A New Approach to the Evaluation of the Lightning Horizontal Electric Field Over a Lossy Ground Based on the Time-Domain Cooray-Rubinstein Formula Fitted by Orthogonal Polynomials
The calculation of lightning return stroke electromagnetic field is the basis for evaluating transmission line lightning-induced voltages. The Cooray-Rubinstein formula in the time domain is widely used to evaluate the horizontal electric field of lightning return stroke on a lossy ground, but the e...
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| Veröffentlicht in: | IEEE transactions on electromagnetic compatibility 2023-06, Vol.65 (3), p.1-9 |
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| container_title | IEEE transactions on electromagnetic compatibility |
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| creator | Wang, Tianhao Jiang, Haolin Lv, Gang Yu, Quanyi Guan, Shanshan |
| description | The calculation of lightning return stroke electromagnetic field is the basis for evaluating transmission line lightning-induced voltages. The Cooray-Rubinstein formula in the time domain is widely used to evaluate the horizontal electric field of lightning return stroke on a lossy ground, but the evaluation of the formula requires high computation cost. Therefore, this study presents a new approach to evaluate the Cooray-Rubinstein formula based on orthogonal polynomial fitting. This method converts the complex convolution in the Cooray-Rubinstein formula into the sum of multiple simple convolutions by using an effective truncation scheme of Legendre orthogonal polynomial and the second Chebyshev orthogonal polynomial. The objective is to realize an efficient evaluation method to the horizontal electric field of the lightning return stroke. On the premise of ensuring the calculation accuracy, the effectiveness and correctness of the proposed method are verified through numerical experiments. Moreover, the application of the time-domain Cooray-Rubinstein formula based on two orthogonal polynomial fitting methods is discussed. Compared with the existing numerical methods for solving the Cooray-Rubinstein formula, the proposed method is easy to implement and efficient, which provides a new idea for evaluating the horizontal electric field of lightning return stroke above the lossy ground in the time domain. |
| doi_str_mv | 10.1109/TEMC.2023.3248600 |
| format | Article |
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The Cooray-Rubinstein formula in the time domain is widely used to evaluate the horizontal electric field of lightning return stroke on a lossy ground, but the evaluation of the formula requires high computation cost. Therefore, this study presents a new approach to evaluate the Cooray-Rubinstein formula based on orthogonal polynomial fitting. This method converts the complex convolution in the Cooray-Rubinstein formula into the sum of multiple simple convolutions by using an effective truncation scheme of Legendre orthogonal polynomial and the second Chebyshev orthogonal polynomial. The objective is to realize an efficient evaluation method to the horizontal electric field of the lightning return stroke. On the premise of ensuring the calculation accuracy, the effectiveness and correctness of the proposed method are verified through numerical experiments. Moreover, the application of the time-domain Cooray-Rubinstein formula based on two orthogonal polynomial fitting methods is discussed. Compared with the existing numerical methods for solving the Cooray-Rubinstein formula, the proposed method is easy to implement and efficient, which provides a new idea for evaluating the horizontal electric field of lightning return stroke above the lossy ground in the time domain.</description><identifier>ISSN: 0018-9375</identifier><identifier>EISSN: 1558-187X</identifier><identifier>DOI: 10.1109/TEMC.2023.3248600</identifier><identifier>CODEN: IEMCAE</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Azimuth ; Chebyshev approximation ; Cooray–Rubinstein (C-R) formula ; Costs ; Electric fields ; Electromagnetic fields ; horizontal electric field ; Lightning ; lightning stroke ; lossy ground ; Magnetic domains ; Mathematical analysis ; Numerical methods ; Numerical models ; orthogonal polynomial fitting ; Polynomials ; Power transmission lines ; Return strokes (lightning) ; Time domain analysis ; Transmission lines</subject><ispartof>IEEE transactions on electromagnetic compatibility, 2023-06, Vol.65 (3), p.1-9</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2023</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c246t-c7367196189ed894b53047cdbbb0a3af28b8e2b130a78eb3c25e7ed3342ada513</cites><orcidid>0000-0002-7173-3450 ; 0000-0002-2126-6110 ; 0000-0003-4168-8502 ; 0000-0001-5458-2462 ; 0009-0007-9872-8305</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/10109270$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/10109270$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Wang, Tianhao</creatorcontrib><creatorcontrib>Jiang, Haolin</creatorcontrib><creatorcontrib>Lv, Gang</creatorcontrib><creatorcontrib>Yu, Quanyi</creatorcontrib><creatorcontrib>Guan, Shanshan</creatorcontrib><title>A New Approach to the Evaluation of the Lightning Horizontal Electric Field Over a Lossy Ground Based on the Time-Domain Cooray-Rubinstein Formula Fitted by Orthogonal Polynomials</title><title>IEEE transactions on electromagnetic compatibility</title><addtitle>TEMC</addtitle><description>The calculation of lightning return stroke electromagnetic field is the basis for evaluating transmission line lightning-induced voltages. The Cooray-Rubinstein formula in the time domain is widely used to evaluate the horizontal electric field of lightning return stroke on a lossy ground, but the evaluation of the formula requires high computation cost. Therefore, this study presents a new approach to evaluate the Cooray-Rubinstein formula based on orthogonal polynomial fitting. This method converts the complex convolution in the Cooray-Rubinstein formula into the sum of multiple simple convolutions by using an effective truncation scheme of Legendre orthogonal polynomial and the second Chebyshev orthogonal polynomial. The objective is to realize an efficient evaluation method to the horizontal electric field of the lightning return stroke. On the premise of ensuring the calculation accuracy, the effectiveness and correctness of the proposed method are verified through numerical experiments. Moreover, the application of the time-domain Cooray-Rubinstein formula based on two orthogonal polynomial fitting methods is discussed. Compared with the existing numerical methods for solving the Cooray-Rubinstein formula, the proposed method is easy to implement and efficient, which provides a new idea for evaluating the horizontal electric field of lightning return stroke above the lossy ground in the time domain.</description><subject>Azimuth</subject><subject>Chebyshev approximation</subject><subject>Cooray–Rubinstein (C-R) formula</subject><subject>Costs</subject><subject>Electric fields</subject><subject>Electromagnetic fields</subject><subject>horizontal electric field</subject><subject>Lightning</subject><subject>lightning stroke</subject><subject>lossy ground</subject><subject>Magnetic domains</subject><subject>Mathematical analysis</subject><subject>Numerical methods</subject><subject>Numerical models</subject><subject>orthogonal polynomial fitting</subject><subject>Polynomials</subject><subject>Power transmission lines</subject><subject>Return strokes (lightning)</subject><subject>Time domain analysis</subject><subject>Transmission lines</subject><issn>0018-9375</issn><issn>1558-187X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpNUcuO0zAUtRBIlIEPQGJhiXWKH3HjLEtpZ5AKRahI7CI7uW09SnyL7cwo_BY_iEtnwerqHp1z7uMQ8pazOees_rBff1nNBRNyLkWpF4w9IzOulC64rn4-JzPGuC5qWamX5FWM97ktlZAz8mdJv8IjXZ7PAU17oglpOgFdP5h-NMmhp3j4h2zd8ZS880d6h8H9Rp9MT9c9tCm4lm4c9B3dPUCghm4xxoneBhx9Rz-aCB3NPheTvRug-ISDcZ6uEIOZiu-jdT4myMgGwzD2JpullDV2oruQTnhEn0d9w37yODjTx9fkxSEXePNUb8iPzXq_uiu2u9vPq-W2aEW5SEVbyUXF6wXXNXS6Lq2SrKzazlrLjDQHoa0GYblkptJgZSsUVNBJWQrTGcXlDXl_9c2_-TVCTM09jiEvExuhhVK1rhnLLH5ltSHfHeDQnIMbTJgazppLNs0lm-aSTfOUTda8u2ocAPzHz2xRMfkXvfONSg</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Wang, Tianhao</creator><creator>Jiang, Haolin</creator><creator>Lv, Gang</creator><creator>Yu, Quanyi</creator><creator>Guan, Shanshan</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>8FD</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0002-7173-3450</orcidid><orcidid>https://orcid.org/0000-0002-2126-6110</orcidid><orcidid>https://orcid.org/0000-0003-4168-8502</orcidid><orcidid>https://orcid.org/0000-0001-5458-2462</orcidid><orcidid>https://orcid.org/0009-0007-9872-8305</orcidid></search><sort><creationdate>20230601</creationdate><title>A New Approach to the Evaluation of the Lightning Horizontal Electric Field Over a Lossy Ground Based on the Time-Domain Cooray-Rubinstein Formula Fitted by