10. Tables Table 1 Natural values of the trigonometric functions sine and cosine sin 0°…sin 15° minute 0 6 12 18 24 30 36 42 48 54 60 degree ,0 ,1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 (1,0) 0 0,00000 00175 00349 00524 00698 00873 01047 01222 01396 01571 01745 89 1 01745 01920 02094 02269 02443 02618 02792 02967 03141 03316 03490 88 2 03490 03664 03839 04013 04188 04362 04536 04711 04885 05059 05234 87 3 05234 05408 05582 05756 05931 06105 06279 06453 06627 06802 06976 86 4 06976 07150 07324 07498 07672 07846 08020 08194 08368 08542 08716 85 5 08716 08889 09063 09237 09411 09585 09758 09932 10106 10279 10453 84 6 10453 10626 10800 10973 11147 11320 11494 11667 11840 12014 12187 83 7 12187 12360 12533 12706 12880 13053 13226 13399 13572 13744 13917 82 8 13917 14090 14263 14436 14608 14781 14954 15126 15299 15471 15643 81 9 15643 15816 15988 16160 16333 16505 16677 16849 17021 17193 17365 80 10 0,17365 17537 17708 17880 18052 18224 18395 18567 18738 18910 19081 79 11 19081 19252 19423 19595 19766 19937 20108 20279 20450 20620 20791 78 12 20791 20962 21132 21303 21474 21644 21814 21985 22155 22325 22495 77 13 22495 22665 22835 23005 23175 23345 23514 23684 23853 24023 24192 76 14 24192 24362 24531 24700 24869 25038 25207 25376 25545 25713 25882 75 (1,0) ,9 ,8 ,7 ,6 ,5 ,4 ,3 ,2 ,1 ,0 degree 60 54 48 42 36 30 24 18 12 6 0 minute cos 75°…cos 90° Natural values of the trigonometric functions sine and cosine sin 15°…30° minute 0 6 12 18 24 30 36 42 48 54 60 degree ,0 ,1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 (1,0) 15 25882 26050 26219 26387 26556 26724 26892 27060 27228 27396 27564 74 16 27564 27731 27899 28067 28234 28402 28569 28736 28903 29070 29237 73 17 29237 29404 29571 29737 29904 30071 30237 30403 30570 30736 30902 72 18 30902 31068 31233 31399 31565 31730 31896 32061 32227 32392 32557 71 19 32557 32722 32887 33051 33216 33381 33545 33710 33874 34038 34202 70 20 0,34202 34366 34530 34694 34857 35021 35184 35347 35511 35674 35837 69 21 35837 36000 36162 36325 36488 36650 36812 36975 37137 37299 37461 68 22 37461 37622 37784 37946 38107 38268 38430 38591 38752 38912 39073 67 23 39073 39234 39394 39555 39715 39875 40035 40195 40355 40514 40674 66 24 40674 40833 40992 41151 41310 41469 41628 41787 41945 42104 42262 65 25 42262 42420 42578 42736 42894 43051 43209 43366 43523 43680 43837 64 26 43837 43994 44151 44307 44464 44620 44776 44932 45088 45243 45399 63 27 45399 45554 45710 45865 46020 46175 46330 46484 46639 46793 46947 62 28 46947 47101 47255 47409 47562 47716 47860 48022 48175 48328 48481 61 29 48481 48634 48786 48938 49090 49242 49394 49546 49697 49849 50000 60 (1,0) ,9 ,8 ,7 ,6 ,5 ,4 ,3 ,2 ,1 ,0 degree 60 54 48 42 36 30 24 18 12 6 0 minute cos 75°…60° Natural values of the trigonometric functions sine and cosine sin 30°…45° minute 0 6 12 18 24 30 36 42 48 54 60 degree ,0 ,1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 (1,0) 30 0,50000 50151 50303 50453 50603 50754 50904 51054 51204 51354 51504 59 31 51504 51653 51803 51952 52101 52250 52399 52547 52696 52844 52992 58 32 52992 53140 53288 53435 53583 53730 53877 54024 54171 54317 54464 57 33 54464 54610 54756 54902 55048 55194 55339 55484 55630 55775 55919 56 34 55919 56064 56208 56353 56497 56641 56784 56928 57071 57215 57358 55 35 57358 57501 57643 57786 57928 58070 58212 58354 58496 58637 58779 54 36 58779 58920 59061 59201 59342 59482 59622 59763 59902 60042 60182 53 37 60182 60321 60460 60599 60738 60876 61015 61153 