Overhead lines a) ja b) 0 kv wood poles c) free standing 0 kv metal tower with I-strings d) free standing 440 kv metal tower with V-strings e) 400 kv metal tower with guy wires 0 kv wood tower with guy wires
Rated data of OH line conductors resistance W/km nominal load carrying capacity A s thermal withstand current ka The corresponding maximum temperatures : I nim I s - copper 70 C 70 C - aluminum 80 C 0 C - aluminum alloy 80 C 60 C - Al steel reinforced 80 C 60 C Thermal time constant t : J - ( t) ( e t / t J0 + - ) ( J - J0) J(t) temperature rise at time t J J 0 steady state temperature rise (constant load) temperature rise in the beginning t time constant - overhead lines t 7 min - underground cables t 5 60 min J J t 0
Temperature rise by short circuit current Temperature rise J ( C) : J p mc t I r mc t () p heating power (per km) I current r resistance (per km) m conductor mass (per km) c heat capacity of the material Example: 5.5 aluminum alloy : Solving I from Eq. () : Þ Þ I I s» Jmc rt,568 0,9 ka 80 45 90 0,67 7 A C kg/km Ws/ C kg W / km s W VA A W V/A Temperature rise for different currents and different times: r 0,67 W/km (80 C) m 45 kg/km c 90 Ws/ C kg J allowed 80 C J J I r t mc : I r t mc I I t t I s?
Example: DT in a MV OH-line during a short circuit fault t 0 t t t t 4 t 5 fault RC RC RC 0,5 0,5 0,5 0 0,5 0 0,5 Data : I s,9 ka I k,0 ka thermal s withstand current fault current t 4 min time constant T max 80 C max operation temperature T maxs 60 C max I s temperature T 0 50 C T a 0 C initial conductor temperature ambient temperature One 0,5 s fault current pulse causes the temperature rise of J : J J s Þ J Dt R I s R I k s 0,96 J s 0,5,0,0,9 0,96 0,96 (60-80) C»,7 C Temperature at time t (t -t 0 << t ; all the heat in conductor) : T 0 T + J 50 +,7 C 97,4 C Cooling in the period t -t : T T a + (T - T ) (- e 0 + 77,4 (- e a -/ 4 ) C ) -(t -t )/ t 50,5 C Heating by re-closing at time t : T T + J 74, C Cooling in the period t -t 4 : T 4 T a + (T - T ) (- e 0 + 54, (- e a -/ 4 ) ) -(t -t ) / t» 4 4, C Heating by re-closing at time t 5 : T 4 5 T + J 65 C
Example: DT in a MV OH-line during a short circuit fault 00 T/ C The run of temperature ~ time : 80 60 40 0 0 t t t t t 4 t 5
Capacitances in the chain of isolators Overhead line isolators a) pin type, b) suspension type, c) long rod type, d) multi-material-type, e) and the cross-section: fiber glass rod, silicon plating, silicon discs, 4,5,6 junctions, 7 terminal piece, 8 filling piece
400 kv chain of suspension insulators. insulator, 8 upper arcing horn, 9 lower arcing horn, armor rod, 5 suspending clamp
Overhead lines with covered conductors Types of OH lines with covered conductors: a) SAX-line (Nokia), b) SAMI-line (Sekko). support, spacer suspender, spacer. narrower right of way needed contact of two phases Þ no disturbance a leaning tree causes fault only after days power arc not able to move - risk of a broken conductor - clamps as arcing horns detection of a broken conductor not easy After a possible fault the line must be checked in case a conductor has been broken!
