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Ky Thuat Dien Cao AP t 2
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1
AI HOC QUOC GIA THANH PHO HO CH MINH TRNG AI HOC BACH KHOA
Hoang Viet
KY THUAT IEN CAO AP
Tap 2
QUA IEN AP TRONG
HE THONG IEN (Tai ban lan th hai co bo sung, chnh l)
NHA XUAT BAN AI HOC QUOC GIA THANH PHO HO CH MINH - 2007
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MUC LUC
Li noi au 5 ......................................................................................................... 5
Chng 1. SET - NGUON GOC CUA QUA IEN AP KH QUYEN ............. 7 1.1 Cac giai oan phat trien cua phong ien set ....................................... 7 1.2 Cac tham so chu yeu cua set - cng o hoat ong cua set .............. 14
Chng 2. QUA TRNH SONG TREN NG DAY TAI IEN .................28 2.1 S truyen song ien t tren ng day khong ton hao ....................... 28 2.2 Hien tng phan xa va khuc xa cua song: qui tac Petersen ............... 32 2.3 S phan s nhieu lan cua song .......................................................... 43 2.4 Vai phng phap tnh toan qua trnh truyen song bang o th ........... 51 2.5 Qui tac ve song ang tr ..................................................................... 59 2.6 Qua trnh truyen song trong he thong nhieu day dan ........................ 63 2.7 S bien dang cua song ..................................................................... 669
Chng 3. BAO VE CHONG SET ANH TRC TIEP CHO HE THONG IEN .................................................................................................75
3.1 Khai niem chung ................................................................................ 77 3.2 Xac nh pham vi bao ve cua cot thu set - mo hnh
A. Kopian .......................................................................................... 77 3.3 Pham vi bao ve cua day chong set .................................................... 84 3.4 Cac yeu cau ky thuat kinh te khi dung he thong cot thu set e
bao ve set anh thang cho tram bien ap va nha may ien ................ 87 3.5. Ly thuyet mo hnh ien hnh hoc ...................................................... 92
Chng 4. NOI AT TRONG HE THONG IEN .........................................112 4.1 Cac khai niem chung ....................................................................... 112 4.2 ien tr tan noi at tan so cong nghiep R~................................... 116 4.3 ien tr tan cua noi at chong set ................................................... 122 4.4 Anh hng cua chat at va thi tiet en ien tr noi at ................ 131 4.5 Cac yeu cau ve kinh te ky thuat khi thiet ke he thong noi at cho
tram va ng day tai ien .............................................................. 133 4.6 Phng phap dien tch e tnh ien tr tan cua li noi at ................. 136
Chng 5. BAO VE CHONG SET CHO NG DAY TAI IEN ............141 5.1 ng loi tong quat e tnh toan ch tieu chong set cua ng day tai
ien ................................................................................................. 135
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5.2 Qua ien ap cam ng ....................................................................... 146 5.3 Set anh trc tiep vao ng day khong co day chong set ............. 150 5.4 Set anh tren ng day co day chong set ...................................... 157
Chng 6. THIET B CHONG SET .................................................................170 6.1 Khai niem chung .............................................................................. 170 6.2 Khe h bao ve ................................................................................. 171 6.3 Thiet b chong set kieu ong ............................................................. 172 6.4 Thiet b chong set van (CSV) .......................................................... 169 6.5 Thiet b han che QA hay CSV khong co khe h ........................... 187
Chng 7. BAO VE CHONG SET TRUYEN VAO TRAM PHAN PHOI IEN ..................................................................................................189
7.1 Khai niem chung .............................................................................. 182 7.2 Bien phap va yeu cau oi vi viec bao ve chong set truyen vao tram .... 182 7.3 S o nguyen ly bao ve tram ........................................................... 188 7.4 Tham so tnh toan cua song set truyen vao tram va cach tnh ch
tieu chu set cua tram ....................................................................... 190 7.5 ien ap tren cach ien cua tram ..................................................... 192
Chng 8. BAO VE CHONG SET CHO MAY IEN QUAY .......................208 8.1 Bao ve cach ien may ien quay chong song set truyen vao theo
ng day tren khong ...................................................................... 201 8.2 Bao ve chong set cho may ien quay au vao ng day tren
khong qua may bien ap ................................................................... 204
Chng 9. QUA IEN AP NOI BO - NHNG TNH CHAT CHUNG CUA QUA IEN AP NOI BO TRONG HE THONG IEN .......218
9.1 Phan loai Qua ien ap noi bo .......................................................... 209 9.2 Van e noi at iem trung tnh cua he thong ien .......................... 211
Chng 10. QUA IEN AP KHI CHAM AT MOT PHA BANG HO QUANG TRONG LI CO TRUNG TNH CACH IEN .......224
10.1 Cham at mot pha on nh ............................................................. 215 10.2 Dien bien cua qua trnh cham at mot pha .................................... 226 10.3 Noi at iem trung tnh qua cuon dap ho quang ............................ 234
Chng 11. QUA IEN AP CONG HNG ..................................................243 11.1 Khai niem chung ............................................................................ 243 11.2 Cong hng ieu hoa ..................................................................... 235
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Cac cau hoi on tap mon hoc Qua ien ap ..................................................260 Tai lieu tham khao ..............................................................................................272
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Li noi au
Cach ien cua trang thiet b ien ap cao khong ch chu tac dung thng xuyen, lau dai cua ien ap lam viec ma con phai chu tac dung trong mot thi gian ngan hoac rat ngan cua nhng ien ap tang cao ot ngot vt xa kha nang chu ng cua cach ien. o la hien tng qua ien ap trong he thong ien.
QUA IEN AP TRONG HE THONG IEN trnh bay nguon goc, dien bien va thong so cua cac dang qua ien ap cung nh cac bien phap nham ngan nga, han che chung e bao ve cho cach ien cua cac trang thiet b ien.
QUA IEN AP TRONG HE THONG IEN c bien soan tren c s cua cuon sach Qua ien ap trong he thong ien dung giang day cho sinh vien nhieu khoa cua nganh He thong ien va c chnh sa, bo sung cap nhat thng xuyen.
Tuy nhien hien tng qua ien ap, ac biet la qua ien ap noi bo rat a dang va phc tap, ma thi lng cho phep oi vi mon hoc co gii han, nen tap sach nay cha the e cap ay u moi dang qua ien ap ma ch neu mot vai dang tieu bieu ien hnh.
Tac gia hoan nghenh va xin chan thanh cam n moi gop y quy bau cua oc gia.
Moi gop y xin gi ve: Bo mon He thong ien Khoa ien - ien t, Trng ai hoc Bach khoa - ai hoc Quoc gia TPHCM. ien thoai: 8 651 821.
TS. Hoang Viet
7
Chng 1
SET - NGUON GOC CUA QUA IEN AP KH QUYEN
1.1 CAC GIAI OAN PHAT TRIEN CUA PHONG IEN SET Set thc chat la mot dang phong ien tia la trong khong kh vi khoang
cach rat ln. Chieu dai trung bnh cua khe set khoang 35 km, phan ln chieu dai o phat trien trong cac am may dong. Qua trnh phong ien cua set tng t nh qua trnh phong ien tia la trong ien trng rat khong ong nhat vi khoang cach phong ien ln. Chnh s tng t o a cho phep mo phong set trong phong th nghiem e nghien cu nhng qui luat cua no va nghien cu nhng bien phap bao ve chong set.
Hien nhien, set khac vi phong ien trong khong kh tien hanh trong phong th nghiem khong ch qui mo ma con ac iem rieng biet cua nguon ien ap cua no tc la nhng am may dong tch ien.
Thc te, s hnh thanh cac cn dong luon luon gan lien vi s xuat hien cua nhng luong khong kh nong am khong lo t mat at boc len. Cac luong khong kh nay c tao thanh hoac do s ot nong mat at bi anh nang mat tri, ac biet cac vung cao (dong nhiet) hoac do s gap nhau cua nhng luong khong kh nong am vi khong kh lanh nang (dong front), luong khong kh nong am b ay len tren. cac vung oi nui cao, cac luong khong kh nong am trn theo sn nui len cao o la dong a hnh. Sau khi a at c mot o cao nhat nh (khoang vai km tr len), luong khong kh nong am nay i vao vung nhiet o am, b lanh i, hi nc ngng tu lai thanh nhng giot nc li ti hoac thanh cac tinh the bang. Chung tao thanh cac am may dong (H.1.1), con c goi la may tch vu (Cumuloninbus).
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Hnh 1.1 S phan bo ien tch trong mot am may dong
T lau, ngi ta a khang nh ve nguon tao ra ien trng khong lo gia cac may dong va mat at chnh la nhng ien tch tch tu tren cac hat nc li ti va cac tinh the bang cua cac am may dong o. Nhng do au co s nhiem ien cua cac hat nc va tinh the bang cung nh s phan li cac ien tch th co nhieu gia thuyet khac nhau va cha c hoan toan nhat tr (trong pham vi cuon sach nay se khong i sau vao cac gia thuyet o). V du, co gia thuyet cho rang, di tac dung cua ien trng cua qua at (qua at mang mot ien tch am khoang 5,410+5C), cac hat nc b phan cc, au di nhan ien tch dng va au tren nhan ien tch am (H.1.2).
Cac giot nc ln, do trong lng cua no ri xuong gap cac ion t do (gan mat at co khoang 600 oi ion trong mot cm3 khong kh, cang len cao mat o ion cang cao) bay cham hn trong khong kh, hap thu cac ion am bang au dng cua no pha trc va ay cac ion dng t do ra xa. Ket qua la giot nc mang ien tch am tha.
Cac giot nc be a phan cc, th b cac luong khong kh ay len pha tren hap thu cac ion dng bang au am cua mnh, ay ion am t do ra xa va do o mang ien tch dng tha. Nh vay theo gia thuyet nay, phan di cua cac am may dong mang ien tch am, phu hp vi thc te la phan ln cac phong ien set xuong at (8090%) co cc tnh am. Nhng gia thuyet nay van
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cha giai thch c mot thc te, la hn mot na the tch cua am may khong phai c tao thanh t cac giot nc ma t cac tinh the bang va bong tuyet ma hnh dang va cau tao cua chung lam cho chung kho co the b phan cc bi ien trng cua qua at.
Tom lai, cac gia thuyet cho en nay eu cha giai thch c mot cach triet e ve nguon ien tch cua cac am may dong va s phan li chung, khien ngi ta ngh rang trong thc te co the co nhieu nguyen nhan ong thi tac ong va rat phc tap.
Nhng co ieu chac chan la trong suot cn dong, cac ien tch dng va ien tch am b cac luong khong kh manh liet tach ri nhau, gan lien vi s phan bo cac tinh the bang tuyet tren tang nh va cac giot nc ma tang ay cua am may dong. S tach ri ien tch nay tuy thuoc vao o cao cua am may, nam trong khoang t 20010.000m, vi tam cua chung cach nhau c khoang t 3005000m. Lng ien tch trong cac am may tham gia vao cn set vao khoang t 1100C va co the cao hn. ien the cua cac am may dong vao khoang 107108V. Nang lng toa ra bi mot cn set khoang 250kWh.
Ket qua quan trac cho thay phan di cua cac am may dong chu yeu cha ien tch am, do o cam ng tren mat at nhng ien tch dng tng ng va tao nen mot tu ien khong kh khong lo. Cng o ien trng trung bnh ni ong nhat thng t khi qua 1kV/cm, nhng ca biet ni mat o ien tch cao, hoac ni co vat dan ien tot nho len cao tren mat at ien trng cuc bo co the cao hn nhieu va co the at en ngng ion hoa khong kh ( mat at tr so nay 2530kV/cm va cang len cao cang giam, o cao mot vai km giam con khoang 10kV/cm) se gay ion hoa khong kh tao thanh dong plasma, m au cho qua trnh phong ien set phat trien gia may dong va mat at.
Qua trnh phong ien set nay gom co ba giai oan chu yeu:
1- Thoat tien xuat phat t may dong mot dai sang m keo dai tng t gian oan ve pha mat at vi toc o trung bnh khoang 105106 m/s. ay la giai oan phong ien tien ao tng t c goi la tien ao bac (stepped leader). Kenh tien ao la mot dong plasma mat o ien tch khong cao lam, khoang 10131014 ion/m3. Mot phan ien tch am cua may dong tran vao kenh va phan bo tng oi eu doc theo chieu dai cua no (H.1.3a).
