Multi-state Electric Field Analysis of 1-tower-double-circuit HVDC Transmission Lines Based On Charge Simulation Method

Transcription

1 Applied Mechanics and Mateials Online: ISSN: , Vol. 5, pp 3-39 doi:0.408/ 04 Tans Tech Publications, Switzeland Multi-state Electic Field Analysis of -towe-double-cicuit HVDC Tansmission Lines Based On Chage Simulation Method ZHOU Quan,a, TU Li,b, BIE Rui,c, FENG Dong,d, FAN You-ping,e Maintenance & Test Cente, CSG EHV Powe Tansmission Company, Guangzhou 50663, China School of Electical Engineeing, Wuhan Univesity, Wuhan43007, China a zhouquan@ehv.csg.cn, b @qq.com, c bieui@whu.edu.cn, d fengdong@ehv.csg.cn, e ypfan@whu.edu.cn Keywods: -towe-double-cicuit DC tansmission lines; chage simulation method; nominal electic field distibution; aangement ways; opeation conditions Abstact. Cuently, thee is little expeience about design of the -towe-double-cicuit DC tansmission lines. But the electomagnetic field distibution unde its lines is complicated. In ode to study the nominal electic field distibution of -towe-double-cicuit DC tansmission lines unde diffeent situations and a vaiety of opeating conditions, the cuents with analytical solutions ae used to simulate the discete o uneven distibuted continuous chage. In the woks within an acceptable ange, the linea equations ae built to solve simulation chage accoding to the electomagnetic theoy. And gound nominal electic field of -towe-double-cicuit DC tansmission lines is calculated. nominal electic field distibution exteme value exteme unde diffeent aangements and nominal electic field distibution unde a vaiety of opeating conditions ae analyzed compaatively. In this pape, the esults show that the aangements of lines have effects on the distibution chaacteistics of nominal electic field in nomal condition. When monopole o bipola o the bipola of one line doesn t wok, the change of nominal electic field is ponounced, but thei extemes educe. Intoduction A lot of eseach, in ecent yeas, have shown that when DC tansmission lines un, it will bing a seies of envionmental poblems of electomagnetic.it compises ion flow, adio intefeence, coona noise and so on. efoe, it is difficult to decide whee to locate and build the DC tansmission coido. As fo High Voltage AC tansmission lines, it is common that diffeent tansmission lines ae placed on the same towe. But this way is elatively ae fo HVDC tansmission lines.in fact, it began to emege gadually. As fo Xin-an DC tansmission lines, pat of the DC lines and gounding lines ae built on the same towe fo lack of land. HVDC poject that Xi-luodu powe tansmitting Guangdong ae being constucted. Two cicuits of lines ae eected on the same towe. Cuently, thee is little expeience about design of the -towe-double-cicuit DC tansmission lines. Its electomagnetic field distibution of the line is complex and not well known. e exist seveal possibilities fo unning condition of the -towe-double-cicuit DC tansmission lines. Howeve, the electomagnetic fields ae aely studied. It is ecognized that seveal methods, based on the pinciple of Maxwell's equations,can be used to calculate the electomagnetic fields. Dealing with electomagnetic field equations can be done eithe by integal discetization o by diffeential discetization. Finite element method, finite diffeence method, the Monte Calo method, the chage All ights eseved. No pat of contents of this pape may be epoduced o tansmitted in any fom o by any means without the witten pemission of Tans Tech Publications, (# , Pennsylvania State Univesity, Univesity Pak, USA-8/09/6,:55:03)

