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Partial shading detection and hotspot prediction in photovoltaic systems based on numerical differentiation and integration of the P - V curves

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IET RENEWABLE POWER GENERATION 2023年第2期17卷 279-295页

作者： Khodapanah, Mohammadali Ghanbari, Teymoor Moshksar, Ehsan Hosseini, Zahra Shiraz Univ Sch Adv Technol Shiraz Iran

Hotspot phenomenon is an expected consequence of long-term partial shading condition (PSC), which results in early degradation and permanent damage of the shaded cells in the photovoltaic (PV) systems. Hence, partial shading detection and estimation of its intensity is a significant factor to predict the possibility of hotspotting process and its occurrence time for PV system protection. In this paper, two partial shading detection indices are introduced based on the extracted power-voltage (P-V$P - V$) curves. The first P-V$P - V$ characteristic is related to the real shaded PV system and the second P-V$P - V$ curve is numerically obtained from the equivalent single-diode circuit model. The proposed PSC detection indices are established according to the difference between the numerical differentiation and integration of the P-V$P - V$ curves from the real PV system and the virtual reference model. These techniques have the advantages to distinguish between temporary and permanent PSC. Moreover, it is possible to estimate the intensity of the shading level and predict the hotspot occurrence time, accordingly. The performance of these methods are confirmed using some simulations and an experimental setup. The results verify the capabilities of the methods for partial shading detection without the requirement of an extra physical cell/module as a reference model.

关键词： Solar power stations and photovoltaic power systems DC-DC power convertors PSC detection indices maximum power point trackers hotspot prediction shaded cells Solar cells and arrays hotspot occurrence time power semiconductor diodes long-term partial shading condition differentiation shaded PV system solar cell arrays integration permanent damage numerical integration and differentiation partial shading detection indices photovoltaic systems photovoltaic power systems hotspot phenomenon numerical differentiation PV system protection shading level

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COMPUTATION OF ELECTROMAGNETIC-FIELDS GUIDED BY A CYLINDRICAL INHOMOGENEITY IN A HOMOGENEOUS MEDIUM OF INFINITE EXTENT

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IEE JOURNAL ON MICROWAVES OPTICS AND ACOUSTICS 1979年第6期3卷 224-230页

作者： MUR, G FONDSE, PJ Department of Electrical Engineering Laboratory of Electromagenetic Research Delft University of Technology Delft Netherlands

A rigorous numerical method is presented for computing time-harmonic electromagnetic fields that are guided by a transparent, lossless inhomogeneity in a homogeneous medium of infinite extent. Geometrically, the inhomogeneity is a cylinder of arbitrary cross-section. The structure is typical for a uniform open waveguide. On using the wave functions of the circular cylinder outside a cylinder that surrounds the inhomogeneity, and on transforming the electromagnetic-field equations inside this cylinder into a system of first-order ordinary differential equations, a two-point differential eigenproblem is obtained that is solved using standard techniques. Results are presented for waveguides with an equilaterally triangular and a rectangular cross-section, respectively. The latter is studied in detail.

关键词： optical waveguide theory EM fields computation Electromagnetic waves: theory differential equations differential eigenproblem Waveguide and cavity theory waveguide theory rigorous numerical method homogeneous medium guided electromagnetic wave propagation numerical approximation and analysis cylindrical waveguides Optical waveguides and couplers numerical methods rectangular waveguides dielectric waveguides numerical integration and differentiation wave functions Waveguides and microwave transmission lines cylindrical inhomogeneity equilateral triangle waveguides uniform open waveguide

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Earth-return path impedances of underground cables. Part 1: numerical integration of infinite integrals

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IEE PROCEEDINGS-GENERATION TRANSMISSION AND DISTRIBUTION 1998年第6期145卷 621-626页

作者： Nguyen, TT Univ Western Australia Dept Elect & Elect Engn Energy Syst Ctr Perth WA 6907 Australia

Although it is generally acknowledged that there is a need to closely formulate the earth-return path impedances of underground cables, research published so far has mainly concentrated on developing approximate formulations, especially for the infinite integrals which arise. Instead of seeking approximations, the paper develops a rigorous method based on direct numerical integration to evaluate the infinite integrals of underground cable earth-return path impedances. The method has immediate practical use in underground cable parameter calculations. It also provides a benchmark by which the accuracy of any proposed approximate method can be assessed. Further, the method can be used to provide training data by means of which infinite integrals can be evaluated using an array of neural networks.