Conductor resistance R r l A ; r r 0,05W 0,079 W mm m mm m (Al) (Cu) Example: 0 mm copper, DC-resistance R 0 000 0,079 W/km» 0,5 W/km By AC the resistance is increased due to the skin effect and in cables also due to the proximity effect Þ additional resistance DR, about - - 6 % for OH lines - - 8 % for cables Resistance is given at +0 C. Temperature dependence : a 0,009 / C (Cu) a 0,0040 / C (Al) Total resistance : [ + a ( J - 0 C) ](R + R) R 0 D
Capacitances of an OH-line r conductor radius h geometric mean height h h h h a, A : geometric mean distances a a a a ; A A A A C k C k C k C 0 C 0 C 0 Positive sequence capacitance C C 0 + C k pe0 c ha ln ra a a a Zero sequence capacitance C 0 pe0 c h æ A ö ln ç r è r ø h h h A A A e 0 vacuum permittivity 8,84 0 - F/m
Example : 0 kv line with conductors in the same plane r 0,007 m h 0 m» a,,,,8 m» A 0,0 0,0 0, 0,06 h, m, m 0 m Positive sequence capacitance: c» pe0 ha ln ra 0,5 0 - ln F m - p 8,84 0 0,8 0,007 0.06 nf 0,5 km F/m Zero sequence capacitance : pe0 p 8,84 0 c h æ A ö 0 æ ln ç ln ç r è a ø 0,007 è - F nf» 4,7 0 4,7 m km - 0,06,8 ö ø F m
OH-line inductance L m 0 m0 p é ê + ln ë4 4p 0-7 d ù r ú û H/m d r d If the distances between the phases are not equal: d eq d d d r d r Example: a 0 kv line with horizontal arrangement:, m, m 50 mm Þ r» 7 mm d,,,»,9 m L m0 p 4p 0 p é d ê + ln ë4 r -7 æ ç è 4 eq + ù ú û ln,9 0,007 ö ø H/m X 0»,mH/km wl -7 pf L» 0,5 W/km (0,5 + 5,9) H/m p 50, 0 - W/km
The inductance of a multi-conductor line L m é 0 ê p ë4n d e de de d e + d ln r n number of sub-conductors d e equivalent distance between the phases and r e equivalent radius of one phase conductors e aa e e ù ú û a e ab a e ab e an b n b n phase phase d r e e n n (r (e e aa' ab e ab' Le an Le an' ) L(e ) L(e na e nb na' e Le nb' n(n-) Le r) nn' )
Zero sequence inductance of an OH-line Inductance in a loop of phase conductors and the ground return: m é 0 ê p ë + H ln r en ù ú û L d d H r e en re d d d r r en phase conductors equivalent radius d distance between phases and H equivalent depth of the ground return current H,85 rm wm 0 In Finland the soil resistivity typically is r m 00 Wm 00,85 p 50 4p 0» 4465 m Þ H -7 m
Example : a 0 kv line, m, m H r 7 mm (50 ) r m 00 Wm Þ H 4465 m r 0,007,,, en» 0,8m The zero sequence inductance for the three phases is: L a» m0 p é ê + ln ë -7 4p 0 é p ê ë,98 mh/km H r en + ù ú û ln 4465 0,8 ù ú û H/m And the zero sequence inductance per phase is: L 0 Þ L X 0 a 5,94 mh/km wl 0 p 50 L 0»,87 W/km
Structures of power cables Belt type cable: conductor, conductor insulation, belt insulation, protection screen Single conductor cable: conductor, conductor screen, insulation, core screen, protection screen, (armoring) H-type cable. Composed of single conductor cables with a common protection screen Multi-screen cable. Composed of single conductor cables with a common plastics screen.
Cable capacitances. Cables with cylindrical field : C R C C C C C Positive sequence C zero sequence C C T S. Belt type cable : C C C C 0 C 0 C 0 C C 0 C Positive sequence C : C0 C C 0 C C 0 + C Zero sequence C C 0 The usually given rated data for cables includes : operational (pos.seq.) capacitance mf/km (C) charging current A/km (U v wc) earth fault current A/km (U v wc0 ) The data is given in tables according to the type and cross-section
The load carrying capacity of power cables The thermal circuit : Heat flow R jv R jv Heat source Thermal resistances : R jv R va R au R um conductor - screen screen - armoring armoring - cable surface cable surface - earth surface conductor R jv R va R au R um metal screen armoring cable surface earth surface Maximum load depends on the allowed insulation temperature : MV-cables normally: (during fault) PVC : 65 C (5) paper: 65 C (50) PE : 65 C (50) PEX : 90 C in air (50) 65 C in soil
Power cable load carrying capacity Maximum load currents are given in standard conditions: in soil : cable in 70 cm depth, soil temperature +5 C and soil resistivity Km/W in air : ambient temperature +5 C, free air flow around the cable The differences to the standard conditions are taken into account by correction coefficients k i : impact of adjacent cables effect of burial depth difference in soil thermal resistivity soil ambient temperature The final loading is the product of std-loading and the correction coefficients.
