813991 4CBC1 Elektrotehnika i Elektromehanika 2009 1
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Електротехніка і Електромеханіка Электротехника и Электромеханика Electrical engineering & Electromechanics 2009'1
Transcript of 813991 4CBC1 Elektrotehnika i Elektromehanika 2009 1
Electrical engineering & Electromechanics
2009'1
Electrical engineering & Electromechanics
-
2009'1
, 6115 30.04.2002 . 2002 . : .. ..., , , .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..., , ..., , ..., , ..., , ..., , , ..., , - , , ..., , ..., , , ..., , , ( ) ..., , , ..., , , , ..., , , ..., , , ..., , ..., , ..., , , ..., , ..., , ..., , , ..., , - , ..., , ..., , ..., , - , , ..., , , ..., , , ..., , , ..., , , ..., , , , . , 21, . , 61002. . (057) 707-62-81. E-mail: [email protected]
, 2009
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4
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1979 [1] (Vilm Klma). . , , , . , , , , ( ) () . . , . n = 4 , (z = 24). () . : A 1 4 (4 - 1), B 3 6 (6 - ), C 5 2 (2 - ). . n z, - , 120 , - 60, . , () [2, 3 (. 4)]. . 1 1 - 3 1 . 4, 4 - 5 2. [2, . 4] () . , . 1 - 3 . 1 , , . . . 2009. 1
1 24 z 1 2 3 4 5 6 7 8 9 10 11 12
1
1 1 1 1 1 1 1 1
2
1 1 1 1 1 1 1 3
3
1 1 1 1 1 1 2 5 1 1 1 4
4
1 1 1 1 1 1
5
1 1 1 1 3 5
[1 (9.b)] i , (1) 2 j = j0 N ki i j0 ; z ; Nki i ; kjn . (1) , Nki , , , j0. , , - , . . 2 . 1. (1). (1) , 6 (244/16). [1]. . j0 + z 1
z k2 = jn
2 N ki
5
2 . 1 1 2 3 4 5 / 1/23 0,958/ 0,958 0,744/ 0,531 0,964/ 0,964 0,744/ 0,744 0,359/ 0,344 2/22 0,837 /0,837 0,837/ 0,433 0,864/ 0,864 0,433/ 0,433 0,250/ 0,376 3/21 0,653/ 0,653 0,830/ 0,407 0,723/ 0,723 0,653/ 0,653 0,205/ 0,126 4/20 0,433/ 0,433 0,750/ 0,433 0,577/ 0,577 0,750/ 0,750 0,661/ 0,250 5/19 0,205/ 0,205 0,609/ 0,454 0,478/ 0,478 0,454/ 0,454 0,830/ 0,467 6/18 0,000/ 0,000 0,433/ 0,433 0,458/ 0,458 0,000/ 0,000 0,599/ 0,376 7/17 0,158/ 0,158 0,278/ 0,360 0,487/ 0,487 0,278/ 0,278 0,531/ 0,168 8/16 0,250/ 0,250 0,250/ 0,250 0,509/ 0,509 0,250/ 0,250 0,901/ 0,250 9/15 0,271/ 0,271 0,344 /0,168 0,493/ 0,493 0,271/ 0,271 0,958/ 0,158 10/14 0,224/ 0,224 0,433/ 0,224 0,437/ 0,437 0,433/ 0,433 0,599/ 0,250 11/13 0,126/ 0,126 0,467/ 0,342 0,367/ 0,367 0,342/ 0,342 0,407/ 0,609 12/24 0,000/ 1,000 0,433/ 0,661 0,333/ 1,000 0,000/ 0,000 0,661/ 0,250
, 1 2, 24*7/25 = 6,72. , . , :zj = j0 + mc jn k2 = 2 N ki i
, (2) 2 m N ki i m ( , m = 3 m = 6); c = 0, 1, 2, , z/m 1. (2) , (24*4/(6*16)). , j0 = 1, m = 6, = 0, 1, 2, 3 , (2) . 2:
, . ( ), , , , "" , , z. z = mn (m=6) , m n . , ni < n . (1) (2). (1) , (5) inv j = z /( m ni ). (2) j0 =1 inv j1 = z /( m ni ), j0 =2 3inv j 2 = inv j 3 = 0.
(6) (7)
k2 jn j = j0 +6c
= 0,958 + 0,158 + 0,126 + 0,205 = 1.
