PROBABILISTIC APPROACH TO FIX THE OVERHEAD LINE POWER TRANFER LIMITS, WITH EFFECTIVE WIND COOLING A dissertation submitted to the Department of Electrical Engineering, University of Moratuwa in partial fulfillment of the requirements for the Degree of Master of Science by D.M.J. ROSHAN KUMARA Supervised by: Eng. W.D.A.S. Wijayapala Eng. D.G. Rienzie Fernando Department of Electrical Engineering University of Moratuwa Sri Lanka 2010 94545 Abstract Open distribution line access and economic uncertainties are the reasons why many utilities are operating their lines at much higher loads than they were initially designed for. Because of this, the effects of higher operating temperatures on the safety and reliability of overheads lines were studied in this dissertation. It is observed that overloading of conductor usually occur during peak hours in according to the average daily load pattern of Sri Lanka. During this time conductor temperature reaches to its maximum. However, conductor temperature may not increase due to the cooling effect on availability of wind. The over temperature causes reduction of the tensile strength of the conductor. The work has been identified in significant areas where improved analytical methods are relevant. Several such methods have been created and their impact is discussed in this report. As such, present conductor ratings are studied in accordance to IEC standard [7] and IEEE standard [5, 6]. Wind data at four different sites have been collected and are used for the analysis. Current variations of three different sites are taken for the study. The probability of over temperature could be determined by applying Rayleigh distribution and cumulative frequency distribution respectively when the wind speed is below 1mls and the current rating is more than 202A. At the second stage, sag at maximum temperature has been calculated for each span. Finally,. Economical optimizations of losses are analyzed. In the first part, allowable loss of strength of Aluminium is analyzed through a probabilistic approach. Accordingly, it is observed that strength of Aluminium is not ever reduced below 90% of its original strength during the conductor lifetime of 50 years. This reduction of strength is negligible. Therefore, effective wind speed can be taken as 1m/s. In the second part, sag variations were analyzed for each span which is presently used in CEB against maximum allowable temperature (90°C) in the absence of wind speed. It is observed that ground clearance is not violated when it is operated at maximum allowable temperature (90°C). Finally, under this method costs and benefits are evaluated with increase of losses against investment incurred in strengthening of the , CEB network. Net present value is analyzed considering present value of expenses (increase of losses of existing system) and present value of savings (investment incurred in strengthening of the CEB network). Net present value is positive for load patterns of Omara, Ratmalwala and Kudagammana. Therefore those projects are financially viable. D E C L A R A T I O N T h e w o r k s u b m i t t e d i n t h i s d i s s e r t a t i o n i s t h e r e s u l t o r m y o w n i n v e s t i g a t i o n . e x c e p t \ Y h e r e o t h e r w i s e s t a t e d . I t h a s n o t < . d r e a d : b e e n a c c e p t e d C o r a n y d e g r e e . < J . n d i s a l s o n o t b e i n g c o n c u r r e n t ! ) s u b m i t t e d f o r a m o t h e r d e g r e e . \ . . ) . l~_?r-~ D . M . . I . R o s h a n K u m a r a D a t e : 2 8 1 1 1 . T a n u a n 2 0 1 0 W e e n d o r s e t h e d e c l a r a t i o n b y t h e c a n d i d a t e . I \ ' . \ · . \ . . C \ . . . . ~~ . \ . E n g . W . D . A S . \ \ i . i a : a p a l a S e n i o r I . e c t u r e r U n i v e r s i t Y o r l'vlor~ltll\\ a ~ . . - - - ) ~- ~ - - - - . / - - - - - .----~ _ . / E n g . D . G . R i e n / i c F e r n a n d o M a n a g i n g D i r e c t o r J \ . m i t h i P o w e r C C l l l S u l \ a n t s ( P \ t ) l . t d D G ~- ' 1 ; . < \ , r : f \ ~ ; : : : : : : : . [~.~ r \ : : - · ' \ : · - ~ ( ) ( ) . ! A c k n o w l e d g e m e n t T h i s \ V o r k h a s b e e n c a r r i e d o u t a t t h e D e p a r t m e n t o f L l c c t r i c a l L n g i n e e r i n g . t ! n i v e r s i t v o f i v l o r a t t l \ \ a . I w o u l d l i k e t o t h a n k m y p r o j e c t s u p c n i s o r . L n g . W . D . A . S . W i j a y a p a l a . s c m o r l e c t u r e r . u n i \ c r s i t y o f M o r a t U \ \ a . f o r h i s g u i d a n c e . s u p p o r t a n d e n c o u r a g e m e n t g i , c n t o m e b c v o n d h i s r o l e o f p r o j e c t f o r c o m p l e t i o n o f t h i s l i n a l d i s s e r t a t i o n s u c c c s s ! " u l h . ~ - - - I a l s o t a k e t h i s o p p o r t u n i t y t o e x t e n d m y s i n c e r e t h a n k s t o p r o j e c t s u p e n i s o r . l · . n g . D . G . R i c n z i e I c r n a n d o . M a n a g i n g D i r e c t o r . ; \ m i t h i P O \ v c r C o n s u l t a n t s ( P \ ' 1 ) L t d \ \ h o a h v a y s d i r e c t e d m e t o t h e c o r r e c t p a t h . g i v i n g t h o u g h t f u l c o m m e n t s a n d e n c o u r a g e m e n t . ' ' h c n c \ c r I d i s c u s s e d t e c h n i c a l i s s u e s t o c a r r y o u t t h i s p r o j e c t s u c c e s s f u l l v . I a l s o t h a n k M r . J ) . ; \ . N . l · c r n a n d o . D e p u t y ( ) c n c r a l M a n a g e r . L n c r g y P u r c h a s e B r a n c h . T r a n s m i s s i o n . C I . B a n d I ' v 1 r . S . B o g a h < : m a t t e . P r o j e c t D i r e c t o r . L S I I P P r o j e c t . R e g i o n 4 . C E B f o r e x t e n d i n g t h e i r s u p p o r t b y p r m i d i n g d a t a t o c a r r y o u t t h i s \ \ o r k . I w o u l d a l s o l i k e t o e x p r e s s m y a p p r e c i a t i o n t o , d ] m y c o l l e a g u e s a n d p a r t i c u l a r ! ) t o B u d d h i k a . S h a n t h a . ( ' h a m i l . S a m a n t h i a n d R a j i \ ! " o r t h e i r e n c o u r a g e m e n t . A l s o I l i k e t o r e m i n d m y b r o t h e r s . K u m u d u . P r a h a t h a n d U d a y a n g a . I n p a r t i c u l a r . I a m g r a t e f u l t o 1 1 1 ) , , i r e N c c d u f o r h e r h ) \ c a n d c o n t i n u o u s e n c o u r a g e m e n t . L a s t b u t n o t t h e l e a s t m y g r a t i t u d e g o e s t o m y d e a r p a r e n t s : G i l b e r t a n d S u \ i n i t i o · t h e i r l o v e . m o r a l s u p p o r t a n d u n d e r s t a n d i n g t i · 0 1 n s t a r t t o e n d o f t h i s c o u r ' · \ l l l C O N T E N T S D e c l a r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A b s t r a c t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 A c k n o w l c d g c m c n 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 \ C o n t e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \ L i s t o f F i g u r c s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \ I l l L i s t o f T a b l e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I : \ A b b r e v i a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : \ 1 I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 1 . 1 B a c k g r o u n d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 2 O b j c c t i \ c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I . 3 S c o p e o i . \ \ o r k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 4 D e t e r m i n a t i o n o f m a x i m u m p e r m i s s i b l e c o n d u c t o r t e m p e r a t u r e P r o h l e n 1 S t a t e m e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M a x i m u m a d m i s s i b l e l o s s o f t e n s i l e s t r e n g t h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I I ~ _ ) 5 3 . 1 U n i t s ~111d i d e n t i f i c a t i o n o f l e t t e r s S \ t n h o l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 . 2 C u r r e n t c a r r y i n g c a p a c i t y o f A C S R R a c o o n c o n d u c t o r s . . . . . . . . . . . 7 3 . 2 . 1 S t e a d y s t a t e h e a t b a l a n c e e q u a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 . 2 . 2 l · u r c e d c m w e c t i o n h e a t l o s s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 . 2 . 3 1 ' \ a t u r a l c o m e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s 3 . 2 . · - l R a d i a t e d h e a t l o s s r a t e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s 3 . 2 . 5 R a t e o f s o l a r h e a t g a i n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l ) 3 . 2 . ( ) C o n d u c t o r e l e c t r i c a l r e s i s t a n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 . 2 l · : q u a t i o n s f o r a i r p r o p e r t i e s . s o l a r a n g l e s . a n d s o l a r h e a t t 1 u x . . . . I 0 3 . 3 . 1 D ) n a m i c v i s c o s i t y o f a i r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 0 3 . 3 . 2 . ' \ i r d c n s i t v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 0 3 . 3 . 3 l h c r m a l c o n d u c t i v i t y o f a i r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 3.3.~ A l t i t u d e o f t h e s u n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I I 3 . 3 . 5 / \ / . i m u t h o f t h e s u n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3 . 3 . ( ) I o t a l h e a t f l u x r e c e i \ c d b y a surl~1cc a t s e a l e v e l . . . . . . . . . . . . . . 1 3 3 . 3 . 7 I o t a l h e a t f l u x e l e v a t i o n c o r r e c t i o n l~1ctor . . . . . . . . . . . . . . . . . . . . . . . . I 5 \ 3 . 4 S a m p l e c a l c u l a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 3 . 4 . 1 S t e a d y s t a t e t h e r m a l r a t i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 3 . 4 . : : ' P r o b l e m s t a t e m e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 _ ) . 4 . ' - ( · o m e c t i o n h e a t l o s s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 ( J 3.4.~ R a d i a t e d h e a t l o s s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 .1.~.:' S o l a r h e a t g a i n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 g 3 . - - U ' S t e a d : s t a t e t h e r m a l r a t i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 g 3 . 5 I n p u t d d t a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v · · · · · · · · . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 3 . 5 . 1 \ \ ' i n d a n d a m b i e n t t e m p e r a t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l l J 3 . 5 . : : ' . \ i r d e n s i t y . ' v i s c o s i t y a n d c o n d u c t i v i t y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 3 . 5 . 