61291 61429 61566 52 38 61566 61704 61841 61978 62115 62251 62388 62524 62660 62796 62932 51 39 62932 63068 63203 63338 63473 63608 63742 63877 64011 64145 64279 50 40 0,64279 64412 64546 64679 64812 64945 65077 65210 65342 65474 65606 49 41 65606 65738 65869 66000 66131 66262 66393 66523 66653 66783 66913 48 42 66913 67043 67172 67301 67430 67559 67688 67816 67944 68072 68200 47 43 68200 68327 68455 68582 68709 68835 68962 69088 69214 69340 69466 46 44 69466 69591 69717 69842 69966 70091 70215 70339 70463 70587 70711 45 (1,0) ,9 ,8 ,7 ,6 ,5 ,4 ,3 ,2 ,1 ,0 degree 60 54 48 42 36 30 24 18 12 6 0 minute cos 60°…45° Natural values of the trigonometric functions sine and cosine sin 45°…60° minute 0 6 12 18 24 30 36 42 48 54 60 degree ,0 ,1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 (1,0) 45 0,70711 70834 70957 71080 71203 71325 71447 71569 71691 71813 71934 44 46 71934 72055 72176 72297 72417 72537 72657 72777 72897 73016 73135 43 47 73135 73254 73373 73491 73610 73728 73846 73963 74080 74198 74314 42 48 74314 74431 74548 74664 74780 74896 75011 75126 75241 75356 75471 41 49 75471 75585 75700 75813 75927 76041 76154 76267 76380 76492 76604 40 50 0,76604 76717 76828 76940 77051 77162 77273 77384 77494 77605 77715 39 51 77715 77824 77934 78043 78152 78261 78369 78478 78586 78694 78801 38 52 78801 78908 79016 79122 79229 79335 79441 79547 79653 79758 79864 37 53 79864 79968 80073 80178 80282 80386 80489 80593 80696 80799 80902 36 54 80902 81004 81106 81208 81310 81412 81513 81614 81714 81815 81915 35 55 81915 82015 82115 82214 82314 82413 82511 82610 82708 82806 82904 34 56 82904 83001 83098 83195 83292 83389 83485 83581 83676 83772 83867 33 57 83867 83962 84057 84151 84245 84339 84433 84526 84619 84712 84805 32 58 84805 84897 84989 85081 85173 85264 85355 85446 85536 85627 85717 31 59 85717 85806 85896 85985 86074 86163 86251 86340 86427 86515 86603 30 (1,0) ,9 ,8 ,7 ,6 ,5 ,4 ,3 ,2 ,1 ,0 degree 60 54 48 42 36 30 24 18 12 6 0 minute cos 30°…45° Natural values of the trigonometric functions sine and cosine sin sin 60°…75° minute 0 6 12 18 24 30 36 42 48 54 60 degree ,0 ,1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 (1,0) 60 0,86603 86690 86777 86863 86949 87036 87121 87207 87292 87377 87462 29 61 87462 87546 87631 87715 87798 87882 87965 88048 88130 88213 88295 28 62 88295 88377 88458 88539 88620 88701 88782 88862 88942 89021 89101 27 63 89101 89180 89259 89337 89415 89493 89571 89649 89726 89803 89879 26 64 89879 89956 90032 90108 90183 90250 90334 90408 90483 90557 90631 25 65 90631 90704 90778 90851 90924 90996 91068 91140 91212 91283 91355 24 66 91355 91425 91496 91566 91636 91706 91775 91845 91914 91982 92050 23 67 92050 92119 92186 92254 92321 92388 92455 92521 92587 92653 92718 22 68 92718 92784 92849 92913 92978 93042 93106 93169 93232 93295 93358 21 69 93358 93420 93483 93544 93606 93667 93728 93789 93849 93909 93969 20 70 0,93969 94029 94088 94147 94206 94264 94322 94380 94438 94495 94552 19 71 94552 94609 94665 94721 94777 94832 94888 94943 94997 95052 95106 18 72 95106 95159 95213 95266 95319 95372 95424 95476 95528 95579 95630 17 73 95630 95681 95732 95782 95832 95882 95931 95981 96029 96078 96126 16 74 96126 96174 96222 96269 96316 96363 96410 96456 96502 96547 96593 15 (1,0) ,9 ,8 ,7 ,6 ,5 ,4 ,3 ,2 ,1 ,0 degree 60 54 48 42 36 30 24 18 12 6 0 minute cos 15°…30° Natural values of the trigonometric functions sine and cosine sin 75°…90° minute 0 6 12 18 24 30 36 42 48 54 60 degree ,0 ,1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 (1,0) 75 96593 96638 96682 96727 96771 96815 96858 96902 96945 96987 97030 14 76 97030 97072 97113 97155 97196 97237 97278 97318 97358 97398 97437 13 77 97437 97476 97515 97553 97592 97630 97667 97705 97742 97778 97815 12 78 97815 97851 97887 97922 97958 97992 98027 98061 98096 98129 98163 11 79 98163 98196 98229 98261 98294 98325 98357 98389 98420 98450 98481 10 80 0,98481 98511 98541 98570 98600 98629 98657 98686 98714 98741 98769 9 81 98769 98796 98823 98849 98876 98902 98927 98953 98978 99002 99027 8 82 99027 99051 99075 99098 99122 99144 99167 99189 99211 99233 99255 7 83 99255 99276 99297 99317 99337 99357 99377 99396 99415 99434 99452 6 84 99452 99470 99488 99506 99523 99540 99556 99572 99588 99604 99619 5 85 99619 99635 99649 99664 99678 99692 99705 99731 99731 99744 99756 4 86 99756 99768 99780 99792 99803 99813 99824 99834 99844 99854 99863 3 87 99863 99872 99881 99889 99897 99905 99912 99919 99926 99933 99939 2 88 99939 99945 99951 99956 99961 99966 99979 99974 99978 99982 99985 1 89 99985 99988 99990 99993 99995 99996 99998 99999 99999 1.00000 1.00000 0 (1,0) ,9 ,8 ,7 ,6 ,5 ,4 ,3 ,2 ,1 ,0 degree 60 54 48 42 36 30 24 18 12 6 0 minute cos 15°…0° Table 2 Resistances and weights of copper wires Diameter Cross section Resistance per km with 15°(288 k) Length of a wire of 1 W Weight per km Length of a wire of 1 kg mm mm 2 W m kg m 0,1 0,0079 2215 0,4514 0,070 14306 0,2 0,0314 553,9 1,856 0,280 3577 0,3 0,0707 246,2 4,062 0,629 1590 0,4 0,1257 138,5 7,222 1,118 894,1 0,5 0,1964 88,62 11,28 1,748 572,2 0,6 0,2827 61,54 16,25 2,516 397,4 0,7 0,3848 45,21 22,12 3,425 292,0 0,8 0,5026 34,62 28,89 4,474 223,5 0,9 0,6362 27,35 36,56 5,662 176,6 1,0 0,7854 22,15 45,14 6,990 143,1 1,1 0,9503 18,31 54,62 8,458 118,2 1,2 1,1310 15,38 65,00 10,07 99,35 1,3 1,3273 13,11 76,28 11,81 84,65 1,4 1,5394 11,30 88,47 13,70 72,99 1,5 1,7671 9,846 101,6 15,73 63,58 1,6 2,0106 8,654 115,6 17,89 55,88 1,7 2,2698 7,666 130,5 20,20 49,50 1,8 2,5447 6,838 146,2 22,65 44,15 1,9 2,8353 6,137 162,9 25,23 39,63 2,0 3,1416 5,539 180,6 27,96 35,77 2,1 3,4636 5,024 199,1 30,83 32,44 2,2 3,8013 4,577 218,5 33,83 29,56 2,3 4,1548 4,188 238,8 36,98 27,04 2,4 4,5239 3,846 260,0 40,26 24,84 2,5 4,9087 3,545 282,1 43,69 22,89 2,6 5,3093 3,277 305,1 47,25 21,16 2,7 5,7256 3,039 329,1 50,96 19,62 2,8 6,1575 2,826 353,9 54,80 18,25 2,9 6,6052 2,634 379,6 58,79 17,01 3,0 7,0686 2,462 406,2 62,91 15,90 3,1 7,5477 2,305 433,8 67,17 14,89 3,2 8,0425 2,164 462,2 71,58 13 79 3,3 8,5530 2,034 491,6 76,12 13,14 3,4 9,0792 1,916 521,8 80,80 12,38 3,5 9,6211 1,809 552,9 85,63 11,68 3,6 10,1790 1,709 585,0 90,59 11,04 3,7 10,752 1,618 617,9 95,69 10,45 3,8 11,341 1,534 651,8 100,9 9,907 3,9 11,946 1,457 686,5 106,3 9,406 4,0 12,566 1,385 722,2 111,8 8,941 4,1 13,203 1,318 758,8 117,5 8,510 4,2 13,854 1,256 796,2 123,3 8,110 4,3 14,522 1,198 834,6 129,2 7,737 4,4 15,205 1,144 873,9 135,3 7,389 4,5 15,904 1,094 914,0 141,5 7,065 4,6 16,619 1,047 955,1 147,9 6,761 4,7 17,349 1,003 997,1 154,4 6,476 4,8 18,096 0,9616 1040 161,1 6,209 4,9 18,857 0,9227 1084 167,8 5,958 5,0 19,635 0,8862 1128 174,7 5,722 5,1 20,428 0,8518 1174 181,8 5,500 5,2 21,237 0,8193 1221 189,0 5,291 5,3 22,062 0,7887 1268 196,4 5,093 5,4 22,902 0,7598 1316 203,8 4,906 5,5 23,758 0,7324 1365 211,5 4,729 5,6 24,630 0,7065 1416 219,2 4,562 5,7 25,518 0,6819 1467 227,1 4,403 5,8 26,421 0,6586 1518 235,1 4,253 5,9 27,340 0,6463 1571 243,3 4,110 6,0 28,274 0,6154 