РАСПРЕДЕЛЕНИЕ ПОТЕНЦИАЛА В ОКРЕСНОСТИ ОПОРЫ ЛИНИИ ЭЛЕКТРОПЕРЕДАЧИ

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<ul><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p> .. </p><p>. - . , . . Matlab. . : , , , , . </p><p> REPARTIIE TRIDIMENSIONAL A CMPULUI ELECTRIC N VECINTATEA </p><p>PILONULUI ELECTRIC Paiuc V.I. </p><p>Institutul de Energetic al AM Rezumat. n lucrare se examineaz o nou abordare a utilizrii metodei volumelor finite pentru a calcula cmpul electric n mediul tridimensional neomogen spaial. S-a formulat problema Dirichlet cu construirea reelei de divizare denumit trianghiularea Delaunay i celulele Voronoi. S-a propus algoritmul de calcul numeric a potenialului i intensitii cmpului electric n spaiul n vecintatea pilonului electric. A fost elaborat algoritmul i programa de calcul n mediul aplicaiei Matlab. Sunt prezentate rezultatele calculelor repartiiei potenialului i a intensitii cmpului electric n spaiu. Cuvinte-cheie: Cmp electric, mediu neomogen, potenial, intensitatea cmpului electric, metod numeric. </p><p>POTENTIAL DISTRIBUTION IN VICINITY OF TRANSMISSION LINE SUPPORT Patsiuk V.I. </p><p>Institute of Power Engineering of the Academy of Sciences of Moldova </p><p>Abstract. The paper examines a new approach to finite volume method which is used to calculate the electric field of spatially inhomogeneous three-dimensional environment. The Dirichlet problem is formulated and the computational grid is constructed on the base of space partition, which is known as Delaunay triangulation with the use of Voronoi cells. To calculate the potential and the electric field strength in the vicinity of the electric line support the numerical algorithm is proposed. We have developed the algorithm and the corresponding software using Matlab application. There are presented some numerical results of calculations of the distribution of potential and of the electric field strength. Keyword: Electric field, inhomogeneous medium, potential, electrical field strength, numerical method. </p><p>1. </p><p> 500 . </p><p>2. </p><p> , ) - : a = 1 a = 6 . . 1 , 2Lx, Ly, Lz, . </p><p>),,( zyxu</p><p>,( yxa</p><p>54</p></li><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p> 500 , . z = 0 . . , x = Lx, x = -Lx z = Lz . y = 0 y = Ly . </p><p>. 1. 500 ),,( zyxu </p><p> ),,()grad(div zyxua , (1) . ),,( zyx , (1) </p><p>. 0(div )grad ua ), zy,(xu</p><p> ),,(),,( zyxzyxu </p><p>, (2) </p><p>55</p></li><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p> ( ) </p><p> 0</p><p>nu . (3) </p><p> E</p><p> u </p><p>, uE grad</p><p>ED a</p><p>[</p><p>. </p><p> : 0] u , , . </p><p>0)],[( nD </p><p>n</p><p> 3. </p><p> (1)-(3) : </p><p>A. , . B. (1) </p><p> . C. . D. . . </p><p> : </p><p> a) </p><p>56</p></li><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p> ) </p><p>. 2. ) ) a) , , </p><p> (advancing front method) [1, 2]. : ( ). : . . . 2 , . </p><p>b) , , </p><p>c) , . </p><p> (), , . </p><p> , . . . 3 13 2012. , , , . , , . </p><p>hT h*hT</p><p>57</p></li><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p> a) </p><p> ) </p><p>. 3. 13 ) 2012 ), </p><p> , . </p><p> Qi, , </p><p> , . </p><p>0P*</p><p>0PK*</p><p>0PK</p><p>0P (1)-(3) -</p><p> ) , ,,( zyxuh hTK . . ) . </p><p>hT ,,( zyxuh</p><p>58</p></li><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p> 4. 4321 PPPPK </p><p> 4321 PPPPK (. 