3 l i n i s s i v i t y a n d a b s o r p t i ' v i t y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 3.5.~ S o l a r h e a t g a i n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 ~ P r o b a b i l i s t i c A p p r o a c h t o A l l o w f o r M a x i m u m A d m i s s i b l e L o s s o f · r c n s i l c S t t · e n g t h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 4 . 1 P r o b a b i l i t : o l ' m e r t e m p e r a t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 4 . 1 . 1 R a : l e i g h p r o b a b i l i t y d i s t r i b u t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 4 . 1 . 2 C u m u l a t i \ c f r e q u e n c y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 4 . 2 C a l c u l a t i o n o f p r o b a b i l i t y o f v \ i n d s p e e d b y a p p l y i n g R a y l e i g h d i s t r i b u t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ; 1 4 . 3 C a l c u l a t i o n o r p r o b a b i l i t : o f O \ c r c u r r e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 4 . 4 P r o b a b i l i t : o f O \ e r t e m p e r a t u r e u p t o g 7 o c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7 4 . 5 M e t h o d o f l i n e t e n s i o n c a l c u l a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 8 5 A p p r o p r i a t e G r o u n d C l e a r a n c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 5 . 1 I n t r o l l u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 5 . 2 S a g a n d t e n s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 5 . 2 . 1 L q u i \ a l e n t s p a n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 5 . 2 . 2 S e l e c t i ( l n ( l f . t e n s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 5 . 2 . ~ S a [ ! . a n d t e n s i o n f o r m u b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 5 . 2 . · } I ) e s i g n c r i t e r i a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~~ _ ) _ 5 . 3 S a m p l e c a l c u l a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . '"\~ _ " ' \ _ 1 5 . 4 C l e a r a n c e f i · o m t h e g r o u n d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 7 5 . 5 l'v1a~imum s a g f o r A C ' S R R a c o o n c o n d u c t o r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 7 \ 1 6 E c o n o m i c a l O p t i m i z a t i o n o f L o s s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 6 . 1 h 1 c r g ) l o s s e s d u e t o i n c r e a s e o r ( ' ( ' ( . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 l ) 6 . 2 P r e s e n t , a l u c o r l o s s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - + 1 6 . : 1 I · : s t i m d t c d c o s t o r r e c o n s t r u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - t l 6 . . ~ 1 P r e s e n t \ a l u c o r s a \ i n g s . . . . . . . . . - + 2 6 . ' - f J - C 0 1 h l l l l 1 C \ i a b i ] i t ) o r t h e p r o j e c t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - + 2 8 C~onclusio;1s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L i s t o f r e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - l 6 A n n e x A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - l 8 i \ n n e x B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - l 9 A n n e x c : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 \ 1 1 L i s t o f F i g u r e s P a g e N u m b e r C h a p t e r 4 F i g u r e 4 . 1 F i g u r e 4 . 2 F i g u r e 4 . 3 F i g u r e 4 . 4 F i g u r e 4 . 5 F i g u r e 4 . 6 F i g u r e 4 . 7 F i g u r e 4 . 8 . \ c t u a l ! ' r e q u e n c y \ s . \ \ i n d s p e e d ~It ~arakkalliya . . . . . . . . . . . . . . . . P r o b a b i l i t y d e n s i t y \ ' S . \ v i n d s p e e d a t N a r a k k a l l i y a . . . . . . . . . . . . . . ( ' u m u l a t i \ e f r e q u e n c y \ S . w i n d s p e e d ( m i s ) a t N a r a k k a l l i y a n i \ \ L · r a g e c u r r e n t \ S . t i m e ( 2 4 h r s ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \ c l u a l l i · e q u e n c ) \ ' S . a \ · e r a g e c u r r e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P r o b a b i l i t y d e n s i t y \ S . m e r a g e c u r r e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( · u m u l a t i \ c l i - c q u e n c ) \ s . m c r a g c c u r r e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . l . l l S S o r s t r e n g t h o r A l u m i n i u m t y p e A 1 a s a f u n c t i o n o r I I I " _ _ ) 2 ) 2 5 2 6 2 ( ) t e m p e r a t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 8 \ I l l L i s t o f T a b l e s P a g e N u m b e r C h a p t e r 3 T a b l e 3 . 1 T a b l e 3 . 2 T a b l e 3 . 3 T a b l e 3 . 4 T a b l e 3 . 5 T a b l e 3 . 6 T a b l e 3 . 7 T a b l e 3 . 8 C h a p t e r - t T a b l e 4 . 1 T a b l e 4 . 2 T a b l e 4 . 3 T a b l e 4 . - 1 - C h a p t e r 5 T a b l e S . ! T a b l e 5 . 2 T a b l e 5 . 3 C h a p t e r 6 T a b l e 6 . 1 T a b l e 6 . 2 T a b l e 6 . 3 T a b l e 6 . 4 T a b l e 6 . 5 T a b l e 6 . 6 l ! n i t s a n d i d e n t i l i c a t i o n o f l e t t e r s v m b o l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ' I \ " J S c o s i t ) . d e n s i t y a n d t h e r m a l c o n d u c t i \ i t y o f a i r . . . . . . . . . . . . . . . . 1 1 S o I a r a / i m u t h c o n s t a n t . C ( i n d e g r e e ) . i s f u n c t i o n o f t h e · · h o u r a n g l e " . t 1 l . a n d s o l a r < v i m u t h \ a r i a b l c . X . . . . . . . . . . . . . . . . . . . . . 1 2 S u l a r a l t i t u d e . l i e . a n d < v i m u t h . l c . . a t v a r i o u s l a t i t u d e s f o r a n a n n u a l p e a k s o l a r h e a t i n p u t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 ( " ; d ' t i c i e n t f o r e q u a t i o n ( 3 . 1 9 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 1 - I o t < t l h e a t t l u - . : r e c e i \ e d l w a surl~tce a t s e a l e v e l n o r m a l t o t h e s u n · s r a v s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 1 - S o l a r h e a t m u l t i p l y i n g l~tctors. K , u ; , 1 1 f o r h i g h a l t i t u d e s . . . . . . . . . 1 5 l . q u i Y a l c n t c o m b i n a t i o n o f w i n d s p e e d a n d d i r e c t i o n f o r e q u a l C O i l \ e c t i \ e c o o l i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 ( ) R < i ) l e i g h p r o b a b i l i t y d i s t r i b u t i o n f o r \ \ i n d s p e e d b e l o \ \ l m / s 2 - 1 - V o l t a g e l e \ C L m g . c u r r e n t a n d m u l t i p l i c a t i o n b c t o r . . . . . . . . . . . . 2 - 1 - P m b a b i l i t ) d i s t r i b u t i o n f o r l o a d m o r e t h a n 2 0 2 ; \ . . . . . . . . . . . . . . . . . 2 7 ( , , n d u c t o r t e n s i o n f o r \ a r i o u s t e m p e r a t u r e s a s a p e r c e n t a g e o f i l \ a i l a b l e l l T S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 P o l e s p a c i n g c h a r t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l \ L 1 x i m u m a l l o \ \ a b l e s a g f o r e a c h p o l e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C t 1 t 1 d u c t o r s a g f o r e a c h s p a n \ S . c o n d u c t o r t e m p e r a t u r e . . . . . . . - , - , _ " ' ! _ " ' ! 3 7 , , _ ) I l . u s s d i J T e r e n c c \ s . e a c h d i s t a n c e a t l l a m b a n t o t a ( ) o n n o r u w a l i n e - 1 - 0 P r L ' s e n t \ a l u e o f e x p e n s e s ( l o s s e s ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - 1 - 1 P r L " s e n t \ a l u e o f s a v i n g s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - 1 - 2 P r e s e n t ' a l u e o f e x t r a c o s t o f l o s s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - 1 - 2 P r e s e n t \ a l u e o f c o n s t r u c t i n g a n e \ \ l i n e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - 1 - 3 N e t p r e s e n t ' a l u e o f e a c h p r o j e c t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - 1 - 3 1 : \ A b b r e v i a t i o n s A C S R Alun~ini~Il~~(\)-ndL~Ic~,t~o-r Stc-,c,-l~R~c,~:ll"C~c-1 - - - - - i f - - - - - - - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - A v g . / \ \ c r a g c - - - - - - - - - - - - - - - - C C C C m r c n t C a r r y i n g C a p a c i t y - - - - - -----------~------ 1 c d f c u m u l a t i \ c d c n s i t \ f u n c t i o n I C E B l c - : c , 1 < ; 1 1 JJc~l~-i-~ity Bm;1~d- - - - - - _ C I G R E h~1tcrnational C o u n c i l o n Larg~D~cu·ical S y s t e m s ~~: I : :~~~-:::------~:-~:-~~-:~~-------------~----_ ~-~ -~ - - - - - 1 • • L - - - - - -------------------~----- - - - - - - - - l E C [ t l l l c r n a t i o n a l F l c c t r o t c c h n i c a l C o m m i s s i o n 1 i l E E E T I l k lnsti-tL~U:-t;-fFl~ctl:ical a m l i·:lcct!:;-;;;-~j::nginecr~ I I I G S S ll;o,;hantn~Ciriclsuh S t a t i o n - . . ~·· 1 L K R . I S n l . a n k a n R u p e e s f - - - - - - - 1 - - - - - - - - - - - - - - - l ' v l a . \ i m u m I M a x . l M i n i m u m J ~ pdf~ 1 il~rohal~~i~)~~icmi~: l~mcl~l;;· _ _ - - - = - = = - - j P r c : ; c n t V a l u c l · a c t o r I ~IJtnnal~ I c,~ii~lrcngth · . n - • l M i n . . \ ~ C h a p t e r 0 1 I n t r o d u c t i o n 1 . 1 B a c k g r o u n d R e c e n t l y . e l e c t r i c a l u t i l i t i e s s h o w m o r e i n t e r e s t i n u t i l i z a t i o n o f d i s t r i b u t i o n n c t \ \ o r k t o t h e i r m a x i m u m c a p a c i t y . T h e r e f o r e a n u t i l i t y h a s t o o p e J 1 m a n y a c c e s s e s \ \ h i c h c a u s e h e a v i e r a n d h c a \ i c r l o a d s o n d i s t r i b u t i o n l i n e s . B u t . e c o n o m i c u n c e r t a i n t i e s h a \ c m a d e m o s t d i s t r i b u t i o n l i n e s a n d u t i l i t i e s \ T r y r e l u c t a n t t o e x p e n d c a p i t a l r e s o u r c e s f o r n e t w o r k r e i n f o r c e m e n t s a n d c o n s t r u c t i o n o f n e w l i n e s . J n t u r n . t h i s h a s r e s u l t e d i n a g r e a t e r n e e d t o o p e r a t e d i s t r i b u t i o n l i n e s a t h i g h c u r r e n t s a n d a t h i g h t e m p e r a t u r e s t h a n i n i t i a l l y d e s i g n e d f o r . T h u s t h e a s s e s s m e n t o f t h e i m p a c t o f t h e s e d e s i r e d i n c r e a s e i n p o w e r t r a n s ! C r c a p a b i l i t ) o n r c l i a b i l i t v a n d s a i C t \ a r c o f i n c r e a s e d a n d \ i t a ! i m p o r t a n c e . W i n d s p e e d a n d \ \ i n d d i r e c t i o n a r c 1 \ \ o i m p o r t a n t \ \ c a t h e r p a r a m e t e r s \ \ h i c h a f ! C c t t h e c o o l i n g o f t h e O \ c r h c a d c o n d u c t o r s . R a t i n g p r a c t i c e s a n d a s s u m p t i o n s a r c \ a r y i n g f r o m u t i l i t y t o u t i l i t y . T h e m o s t o f c o m m o n p r a c t i c e t o c a l c u l a t e l i n e r a t i n g a t h i g h e s t a m b i e n t t e m p e r a t u r e . f u l l s o l a r r a d i a t i o n a n d c i T c c t i \ c \ \ i n d s p e e d o f 0 . 