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Hnh 1.3 Cac giai oan phong ien set va bien thien cua dong ien set theo thi gian
a) Giai oan phong ien tien ao (1) b) Tia tien ao en gan mat at, hnh thanh khu vc ion hoa manh liet (2) c) Giai oan phong ien ngc hay phong ien chu yeu (3) d) Phong ien chu yeu ket thuc, dong set at gia tr cc ai (4)
Thi gian phat trien cua tia tien ao moi t keo dai trung bnh khoang 1s, tng ng tia tien ao dai them trung bnh c khoang vai chuc met en bon nam chuc met. Thi gian tam ngng phat trien gia hai t lien tiep khoang 3090s.
ien tch am t may tran vao kenh tien ao bang Q = l vi l la chieu dai kenh. ien tch nay thng chiem khoang 10% lng ien tch chay vao at trong mot lan phong ien set. Di tac dung cua ien trng tao nen bi ien tch am cua may dong va ien tch am trong kenh tien ao, se co s tap trung ien tch cam ng trai dau (ien tch dng) tren vung mat at pha di am may dong. Neu vung at pha di co ien dan ong nhat th ni ien tch tap trung se nam trc tiep di kenh tien ao. Neu vung at pha di co ien dan khac nhau th ien tch cam ng se tap trung chu yeu vung ke can, ni co ien dan cao nh vung quang kim loai, vung at am, ao ho, song ngoi, vung nc ngam, ket cau kim loai cac nha cao tang, cot ien, cay cao b t trong ma... va ni o thng la ni o bo cua set.
Cng o ien trng au kenh tien ao trong phan ln giai oan phat trien cua no (trong may dong), c xac nh bi ien tch ban than cua kenh
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va cua ien tch tch tu am may. ng i cua kenh trong giai oan nay khong phu thuoc vao tnh trang cua mat at va cac vat the mat at, phng co cng o ien trng cao nhat phu thuoc vao nhieu nhan to ngau nhien phc tap. Ch khi kenh tien ao con cach mat at mot o cao nao o (o cao nh hng), th mi thay ro dan anh hng cua s tap trung ien tch mat at va cac vat dan nho khoi mat at oi vi hng phat trien tiep tuc cua kenh. Kenh se phat trien theo hng co cng o ien trng ln nhat. Nh vay, v tr o bo cua set mang tnh chon loc. Trong ky thuat, ngi ta a li dung tnh chon loc o e bao ve chong set anh thang cho cac cong trnh, bang cach dung cac thanh hoac day thu set bang kim loai c noi at tot, at cao hn cong trnh can bao ve e hng set phong vao o, han che kha nang set anh vao cong trnh.
nhng vat dan co o cao ln nh cac nha choc tri, cot ien ng day cao ap, cot anten cac ai thu phat thanh, truyen hnh, bu ien... th t nh cua no, ni ien tch trai dau tap trung nhieu lam cho cng o trng cuc bo tang cao cung se ong thi xuat hien ion hoa khong kh, tao nen dong tien ao phat trien hng len am may dong. Chieu dai cua kenh tien ao t di len nay tang theo o cao cua vat dan, co the at en o cao mot vai tram met va tao ieu kien de dang cho s nh hng cua set vao vat dan o. Qua trnh nay thng c goi la qua trnh phong ien on set. Nhng au thu set the he mi xuat hien vao nhng nam cua thap ky 80 va 90 the ky chnh la a ng dung hieu ng nay e tang kha nang on bat kenh tien ao t tren may dong xuong, han che xac suat set anh vao cong trnh c bao ve.
2- Giai oan phong ien chnh (hay phong ien ngc). Khi kenh tien ao xuat phat t may dong tiep can mat at (thi gian vao khoang 20ms) hoac tiep can kenh tien ao ngc chieu, th bat au giai oan phong ien ngc hay phong ien chnh, tng t nh cac qua trnh phong ien ngc trong chat kh ien trng khong ong nhat (H.1.3.b). Trong khoang cach kh con lai gia au kenh tien ao va mat at (hoac gia hai au kenh tien ao ngc chieu) cng o ien trng tang cao gay nen ion hoa manh liet khong kh, dan en s hnh thanh mot dong plasma mi, co mat o ien tch cao hn nhieu so vi mat o ien tch cua kenh tien ao 16 19 310 10 /( )ion m , ien dan cua no tang len hang tram, hang ngan lan, ien tch cam ng t mat at tran vao dong ngc nay trung hoa ien tch am cua kenh tien ao trc ay va thc te au dong mang ien the cua at, lam cho cng o ien trng khu vc tiep giap cua hai dong plasma ngc chieu nhau tang len gay ion hoa manh liet khong kh
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khu vc nay va nh vay au dong plasma ien dan cao tiep tuc phat trien ngc len tren theo ng a c don san bi kenh tien ao. Toc o cua kenh phong ien ngc vao khoang 7 81 5 10 1 5 19 /, , m s (bang 0,05 0,5 toc o anh sang) tc la nhanh gap tren tram lan toc o phat trien cua dong tien ao (H.1.3c). V mat o ien tch cao ot nong manh liet nen kenh phong ien chnh sang choi chang (o chnh la tia chp). Nhiet o trong kenh phong ien co the en vai ba chuc ngan oC, (gap vai ba lan nhiet o tren be mat mat tri). Va s dan n ot ngot cua khong kh bao quanh kenh phong ien chnh tao nen nhng t song am manh liet, gay nen nhng tieng no chat chua (o la tieng sam) va tieng ren am keo dai. ac iem quan trong nhat cua phong ien chnh la cng o dong ln. Neu v la toc o cua phong ien chu yeu va la mat o ng cua ien tch th dong ien set se at gia tr cao nhat khi kenh phong ien chnh len en am may dong va bang sI v.= (H.1.3d). o chnh la dong ngan mach khoang cach kh gia may-at, co tr so t vai kA en tren vai tram kA.
3- Giai oan ket thuc c anh dau khi kenh phong ien chnh len ti am may, ien tch cam ng t mat at theo len, tran vao va trung hoa vi ien tch am cua am may, mot phan nho cua so ien tch con lai cua may se theo kenh phong ien chay xuong at va cung tao nen cho set anh mot dong ien co tr so giam dan tng ng phan uoi song cua xung dong set. S toa sang m dan. Trong 50% cac trng hp, s thao ien tch xuong at nay tao nen mot dong khong oi khoang 100A, keo dai co the en 0,1s. Do thi gian keo dai nh vay nen hieu ng nhiet do no gay nen cung khong kem phan nguy hiem cho cac cong trnh b set anh.
Ket qua quan trac set cho thay rang, mot cn set thng gom nhieu lan phong ien ke tiep nhau, trung bnh la ba lan, nhieu nhat co the en vai ba chuc lan. Thi gian gia cac lan phong ien ke tiep nhau trung bnh khoang 3050ms, nhng co the keo dai en 0,1s neu co dong khong oi trong giai oan ket thuc. Cac lan phong ien sau co dong tien ao phat trien lien tuc (khong phai tng t nh lan au), khong phan nhanh va theo ung qu ao cua lan au nhng vi toc o cao hn 62.10 /( )m s , thng goi la tien ao hnh kim (needle leader) cung con co ten goi la tien ao hnh mui ten (dart leader). Moi lan phong ien tao nen mot xung dong set. Cac xung set sau thng co bien o be hn, nhng o doc au song cao hn nhieu so vi xung au tien. Mot cn set co the keo dai en 1,33s.
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1- Giai oan tien ao; 2- Giai oan phong ien chu yeu;
3- Giai oan sau phong ien - sang m; 4- Tia tien ao hnh mui ten hoac hnh kim; 5- Giai oan tien ao cua cac cu set ke tuc; 6- Dong ien tien ao;
7- Dong ien chu yeu; 8- Dong ien trong giai oan sang m
Hnh 1.4 Qua trnh phat trien cua phong ien set
S phong ien nhieu lan cua set c giai thch nh sau: am may dong co the co nhieu trung tam ien tch khac nhau, hnh thanh do cac dong khong kh xoay trong may. Lan phong ien au tien, d nhien se xay ra gia at va trung tam ien tch co cng o ien trng cao nhat.
Trong giai oan phong ien tien ao th hieu the cua trung tam ien tch nay vi cac trung tam ien tch khac ke can thc te khong thay oi ang ke va t co anh hng qua lai gia chung. Nhng khi kenh phong ien chu yeu a len en may th trung tam ien tch au tien cua am may thc te mang ien the cua at lam cho hieu the gia trung tam ien tch a phong vi cac trung tam ien tch lan can tang len va co the dan en phong ien gia chung vi nhau. Qua trnh nay xay ra rat nhanh. Trong khi o th kenh phong ien cu van con mot ien dan nhat nh do s kh ion cha hoan toan, nen phong ien tien ao lan sau theo ung qu ao o, lien tuc va vi toc o cao hn lan au. Phong ien set cung co the xay ra gia cac am may mang ien tch khac nhau hoac gia cac trung tam ien tch cua mot am may lng cc, tuy nhien qua ien ap trong he thong ien, hoa hoan hoac h hong cac cong trnh tren mat at ch xay ra khi co phong ien set ve pha mat at. V vay, ay ch xet en set gia may dong va mat at cung tac hai cua no oi vi he thong ien. Set may - at cung co the xay ra vi tien ao mang ien tch dng xuat phat t phan mang ien tch dng cua am may, nhng rat hiem thay. Loai set dng nay ch co mot xung duy nhat, co bien o dong va tong ien tch rat ln, thi gian song keo dai. Tac dung pha hoai cua no rat ln, ac biet la hieu
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ng nhiet cua no.
1.2 CAC THAM SO CHU YEU CUA SET - CNG O HOAT ONG CUA SET Dong ien set nh hnh 1.5, co
dang mot song xung. Trung bnh trong khoang vai ba micro giay, dong ien tang nhanh en tr so cc ai tao nen phan au song va sau o giam xuong cham cham trong khoang
20 100 s , tao nen phan uoi song.
S lan truyen song ien t tao nen bi dong ien set gay nen qua ien ap trong he thong ien, do o can phai biet nhng tham so chu yeu cua no.
- Bien o dong ien set vi xac suat xuat hien cua no. - o doc au song dong ien set hoac thi gian au song s vi xac suat
xuat hien cua no. - o dai song dong ien set s (tc thi gian cho en khi dong set giam
con bang 1/2 bien o cua no). - Cc tnh dong ien set.
Ngoai ra, phai biet cng o hoat ong trung bnh cua set tc la so ngay co dong set trung bnh hoac tong so gi co dong set trung bnh trong mot nam moi khu vc lanh tho va mat o trung bnh cua set trong khu vc o, tc la so lan set anh vao mot n v dien tch mat at (1km2) trong mot ngay set. nhieu nc phat trien a xay dng c ban o phan vung hoat ong cua set.
1.2.1 Bien o dong ien set va xac suat xuat hien cua no Dong ien set co tr so ln nhat vao luc kenh phong ien chnh len en
trung tam ien tch cua am may dong. Neu ni (vat) b set anh co noi at tot, ien tr noi at khong ang ke, th tr so ln nhat cua dong ien set, nh a trnh bay tren, bang .si v= . Nhng neu ien tr noi at cua vat b set
anh co mot tr so R nao o th dong ien set qua vat o se giam theo quan he:
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. oso
zi v
z R=
+
vi zo la tong tr song cua khe set, co tr so trong khoang 200 500 , trung bnh 300 . Nh vay, neu ien tr noi at R thay oi t 0 30 th dong ien qua
vat b set anh ch giam khoang 10%. ien tr noi at cua cot va day thu set trong he thong ien thng t khi qua 20 30 , nen trong tnh toan co the lay gan ung tr so cc ai cua dong ien set .si v= .
Hnh 1.6 Thiet b xac nh bien o dong ien set
e o bien o dong ien set t lau ngi ta dung rong rai trong he thong ien thiet b ghi t. o la nhng thanh hnh tru bang bot sat t tron vi keo cach ien ep lai. Thanh c gan vao cot thu set hay cot ien, song song vi ng sc cua t trng dong ien set chay qua cot khi b set anh.
Nh lam bang vat lieu sat t nen thanh duy tr mot o t d ln. Cuoi mua set ngi ta thao thiet b ghi t, o lng t d va xac nh c dong ien set ln nhat a chay qua cot. o chnh xac cua thiet b t nay khong cao nhng nhc iem nay c bu lai bi so lng rat ln thiet b at trong he thong ien (en hang chuc ngan chiec).
Ket qua o ac trong nhieu nam nhieu ni cho thay bien o dong ien set bien thien trong pham vi rat rong, t vai kA en tren vai tram kA, nhng phan ln thng di 50kA va rat hiem khi vt qua 100kA.
Trong tnh toan chong set co the dung qui luat phan bo xac suat bien o dong ien set gan ung sau, cho vung ong bang:
16
/ /26 6010s ss
i iiv e
= =
tc: 26
lns
si
iv = hay
60lg
s
si
iv = (1.1)
vi siv la xac suat xuat hien dong ien set co bien o bang hoac ln hn is.