2
2
2
2
(3)
, j0 = 1, 2, 3, m = 3, c = 0 - 7, j =1+3c jn k 2 = 2.
(4)
, (4) (j0 = 1, 2, 3) j0. ( , . 2 ) . 2. , , . 1, . 2 , , . , (2) , , , . 1 , , - . (2) , j0 = 1, , j0 = 2. , , [1], . (1) (2) j0.
(7) , , j0 = 2 j0 = 3 (. (2)), . , ni , 3ni +1. (2) (8) inv = z /( m ni + 1). , (2): j0 = 1 inv j1 = z /(m ni + 1) 2V2 , j0 = 2 3inv j 2 = inv j 3 = z /( m ni + 1) 2 .
(9) (10)
(10) , , j0 = 2 j0 = 3 (. (2)), ni. , ni - , 3ni +2. : . 2009. 1
6
; . : j0 = 1 (11) inv j1 = z /( m ni + 2) 2 inv j 2 , j0 = 2 3inv j 2 = inv j 3 = z /( m ni + 2) 2 .
(12)
: j0 = 1 inv j1 = z /( m ni + 2) 2 inv j 2 , j0 = 2 3inv j 2 = inv j 3 = 2 z /( m ni + 2) 2 .
(13) (14)
p ; m = 6; n = z/m. . z = 24 60 y = 11 . 1. . 3 . (2.49) gp =(1+1+1+0,8662)/4 = 0,9375. (16) : k21 + k27 + k213 + k219 = 0,949472 + 0,095912 + 0,016452 + + 0,162902 = 0,9375. 1 1 1 2 1 1 3 3 4 1 1 1 2
(1) - (14) . , [2] , [1]. [1] , :0
c =0
z 1
2 k1+ c =
1 z Fk z k =1 2 F0
2
1,
(15)
; k1+c z ; Fk ; 2F0 - . (15) - . , (15) z, gp, . [1]. , , , , , . (15) , [2] ( ):n 1 c =0 k 2 +cm =
, . [4, 5], : F ko / . (17) , , , , . , >> z ( z - ) - . , , < z, . [5] =1
d =
( k0 / ) 2 ( k0 p / p ) 2 ( k0 / ) 2( k0 p / p ) 2 = =1
( k0 p / p ) 2
1, (18)
1 n Fk , n k =1 2 F0
2
(16)
k , , () 1 z/2 ( , , - , ); . 2009. 1
p . (18), . , . , , . .
7
(18) , (18) . [4, 5, 6, 7], , , . - : , . [6], . (18) z. zz / 2 1 =1 2 k0 p
: 1. - , . 2. . 3. . , , [6, 7], . 4. - [2] . [1] Klima V. On the theorem of the sum of squares of winding factors invariance // Acta tech. Csav. -1979. p. 365 - 388. [2] .. . -: . -2003. - 396 . [3] .. // . -1989. -. 7. - . 28-35. (. . . ). [4] ., . . - , , 1963. 981 . [5] - . . - . - .: , 1959. -766 . [6] .. // . 1984. - 11. 36 - 43. [7] .. - // . 2001. - 10. . 9 17. 01.09.2008
d =
A k02/ p2
1,
(19)
z( z 1) / 2 =1 2 k0 p
d =
2 A k 0
/ p2
1,
(20)
A = ( /( z sin( / z )) 2 . (21) A , , z/2 z (z-1)/2 - . (19), (20) (21) , , ` = p ( ,
2 d = p 2 A p / k 0 p 1.
(22)
, z m ( m - ) (22) , , , .
8
. 2009. 1
621.313.33:621.318.123
.., ..., ., .., .., .. , 94204, ., , . , 16, , " ", . (06442) 2-05-64, (06442) 2-68-87, E-mail: [email protected]. , , . , , .
() , , () , . , . , , , , , , , . [1, 2]. , , . . . () () : . 2009. 1
. ; . ', , ' . ' , . , () (). f, 2 , , n = 1 (1 s), 1 = 60 f1/p s . f2 = f1 s. 2 - , : f 2 = (n p n ) = (1 s ) 1 f1 = s f1 , (1) 60 S : t p 1 [M . (t ) M C ]dt 1 , (2) S = 1 p H t t - " "; ( t - t ) , ; M . = ( M ( ) M ( ) ) ; p , p () () . "+" , "-" - . - , .