6 1 m s . N e v e r t h e l e s s t h e I I T F / C I C J R L s u n c ) s h o w s t h a t m e r t h e p a s t d e c a d e . n u m b e r o f u t i l i t i e s h a s i n c r e m e n t a l l y i n c r e a s e d t h e i r l i n e r a t i n g s b y r e l a x i n g s o m e o f t h e r a t i n g a s s u m p t i o n s . S o m e u t i l i t i e s n m \ a s s u m e t h a t a n c i T c c t i v c w i n d s p e e d o f 0 . 9 J m i s . o r e w n h i g h e r . T h i s d i s s e r t a t i o n l ' o c u s c s o n t h e i m p r o v e m e n t o f p o w e r t r a n s f e r l i m i t s o n e x i s t i n g d i s t r i b u t i o n l i n e s \ \ i t h c f l c c t i \ c \ \ i n d c o o l i n g . 1 . 2 O b j c c t i n T o c a r r y o u t a n i m c s t i g a t i o n f o r i m p r m c m c n t o f p m v c r t r a n s ! C r l i m i t s ( m c r l o a d i n g c a p a b i l i t y ) o n e x i s t i n g d i s t r i b u t i o n l i n e s \ \ i t h c i T c c t i v c w i n d c o o l i n g . 1 . 3 S c o p e o f w o r k I h e s c o p e o f t h i s \ v o r k a r c g i v e n b e l o w . • ! • I m c s t i g a t c c o n d u c t o r r a t i n g a n d c o l l e c t ' ' i n d d a t a o f s e v e r a l s p e c i f i c a r e a s . • ! • F i n d t h e p o s s i b i l i t i e s t o f i x a ' v \ i n d s p e e d t o u p r a t e t h e c o n d u c t o r r a t i n g . • ! • F i n d t h e p o s s i b i l i t y t o a d o p t a n c ' v \ r a t i n g o n p r o b a b i l i s t i c p o s s i b i l i t y o n c o n d u c t o r r a c i n g ( ) \ c r t e m p e r a t u r e . • ! • T o s t u d : g r o u n d c l e a r a n c e v i o l a t i o n s ' v v h c n o p e r a t i n g ' - m h i g h e r t e m p e r a t u r e s . • ! • P o s s i b i l i t i e s t o a d o p t t h e n C \ \ r a t i n g c o n s i d e r i n g r e l a t e d l o s s e s . 1 . 4 D e t e r m i n a t i o n o f m a x i m u m p e r m i s s i b l e c o n d u c t o r t e m p e r a t u r e , \ s p e r t h e I H ' S t a n d a r d 1 5 9 7 - 1 9 9 5 1 7 1 a n d 1 1 · : 1 - . L S t a n d a r d 7 3 8 - 2 0 0 6 1 6 ] . m a x n n u m t e m p e r a t u r e l i m i t i s s c l e e t c c L • ! • I n o r d e r t o m i n i m i z e l o s s o f t e n s i l e s t r e n g t h o f c o n d u c t o r • ! • r o k e e p a p p r o p r i a t e c l e a r a n c e • ! • l~conomical o p t i m i z a t i o n o f l i n e l o s s . o r a c o m b i n a t i o n o f a b o , · e . . . , C h a p t e r 0 2 P r o b l e m S t a t e m e n t O p e n d i s t r i b u t i o n l i n e a c c e s s a n d e c o n o m i c u n c e r t a i n t i e s a r c t h e r e a s o n s \ \ h \ m a n \ u t i l i t i e s a r c o p e r a t i n g t h e i r l i n e a t m u c h h i g h e r l o a d s t h a n t h e y v v c r e i n i t i a l l ) d e s i g n e d f o r . B e c a u s e o r t h i s . t h e c i T e c t s o r h i g h e r o p e r a t i n g t e m p e r a t u r e o n t h e s a ! C l \ a n d r e l i a b i ! i t i e s o f 0 \ c r h e a d l i n e s \ \ e r e s t u d i e d . C u r r e n t c a r r y i n g c a p a c i t y o r conductor~. m a i n l y d e p e n d o n i n t e n s i t y o r s o l a r r a d i a t i o n . s o l a r a b s o r p t i o n c o c i T i c i e n t . e m i s s i ' i t y c o e f l i c i c n t . a m b i e n t t e m p e r a t u r e . c u n d u c t o r d i a m e t e r . e l e c t r i c a l r e s i s t a n c e . \ \ i n d s p e e d a n d \ \ i n d d i r e c t i o n . W i n d s p e e d a n d \ \ i n d d i r e c t i o n a r c t \ \ O i m p o r t a n t \ \ C a t h e r p a r a m e t e r s \ v h i c h a f f e c t t h e c o o l i n g o f t h e o v e r h e a d c o n d u c t o r . R a t i n g p r a c t i c e s a n d a s s u m p t i o n s v · a r : h o m u t i l i t ; t o u t i l i t y . T h e m o s t c o m m o n p r a c t i c e i s t o c a l c u l a t e l i n e r a t i n g a t h i g h e s t a m b i e n t t e m p e r a t u r e . f u l l s o l a r r a d i a t i o n a n d c i T e c t i v c \ \ i n d s p e e d o r 0 . ( ) 1 1 w ' s . I t i s n o t e d t h a t A C S R R a c o o n c o n d u c t o r ' s C C C b e c o m e 2 0 2 ; \ a t t h e t e m p e r a t u r e o f 8 0 ° ( a n d a t s t i l l a i r c o n d i t i o n s . a n d 2 2 1 ; \ a t t h e \ \ i n d s p e e d 1 m / s a n d z e r o \ \ i n d a n g l e . I l o w e v e r . i n t h e a b s e n c e o f \ \ i n d s p e e d c o n d u c t o r t e m p e r a t u r e r e a c h e s t o 8 7 ' C . H y a n a l y z i n g w i n d d a t a o f s e \ e r a l a r e a s . i t i s o b s c n n l t h a t m o s t o r t i m e w i n d s p e e d i s m o r e t h a n I m s . ; \ s s u c h . p r o b a b i l i t y o r m e r t e m p e r a t u r e c o u l d b e d e t e r m i n e d b \ a p p l y i n g R a y l e i g h d i s t r i b u t i o n \ \ h e n \ \ i n d s p e e d i s b e l o \ \ 1 m / s . F u r t h e r . i t i s n o t e d t h a t l i n e i s b e c o m i n g m c r l o a d c d d u r i n g p e a k h o u r s . P r o b a b i l i t y o r o v e r l o a d i n g c o u l d b e d e t e r m i n e d b y a p p l y i n g c u m u l a t i v e f r e q u e n c y \ \ h e n i t i s m o r e t h a n 2 0 2 ; \ . O v e r t e m p e r a t u r e o f c o n d u c t o r c a n o c c u r d u e t o ' ' i n d s p e e d s b e l o v , 1 m i s a n d c o n d u c t o r l o a d i n g m o r e t h a n 2 0 2 ! \ . T h i s d i s s e r t a t i o n f o c u s e s o n t h e p r o b a b i l i s t i c a p p r o a c h f o r t h e i m p r o \ e m c n t o f p o w e r t r a n s f e r c a p a b i l i t y o f e x i s t i n g R a c o o n . , · ' d i s t r i b u t i o n l i n e s u p t o 2 2 0 ; \ " ' i t h c t T c c t i v c w i n d c o o l i n g a n d t o s t u d y t h e b c h m i o r o f t h e c o n d u c t o r o n O \ c r l o a d i n g a n d p o s s i b l e m c r t e m p e r a t u r e s t h a t t h e c o n d u c t o r m a : u n d e r g o . F u r t h e r t h e a d n m t a g c s a n d d i s a c h a n t a g c s t h a t m i g h t b e e x p e r i e n c e d h ) t h e s u p p l y a u t h o r i t ) o n e c o n o m i c \ i a b i l i t y h m c b e e n s t u d i e d . A C S R R a c o o n c o n d u c t o r i s t h e m o s t c o m m o n ! : u s e d c o n d u c t o r i n t h e e x i s t i n g d i s t r i b u t i o n s y s t e m o r C F B . T h e r e f o r e t h i s c o n d u c t o r \ v a s c h o s e n C o r t h e c a l c u l a t i o n i n t h e s t u d v . ~ C h a p t e r 0 3 M a x i m u m A d m i s s i b l e L o s s o f T e n s i l e S t r e n g t h T h e p a s s a g e o f e l e c t r i c c u r r e n t t h r o u g h a c o n d u c t o r c a u s e s a r i s e i n t e m p e r a t u r e \ \ h i c h c a n h m c a n n e a l i n g c i T c c t o n A l u m i n i u m c a u s i n g a l o s s o f s t r e n g t h . T h e a m o u n t o f s t r e n g t h t h a t i s l o s t d e p e n d s o n t h e t e m p e r a t u r e a n d _ d u r a t i o n . a n d t h e c ! T c c t i s c u m u l a t i v e . i . e 1 0 h r s e a c h y e a r o f 1 0 y e a r s h a s s i m i l a r e f f e c t t o h e a t i n g t h e c o n d u c t o r c o n t i n u o u s l y f o r 1 0 0 h r s a t t h e s a m e t e m p e r a t u r e 1 7 1 . I t i s a n o r m a l p r a c t i c e t o l i m i t o p e r a t i n g t e m p e r a t u r e s t o 8 0 ° C a n d c m c r g c n c : l o a d t e m p e r a t u r e t o 1 2 5 " C f o r ; \ C S R c o n d u c t o r s . B y a n a l y z i n g l o a d p a t t e r n o f C E B n e t w o r k a n d ' ' i n d s p e e d d a t a o f S r i L a n k a . i t i s n o t e d t h a t \ \ h e n \ \ i n d s p e e d b e c o m e b e l o w I m / s a n d c u r r e n t b e c o m e s m o r e t h a n 2 0 2 A . i t c a u s e s O \ c r t e m p e r a t u r e o f c o n d u c t o r . S i n c e t h e s e t \ \ O e v e n t s a r c i n d e p e n d e n t . p r o b a b i l i t y o f 0 \ c r t e m p e r a t u r e o f c o n d u c t o r c a n b e c a l c u l a t e d h y m u l t i p l i c a t i o n o f a b o v e p r o b a b i l i t y o f o c c u r r e n c e o f t h e a b o v e l \ \ o c \ c n t s . T h i s c h a p t e r d e s c r i b e s t h e m a t h e m a t i c a l f o r m u l a t i o n t o C \ a l u a t c t h e c u r r e n t c a r r : i n g c a p a c i t y o f a b a r e c o n d u c t o r . l h e r e a r c m a n y m e t h o d s f o r c a l c u l a t i o n o f l i n e l o a d i n g . M o s t c o m m o n l y u s e d m e t h o d u s e s t h e c o n d u c t o r t e m p e r a t u r e t o s o l v e t h e h e a t b a l a n c e e q u a t i o n t o C \ a l u a t c t h e c u r r e n t c a r r y i n g c a p a c i t ) . 3 . 1 U n i t s a n d i d e n t i f i c a t i o n o f l e t t e r s y m b o l s - · · · , - - - - - - · - · - - - - - - - - - - - - - - - ---~ S y m b o l A ' - · · · c ] ) I ! , - - f f e I - - K u n g l c D e s c r i p t i o n S I l 1 n i t s I P r o j c · - - · · - · - - - - + - - - _ _ , - c t c d a r e a o f c o n d u c t o r p e r u n i t l e n g t h m - / m ! - - - - - · - · - - - - S o l a r a : t i m u t h c o n s t a n t d e g r e e r - - - - · - - - - - - - - - - - - - - - - - - - - - · C o m ! u c t o r d i a m e t e r m m / \ J t i t L d e o f s u n d e g r e e 1 - - - · - - - - - - · · - - - - - - - - - - - - - - - I J c \ ~1 t i o n o f c o n d u c t o r a b o \ ' c s e a l c \ c l 1 1 1 - + - - - - - - - - - - C o m ! ; \ r - - - - - \ \ ' i n d · - - u c t o r c u r r e n t d i r e c t i o n i~lCtor _ - _ _ _ _ _ _ j T a b l e 3 . 1 l l n i t s a n d i d e n t i f i c a t i o n o f l e t t e r s y m b o l s 5 i [ - - - - - - - D e s c r i p t i o n - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 S o l a r a l t i t u d e c o r r e c t i o n f~tctor S y m b o l K \ D i ( / f · · - - - - - - - - - - - - - - - - k ; r h r m a l c o n d u c t i \ i t ) o r a i r a t t e m p e r a t u r e l " t i l t l l r a t D e _ r c c s o r l a t i t u d e / \ ' D a o r t h c \ c a r 1 S I l l n i t s 1 ~--j i ' ( ' l \ V ' m ' : - - - - - - - j d e g r e e s ----~ I - - - - 1 q C / 1 • q c J , q , : - . C j , C o 1 \ c c t c d h e a t l o s s p e r u n i t l e n g t h • . I ~/m _ j I q , " - - - I L / s I Q , 1 . . . ~ I R{7~) T , , · - l ; l t i l l l l r l m t · - - I r / " 1 ' . ; , 1 ' 1 1 - - - - - R a - - - - - - l i e T o - - · T o C O l i \ C · · - i \ 1 T - - - - - - - C o ( 1 c - - - - - - - T v l i r e s . . i a t c d h e a t l o s s r a t e p e r u n i t l e n g t h t t g a i n r a t e t i - m n s u n ---~~--·· - - - d l s o l a r a n d s k ) r a d i a t e d h e a t f 1 u : - - : r a t e < t l s o l a r a n d s k y r a d i a t e d h e a t J l u : - - : r a t e c l c \ a t i o n - c c t c d · - - - - - I w m I \ \ m \ \ ' i m : : r - \ \ ' i m - - - - · - - - - - · - · - - - - - 1 r e s i s t a n c e o r c o n d u c t o r a t t e m p e r a t u r e . ~~ U / m , · - - - - - - - - - - b i c n t t e m p e r a t u r e - - - - - - - - - - - - - - - - - - - 1 d u c t o r t e m p e r a t u r e · l a ) / . 