V du: xac suat phong ien set co bien o dong ien set 60si kA
bang:
60 160
lgsiv = = ; 0 1 10, %
siv = =
Co ngha la trong tong so lan set anh ch co 10% so lan set co bien o dong ien set t 60 kA tr len. Dong ien set co bien o t 100 kA tr len thng rat hiem xay ra, nen ch phai dung en khi thiet ke chong set cho nhng tram phan phoi vo cung quan trong.
Hnh 1.7 Xac suat phan bo dong set co bien o bang va ln hn is
nhng vung oi nui, bien o dong ien set thng be hn so vi nhng vung ong bang khoang vai lan, do khoang cach t at len cac am may dong ngan hn nen phong ien set a co the xay ra, ngay khi mat o ien tch cua cac am may con be hn. Noi mot cach khac, ay, xac suat xuat hien dong ien set co bien o ln thap hn
3010s
s
i
iv
= hay 30
lgs
si
iv = (1.2)
17
1.2.2 o doc au song dong ien set va xac suat xuat hien cua no
Viec xac nh bang thc nghiem o doc au song hoac o dai au song dong ien set kho khan hn nhieu, v vay lng so lieu thc nghiem ve nhng thong so nay tng oi t.
e o o doc dong ien set, ngi ta thng dung mot khung bang day dan treo canh cot thu set. Cac au day cua khung noi vao mot hoa ien ke e o bien o cua ien ap (xem Ky thuat ien cao ap, tap 1, chng 4 trang 133 - 134).
Khi set anh vao cot thu set vi o
doc dong ien set sdi
adt
= th trong
khung se cam ng nen mot sc ien
ong bang sdi
Mdt
vi M la he so ho cam
gia day dan dong ien set cua cot thu set vi khung.
Hoa ien ke ghi c bien o ien
ap gia cac au ra cua khung: max( )sdiu Mdt
=
Biet c u co the xac nh c o doc ln nhat cua song dong ien set a chay qua cot:
max max( ) ,sdia kA sdt
= /
o doc au song dong ien set cung thay oi trong mot pham vi rong va cung c cho di dang ng cong xac suat. Thng dung ng cong thc nghiem sau.
Cho vung ong bang: 15 7 3610/ , /a aav e
= = (1.3)
hay 15 7 36
ln ; lg,a aa a
v v= =
trong o va la xac suat xuat hien dong ien set co o doc au song dong ien bang va ln hn a.
18
nhng vung nui cao, xac suat xuat hien dong ien set co cung o doc au song thng thap hn va co the xac nh theo:
18 /7,8210 /a aav e
= = (1.4)
Ket qua o ac cho thay phan ln song dong ien set co thi gian au song t 1 10s s = thng gap la t 1 4 s va o dai song trong khoang
20 100s s = . Trong tnh toan thiet ke thng lay thi gian au song 1 2,s s = va o dai song trung bnh la 50 s tng ng vi dang song
chuan (song 1,2/50).
Hnh 1.9 ng cong xac suat o doc au song dong set
Ve quan he gia o doc au song va bien o dong ien set, cho en nay vi nhng so lieu o c, ngi ta van cha tm thay co mot quan he toan hoc ro rang, chat che. Co khuynh hng tuy khong ro rang, la o doc au song tang khi bien o dong ien set tang. Trong tnh toan khi ong thi phai xet anh hng cua ca o doc au song va bien o, ngi ta coi chung nh la nhng ai lng ngau nhien oc lap va dung xac suat phoi hp:
- oi vi vung ong bang:
60 36lg ( , ) ( )ss
i av i a = + (1.5)
hay 26 15 7
ln ( , ) ( ),
ss
i av i a = +
- oi vi vung oi nui cao:
19
30 18lg ( , ) ( )ss
i av i a = + (1.6)
g ien tch tan vao at trong thi gian phong ien set nhieu lan thay oi trong pham vi t 0,1C100C va co the ln hn, tr so trung bnh vao khoang 20C. Chnh lng ien tch tan vao at trong thi gian phong ien set nay ong mot vai tro ang ke trong s duy tr ien tch am cua qua at.
g Ve dang tnh toan dong ien set, tuy tng trng hp cu the co the dung cac dang n gian hoa nh sau:
Hnh 1.10 Cac dang song tnh toan dong ien set
a) Dang song hnh thang si at= (H.1.10a) dung khi qua trnh can xet
chu anh hng chu yeu cua phan au song, con s giam dong ien sau tr so cc ai theo qui luat nay hay qui luat kia khong co anh hng ang ke en qua trnh. V du nh khi xet qua trnh song trong cuon day may bien ap.
b) Dang ham mu /t Ts si I e
= (H.1.10b) dung khi tnh toan cac qua trnh
phat trien cham, nh khi tnh hieu ng nhiet cua dong ien set, trong o s tang dong ien au song theo qui luat nay hay qui luat kia thc te khong co anh hng nhieu en ket qua.
T la hang so thi gian cua s giam dong ien: 0 7,sT
=
vi s la thi gian toan song (tc la thi gian tnh en khi dong ien giam con
bang mot na bien o).
1.2.3 Cng o hoat ong cua set - mat o set
Cng o hoat ong cua set c bieu th bang so ngay trung bnh co
20
dong set hang nam hoac bang tong so gi trung bnh co dong set hang nam.
Cng o hoat ong cua set rat khac nhau cac vung kh hau khac nhau. Khuynh hng chung la cng o hoat ong cua set tang dan t cac mien a cc en mien nhiet i xch ao, ni co o am khong kh va nhiet o cao hn, tao ieu kien de dang cho s hnh thanh may dong.
Theo so lieu thong ke cua nhieu nc, so ngay set hang nam cac vung nam, bac cc vao khoang 23, vung on i khoang 3050, vung nhiet i khoang 75100 va vung xch ao khoang 100150.
Tuy nhien, khuynh hng tren cung khong phai la tuyet oi. Thc te ngay trong cung mot mien kh hau, cng o hoat ong cua set cung co the khac nhau nhieu, do cac ieu kien kh tng thuy van a chat cua tng khu vc tieu kh hau thay oi phc tap.
Tren toan bo be mat qua at trong moi giay xay ra khoang 100 lan phong ien set, tc moi ngay co khoang 89 trieu lan set anh xuong mat at.
- Mat o cua set la so lan set anh trung bnh tren mot n v dien tch mat at 21( )km trong mot ngay set hoac trong mot gi set. So lieu nay cung thay oi theo vung lanh tho.
1.2.4 Cc tnh cua set
So lieu quan trac set nhieu nc trong nhieu nam cho thay, song dong ien set mang cc tnh am xuat hien thng xuyen hn va chiem khoang 8090% toan bo so lan phong ien set.
1.3. TNH HNH DONG SET VIET NAM Theo tai lieu tham khao [12] Viet Nam la mot nc thuoc vung kh hau
nhiet i nong am, ma nhieu, cng o hoat ong cua dong set rat manh. Thc te set a gay nhieu tac hai en i song con ngi, gay h hong thiet b, cong trnh. La mot trong nhng tac nhan gay s co trong van hanh he thong ien va hoat ong cua nhieu nganh khac.
cac vung lanh tho vi ieu kien kh hau, thi tiet va a hnh khac nhau th ac iem ve hoat ong dong set khac nhau, mat khac, ieu kien trang b ky thuat khac nhau th mc o thiet hai do set gay ra cung khac nhau. V vay, ngoai viec tiep nhan cac ket qua nghien cu cua the gii, moi nc can phai t tien hanh ieu tra, nghien cu ve ac tnh hoat ong dong set va cac thong so phong ien set tren lanh tho cua mnh e t o e ra nhng bien
21
phap phong, chong set thch hp, hieu qua.
Viet Nam van e nghien cu set a c at ra t lau nhng no ch thc s c trien khai co hieu qua sau khi xay dng xong tram nghien cu set (Gia Sang - Thai Nguyen (1987) vi nhieu trang thiet b kha ong bo e tien hanh nghien cu tong hp ve set.
1.3.1. ac iem va phan bo dong tren lanh tho Viet Nam
1. Phan hoa mua cua dong
Dong co kha nang xuat hien hau nh quanh nam cac vung, song thi ky tap trung nhat la vao mua ma. Cung co the goi o la mua dong. T ket qua thong ke cua hn 100 tram nghien cu set, co the rut ra mot so nhan xet sau:
- phan pha ong Hoang Lien Sn, dong phat trien manh t thang 4, cc ai vao thang 7 hoac thang 8 vi so ngay dong trung bnh moi thang len ti tren 10 ngay, sau o giam nhanh, ti thang 10, so ngay co dong ch con 2-3 ngay. Cac thang mua dong so ngay dong xuat hien khong ang ke.
- Tay Bac, mua dong en sm hn, cc ai hang nam cung xay ra sm hn. Thang 3, dong a phat trien kha manh, trung bnh 4-6 ngay vi khoang 20-25 gi co dong. So ngay co dong cc ai vao thang 4 en thang V vi khoang 11-15 ngay va 40-70 gi dong. Mua ong co the coi la bat au t thang 3 en thang 9. Ba thang t dong nhat la 6, 7, 1.
- Ven bien Trung Bo, bien trnh nam cua dong co en 2 cc ai. Cc ai chnh ri vao thang 7-9 va cc ai th 2 ri vao thang 5 nhng tr so chenh nhau ch khoang 0,5-1 ngay. Cac thang 6, 7 so ngay dong giam ang ke ch con khoang 2-3 ngay vi so gi dong 3-6 gi. Mua dong keo dai 7 thang t thang 6 en thang 10), cac thang mua ong kha nang xuat hien dong rat nho.
Bang 1.1: So ngay co dong tai mot so tram tieu bieu (trung bnh thang va nam)
Thang Tram
1 2 3 4 5 6 7 8 9 10 11 12 Nam
Sn La 0.6 1.9 4.2 11.2 11.3 11.2 10.0 9.6 6.3 2.2 0.5 0.1 69.2
H.Giang 0.1 0.8 3.1 7.5 9.4 11.7 14.5 12.7 6.3 1.9 0.6 0.0 68.6
T.Nguyen 0.2 1.0 2.3 6.0 9.2 10.8 11.3 11.5 6.3 2.6 0.3 0.1 61.6
Ha Noi 0.2 0.6 1.6 5.9 9.0 8.8 9.8 8.8 5.4 1.9 0.4 0 52.4
Vinh 0.1 0.7 2.5 5.0 6.5 3.8 3.3 6.1 5.9 3.4 0.4 0.1 37.8
a Nang 0 0.2 0.7 3.1 3.8 3.1 3.5 2.6 3.9 3.0 0.5 0 21.4
22
Quy Nhn 0 0 0 1.0 3.4 2.9 2.1 2.2 4.7 2.2 0.7 0 19.2
Nha Trang 0 0 0 0.5 2.1 1.9 1.1 1.5 3.1 1.7 1.1 0 13.0
T.S.Nhat 0 0.3 0.2 2.0 11.0 8.0 13.0 9.0 9.0 8.0 6.0 1.0 67.5
Can Th 0.1 0.2 0.8 4.2 9.2 5.6 5.8 5.2 8.5 7.8 3.5 0.2 51.1
Rach Gia 0.3 0.4 1.8 7.5 13.6 7.8 7.5 7.0 10 9.8 6.9 1.2 73.8
Trng Sa 0.2 0.2 0.2 1.2 2.8 2.1 2.1 2.5 2.5 1.8 1.7 1.2 18.5 Hoang Sa 0 0 0.1 0.3 0.5 0.8 0.3 1.1 1.0 0.2 0.1 0 4.4
Khu vc Tay Nguyen, cung vi bien trnh 2 nh nhng cc ai chnh ri vao thi ky au, tap trung vao thang 5. Cc ai th 2 ri vao thang 9. Thi ky gia 2 cc ai, thang 6-8, so ngay dong giam i tren 50% so vi thang 5 va 9.
Mua ong keo dai t thang 4 en thang 10, cac thang mua ong kha nang xuat hien dong cung rat nho.
Vao Nam Bo, bien trnh nam cua dong co net tng t nh Tay Nguyen. Cc ai chnh cung ri vao thang 5, cc ai th 2 ri vao thang 9, nhng sau thang 9 dong van con phat trien manh, ti tan thang 9 so ngay co dong van xap x thang 4. Ch mai ti thang 12 tr so nay mi giam han xuong, khac vi Tay Nguyen. Mua ong keo dai t thang 4 en thang 10.