2 3 Sustainable Enegy simulation method have been applied in the field. Among them, the chage simulation method has some advantages in the following five aeas: electic field ange calculation, bounday shape, field dimensions, media type, the electic field stength calculation. Calculation Method basic pinciple of the chage simulation method. chage simulation method is based on the uniqueness theoem of the electomagnetic field, whee continuously distibuted fee chage and bound chage ae equivalent to N discetely simulated chage outside of the calculation field. Fist, calculate the magnitude of each simulated chage, accoding to the condition that the bounday conditions emain unchanged. Second, seek the amount of simulated chage to establish linea equations and solve them by discete field intensity ( ϕ, E ) geneated by each simulated chage. n, supeimposed discete field intensity ( ϕ, E ) by the pinciple of supeposition. Finally, get the spatial electic field distibution geneated by the oiginal continuously distibuted chage. As above, the mathematical model is come down to the definite poblem of Poisson equation o Laplace equation, whee electic potential function is efeed to as the unknown quantity. As a matte of fact, Chage Simulation Method can be classified as Image Method due to its essence. But compaed to Image Method, Chage Simulation Method is supeio to Image Method in the numeical pocessing and othe field. Because of this fact, the Chage Simulation Method, which has bette popety, is widely used in the pactical poject. basic equations of Electic potential: ρ ϕ ϕ ε Fist bounday condition: L = = 0 () ϕ = f ( ) P () ϕ Inteface conditions of diffeent mediums: ϕ ε ε = 0, ϕ = ϕ (3) n n basic assumption of nominal electic field calculation. In calculating electic field unde -towe-double-cicuit DC Tansmission Lines, simplify calculation model on condition of meeting the computing needs. ) Conside the electic field geneated by the line conducto as the electostatic field; ) Calculate the maximum sag plana of infinitely long and staight conduct wie; 3) Ignoe the impact and end effects of the towe and the suounding objects; 4) Ignoe the impact of lightning conducto when study the distibution of the gound electic field; 5) Assume that the gound Is a good conducto plana and the potential is zeo potential. Electic Field Calculation Of -towe-double-cicuit DC Tansmission Lines Based On Chage Simulation Method Chage Simulation selection and the match point set. key point to calculate the electic field by the Chage Simulation Method is the electic potential coefficient matix [P] calculation while the electic potential coefficients is decided by the type and location of the simulated chage. Not only should the simulated chage selection be consistent with the actual situation, but also be convenient to calculate the electic potential and the electic field stength with analytic fomula. Accoding to the stuctual chaacteistics of -towe-double-cicuit DC tansmission lines, the simulated chage is chosen to be infinitely long linea chage.

3 Applied Mechanics and Mateials Vol ) Infinitely long linea chage A( x, y) +Q( x, y ) A( x, y) Q( x, y ) A ( x, y ) Q( x, y) Fig. Infinitely long linea chage Fig. Infinitely long linea chage consideing the gound bounday conditions As shown, linea electic chage Q is in the Catesian coodinate system while is a point of A potential efeence. electic potential geneated by Linea Electic Chage at 0 an abitay point A( x, y) is: ϕ Q πε 0 = ln (5) Whee, ae espectively the distance fom linea electic chage Q to A( x, y) and A( x0, y0 ). efoe, the coesponding electic potential coefficients: ln 0 p = (6) πε deivation fom Gadient elationship between the electic field stength and the electic ϕ ϕ potential: E = ϕ = ( i + j) = fxi + f y j (7) x y ϕ efoe, the field stength coefficients: x x ϕ y y fx = =, f y = = (8) x πε y πε ) Infinitely long linea chage which consides the gound bounday conditions A necessay bounday condition to conside is the gound, whose electic potential is zeo when calculating the electic field of -towe-double-cicuit DC Tansmission Lines. Image Method is suggested to be applied in the calculation. To satisfy the bounday conditions of the gound, it is pacticable to employ a linea electic chage of opposite sign which has the same magnitude. As shown, linea electic chage + Qand Q ae in the Catesian coodinate system while the electic potential of the hoizontal axis is zeo. electic potential geneated by Linea Electic Chage at an abitay point (, ) Whee, 0 0 A x y is: ϕ = ln (9) πε ae espectively the distance fom Linea Electic Chage Q to A( x, y) and (, ) ln A x y. efoe, the coesponding electic potential coefficients: P = (0) πε deivation fom Gadient elationship between the electic field stength and the electic potential: ϕ ϕ E = ϕ = ( i + j) = fxi + fy j () x y Thus, the field stength coefficients: ϕ ( x x x x ϕ x ), ( y y y f = = f y ) y = = x πε y πε Q 0 0 ()

4 34 Sustainable Enegy Calculation pocess of Chage Simulation Method. Chage Simulation Method is applied as follows: ) n simulated electic chage ae set outside computing field Q ( j =,,..., n) ; ) Matching points M ( i =,,..., n) ae set on the conducto whose bounday conditions has been i given.thei quantity ae equal to the numbe of simulated electic chage. Electic potential expessions ae established and equations of linea simulated electic chage ae constituted accoding to the pinciple of supeposition. ϕ = P Q + P Q + P nqn ϕ = P Q + P Q + P nqn ϕ = P Q + P Q + P Q n n n nn n ; [ P][ Q] = [ ϕ] (3) Whee the element of the coefficient matix means the electic potential value of jth unit chage simulation souce geneated by ith matching point. 3)Solve equations of linea simulated electic chage and calculate the value of all the simulated electic chage[ Q ]; 4)Take anothe N check point at the suface of the conducto to check calculate accuacy. If non-compliant, then evised the chage simulation (position and numbe) until the accuacy equiements ae met; 5) electic potential o electic field of any field point A can be solved at the coesponding analytic elational expession that is based on the chage simulation discete solution[ Q] which is final calculated. calculation flow chat of chage simulation method is shown in Fig.3. j Fig.3 calculation flow chat of chage simulation method Nominal Electic Field Analysis of Lines Unde Vaious Aangement. nominal electic field unde -towe-double-cicuit DC tansmission lines is simulation calculated with softwae pogamming of MATLAB and Chage Simulation Method.

