Available online at www.sciencediect.com ScienceDiect Enegy ocedia 85 (016) 170 177 Sustainable Solutions fo Enegy and Envionment, EENVIRO - YRC 015, 18-0 Novembe 015, Buchaest, Romania The modelling of the electic field geneated by the electical tanspot lines Eleonoa Daie a, Robet ecsi a * a The Faculty of Building Sevices and Equipment, Technical Univesity of Civil Engineeing of Buchaest, Lacul Tei Bvd., no. 1 14, RO 00396, secto, Buchaest, Romania Abstact This pape pesents the basic concepts egading the electostatic effect of the electical tanspot lines on the electical lines located on the same electical suppot pilla. The influence of the electical tanspot lines on the neighbouing lines can be: electostatic, given by the electostatic field and electomagnetic, given by the electomagnetic field. Depending on the position and the configuation of the electical lines, the induced voltages and the electic field can be calculated analytically o numeically (by using the Quick Field application).two configuations ae analysed analytically: inducto line one-wied induced line and one-wied inducto line two-wied induced line. The gaphical esults (the electical potential and the electical field of the one-wied inducto line and one-wied induced line) of the expeimental simulations (inducto line one-wied induced line and one-wied inducto line) ae pesented in the Quick Field application. 016 The Authos. ublished by Elsevie Ltd. This is an open access aticle unde the CC BY-NC-ND license 015 The Authos. ublished by Elsevie Ltd. (http://ceativecommons.og/licenses/by-nc-nd/4.0/). ee-eview unde esponsibility of the oganizing committee EENVIRO 015. ee-eview unde esponsibility of the oganizing committee EENVIRO 015 Keywods: Electical line; simulation; electostatic field; electomagnetic field; numeical analysis 1. Intoduction In the liteatue [1-6] it is well-known that the electical tanspotation lines ceate electomagnetic fields aound themselves, fields that induce voltages in those electical lines that ae located on the same suppot pillas. The induced voltages ae epesenting a pat of the tanspotation lines voltage atings and can each dangeous values [1- * Coesponding autho E-mail addess: obet.pecsi@gmail.com 1876-610 016 The Authos. ublished by Elsevie Ltd. This is an open access aticle unde the CC BY-NC-ND license (http://ceativecommons.og/licenses/by-nc-nd/4.0/). ee-eview unde esponsibility of the oganizing committee EENVIRO 015 doi:10.1016/j.egypo.015.1.33
Eleonoa Daie and Robet ecsi / Enegy ocedia 85 (016) 170 177 171 & 4], thei effects being able to cause the faulty opeation of the telecommunication signalling and electic shocks [1]. The electical field geneated by the electical tanspotation lines (heeinafte called inducto lines) is depending on these lines position and configuation and on the othe electical lines being on the same suppot pilla (heeinafte called the induced lines) position and configuation. We shall analyse two cases: one-wied inducto and induced lines; one-wied inducto line and two-wied induced lines.. One-wied inducto and induced lines Figue 1 [5] shows a one-wied inducto line togethe with a one-wied induced line. It is supposed that the inducto line is chaged with the q [Cb/m] chage and has the potential of U[V]. Aound it an electic field is geneated, field that detemines in point, a point fom the induced line s suface the potential. The value of this potential can be calculated with the following equation [1]: U U ln j ln j* (1) The potential can be calculated with the equation [1], [], [3]: U UCC UC0, () whee and ae the capacities fomed between the inducto line s wie and the induced line s wie, espectively netween the induced line s wie and the eath. Fom this las equation () we can calculate the voltage : C C U U C 0 C C (3).1. The calculation of the electic field s intensity The calculation of the electic field s intensity in a point (figue 1) being in the electical field of a electical chage (the specific chage fo the length unit of the electical line) being at the height of ove the eath s level can be made with the following equation [4]: E j q j j j* 0 j j*, (4) whee ae the distances between the point,whee is located the chage and the point and, espectively between the point whee is located the chage and the point. The vetical - - and the hoizontal - components of the E electical field ae calculated in a simila way:
