THE REGRESSION MODEL OF TRANSMISSION LINE ICING BASED ON NEURAL NETWORKS

Transcription

1 The 4th Intenatonal Wokshop on Atmosphec Icng of Stuctues, Chongqng, Chna, May 8 - May 3, 20 THE REGRESSION MODEL OF TRANSMISSION LINE ICING BASED ON NEURAL NETWORKS Sun Muxa, Da Dong*, Hao Yanpeng, Huang Xaotng School of Electc Powe, South Chna Unvesty of Technology, Guangzhou, Chna *Emal:dda@scut.edu.cn Abstact: Ths pape addesses the egesson model of the tansmsson lne cng based on BP Neual netwoks. The Model s bult fo estmatng the ce heght on powe lne. The feld data used fo the egesson model comes fom the Ealy Wanng System fo Dsastes (Icng) of Chna Southen Powe Gd, whch ncludes the ambent tempeatue, elatvely humdty, mean wnd speed, wnd decton, atmosphec pessue and the equal ce heght. The esults fom the applcaton of the BP model ae n well ageement wth the feld data, ndcatng that the model can be vey useful both fo estmatng the cng loads on tansmsson lnes, and alam the comng cng events when a futhe shot-tem foecastng system fo the feld clmate data s avalable.bstact of the submtted pape. The abstact should be accodng to the text and algnment fomattng. model buld by BP neual netwoks, especally n the cold egons, ae stll needed.. INTRODUCTION The cng on tansmsson lne was and s stll a poblem fo powe netwoks. Afte the cng dsaste n 2008, an mpotant task fo the South Chna Powe Gd s to pefect the cng alam system of ove head tansmsson lnes. Ou wok s n pupose to gve egesson models to estmate the equal heght of powe lne cng, usng the mco-clmate data of each towe montoed by the Ealy Wanng System fo Dsastes (Icng) of Chna Southen Powe Gd, whch ncludes the ambent tempeatue, elatvely humdty, mean wnd speed, wnd decton, atmosphec pessue and equal ce heght. The models ae expected to be used n shot-tem alam system of the ce events n the futue. We use BP neual netwoks as the leanng machne to fnd the best egesson functons. Expements show that the BP models estmate the cng events n the test sets vey well. Specfcally, we bult a BP neual netwok fo each sepaated montoed towe. In ths pape, the statstcal leanng theoy s ntoduced n ths pape to gve a theoetcal decton fo buldng the BP netwoks. Then the data pepocessng technques was caefully used. In the end of the pape, we gve the expements and esults of ou models, and make a shot concluson. 2. RESULTS AND DISCUSSION The esults show that the BP neual netwoks estmate the powe lne cng well, although the accuacy of the egesson models change fom towe to towe. 3. CONCLUSION Expements and esults show that the BP neual netwok estmates the cng events well. Howeve, moe data and expements ae equed, as the cng events we have collected s stll ae, and fo most towes, the maxmum ce heght we have obseved s vey low, e.g., less than cm. Thus, moe tests fo the effectveness of the egesson Fgue : An cng event at a montoed tansmsson lne n Guangx Povnce n The Towe Numbe Table : Estmatng the Icng Events. The numbe of The best neuon the cng data numbe n the hdden laye The mean squae eo REFERENCES [] Savadjev K, Fazaneh M. Modelng of Icng and Ice Sheddng on Ovehead Powe Lnes Based on Statstcal Analyss of Meteoologcal Data, IEEE Tans Powe Delvey, 2004, vol. 9(2), pp [2] Fazaneh M, Savadjev K. Statstcal analyss of feld data fo pecptaton cng acceton on ovehead powe lnes, IEEE Tans Powe Delvey, 2005, vol. 20(2), pp [3] Laouche E, Rouat J, Bouchad G, et al. Exploaton of Statc and Tme Dependent Neual Netwok Technque fo the Pedcton of Ice Acceton on Ovehead Lne Conductos, 9th Intenatonal Wokshop on Atmosphec Icng of Stuctues. Cheste, Unted Kngdom, Sesson 2, [4] Makkonen L. Modelng Powe Lne Icng n Feezng Pecptaton. Atmosphec Reseach, 998, vol. 46, pp [5] Shao J, Laux S J, Tano B J, Pettfe R E W. Nowcasts of tempeatue and ce on ovehead alway tansmsson wes. Meteoology Appcatonl, 2003, vol. 0,pp [6] Maalbash-Zamn S. Developng Neual Netwok Models to Pedct Ice Acceton Type and Rate on Ovehead Tansmsson Lnes. TI&temp=0 [7] Fazaneh, Masoud (Ed.), Atmosphec Icng of Powe Netwoks, CA: Spnge, [8] Pang-Nng Tan, Mchael Stenbach, Vpn Kuma, Intoducton to Data Mng. CA: Peason Addson-Wesley, [9] Jawe Han, Mchelne Kambe, Data Mnng, Second Edton : Concepts and Technques. CA: Mogan Kaufmann, 2006.