2 - - - - - 1 - - - - · - - - - - _ _ . . . j ' ' C I - - - - - l - 1 - - C ( ' - - - 1 + - , T I I · 1 1 i m u m c o n d u c t o r t e m p e r a t u r e ! ' o r \ \ h i c h a c ' \ ' I . . f " I I s t a n c e 1 s s p c c 1 1 c c ! - - - - - · - - - - - - - 1 M a r e s : - - : i m u m c o n d u c t o r t e m p e r a t u r e ! ' o r w h i c h a c o c I s t a n c e i s s p e c i f i e d I S p c c d o r a i r s t r e a m a t c o n d u c t o r - - · / A · / i ~ . . _ , · · · ~I , " · ' m u t h o r s u n : \ / i m u t h o r l i n e 1 S o l a r a b s o r p t i Y i t y ( 0 . . 2 3 t o 0 . 9 1 ) d e g r e e s d e g r e e s f--~-· +----·-·-··------~--~- 1 r 5 1 S o l m d e c l i n a t i o n ( 0 t o 9 0 ) d e g r e e s - - - ·--·------~- 0.2~ t o 0 . 9 1 ) - - c c n \ \ i n d a n d a : - - : i s o r c o n d u c t o r d e g r e e s I - - - - - - - - - - , . I m i s s i \ i t \ " - - - - - - - - r p ; 1 \ n g l c b e t I f J A n g l e b e t e c n \ \ i n d a n d p e r p e n d i c u l a r t o c o n d u c t o r d e g r e e s I a : ' \ I S -·--------~ P ; D c n s i t \ o k g . m ' 1 1 1 ' - - · - - - - - - - - - · 0 F f T c c l i \ e 1 g l c u f ' i n c i d c n c e o f t h e s u n · s r a y s d e g r e e s - - - f l r l ) y n a m i c s c o s i t : o f a i r P a s · - - - - · · - - - - - - - - - - - - - · · - - - - - - - ( J ) ! l o u r s l i · o - - - - I X S o l a r < v i m L -------~~ dcor~'CS b - - - - - - - - - - 4 - - - - - - - - - - - - - - l o c a l s u n n o o n t i m e s 1 5 t t h v a r i a b l e T a b l e 3 . 1 l l n i t s a n d i d e n t i f i c a t i o n o f l c t t c r s y m b o l s ( c o n t i n u e d ) 6 3 . 2 C u r r e n t c a r r y i n g c a p a c i t y o f A C S R R a c o o n c o n d u c t o r s T h e C C C o f a c o n d u c t o r i s t h e m a x i m u m s t e a d \ s t a t e c u r r e n t i n d u c i n g a g 1 \ e n t e m p e r a t u r e r i s e i n t h e c o n d u c t o r . f o r g i \ e n a m b i e n t c o n d i t i o n s . 3 . 2 . 1 S t e a d y - s t a t e h e a t b a l a n c e e q u a t i o n T h e s t e a d y - s t a t e t e m p e r a t u r e r i s e o f a c o n d u c t o r i s r e a c h e d v v h e n c \ c r t h e h e a t g a i n e d b y t h e c o n d u c t o r ! i · o m \ a r i o u s s o u r c e s i s e q u a l t o t h e h e a t lossc~. T h i s i s e x p r e s s e d b ) e q u a t i o n g i \ c n b c l o \ \ 1 6 1 . q c + q r = C f s + (l.RCJ~) ( 3 . I ) C f c i s t h e c o n v e c t i o n h e a t l o s s q r i s t h e h e a t l o s s b y r a d i a t i o n o f t h c c o n d u c t o r q _ , . i s t h e s o l a r h e a t g a i n b y t h e c o n d u c t o r surf~1cc ( 2 R ( 1 J i s t h e h e a t g e n e r a t e d b ) J o u l e c f T c c t N o t e t h a t m a g n e t i c h e a t g a i n . c o r o n a h e a t g a i n . e \ a p o r a t i v e h e a t l o s s e s a r c n o t t a k e n i n t o a c c o u n t i n e q u a t i o n ( 3 . 1 ) . 3 . 2 . 2 F o r c e d c o m e c t i o n h e a t l o s s [ ( / ) \ ) 0 . : ) 2 ] q c l = 1 . 0 1 + 0 . 0 : - 3 7 2 1 : ; 1 1 1 v f<;f ~--~ ~ C i f x > 0 --~ > - - - - - - - - ( ( _ l e g r e e s ) - - - - + - _ _ -~ degre~~- - - - - - - - - - _ _ 1 _ _ _ _ _ _ - _ 1 _ 8 c _ J ,~ < • l ( J _ _ _ _ 1 _ _ _ _ _ _ _ _ _ o _ _ _ _ _ _ j c _ _ _ _ ( ) _ < l • l < .!~ _ _ _ _ L _ - - _ _ - - - · _ 1 g ( ) _ j _ _ T a b l e 3 . 3 S o l a r a z i m u t h c o n s t a n t , C ( i n d e g r e e ) , i s a f u n c t i o n o f t h e " h o u r a n g l e " , w , a n d s o l a r a z i m u t h v a r i a b l e , X 1 2 ----··-~ ---·~---· · - - - · - · · · · r 1 L o c a l s u n t i m e [ i 1 L a t i t u d e l~ 1 0 : 0 0 a . m . _ l - _ _ ' ' i o o n ~- ~~--~- 2 : 0 0 p . m . _ _ l L ( D e g r e e s N ort!12_fi_I~--L~~ L ~+I -~~-- _ L I ( _ l Z r I I ~j I x o . ' " 1 ' ) I . , . , I . , . , I X O I . , ; . " ' 2 7 - , - ( } I I - j · . . . . : - ' . . : -_ _ I -~ ' ~+--- - - + - - - : 2 . : : : - _ L _ ) I _ ) ) l l _ _ _ _ _ : l _ Q _ _ _ _ -~ t = 3 2 _ ( _ - + 3 __l_l~(~ _ J _ - + Q _ 1 3 2 3 1 3 5 o l ' - 6 0 _ _ _ L - + X _ _ i Q _ _ _ ; _ 5 3 : I X O _ _ ~-+X 3 1 7 350~ r - - - - - - - - - 5 _ 0 _ \ _ 5 5 l 5 2 -~-63 j_1~) _ j 5 5 I 3 0 X I 3 5 0 _ j - 4 1 1 I 6 0 t 6 6 _ + 7 2 _ ~~ I S O _ i 6 0 I 2 9 4 I 3 5 0 I I - ] 0 I 6 2 L X J I~-~~ 1 - 1 8 0 I - 6 2 2 7 7 ] 5 0 f - - - - - - - 2 0 ~ 6 2 ~--=-96 ~ < ) ( ) _ I X I I l = 6 2 _ 1 ~64 _ 2 0 _ l l - 1 ( ) I 6 1 I l ) 7 L X 8 1 x o ~ 6 1 2 6 3 5 0 - - - ( - ) J-60-~~)1 L 9 o - -1xo~ - 6 ( ) 2 6 9 1 8 0 1 I 0 I 6 1 l - 8 5 I 8 9 I X I I I 6 1 ' 2 7 5 I I I ( ) ! 2 0 r 6 2 1 _ 8 5 r _ _ ' J O _ _ 1 8 0 J ~ 6 2 1 2 7 5 1 1 4 ( ) _ 1 f..----~~3_0_ l 62_\--~2__ + - 8 ] ~ ~ 8 0 I - 6 2 I 2 6 1 I I 7 ( ) _ I r---~~4_0 . \ ~~ -~~ ~J_n_l _J_~o _ _ _ l _ _ _ _ ~o- I 2 4 5 i 170~ 5 0 ---\-55--~-~~-. i _ < J J r 8 1 1 I " - . 5 - . - . r 2 3 2 I l ! _ ( ! _ j 6 0 J-~-_l~137 [ _ _ 5 3 -~X~l_j___!X_. i 2 2 3 1 7 0 ~ 7 0 -+~)- L 1 - + 3 -~ - + 3 I 1 ~_j__40 I 2 1 7 1 7 0 i '--~~x_o_ 1 3 2 L _ I : 2 _ _ L 3 3 ~~~-1_32 1 2 1 3 1 7 0 1 T a b l e 3 . - t S o l a r a l t i t u d e , l i n a n d a z i m u t h , Z c , a t v a r i o u s l a t i t u d e s f o r a n a n n u a l p e a l \ . s o l a r h e a t i n p u t 3 . 3 . 6 T o t a l h e a t f l u x r e c e i v e d b y a s u r f a c e a t s e a l e v e l ( T a b l e 3 . 5 a n d T a b l e 3 . 6 ) T h e t o t a l h e a t f l u x d e n s i t y a t s e a l c \ c l i s d e p e n d e n t o n b o t h t h e s o l a r a l t i t u d e a n d a t m o s p h e r i c c l a r i t y . T h e h e a t f l u x recein~d b y a surl~lce a t s e a l e v e l a s s h O \ m i n t a b l e 5 m a y b e r e p r e s e n t e d b y t h e C o l l e ) \ \ i n g r e g r e s s i o n e q u a t i o n 1 6 1 . y - t o t a l h e a t ! l u x . ( ) , ( \ \ / m 2 ) X = s o l a r a l t i t u d e . l i e ( d e g r e e ) Q s = A + B H c + C H / + C H / + C H / + C H c 5 + C H / ' ( 3 . 1 9 ) 1 3 ~-- - - C l e a r a t m o s p h e r e - - ~~--~-- - - ----~~~~~ _ _ -~--------~---- ~---~ - - - - - - - - -~ _ . . Q . 2 : i 9 1 I ' \ - - - - - - - - ! ~---- - - - - - G - - - - - - -~- - - ( ; . 1 X O . . t - t i i ---~ - - c - - - - - - - --1--~-- - - - - - - 1 t ) " l ' l ( ) - - - - - - - 1 C - - - 6 - - - - - t - - = - -_--.1-.~!~~2l~J-(r- - j ~-----·---- ~~- - - - - - - - = t _ _ _ - . 1 . 6 1 1 1 X : - ; I ( f _ _ I - - - - - - - - - F . - - - - - I . - - 1~9..t1 l X : - - ; l O · : - _ _ _ j ~ - - - - - c i - + - - - - - t . 0 7 W X : - - ; H r _ _ _ _ _ _ _ : r - - - - I n d u s t r i a l a t m o s p h o r c . - - - 1 _ _ - _ _ -~- 1 L----------~- - - 5 . . , J 8 ' 1 J I ~ ~-~\~3 - - - - - - - - _1~:2-(]o I ' · · · · - - c - - - 6 . 6 1 . 1 8 : - - ; 1 o · , 1 D ~ _ - 3 . I _ h ? _ ? : - - ; H r - 1 - -~ i -----~- i - - - - - - _ - . -~ru ~~(::~~~/~', -~ - ( ) - - - - · i 1 . 3 2 3 6 x 1 0 ' _ j - - - - - - - · - - - - _ _ L _ _ - - - - - - - - - - - - - - - - - - - - T a b l e 3 . 5 C o e f f i c i e n t f o r e q u a t i o n ( 3 . 1 9 ) D e g r e e s s o l a r a l t i t u d e I Cle~;;:·atmosphere 1 Imlust~ial a t m o s p h e r e I f--~--- + - - - - - - - - - · - - , - - - _ _ _ ; - - - - - - - ~ > - - - - - llr(d~~------- l - _ _ _ Q , ( W / m - ) Q , ( W / m - ) I I . : : ; , . . , - f ] . . , ( ~ I • _ _ ) _ ) ) i f---~~~-------- - - - - - - - - - - - - - - - - - - - --~ 1 0 4 3 3 2 . . t 0 ! f--~~~~- - - - -~~~-- - - - - - - - - . - - - _ _ _ _ _ _ _ _ - - - - - - j - - - - I e . - ! 1 5 I - v - , . . , 1 v 1 ) o . ) . L O / 4 0 . . t s 5 0 6 0 7 0 8 0 - - - - - i 6 9 3 4 2 2 ! -~~~~~-~ s o 2 1 - 8 2 9 5 7 1 I - - - - - - - - - - - X 7 7 9 1 : ) - - 1 - - - - - - - - - - 1 I - - - - - - I 9 4 1 I - - - - - - - - - - - t - - - - - - · - % 9 - - - - - - - - · - - - - - - · · - - - - - - - t - - - 1 0 0 0 1 0 2 0 - - - - - - - - - - 1 0 3 0 1 0 4 0 ~----- 6 1 9 6 6 2 6 9 4 7 2 7 7 7 1 8 0 9 8 3 3 I i - - - - - , I - - - 1 _ _ _ j I J 9 0 L - - - - - - - - - - - - · · · X 4 9 _ j - - - - - - ---~------·-- T a b l e 3 . 6 T o t a l h e a t f l u x r e c e i v e d b y a s u r f a c e a t s e a l e v e l n o r m a l t o t h e s u n ' s r a y s 1 4 3 . 3 . 7 T o t a l h e a t f l u x e l C \ a t i o n c o r r e c t i o n f a c t o r ( T a b l e 3 . 6 ) Q 1 · e = K s o l m · Q s ' A ' h e r e K 1 o l a r = ! 1 + B f l c + C l l e 2 . \ B l . l . . f g x I ( r 1 C - 1 . 1 0 8 x 1 0 . s E l e v a t i o n aht~c--,;ealcvcl H , ( , . ; ) - I M " J t i p l i c r s - r~r v a l u e s i n T a b l e 3 . 5 0 I 0 0 ~- --~ . . ~~:~-:::-) - _ • . - . - - ~= I - - - - - - . · - . ~ : - : : : ~- 4 0 0 0 1 . 2 R ' - - - - - - - - · - -~---- - - · · - · , _ _ _ _ _ _ _ _ _ _ ] T a b l e 3 . 7 S o l a r h e a t m u l t i p l y i n g f a c t o r s , / ( 1 1 1 t a r f o t · h i g h a l t i t u d e s 3 . . 4 S a m p l e c a l c u l a t i o n s 3 . . 4 . 1 S t e a d y s t a t e t h e r m a l r a t i n g T h e c a l c u l a t i o n o f s t e a d y - s t a t e t h e r m a l r a t i n g g i \ c n a m a x i m u m a l l o w a b l e c o n d u c t o r t e m p e r a t u r e . \ \ C a t h e r c o n d i t i o n s . a n d c o n d u c t o r c h a r a c t e r i s t i c s m a y h e p e r f o r m e d h y t h e c o m p u t e r p r o g r a m i n c \ n n c x A \ 5 \ . l l c m c \ C L s i n c e t h e p r o c e s s d o c s n o t r e q u i r e i t e r a t i v e c a l c u l a t i o n s . i t c a n h e d o n e h y h a n d . D o i n g s o d e m o n s t r a t i o n s t h e u s c o f t h e f o r m u l a s a n d y i e l d s s o m e i n s i g h t i n t o t h e c a l c u l a t i o n p r o c e s s . N o t e t h a t i n t h e f o l l o w i n g . t h e n u m b e r o f s i g n i f i c a n t d i g i t s d o c s n o t i n d i c a t e t h e a c c u r a c v ( ) f t h e f o r m u l a . 3 . 4 . 2 P r o b l e m s t a t e m e n t F i n d t h e s t e a d y - s t a t e t h e r m a l r a t i n g ( C C C ) f o r A C S R R a c o o n c o n d ' f o l l o w i n g c o n d i t i o n s . a ) W i n d s p e e d ( V " ) i s l m s p e r p e n d i c u l a r t o t h e , . b ) F m i s s i v i t y ( f : l i s O J J 1 6 c ) S o l a r a b s o r p t i \ i t ) ( u ) i s 0 . 5 d ) / \ m b i c n t a i r t e m p e r a t u r e i s 3 0 ° C c ) M a - . : i m u m a l l r m a h l c c o n d u c t o r t e m p e r a t u r e is~()'(· f ) C o n d u c t o r o u t s i d e d i a m e t e r ( ] ) ) i s 1 2 . 