1625 251,6 3,974 6,1 29,225 0,5974 1680 260,1 3,845 6,2 30,191 0,5763 1735 268,7 3,722 6,3 31,172 0,5582 1792 277,4 3,604 6,4 32,170 0,5409 1849 286,3 3,493 6,5 33,183 0,5244 1907 295,3 3,386 6,6 34,212 0,5086 1966 304,5 3,284 6,7 35,257 0,4935 2026 313,8 3,187 6,8 36,317 0,4791 2087 323,2 3,094 6,9 37,393 0,4653 2149 332,8 3,005 Table 3 Specific resistance and conductivity of essential materials at 20° C (193 K) Material Spec. Resistance Conductivity Aluminium, soft 0,028 36 Lead 0,2 5 Gold 0,022 45 Copper E-Cu, soft 0,01754 57 Brass Ms 58 0,059 17 Brass Ms 63 0,071 14 Nickel silver NiMs 0,5…0,15 2,0…6,7 Platinum 0,098 10,2 Mercury 0,960 1,042 Silver 0,01629 61,4 Steel, ingot iron 0,12 8 Grey iron 1 1 Tungsten 0,059 17 Zinc 0,062 16 Resistance alloy: Chrome nickel 1…1,2 1…0,83 Constantan (WM 50) 0,5 2 Manganin 0,4 2,5 Niccolite 0,5 2 Al-Cr-Steel 1,4 0,7 Arc lamp carbon 13…100 0,08…0,01 Table 4 Temperature coefficient Material Temperature coefficient of an electrical resistance between 0° and 100° C (173 and 273 K) Aluminium +0,0037 Aluminium bronze +0,001 Lead +0,00417 Iron +0,0045 Electron Constantan 0,00005 Copper +0,0043 Manganin +0,00001 Brass +0,0015 Molybdenum +0,0043 Nickel silver +0,00007 Nickel +0,0041 Niccolite +0,00022 Platinum +0,0039 Platinum-Rhodium (10 % Rh.) +0,0017 Mercury +0,00090 Silver +0,0036 Steel +0,0045… 0,005 Tantalum +0,0034 Bismuth +0,0037 Tungsten +0,004-1 Zinc +0,0039 Tin +0,0042 Table 5 Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for lines with copper conductor and plastic, silicone-rubber or glass-silk insulation Conductor cross-sectional area Current-carrying capacity Rated current of overcurrent protection device A A mm 2 1 2 3 4 1 2 3 4 0,5 12 10 9 8 10 10 6 6 0,75 16 13 12 11 16 10 10 10 1,0 20 17 15 14 20 16 10 10 1,5 26 22 20 18 25 20 20 16 2,5 36 31 27 24 36 25 25 20 4 50 43 38 34 50 36 36 25 6 63 54 50 46 63 50 50 36 10 86 74 64 59 80 63 63 50 16 117 101 87 80 100 100 80 80 25 155 133 116 105 125 125 100 100 35 192 165 144 130 160 160 125 125 50 240 206 180 163 224 200 160 160 70 300 259 225 204 300 250 224 200 95 365 314 274 248 355 300 250 224 120 425 366 319 289 425 355 300 250 150 480 413 360 326 425 355 355 300 185 542 466 406 368 500 425 355 355 240 640 551 480 435 600 500 425 425 300 735 633 551 500 600 600 500 500 These values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems). Pay attention to the current-carrying capacity factors according to the Tables 9 to 12. Table 6 Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for lines with aluminium conductor and plastic, silicone-rubber and glass-silk insulation Conductor cross- sectional area Current-carrying capacity Rated current of overcurrent protection device A A for number of cores carrying current in operation mm 2 1 2 3 4 1 2 3 4 2,5 27 23 30 18 25 20 20 16 4 37 32 28 24 36 25 25 20 6 50 43 37 34 50 36 36 25 10 67 57 50 46 63 50 50 36 16 90 77 67 61 80 63 63 50 25 120 103 90 81 100 100 80 80 35 148 127 111 100 125 125 100 100 50 187 161 140 127 160 160 125 125 70 231 200 173 154 200 200 160 125 95 282 243 212 191 250 224 200 160 120 328 283 246 223 224 200 150 376 325 283 249 355 300 250 224 185 480 370 322 292 425 355 300 250 240 502 492 376 342 500 425 355 300 300 578 497 433 395 500 425 425 355 Use: With more than one conductor (core), the current-carrying capacity and the rated current of the overcurrent protection device are reduced as stated above. The values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems). Pay