9
, ' ( ) . , , , . , . - . , , , , . . , , , . (. 1).
, Excel. ' MATHCAD, . MATHCAD - (), . - , 2i , . (t), fft (V), V - , (t). - ( , ). , ', , . . , (), , 3 : ; ; - " " (s = 1); ; . . 2 6. ' . 7 11.
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5%; U U ( = ) 40. , . . ( ) . = 1,5,7,9... . . = 2,8,14... = 4,10,16. , . k = 1,5,7... , 3-. . , 8-. 5- 7- . S=1 , . n = n1 7 ( S = 6 7 ) (M7 = 0). . , 0 < S 1 , . ' , . . , ( , ) .
(), . . , , . , . . . 1. , . 2. , 0 < S 1 , . ' , . 3. . . 4. , . [1] .. : / .. . : , 2008. 259 . [2] .., .., .. . // . . . . -. : , 2007, - .24. . 370-383 [3] . Mathcad 2001: . .: , 2001. 624 .: . 15.09.2008
12
. 2009. 1
621.313.175.32
- .. , 61050, , . , 7, . (057) 730-19-96 .., ... , 61002, , ., , 12, . (057) 731-95-28, E-mail: [email protected] - - MathCAD 2001 - , . - - MathCAD 2001 - , .
. , . () , . - . I . . bn hn - MathCAD 2001: S1:=lspline(b,h) (1) H(B):=interp(S1,b,h,B) (2) B . , , , . , , B : . 2009. 1
i = Bi l W ;FFei = [2 h z1 H ( Bi K z1 ) + 2 h z 2 H ( Bi K z 2 ) +
(3)
+ ( D 2 hz 2 ) H Bi + D H
[
bz 2 K z 2 + ( D 2 hz 2 ) 2
]
(
Bi K z1 k2 Fi =Ii =
) ]
, (6) W ; l ; W ; FFe, F ; ; hz1, hz2 ; D, D , ; bz2 ; k2 ; r s r 1 s r , K z1 = s ; K z2 = s 1 s r s r r s , r - . (. 1, ) (1,2) (i).
4 10 7 Fi + FFei
100; 2 Bi 2
(4)
;
(5)
13
. 1. (i,) 180, 126, 108, 84, 72, 60 0 (c , )
(i,) , [1, 2, 4, 5, 8, 9, 11] : "" ; "" ; , . [1, 2] . , , . [5] "" , , , . [11] . , , . , , . , () ( -
.. . , . 1,8). [3, 6, 9, 11], - [2, 7], [10]. . , [5, 8], , . , [11]. :0 l W 2 , (7) FFeK 0 l W 1 + () k L() ; , ( ) = 0.5 [ max + min ( max min ) cos( )] L( ) =
, 0 = 410 7 . , . , ( ). : k (1.001 ik ) (ik ) . (8) = ik 0.001 ik , i () (. 2) , - -. (7) i [L( )] . (. 3) ( ) (10) (10) ( ) = i [ L( )] L( ) i [ L( )] .
{
}
(10) : L( ) i i i . (i , ) = (i ) ( ) i > i . 2009. 1
14
. . , (11)U 1.41 P (11) 1 . 2 f UI , , 1,41. (. 5) . , 1,68. =2
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(. 1) . 1 5 50 . (. 4).
. :
Y3Y0 1Y2 2 (Y Y ) Y Y . (12) 1 4 1 4 : i= . (13) L (12) : Y Y0 i() = 3 + 2 (Y1 Y4)2 2 Y0in + Y1in Y2 n Y3nin Y4 nin = 1 . (14) n = 1.5 . "" . (14) Y0, Y1, Y2, Y3 Y4 (. 6). . (12, 13) . 180 :
2
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. 2009. 1
15
I=
2 180 (in )2 tn , T n =0
(15)
T - , in - , tn , . K = I max / I . , K (. 7).