4) . </p><p> hT ),,( zyxP</p><p>4,1),,( iyxNi , : 1 </p><p> 0: . </p><p> : </p><p>kiki</p><p>,0,1</p><p>(PN ki )</p><p> iiiii wzwywxwzyxN ,4,3,2,1),,( . (4) </p><p> , , iw ,1 iw ,2 iw ,3 iw ,4 4,1, iwi . </p><p> iw 4 4,1, ifwA ii . </p><p> A 4,1),,,( izyxPP iiiii </p><p>1111</p><p>444</p><p>333</p><p>222</p><p>111</p><p>zyxzyxzyxzyx</p><p>A </p><p>ki</p><p>ffffff ikiiiii ,0),,,,( ,,4,3,2,1</p><p> ki,1</p><p>)</p><p>)</p><p>. </p><p> , ( ) </p><p> ) , i = 1, 2, , n, n+1, , n1, n n1 . -, .. , . </p><p>,,( zyxi</p><p>iP,,( zyxh</p><p>,,( zyxi</p><p>u</p><p> . (5) </p><p>1</p><p>1),,(),,(</p><p>n</p><p>iiih zyxuzyxu</p><p>59</p></li><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p> , ui (4) </p><p> : ) iiiih uzyxu,,( iiii zyxP ),,( . , (1)-(3) </p><p> , . (5) (1) ),,( zyxk </p><p> nkdVdVu kkha ,1,)grad(div </p><p>; (6) </p><p> ; (7) kn</p><p>iikik</p><p>n</p><p>iiia udVu </p><p>~)grad(div11</p><p>11</p><p> dVdVdV kiakiakikk </p><p>gradgrad)grad(div;~ . </p><p> , (7) </p><p> , kn</p><p>iikiu </p><p>1nk</p><p>n</p><p>niikikk ,1,</p><p>~ 1</p><p>1 </p><p>. (8) </p><p> , , (6) </p><p> , . </p><p> ) : , .. - . (6) </p><p>)</p><p>)</p><p>)</p><p>,,( zyxk</p><p>,,( zyxk</p><p>,,( zyxk</p><p>)()( 20</p><p>2 LW,,( zyxk</p><p>*hT</p><p>kP</p><p> nkdVdVu kkha ,1,)grad(div </p><p> (9) </p><p> , ) ,,( zyxk</p><p>*kP</p><p>K , (10) </p><p>**</p><p>)grad(divkPkP KK</p><p>ha dVdVu</p><p> . *</p><p>kPK kP </p><p> hu</p><p>60</p></li><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p>) . Oxyz ,,()grad(div zyxua . *</p><p>kPK</p><p> grada</p><p> , (10) </p><p> . (11) *</p><p>),,(kPK</p><p>dVzyx*</p><p>)(divkPK</p><p>dVu</p><p> (11) </p><p> S*</p><p>gradkP</p><p>a*</p><p>)grad(divkP KK</p><p>a dudVu </p><p>**</p><p>),grad(kPkP K</p><p>aK</p><p>a dSnudSnu , (12) </p><p> ; *</p><p>kPK *</p><p>kPK n </p><p> , u . (11) </p><p>*kP</p><p>K nu /</p><p>a nu</p><p>*0PK</p><p> **</p><p>),,(kPkP KK</p><p>dVzyxdS . (13) </p><p> , (1)-(3) </p><p> (13) . , . , - (8). </p><p> (. 3) 0P 8,0, iPi </p><p> ; 12,1, iSi , iPP0 ; </p><p>12,1, iM i iPP0 . </p><p> (13) : iS</p><p>*0PK</p><p>12</p><p>1 0</p><p>012 )()(</p><p>)(*0</p><p>ii</p><p>i</p><p>iia</p><p>iKa S</p><p>PPPuPu</p><p>MdSnudS</p><p>nu</p><p>P</p><p>1 S</p><p>a</p><p>i</p><p>, </p><p> iPP0 iPP0 . </p><p> (12) </p><p>61</p></li><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p> , 00 )(),(</p><p>*0</p><p>VPdVyxPK</p><p> V0 . (13) </p><p>*0PK</p><p> 0012</p><p>1 0</p><p>0 )()()(</p><p>)( VPSPP</p><p>PuPuMi</p><p>ii</p><p>iia </p><p>. </p><p> 0P </p><p> ; (14) 0012</p><p>100 )()()( VPPuPu</p><p>iii </p><p>12</p><p>10</p><p>0</p><p>;12,1,)(i</p><p>ii</p><p>iiai i</p><p>PPSM . </p><p> (14), </p><p> , , (2). , , (14) i (14). . , , . (13) ( 9 25), . . , . </p><p> ) </p><p> . v </p><p>,,( zyxuhugradEEEE zyx ),,(</p><p>E</p><p>, , E</p><p>. const),,( zyxu const),,( zyxv</p><p>),, zyx </p><p>. </p><p>(v</p><p> , (15) ),,(</p><p>),,( 000</p><p>),(zyx</p><p>zyxzyx dzEdyEdxEyxv </p><p> , . </p><p>000 ,, zyx</p><p>62</p></li><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p> , . </p><p> C </p><p> 21 uu</p><p>qC</p><p> , (16) </p><p> . q , V, </p><p>)( 21 uu </p><p>VS E</p><p>SS</p><p>SduSdEq</p><p>grad </p><p>SS</p><p>dSnudSnu )(grad . (17) </p><p> S , ; ; . </p><p>n</p><p>4. </p><p>Matlab. </p><p> . 5. </p><p> ),,( zyxu ],,[:),,( xx LLxzyxP ],0[],,0[ zy LzLy Lx = Lz = 160 , Ly = 200 . . 5. 3 400/51, r0=1,13 c, 40 , 17,3 . 10,05 . </p><p>63</p></li><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p> . </p><p> 4 , 0,14 . 33024. 1909507 . </p><p> 6. 6 ( ) () y = 36,23; 1,37; 0,675 0 . , y = 36,23 y = 200 , .. 36,23 . y = 0 264,9 /. y = 36.23 193,9 /. </p><p> (16), (17) . </p><p>y =152,4 : / </p><p>27.780.161.080.115.780.161.080.127.7</p><p>C</p><p>y =0,675 : /. </p><p>32.1088.025.088.039.1088.025.088.032.10</p><p>C</p><p> y = 36.23 y = 1.37 </p><p>64</p></li><li><p>PROBLEMELE ENERGETICII REGIONALE 3(23) 2013 ELECTROENERGETIC </p><p>65</p><p> y = 0.675 y = 0 </p><p> . 6. ( ) () </p><p> y = 36,23; 1,37; 0,675 0 </p><p>1. ),,( zyx u , </p><p> ),( yxa - . </p><p>2. . . </p><p>3. , - . . </p><p>4. , . </p><p> [1] .., .. </p><p> . , . 5, N 2, 2000, . 82-91 </p><p>[2] .. (). http://ps300.narod.ru/fr3d/mesh.htm </p><p> .. - , . : , , , . 100 , 1 10 . E-mail: patsiuk@mail.ru </p><p>http://ps300.narod.ru/fr3d/mesh.htmmailto:patsiuk@mail.ru</p></li></ul>

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