2 The Regesson Model of Tansmsson Lne Icng Based on Neual Netwoks Sun Muxa, Da Dong *, Hao Yanpeng, Huang Xaotng School of Electc Powe South Chna Unvesty of Technology Guangzhou, Chna Abstact Ths pape addesses the egesson model of the tansmsson lne cng based on BP Neual netwoks. The Model s bult fo estmatng the ce heght on powe lne. The feld data used fo the egesson model comes fom the Ealy Wanng System fo Dsastes (Icng) of Chna Southen Powe Gd, whch ncludes the ambent tempeatue, elatvely humdty, mean wnd speed, wnd decton, atmosphec pessue and the equal ce heght. The esults fom the applcaton of the BP model ae n well ageement wth the feld data, ndcatng that the model can be vey useful both fo estmatng the cng loads on tansmsson lnes, and alam the comng cng events when a futhe shot-tem foecastng system fo the feld clmate data s avalable. Keywods-Tansmsson lne cng; egesson model; BP neual netwok; feld data I. INTRODUCTION The cng on tansmsson lne was and s stll a poblem fo powe netwoks. Afte the cng dsaste n 2008, an mpotant task fo the South Chna Powe Gd s to pefect the cng alam system of ove head tansmsson lnes. Thus, the Ealy Wanng System fo Dsastes (Icng) of Chna Southen Powe Gd,.e., EWSD of CSG, a system montos the clmate and othe paametes of the powe lnes n south chna has been bult n fve povnces of south Chna. Ths system gves the mco clmate data of each montoed towe, ncludng the ambent tempeatue, elatvely humdty, mean wnd speed, wnd decton, atmosphec pessue and equal ce heght. Ou wok s n pupose to gve empcal cng models to estmate the equal heght of powe lne cng, so that a shot tem cng alam system mght be establshed wth the help of a numecal mco clmate foecast system n the futue. Consdeng the success of the addtve model based on the data fom the Mont Bela test ste, we use egesson models and the clmate data povded by the montong system to estmate the powe lne cng. We use BP neual netwok as the leanng machne to fnd the best egesson functon. Expements show that the BP models estmate the cng events vey well, whch wee ndependent fom the tanng data sets. As the BP netwoks can update themselves onlne by tanng themselves automatcally, they have a sgnfcant potental to be appled n the pactcal powe lne cng estmatng. Specfcally, we bult a BP neual netwok fo each sepaated towe, fo the montoed towes ae dstbuted n such dffeent geogaphc and atmosphec envonment, and the coelaton between ce heght and the nput clmate vaables seems dependent fom the locaton of the montoed towe, as the mpotant clmate paametes, such as the cng ate and the pecptaton ate ae absent hee. As the cng events fo each towe s qute lmted, the poblem s to buld the egesson functons by BP netwok at the lowest sk wth lmted data samples. Thus, the statstcal leanng theoy s ntoduced, whch gves a theoetcal decton fo buldng the BP netwok, and seveal data pepocessng technques was used. In ths pape, we wll fst dscuss the data and ts pepocessng, then ntoduce ou egesson model based on BP neual netwoks, and n the end, gve the expements and esults of ou models, and make a shot concluson. II. THE REGRESSION MODEL BASED ON BP NEURAL NETWORKS A. The basc egesson model fo tansmsson lne cng Accodng to the statstcal leanng theoy, the basc egesson estmaton poblem fo a leanng machne k s to mnmze the sk functonal 2 R( α) = ( f( x, α) y) df( x, y) () whee x s the vecto of the ndependent vaables, y s the dependent vaable, F( x, y) s the unted pobablty dstbuton of x, y,and α s the paamete. The condtonal expectaton functon of F( x, y) f ( x, α ) = ydf( y x) (2) 0 mnmzes the sk functonal R( α ), so that the key fo the leanng machne k to mnmze R( α ) s to estmate f( x, α0) n the set { f( x, α) α Λ k }, whee Λk s a set of paamete α gven by k. The leanng machnes use empcal data to mnmze R( α ). As the sk functonal of the set of the empcal data M = {( x, y) =,2... l} (l s the numbe of the data samples, and ( x, y) s usually assumed as ndependent and dentcally obsevatons of F( x, y) ), o the Empcal Rsk Functonal