- . .. - // , 1998. - 6. . 50-53. [2] .. - . 1 // . 1999. - 12. . 32-41. [3] .. - . -: 2003. 149 . [4] .. - // , 2001. - 5. . 41-47. [5] .., .. . .: , 2003. 70 . [6] .., .., .., .. // , 1998. - 6. . 35 43. [7] Krishnan R. Switched Reluctance Motor Drives. Modeling, Simulation, Analysis, Design and Applications. CRC Press, 2001. 398 p. [8] Miller T.J.E. Switched Reluctance Motor and their Control. Magna Physics Publishing and Clarendon Oxford Press, 1993. 203 p. [9] .. - // , 2003. - 4. . 72-76. [10] .. - . // . 2002. - 1. . 37-43. [11] .. . : " ", 2006. - 440 . 02.06.2008 [1]
. 6. ( , )
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16
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621.313
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, . , . 120- . , , . : 1. . 2. ( ). 3. . 4. . - . . , - . , , . , , 2 p1 2 p2 - , ( ) . [1, 2]. . 2009. 1
, . , ( 2 p1 = 4 ), 2 p2 - , , 2 p2 = 2,6,8. , 2 p2 = 2. 2 p1 2 p2 = 4 2 , 2 p2 2 p1 . 2 p1 2 p2 . . 1 , . 1 21-, 21 = 4 (. 1), 2 - 22-, 22 = 2 (. 1), , 1, = 0,52 = 1. . . 1 240 . 21- , 2 120 . 22 , 1 = 2, , , . 1 2 . , . . , . , , , . , . , . 1, , , 1 2, 1 2. -
17
( ), . , . , , . 2 21- 1, , 2, , . , Z1+Z2 , , s 2 .
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22- , , . 3.
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, . , [3]. 250LC4 132 660/1140, " ". 368 , 244 , 580 , =0,9 , Z1=48, Z2=42, , =9 (1-10), 4+4, W1=64, 2,87,1. , d=9 , , 34,3 , 8,12,9 . . : d=9 , .
. 3.
22, , 2, . 2. . 8+8 1,47,1. . . 21- (21=4), , , , . 21- , 22- (22=2), 2, 2. 22- . . 2009. 1
18
60 f1 n = 0 n = . p1 + p260 f1 n = n1 p1 + p2 , . , . 23 , ,
n =
0,51 . 2 250LC4: , , , "", . . . , , , . , .
250LC4
P, U, , cos , % S, % / / / ., 1, 2, , ., ., , 1, R. 20 0, , ,
132 660/1140 152,2/87,9 0,82 92,5 1,1 6,4 2,8 3,0
7,5 2,8 3,0
0,111 865
132,09 660/1140 146 0,853 93,02 0,94 6,1 2,73 3,42 96 3,26 1,27 3,42 1,25 0,71 9,91 142 0,1095 59 0,9
132,34 660/1140 148 0,84753 92,55 0,97 7,817 3,356 4,28 98 3,35 1,32 3,42 1,85 0,715 10,655 142,995 0,111 60 0,9
132,940 660/1140 148 0,84753 92,968 0,97
3,35 1,32 3,42 1,25 0,715 10,055 142,995 0,111 60 0,9
1. 23%. 2. .
1. .., .. . .: . 1973. . . 648 . 2. - . . : . .: , 1980. 928 ., . 3. .. . .: , 1993. 203 . 31.08.2008
. 2009. 1
19
621.313.12
- .., ..., .., ... " " , 61002, , . , 21, "", " " . (057) 707-65-14, e-mail: [email protected] .. - , , 94000, , . , 53, e-mail: [email protected] - , . - , .
- () , [1, 2]. , , , , . . 1. (A-A, B-B, C-C) () ( i f , ia , ib , ic ). . 1 , . : 80,4 128 , 0,3 , , 52; 52 50 ; 0,95. , , . 2. , . 2, ea , eb , ec , . 3, e = zr ,
z r . e , , n e = et , e = z r - 30 ; n /, t .if ib ia if++
ib
ic i f C++ +
if++
B
if
ic+
ia if
A if ia ic if C B if
A if ia ib
+
if
ic ib if
+
+
+
. 1.
. 2.
. , , -. . 2009. 1
20
3
2 3
4 3
2
5 3
7 3
e = 0 3 +
e = 3 + 3 + +
. 3.
e = 3 + + 2 3 +
e = 2 3 + 2 3 + +
. , , (). , 2, 0 2 + + , v . - , . (. 2) , , . 4. e = 0 3 + a c V4 V5 (. 4,). e = 3 + , ec , : V5 V1 (. 4,). e = 3 + + c V5 , e = 3 + + 2 3 + , a (. 4,). e = 2 3 + , eb , , V4 V6, b (. 4,). a b. e = 2 3 + + + a b, . , , . 3. . 2009. 1
. 4.