2. Tan suat xuat hien dong trong ngay
Da tren nguon so lieu khai thac chi tiet ve thi gian co dong tai tram trong 10 nam (1981-1990) mot so iem tieu bieu (Bang 1.2) va bieu o bien trnh ngay tan suat co dong (H.1.11) ta co the i en mot so nhan xet:
Bang 1.2 Thi gian co dong trung bnh (gi)
Thang Tram
Mua ong Mua he Nam
9 12 1 6 77 8
Sn La 0.650 0 2.525 34.17 35.70 32.72 224.9
Ha Giang 4.525 0 0.425 43.80 60.23 43.35 262.0
Thai Nguyen
1.675 0 0.175 26.13 38.00 31.70 187.9
Ha Noi 2.225 0 0.500 27.77 28.66 24.85 154.0
Vinh 1.250 0 0.050 4.43 5.45 7.88 57.1
a Nang 0.700 0 0 4.35 2.85 2.55 31.8 Nha Trang 1.250 0 0 2.93 0.38 1.13 15.3
B.M.Thuot 4.500 0 0 5.30 5.38 2.20 45.1
23
- tat ca cac vung, hang ngay dong phat trien chu yeu vao thi gian buoi chieu va toi, sau 13 gi. Thi gian t co kha nang xuat hien dong nhat ri vao buoi sang (5-10 gi).
- Bien trnh xuat hien dong hang ngay tren cac khu vc cung co nhng net rieng. na phan pha Bac, sau 24 gi kha nang xuat hien dong con kha ln, trong khi o cac khu vc pha Nam tr so nay nho hn ro ret.
- Thi gian co kha nang xuat hien dong ln nhat trong ngay thng ri vao khoang 18-20 gi. Tuy nhien, cung co ni sm hn nh a Nang 15-16 gi...
- cac khu vc sau trong noi a, tan suat toi a trong moi khoang gi ti 15-16% trong khi cac khu vc ven bien t dong ch khoang 3-5%.
Hnh 1.11 Bien trnh ngay tan suat co dong
Ngoai ra, so ngay co dong hang nam bien oi kha ln t nam nay qua nam khac. Nam co so ngay dong cc ai gap 4-5 lan nam co so ngay dong cc tieu.
1.3.2. Phan vung mat o set Viet Nam
T cac nguon so lieu khac nhau ve ngay dong, gi dong, so lan set anh xuong cac khu vc, ngay gi xuat hien va ket thuc dong hang nam, qua x ly, tnh toan a phan ra c 5 vung ac trng ve cng o hoat ong dong set tren toan
24
bo lanh tho Viet Nam, bao gom:
1. Khu vc ong bang ven bien mien Bac (khu vc A).
2. Khu vc mien nui trung du mien Bac (khu vc B).
3. Khu vc mien nui trung du mien Trung (khu vc C).
4. Khu vc ven bien mien Trung (khu vc D).
5. Khu vc ong bang mien Nam (khu vc E).
Bang 1.3 Cng o hoat ong dong set tai cac khu vc Khu vc Ngay dong TB
(ngay/nam) Gi dong TB
(gi/nam) Mat o set TB
(lan/km2.nam)
Thang dong cc ai
A 51.1 219.1 6.47 VIII
B 61.6 215.6 6.33 VII
C 47.6 95.2 3.31 V va VIII D 44.0 89.32 3.55 V va VIII
E 60.1 126.21 5.37 V va IX
Xuat phat t cac so lieu ve ngay gi dong trong nam oi vi 5 khu vc lanh tho Viet Nam, co the tnh toan a ra cac gia tr d kien ve mat o phong ien xuong at cho cac khu vc nh sau:
Bang 1.4 Tr so d kien mat o set theo khu vc:
So ngay dong
Khu vc A Khu vc B Khu vc C Khu vc D Khu vc E
20 40 2.43 4.86 2.1 4.2 1.2 2.4 1.22 2.44 1.26 2.52
40 60 4.86 7.29 4.2 6.3 2.4 3.6 2.44 3.65 2.52 3.78
60 80 7.29 9.72 6.3 8.4 3.6 4.8 3.65 4.87 3.78 5.04
80 100 9.72 12.16 8.4 10.5 4.8 6.0 4.87 6.09 5.04 6.3 100 120 12.15 14.58 10.5 12.6 6.0 7.2 6.09 7.31 6.3 7.56
Nhan xet:
- Khu vc ong bang ven bien mien Bac (khu vc A): cng o hoat ong dong set manh nhat. Nhng thang co nhieu dong set t thang 5 en thang 9, cc ai la thang 8. Trung bnh mot ngay set keo dai 4.05 gi.
- Khu vc mien nui trung du mien Bac (khu vc B): la khu vc co cng o hoat ong dong set manh, nhng thang co nhieu dong set t thang 3 en thang 9, manh nhat la cac thang 5, 6, 7, 8, cc ai la thang 7. Khu vc nay co
25
thi gian mua set dai nhat. Trung bnh mot ngay set dai 3,5 gi.
- Khu vc mien nui trung du mien Trung (khu vc C): la khu vc t set hn, bien trnh hoat ong dong set that thng, mua set thng keo dai t thang 2 en thang 9, manh nhat vao thang 5 sau o giam dan roi lai tang manh dan vao thang 8, thang 9. Bien trnh dong co 2 nh vao thang 5 va thang 8. Gi dong trung bnh trong ngay dong cua khu vc la 2 gi.
- Khu vc ven bien mien Trung (khu vc D): la khu vc co ac iem hoat ong dong set gan giong khu vc cao nguyen mien Trung. Tuy nhien mc o hoat ong dong set tang dan vao cuoi mua set. Khu vc nay ve bien trnh dong co 2 cc ai so ngay dong vao cac thang V, thang VIII. Mua set keo dai t thang II en thang XI. Gi dong trung bnh trong mot ngay dong la 2,03 gi.
- Khu vc ong bang mien Nam (khu vc E): la khu vc co so ngay dong ln. Tuy nhien gi dong trong ngay dong thng ngan hn. Mua dong chu yeu tap trung vao thi gian t thang V en thang X. Manh nhat vao thang V sau o giam dan en thang VIII, thang IX lai tang cng tr lai. Thi gian gi dong keo dai trung bnh la 2,1 gi.
1.3.3. Phan bo xac suat bien o va o doc dong set Viet Nam
T cac ket qua o lng cac thong so phong ien set xuong at bang to hp dao ong ky t ong va bang cac bo ghi t tnh co the thay rang:
- Xac suat xuat hien cac cu set co cng o manh tai Viet Nam la tng oi thap.
- 90 97max ,I kA= va 65 8max , /A kA s= (theo dao ong ky t ong).
- ng cong phan bo xac suat bien o va o doc dong set khong co ot bien va nam trong mien tap hp cac ng phan bo tai cac vung khac nhau tren the gii.
Ket luan
Viet Nam la nc nam trong vung kh hau nhiet i am, kh hau nay rat thuan li cho s phat sinh, phat trien cua dong set. Do anh hng cua che o gio mua va a hnh oi nui va ong bang xen ke, nen phan bo dong tren cac vung lanh tho khong eu, cac vung bien va ven bien t dong, ac biet la ven bien Nam Trung Bo.
Cac vung sau trong at lien dong phat trien nhieu hn, mot so khu vc hnh thanh cac trung tam dong, ac biet phan tay bac cua Nam Bo.
26
Hnh 1.12 ng phan bo xac suat bien o dong set.
27
Hnh 1.13 ng phan bo xac suat o doc dong set.
28
Chng 2
QUA TRNH SONG TREN NG DAY TAI IEN
2.1 S TRUYEN SONG IEN T TREN NG DAY KHONG TON HAO Nguon gay nen qua ien ap kh quyen trong he thong ien la phong ien
set gia may dong va mat at.
Cung nh bat c mot kch ong ien t nao vao he thong ien (cac qua trnh ong cat bnh thng, cac trng hp ngan mach, s co...) phong ien set gay nen song ien t, toa ra xung quanh vi toc o rat ln, trong khong kh toc o o tng ng vi toc o anh sang. Song ien t xuat phat t ni set anh truyen doc theo ng day tai ien, gay nen qua ien ap tac dung len cach ien ng day.
Trng hp set anh trc tiep vao day dan cua ng day, th tr so cua qua ien ap tuy thuoc bien o dong set co the en hang trieu, tham ch hang chuc trieu Volt, vt qua nhieu lan mc cach ien xung cua cach ien ng day bat c cap ien ap nao.
Trng hp set anh gan ng day, gay nen qua ien ap cam ng, co bien o tng oi be, cao nhat khoang vai tram ngan volt, nen thc te ch nguy hiem oi vi cach ien ng day cua cac cap ien ap t 35kV tr xuong.
Song qua ien ap xuat hien tren ng day truyen en tram bien ap se tac dung len cach ien cua cac thiet b trong tram. e bao am s lam viec lien tuc cua ng day va s an toan oi vi cac thiet b cua tram, do o can phai co nhng bien phap chong set co hieu qua va thch hp cho ng day
29
tai ien va tram phan phoi.
Hien tng qua ien ap va cac bien phap ngan nga qua ien ap eu co c s tren qua trnh truyen song tren ng day va phu thuoc vao cac s o au day. V vay, trong chng nay trc het can nghien cu qua trnh truyen song o.
Qua trnh truyen song ien t tren ng day ien ap cao bao gi cung kem theo ton hao tren ien tr tac dung ( )or cua mach truyen song (day dan
va at), ton hao dong ien ro tren cach ien ng day va ton hao vang quang ( )og (H.2.0). Tuy nhien, e n gian qua trnh tnh toan trong thc te
thng bo qua nhng ton hao nay, chap nhan nhng li giai gan ung nghieng ve pha an toan. Nh vay, qua trnh truyen song ch con chu s chi phoi cua ien dung Co oi vi at va ien cam Lo (theo n v chieu dai) cua ng day.
Hnh 2.0 S o thay the thong so rai mo ta qua trnh truyen song tren ng day tai ien
He phng trnh vi phan bieu dien qua trnh truyen song tren ng day khong ton hao co dang nh sau:
o
o
u iL
x ti uC
x t
=
=
(2.1)
hay
2 2
2 2
2 2
2 2
o o
o o
u uL C
x t
i iL C
x t
=
=
(2.2)
Vi (2.2) moi phng trnh ch con cha mot bien so u hoac i.
30
Nghiem tong quat cua chung di dang song chay nh sau: ( ) ( )u u u f x vt f x vt+ + = + = + + (2.3)
1 [ ( ) ( )]i i i f x vt f x vtZ
+ + = + = + 1 ( )u u
Z+
= (2.4)
vi: /o oZ L C= - tong tr song cua ng day khong ton hao () 1
o o
cv
L C= =
- toc o truyen song (m/s)
c - toc o anh sang, bang / /83 10 hay 300mm s s , - he so ien moi va he so t tham cua moi trng quanh day dan. oi vi ng day cap, loi cap c boc chu yeu bang giay tam dau co
1 4, = , do o /1502
cv m s = .
oi vi ng day tren khong, moi trng quanh day dan la khong kh co 1 1; = = do o /300v c m s= = Ap va dong gom hai thanh phan xep chong len nhau: - Song ( )u f x vt+ += truyen theo chieu dng cua truc x c goi la song thuan. - Song ( )u f x vt = + truyen theo chieu ngc lai nen c goi la song ngc. Bieu thc (2.3) va (2.4) cho biet ham toa o cua song ap va dong tai mot
thi iem t a cho ( )xtv
: dang song chay.
Cung co the mo ta cac song tren nh la nhng ham thi gian tai mot iem x a cho cua ng day, tc la dang song ng. Song thuan trong trng
hp nay co dang ( )xf tv
+ va song ngc ( )xf t
v + , trong o t la thi gian
tnh t luc bat au qua trnh qua o tai thi iem t = 0. Gia song ap va dong, thuan cung nh ngc co quan he vi nhau theo:
uiZ
++
= va uiZ
=
Can lu y la song ap va song dong ngc luon luon trai dau vi nhau. Trong qua trnh truyen song moi ng day khong ton hao co the ac
trng bi hai thong so: - Hoac ien cam Lo va ien dung Co theo n v chieu dai ng day.
31
- Hoac tong tr song Z va toc o truyen song v.
oi vi ng day tren khong khong ton hao, moi pha co mot day dan th:
/722 10ln ,ddodd
hL H m
r
= (2.5)
29
1 1
22 9 10
,
lno
ddo
dd
C F mhc L
r
= = /
(2.6)
T o 260 ln ,ddoo dd
L hZ
C r= = (2.7)
vi: ddh - o treo cao trung bnh cua day dan so vi mat at, m
rdd - ban knh day dan, m.
Tong tr song Z phu thuoc vao o treo cao va ban knh day dan cua ng day, nhng mc phu thuoc khong nhieu v di dang ham logarit (can lu y la Z khong phu thuoc vao chieu dai cua ng day), thay oi trong khoang t 450550 oi vi ng day co pha khong phan chia, va t 250400 oi vi ng day co pha phan chia.
Tong tr song cua ng day cap, do Co ln va Lo be nen nam trong khoang t 540 tuy theo tiet dien loi, ien ap nh mc va cau tao cua cap (Ucao, cong suat ln Z be do Lo giam, Co tang).
oi vi ng day khong ton hao, toc o truyen song v hau nh khong thay oi oi vi mot moi trng truyen song nhat nh, tc la bang toc o anh sang oi vi ng day tren khong va bang na toc o anh sang oi vi ng day cap.