关键词： underground cable parameter calculations electric impedance numerical integration and differentiation earth-return path impedances power cables underground cables neural network array Power cables numerical integration training data integration infinite integrals

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INTEGRATOR DESIGN FOR A DIFFERENTIAL ANALYZER

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RADIO AND ELECTRONIC ENGINEER 1976年第12期46卷 593-604页

作者： FORSYTHE, W HOUSEMAN, SL LOUGHBOROUGH UNIV TECHNOL DEPT ELECTR & ELECT ENGN LOUGHBOROUGH LE11 3TU LEICESTERSHIRE ENGLAND

The paper sets out to examine various integration algorithms, suitable for implementation in the form of serial binary arithmetic, and concludes that only first-order integration is practicable at the present time and that only first-order prediction is necessary or *** examination is made of the errors inherent in digitizing the main functions of the traditional analogue computer (integration, multiplication, division) and some conclusions reached about the feasibility of building a digital differential analyser given the current state of technology.

关键词： errors integration digital differential analysers first order integration multiplication first order prediction serial arithmetic digital analogue computer digital differential analyser integration algorithms digitizing division total transmission analogue computer numerical integration and differentiation increment transmission

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COMPUTER-AIDED-DESIGN OF THYRISTOR CIRCUITS - SPARSE-NETWORK TABLEAU APPROACH

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PROCEEDINGS OF THE INSTITUTION OF ELECTRICAL ENGINEERS-LONDON 1979年第5期126卷 369-374页

作者： PRENDERGAST, EJ JACKSON, RD Engineering Department Cambridge University Cambridge UK

Developments in sparse-matrix handling techniques have resulted in the emergence of the network tableau as an important method for a computer solution of network equations. This paper considers the use of the tableau method for the computer-aided design of thyristor circuits and illustrates the method with two examples. The tableau method is described briefly, the problems of sparse-matrix handling, numerical integration and thyristor modelling are introduced.

关键词： circuit CAD semiconductor device models thyristor modelling Computer-aided circuit analysis and design sparse matrix handling Electronic engineering computing Power engineering computing numerical integration network equations thyristors numerical integration and differentiation Thyristors and silicon controlled rectifiers computer aided design thyristor circuits sparse network tableau approach numerical methods Power convertors and power supplies to apparatus computer solution numerical analysis

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Earth-return path impedances of underground cables. Part 2: Evaluations using neural networks

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IEE PROCEEDINGS-GENERATION TRANSMISSION AND DISTRIBUTION 1998年第6期145卷 627-633页

作者： Nguyen, TT Univ Western Australia Dept Elect & Elect Engn Energy Syst Ctr Perth WA 6907 Australia

The aim of the paper is to train an array of neural networks to provide a procedure with high accuracy and low computing time requirement for evaluating the earth-return path impedances of underground cables. The training set required is formed by using a direct numerical integration method to evaluate the infinite integrals in the earth-return path formulations. The training is extensive but, once completed, it is valid for any cable configuration as it arises. The training leads to a universal set of weighting coefficients for an array of networks each of which has three input nodes, one output node and two hidden layers. Set up with these coefficients, the computing time requirements in calculating sets of series-path parameters for underground cables is reduced by a factor of about 1000 from that using a direct numerical evaluation of infinite integrals.

关键词： underground cables hidden layers neural nets Power engineering computing power engineering computing numerical integration and differentiation power cables neural network array Knowledge engineering techniques integration Neural computing techniques infinite integrals numerical analysis neural network training learning (artificial intelligence) earth-return path impedances weighting coefficients Power cables direct numerical integration method

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Accuracy and numerical stability of high-order polar harmonic transforms

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IET IMAGE PROCESSING 2012年第6期6卷 617-626页

作者： Singh, C. Upneja, R. Punjabi Univ Dept Comp Sci Patiala Punjab India

Invariant moments and transforms are a special kind of statistical measure designed to remain constant after some transformations, such as object rotation, scaling, translation or image illumination changes, in order to improve the reliability of a pattern recognition system. Polar harmonic transforms (PHTs) are one of such image descriptors based on a set of orthogonal projection bases, which are better rated in comparison with other moments and transforms because they possess less redundant information. PHTs suffer from geometric error and numerical integration error. Geometric error is caused when a square image is mapped into a unit circular disk, which cannot exactly match the square domain. numerical integration error is caused when the integration is approximated by zeroth-order summation. We propose a computational framework based on numerical integration approach that reduces the geometric error and the numerical integration error simultaneously. The effect of the improved accuracy in the PHTs is analysed for rotation invariance, scale invariance and image noise. Various numerical experiments demonstrate that the effect of these errors is much more prominent in small images and, therefore the proposed method is suitable for applications involving small images, such as in optical character recognition and template-matching applications.