: d , (1) u = r i + dt = a, b, c ; u, i, , r ; ; . : d f u f = rf i f + , (2) dt , f. : a = l a ia + mab ib + mac ic + maf i f ; b = lb ib + mba ia + mbc ic + mbf i f ; c = lc ic + mca ia + mcb ib + mcf i f ; f = l f i f + m fa ia + m fb ib + m fc ic .
(3)
l m , (1) (2). l m . - [3]. FEMM [4]. , -
21
, . , . (3) , . ( ), a, . 5 . 6, (max [3]).
l f 15. l a lb lc m fa , m fb m fc , , , .0,018 0,016 0,014 0,012 0,01 0,008 0,006 0,004 0,002 0 5 10 15 20 25 30 35 40
lf
mfa
mfc
mfb
45
. 7. I f = 4 A
. 5. = 0 I f = 6 A (max=0,008857 /)
, . ( z s = 6 , z r = 8 ) ( . 1), . : l a = l0 + l m cos e ; lb = l0 + l m cos( e 2 3); (4) lc = l0 + l m cos( e + 2 3), l0 = 0,5(la max + la min ) , lm = 0,5(la max la min ) - -
; la max , la min - . (5) l f = l f 0 p + l fmp cos 3 e . : mab = m0 mm cos( e + 3);. 6. I a = 4 A = 7,5 (max=0,004471 /)
. 7. m fa , m fb m fc 45, 15.
mca = m0 + mm cos( e 3). : maf = m0 f + mmf cos e ;mbf = m0 f + mmf cos( e 2 3); mcf = m0 f + mmf cos( e + 2 3).
mbc = m0 + mm cos e ;
(6)
(7)
. 2009. 1
22
(5), (6) (7) (4). - , [3] , : l 0 = 5,22 ; l m = 3,80 ; l fmp = 1,08 ; l f 0 p = 16,66 ;m0 f = 5,41 ; mmf = 3,92 ; m0 = 0 ,102 ; mm = 0,059 .
, (6) , , , (4), (5) (7). , (. 3 . 4). , , (1), (2) (3) (4)-(7). e = 0 3 + , a c (. 4,), : di f di C1 c + C 2 = C3 ; dt dt (8) di f dic C2 + C4 = C5 , dt dt C1 = 2(l 0 m 0 ) + l m cos ( e + 3) 2m m cos ( e 3) ; C3 = (2r + R )ic + l m e ic sin( e + 3) C 2 = 2m0 f + mmf cos ( e + 3) ; C4 = l fop + l fmp cos 3 e ;
A3 = m0 f + mmf cos e ; A4 = l0 + lm cos( e + 2 3) ; mm e ic sin( e 3) + mmf e i f sin e L1 = (r + R )ia + l m e ia sin e ;
di f dia di + A2 c + A3 = L1 ; dt dt dt di f di di (10) A2 a + A4 c + A5 = L2 ; ; dt dt dt di f di di A3 a + A5 c + F f = Lf , dt dt dt A1 = l0 + lm cos e ; A2 = m0 + mm cos( e 3) ; A1
+ mmf e i f sin( e + 2 3);+ mmf e ic sin( e + 2 3) .
L2 = ric + l m e ic sin( e + 2 3) mm e ia sin( e 3) +
A5 = m0 f + mmf cos( e + 2 3) ; F f = l fop + l fmp cos 3 e ;
L f = U f r f i f + 3l fmp e i f sin 3 e + mmf e ia sin e +
(10) (8) . ic = 0 . e = 3 + + 2 3 + a (. 4,) , , : di f di C1 a + C 2 = C3 ; dt dt (11) di f dia C2 + C4 = C5 , dt dt C1 = l0 + lm cos e ; C2 = m0 f + mmf cos e ;C3 = (r + R )ia + l m e ia sin e + mm f e i f sin e ; C5 = U f r f i f + mmf eia sin e + 3l fmp ei f sin 3 e .C4 = l fop + l fmp cos 3 e ;
2mm e ic sin( e 3) + mmf e i f sin( e + 3);
C5 = U f r f i f + mmf eic sin( e + 3) + 3l fmp ei f sin 3 e .
(8) : ic = 0 , e = 0 , i f = U f r f . c, :ec = c f t mc f i f = = t
(
)
mm f ei f sin ( + 2 3) mo f + mm f cos( + 2 3)
[
] dt
di f
(9) 0.