Cac thong so ac trng cho ng day khong ton hao co quan he vi nhau theo:
1o
o
L v Z
C vZ
=
=
hay /
1o o
o o
Z L C
vL C
=
=
(2.8)
V v a biet oi vi mot loai ng day nhat nh nen e xac nh Z ch can mot phep o duy nhat, hoac ien dung Co hoac ien cam Lo cua ng day. V vay thng dung hai thong so Z va v e ac trng cho ng day khong ton
32
hao.
Trng hp ng day dai vo tan se khong co song ngc, tc song t cuoi ng day tr ve, nh vay ap va dong tai mot iem tren ng day c xac nh duy nhat bi thanh phan song thuan, tc la theo qui luat cua song tac dung t au ng day:
( , ) ( )u x t f x vt+=
1( , ) ( )i x t f x vt
z+
=
2.2 HIEN TNG PHAN XA VA KHUC XA CUA SONG: QUI TAC PETERSEN Gia thiet cac song thuan: u , i+ + truyen theo mot ng day co tong tr
song Z1 en iem A th chuyen sang mot moi trng khac co tong tr song Z2 (H.2.1).
Hnh 2.1 S o truyen song
Biet rang tong tr song bang ty so cua song ap va dong /Z u i= ma 2 1Z Z nh vay song ap va dong truyen sang moi trng Z2 a thay oi, co
ngha la tai iem nut A co hien tng phan xa va khuc xa cua song.
S thay oi cua song ap va dong khi co s thay oi moi trng truyen song phan anh s phan bo lai nang lng ien va t trng cua song trong cac
phan t ien cam va ien dung cua mach 2 21 12 2E M o o
W W W C U L I= + = + .
Neu do s chuyen oi moi trng truyen song, ap tang dong giam (trng hp 2 1Z Z> ) th co ngha la mot phan nang lng t trng a chuyen thanh nang
33
lng ien trng.
Trong trng hp nay, oi vi iem nut A, song thuan c goi la song ti, ky hieu la ,t tu i . Song ngc c goi la song phan xa, ky hieu ,p pu i .
Con song truyen sang moi trng Z2 c goi la khuc xa, ky hieu ,k ku i .
Vi cach ky hieu nay, co the viet lai nghiem cua phng trnh truyen song tren ng day khong ton hao ((2.3) va (2.4)) di dang sau:
k t pu u u= + (2.9)
1
1( )k t p t pi u u i iz
= = + (2.10)
hay 1 k t pz i u u=
T (2.9) va (2.10) suy ra quan he gia song ap va dong khuc xa tai A vi song ti nh sau:
1 2k k tu i z u+ = (2.11)
Bieu thc nay tng ng vi s o thay the gom nguon ien ap bang 2 lan song ti 2 tu cung cap cho hai tong tr song
1 2,z z mac noi tiep nhau (H.2.2). o chnh la s o thay the theo qui tac Petersen, dung e xac nh song ap va dong khuc xa khi moi trng truyen song thay oi.
Trong phng trnh (2.11) neu thay the
2
kk
ui
z= th co the suy ra quan he gia song ap khuc xa va song ap ti nh
sau: 1
2
1 2( )k tz
u uz
+ = hay /
2
1 2 2 1
22
1k t tz
u u uz z z z
= =
+ +
Khi a tnh c song khuc xa th theo (2.9) suy ra c quan he gia song ap phan xa va song ap ti theo:
2 2 12 1 2 1
21( )p k t t t
z z zu u u u u
z z z z
= = =
+ +
Nh vay: 22 1
2ku
t
u z
u z z= =
+ (2.12)
34
2 12 1
pu
t
u z z
u z z
= = +
(2.13)
He so t le kut
u
u = c goi la he so khuc xa cua song ap t 1Z sang 2Z ;
pu
t
u
u = c goi la he so phan xa cua song ap t iem nut A tr ve moi trng z1.
Cung vi phng phap tng t, neu thay 2k ku i z= va 1t tu i z= vao bieu
thc (2.11) se suy ra c quan he gia song dong ti va dong khuc xa nh sau:
12 1 1
1 2
22( )k t k t
zi z z i z i i
z z+ = =
+
Biet c ik, theo bieu thc (2.10) suy ra quan he gia dong phan xa va dong ti.
1 1 2
1 2 1 2
21( )p k t t t
z z zi i i i i
z z z z
= = =
+ +
Cac he so ty le:
1 1 2
1 2 1 2
2va
pki i
t t
ii z z z
i z z i z z
= = = =+ +
(2.14)
c goi la he so khuc xa cua song dong t 1Z sang 2Z va he so phan xa cua song dong t nut A tr ve 1Z . Co the nhan thay de dang quan he gia va
1
1u u
i i
= +
= + (2.15)
va trong moi trng hp luon dng, con co the dng hoac am tuy theo tng quan gia 1 2 va zz .
e biet pham vi bien thien cua va , xet cac trng hp gii han: - Khi 2 0z = , (tc ng day co tong tr song z1 b ngan mach cham at) th 0 1;u u = = tc la ap tai iem nut bang khong do song ap phan xa am toan phan va 2 1,i i = = + tc la dong tai iem nut tang gap oi do song dong phan xa dng toan phan. - Khi 2z = tc ng day co tong tr song z1 b h mach th
35
2 1,u u = = tc la ap tai iem nut tang gap oi do song ap phan xa dng toan phan, con 0 1,i i = = tc la dong tai iem nut bang khong do song dong phan xa am toan phan.
- Khi 2 1z z= th: 1 0
1 0
;
;u u
i i
= =
= =
tc la song truyen qua iem nut lien tuc ma khong co phan xa.
Tom lai, cac he so khuc xa va phan xa bien thien trong pham vi nh sau: 0 2 ; 1 1
Trong trng hp tong quat, z2 co dang so phc, th co the viet qui tac Petersen di dang toan t Laplace tng ng vi s o thay the (H.2.3).
Hnh 2.3 S o thay the theo quy tac Petersen di dang toan t Laplace
1 2( ) ( ) ( )k tku p i p z u p+ =gg g (2.16)
T o, tnh c:
2
2 1
2 ( )( ) ( ) ( ) ( )
( ) t tukz p
u p u p p u pz p z
= = +
g g g (2.17)
2 1
2 1
( )( ) ( ) ( ) ( )
( ) t tupz p z
u p u p p u pz p z
= = +
g g g (2.18)
T nghiem di dang toan t bien oi ve dang goc theo cac qui tac toan
hoc a biet ( ) ( )u p u tg
Mot vai v du ve ng dung qui tac Petersen.
2.2.1 Song truyen en tram noi vi nhieu ng day
Gia thiet co n ng day giong nhau au vao thanh gop cua tram va song truyen vao tram theo mot trong cac ng day o (H.2.4a).
36
Hnh 2.4: Song truyen theo mot trong n ng day vao tram
T s o thay the (H.2.4b) co the suy ra mot cach de dang ien ap tren thanh gop cua tram.
2
21
1
( )
A k t t
z
nu u u uz nzn
= = =
+
(2.19)
T o, co the rut ra vai nhan xet: - Song en mot tram cut (n=1), qua ien ap tren thanh gop co bien o
gap oi song qua ien ap truyen tren ng day: 2k tu u= . o la ieu kien
nang ne nhat oi vi cach ien cua cac thiet b au vao thanh gop cua tram. - Song en mot tram chuyen tiep (n=2), qua ien ap tren thanh gop co bien
o bang tren ng day k tu u= co ngha la song se i ngang qua tram khong
co thay oi g ve bien o. Cach ien cua thiet b cua tram chu mc qua ien ap tng ng qua ien ap tren ng day.
- So ng day au vao thanh gop cua tram cang nhieu (n>2) th ien ap tren thanh gop cua tram cang giam. ieu kien lam viec cua cach ien cua tram cang nhe nhang hn.
o la nhng ieu can lu y trong viec bao ve chong set truyen vao tram.
2.2.2 Trng hp gia hai moi trng truyen song co mac song song mot ien dung hoac noi tiep mot ien cam
o la nhng trng hp thng gap khi thanh gop cua tram co mac song song mot ien dung C (H.2.5a) hoac ng day co song truyen c au vao thanh gop cua tram qua mot cuon ien cam L (H.2.5b).
37
Hnh 2.5
Gia thiet song truyen theo ng day Z1 co dang vuong goc, o dai song vo han: t ou u const= =
Can xac nh ien ap tac dung len thanh gop cua tram. Tren cac s o thay the theo qui tac Petersen, ien ap tren thanh gop cua
tram chnh la ien ap tren tong tr song tng ng Z2 cua tong tr song cua (n1) ng day con lai.
V C va L la nhng phan t phc nen ay co the dung phng phap toan t Laplace e tnh ien ap khuc xa va phan xa.
1- ien ap khuc xa
- oi vi s o co ien dung song song (H.2.5a) phng trnh can bang ien ap co dang:
12
2 2( )c ct c odu u
u C z u udt z
= + + =
11
2
2 2 ct o c cdu z
u u Cz u udt z
= = + +
Bien oi ra dang toan t Laplace:
11
2
2 . . . ( ) ( ) ( )o c c cu z
C z p u p u p u pp z
= + +g g g
38
Suy ra:
1 2
2 1 2
1 21 2
1 2
2 .( )
( ). .
c o
z z
z C z zu p u
z zz zp p
C z z
+
=
+++
g
Bien ve dang goc:
Biet qui tac bien oi ngc ve dang goc cua 1[ ].( )
ata ep p a
+B se
tnh c ien ap tac dung tren ien dung C hay cung chnh la ien ap tren thanh gop:
/o u 1( ) ( ) ( )
Ct Tk cu t u t e
= = (2.20)
trong o:
2
1 2
1 2
1 2
he so khuc xa cua song ap trc tiep t sang 1 2
khi khong chu y en anh hng cua ien dung C
hang so thi gian truyen song qua ien dung C
2
(2.21)
(2.22
:
. .:c
z zz
z z
C z zT
z z
=+
=
+)
- oi vi s o co ien cam noi tiep (H.2.5b) phng trnh can bang ien ap co dang:
1 22 2t odi
u u iz L izdt
= = + +
Bien oi ra dang toan t Laplace:
1 22
( )( )ou
i p z pL zp
= + +g
Suy ra: 1 2
12( ) ou
i pp z z pL
=
+ +
g
ien ap tai iem A (tai thanh gop) bang:
1 2
22
1 21 2
2( ) ( ) ( ).
( )okA
z zz Lu p u p i p z u
z zz zp p
L
+
= = =
+++
gg g
Bien oi ngc ve dang goc, se co ien ap tac dung tren thanh gop: / 1( ) ( )Lt Tk ou t u e
= (2.22)
vi: 21 2
2z
z z =
+ - he so khuc xa cua song ap trc tiep t z1 sang z2
39
khi khong chu y en anh hng cua ien cam L TL - hang so thi gian truyen song qua ien cam L:
1 2L
LT
z z=
+ (2.23)
T (2.20) va (2.22) thay rang trong ca hai trng hp, ien ap tren thanh gop (khuc xa) eu co dang giong nhau, ch khac nhau hang so thi gian T. Neu cha ke en anh hng cua ien dung C va ien cam L, ien ap khuc xa qua thanh gop van gi dang song vuong goc va bien o bang:
2
1 2
2k o o
zu u u
z z= =
+
ien dung C va ien cam L co tac dung lam giam o doc au song khuc xa tng ng vi cac hang so thi gian L va TCT (H.2.6), nhng trng hp song ti dai vo han th chung khong co anh hng en bien o cua song khuc xa.
oi vi tram au vi ng day tren khong th nen dung tu ien au vao thanh gop, con oi vi tram au vi ng day cap th nen dung cuon ien cam v hieu qua giam o doc au song se tot hn.
V du: a) ien dung cua thanh gop va cua cac thiet b au vao thanh gop cua tram thng co tr so trong khoang (15) 310 F . Khi o, oi vi mot tram cut au vi ng day tren khong (z=500) th hang so thi gian:
31 5 10 500 0 5 2 5( ) ( , , )CT s
= = , con oi vi tram cut au vao ng day cap, do ng cap co tong tr song be nen TC be hn hang chuc en hang tram lan. Neu au vao thanh gop mot tu co C = 0,51 F th hang so thi gian TC trng hp tram cut au vi ng day tren khong se tang len en
250 500CT F= con trng hp ng day cap TC ch tang en khoang 10 20 s .
b) ien cam cua cac cuon khang ien au gia ng day va thanh gop tram co tr so thng vao khoang (25) mH. Nh vay oi vi mot tram chuyen tiep (n=2) au vi cac ng day tren khong 1 2 500( )Z Z= = th hang so thi
gian 2 5 500 2 51000
( )LT s
= = . Neu tram au vi cac ng day cap th TL
co the tang len gap tram lan, 100 500LT s=
40
Con oi vi tram cut, tc 2 L th T 0Z = = , cuon ien cam khong co tac dung giam o doc au song khuc xa na.