Orthogonal Polynomials</title><author>Wang, Tianhao ; Jiang, Haolin ; Lv, Gang ; Yu, Quanyi ; Guan, Shanshan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c246t-c7367196189ed894b53047cdbbb0a3af28b8e2b130a78eb3c25e7ed3342ada513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Azimuth</topic><topic>Chebyshev approximation</topic><topic>Cooray–Rubinstein (C-R) formula</topic><topic>Costs</topic><topic>Electric fields</topic><topic>Electromagnetic fields</topic><topic>horizontal electric field</topic><topic>Lightning</topic><topic>lightning stroke</topic><topic>lossy ground</topic><topic>Magnetic domains</topic><topic>Mathematical analysis</topic><topic>Numerical methods</topic><topic>Numerical models</topic><topic>orthogonal polynomial fitting</topic><topic>Polynomials</topic><topic>Power transmission lines</topic><topic>Return strokes (lightning)</topic><topic>Time domain analysis</topic><topic>Transmission lines</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Tianhao</creatorcontrib><creatorcontrib>Jiang, Haolin</creatorcontrib><creatorcontrib>Lv, Gang</creatorcontrib><creatorcontrib>Yu, Quanyi</creatorcontrib><creatorcontrib>Guan, Shanshan</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>IEEE transactions on electromagnetic compatibility</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Wang, Tianhao</au><au>Jiang, Haolin</au><au>Lv, Gang</au><au>Yu, Quanyi</au><au>Guan, Shanshan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A New Approach to the Evaluation of the Lightning Horizontal Electric Field Over a Lossy Ground Based on the Time-Domain Cooray-Rubinstein Formula Fitted by Orthogonal Polynomials</atitle><jtitle>IEEE transactions on electromagnetic compatibility</jtitle><stitle>TEMC</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>65</volume><issue>3</issue><spage>1</spage><epage>9</epage><pages>1-9</pages><issn>0018-9375</issn><eissn>1558-187X</eissn><coden>IEMCAE</coden><abstract>The calculation of lightning return stroke electromagnetic field is the basis for evaluating transmission line lightning-induced voltages. The Cooray-Rubinstein formula in the time domain is widely used to evaluate the horizontal electric field of lightning return stroke on a lossy ground, but the evaluation of the formula requires high computation cost. Therefore, this study presents a new approach to evaluate the Cooray-Rubinstein formula based on orthogonal polynomial fitting. This method converts the complex convolution in the Cooray-Rubinstein formula into the sum of multiple simple convolutions by using an effective truncation scheme of Legendre orthogonal polynomial and the second Chebyshev orthogonal polynomial. The objective is to realize an efficient evaluation method to the horizontal electric field of the lightning return stroke. On the premise of ensuring the calculation accuracy, the effectiveness and correctness of the proposed method are verified through numerical experiments. Moreover, the application of the time-domain Cooray-Rubinstein formula based on two orthogonal polynomial fitting methods is discussed. Compared with the existing numerical methods for solving the Cooray-Rubinstein formula, the proposed method is easy to implement and efficient, which provides a new idea for evaluating the horizontal electric field of lightning return stroke above the lossy ground in the time domain.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TEMC.2023.3248600</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0002-7173-3450</orcidid><orcidid>https://orcid.org/0000-0002-2126-6110</orcidid><orcidid>https://orcid.org/0000-0003-4168-8502</orcidid><orcidid>https://orcid.org/0000-0001-5458-2462</orcidid><orcidid>https://orcid.org/0009-0007-9872-8305</orcidid></addata></record> |
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| source | IEEE Electronic Library (IEL) |
| subjects | Azimuth Chebyshev approximation Cooray–Rubinstein (C-R) formula Costs Electric fields Electromagnetic fields horizontal electric field Lightning lightning stroke lossy ground Magnetic domains Mathematical analysis Numerical methods Numerical models orthogonal polynomial fitting Polynomials Power transmission lines Return strokes (lightning) Time domain analysis Transmission lines |
| title | A New Approach to the Evaluation of the Lightning Horizontal Electric Field Over a Lossy Ground Based on the Time-Domain Cooray-Rubinstein Formula Fitted by Orthogonal Polynomials |
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