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Methods of Numerical Integration

Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.

Integral transforms and their applications

Power utilities are struggling to reduce power failure incidents in substations and their components to operate more reliably and economically [1]. Many power failures are produced directly or indirectly because of the insulation system of utility components [2], [3]. The selection of the insulation should ensure power plant operational continuity along with completely resolving or significantly limiting the actual power system's failures [4]. Gas insulated substations (GIS) have the best insulation performance which ensures achieving minimum failure incidents, although at high installation cost. The most common insulating gas used in GIS is Sulfur hexafluoride (SF 6 ) gas, which is widely used as an effective electrical insulation as well as an arc-quenching medium [5]. Basic GIS and gas insulated transmission lines (GITL or GIL) consist of a conductor supported by solid insulators inside an enclosure filled with SF 6 gas or its mixture [6].

Partial discharge detection and diagnosis in gas insulated switchgear: State of the art

Condition monitoring of an operating apparatus is essential for lifespan assessment and maintenance planning in a power system. Electrical insulation is a critical aspect to be monitored, since it is susceptible to failure under high electrical stress. To avoid unexpected breakdowns, the level of partial discharge (PD) activity should be continuously monitored because PD occurrence can accelerate the aging process of insulation in high voltage equipment and result in catastrophic failure if the associated defects are not treated at an early stage. For on-site PD detection, the ultra-high frequency (UHF) method was employed in the field and showed its effectiveness as a detection technique. The main advantage of the UHF method is its immunity to external electromagnetic interference with a high signal-to-noise ratio, which is necessary for on-site monitoring. Considering the detection process, sensors play a critical role in capturing signals from PD sources and transmitting them onto the measurement system. In this paper, UHF sensors applied in PD detection were comprehensively reviewed. In particular, for power transformers, the effects of the physical structure on UHF signals and practical applications of UHF sensors including PD localization techniques were discussed. The aim of this review was to present state-of-the-art UHF sensors in PD detection and facilitate future improvements in the UHF method.

Application of UHF Sensors in Power System Equipment for Partial Discharge Detection: A Review

The condition of the internal cellulosic paper and oil insulation are of concern for the performance of power transformers. Over the years, a number of methods have been developed to diagnose and monitor the degradation/aging of the transformer internal insulation system. Some of this degradation/aging can be assessed from electrical responses. Currently there are a variety of electrical-based diagnostic techniques available for insulation condition monitoring of power transformers. In most cases, the electrical signals being monitored are due to mechanical or electric changes caused by physical changes in resistivity, inductance or capacitance, moisture, contamination or aging by-products in the insulation. This paper presents a description of commonly used and modern electrical-based diagnostic techniques along with their interpretation schemes.

Electrical-Based Diagnostic Techniques for Assessing Insulation Condition in Aged Transformers

Partial discharge (PD) measurements provide valuable information for assessing the condition of high voltage (HV) insulation systems, contributing to their quality assurance. Different PD measuring techniques have been developed in the last years specially designed to perform on-line measurements. Non-conventional PD methods operating in high frequency bands are usually used when this type of tests are carried out. In PD measurements the signal acquisition, the subsequent signal processing and the capability to obtain an accurate diagnosis are conditioned by the selection of a suitable detection technique and by the implementation of effective signal processing tools. This paper proposes an optimized electromagnetic detection method based on the combined use of wideband PD sensors for measurements performed in the HF and UHF frequency ranges, together with the implementation of powerful processing tools. The effectiveness of the measuring techniques proposed is demonstrated through an example, where several PD sources are measured simultaneously in a HV installation consisting of a cable system connected by a plug-in terminal to a gas insulated substation (GIS) compartment.

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Application of HFCT and UHF Sensors in On-Line Partial Discharge Measurements for Insulation Diagnosis of High Voltage Equipment

Nowadays, many researchers are focusing on on-line condition monitoring of high-voltage insulated cable systems to prevent failures. With the aim of reducing the voltage induced in the cable sheaths, cross-bonding (CB) grounding cable systems are used in long distance power transmission land lines. This paper proposes a new criterion for the detection and localization of defects that might occur in the cable sheath when a CB configuration is adopted. The proposed criterion can be applied at different levels of load current. For the application of the criterion, the cable system under evaluation is modeled using the alternative transient program (ATP) software. Various practical cases were studied, showing the effectiveness of the criterion for the detection and localization of different types of defects in simulated cable systems. Furthermore, in order to validate the criteria adopted for the defect detection, based on the ATP model, a real defected case was evaluated. The results obtained proved that this criterion is suitable for the detection and localization of defects in the cable sheaths, when on-line measurements are performed in monitoring applications.

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Detection and Localization of Defects in Cable Sheath of Cross-Bonding Configuration by Sheath Currents

In order to remove the present IEC 60060-1 and IEEE Standard 4 ambiguities in the evaluation of the test voltage when oscillations and/or an overshoot appear superimposed in a lightning impulse, at the end of the 1990s, a European Project within the Standard, Measurement and Testing (SMT) program was developed by KEMA (Netherlands), Schering Institute (Germany), LCOE (Spain), and NGC (United Kingdom) in coordination with the CIGRE Working Group 33.03. The conclusion of this European Project is a new evaluation method called test voltage function K(f) derived on the breakdown behavior of different dielectric media, that removes the standard ambiguity to determine the test voltage of an impulse with oscillations and/or an overshoot. This paper presents the experimental results of the project and deals in depth with the definition of K(f).

Determining the test voltage factor function for the evaluation of lightning impulses with oscillations and/or an overshoot

Definitions of standards IEC 60 and IEEE Std 4 are insufficient for the evaluation of lightning impulse parameters of waveforms with oscillations and/or overshoot. This has brought about different interpretations in the estimation of these parameters, especially when using digital recorders. Large discrepancies have resulted from the different interpretations. The working group 33.03 of CIGRE has collected various opinions about this problem. These are presented, analysed and discussed in this paper. Different ways of determining mean curves of impulses with oscillations and/or overshoot are proposed. In addition, different alternatives for the definitions of overshoot amplitude and duration are suggested for impulses with overshoot. The problems and alternative solutions are discussed in the light of analyzing three impulses of the IEC Test Data Generator. This illustrates clearly the need to change the above mentioned standards. Simple, easily applicable, reproducible and technically justified definitions are required in order to take advantage of the accuracy and facilities of digital recorders in impulse measurements. This paper offers the basis for further discussion on the subject before WG 33.03 of CIGRE makes its final proposal. Further studies with practical test impulses are still needed.

Evaluation procedures for lightning impulse parameters in case of waveforms with oscillations and/or an overshoot

A new algorithm has been proposed to calculate the parameters of full lightning voltage impulses. The new algorithm enables the application of the test voltage factor (also referred to as k-factor ...

Fernando Garnacho

Papers

Application of HFCT and UHF Sensors in On-Line Partial Discharge Measurements for Insulation Diagnosis of High Voltage Equipment

Detection and Localization of Defects in Cable Sheath of Cross-Bonding Configuration by Sheath Currents

Determining the test voltage factor function for the evaluation of lightning impulses with oscillations and/or an overshoot

Evaluation procedures for lightning impulse parameters in case of waveforms with oscillations and/or an overshoot

International comparison of software for calculation of lightning impulse parameters based on a new processing algorithm