Hnh 2.7 Tac dung giam bien o song khuc xa oi vi song co o dai song s ngan
ien dung va ien cam co tac dung giam ang ke bien o song khuc xa ch khi o dai song ti s be hn nhieu so vi hang so thi gian T. Trong trng hp nay song ti vi o dai song s co the coi nh xep chong cua hai song o dai vo han cung bien o nhng khac dau va lech nhau mot thi gian s (H.2.7). Va nh vay ien ap khuc xa la tong cua hai thanh phan 'ku cua song dng va ''ku cua song am co o dai song vo han:
'''k k ku u u= +
Bien o cua uk xuat hien thi iem st = bang:
1 v /( )s Tkmax o su U e T
= = tc 1sT
=
nen co the tnh gan ung: 1/s T seT
Do o: oUmaxs
ku T
(2.24)
Nh vay, trong thc te ien dung va ien cam au vao thanh gop cua tram co the giam rat nhieu bien o va o doc cua cac song cat truyen vao tram.
2- ien ap phan xa
Tren ay a noi en tac dung giong nhau cua ien cam va ien dung oi vi song khuc xa. Nhng trong hai trng hp, song phan xa khac nhau nhieu.
g Trng hp s o co ien dung song song: / /1 1( ) ( )t Tc t Tcp k t o o ou u u U e U U e
= = = (2.25)
41
thi iem ban au 0 0 ( )p o tt u U u= = = song phan xa am toan
phan. Nh vay la thi iem ban au, ien dung co tac dung tng ng ngan
mach ng day (H.2.8).
Hnh 2.8 Song phan xa tai thanh gop co au vi ien dung song song
Khi t , up at en tr so on nh bang:
1( ) ( )p o ou U U = = 2 12 1
oz z
Uz z
=
+
Tren ng day song ti 1( )z , khi a co song phan xa tr ve th ien ap bang:
/1 1 ( ) ( ) ( ) ( )Ct T
t p o ou t u t u t U U e
= + = +
1 1/( ) ( )Ct Tou t U e
= (2.26)
co dang giong nh song khuc xa. Nh vay, ien dung co tac dung giam o doc au song ca ve hai pha ca tram lan ng day (H.2.8).
g Trng hp s o co ien cam noi tiep, ien ap khuc xa iem B (trc cuon cam) bang.
221 2 1 2
22 ( )( )( ) ( )
( )B oz pLu p
u p z pL Uz z pL p z z pL
+= + =
+ + + +
gg
42
Hnh 2.9 Song phan xa t cuon cam L tr ve ng day z1
Bien oi ve dang goc:
/2( ) [ ( ) ]Lt TB ou t U e
= + (2.27)
Do o song phan xa bang:
( ) ( ) ( )p B tu t u t u t= /1 2[ ( ) ]Lt Tou e
= + (2.28)
Khi 0 0( )p o tt u u u= = = tc la song ap phan xa dng toan phan t
cuon cam, tng ng nh t cuoi ng day b h mach.
Khi t ; 2 12 1
( )p o oz z
u U Uz z
= =+
Tren ng day 1z khi a co song phan xa tr ve th ien ap bang tong cua song ti va song phan xa:
/1 1 2( ) ( ) ( ) [ ( ) ]
Lt Tt p o ou t u t u t U U e
= + = + + /2[ (( ) ]Lt ToU e
= +
(2.29) Khi 1 10 u 2 maxot U u= = = ; 1 ot u U =
thi iem ban au, do song ap phan xa dng toan phan nen ien ap tren ng day z1 tang len gap oi. Tnh chat nay cung c ng dung e lam tang o nhay cua thiet b chong set (Chng 7).
2.2.3 Song tac dung len mach dao ong
Trng hp song ut tac dung len mot mach dao ong tao thanh bi ien cam L va ien dung C (H.2.10a) th theo s o thay the (H.2.10b) phng trnh can bang ien ap co dang
2 t cdi
u L udt
= +2
22c c o
d uLC u U
dt= + =
Vi song ti co dang t ou U const= = th phng trnh tren co the viet
di dang toan t Laplace
22 ( ) ( )o c cU
LCp u p u pp
= +g g
43
Suy ra: //2
12
1( )
( )c o
LCu p U
p p LC=
+
g2
2 22
( )oUp p
=
+
Hnh 2.10 Song t ou U const= = tac dung len mot mach dao ong
Bien oi ve dang goc:
2 1 ( ) ( cos )c ou t U t= , vi /1 LC = (2.30)
Nh vay, ien ap tren ien dung C gom hai thanh phan xep chong len nhau:
Thanh phan khong chu ky 2Uo khong oi; Thanh phan 2( cos )oU t bien thien theo chu ky:
2 2T LCpi= = pi
Khi 2
Tt = th 4maxc c ou u U= =
o doc cua song tac dung len ien dung at tr so cc ai tai 4
Tt = va
bang 12max( )o
odU
Udt LC
= . Nh vay, o doc cua song tang khi giam tr so L
hoac (va) C cua mach dao ong.
2.3 S PHAN XA NHIEU LAN CUA SONG Gia hai ng day tong tr song 1 2 va zz co mac noi tiep mot oan
44
ng day ngan co chieu dai l va tong tr song zo. Song truyen qua cac moi trng o se co s phan xa nhieu lan tai cac iem nut A va B. Can xac nh ien ap hai iem nut o theo thi gian.
Gia thiet ng day 1 2 zz va co chieu dai ban vo han, tc la khong co song phan xa t au ng day z1 va t cuoi ng day z2 tr ve. Qua trnh truyen song c minh hoa trong hnh 2.11. Trong o cac he so khuc xa va phan xa c xac nh nh sau:
He so khuc xa
T z1 sang zo: 101
2 o
o
z
z z =
+
T zo sang z2: 2022
2
o
z
z z =
+
T zo sang z1: 1011
2
o
z
z z =
+
He so phan xa
T B ve zo: 220 022
1o
o
z z
z z
= = +
T A ve zo: 110 011
1o
o
z z
z z
= = +
45
Hnh 2.11 S phan xa nhieu lan cua song
Neu vo la toc o truyen song trong moi trng zo th thi gian e song i t A en B bang / ol v =
Chon thi iem khi song ti iem A lan au tien lam goc thi gian. ien ap iem A khi song co dang bat ky. Khi 0< t
46
2 210 20 01 10 20 10 202 4 6[ ( ) [ ( ) ( ) ( )Au u t u t u t u t= + + + 3 310 20 10 208 2 1( ) [ ( ) ]}
k ku t u t k+ + + + +K K (2.31) va tng t ien ap tai iem B bang:
2
10 02 10 20 10 20
10 20
3 5
2 1
[ ( ) [ ( ) ( ) ( )
( ) ( ( ) ) ]}
B
k
u u t u t u t
u t k
= + + ++ + +
K
K (2.32)
Trng hp song tac dung co dang au song vuong goc, o dai song vo tan, tc ( ) ou t U const= = th ien ap iem A va B se bang:
210 01 20 10 20 10 20 10 201 1[ [ ( ) ( ) ]}k
A ou U= + + + + + +K K (2.33) 210 02 10 20 10 20 10 201[ ( ) ( ) ]
kB ou U= + + + + +K K (2.34) Bieu thc trong dau ngoac vuong [ . . . ] la mot cap so nhan hoi tu v
cong boi 10 20 1 < . Neu so lan phan xa tang len vo cung th tong cua chung at en tr so gii han bang:
210 20 10 20 10 2010 201
11
1( ) ( )
nnn = + + + + =
K
Ket qua la: 20 011010 20
11
[ ]A ou U
= +
10 0210 20
1
1[ ]B ou U=
nhng: 20 01 10 20 20 01 20 01 10 20 02
10 10 20 10 20 10 20 10 20
1 1 11
1 20 1 1 1 1
( ) + + + + = = = =
Do o, khi so lan phan xa tang len vo cung tc la khi t , th ien ap iem A va B se tien en cung mot gii han va bang:
10 0210 201
A B ou u U
= =
ma: 10 02 2 2 121 210 20 1 2 2 1 2
1 2
2 2 21
11 ( )( )
o
o oo
o o
z z z
z z z zz z z z z z
z z z z
= = =
+ + +
+ +
12 la he so khuc xa t z1 sang z2 khi khong co zo.
47
Cuoi cung ta co:
12A B ou u u= = (2.35)
Nh vay, khi qua trnh tien ti on nh ( )t th anh hng cua phan t zo se mat, ien ap hai iem nut A va B se tien en cung mot tr so gii han nh khi song khuc xa trc tiep t z1 qua z2. Tuy nhien, qua trnh bien thien cua ien ap tai A va B trong thi gian qua o, tuy tng quan gia tong tr song cua cac phan t, co nhng ac iem rieng cua no. Ta se lan lt xet cac trng hp sau ay.
2.3.1 oan day gia co tong tr song zo nho hn tong tr song z1 va z2 (H.2.12) Trong trng hp nay: 1oz z< ; 2oz z<
101
21o
o
z
z z =
+
2022
21
o
z
z z = >
+
1101
0o
o
z z
z z
= >+
2202
0o
o
z z
z z
= >+
do o: 10 20 01 200 va 0 > >
Cac so hang trong chuoi so uA va uB eu dng. Nh vay, qua trnh tien ti on nh cua chung la qua trnh tang dan ien ap theo tng cap, moi cap cach nhau khoang thi gian /2 2 ol v = (H.2.12).
Khi zo rat be so vi z1 va z2 th qua trnh truyen song tng t nh khi gia z1 va z2 co mac mot ien dung song song, co the thay the oan zo bang mot ien dung tng ng va ien ap uA va uB se bang ien ap khuc xa qua ien dung tng ng Ct.
1vi ( )t o oo o o o o
lC C l C
z v z z v
= = = =
/12 1( )Ct
A B ou u U e
= =
48
vi: /
/1 2 2
1 2 2 11t o
c
C z z z z
z z z z
= = + +
Trng hp nay co the gap trong thc te, khi song truyen t ng day tren khong qua oan cap vao tram. oan cap co tac dung nh mot ien dung, lam giam o doc au song, tang an toan cho cach ien doc cua may bien ap va thiet b ien trong tram.
2.3.2 oan day gia co tong tr song zo ln hn tong tr song z1 va z2 cua cac ng day hai ben (H.2.13)
Trong trng hp nay: 1oz z> ; 2oz z>
>10 1 zo > z2
49
Cac he so phan xa 10 va 20 khac dau nhau. Trong cong thc uA va uB cac so hang cua chuoi so luon oi dau. Bien thien cua uA va uB theo thi gian co dang nhng dao ong tat dan quanh tr so gii han 12 oU , do o co the
xem nh song truyen trong mot mach dao ong. Hnh 2.14 di ay cho dang ien ap tai iem B trong hai trng hp: 2 1 12 1Z Z> > va
2 1 12 1Z Z< < .
Hnh 2.14
Chu y: 2 1 122121 2 2 1 12
12
1
I
II
z zz
z z z z
> > =
+ <
+; 202
2
21
o
z
z z = >
+ 1maxB B ou u u = >
Khi 1 2oz z z> > th oi vi moi trng 2 , oz z co tac dung nh mot ien
cam, con oi vi 1, oz z co tac dung nh mot ien dung. Trng hp nay tng
ng vi s o thay the (H.2.14b). Trng hp 1 2oz z z< < tng ng vi s o thay the hnh 2.14c.
Trong cac s o thay the nay:
t oL L l= ; 2o
tC l
C =
50
ooo
Lz
C= ; 21
2
1 1 1
4( )
t t t t
z
L C C z L =
V du, ngi ta a tnh c ien ap tren ien dung Ct cua s o hnh 2.14c khi co song vuong goc dai vo tan tac dung bang:
21 2
21[ cos( )]
cos
t
B Ct oz e
u u U tz z
= =
=
tc la gom mot dao ong tat dan xep chong len tr so on nh 12oU vi:
He so tat dan: 12
1 1
2( )t t
z
C z L = +
Goc lech pha: tg =
Tan so dao ong: 2 2 14 2/
o
o
v
T l v l
pipi pi = = =
Tr so ien ap ln nhat tac ong len z2 xay ra sau mot na chu ky cua dao ong, tc la khi t = pi
Nh vay: 21 2
21max ( )C o
zu U e
z zpi/
= ++
hay 1 21 1
2 2
2 21 1
1 1
max ( ) ( )z zC
o
ue e
z zUz z
pipi /
= = ++ +
vi 1 2z z= th max( )C ou U qua ien ap khong cao lam.