attention to the current-carrying capacity factors according to the tables 9 to 12. Table 7 Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for rubber-insulated lines with copper conductor Conductor cross-sectional area Current-carrying capacity Rated current of overcurrent protection device A A for number of cores carrying current in operation mm 2 1 2 3 4 1 2 3 4 0,5 11 9 9 8 10 6 6 6 0,75 15 12 11 10 10 10 10 10 1 19 16 14 13 16 16 10 10 1,5 24 21 19 17 20 20 16 16 2,5 34 29 25 23 25 25 25 20 4 47 41 36 32 36 36 36 25 6 60 51 47 43 50 50 36 36 10 82 70 61 56 80 63 50 50 16 111 96 83 76 100 80 80 63 25 147 126 110 100 125 125 100 100 35 182 157 137 124 160 125 125 100 50 229 196 171 155 224 160 160 125 70 285 246 214 194 250 224 200 160 95 347 300 260 236 300 300 250 224 120 404 348 303 274 355 300 300 250 150 456 393 342 310 425 355 300 300 185 515 442 385 350 500 425 355 300 240 608 523 456 413 600 500 425 355 300 700 602 523 475 600 600 500 425 Use: With more then one conductor (core), the current-carrying capacity and the rated current of the overcurrent protection device are reduced as stated above. The values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems). Pay attention to the current-carrying capacity factors according to the Tables 9 to 12. Table 8 Values of current-carrying capacity and maximum permissible rated current of the overcurrent protection device for rubber-insulated lines with aluminium conductor Conductor cross-sectional area Current-carrying capacity Rated current of overcurrent protection device A A for number of cores carrying current in operation mm2 1 2 3 4 1 2 3 4 2,5 26 22 19 17 25 20 16 16 4 35 30 27 23 25 25 25 20 6 47 41 35 32 36 36 25 25 10 63 54 47 44 63 50 36 36 16 85 73 64 58 80 63 63 50 25 144 98 85 77 100 80 80 63 35 141 121 105 95 125 100 100 80 50 178 153 133 121 160 125 125 100 70 220 190 164 146 200 160 160 125 95 268 231 202 182 250 224 200 160 120 312 269 234 212 300 250 224 200 150 358 309 269 236 355 300 250 224 185 408 351 306 278 355 300 300 250 240 477 410 358 325 425 355 355 300 300 550 472 412 374 500 425 355 355 Use: With more than one conductor (core), the current-carrying capacity and the rated current of the overcurrent protection device is reduced as sated above. The values also apply to three-phase four-wire systems with neutral conductor and separate protective conductor (five-wire systems). Pay attention to the current-carrying capacity factors according to the Tables 9 to 12. Current-carrying capacity factors These are factors by which the values of current-carrying capacity given in the Tables 6 to 8 have to be multiplied when special conditions are given. These conditions may be: – bundled lines installed freely in air – bundled lines installed in pipes or conduit subways – multicore lines with more than 4 conductors (cores) – multicore lines installed in a piled-up arrangement which are loaded at the same time – ambient temperatures which deviate from 25° C (298 K) and are higher If multicore lines are fastened individually by means of spacing clips side by side, the current-carrying capacity factor of 0,9 is applicable irrespective of the number of lines placed side by side. In the case of ambient temperatures higher than 25° C (298 K), the limiting temperature for the conductor of the line used must be taken into consideration. There are limiting temperatures of conductors · of 60°C (333 K), · of 70°C (343 