2 7 m m g ) C o n d u c t o r a c r e s i s t a n c e I R ( J e l l i s : R ( ~ooc) 0 . 4 3 1 0 (k~2im) R ( 8 0 ° C ) 0 . 5 1 9 2 ( k £ 2 / m ) h ) T h e l i n e r u n s i n a n 1 ; a s t - W e s l d i r e c t i o n s o a / . i m u t h o f l i n e . / 1 9 0 ° i ) L a t i t u d e i s 1 0 ' 1 N o r t h j ) T h e a t m o s p h e r e i s c l e a r k l S o l a r a l t i t u d e O l e ) r o r 1 2 : 0 0 1 \ o o n o n l ) / \ \ c r a g e c o n d u c t o r e l c \ a t i o n 1 O O m 3 . . t . 3 C o n v e c t i o n h e a t l o s s ( q , ) T h e n a t u r a l c o m e c t i o n h e a t l o s s i s c a l c u l a t e d b y m e a n s o f e q u a t i o n s ( 3 . 6 ) . S e c W h e r e D 1 2 . 2 7 m m r c - 8 0 ° C T a - 3 0 ° C B O + 3 0 ' I [ u m = 2 = s s o c P t 1 . 0 7 6 k g / m ' ( T a b l e 3 . 2 ) q e n = 0 . 0 2 0 5 X ( 1 . 0 7 6 ) 0 ' i X 1 2 . 2 7 ° 7 5 X ( B 0 - 3 0 ) 1 2 5 q c n = 18.5~ W 1 m S i n c e t h e \ V i n d s p e e d i s g r e a t e r t h a n / . e r o . t h e f o r c e d c o m c c t i o n h e a t l o s s f o r p e r p e n d i c u l a r \ \ i n d i s c a l c u l a t e d a c c o r d i n g t o e q u a t i o n ( 3 . 2 ) a n d ( 3 . 3 ) . c o r r e c t e d C o r w i n d d i r e c t i o n a n d c o m p a r e d t o t h e n a t u r a l a n d f o r c e d h e a t c o n v e c t i o n i s u s e d t o c a l c u l a t e t h e t h e r m a l r a t i n g . W h e r e D ~ 1 2 . 2 7 m m V , , 1 m / s l c 8 0 ° ( ' 1 6 1 , . • 3 0 o c B O + 3 0 T r u m = 2 = 5 5 o c : f l r 1 . 9 8 x ] ( r ' P a s ( ' ! a b l e 3 . 2 ) P t - 1 . 0 7 6 k g / m ; ( ! a b l e 3 . : ? . ) k 1 0 . 0 2 8 3 ' N / ( m ° C ) ( T a b l e 3 . : ? . ) F r o m e q u a t i o n ( 3 . 2 ) [ 1 2 . 2 7 X 1 . 0 7 6 X 1 O . S Z ] q c 1 = 1 . 0 1 + 0 . 0 3 7 2 ( " ) 0 . 0 2 B 3 X 1 . 9 B X 1 0 - ' • : ? . 2 . 3 6 \ V 1 m F r o m e q u a t i o n ( 3 . 3 ) 0 . 3 B B X ( B O - 3 0 ) · = l 0 . 0 1 1 9 ( l Z . ' 2 . 7 X l . 0 7 ( , x J ) o . r , ] X ( ) . ( ) 2 B 3 q c z l . ' J H X 1 0 - ' X 0 . 3 B B X ( B O - 3 0 ) 2 0 . - 1 - 0 w 1 1 1 A s i n s t r u c t e d i n 3 . 1 . 2 . s e l e c t t h e l a r g e r o r t h e t \ V O c a l c u l a t e d c o n v e c t i o n h e a t l o s s e s . q , - 2 2 . 3 6 W / m S i n c e t h e \ \ i n d s p e e d i s a l o n g t h e a x i s o f t h e c o n d u c t o r . t h e \ \ i n d d i r e c t i o n m u l t i p l i e r . I C u a t e i s 0 . 3 8 8 . a n d t h e f o r c e d c o m c c t i o n h e a t l o s s . I h e r d ( H · e . t h e ! ( n e e d c o m e c t i o n " h e a t l o s s \ \ i l l b e u s e d i n t h e c a l c u l a t i n g o f t h e n n a l r a t i n g . 3 A A R a d i a t e d h e a t l o s s ( q r ) T h e r a d i a t e d h e a t l o s s i s c a l c u l a t e d \ \ i t h e q u a t i o n ( 3 . 8 ) . W h e r e . D = 1 2 . 2 7 m m E - 0 . 6 T c ~- s o o c T a 3 0 ' T q r = 0 . 0 1 7 B X 1 2 . 2 7 x 0 . 6 x ~-(BO + 2 7 : 1 ) 1 - _ ( 3 0 + 2 7 3 ) 1 - ] 1 0 0 1 0 0 q r = 9 . 3 0 \ V 1 m 1 7 3 . 4 . 5 S o l a r h e a t g a i n ( q , ) l h e c o n d u c t o r i s a t 1 o o c N o r t h l a t i t u d e : A p p r o x i m a t e v a l u e s o ! ' I l , a n d / , c a n b e o b t a i n e d l i · o m T a b l e 3 . 3 a n d 3 . - 1 - . F r o m T a b l e 3 . 3 . t h e s o l a r a l t i t u d e . I I , a n d t h e s o l a r z v : i m u t h . / , c a n b e d e t e r m i n e d a s f o l l o w s : l l , a t 1 2 : 0 0 n o o n H 9 c / , a t 1 2 : 0 0 n o o n 1 X O ' ) I r o m t a b l e 3 . 5 f o r I I , X l ) u \ \ i t h c l e a r a t m o s p h e r e : ( ) , ~ 1 0 3 9 \ . \ ' 1 m 2 ( B y i n t e r p o l a t i o n ) / 1 · 9 0 ° o r 2 7 0 ° 0 a r c o s j c o s ( X 9 ° ) c o s ( 1 X 0 ° - 9 0 ° ) j 9 0 ° \ \ ' h e r e u . c 0 . 5 A ' · D / 1 0 0 0 1 2 . 2 7 ' 1 0 0 0 0 . 0 1 2 2 7 m K , 0 J a r · 1 . 0 C f s = 0 . 5 X 1 0 3 9 X s i n ( 9 0 ° ) X 0 . 0 1 2 2 7 q~=6.37Wjm 3 . 4 . 6 S t e a d y s t a t e t h e r m a l r a t i n g U s i n g E q u a t i o n ( 3 . I ) . t h e t h e r m a l r a t i n g c a n b e f o u n d \ \ h e r e : C J c = 2 2 . : 1 6 W j m q , = 9 . 3 0 W j m C J s = 6 . 3 7 W / m R U W ° C ) 5 . 1 9 2 X 1 c r 1 £ 2 / m / 2 2 . 3 6 + 9 . 3 0 - 6 . 3 7 I - I - J 5 . 1 9 2 x 1 0 · ' l l = 2 2 1 A ! ' h e p r o g r a m l i s t e d i n J \ n n c x J \ c a n a l s o b e u s e d t o c a l c u l a t e t h e s t e a d y - s t a t e t h e r m a l r a t i n g . ! X ~: 3 . 5 I n p u t d a t a C a r e f u l s e l e c t i o n o r i n p u t d a t a f o r c u r r e n t - t e m p e r a t u r e r e l a t i o n s h i p i s a s i m p o r t a n t a s t h e m e t h o d o f c a l c u l a t i o n i t s e l f . a n d r e q u i r e s c o n s i d e r a b l e e n g i n e e r i n g j u d g m e n t i n t h e s e l e c t i o n o r \ a l u c s I ( H e a c h o f t h e \ a r i a b l e s . T h e s e \ a r i a b l c s a r c d i s c u s s e d s e p a r a t e h e a d i n g . w i t h s u g g e s t i o n s g i v e n o n h e m t o s e l e c t \ a l u c s t o s u i t p a r t i c u l a r c i r c u m s t a n c e s . S o m e s u g g e s t i o n s a r c g i v e a s t o \ \ h a t f~tctors s h o u l d b e c o n s i d e r e d w h e n i t i s n c c e s s a n t o m a k e d e c i s i o n s . 3 . 5 . 1 \ V i n d a n d a m b i e n t t e m p e r a t u r e \ \ ' c a t h c r c o n d i t i o n s h m c a c o n s i d e r a b l e c J ' f c c t o n t h e t h e r m a l l o a d i n g o f b a r e o v e r h e a d c o n d u c t o r s . T h e \ \ C a t h e r p r o v i d e s c o o l i n g p r i n c i p a l l y b y m e a n s o f c o n v e c t i \ e h e a t l o s s ( c i c l t o s u r r o u n d i n g a i r . T h e d e g r e e o f c o o l i n g d e p e n d s o n t h e a i r t e m p e r a t u r e a n d t h e w i n d \ c l o c i t y c o m p o n e n t p e r p e n d i c u l a r t o t h e c o n d u c t o r . T h e e f f e c t o f w i n d d i r e c t i o n r e l a t i \ c t o t h e c o n d u c t o r i s c o n c l u d e d i n t h i s s t a n d a r d a s e q u a t i o n ( 3 . 4 - a n d 3 . 5 ) . F o r a g i v e n \ \ l ! l d s p e e d . \ \ i n d s b l m v i n g p a r a l l e l r e s u l t i n a 6 0 ° / c > l o w e r c o m c c t i v e h e a t l o s s t h a n w i n d s h l c m i n g p e r p e n d i c u l a r t o t h e c o n d u c t o r . ! I e i g h t o r c o n d u c t o r s a b m c g r o u n d J s s i g n i t i c a n t i n t e r m s o f \ \ i n d s h i e l d i n g . 3 3 k V l i n e s ( \ \ h e r e t h e g r o u n d c l e a r a n c e i s g r e a t e r ) m a y b e e x p e c t e d t o b e l e s s s h i e l d e d b y t r e e s a n d t e r r a i n t h a n l m \ - \ o l t a g c l i n e s . i l -~~- \ V i n d d i r e c t i o n r e l a t i v e t o c o n d u c t o r a x i s W i n d s p e e d ( m / s ) ( d e g r e e s ) ~ -·--------~-~-~- 0 . 6 9 0 0 . 8 - + 5 I ~--- c~~~~· = - - - - - - 2 2 . 5 -~---- 0 T a b l e 3 . 8 E q u i v a l e n t c o m b i n a t i o n o f w i n d s p e e d a n d d i r e c t i o n f o r e q u a l c o m e c t i v c c o o l i n g 945~5 ] C ) 3 . 5 . 2 A i r d e n s i t y . v i s c o s i t y a n d c o n d u c t i v i t y T h e d e n s i t y . \ i s c o s i t : a n d c o n d u c t i \ i t y o f a i r a r c u s e d i n t h e c a l c u l a t i o n l o s s e s a n d c a n h e o b t a i n e d f r o m I a b l e 3 . 2 . 3 . 5 . 3 E m i s s i v i t y a n d a b s o r p t i v i t y F m i s s i \ it~ a n d a b s o r p t i \ i t y i n c r e a s e ! " r o m a b o u t 0 . 2 t o ( ) l ) \ V i t h a g e . ! h e e x a c t r a t e ( 1 r i n c r e a s e d e p e n d s o n t h e J c , c l o f a t m o s p h e r i c p o l l u t i o n a n d t h e l i n e ' s o p e r a t i n g \ o l t a g c . V a l u e s o f 0 . 5 f o r s o l a r a b s o r p t i \ i t y ( u . ) a n d 0 . 6 f o r I . m i s s i \ i t y ( i : ) . h a s b e e n u s e d f o r / \ C S R ( R a c o o n ) C o n d u c t o r . 3 . 5 . 4 S o l a r h e a t g a i n i \ s i m p l e m e t h o d f o r t h e c a l c u l a t i o n o r s o l a r h e a t g a i n i s p r o Y i d c d b : e q u a t i o n ( 3 . 9 ) a n d ( 3 . 1 0 ) . T h e m o s t c o n s c n a t i Y c r e s u l t s a r c o b t a i n e d b y a s s u m i n g a n a n g l e o r i n c i d e n c e o f 9 0 ° . ' ' h i c h \ \ i l l g i \ c t h e l o w e s t v a l u e o r c u r r e n t c a r r y i n g c a p a c i t y a n d w i l l b e a p p r o p r i a t e ! " o r m a n y p u r p o s e : ; . S o l a r h e a t i n p u t t o b a r e o \ · c r h c a d c o n d u c t o r c a n c a u s e a c o n d u c t o r t e m p e r a t u r e r i s e a b o v e a i r t e m p e r a t u r e o r u p t o 1 5 ° C i n s t i l l a i r . l l o \ \ C \ c r . m o r e t y p i c a l l y . p e r i o d s o f m a x i m u m s o l a r h e a t i n p u t a r c associ~11cd \ V i t h s i g n i l i c a n t \ \ i n d a c t i \ i t : a n d t h e a c t u a l t e m p e r a t u r e r i s e m e a s u r e d ! o r b a r e c o n d u c t o r s i n O \ ' C r h c a d t r a n s m i s s i O n l i n e s s e l d o m e x c e e d s 5 o c t o 1 ( ) " ( · . 2 0 C h a p t e r 0 4 P r o b a b i l i s t i c A p p r o a c h t o A l l o w f o r M a x i m u m A d m i s s i b l e L o s s o f T e n s i l e S t r e n g t h . t . l P r o b a b i l i t y o f o v e r t c m p c n t t u r t - T h e p r o b a b i l i t y o r o \ n t e m p e r a t u r e c o u l d b e d e t e r m i n e d b y a p p l y i n g R a y l e i g h d i s t r i b u t i o n a n d c u m u l a t i ' e t i · c q u e n c \ r c s p e c t i \ c l y ' ' h e n \ \ i n d s p e e d i s b e l o w 1 m / s a n d c o n d u c t o r c u r r e n t r a t i n g i s m o r e t h a n : : ? . 0 2 ! \ . . t . l . l R a y l e i g h p r o b a b i l i t y d i s t r i b u t i o n T h e p r o b a b i l i t y t h e o r y a n d s t a t i s t i c s . t h e R a y l e i g h d i s t r i b u t i o n i s a c o n t i n u o u s p r o b a b i l i t y d i s t r i b u t i o n . R a y l e i g h p r o b a b i l i t y d e n s i t y f u n c t i o n ( p d f ) i s \ 1 6 j f x ( - x 2 ) ( x : 0 ) = 0 2 e x p 2 C Y 2 f o r x E I 0 , o c ) . 0 > 0 C u m u l a t i v e d i s t r i b u t i o n f u n c t i o n ( c d l ) i s \ 1 6 \ 1 - e x p (;~:) . 4 . 1 . 2 C u m u l a t i v e f r e q u e n c y T h e c u m u l a t i v e f r c q u e n c y i s t h e f r e q u e n c y \ \ h e r e t h e ' a l u e o r a v a r i a b l e Y i s l e s s t h a n a r e f e r e n c e \ a l u c X . T h e c u m u l a t i v e l ' r c q u e n c y F e ( Y < X ) i s f o u n d t i · o m F e ( Y < X ) M x / N . \ \ h e r e M x i s t h e n u m b e r o f d a t a Y w i t h a \ · a l u c l e s s t h a n t h e r e f e r e n c e v a l u e X . a n d N i s t h e t o t a l n u m b e r o f d a t a . C o n s i d e r i n g X a s a \ a r i a b l c . F e ( Y < X ) c a n b e c a l l e d t h e c u m u l a t i v e i i c q u c n c y f u n c t i o n u r c u m u l a t i v e l ' r c q u c n c y d i s t r i b u t i o n o f Y . T h e p r e v i o u s e x p r e s s i o n m a y b e b r i c t l y ' ' r i t t e n a s F e M I N . A s t h e m i n i m u m v a l u e o f M i s z e r o a n d t h e m a x i m u m i s N . t h e \ a l u c o f l · c r a n g e s b c l \ \ e c n 0 a n d I o r 1 0 0 % 2 1 I h e c u m u l a t i v e f r e q u e n c y c a n a l s o h e c a l l e d t h e f r e q u e n c y o f n o n - c x c e e d a n c e . T h e l r c q u c n c ) o f e x c c e d a n c e l e i s f o u n d ! r o m 1 F c l 1 7 ! . . t . 