17 Eleonoa Daie and Robet ecsi / Enegy ocedia 85 (016) 170 177 q h h h h Ez E x j j j 0 h x h x q j x x 0 h x h x (5) Fig. 1 One-wied inducto line and one-wied induced line. By using the Maxwell equations fo the electical chages, we find [5]: UKq (6) whee [U] is the colon matix of the voltages fomed between the wies and the eath, [K] is the squae matix of the potential coefficients and [q] is the colon matix of the wies electical chages. 3. One-wied inducto lines and two-wied induced line This is the case of the telecommunication lines with two electic wies (figue ) [1], [4]. Fig. : One-wied inducto line and two-wied induced line
Eleonoa Daie and Robet ecsi / Enegy ocedia 85 (016) 170 177 173 3.1. The calculation of the induced voltages If the telecommunication line would be on the same suppot pilla with the induced line, each wie (1, ) have had the potential against the eath as calculated with equation (1). Between the two wies thee is no potentialdiffeence due to thei symmetical position [1]. In opeation thee ae two limit-situations, depending on the two lines elative positions: the fist one is that when the two lines ae on the same suppot pilla and the second one is that when the two lines have a geat distance between them. In the fist case, we can wite: h h j* j (7) Thus, equation (1) becomes: U h U ln h ln (8) whee. In the second case, we can wite fo the distances: h h j* j 4 j (9) Because the distance between the lines is big, the equation (1) becomes: U U h h j x ln (10) By analysing the equation (7), we can notice that the electostatically induced voltage is popotional with the height of the inducto line and with the height of the induced line (, espectively ) and is invese popotional with the distance between them ( ). By equation (10) we can detemine the induced voltages and [1]: hh U 1 U a ; U U h ln 1 1 hh a d h ln (11) 4. The numeical analysis fo the detemination of the powe lines electostatic effect 4.1. Genealities Quick Field [7] is a softwae aimed fo solving electical field and magnetic field poblems, based on the method of the finite elements, which is a numeical (appoximation) method fo solving the patial deivatives equations.
174 Eleonoa Daie and Robet ecsi / Enegy ocedia 85 (016) 170 177 It is consideed a ange of field D, whee is distibuted an electostatic field, descibed by a Laplace equation type (, whee V is the electostatic potential, to be detemined. [7] Fo solving this equation, we must know the values of the potential V, on the ange s bode. If the values of the potential on the bode s ange ae known, this means that we have the Diichlet type conditions [7]. Fo solving this equation with the finite elements method, the domain of the field is digitized by using the finite elements netwok [7]. 4.. Modelling and Simulation The numeical model fo the one-wie inducto line and the one-wied induced line, without consideing losses, is shown in Figue 3, analysis that solves an electostatic question, the model being plane-paallel. Electostatic analysis is used to analyse a vaiety of capacitive systems such as tansmission lines. Geneally, the quantities of inteest in electostatic analysis ae voltages and electic fields. The QuickField pogam is able to pefom a linea electostatic analysis fo D models and it is based on oisson's equation. The following options ae available fo electostatic analysis: mateial popeties (ai, othotopic mateials with constant pemittivity); loading souces (Voltages Bounday conditions; ost-pocessing esults: voltages, electic fields. We conside an inducto line (voltage ating of 0 kv, fequency of 50 Hz), in ai, located at the height of 8 metes above the gound and an induced line (voltage ating of 50 V), located at the height of 5 metes above the gound. The two lines ae mounted on electicity suppot pillas (the distance between them being of 0 metes). The voltage electostatically induced by the inducto line into the induced line is detemined numeically (figue 4). Analytically, the electostatic voltage induced by the inducto line in the induced one, fom a distance of 0 metes has the value of U = 0,5 kv (equation (10)). Is both the lines have been on the same electicity suppot pilla, the electostatic voltage induced by the inducto line in the induced one would be U = 3,7 kv (equation (8)). The esulting induced voltage is vey high and is able to impai the insulation of the induced line. The electic potential coesponding to the numeical model illustated in figue 3 is shown in figue 4. The electostatic potential vaiation, between the one-wied inducto line and induced line is shown in figue 5. Fig. 3 Numeical Model fo the one-wied inducto line and one-wied induced line (the induced line is situated at a cetain distance fom the inducto line).