3 R ( ) emp α = l 2 [ f ( x, α) y ] (3) l = s usually nconsstent wth R( α ), we have the SRM pncple fo leanng machnes such as BP neual netwok, whch ponts out we should take a ndect way by mnmze Rs (, l k), the bounds of the genealzaton ablty of the leanng machnes, as R (, lk) = R ( α ) +Φ ( l/ h) (4) s emp emp, k k R (, l k) R( α ) (5) s emp, k Whee αemp,k mnmzes R ( ) emp α n the functon set A k, and the symbol Φ( l / h k ) s the confdence nteval, whch decded by l, and the VC dmenson of leanng machne k. B. The BP neual netwok Fgue. a BP neual netwok wth one hdden laye. The Hecht-Nelsen Theoem shows that a BP neual netwok wth at least one hdden laye could appoxmate any contnuous functon. The fttng functon of BP neual netwok wth one hdden laye s n n f ( x, α) = N ( x) = w S( u ) = = T whee u = λ( w x b ), x s the nput vecto, y s the output vaable, and n s the numbe of the hdden laye neuons. Fo the hdden neuon, N ( x ) s the output of the neuon, wth the sgmod functon Su ( ), and the neuon paametes λ, w,, w2,, b. In ths pape, we use BP netwok wth one hdden laye to ft the egesson functons. The steps to mnmze Rs (, ln ) (The hdden laye neuons numbe n fxes the stuctue of the BP netwok wth one hdden laye) fo the BP netwoks s: Step. Choose a small n, so that the confdence nteval Φ( l / h n ) s fxed. 2 (6) Step3. Fo each n, calculate the empcal sk functon R ( ) test α fo the test data set whch s ndependent of the tanng data set. Assume that R ( test α ) R (, ) s l n, the numbe of the hdden neuons n 0 whch mnmze Rs (, l n) s got. Hee, f( x, αemp,n 0 ) s the best estmaton gven by the BP netwok wth one hdden laye of f( x, α0). III. PREPARE YOUR PAPER BEFORE STYLING A. The nput data The montong system of the EWSD of CSG povdes vaous data. Fo neual netwoks, the nput data, ncludng the ndependent vaables and the dependent vaable, should be caefully chosen. Because of the absent of the cng ate and the pecptaton ate, we chose the equal ce heght H athe than the ce accumulatng ate as the dependent vaable. Fo the cng alam system n futue, the ndependent vaables should be easy to foecast n shot tem. Thus, we chose the avalable clmate vaables as the ndependent vaables, ncludng the ambent tempeatuet, elatvely humdtyw, mean wnd speedv, wnd decton A, and the atmosphec pessue P. The montong system takes sample of the clmate vaables evey 0 o 5 mnute. The database s conssted of all the data montoed fom the yea 2008 to 200. The contnuous cng events n the database consttute the tanng set and test set fo the BP neual netwoks. B. The devaton detecton n databases Whle the database contans dffeent knds of eo, the devaton detecton technques ae equed. The eo data we have commonly obseved n the database ncluded the solate ponts and the contnuous beakdown caused by hadwae falue. To fnd the two knds of eo n the data flow, we desgned a devaton detecton algothm n tme sees, whch s based on the statstcal analyss of the clmate vaables. The algothm uses a sees of confdence ntevals to check whethe the value o the nceasng ate of a data s out of them. Then, the cteons whch classfy the two knds of eo ae used to classfy the eo data. We also use the k-neaest neghbohood algothm to detect the outles left n the database afte usng the devaton detecton algothm. As the cng data s vey ae, the two algothms ae used n the whole database athe than n each tanng and test set. The esults of these two algothms ae showed n fg. and fg 2. Step2. Fo each possble n, mnmze R emp ( α ), and get the fttng functon f( x, α emp, n )