2 C a l c u l a t i o n o f p r o b a b i l i t y o f " i ; a l s p e e d b y appl~ i n g R a y l e i g h d i s t r i b u t i o n W i n d d a t a a t 1 0 m a b m c g r o u n d l c \ c l o f f c \ \ s i t e s h a s b e e n c o l l e c t e d f r o m L n e r g y P u r c h a s e b r a n c h . C T B a n d t h o s e d a t a h a \ e b e e n u s e d ! ' o r t h e p r o b a b i l i s t i c a n a l y s i s . A c t u a l t i - c q u e n c y o r \ \ i n d s p e e d f ( ) r a p e r i o d o f o n e y c a r - ( 2 0 0 1 ) a t N a r a k k a l l i v a i s i n d i c a t e d i n f i g u r e 4 . 1 . 4 0 0 0 3 5 0 0 > 3 0 0 0 u ~ 2 5 0 0 0 " ~ 2 0 0 0 u . . ~ 1 5 0 0 . . . . u < ( 1 0 0 0 5 0 0 0 A c t u a l F r e q u e n c y V s . W i n d S p e e d ( m / s } a t N a r a k k a l l i y a 0 . 5 1 . 5 2 . 5 3 . 5 4 . 5 5 . 5 ( j 5 7 . 5 8 . 5 9 . 5 1 0 . 5 1 1 . 5 1 2 . 5 1 3 . 5 1 4 . 5 1 5 . 5 W i n d S p e e d ( m / s ) F i g u r e . t . l A c t u a l f r e q u e n c : , v s . w i n d s p e e d ( m / s ) a t N a r a k k a l l i y a . B y a p p l y i n g R a y l e i g h d i s t r i b u t i o n l " l 1 r a b O \ e v , i n d s p e e d d a t a i s i n d i c a t e d i n f i g u r e 4 . 2 . ! ' ) > : ! : : ! " ' c 0 . 2 5 0 0 0 . 2 0 0 0 ~ 0 . 1 5 0 0 > . : ! : : : : g 0 . 1 0 0 0 . . c 0 . . . c . . 0 . 0 5 0 0 0 . 0 0 0 0 P r o b a b i l i t y D e n s i t y V s . W i n d S p e e d { m / s ) a t N a r a k k a l l i y a 0 . 5 1 . 5 2 . 5 3 . 5 4 . 5 5 . 5 6 . 5 7 . 5 8 . 5 9 . 5 1 0 . 5 1 1 . 5 1 2 . 5 1 3 . 5 1 4 . 5 1 5 . 5 W i n d S p e e d ( m / s ) F i g u r e . . f . 2 P r o b a b i l i t y d e n s i t y Y S . w i n d s p e e d ( m / s ) a t N a r a k k a l l i y a CumulatiH~ d i s t r i b u t i o n f o r w i n d s p e . _ : d d a t a i s i n d i c a t e d i n f i g u r e 4 . 3 b y a p p l y i n g R a y l e i g h d i s t r i b u t i o n . > u c 1 . 2 0 0 0 1 . 0 0 0 0 ~ 0 . 8 0 0 0 0 " Q J . . . u . . Q J 0 . 6 0 0 0 > · . ; ; r o E o . 4 o o o : I u 0 . 2 0 0 0 0 . 0 0 0 0 C u m u l a t i v e F r e q u e n c y \ i s . W i n d S p e e d { m / s ) a t N a r a k k a l l i y a ,'-'=""-·"'·''"'"'-~''''<\, ~· 0 . 5 1 . 5 2 . 5 3 . 5 4 . 5 5 . 5 6 . 5 7 . 5 8 . 5 9 . 5 1 0 . 5 1 1 . 5 1 2 . 5 1 3 . 5 1 4 . 5 1 5 . 5 W i n d S p e e d ( m / s ) F i g u t · e . . f . 3 C u m u l a t i v e f r e q u e n c y v s . w i n d s p e e d ( m / s ) a t N a r a k k a l l i y a F i g u r e · - 1 - . 3 s h o w s t h a t t h e e u m u l a t i n · ! i n t u e n c y o r \ \ i n d s p e e d b e l m \ 1 m / s i s 0 . 0 5 1 8 a t \ f a r a k k a l i y a . i \ b m e c a l c u l a t i o n s \ \ C I T r e p e a t e d f o r a f e w s i t e s o r S r i L a n k a a n d s u m m a r y o f p r o b a b i l i t y i s g i v e n i n T a b l e 4 . 1 . 2 3 - - - - - , - - -~~- - - - - - - S i t e I V a r i a n c e o f n o r m a l ( u ) N a r a k k a l l i y a 3 . 0 7 I S e v a n a o - - l - 1 ' - - l - - ~:::-'d - - Kaju\~~~tt~l - 2 . 8 1 2 . 0 0 I r i J . l a \ \ i l~a~~L M . . . . - . . , I } _ ) . .:...~ - - - - - - - - - 0 . 0 5 1 X -~---- 0 . 0 ( ) 1 2 T a b l e . t . t R a y l e i g h p r o b a h i l i t : • d i s t r i b u t i o n f o • · " i n d s p e e d b e l o w l m / s I t i s n o t e d t h a t t h e h i g h e s t p r o b a h i l i t : o f w i n d s p e c . d b e l o w I t n l s i s 0 . 1 1 7 8 a t K a j L I \ \ a t t a i n H a m b a n t o l < t D i s t r i c t . . t . 3 C a l c u l a t i o n o f p r o b a b i l i t y o f m e r c u r r e n t A v e r a g e c u r r e n t d i s t r i b u t i o n f o r 2 4 l i 1 s o f t h r e e s i t e s i n l l a m b a n t o t a D i s t r i c t i s i n d i c t e d i n f i g u r e 4 . 4 a n d t h o s e a r c t a k e n a s c u r r e n t d i s t r i b u t i o n p a t t e r n o r C E B . ; \ \ T r a g e c u r r e n t \ \ a s m u l t i p l i e d b y l~1ctor i n o : d e r t o r e a c h m a x i m u m \ a l u c a s 2 2 0 A . - - - - - f - - M i n . - , - - - \ M a x . 1 - M i n . M i n . \ ' o l t a o e I I , _ . , A Y g . 1 A v g . M u l t i p l i c a t i o n A v g . i 1 \ \ g . l e n : ! 1 I 1 1 c u t - r c ; . t I < c u r r e n t f a c t o t · c u r r e n t I c m - r e n t ( ( V ) i I I ( A ) ( A ) I ( ; \ ) I A ) 2 3 0 - r - - - - - - s - - 1 1 3 1 I 7 ( 7 - - - r - 1 3 2 1 9 n o _ _ t 1 1 1 2 4 • 1 . 7 7 I 1 9 m 2 3 1 1 1 _ - 4 R ~±-~~ 7 9 r 1 8 2 1 9 S i t e O m a r a R a t m a l \ \ a l a \ K u d a g a m m a n a ~~~_L__- T a b l e . t . 2 V o l t a g e l e v e l , . ~'g. c u r r e n t a n d m u l t i p l i c a t i o n f a c t o r 2 4 ~ . . . . . r : : : ~ . . . . . : : : l u 2 5 0 2 0 0 1 5 0 A v e r a g e C u r r e n t V s . T i m e ( 2 4 h r s ) O m a r a - 1 \ a t m a l w a l a l < u d d a g a m m i l i l a ~ 1 0 0 / A , . . . . r o . . . . . Q ) > < 1 : I '\'~ 5 0 P ····~·· v ' / . . . ~'.J.f" • . . . • . v ~- w 0 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o C ) L f ) 7 r Y ! N r l 0 L f ) 7 r Y 1 N r l C ) L f ) 7 r Y 1 N r l 0 l f ) 7 r Y 1 N c - l C l l f ) 7 r Y 1 N o o r l N m ~ L f ) L f ) ~ ~ o o m o o r i N m ~ L f ) L f ) ~ ~ o o m o o r i N m r l r l r l r l r l r l r l r l r l r l r l r l 0 J N N N N T i m e ( h r s ) F i g t ; r c 4 . - l Av~ragc c u r r e n t v s . t i m e ( 2 4 h r s ) A c t u a l l i " c q u e n c y \ s . a v e r a g e c u r r c m d i s t r i b u t i o n f o r a b t n ' e t h r e e s i t e s i s i n d i c a t e d i n f i g u r e 4 . 5 A c t u a l F r e q u e n c y V s A v g . C u r r e n t 8 0 7 0 O m a r a 6 0 R a t m a l w a l a > 5 0 u r : : : K u d a g a m m a n a Q ) 4 0 : : : l ~ Q ) 3 0 L L . 2 0 1 0 0 1 0 2 0 3 0 4 0 s u 6 0 7 0 8 : ; 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 0 1 6 0 1 7 0 1 8 0 1 9 0 2 0 0 2 1 0 2 2 0 A v e r a g e C u r r e n t ( A ) Figun~ . . t . 5 A c t u : ; l f r e q u e n c y v s . a v e r a g e c u r r e n t P r o b a b i l i t y d e n s i t y r o r ~lbO\C c u r r c : l 1 t \ a r i a t i o n d a t a i s i n d i c a t e d i n f i g u r e 4 . 6 . l w a p p l y i n g R a y l e i g h d i s t r i b u t i o n . 2 5 > . . . . . 0 . 0 1 6 0 0 0 . 0 1 4 0 0 0 . 0 1 2 0 0 -~ 0 . 0 1 0 0 0 Q J C l -~ 0 . 0 0 8 0 0 . . c r o - g 0 . 0 0 6 0 0 . . . . c . . 0 . 0 0 4 0 0 0 . 0 0 2 0 0 0 . 0 0 0 0 0 P r o b a b i l i t y : _ : c n s i t y V s A v a r a g e C u r r e n t 0 0 0 0 0 0 0 c - < N r Y " l ¢ L f ) C O r ' - O m a r a R a t m a l w a l a K u d a g ; 1 m m a n a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 m o , . . . , N m g - L f ) c o r - - o o m o , . . . , N , . . - < , . . - < c - < ~ ~ c - < c - < c - < ~ c - < N N N A v e r a g e C u r r e n t ( A ) F i g u r e - L 6 P r o b a b : ; i t y d e n s i t y v s . a v c n t g e c u r r e n t C u m u l a t i \ C d i s t r i b u t i o n r o r a b o \ " C l " i l T C n t \ a r i a t i o n d a t a i s i n d i c a t e d i n f i g u r e - l - . 7 b y a p p l y i n g R a y l e i g h d i s t r i b u t i o n . > u 1 . 2 0 0 0 1 . 0 0 0 0 ~ 0 . 8 0 0 0 : : J 0 " " ~ u . . Q J 0 . 6 0 0 0 : > · . ; ; r o : : J E 0 . 4 0 0 0 : : J u 0 . 2 0 0 0 0 . 0 0 0 0 C u m u l a t i v e F . . ; q u e n y V s A v e r a g e C u r r e n t · O m a r a R a t m a l w a l a l < u d a g a m m a n a 1 0 2 0 3 0 4 0 5 0 6 0 7 0 [ 1 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 1 ) 0 1 5 0 1 6 0 1 7 0 1 8 0 1 9 0 2 0 0 2 1 0 2 2 0 A v e r a g e C u r r e n t ( A ) F i g u r e - L 7 C u m u l a L , e f r e q u e n c y v s . ~n e r a g e c u r r e n t 2 6 - . . , f r e q u e n c y l . . I C u r n u l a t n e ! - b · t h t h t \ I A ) I - - , ) r 1 . a y l c i g h p r o ' . ( I > 2 0 2 I I V a r i a n c e o l . . 2 0 2 A ) I ! S i t e I nor~,a~ ( q ) - ( ) . ( 1 ( 1 0 ' \ t = = · - ( l . 0 5 9 0 _ _ j ( I > \\(\3J,~ ~-.---+ . t 9 . l l _ 1 o . o o o 9 4 . · - - o . o 1 3 9 _ I O m a J c l _ 5 3 . 9 7 _ ( ) . 0 0 0 0 1 - · - - R a t m a l \ ' . a l a ~.94 - T a b l e " ' · 3 P r o b a b i l i t y ( : . , t r i h u t i o n f o r l o a d m o r e t h a n 2 0 2 A I t i s n o t e d t h a t R a y l e i g h p r o b a b i l i t , i s I O \ v c r t h a n cwm~lative f r e q u e n c y . T h c r c f " o r c c u m u l a t i Y c f r e q u e n c y i s t a k e n a s I Y t s o n a b l c \ a l u e o f p r o b a b i l i t y u r a b o v e 2 0 2 / \ f o r m o r e a c c u r a c y . H o w c \ c r . t h e h i i : _ ' t : c s t v a l u e o f p r o b a b i l i t y o c c u r s a t R a t m a h \ a l a a s 0 . 0 5 9 0 . 4 . 4 P r o b a b i l i t y · o f o v e r t c m p c r a t u . - . · u p t o 8 7 ° C O v e r t e m p e r a t u r e o f / \ C S R ( R a c o c . J c o n d u c t o r m a : i w c o m e d u e t o t h e c o m b i n a t i o n o [ • W i n d s p e e d s h o u l d b e b e l o \ \ 1 1 : . s a n d • C C C s h o u l d b e m o r e t h a n 2 0 2 ! \ • S i n c e \ V i n d s p e e d a n d c c c · a r c i n d e p e n d e n t e \ e n t s . p r o b a b i l i t y o f 0 \ e r t e m p e r a t u r e ( P 1 ) c a n b e c d c u l a t . i b ) m u l t i p l i c a t i m 1 o ! " t h c t w o p r o b a b i l i t i e s . • P ; ( 1 \ , - 1 1111~; ' - ; ( I > 2 0 2 / \ ) 0 . 1 1 7 S x ( U 5 9 0 6 . 9 5 x ] ( r ' • T i m e p e r i o d o f O \ c r t e m p e r a t u r e p e r ) c a r 6 . 9 5 x 1 o - ' · ' 4 x 3 6 5 h r s ( J 1 I ; 1 ' - ; • T i m e p e r i o d o f o \ · c r t e m p c r a t u r , · o r l i i C t i m e ( 5 0 )''~lr) 6 1 : - ; 5 ( ) h r s 3 0 : 0 : . ( ) h r s . • T i m e p e r i o d o f O \ c r t c m p c r a t u r . · p e r y e a r \ V i t h s a ! C t y m a r g m 6 l h r s . \ 2 . : ' 1 5 2 h r s • T i m e p e r i o d o f o \ c r t c m p c r a t u r , · : i J r l i f e t i m e ( 5 0 ye~\r) w i t h s a f c t ) m a r g i n 3 0 5 ; ) h r s . \ _ ) 7 C J 2 : ; h r s . 2 7 T h e p e r c e n t a g e r e d u c t i o n i n ten~ ~' s t r e n g t h o f ' , \ l u m i n u m t y p e , \ 1 a t d i ! T e r e n t t e m p e r a t u r e a n d d u r a t i o n s h s h o ' . , 1 f i g u r e 4 . 8 . T h e s e f i g u r e s a r c b a s e d o n d a t a a s s e m b l e d f r o m \ a r i o u s s n u n > . . : s a m i : • : s t r e s u l t s 1 7 1 . 1 0 0 _.""~·80 " ( - " * ' 9 5 - . l : . . . . . b . ( ) 9 0 t : Q ) , _ -i~-100"( . . . . . 8 5 V I b . ( ) t : t : 8 0 r o E 7 5 1 2 5 " C Q ) , _ . . . . . 