K) and · of 180°C (453 K). If several current-carrying capacity factors are applicable, then the values of current-carrying capacity given in the Tables 6 to 8 must be multiplied by all of the applicable factors. The rated current of the overcurrent protection device must be specified according to the newly calculated current-carrying capacity when factors of the current-carrying capacity are used. In this event, the rated current of the overcurrent protection device must be below the value of the newly calculated current-carrying capacity of the line. Table 9 Current-carrying capacity factors for single-core lines bunched and laid out as open-wire line, in pipe trench or service duct or for multi-core lines with more than 4 cores Number of lines or cores Current-carrying capacity factor 2 0,85 3 0,75 4 0,68 5 0,62 6 0,58 7 0,55 8 0,53 9 0,50 10 0,48 15 0,42 20 0,38 25 0,35 30 0,33 35 0,31 40 0,30 45 0,29 50 0,28 Table 10 Current-carrying capacity factors for bunched multi-core lines Number of multi-core lines Current-carrying capacity factors in case of open-air bunching direct side-by side arrangement on walls or ceilings bunching in pipe trench or service duct 2 0,89 0,83 0,81 3 0,80 0,76 0,75 4 0,73 0,73 0,69 5 0,69 0,71 0,65 6 0,66 0,70 0,62 7 0,63 0,69 0,60 8 0,61 0,69 0,58 9 0,59 0,68 0,56 10 0,57 0,68 0,55 15 0,50 0,66 0,49 20 0,47 0,64 0,46 25 0,44 0,62 0,43 30 0,42 0,60 0,41 35 0,40 0,59 0,40 40 0,39 0,58 0,39 Table 11 Factors of current-carrying capacity in dependence of constant ambient temperatures for lines with a conductor limiting temperature in continuous operation of 60° C (333 K) and 70° C (343 K) Ambient temperature Current-carrying with a conductor capacity factors for lines limiting temperature of °C (K) 60°C (333 K) 70°C (343 K) 5 (278) 1,25 10 (283) 1,19 15 (288) 1,13 20 (293) 1,07 25 (298) 1,00 30 (303) 0,92 0,94 35 (308) 0,83 0,87 40 (313) 0,74 0,80 45 (318) 0,63 0,72 50 (323) 0,51 0,64 55 (328) 0,36 0,55 60 (333) – 0,46 65 (338) – 0,37 Table 12 Factors of current-carrying capacity in dependence of constant ambient temperatures for lines with a conductor limiting temperature of 180°C Ambient temperature Current-carrying capacity factor Ambient temperature Current-carrying capacity factor °C (K) °C (K) 55 (328) 1,00 120 (393) 0,69 60 (333) 0,98 130 (403) 0,63 70 (343) 0,94 140 (413) 0,56 80 (353) 0,90 150 (423) 0,49 90 (363) 0,85 160 (433) 0,40 100 (373) 0,80 170 (443) 0,28 110 (383) 0,75 175 (448) 0,20 Example: A seven-core plastic-insulated line with copper conductor o and a conductor rated cross-sectional area of 1,5 mm is to be installed at a constant ambient temperature of 35°C (308 K). What is the current-carrying capacity of the line with a conductor limiting temperature of 70°C (343 K)? Solution : According to Table 5, the current-carrying capacity of one core is 26 A. For 7 cores, the factor of current-carrying capacity is 0,55; at a constant ambient temperature of 35°G (308 K) the factor of current-carrying capacity is 0,87 (conductor limiting temperature 70°C or 343 K) according to Table 10. Actual current-carrying capacity 26 A · 0,55 · 0,87 = 12 A. Rated current for the overcurrent protection device is 10 A. Table 13 Limiting temperature for conductors Type of cable Conductor limiting temperature °C (K) continuously at short-circuit 1-kV plastic cable 70 (343) 180 (453) 10-,20-,30-kV plastic cable 70 (343) 200 (473) 1-kV solid-type cable 80 (353) 200 (473) 10-kV solid-type cable 