5 Applied Mechanics and Mateials Vol location of chage simulation, matching point and check point is shown in Fig.4. stuctue and size of -towe-double-cicuit DC tansmission lines towe ae shown in Fig. 5. Fig.4 location of chage simulation, Fig.5 Towe size chat of matching point and check point -towe-double-cicuit DC tansmission lines Table Gound nominal electic field calculation paamete table of -towe-double-cicuit DC tansmission lines Paamete the adius of lines/mm spacing of splitting/m numbe of splitting Value spacing of pole(m) the height of the fist line/m the height of the second line/m opeating voltage/kv Shown in the figue ±500 e ae fou main aangement of -towe-double-cicuit DC tansmission lines in the simulation analysis without consideing the way of hoizontally aanged. Fou kinds of aangement ae shown in Fig.6. Fig.6 4 aangements of -towe-double-cicuit DC tansmission lines In nomal opeation mode, it is suggested that nominal electic field distibution of -towe-double-cicuit DC Tansmission Lines unde aangement of fou is vaious. simulation distibution is shown in Figue 7.

6 36 Sustainable Enegy Nominal Electic Field Distibution On gound (KV/m) Nominal Electic Field Distibution On gound (KV/m) Distance fom the cente point of lines(m) Distance fom the cente point of lines(m) Nominal Electic Field Distibution On gound (KV) Nominal Electic Field Distibution On gound (KV) Distance fom the cente point of lines(m) Distance fom the cente point of lines(m) Fig.7 nominal electic field distibution on the gound of aangement A/B/C/D It is shown in Fig.7 that the aangement geatly influence the distibution of the nominal electic field. Details ae as follows. minimum value of the nominal gound electic field is 500V / m in the case of aangement B. exteme value appeas on the position 9m away fom the towe at the left and ight sides. Similaly, the maximum value of the nominal gound electic field is 400V / m in the case of the aangement C. Consideing the minimum gound electic field intensity, aangement B is the optimal method. Nominal Electic Field Analysis Of Lines Unde Diffeent Opeating States. opeating conditions of DC tansmission lines ae vaious. Obviously, it is possible of unipola outage, bipola outage and even all the outage in sevee cases to occu, due to lightning, line failue, convete tansfome failue, maintenance, etc. If the opeating condition of the DC tansmission lines changes, the elative paametes of lines will eact coespondingly. state of one bipola out of wok. Fo -towe-double-cicuit DC tansmission lines, thee ae two main opeating conditions including the fist bipola lines out of wok and the second bipola lines out of wok. In such situation, the gound nominal electic field distibution of -towe-double-cicuit DC tansmission lines unde the aangement of the fou cases ae vaious. simulation esults ae shown in Fig.8 and Fig.9. Fig.8 nominal electic field distibution in the condition of the fist bipola lines out of wok Fig.9 nominal electic field distibution in the condition of the second bipola lines out of wok

7 Applied Mechanics and Mateials Vol state of one unipola out of wok. Fo -towe-double-cicuit DC tansmission lines, thee ae fou main opeating states including the fist positive line out of wok, the fist negative line out of wok, the second positive line out of wok and the second negative line out of wok. In such situation, the gound nominal electic field distibution of -towe-double-cicuit DC tansmission lines unde the aangement of the fou cases ae vaious. simulation esults ae shown in Fig.0, Fig., Fig. and Fig.3. Fig.0 Nominal electic field distibution in the condition of the fist positive line out of wok Fig. nominal electic field distibution in the condition of the fist negative line out of wok Fig. nominal electic field distibution in the condition of the second positive line out of wok Fig.3 nominal electic field distibution in the condition of the second negative line out of wok It can be obseved in Fig.0-3 that the gound nominal electic field distibution of -towe-double-cicuit DC tansmission lines unde the aangement of the fou cases ae geatly diffeent when the opeating condition is one unipola out of wok. In this case, compaed to the nomal opeating state, the maximum value of the nominal electic field is much lage. Fo example, maximum value of the nominal gound electic field is 6000V / m in the case of the aangement C when the condition is the second negative line out of wok. Howeve, the value of the nominal gound electic field in the case of the aangement C becomes the minimum. efoe, it is necessay to take both the opeating state and the aangement of lines into account fo educing the gound electic field intensity. state of all pola out of wok. Fo -towe-double-cicuit DC tansmission lines, thee ae fou main opeating conditions: ) the fist negative line and the second negative line out of wok ) the fist positive line and the second positive line out of wok