7 0 t : Q ) u , _ 6 5 Q ) a . ~~-150"( 6 0 0 . 1 1 1 0 0 l l u o 1 0 0 0 0 : i m e { h r s ) F i g u t · e . t . S L o s s o f s t r e n g C 1 o f A : . , n i n i u m t y p e A t :l~; a f u n c t i o n o f t e m p e r a t u r e A c c o r d i n g t o t h e a b O \ c f i g m e . i t i s , l S C r v e d t h a t l o s s n l s t r e n g t h o r A l u m i n i u m i s n o t e v e r r e d u c e d b e l o \ \ 9 5 % i n t h e I i i t i m e a n d i t i s n o t r e d u c e d b c l m \ 9 0 % \ v i t h 2 . 5 s a i d ) m a r g i n . 4 . 5 M e t h o d o f l i n e t e n s i o n c : l c u l : : . m S t r a n d i n g D i a m e t e r . . 1 - . ( ) 9 m m n o o f s t r a n d s t e e l n o o r s t r a n d Aluminit:t~l 6 M i n i m u m L J T S o r . \ I \ \ i r e 1 6 5 N / m m · P e r c e n t r e m a i n i n g ~trc:1gth o l A l u m i n i u m M i n i m u m l J I s a t 1 % C : \ . t e n s i , . o r s t e e l 1 1 0 0 N / m m 7 [ 3 . 1 4 U T S o l ' R a c o o n C o n d u c t o r U T S o r R a c o o n C o n d u c t o r 1 ( J 5 . 7 t X ( 4 . 0 9 / 2 ) 2 X ( J 1 1 ( ) ( ) x 7 t X ( 4 . 0 9 1 2 / 2 7 4 l N ( t a k e n a s 2 7 0 5 d a N ) 2 8 \ h e t ' t l l l o \ \ i n g t a b l e i n d i c a k s t h e I S o f R a c o o n c o n d u c t o r a g a i n s t p e r c e n t a g e o f r e m a i n m g s t r e n g t h o f A h t r . l i n i u m h t r t h e r . i t h a s he,~n c a l c u l a t e d t h a t c o n d u c t o r t e n s i o n f o r t e m p e r a t u r e s f r o m 1 5 c ( t o 6 5 o c a n d i t s r e k Y a n t p e r c e n t a g e o f a Y a i l a b l c l ' T S . l l c n c e . i t i s o b s e n e d t h a t l l - ; o f s t r e n g t h o f . \ l u m i n i u m u p t o 9 0 ~~() c a n b e a l l l m e d . , - - - - - - - - - - : 16~\ ~~~ I 1 ( ) ( ) 1 1 < 1 9 5 % 9 0 ' 1 < ) , - - I 2 7 · 1 7 0 N 2 6 R 1 9 N I 2 6 1 6 9 ' I _ \ _ - _ - - I R - _ - ~ 1 9 _ 1 9 j - 1 1 6 _ _ : 1 6 i _ 1 7 _ I 1 1 2 1 2 1 1 2 ! ' I I t 9 - \ 9 I q ' I I - - 1 - - 6 - - - - - - - I I - E = E - - - - - - 5 - 5 - - - - - - +-----~~ _ _ _ _ _ s _ _ _ s J -~ P e r c e n t a g e o f r e m a i n i n g : ; r e n , _ ' , l - - - - - - - - - I \ A l u m i n i u r H ~ailablc U T S o l ' ~cou~~( ~~c. r - - - - ( , m d u c t o r 1 ( ' o ; ; d u c t , l < \ t e m p e r a t u r e ( ° C ) \ t c n ; i o n ( 1 ' \ ; I 1 5 t - - - - \ 9 9 2 _ _ _ I I 1 - r - - 2 0 1 I I 1 0 1 - - 2 2 ( 1 - 1 - ! I 1 - - - · - ~,-, - . - - - - - \ - - 1 - 0 i _)--1-~\ r - - - - - 5 - 0 - - - - - j - - - - ~-77-5 - ~-=-__: :~----1- _ - . - I;;)~ _ _ _ _ _ _ L _ _ _ - - - - - - - - 1 Y o U T S o ; ; ) U T S % U T S 7 7 T a b l e - t . 4 C o n d u c t o r L . 1 s i o : 1 , r v a r i o u s t e m p e r a w r e s a s a p e r c e n t a g e o f ' > a i l a h l c l J T S 2 9 C h a p t e r 0 5 A p . · r o p r i a t e ( ; r o u n d C l e a r a n c e 5 . 1 I n t r o d u c t i o n M a x i m u m a l l o w a b l e c o n d u c t o r k l : . 1 c r a t u r e i s t y p i c a l ! ; s e l e c t e d s o a s t o l i m i t e i t h e r l o s s o f s t r e n g t h o f t h e c o r . d u c t o r i u e t o a n n e a l i n g u : · ' A l u m i n i u m o r t o m a i n t a i n a d e q u a t e g r o u n d c l e a r a n c e . 5 . 2 S a g a n d t e n s i o n . C o n d u c t o r s a g o n a J 1 a t t e r r a i n i s m : < i m u m a t m i d - s p a n . h 1 r t h e L t h i s s a g w i l l i n c r e a s e w i t h t e m p e r a t u r e a n d b e a m a x i m u 1 . ~lt m a x i m u m o p e r a t i n g t e m p e r a t u r e . 5 . 2 . 1 E q u i v a l e n t s p a n T h e e q u i v a l e n t s p a n i s c a l c u l a t e d i 1 : l r d c r t o u s c s a g a n d t e n s i o n c h a r t s . T h e t e n s i o n i s u n i f o r m b e t w e e n t \ \ O s e c t i o n p t ) · s a n d s u p p o r t e d < l l 1 i n t e r m e d i a t e p o l e s . T h e e q u i v a l e n t s p a n t h a t r e s u l t s l i - o m t . , s u n i f o r m t e n s i o n i , ; c a l c u l a t e d \ \ i t h t h e t < . m m d a b e l o w . S e W h e r e : S i ' + S } . + S:~ + e t c S 1 + S 2 + s · , + e t c S 1 . S 2 . s , . e t c a r c t h e i n d i \ i d u a l sp~: l e n g t h s b e t w e e n s e c t i o n p o l e s . ( 5 . 1 ) H a v i n g d e t e r m i n e d t h e s~lgs a1~· t e n s i o n o n t h e c q u i n 1 l c n t s p a n a t \ a n o u s t e m p e r a t u r e s . t h e s a g s o n t h e a c t t w l . p a n c a n b e d e t e r m i t t c d f r o m t h e f o r m u l a : . S a g o n c q u i v < . 1 ! 1 t S p a n x ( A c t u a l S p a n L c n g t h ) 2 S a g o n a n y s p a n = · · . ( c ( : : v a l e n t s p a n l c n g l h ) 2 ( 5 . 2 ) 3 0 W h i l e f i x i n g t h e s p a c i n g . i t s h m t l ; , c a s u n i f o r m a s p ( ) s s i b l c s u b j e c t t o m a i n t a i n o r m i n i m u m g r o u n d c l e a r a n c e . T h e . 1 a x i m u m s a g f o r d i f f e r e n t p o l e h e i g h t s c a n b e o b t a i n e d r r o r n t h e s a g t a b l e . 5 . 2 . 2 S e l e c t i o n o f t e n s i o n C o n d u c t o r s a g a n d t e n s i o n ' a r y i n : : o r d a n c e w i t h t h e r , > l ! o v , i n g p a r a m e t e r s . • T h e m a x i m u m s a g \ \ i l l o c c m : - L d c l " i n e d m a x i m u 1 1 1 o p e r a t i n g t e m p e r a t u r e 9 0 ' T \ \ i t h n o \ \ i n d . • T h e m a x i m u m t c n s i o l l \ \ i l l o c . r a t t h e d e f i n e d C O l t d u c t o r \ \ i n d l u a d i n g o r 0 . 5 7 5 k l \ 1 m 2 a n d m i n i m u m t e m p e r a \ \ : o r 1 5 ° C 1 4 1 . • C o n s t a n t c o n d u c t o r t e n s i o n o~: .c~·s a t t h e d e f i n e d n o r m a l e v e r y d a y t e m p e r a t u r e o r 3 0 ° C . T h i s t e n s i o n i s t e r m e d c:~,cryday t e n s i o n ( ! ~DT) a n d t h e c o r r e s p o n d i n g s t r e s s i s c \ c r y d a y strc~s (ED~; • i \ ' c r a g c t e n s i o n o f t h e c o n d ' : · o r s s h a l l b e l i m i k J t o 1 7 ( 1 ; ; > o r t h e U T S o f t h e c o n d u c t o r 1 4 1 . • l ' v b x i m u m a l h m a b l c s t : · c s s \ ' , \ \ i n d a n d l m \ t e m p e r a t u r e s h a l l b e l i m i t e d t o 4 0 % U T S 1 4 1 . 5 . 2 . 3 S a g a n d t e n s i o n f o r : n . l l a T h e s a g a n d t e n s i o n r c l a t i o m : h i p i s · ' e n b y : T o X [ c o s h c ; / - 1 ) I s = ( ) - w O r a p p r o x i m a t e f o r m u l a w l 2 5 = - B ' / ' W h e r e : S i s s a g ( m ) T o i s i n i t i a l t e n s i o n a t l o v , c s t p o i n t · . ) 1 1 ' i s c o n d u c t o r w e i g h t ( N 1 1 1 1 ) 1 i s s p a n o r h o r i z o n t a l dis~,u~ce b e . . . · e n t v , o s u p p o r t s ( 5 . 3 ) ( 5 . 1 ) 3 1 T i s c o n d u c t o r t e n s i o n A f t e r a c o n d u c t o r h a s b e e n ! i x e d : . . o a p o s i t i o n . t h e u : n s e q u c n t v a r i a t i o n i n sag(~) d u e t o \ \ i m l p r e s s u r e a n d t e m p e r a L · v a r i a t i o n s c a n b e c a l c u l a t e d f r o m : T l x [ T 1 - C T c - x i \ E C 0 1 - O z ) - . · : F 2 1 2 / 2 4 T n I = I ( / \ E F f l 2 ) l / 2 4 ( 5 . 5 ) T l x I T r - C T c - x i \ E ( 0 3 - 0 2 ) - : · : F i l 2 / 2 4 T n J = [ (/\EF~l 2 ) l / 2 4 ( 5 . 6 ) W h e r e : T 1 c o n d u c t o r t e n s i o n i n i n i t i a i , m d i t i o n ( d a N ) · 1 c c o n d u c t o r t e n s i o n i n c v · e n . \ c o n d i t i o n ( d a N ) T 1 c o n d u c t o r t e n s i o n i n f i n a l · . · . 1 d i t i o n ( d a N ) X c o c f " f i c i c n t o f t h c r m d c x p : . 1 0 n i \ c o n d u c t o r a r e a ( m m ~) E Y o u n g ' s m o d u l e s ( c h N / m : E - ) 1 c o n d u c t o r t e m p c r a t L ! r c i n 1 . i a l c o n d i t i o n ( ° C ) 0 2 c o n d u c t o r tcmper~1tuc i n v - r y d a y c o n d i t i o n ( ' ( · ) 0~ c o n d u c t o r t c m p c r a t u e i n l . . : l c o n d i t i o n ( ° C ) F 1 r e s u l t a n t w i n d a n d \ \ e i g h t : c c i n i n i t i a l c o n d i t i o n ( d a N / m ) h r e s u l t a n t w i n d a n d \ \ e i g h t ! : c i n e v e r y d a y c o n d i t i o n ( d a N / m ) F l r e s u l t a n t \ v i n d a n d \ \ e i g h t • . c c i n f i n a l c o n d i t i o n ( d a N / m ) 5 . 2 . 4 D e s i g n c r i t e r i a r C l m d u c t o r t e n s i o n • A t e \ c r y d a y t e m p e r a t u r e t l . : o n d u c t o r t e n s i o n s h a l l b e 1 ] 0 / o o r l 1 T S . • ! \ t t h e s e t e n s i o n s a t I D T t l . ~cnsions a p p l i c a b k a t t h e l o v v c s t t e m p e r a t u r e a n d m a x i m u m w i n d c a l c u l a t e d . I c h e c k e d w i t h t h e m a x i m u m p o l e t o p l o a d i n g , . . - T h e g r o u n d c l e a r a n c e i s c h e c k w i t h t h e s p e c i f i e d m i n i m u m c l e a r a n c e , . S o i l t y p e o f f o u n d a t i o n s h a s b 1 t a k e n a s g o o d s o i l f o r t h e a b o v e c a l c u l a t i o n s 3 2 5 . 3 S a m p l e c a l c u l a t i o n s C o n s i d e r t h e f o l l o \ \ i n g p o l e s p a c i 1 ~hart: -~>~e n o = l - - C = - 1 ----~-~ - + t i a t i v e s p a n 7 0 1 2 0 1 8 0 . ; p a n ] C u m u ~:: I 5 0 ~--1-~~-- 6 0 ) I - - - - c ; - - - - 1 - - - 1 ~ - - 7 _ _ _ j 2 f 0 2 5 0 2 9 0 4 0 3 0 ~-+---~- 4 0 T a b k _ i P o l e s p a c i n g c h a r t E q u i v a l e n t s p a n : U s i n g F q u a t i o n ( 5 . 1 ) . t h e e q u i \ a k < , a g c a n h e c a l c u l a t e d a s : S e \ j 2 X 3 0 3 + 3 X 1 · 0 3 + 5 0 : l 2 X 3 0 + 3 X 1 0 + 5 0 - S e = 1 5 m C a l c u l a t e e v u y d a y t e n s i o n ( T e ) : N o w a s s u m e t h e F D I a t : 1 0 o c a s T a k e l I S E D T ( I , : ) 2 7 0 5 0 N 2 7 ( ) 5 ( ) X 0 . 1 7 4 5 9 8 . 5 N G r a v i t a t i o n a l f o r c e Y o u n g ' s m o d u l u s T h e r m c d e x p a n s i o n c o c l ' f i c i e n t C r o s s s e c t i o n a r e a W e i g h t o f c o n d u c t o r D i a m e t e r o f c o n d u c t o r T e m p e r a t u r e a t i n i t i a l c o n d i t i o n . ( E v e r y d a y t e m p e r a t u r e . C c , · , o : ' 0 ; ) o f U T S . 9 . 8 0 6 6 5 m / s 2 7 9 4 6 d a N / m n , : ' 0 . 0 0 0 0 1 9 0 8 ; o c " C ) 1 . 9 9 mm~ 0 . 3 1 2 9 k g / m 1 2 . 7 m m l 5 ° C 3 0 o c " ' " ' _ , _ , T e m p e r a t u r e a t f i n a l c o n d i t i o n , C 1 W i n d p r e s s u r e 9 0 ° C 5 7 . 5 d a N / m 2 W e i g h t o r c o n d u c t o r ' ' e i g h t o : · m l u c t o r x C i r a \ ' i t a t i o n a l f o r c e / 1 0 0 . 3 1 2 9 k ~ x 9 . 8 0 6 6 5 m / s 2 0 . 3 0 6 8 5 ' · . i m W i n d l~ll'CC a t i n i t i a l c o n d i t i o n v \ ' i n d p r e s s u r e \ . di~lmetcr o r c o n d u c t o r ( m ) 5 7 . 5 d a N / m 2 x 0 . 0 1 2 7 m 0 . 7 3 0 2 5 d a N / m W i n d l " o r c c a t e \ · c r y d a ) c o n d i t i o n 0 (da~lm) W i n d f o r c e a t f i n a l c o n d i t i o n 0 ( d a N / m ) R e s u l t a n t \ \ i n d a n d \ \ e i g h t f o r c e " . 