1 2z z> th qua ien ap tham ch con nho hn na max( )C ou U< Nhng vi 1 2z z< tc khi song i t moi trng co tong tr song be sang
moi trng co tong tr song ln, th qua ien ap co tr so ang ke. V du, z1 = 50 la tong song cua ng day cap, con 2 5 000.z = la tong tr song cua cuon day may bien ap th:
50 50002 1 3 46 lan50
15000
max ( ) ,C
o
ue
U/
pi= + =+
Tom lai, neu cac tong tr song mac noi tiep nhau 1 2, ,oz z z hoac ln dan
hoac be dan th co the gay nen dao ong rieng tat dan gom mot chuoi nhng t song vuong goc truyen vao li. Nhng dao ong cao tan nay co the gay cong hng trong mot mach cuc bo nao o neu nh tan so cua chung phu hp
51
vi tan so cua nguon. Qua ien ap cong hng co the lam h hong cach ien cua cac cuon day MBA va may ien. Do o can phai tranh nhng dang s o kieu o.
2.4 VAI PHNG PHAP TNH TOAN QUA TRNH TRUYEN SONG BANG O TH
2.4.1 Phng phap cac ng ac tnh
Hnh 2.15
e giai bai toan truyen song qua nhieu moi trng vi cac dang song n gian (song vuong goc, xien goc, song ham mu), con co the dung phng phap o th - phng phap cac ng ac tnh sau ay.
Song truyen t ng day Z1 sang ng day Z2 qua mot oan ng day tong tr song Zo, chieu dai l (H.2.15a). S o thay the theo qui tac Petersen cho hnh 2.15b; cac tr so cua ap A (theo thi gian) phai nam tren ng thang 12A oU U Z i= (ng 1). Con tr so uB nam tren ng 2BU Z i=
(ng 2, (H.2.15c). Ngoai ra, ap va dong tai bat c iem nao tren oan Zo, ke ca tai hai iem
A va B, eu co the bieu dien di dang tong cua cac song thuan (xuat phat t A) va song ngc (xuat phat t B):
u u u+ = + ; o o
u uiZ Z
+
= hay oZ i u u+
=
Suy ra: 2 3
2 4
( )
( )
B o
A o
U u Z i ng
U u Z i ng
+
=
= +
52
ng 3: xuat phat t A en B goi la ac tnh thuan ng 4: xuat phat t B en A goi la ac tnh ngc Tr so cua uA cho bi giao iem cua ng 1 va ng ac tnh ngc 4,
con uB la giao iem cua ng 2 va ng ac tnh thuan 3 nh trnh bay trong hnh 2.15c.
Cach tien hanh
Hnh 2.16 Trng hp 1 2;o oz z z z> >
Ve hai he truc toa o u(i) va u(t) ben canh nhau. Tren he truc u(i) hnh 2.16a ve cac ng ac tnh uA va uB. Giao iem M cua chung cho tr so gii han cua uA va uB khi so lan phan xa n tang vo cung (tc la khi t ):
2 121 2
2( ) ( )M A B o o
zu u t u t U U
z z= = = =
+
Chon goc thi gian t = 0 khi song en iem A lan au tien. Trong khoang thi gian /0 2 ( )ot vi l v = cha co song phan xa t B ve, tc u
= 0, nen ac tnh ngc luc nay bang A ou z i= qua goc toa o.
Giao iem A1 cua no vi ng 12A ou U z i= cho ien ap uA1 tai nut A trong khoang thi gian nay.
That vay, t 1 11
2A o
A o
u U z i
u z i
=
= suy ra 1 10
1
2 oA o o
o
zu U U
Z Z= =
+
53
Song uA1 truyen en B theo ac tnh thuan
1 102 2B A o o ou u z i U z i= =
Giao iem cua no vi ng B ou z i= tai iem B1 cho ien ap uB1 tai
iem B thi iem t = . Tr so cua no c xac nh bi:
1 101 2
2B o o
B
u U z i
u z i
=
= suy ra 21 10 10 02
2
2B o o
o
zu U U
z z= =
+
Song UB1 phan xa ve A theo ac tnh ngc, luc nay bang 1 10 022 2A B o o ou u z i U z i= + = +
Giao iem A2 cua no vi ng 12A ou U z i= cho tr so ien ap uA2 tai
A luc t = 2 c xac nh theo:
2 10 022 1
2
2A o o
A o
u U z i
u U z i
=
= suy ra 2 10 01 20A ou U=
Co the chng minh tiep tuc tng t.
Thc ra trong cach ve co the tien hanh n gian hn: T iem B1 ve ng thang co o doc zo, no cat ng 12UA ou z i= tai
A2. Bay gi qua iem A2 ve ac tnh thuan mi vi o doc zo), giao iem B2 cua no vi ng 2Bu z i= cho ien ap tai nut B tai thi iem t = 3. C tiep tuc qua trnh ve cac ac tnh thuan va nghch tng t, cho en khi cac iem
,n nA B tiem can vi giao iem M, tr so cua no cho gia tr ti han cua uA va uB,
khi so lan phan xa tang len vo cung.
Hnh 2.16b cho quan he uA va uB theo thi gian. Bang phng phap nay co the xac nh uA va uB theo t trong moi tng quan khac nhau gia
1 2 va, oz z z (H.2.17) tng t nh trong phng phap giai tch a xet muc
2.3.
54
Hnh 2.17-1
Hnh 2.17: Bien thien cua Au va Bu theo thi gian khi tng quan gia 1, oz z va 2z khac nhau
Neu z2 la mot ien tr khong ng thang (tc tr so R phu thuoc vao i) va a biet ac tnh Volt-Ampe (tc u = f(i) cua no, th phng phap giai bang o th cung hoan toan tng t (H.2.18).
55
Hnh 2.18 Bien thien cua Au va Bu theo t khi 2z la mot phan t phi tuyen
1- Xac nh bang o th ham: /t Ty e=
Phng phap o th da tren c s la: hnh chieu tren truc t cua ng tiep tuyen tai moi iem cua ng cong y(t) co chieu dai bang T. Chia truc t thanh nhng khoang thi gian T (nen chon T la mot c so cua T) T cang nho cang chnh xac.
Trc tien t iem y = 1, ve ng thang noi vi iem t1 = T. Giao iem cua ng thang o vi ng thang t T= cho iem y1, tung o cua no la 1 ( )y y T= . Noi y1 vi iem 2t t T= + , cat ng 2t T= tai y2 co tung o 2 2( )y y T= va c tiep tuc nh the.
2- Xac nh ien ap tac dung len mot ien dung C cuoi ng day khi co song 1 ou U const= = tac dung
Nh a biet 2 1 /( )t Tc ou U e
= . Phng phap o th e xac nh cu
c tien hanh tng t nh tren. Cach ve: Chon truc tung theo / ou U va truc hoanh theo t.
56
Tren ng thang song song vi truc t qua iem co tung o bang 2 xac nh iem 1t = T
T goc toa o ve ng thang noi lien vi iem t1, ng thang nay cat ng t T=
1 1; ( )cu u u T= , t 1u ve ng thang noi lien vi iem 2t T T= + ng thang o se cat ng
2t T= 2u , tung o cua
2 2( )u u T= va c tiep tuc nh vay.
3- Xac nh ien ap tac dung len mot ien tr khong ng thang cuoi ng day khi song tac dung co dang bat ky (H.2.19)
Hnh 2.19
Gia thiet song ti ( )tu t co dang bat ky truyen theo ng day co tong tr song z tac dung len mot ien tr khong ng thang R co ng ac tnh V-A: ( )Ru f i= a biet. Theo qui tac Petersen co s o thay the nh hnh
2.19a va ien ap ( )Ru t c xac nh bi quan he:
2 ( ) ( ) ( )t Ru t u t zi t= + (2.32)
Bang phng phap o th co the xac nh ( )Ru t nh sau:
Tren goc th I ve he truc toa o u, i. Tren o ve ng ac tnh V-A cua ien tr khong ng thang, ( )Ru f i= va ng bieu dien ien ap giang tren tong tr song z cua ng day zi. Cong tung o cua hai ng ac tnh o vi
57
nhau se co ng cong Ru zi+ bieu dien ve phai cua phng trnh (2.32).
Tren goc th II ve truc toa o u, t. Tren o ve dang song ti ut(t) va 2ut(t). Tai mot thi iem t nao o se xac nh c iem a tren ng 2 ( )tu t , t a ke ng thang song song truc hoanh se xac nh c iem b tren ng cong Ru zi+ . T b ve ng thang song song vi truc u, no se cat ac tnh V-
A cua ien tr khong ng thang ( )Ru f i= tai c. T c ve ng thang song song vi truc hoanh va xac nh c iem d ng vi thi gian t.
Tung o cua iem d chnh la ien ap tren ien tr R tai thi iem t. Thay oi thi iem t se lan lt xac nh c nhng iem d tng ng cua ng cong ( )Ru t . Song phan xa t ien tr khong ng thang tr ve ng day c xac nh theo quan he:
( ) ( ) ( )p R tu t u t u t= ; ( )p k tu u u=
2.4.2 Song dang bat ky tac dung len chong set van at cuoi ng day (H.2.20)
Chong set van gom khe h phong ien K co ac tnh Volt-giay a biet ( )csvu t noi tiep vi mot ien tr khong ng thang R co ac tnh Volt-Ampe
a cho: csv (i )csvu f=
Hnh 2.20
Trc khi khe h K phong ien tc cuoi ng day h mach, do o: 0x csvi i= =
va 2 x t csvu u u= =
Khi khe h K phong ien, thi iem phong ien tp c xac nh bi giao iem cua ng cong 2 x tu u= vi ac tnh Volt-giay cua khe h K. Luc nay ien tr khong ng thang R c ghep noi tiep vao mach; ien ap tac dung len chong set van c xac nh theo qui tac Petersen 2 t csv csvu u zi= + (H.2.21). csvu bay gi thc chat la ien ap tac dung len ien tr khong ng
thang R cua chong set van, thng c goi la du cua chong set van. Cach
xac nh ( )csvu t tng t nh trng hp a xet tren. Hnh 2.21 cung trnh bay
cach xac nh dong qua CSV theo t: ( )csvi t .
58
Hnh 2.21 Cach xac nh bang o th ( )csvu t va ( )csvi t
2.4.3 Phng phap tiep tuyen Thc chat cua phng phap nay la cach giai bang o th phng trnh vi
phan cua ham v(t) co dang
( )dy
ay f tdt
+ = (2.33)
V du: Gia thiet co mot song ien ap u(t) dang bat ky cho trc truyen theo ng day co tong tr song z tac dung len mot ien dung C cuoi ng day (H.2.22a). Can xac nh ( )cu t .
Hnh 2.22 Song Ut dang bat ky tac dung len ien dung C
at cuoi ng day
V song co dang bat ky nen dung phng phap giai tch se rat phc tap, con dung phng phap o th se n gian hn nhieu.
S o thay the theo qui tac Petersen cho hnh 2.22b. Theo o lap c phng trnh can bang ien ap sau:
2 ( ) cu t Zi u= + vic c
cdu du
ZC u i Cdt dt
= + =
Thay CZ = T, hang so thi gian nap ien cho ien dung C va bien oi phng trnh ve dang chuan se co:
59
1 12 ( )c c
duu u t
dt T T+ = (2.34)
Cach xac nh uc bang o th tien hanh nh sau (H.2.23) g Tren he toa o vuong goc ( , )u t goc O ve ng cong 2u(t) (a biet dang
u(t), tai moi thi iem t nhan tung o vi 2). g Ve he toa o vuong goc ( , )cu t co goc 0 lui sau goc 0 cua he toa o (u,t)
mot thi oan T = Cz.
g Chia truc thi gian t va t thanh nhng khoang t bang nhau (t nen la c so cua T, chia cang nho th hnh ve cang chnh xac), tren truc 0t ky hieu bang 1 2 3, , nt t t tK . Con tren truc t ky hieu bang 1 2 3, , nt t t t K .
g Cac ng thang 1 2, , nt t tK cat ng cong 2u(t) tai nhng iem 1,2... n.
g at tren truc uc mot tr so bang tr so ien ap ban au tren ien dung 0( )cu (trng hp tong quat).
g Noi iem 0( )cu vi goc O cua he toa o (u,t) ni ng cong 2u(t) co tr so ban au (t = 0). oan nay cat ng 1t iem 1.
g T iem 1 ke oan thang noi lien vi iem 1. oan 1 1 cat ng 2t iem 2.
g Noi 2 vi 2, oan 2 2 cat ng 3t tai 3.
g Qua trnh tiep theo c lap lai tng t nh vay. Cuoi cung co c ng gay khuc qua cac iem 0( )cu , 1,2... n, o chnh la ng cong ( )cu t can
tm. g e chng minh ieu o, ta xet tam giac vuong 3 33 : iem 3 co tung o bang
2u(t), iem 3 gia thiet la nghiem cua bai toan co tung o la ( )cu t , chieu dai
canh 3 3' ''=T. Nh vay 233
3 3
( ) ( )cu t u ttgT
= =
. Mat khac t phng
trnh chuan (2.34) cung co 2 ( ) ( )c cdu u t u t
dt T
= . Tom lai cdu
tgdt
= , ieu nay chng to ng gay khuc 1, 2, 3, chnh la li giai cua bai toan.