关键词： integration numerical integration error statistical analysis optical character recognition scale invariance PHT statistical measure unit circular disk Computer vision and image processing techniques image processing template-matching invariant moment geometric error object rotation zeroth-order summation Optical, image and video signal processing Integral transforms numerical stability numerical integration and differentiation image noise pattern recognition Integral transforms in numerical analysis object scaling image illumination transforms orthogonal projection bases rotation invariance high-order polar harmonic transform image descriptor

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REFLECTION COEFFICIENT AT THE FEED OF A RADOME-COVERED REFLECTOR ANTENNA

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IEE PROCEEDINGS-H MICROWAVES ANTENNAS AND PROPAGATION 1982年第4期129卷 145-152页

作者： CORY, H CLARRICOATS, PJB UNIV LONDON QUEEN MARY COLL DEPT ELECT & ELECTR ENGNLONDON E1 4NSENGLAND

The reflection coefficient at the feed of a paraboloidal reflector antenna covered with a paraboloidal radome is evaluated by the power-coupling theorem. An asymptotic value of the reflection-coefficient expression leads to a simple physics interpretation of the result. The asymptotic value is favourably compared with that obtained by numerical integration. A comparsion between theoretical and experimental results is given in a companion paper.

关键词： integration reflection coefficient Antenna theory numerical integration antenna radiation patterns Single antennas asymptotic value power-coupling theorem radome-covered reflector antenna reflector antennas paraboloidal reflector antenna numerical integration and differentiation antenna theory

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FINITE-ELEMENT ANALYSIS OF LINEAR INDUCTION MACHINES

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PROCEEDINGS OF THE INSTITUTION OF ELECTRICAL ENGINEERS-LONDON 1979年第7期126卷 677-682页

作者： ALWASH, JHH ALRIKABI, JAH MIL TECH COLL DEPT ELECT & ELECTR ENGNBAGHDADIRAQ UNIV BAGHDAD COLL ENGNDEPT ELECT ENGNBAGHDADIRAQ

The paper presents a 2-dimensional finite-element analysis applicable to all practical forms of the plate-rotor, flat, linear induction motor. The analysis accounts for longitudinal end effects, finite plate thickness, slotting and discrete winding distribution; it yields detailed space profiles of the flux density and other distributions. The finite-element formulation is presented for the actual slotted model as well as the stator current-sheet representation. The problem of induction in moving media is treated by the extension of previous finite-element machine applications. The formulation results in a set of linear equations which are solved by a modified version of Liebmann's extrapolated process; the solution algorithm employs power mismatch in the machine to indicate accuracy, and nonlinear extrapolation to speed up convergence. The theory is supported by experimental findings.

关键词： electric machine analysis computing Linear machines slotting Asynchronous machines Differential equations (numerical analysis) partial differential equations induction motors linear motors finite plate thickness linear induction motor space profiles linear induction machines Electric actuators and final control equipment slotted model linear equations flux density numerical integration and differentiation power mismatch finite element analysis Liebmann's extrapolated process discrete winding distribution longitudinal end effects

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numerical-integration ALGORITHMS IN POWER SYSTEM DYNAMIC ANALYSIS

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PROCEEDINGS OF THE INSTITUTION OF ELECTRICAL ENGINEERS-LONDON 1974年第6期121卷 467-473页

作者： HUMPAGE, WD WONG, KP LEE, YW UNIV MANCHESTER INST SCI & TECHNOL POWER SYST LAB POB 88 MANCHESTER M60 1QD ENGLAND UNIV BRISTOL DEPT ELECT ENGN BRISTOL ENGLAND

The outcome of recent test applications of a range of integration algorithms to models representative of those now widely encountered in large- scale power- system dynamic analysis is reported. The paper collects together the main requirements of practical dynamic analysis, and it gives the principal schemes and solution strategies that might be used in meeting these requirements. Plant equation sets are summarised in a form that is of general application and interpretation in large analysis schemes, and, for these sets, comparative studies are made of the performance of explicit and implicit methods of single- and multiple-step sequences of numerical integration. In total, some ten different methods have been included in the evaluations, and, for most of these, two, and, in some cases, three, alternative modes of implementation are studied and compared. Methods of decomposition are invoked to allow different step lengths, and, where required, different integration methods, to be associated with individual subsets of significantly different response rates. Finally, the likely role of automatic algorithm control in this area of applied analysis in power systems is discussed

关键词： numerical integration algorithms numerical analysis numerical integration and differentiation dynamic analysis Power engineering computing Power systems electrical engineering applications of computers computer aided analysis power systems integration

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