a general description of wavelet application in the selected areas of power systems. There are more works in these areas; however, no details will be entered due to space issues and that the approach to the topic used WT is similar.
\nWavelet publication percentage in different power system areas.
Partial discharges are difficult to detect because of their short duration, high frequency, and low amplitude. However, the use of WT can not only detect them but also isolate them by frequency bands for their study, performing a multi-resolution analysis. An important study is the filtering of noise in PD signals. In this sense, [15, 16] propose the recognition and categorization of PDs, for the study of transformer failures.
\nIn [15], an adaptive filter is used to obtain PD without noise or interference for online studies. In [16], it is posed by means of a sophisticated equipment to obtain the currents and through WT to filter the PD and to be able to carry out its later study. If we follow the line of online monitoring, it can be seen in [17] that using a high-frequency transducer, the PD can be extracted to obtain analysis in transformers in service. We talked about how to get them and how to remove the noise in the signals, we just need to locate them. Ref. [18] proposes a PD injection method in preestablished nodes to obtain the plant model to measure at separate points.
\nThis section could be assembled considering different places of application of the WT, from generation to service transformers. In the generation, [19] shows us a study in the transients of the generation turbines where they perform an exhaustive analysis using a wavelet neural network to obtain the output values to adjust the turbine and obtain a correct operation.
\nWorks [20, 21, 22] propose the use of WT for applications in high voltage lines (EHV) and the power system. In [20], WT used for the study of the electric field in the conductors can obtain the waveform of the current and voltage that facilitates the study of faults with which a filter for the study of harmonics can be designed. In [21], using the entropy energy, it is possible to obtain parameters of systems that change with certain sensitivity and design a protection that can reduce the capacitive effects in the bars and in the high-frequency traps. Ref. [22] proposes to use several scales of different frequencies to decompose the harmonics for the detection, localization, and segmentation of them. With this, we can estimate the energy and overvoltage caused and discern between impulsive and oscillatory transients. Ref. [23] presents an analysis on which is the best wavelet mother for the measurement of harmonics in electrical systems. Ref. [24] proposes an empirical wavelet transform for harmonic detector under dynamism conditions of the system. Ref. [25] presents a method for detecting and classifying faults in transmission lines by combining DWT and neural networks.
\nFinally, the characteristic impedance of a transformer can be obtained through its transient response [26]. With this, we can easily make a verification of the state of the transformer using the WT coefficients.
\nIn the search for shorter downtimes and the maximization of the life time of the energy system equipment, it repeats itself to increasingly finer methods for analysis. In the recent years, we have begun to analyze the protections of voltage transformers (TT) and current transformers (CT) by WT [27]. This was done previously in the use of the Fourier Transform (FFT) and the current protections of the internal fault current. Refs. [28, 29, 30, 31] study the differentiation of these currents by theoretical methods. This means that the test in the field is not done but the results of the simulations give positive results, an exception of [31] where the methods are applied to a test TT. For the development of differential protections, [30, 32, 33, 34] analyze the transients and extract the predominant signal from the internal fault; the method has been tested with different faults and an efficient algorithm for online analysis has been obtained. In [33, 34, 35, 36, 37, 38, 39, 40, 41], WT is used for fault diagnostic and transient event identification in transformer operation.
\nThere has been a great effort in different works to evaluate the different mother wavelet. Thus, [33, 34] present a comprehensive analysis involving an important number of wavelets to prove the efficiency in power transformer protection.
\nAnother important part is between disruptive currents and fault currents in the earth, where the results were analyzed with computer programs [42, 43].
\nThe bus zone protection scheme is considered for the detection of transient current in [44]. In the electric machine area, [45] proposed the use of the WT for fault diagnostic using current signal. The transmission line fault detection with WT in the presence of wind power generation is studied in [46, 47] approach, a study on fault detection in compensated transmission line (TCSC technology). In [48], wavelet analysis is used for fault detection in hybrid energy source.
\nWith the increase of the use of electronic equipment, it has become a necessity to study the quality of energy. The loads, having a stationary or non-stationary state, are no longer easily analyzed, so we resort to mathematical tools capable of classifying and characterizing these states. In this network, transient disturbance occurring in the network can be classified as voltage drops, voltage increases, momentary interruptions, harmonics, and transients, among others.
\nThe main topics of study are the harmonics; these are present in the waves and are common to see in the electrical networks, and so the first step would be to identify them and isolate their behavior in order to eliminate these disturbances. Ref. [49, 50, 51], using WPT, perform a method in which the fundamental harmonic and higher order harmonics can be extracted, which is a method applicable to energy networks for monitoring them. For the same application [52], they have formulated using CWT, an algorithm used to identify the variations of frequency, harmonics, sub harmonics, and inter harmonics.