60
Hnh 2.23 Xac nh ien ap tren ien dung C
bang phng phap tiep tuyen
61
2.5 QUI TAC VE SONG ANG TR
Hnh 2.24 Qui tac song ang tr
Trong thc te, thng gap nhieu trng hp song truyen ong thi tren nhieu ng day en mot iem nut. Van e c at ra la can xac nh tr so qua ien ap xuat hien tai iem nut. Hnh 2.24a trnh bay mot trng hp tong quat:
g Co n ng day, tong tr song lan lt la 1 2, ,i nz z z zK (gia cac ng day khong co tong tr song tng ho, tc 0ikz = ) au vao
iem nut A. g Tai A co noi vi tong tr tap trung z, co the la ng thang hoac khong
ng thang, co cac ac tnh Volt-giay hoac Volt-Ampe a biet. g Song truyen theo ng day zi en nut A c ky hieu bang
1 2( , ,..., )iAu i n= va song phan xa t A tr ve iz c ky hieu bang Aiu .
g Can xac nh ien ap tai iem nut ( )Au t va cac song phan xa t A tr ve lai cac ng day Aiu .
ieu kien b tai nut A cho cac quan he sau: 1 1 2 2A A A A A iA Aiu u u u u u u= + = + = +K (2.35)
1
( )i n
A iA Aii
i i i=
=
= + (2.36)
Biet rang: 1 1
;iA AiiA Aiu u
i iz z
= = va t (2.35) suy ra: Ai A iAu u u=
Thay cac gia tr nay vao bieu thc (2.36):
62
1 1
12( )n n
iA A iA iAA A
i i i ii i
u u u ui u
z z z z= =
= = (2.37)
Chia ca hai ve cua (2.37) cho 1
1n
ii z= va sap xep lai th t cac so hang ta co:
1 11 1 1
1 1 12 ( ) ( )n n n
iA A Ai i ii i i
u u iz z z
= = =
= +
ma 1 1 21
1( )n
n tii
z z z zz
=
= // // = K
va at 11 1 1
1 1( )
n n nt
iA iA tAi i ii i i
zu u uz z z
= = =
= =
th bieu thc c viet lai di dang
2A A t tAu i Z u+ = (2.38)
vi: zt - tong tr song ang tr cua tat ca n ng day au song song tAu - song ang tr cua tat ca song ti 1 2, ,A A nAu u uK en nut A theo
ng day co tong tr song ang tr tz . Can lu y, khi tnh tAu tai mot thi iem t nao o th ch ke en nhng
song iAu nao a en A tai thi iem o. Cac song khac cha en A eu coi
nh bang khong. Bieu thc (2.38) c goi la qui tac song ang tr, tng ng vi s o
thay the hnh 2.24b. Nh vay, qui tac song ang tr cho phep chuyen mot bai toan phc tap:
song truyen ong thi theo nhieu ng day khac nhau en iem A, thanh mot bai toan n gian hn nhieu - mot song ang tr tAu truyen theo ng day ang tr co tong tr song tz en iem nut A.
Theo s o thay the (H.2.24b) co the tnh ien ap tai iem nut A theo.
2 .A tA tA tAt
zu u u
z z= =
+
trong o 2tAt
z
z z =
+ goi la he so khuc xa ang tr tai nut A, va dong qua
tong tr Z bang: AAu
iz
=
63
Song phan xa t iem nut A ve ng day zi suy ra t ieu kien b (2.35):
Ai A iAu u u=
2.6 QUA TRNH TRUYEN SONG TRONG HE THONG NHIEU DAY DAN
2.6.1 Trng hp tong quat
Tren ay chung ta ch mi khao sat qui luat truyen song tren ng day mot day dan, o song dong thuan truyen theo day dan, con song dong ngc theo ng at. Trong thc te, ng day tai ien la mot he nhieu day dan gom ca cac day pha va day chong set va qua trnh truyen song ien t trong he nhieu day phc tap hn nhieu, do co quan he tng tac cua trng ien t gia cac day song song vi nhau o.
Trong nhieu trng hp, co the thay the he nhieu day bi mot day ang tr, nhng can phai tnh en cac ac iem cua s truyen song trong he nhieu day.
e n gian hoa s nghien cu qua trnh truyen song trong he nhieu day dan, trc tien cung bo qua ton hao nang lng trong day dan, trong at va ton hao vang quang xung. Vi gia thiet nay, song tren tat ca cac day dan truyen vi cung mot toc o (bang toc o anh sang oi vi ng day tren khong), khong b bien dang va co dang song phang, co ngha la khong co thanh phan vect ien trng E va t trng H theo chieu truc ng day. Do o e phan tch qua trnh truyen song trong he nhieu (n) day dan, co the xuat phat t he phng trnh Maxwell quen thuoc cho he day dan co ien tch tnh.
1 11 1 12 2 1
2 21 1 22 2 2
1 1 2 2
n n
n n
n n n nn n
u q q q
u q q q
u q q q
= + + +
= + + +
= + + +
KK
K
(2.39)
trong o: 1, , nu uK - ien the oi vi at cua cac day dan 1, , nq qK - ien tch tren n v chieu dai cua cac day dan ik - he so the, c xac nh theo cac kch thc hnh hoc
cua ng day (H.2.25).
64
1 2
2
1
2
ln ( )
ln ( )
kkk
o k
kiik
o ki
hm F
r
Dm F
d
= /
pi = / pi
(2.40)
vi: rk - ban knh day dan th k, m kh - o treo cao trung bnh cua day dan k, m
dki - khoang cach gia cac day dan k va i, m Dki - khoang cach gia day dan k va anh soi qua mat at cua day dan i,
m. V ki ikd d= va ki ikD D= nen ki ik =
ien trng tao nen bi ien tch tnh la ien trng tnh.
e chuyen ien trng tnh sang ien trng trang thai song phang, tng tng gan cho no mot toc o chuyen dch v khong oi doc ng day. Bang cach nhan va chia cac so hang cua ve phai cua he phng trnh Maxwell (2.39) vi van toc chuyen dch v cua song, ong thi thay the .k kq v i= la song dong truyen theo day dan k, va thay /ki kiv z = v ty so nay
co th nguyen cua tong tr, ta nhan c he phng trnh truyen song cho he n day dan.
Hnh 2.25
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1 11 1 12 2 1
2 21 1 12 2 2
1 1 2 2
n n
n n
n n n nn n
u z i z i z i
u z i z i z i
u z i z i z i
= + + +
= + + +
= + + +
KK
K
(2.41)
vi /kk kkz v= - tong tr song ban than cua day dan k, no bieu hien quan he gia song ap va dong trong day dan k
/ki kiZ v= - tong tr song tng ho gia cac day dan k va i, no bieu hien quan he gia dong trong day i vi song ap ma no cam ng tren day dan k.
oi vi ng day tren khong /83 10v c m s= = th:
2 260 138
60 138
ln lg
ln lg
k kkk
k k
ik ikki ik
ik ik
h hz
r r
D Dz z
d d
= =
= = =
(2.42)
Co the nhan thay de dang la k v rkk ki ikz z d> = . oi vi ng day tren khong tong tr song tng ho thng nam trong gii han t 100200.
He phng trnh (2.41) gom n phng trnh vi 2n an so, so phng trnh con lai se c xac nh t cac ieu kien b trong cac trng hp cu the. Sau ay la mot vai v du minh hoa.
2.6.2 Cac day dan cung c noi vao mot nguon phat song
Hnh 2.26 Ba day dan cung c noi vao nguon song
ay la mot v du thc te co the xay ra khi set anh gan ng day, gay nen song cam ng tren tat ca day dan tren ng day.
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Trong trng hp nay ien ap tren day dan co the coi mot cach gan ung eu bang nhau va bang Uo. Gia th ng day co ba day dan co cung ban knh va treo tren cung mot o cao (nh ng day co cot hnh pi) th:
11 22 33
12 23 13
z z z
z z z
= =
= >
Trong trng hp nay ieu kien b la 1 2 3 ou u u U= = = .
Do o, t he ba phng trnh truyen song:
1 11 1 12 2 13 3
2 21 1 22 2 23 3
3 33 1 32 2 33 3
o
o
o
u U z i z i z i
u U z i z i z i
u U z i z i z i
= = + +
= = + +
= = + +
Suy ra: 11 121 3 2 211 11 13 122
oz z
i i Uz z z z
= =
+ ; 11 13 122 12 2
11 11 13 12
2
2o
z z zi U i
z z z z
+ = se en cham tng ng so vi trng
hp khong co vang quang mot khoang thi gian t(u) xac nh nh sau:
1 2 1( ) ( )( )vq o o
l l lt u Bu
v u v v = = +
V 2Bu= 1 (t oq q= (1+Bu) suy ra 1 1o
qBu
q= = ) co the tnh gan
ung 1 2 1Bu Bu+ + (khai trien nh thc Newton), do o:
( )o
lt u Bu
v (2.51)
Bang cach xac nh thi gian cham tre cua tng bang song co the xac nh gan ung s bien dang au song (H.2.33b).
V du: Tai ni xuat hien qua ien ap (x = 0) song co dang au song khong vuong goc 0( )s = bien o khong oi 0 5,u u= th sau khi truyen qua
mot oan x = l th di tac dung cua vang quang xung au song b keo dai, thi gian au song bang
0 5,slBuc
(2.52)
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do o o doc au song bang 0 5,s
u ca
Bl= =
(2.53)
Khi ng cong bien dang au song cat phan uoi song, iem giao nhau cho bien o cua song sau khi a truyen qua oan ng x = l. Trng hp song co o dai song ngan nh trng hp song cat th bien o cua song giam ro ret di tac dung cua vang quang xung.
phan uoi song, vang quang khong tiep tuc phat trien, cac dong plasma giam dan o dan ien, vang quang se tan dan. Co the coi mot cach gan ung nh la uoi song khong b bien dang.
Hnh 2.34 Quan he B = f(d) oi vi song am
Quan he B = f(d) oi vi song cc tnh am cho hnh 2.34, hay co the lay theo cac tr so trung bnh:
3 10 5 10,BkV
= vi d = 1215mm (tng ng vi D 110kV)
3 10 3 10,BkV
= vi d = 2530mm (tng ng vi D 220kV)
3 10 2 10,BkV
= vi d = 4060mm (tng ng vi D 330380kV)
Trong tnh toan chong set, ngi ta con dung mot cong thc gan ung, qui s bien dang cua au song di tac dung cua vang quang xung khi en tram, thanh mot au song xien goc tng ng theo cong thc thc nghiem sau:
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0 5 0 008 max( , , ) ,t odd
ul s
h = + + (2.54)
vi: o - thi gian au song tai ni xuat phat, s umax - bien o song, kV; htb - o treo cao trung bnh cua day dan, m
l - chieu dai cua oan ng day (ti tram) ma song truyen qua, km.
V du: tai ni xuat phat song co dang vuong goc o=0, bien o 1000maxU kV= sau khi truyen qua oan ti tram co chieu dai
l=1km, day dan co o treo cao trung bnh 10tbh m= th song b bien dang va
co au song tng ng bang:
0 5 0 8 1 3, , ,tb s = + =
Nh vay s bien dang cua song di tac dung cua vang quang xung ln hn nhieu so vi s bien dang do ton hao bi ien tr tac dung cua at.
* Vang quang xung lam giam tong tr song cua day dan va lam tang he so ngau hp.
Thanh phan dong ien vang quang tng ng vi mot bang song du co the viet:
1vqvq
di duz
=
vi vqz la tong tr song cua day dan co vang quang xung khi ien ap tac
dung co tr so bang u tng ng vi o cao cua bang song a chon:
1 2 1 2
'( )
o o ovq
o
L L zz
C C Bu Bu= = =
+ +
Dong ien vang quang tong se bang
0 0
1 11 2
vqi u
vq vqvq o o
u u Bui di Bu du
z z z
+= = = +
vi zo la tong tr song cua day dan khi khong co vang quang.
Nh vay: 1o
vq
zz
Bu=
+ (2.5
Co ngha la khi co vang quang xung, tong tr song ban than cua day dan b giam. Neu bien o song t 10001500 kV th tong tr song giam khoang 1020% va t vai nghn kV th tong tr song co the giam en 3040% va hn.
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He so ngau hp gia hai day dan 1 va 2 khi cha co vang quang c xac nh theo.
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