(11) , (10). e = 2 3 + , b (): b f mb f i f eb = = = t t (12) = m mf e i f sin ( 2 3)
(
)
V4-Va- a--V1-R, Vc - c -V5-V1 (.4,). e = 3 + 3 + + :
mof + m mf cos( 2 3)
[
] di f dt
0.
e = 2 3 + 2 3 + + b (. 4,) :
. 2009. 1
23
A3 = m0 f + mmf cos e ; A4 = l0 + lm cos( e 2 3) ; + mmf e i f sin e ;
di f dia di + A2 b + A3 = L1 ; dt dt dt di f di di (13) A2 a + A4 b + A5 = L2 ; dt dt dt di f di di A3 a + A5 b + F f = Lf , dt dt dt A1 = l0 + lm cos e ; A2 = m0 mm cos( e + 3) ; A1
L1 = (r + R )ia + l m e ia sin e mm e ib sin( e + 3) +A5 = m0 f + mmf cos ( e 2 3) ; F f = l fop + l fmp cos 3 e ;. 8.
+ mmf e i f sin( e 2 3);+ mmf e ib sin( e 2 3) .
L2 = rib + l m e ib sin( e 2 3) mm e ia sin( e + 3) +
L f = U f r f i f + 3l fmp e i f sin 3 e + mmf e ia sin e +
(13) (11) . ik = 0 , ia = ib . e = 2 3 + + + a b . , , , . 3. . - . . 8 . 9 . i0 , ( i0 ), . , . 3 e = 2 . . , . , , - , ( , ).
. 9.
, , . , . 9 , , . [1] .., .. // "". 2002. - 4. . 49-52. [2] .., .. // . - 2007. 4. . 9-12. [3] .., .. // .-2006.-2. - . 40-46. [4] Meeker D. Finite Element Method Magnetics. Version 4.0. Users Manual, January 26, 2004 // http://femm.berlios.de, 2003. 01.07.2008
24
. 2009. 1
621.316.933.064.4
.., .., . " " , 61002, , . , 21, "", " " . (057) 707-64-84, . . . . . .
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, . . . . , , (. 1).
. 1. ,
, . , : - ; - ; - ; - , 6 .. ,
25
, [1,2]. , , dW dQTO dQ0 = , (1) dt dt dt dW dt dQTO ; dt dQ0 ; , dt . , (1) , , . . , . , . . , , .. , . , , . , , , . , , , . , S , , : (1); (2); (3), (. 2).
q l
1
3
2
. 2. : 1 ; 2 ; 3
l S, V, m: l = (T ) , (2) q ; q 2 V = Sl = r0 ( ) , (3) q r0 ; 2 m = r0 ( ) , (4) q : Q = mQ0 , (5) Q0 , . , V, :Q = qSt , (6) t , , : t = j Q0 , (7) q2 j . : q2 = . (8) t j Q0 ( ) , , . : dT + k (T T0 )dS , j 2dV = cj (9) dt ; ; k n=
26
. 2009. 1
; , 0 () . - dV, ; , . dT / dt > 0 dV . , . , . , . , : , , , , . [3] , , : (10) q , , k ; q , , , ; q , ; qi , , , , -
ji , je , ; je ; A0 ;
; E k ; k ; U k ; mi , m , , . [4, 5] , , . , . , 10-1000 , . , . , . , , . , , . , , , . [1] .., .. ., . . . " ",-, , 1993. - C. 230-235. [2] .., .., .., .. . . . , 1978 , 1.- . 8285. [3] .., .., .. . // , 1985, .11. - . 74-78. [4] .., .. . - .: , 1973.479 . [5] .. .- : , 1983 361 . 25.04.2008
k q + q + q = qi + qe + qR + qa ,
; qe , , : , , , , -
; , : , , , , . , , : j = je + ji je ; e eEk je = A0T 2 exp kT
qR
(
) ;
1 2 5 2 Ek = 7,6 10 U k ji
1 2 mi je , me
(10)
. 2009. 1
27
621.314
.., ..., ., , 83000, , . 58, , "" .(062) 304-90-28, Email: [email protected] . . . .
() . . [1], [2] .. , . . , , [3] . . . () [1], , . (5, 7 ..), . . , , . 600 . "" , .
: . : - ; - ; - , . n () . , . , , , U(1) I(1). , U(1). i=1n, (. 1) : i 1