8 38 Sustainable Enegy 3) the fist positive line and the second negative line out of wok 4) the fist negative line and the second positive line out of wok In such situation, the gound nominal electic field distibution of -towe-double-cicuit DC tansmission lines unde the aangement of the fou cases ae vaious. simulation esults ae shown in Fig.4, Fig.5, Fig.6 and Fig. 7. Fig.4 nominal electic field distibution in the condition of the fist negative line and the second negative line out of wok Fig.5 nominal electic field distibution in the condition of the fist positive line and the second positive line out of wok Fig.6 nominal electic field distibution in the condition of the fist positive line and the second negative line out of wok Fig.7 nominal electic field distibution in the condition of the fist negative line and the second positive line out of wok It can be implied in Fig.4-7 that the gound nominal electic field distibution of -towe-double-cicuit DC tansmission lines unde the aangement of the fou cases ae geatly diffeent when the opeating condition is all the outage. Compaed to the nomal opeating state and the two unning conditions above, the maximum value of the nominal electic field is much lage. Fo example, all the exteme value of the nominal gound electic field ae highe than 5000V / m unde the aangement of the fou cases when the condition is the fist positive line and the second positive line out of wok. Futhe obsevated, the maximum value of the nominal gound electic field is 8500V / m in the case of the aangement C when the condition is the fist positive line and the second positive line out of wok. Conclusions. ) Chage Simulation Method can be used to calculate the nominal electic field unde -towe-double-cicuit DC tansmission lines due to thei many advantages of speediness and simplicity. But in fact, it is suitable to be applied to the poject which needs less demanding pecision. )In this pape, the aangement of lines has a geat impact on the gound nominal electic field unde -towe-double-cicuit DC tansmission lines. exteme value of the nominal electic field in the case of the aangement B is the least while that in the case of the aangement C is the lagest.

9 Applied Mechanics and Mateials Vol Fom the simulation esults,it seems that the aangement B has been poved to be supeio to the othe thee kinds of aangement. 3) unning state of -towe-double-cicuit DC tansmission lines has also been poved to have a geat impact on the gound nominal electic field. gound nominal electic field distibution of -towe-double-cicuit DC tansmission lines unde the aangement of the fou cases ae also complex and changeable. exteme value of the electic field ae two o thee times as much as which is unde nomal opeating conditions. Though the simulation model significant esults showing that the unning state of -towe-double-cicuit DC tansmission lines is also an impotant consideation in consideing the limits of the electic field has been povided. Refeences [] SHENG Jianni. Engineeing Electomagnetic field numeical analysis [M]. Fist edition, Xi'an, Xi'an Jiaotong Univesity Pess, 99. [] DAI Xijie. HVDC foundation[m]. Beijing, Wate Consevancy Electical Powe Pess, 990: [3] WU Guifang,LU Jiayu,SHAO Fangyin. A highe voltage level tansmission of electomagnetic envionmental eseach [J]. Chinese Association 004 Annual Meeting of electicity sub-venue-cum-chinese Society fo Electical Engineeing 004 Confeence Poceedings, , China Hainan. [4] FU Binlan. Ge - Shang ± 500kV DC tansmission line envionmental impact [J]. Chinese Powe, 995,:7-,45. [5] U.S. Banville Powe Authoity woking goup of ecological eseach. Electic tansmission lines and Ecological Effects [M]. Beijing: Ministy of Wate Resouces Reseach Institute Publishing, 987. [6] B.L.Qin, J.N.Sheng, Z.Yan, G.Gela. Accuate calculation of ion flow field unde.hvdc bipola tansmission lines [J]. IEEE Tansactions on Powe Delivey, 988, 3(l): [7] Ming Yu,E.Kuffel. A New Algoithm fo Evaluating the Fields Associated with HVDC Powe Tansmission Lines in the Pesence of Coona and Stong Wind[J].IEEE Tansactions on Magnetics,993,9(): [8] W.Janischewskyj, G. Gela, Finite element solution fo electic fields of coonating DC tansimission lines [J]. IEEE Tansactions on Powe Appaatus and Systems. 979, PAS-98(3): [9] H.Yala, Y.Zebboudj. Analysis of cuent and electic field distibutions beneath a Positive DC wie-to-plane coona [J]. UPEC 00, 37th Intenational Univesities Powe Confeence, Staffod, United Kingdom, 00, Sep.9-,