4 Fgue 2. the Devaton Detecton n Tme Sees. Fgue 4. An cng event at a montoed tansmsson lne Guzhou Povnce n Fgue 3. the Outle Detecton based on k-neaest Neghbohood Algothm. C. The epa and smooth of data The data lost o dstngushed by the devaton detecton technques needs to be epaed. We use the tanng d has to be nomalzed to epa the data. As the epaed data s stll wth some andom measue eo, we use the movng aveage method to smooth the data flow. D. The nomalzaton of data The tanng data fo BP netwok usually has to be nomalzed. Hee, we use the lnea nomalzed method, whee the nomalzed data u = ( u u )/( u u ) (4) G mn max mn u mn Hee, u s the ognal data value, s the mnmum value of u, u s the maxmum value of u. max IV. THE EXPERIMENTS AND RESULTS In ths pape, we use the BP neual netwok to estmate the cng events n the test set fo the 4 classcal montoed tansmsson lne at dffeent place of south chna. The esults ae showed n Fg. 3, Fg. 4 and Tab.. Fgue 5. An cng event at a montoed tansmsson lne n Guangx Povnce n The Towe Numbe TABLE I. The numbe of the cng data ESTIMATING THE ICING EVENTS. The best neuon numbe n the hdden laye The mean squae eo The esults show that the BP neual netwoks estmate the powe lne cng well, although the accuacy of the egesson models change fom towe to towe, and occasonally they does not wok such well, e.g., at the lne No.4. One eason explans ths phenomenon s that the cng data, especally the data of the classcal cng events s stll vey ae, so that the pefomance of BP neual netwok would not always be steady. Anothe eason s that the mpotant chaactes of the tansmsson lne cng events, e.g., the cng ate, s absent hee. We could expect a egesson model wthout the nput I would have a hghe sk, though qute enough fo a shot-tem cng alam system.

5 V. DISCUSSION Ths pape deals wth egesson model based on BP neual netwok fo estmate the powe lne cng. The nput of the neual netwok ncludes the ambent tempeatue, elatvely humdty, mean wnd speed, wnd decton, atmosphec pessue and equal ce heght. The data we use was caefully pepocessed. Expements and esults show that the BP neual netwok estmates the cng events well. Howeve, moe data and expements ae equed, as the cng events we have collected s stll ae, and fo most towes, the maxmum ce heght we have obseved s vey low, e.g., less than cm. Thus, moe tests fo the effectveness of the egesson model buld by BP neual netwoks, especally n the cold egons, ae stll needed. ACKNOWLEDGMENT Ths wok was suppoted by the Natonal Key Suppotng Pogam fo Sc & Tech Reseach dung the st Fve-Yea Plan Peod of Chna (2009BAA23B0-8) and the Natual Scence Foundaton of Guangdong Povnce, Chna ( ). Refeences [0] Savadjev K, Fazaneh M. Modelng of Icng and Ice Sheddng on Ovehead Powe Lnes Based on Statstcal Analyss of Meteoologcal Data, IEEE Tans Powe Delvey, 2004, vol. 9(2), pp [] Fazaneh M, Savadjev K. Statstcal analyss of feld data fo pecptaton cng acceton on ovehead powe lnes, IEEE Tans Powe Delvey, 2005, vol. 20(2), pp [2] Laouche E, Rouat J, Bouchad G, et al. Exploaton of Statc and Tme Dependent Neual Netwok Technque fo the Pedcton of Ice Acceton on Ovehead Lne Conductos, 9th Intenatonal Wokshop on Atmosphec Icng of Stuctues. Cheste, Unted Kngdom, Sesson 2, [3] Makkonen L. Modelng Powe Lne Icng n Feezng Pecptaton. Atmosphec Reseach, 998, vol. 46, pp [4] Shao J, Laux S J, Tano B J, Pettfe R E W. Nowcasts of tempeatue and ce on ovehead alway tansmsson wes. Meteoology Appcatonl, 2003, vol. 0,pp [5] Maalbash-Zamn S. Developng Neual Netwok Models to Pedct Ice Acceton Type and Rate on Ovehead Tansmsson Lnes. TI&temp=0 [6] Fazaneh, Masoud (Ed.), Atmosphec Icng of Powe Netwoks, CA: Spnge, [7] Pang-Nng Tan, Mchael Stenbach, Vpn Kuma, Intoducton to Data Mng. CA: Peason Addson-Wesley, [8] Jawe Han, Mchelne Kambe, Data Mnng, Second Edton : Concepts and Technques. CA: Mogan Kaufmann, 2006.