The effect of adjacent cables in the soil to the ampacity of cables number of adjacent 4 5 6 8 0 cables correction factor when the free distance between cables is a) 0 mm 0,79 0,69 0,6 0,58 0,55 0,50 0,46 The effect of burial depth in soil depth rated voltage in soil 0,6/ kv 6/0 40/69 m kv 0,5 0,7,0,0 0,7 0,9 0,97 0,99 0,9, 0,95 0,98,, 0,9 0,96,,5 0,9 0,95 b) 70 mm 0,85 0,75 0,68 0,64 0,60 0,56 0,5 c) 50 mm 0,87 0,79 0,75 0,7 0,69 0,66 0,64 The effect of soil thermal resistivity Soil thermal resistivity Km/W 0,7,0,,5,0,5,0 0,6/ kv up to 5 mm, 0,94 0,87 0,78 0,7 0,67 5 95 mm, 0,9 0,86 0,76 0,70 0,64 0 500 mm,4 0,9 0,85 0,75 0,69 0,6 6/0 kv up to 5 mm,09 0,95 0,88 0,80 0,74 0,69 5 95 mm, 0,94 0,87 0,78 0,7 0,66 0 500 mm, 0,9 0,86 0,77 0,70 0,65 /0 kv up to 5 mm,08 0,96 0,90 0,8 0,75 0,70 5 95 mm,0 0,95 0,89 0,79 0,7 0,67 0 500 mm, 0,94 0,88 0,78 0,7 0,66 8/0-4,6/60 kv up to 95 mm,08 0,95 0,90 0,8 0,76 0,7 0 500 mm,09 0,95 0,89 0,80 0,74 0,69
Examples of the soil thermal resistivities Dry sand (water content 0 %),0 Km/W Dry gravel and clay,5 " Half dry gravel and sand (water content 0 %), " Half dry clay and wet gravel,0 " Wet clay and sand (water content 5 %) 0,7 " The effect of soil ambient temperature Soil temperature C 5 0 5 0 5 0 90 C conductor temp.,06,0,0 0,96 0,9 0,89 80 C ",07,04,0 0,96 0,9 0,88 70 C ",09,04,0 0,95 0,90 0,85 65 C ",0,05,0 0,95 0,89 0,84
Example: Three cables APAKM 85 0,6/,0 kv with 7 cm distances in soil: in 90 cm depth half dry gravel soil soil temperature +0 C std-loading 50 A / cable Correction coefficients : cables Þ k 0,75 90 cm Þ k 0,97 soil resistivity Þ k 0,9 soil temperature Þ k,04 Þ Maximum allowed load current is I n» k k k k 4 50 0.75 0.97 44 A 0.9.04 A
Power line electrical fields and health risks WHO v. -8 : safe limit is 0 kv/m exception : users of artificial pacemaker (heart) 0 kv lines: maximum value in practice about kv/m 400 kv double lines ~0 kv/m, can be reduced by a proper phase location. EU Comission recommendation 59 year 999: -5 kv/m for longer duration -5 kv/m temporarily Electrical field strength at the earth level in the vicinity of power lines. ) 4) 400 kv, lowest conductors 0 m from earth 5), 6) 0 kv, lowest conductors 8 m from earth ), 5) phase conductors located symmetrically ) phase order reversed in the other pole ) phase order reversed in other sub-conductor 4) poles with guy wires, d distance from center
Magnetic fields and health risks WHO v. -8 : safe limit 0, mt risk of cancer when 0, mt? compare with the earth magnetic field~0 mt under an overhead line max value 0 40 mt - at 0 m distance attenuated to 0 % - at 00 m distance 0, mt - Buildings do not attenuate! EU Comission recommendation 59-00 ut for longer time -500 ut temporarily Magnetic fields of overhead lines at the earth surface level ), ) 400 kv, 000 A / circuit ) 0 kv, 000 A ) double lone ), ) towers, d distance from the center