\nA practical application of the CWT is the real-time monitoring of voltage and current signals for the rapid detection and elimination of transient events that may worsen the quality of the electric service. Previously, the first subject of study in terms of energy quality was established, but this is only a small part of the faults found in the energy system. Faults must be identified in order to perform an efficient analysis and be able to act on them as soon as they occur.
\nIn the papers presented in [42, 53, 54, 55, 56, 57, 58, 59, 60, 61], their main theme coincides and is to classify the faults that can be obtained from the analysis of the voltage wave through WT. Broadly speaking, it can be highlighted that they obtain the range of frequency, amplitude, time of action, waveform, etc. Although their methods differ in the application of the WT, the essence of the study is the same. One step beyond performing fault classification studies is to achieve a practical application for the in-service power network. In [62], it implements a DSP for the continuous study of energy. Ref. [63] uses an FPGA for continuous analysis of system disturbances. In [42], through a wavelet neural network and a self-organizing arrangement system, it obtains automatic equipment for the detection and suppression of multiple faults in the network.
\nOther areas of power quality are studied using the WT characteristic. In [64, 65], the power quality events are characterized and classified using wavelet transformation. The power quality disturbance detection in grid-connected wind energy system is development with wavelet and S-transform. In [66] is presented a comparative analysis of power quality event using wavelet for real time implementation and [67] tested measurement system to electric energy quality together digital signal processor.
\nThe voltage variation is a usual problem in electric system which affects the quality power. Ref. [68] addresses this problem from distributed energy resources.
\nThis analysis is the key to a correct distribution of energy in the electricity grid. Basically, a prediction is made of how the loads will behave in short- or medium-term horizons. In this sense, the behavior of the load can refer to disconnections of large equipment, circuits that have transients in start, devices with low power factor, etc. This analysis can be done through WT and some complement to make the prediction.
\nWe have cases like [69] that use a linear correlation for the load forecast. This is a more conventional method compared to the other two. In recent years, there is much talk of NN and machine learning to such a point that [70, 71, 72, 73, 74, 75, 76, 77, 78, 79] use machine learning to train a WT-based neural network. The load forecasting in the short-term used WT theory is presented in [80, 81]. Thus, it can be observed that this application is widely studied.
\nFrom another point of view, we have a prediction system based on fuzzy logic in [82], and finally, in the current year, a neural network with fuzzy logic based on WT is launched for the short-term study, which may be the foot to what is coming to the future.
\nMainly, the WT is used in power systems and RMS measurements, both voltage and current. As for the measurement systems of active, reactive, or apparent power, a decomposition and classification of those waves present in the fundamental are achieved. In [83], it analyzes how the variations of the loads influence the tension, as much as it falls as in descents or in blinking. Then in [23], it approximates the RMS value of the harmonics present in the voltage and current waves by means of statistics; with this purpose, the improvement of harmonic detection and measurement systems is sought. In [84], a method for determination and correction of measurement anomaly based in WT is proposed.
\nWavelet transform is a powerful signal processing tool that transforms a time-domain waveform into time-frequency domain and estimates the signal in the time and frequency domains simultaneously. So, it is mostly used in electric power systems analysis.
\nThis chapter carries out an approach on the WT application in EPS in order to facilitate the search for information in this area. Therefore, a classification of the different fields of EPS applications was made. A summary description for each WT application area is presented with the main objective of showing the applications of this tool in the resolution of typical problems of the energy system.
\nThe works analyzed show that the Daubechies family was used in most of the applications in power systems analysis, especially in protection area. However, the type of mother wavelet and the decomposition level number may be changed and therefore may not be generalized to all the cases.
\nThe use of WT together with artificial intelligence tools (neural networks, fuzzy logic, genetic algorithms, etc.) was presented as a promising methodology to diagnose faults in electrical systems.
\nMost of the works analyzed results of computational simulations. It is expected that in the short term, the functionality of WT it is will comprobed in real situations.
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\n\nThe Social Media Community Manager and Marketing Assistant will report to the Senior Marketing Manager. They will work alongside the Marketing and Corporate Communications team, supporting the preparation of all marketing programs, assisting in the development of scientific marketing and communication deliverables, and creating content for social media outlets, as well as managing international social communities.
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\n\nTo apply, please email a copy of your CV and covering letter to hogan@intechopen.com stating your salary expectations.
\n\nNote: This full-time position will have an immediate start. In your cover letter, please indicate when you might be available for a block of two hours. As part of the interview process, all candidates that make it to the second phase will participate in a writing exercise.
\n\n*IntechOpen is an Equal Opportunities Employer consistent with its obligations under the law and does not discriminate against any employee or applicant on the basis of disability, gender, age, colour, national origin, race, religion, sexual orientation, war veteran status, or any classification protected by state, or local law.
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