Eleonoa Daie and Robet ecsi / Enegy ocedia 85 (016) 170 177 175 Fig. 4 Colou map fo electical potential of the one-wied inducto line and one-wied induced line. Fo the distant lines, we can conside that the distance measued along the aows is equal to the distance between the lines axes (as shown in figue 1). Figues 5 and 6 show the vaiation of the induced voltage and of the electic field s intensity between the inducto line the induced one, fo the analysed model. Fig. 5 - Electostatic potential vaiation, between the one-wied inducto line and one-wied induced line. Fig. 6 - Electic field vaiation, between the one-wied inducto line and one-wied induced line. The consideed inducto line ceates aound itself an intense electomagnetic field (1,55 x106 [V/m]), which induces voltages with effects that could be distubing fo the induced line.
176 Eleonoa Daie and Robet ecsi / Enegy ocedia 85 (016) 170 177 Figue 7 pesents the equilines of otential, the vectos of Stength (E), the colou Map of Stength (E) and the discetization netwok. Fig. 7.- Equilines of otential, vectos of Stength (E), colou Map fo stength and the discetization netwok fo the consideed numeical model. Fig. 8.- Colou map fo electical potential of the one-wied inducto line and one-wied induced line, deceasing the distance between them. In Figue 8, thee is shown the electostatic potential fo the one-wied inducto line and one-wied induced line, deceasing the distance between them. Analytically we can notice that the electostatic induced voltage (U =0,9 kv) is highe as the distance between the two lines deceases (to 15 metes) (equation (10)). So, the induced electostatic voltage is highe when the distance between the two lines is lowe. 5. Conclusions The electostatic influence of the electical tanspotation lines is detemined by the electic field geneated by the chages of the electic wies. This influence is pesent both at the ceep opeation and at the load opeation. Depending on the configuation of the two lines (inducto and induced, one-wied and two-wied) thee ae moe cases which can be diffeentiated and diffeently analysed analytically (equations (7-11)) and numeically (figues (3-8)). The induced voltage is popotional with the distance between the wies of the inducto lines (equations (7-11)). If the induced line is located on the same electicity suppot pilla with the inducto line (figue ), each wie 1, have a voltage to the gound that can be calculated with the equation (8). Between the two wies thee is no potential-diffeence, due to the symmetical elative position.
Eleonoa Daie and Robet ecsi / Enegy ocedia 85 (016) 170 177 177 Fo the decease of the electostatically induced voltages, thee ae measues like: the avoidance of the one-wied telecommunication lines; the diffeent positions of the electical tanspotation lines and the telecommunication lines; the stengthening of the telecommunication lines insulation, when they ae in the tanspotation lines neighbouhood; the sceening of the telecommunication lines of those sections, whee thee ae paallel intesection with the tanspotation lines. Refeences [1] I. Vulcu, Instalaţii de tanspot şi distibuţie a enegiei electice, Ed. Matix Rom, Bucueşti, 006. [] A. Buta, Tanspotul şi distibuţia enegiei electice, Ed. I.. Timişoaa, 1990. [3] O. Cişan, Sisteme electoenegetice, Ed. Didactică şi edagogică, Bucueşti, 1979. [4] H. Albet, Calitatea enegiei electice la consumato o poblemă pioitaă, Măsuăi şi Automatizăi, N.1, 005. [5] G. Dăgan, Tehnica Tensiunilo Înalte, vol. III, Ed. Academiei Române, Bucueşti, 003. [6] A. Maincu, M. Geconici, Câmpul electic şi magnetic în vecinătatea unei linii electice de înaltă tensiune şi posibilele efecte asupa sistemelo biologice, The 5th Intenational owe Systems Confeence, Timişoaa, România, 003, pp. 357-36. [7] QuickField 5.9.