55 (328) 165 (438) 20-kV solid-type cable 55 (328) 145 (418) 30-kV solid-type cable 45 (318) 130 (408) When selecting cables with respect to their current-carrying capacity, the following factors must be taken into consideration: – The thermal resistance of the soil; it is dependent on the type of soil and the moisture content of the soil. – Loaded cables, heating lines and the like installed in close vicinity. – Heat retention due to air cushions, protective covers, in ducts, pipes or nests of tubes. Table 14 Current-carrying capacity of 1-kV solid-type cables for individual installation, with reduced solid sheath and fully saturated impregnation Rated cross-sectional area of conductor Single -core cables Two-core cables Three-core and four-core cables mm 2 Cu Al Cu Al Cu Al 1,5 – – 30 – 25 – 2,5 – – 35 30 30 25 4 – – 45 35 40 30 6 – – 60 45 55 40 10 – – 85 65 75 60 25 – – 145 115 125 100 50 285 230 215 175 185 150 70 350 280 260 210 225 180 120 495 395 350 280 315 250 185 630 510 450 360 410 330 240 740 590 525 420 475 380 300 840 675 590 470 545 435 400 1000 800 700 565 645 515 500 1140 910 – – – – 1000 1740 1390 – – – – Table 15 Current-carrying capacity of three unarmoured single-core solid-type cables with lead sheath, fully impregnated, in three-phase systems, separately lying side by side Nominal cross-section of the conductor 1 kV Current – carrying capacity in A mm 2 Cu Al 50 250 200 70 300 240 120 410 330 185 510 405 240 575 460 300 640 510 400 725 580 500 790 630 1000 950 805 The values of Table 15 are applicable to cables lying side by side in a clearance of about 7 cm, in consideration of the metallic sheath losses in case of cable sheaths short-circuited at both cable ends. The current-carrying capacity of three unarmoured single-core cables with A1-sheath separately lying side by side amounts to 90 % of the values according to Table 15. Table 16 Current-carrying capacity of three unarmoured single-core solid-type cables with lead sheath, non-draining, in three-phase systems, separately lying side by side Nominal cross-section of the conductor 1 kV mm 2 Current-carrying capacity in A Cu Al 50 250 200 70 300 240 120 410 330 185 510 405 240 575 460 300 640 510 400 725 580 500 790 630 1000 950 805 The values of Table 16 are applicable to cables lying side by side in a clearance of about 7 cm, in consideration of the metallic sheath losses in case of cable sheaths short-circuited at both cable ends. The current-carrying capacity of three unarmoured single-core non-draining cables with Al-sheath separately lying side by side amounts to 90 % of the values according to Table 16. The current-carrying capacity of three touching single-core non-draining cables with Al-sheath arranged in a triangle amounts to 105 % of the values according to Table 16. Table 17 Current-carrying capacity of 1-kV-plastic cables Nominal cross-section of the conductor Single-core cables Two-core cables Three- and four-core cables Current-carrying capacity in A mm 2 Cu Al Cu Al Cu Al 1,5 – – 25 – 20 – 2,5 – – 30 25 25 20 4 – – 40 50 35 25 6 – – 55 40 45 35 10 – – 75 55 65 50 25 – – 120 95 110 90 50 260 210 – – 165 125 70 315 250 – – 200 155 120 445 360 – – 285 220 185 570 455 – – 370 285 240 665 530 – – 430 335 300 755 605 – – – – 400 880 720 – – – – 500 990 800 – – – – The carrying capacity specified in the Tables 14…17 is to be reduced to the following specified percentages in case of deviations from the mentioned conditions of installation. Table 18 Reduction in case of bunched multi-core cables in three-phase systems and cables in direct current systems Number of cables in the trench 2 3 4 5 6 8 10 Carrying capacity in % 90 80 75 70 65 62 60 The carrying capacity of cables under protective hoods diminishes to 90 % of the values found out in application of other reductions (see Tables 18…25). The reductions are applicable to cables lying side by side in a clearance of about 7 cm. Table 19 Reduction in case of bunched single-core cables in three-phase systems Number of systems in the trench 2 3 4 Carrying capacity in % 80 75 70 The reductions are applicable to single-core cables lying side by side in a clearance of about 7 cm. The values of the Tables 20 and 21 are applicable to cables in unarmoured cement pipes in the earth with a clear interior diameter of about 150 mm and 20 mm wall thickness in an horizontal arrangement with reciprocal touch and an outer diameter of 50 mm. Table 20 Reduction in case of multi-core cables and single-wire cables in single pipes bunched in a triangle Number of pipes 1 2 3 4 5 6 7 8 9 10 Carrying capacity of the cables in % 80 72 68 65 63 61 60 59 58 57 Table 21 Reduction, in case of single-core cables in single pipes in three-phase systems Number of pipes 3 6 9 Number of systems 1 2 3 Carrying capacity of the cables in % 85 76 72 Table 22 Reduction in case of bunched cables in the open air Cable distance Carrying capacity in % 3 cables or 3 cable systems 6 cables or 6 cables systems Space between the cables is equal to the cable diameter 93 87 No space between the cables (reciprocal touch) 81 74 Table 23 Reduction in case of an ambient temperature for plastic cables deviating from 20°C Rated voltage Carrying capacity in % in case of an ambient temperature of °C kV 5 10 15 20 25 30 35 40 1 115 110 105 100 95 89 84 77 Example of calculation: For the transmission of 1,25 MVA with an operating voltage of 6 kV three-phase current a cable is required. This cable is to be hung by means of an auxiliary cable side by side with two cables hanging already in a shaft. The space between the cables is equal to the cable diameter. The ambient temperature is 30°C. Solution: A three-core cable with screened cores and with non-draining, intensified insulation is to be chosen. Table 24 Reduction in case of an ambient temperature for solid-type cables deviating; from 20 % Rated voltage kV Carrying capacity in % in case of an ambient temperature of °C 5 10 15 20 25 30 35 40 1 112 108 104 100 96 91 87 82 10,20 120 113 107 100 93 85 76 65 30 126 118 110 100 90 78 63 45 Occuring factors of reduction: – 93 % for laying three cables side by side (space between the cables = cable diameter, see Table 22). – 85 % for raised ambient temperature of 30 % (see Table 23). Total reduction factor = 0,93 · 0,85 » 0,79 Table 25 Continuous carrying capacity of the most important overhead-line materials for an over temperature of 40°C Cable cross section Copper Pure aluminium Aldrey Steel-aluminium 1:6 1:4 mm 2 A A A A A 16 115 92 88 – – 25 151 121 115 – – 35 174 149 142 145 225 50 1) 234 187 178 170 300 50 2) 231 185 176 – – 70 282 226 215 235 355 95 357 283 269 290 440 120 411 329 313 345 505 150 477 382 363 400 560 185 544 435 414 455 650 240 3) 630 502 479 – – 240 4) 641 513 488 530 770 300 747 598 568 615 – 1) 7-wire (1 layer) 2) 19-wire (2 layers) 3) 37-wire (3 layers) 4) 61-wire (4 layers)
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