1 c o n d i t i o n ( ( W e i g h t . c o n d u c t o r 2 \ \ V i n d C o r e e a t i n i t i a l c o n d i t i o n 2 ) ) 1 2 h ( ( C U 0 6 8 . l ' 0 . 7 3 0 2 5 - ) ) ' 0 . 7 9 2 0 9 · ) d a N / m R e s u l t a n t ' ' i n d a n d \ \ e i g h t f o r c e < : W e i g h t o r c o n d u c t o r h R e s u l t < m t \ \ i n d a n d \ \ e i g h t f o r c e < i ' -~ 0 . 3 0 6 8 5 d a N / m W e i g h t o r c o n d u c t o r 0 . 3 0 6 8 5 d a N / m U s i n g e q u a t i o n ( 5 . 5 L t h e i n i t i a l a t 1 1 c a n b e c a l c u l a t e d . T h i s i s a t h i r d o r d e r p o l y n o m i a l i n t e r m s o i " 1 1 . T h e 1 - . o l · t h i s p o l y n o m i a l c a n b e c a l c u l a t e d b y s o h · i n g t h i s c q u a t i o n b y i t c r a t i \ C m e t h o d : i 1 c F x c c l p r o g r a m l i s t e d i n J \ n n e x B c a n b e u s e d t o c a l c u l a t e t h e 1 1 • T 1 7 1 6 . 8 6 5 5 0 7 3 9 9 5 8 1 d a N U s i n g e q u a t i o n ( 5 . 6 ) . t h e f i n a l s~ : t 1 1 c a n b e c a l c u l a t e d . T h i s i s a l s o a t h i r d o r d e r p o l y n o m i a l i n t e r m s o l · i 1 . T h e r , · t : . o f t h i s p o l y n o m i a l c a n b e c a l c u l a t e d b y s o h i n g t h i s e q u a t i o n b y i t e r a t i ' c m e t h o d . l : 1 c l~xccl p r o g r a m l i s t e d i n 1 \ n n e x B c a n b e u s e d t o c a l c u l a t e t h e T r . T 1 1 0 6 . 5 8 2 2 3 4 9 1 7 7 8 7 d a N 3 4 U s i n g e q u a t i o n ( 5 . : : 1 ) . t h e s a g a t c~ : h c o n d i t i o n c a n h e c a l c u l a t e d a s : , 1 , : 1 ( w l 1 ) \ 1 X \ C O S 1 " 2 ' G - E q u i v a l e n t s a g a t ' I \ ( m ) v v . . 7 1 6 . : 6 5 5 x [ c o s h ( 0 . 7 9 2 0 9 9 x ! J . 5 ) j l~quJvdlent s a g a t ' I \ ( m ) = _ _ 2 x 7 \ A . B A 5 5 - 1 0 . 7 9 2 0 9 9 Equiv~lienl s a g a t T 1 = 0 . 2 9 l 1 1 1 Equiv~lient s a g a t T c ( m ) T c x co~;h(~-1)j w E q u i v a l e n t s a g a t T c ( m ) o.306n:;x~-5 ) [ ~59. l S >~[cosh ( 2 x ! J . 5 9 . B 5 - 1 0 . 3 0 6 8 5 E q u i v a l e n t s a g a t T c = ( ) . 1 7 . ) 1 1 1 E q u i v ; l i e n t s a g a t T 1 ( 1 1 1 ) ' f j Y l c o s h ( T J ; - 1 ) j w l ( o.:~06B5x~5 _ 1 ) [ 1 O G ) 8 2 2 3 x c o s h 2 x 1 0 6 . 5 B 2 2 3 E q u i v a l e n t s a g a t T 1 ( m ) 0 . 3 0 6 8 5 E q u i v a l e n t s a g a t T 1 = 0 . 7 ( ; ; 1 1 1 S a g o n a n y s p a n U s i n g e q u a t i o n ( 5 . 2 ) . t h e equi\a~ : 1 t s~tg o n a n ; s p a n c a n b e c a l c u l a t e d a s : I n i t i a l s a g a t T 1 I n i t i a l s a g a t T 1 c 0 ) : _ 0 . 2 9 1 > < ( S ) L 0 . 1 2 9 3 1 1 1 c : ; 0 ) ' E v e r y d a y s a g a t T c = 0 . 1 7 6 x ( i S r : - - E v e r y d a y s a g a t T e = 0 . 0 7 8 2 r~·. F i n a l s ; 1 g a t T 1 F i n a l s : 1 g a t T 1 : . i O ) 0 . 7 5 B ~<- ! S f o . : - n e J r . , 3 5 V e r t i c a l s a g a t i n i t i a l c o n d i t i o l l : m ) . , , Jnili~; s a g ~1t T 1 x w e i g h t o f c o n d u c t o r ( d a N / m ) V e r t 1 c l l s a g a t I = - - - - - - - - - - - - - - - - - - - - - 1 r e s u l t a n t · ; i n d a n d w e i g h t f o r c e a t T 1 c o n d i t o n ( d a N / m ) V e r t i c l l s a g a t T 1 = C . l 2 9 3 x(L306~l5 ( d a N / m ) 0 . 7 9 2 ( 99(d~1N/m) V e r t i c c d s a g a t T 1 = 0 . 0 5 0 1 m V e r t i c a l s a g a t c v c r y d : t : . c o n d i t . m ( m ) . , , l n i t i < s a g ~1t T c x w e i g h t o f c o n d u c t o r ( d a N / m ) V e r t 1 c a l s a g a t I , = - - - ----~--------------- c P , c s u l t a n t v i n d a n d w e i g h t f o r c e a t E D c o n d i t o n ( d a N / m ) 0 . 0 7 B 2 x O 3 0 6 : l 5 ( d a N / m ) V e r t i c a l s a g a t T c = 0 . 3 0 6 l 5 ( d a N / m ) V e r t i e < l i s a g a t T e = 0 . 0 7 8 2 m V e r t i c a l s a g a t f i n a l c c E d i t i o n ( u ) V e r t i c a l s a g a t T r = ~.: ; u l t a n t \ · i n d : . n d w e i g h t f o r c e a t ' ! \ c o n d i t o n ( d a N j m ) c . : \ 3 6 9 X ( . 3 3 C ) ( d a N / m ) V e r t i c c 1 l s a g a t T r = 0.3369(d<~f'-J/m) V e r t i c a l s a g a t T r = O . : n 6 9 m A s p e r L k s i g n c r i t e r i a . l 1 1 c m a x i n : u m l\~nsion o c c u r s a t l 5 ° C a n d g i v e n m a x i m u m a i r p r e s s u r e c o n d i t i o n s s h < : : b e l i m i t < d t o . ; ( ) 0 ; ( J l J l S . 716.~ 6 5 : T 1 a s p e r c e n t a g e o f t r : : · = - - - - 2 7 l 5 T 1 a s p e r c e n t a g e o f lJT~; = 2 7 % < 1 \ l ) ( Y c J A v e r a i : ' - c t e n s i o n o r t k c o n d u c o r s s h a l l b e l i m i t e d t o 1 7 % o f ' t h e U T S o f t h e c o n d u c t o r . 459.~:5 T a s n c r c c n t a g e o f U T : : = - - - c t 2 7 0 ) T e a s p e r c e n t a g e o f tn·~: = 1 7 % = 1 · . ' % 1 0 6 . 5 8 2 2 T f a s p e r c e n t a g e o f l J T S = - - - - 2 7 0 5 T r a s p e r c e n t a g e o f L n : ; = 4 % 3 6 S A C l e a r a n c e f r o m t l ; , ' G r o u n d ( ) \ e r h l · a d l i n e c o n d u c \ · : · s s h a l l l c S ( ) l o c a t e d t h a t t h e i r g r o u n d c l e a r a n c e ! 4 ] i n a n y d i r e c t i < m f r o m a n y p o : ; ; ' i o n a f t e r s a g c : n d e r t h e i n f l u e n c e o f l o a d c u r r e n t s h a l l n o t b e l e s s t h e m t h e d i s t a n c e ( l . : · o l l o w s . ~1aximum a l l o w a b l e S : · ! ' P o l e l ! c i g l : t - B u r i e d L e n g t h - C l e a r a n c e . p e o f g r J u n ! l 1 \ ' o l t a g e f - - - . · · \ ; \ e n : ; t h e r o a d o r I • c l e a r a n : e s t r c c ' ' C l e a r a n c e ( n r ) 6 . 1 M a x . a l l o w a b l e s a g ( m ) 1 0 m p o l e - 2 . 2 1 1 m p o l e 3 . 1 6 5 0 V t o 1 1 k V ~1 a ; o t h e r p l a c e s - · - - + - - - - - - I . ) _ _ f - - - - - P l a c : i n a c c e s s i b l e t o 4 . ( ) \ C h i · d a r t r a t T i . . : ! \ e r e : ; t h e r o a d o r 1 0 m p o l e 1 . 9 i r - \ s t r c ' · 6 . 4 1 1 m p o l c 2 . 8 i ------~ T a b \ · : ; . 2 M a x i m m . : a l l o w a b l e s a g f o r e a c h p o l e ll:~o m v f . . - - - - - - - - 1 n a 1 · o t h e r p l a c e s l - - - - - - - - P l a c · i n a c c e s s i b l e u y c h i · : l a r t r a f f i : 6 . 1 4 . 9 5 . 5 M a x i m u m s a g f o r C S R R~H~OOL . : o n d u c t o r U s i n g d b O Y C C o r m u l a . : g a n d t c n s i o : 1 w e r e c a l c u l a t e d i n e a c h e q u i Y a l c n t s p a n a n d s u m m a r ) i s g i \ e n b c l o · [ L ' I ' " : 1 i . \ a l e n t 1 _ _ a n ( m ) ~==-f') t = - = ' ) ( ) C . J u c t o r t e r . . \ . ' r a t u r e J o e . ; ) o c 3 0 m \ _ 0 . 3 4 6 0 m 0 . 7 6 C o n d u c t o r s a g ( m ) f o r s p a n 4 ( m 5 0 m 6 0 m 0 . 6 0 0 . 9 3 1 . 3 5 7 ( l m 8 0 m 9 0 m 1 . 0 3 1 . 3 5 1 . 7 1 T a b l e 5 . 3 C o L . c t o r s a g f o r e a c h s p a n v s . c o n d u c t o r t e m p e r a t u r e 3 7 I t c a n b e : o b s c n c d t h a t : c m a x t m u m ;~1g 1 . 7 1 m i s l e s s t h a n m a x i m u m a l l c m a h l c s a g l . Y m l u r I 0 m p o l e . : : r e f o r e . t h e t . < o u n d c l e a r a n c e i s n o t \ ' i o l a t c d \ \ h e n o p e r a t i n g o n h i g h e r t e m p e r a t u r e , · ( ) 0 ° C . A l s o s~.g m a y i n c r e a s e o n w i n d s p e e d b c l o v v 1 m / s a n d m a x i m u m l o a d i n g m o r : h a n 2 0 2 . \ . P : . 1 b a b l c o c c u r r e n c e o f t h i s i s g i \ c n i n c h a p t e r 0 4 a s 3 0 5 0 h r s f o r a c o m h : ( ) J " l i f e t i m e . 3 8 C h a p t e r 0 6 E c o n o m i c a l O p t i m i z a t i o n o f L o s s e s C o s t s a n d h e n e l i t s s h a l l b e e \ a l u a t e d \ V i t h i n c r e a s e 0 r l o s s e s a g a i n s t i m e s t m e n t s i n c u r r e d i n r e c o n s t r u c t i n g o r t h e C F B n e t \ \ o r k . I t i s n o t e d t h a t i m e s t m e n t c a n h e p o s t p o n e d a t l e a s t 4 y e a r s \ \ h e n a n n u a l g r c ) \ \ t h r a t e i s c o n s i d e r e d a s 2 . 5 ° 1 o . T h i s s i m u l a t i o n i s d o n e b y u s i n g S y n c r G E F s o t i v , a r e \ \ h i c h i s p r e s e n t l y u s e d ! ' o r d i s t r i b u t i o n p l a n n i n g o f C F B . 6 . 1 E n e r g y l o s s e s d u e t o i n c r e a s e o f C C C I f i t i s r e q u i r e d t o r e p l a c e R a c o o n c o n d u c t o r . n e x t a \ a i l a b l c c o n d u c t o r o r C L B i s I . y n x c o n d u c t o r . T h c r c C o r e . l o s s c o m p a r i s o n h a s b e e n c a l c u l a t e d b y s i m u l a t i n g R a c o o n a n d L y n x c o n d u c t o r s f o r l l a m b a n t o t a F 3 ( i o n n o r U \ \ a l i n e . I J . · , x~~· p~ { ~- \ l 1 _ _ : / ~ : ' I J]~ 1 ~·.:11 •\:.:·~~ ~:)' · . . . i I ' . - j i t . • - , . - H - , _ , · , \ 1 I J - ! J ' ' ' 1 : : : - 1 1 / 1 < 1 - · 1 1 · 1 . \ 1 1 1 1 ' 1 . - j ~~ r · w : . · L , 1 1 I ' : ' I J ' · I J : · _ . u . . · _ , : J':·~"\ : - : \ , 1 1 . ' I I \ ' 1 " \ · . ; w ; : ' . . .t;tc(j·~-J:: · _ , . . - ~·r~·,-, I I I . . ' . " r ' ' " " • . , I \ _ ;;~;~r' 1 ~ 1 , 1 J · 1 K J . ~· I . : - r - · ~ · 1 · : . . . 1 1 · · • ' . I ·-.;-,'.;':-~:?:) ' • l _ _ l l 1 - ' 1 • . . - t , . . , ' f -. . . - 1 ' 1 1 ~:~.!~ . I I · . · ' . - j . I I 1 [ l l J pi~ I I I C J S S F i g u r e 6 . 1 l l a m h a n t o t a F 3 G o n n o r u w a l i n e ~9 H am ba nt ot a 1 ' 1 Y ea r 21 1 < 1 Y ea r 3n 1 Y ea r ~"'Y ear ~~ F3 G on no ru \v a D is t lin e R ac oo n L yn x di ff er en ce R ac oo n L yr n di ff er en ce R ac oo n L yn x di ff er en ce R ac oo n L yn x di ff er en ce Se ct io n kV I kW l.;W kW kW l.;W kW kW kW kW kW kW kW ~ :\ ar ne 72 96 24 47 39 3.1 17 1 70 I 0 I i 17 9 74 10 5 18 8 77 Il l 19 8 81 11 7 I I 1 70 79 48 92 2 0.9 89 36 53 i 93 38 55 98 40 I 58 10 3 42 61 I 75 11 61 63 32 10 .3 16 7 9 17 I 7 10 16 7 i 9 19 8 II I I I To ta l 1 4.3 I 27 6 i 28 9 11 9 30 2 12 4 \ 32 0 13 1 I I 11 3 16 3 17 0 17 8 I 18 9 I T ab le 6 .1 - Lo ss d if fe re nc e v s. e a c h di st an ce a t H am ba nt ot a G on no ru w a lin e +- ~ 6 . 2 P r e s e n t v a l u e o f l o s s e s F o l l o w i n g d a t a a r c u s e d t o c a l c u l a t i o n o f p r e s e n t \ a l u c o f e n e r g y l o s s e s 0 \ e r c u r r e n t t i m e p e r d a y U n i t c o s t 0 . 8 4 h r s ( t a k e n f r o m l o a d p a t t e r n o f O m a r a ) 1 4 . 0 0 L K R / k W h 1 3 1 A n n u a l t a r i f f i n c r e m e n t 1 0 ( Y c ) D i s c o u n t r a t e 1 5 ° i t J ~- T o t a l l o s s - P V o f A d d i t i o n a l l l n i t c o s t T o t a l c o s t Y e a r p e r y e a 1 · P V F e x p e n s e s l o s s ( k W ) ( L K R ) ( L K R ) ( k W h ) ( L K R ) 1 1 6 3 4 9 9 7 6 1 4 . ( J 0 6 9 9 . 6 6 1 0 . 8 7 0 6 0 8 . 4 0 I J I 1 7 0 5 2 1 2 2 1 5 . 4 0 8 0 2 . 6 7 9 0 . 7 5 6 6 0 6 . 9 4 0 I I - - , 1 7 8 5 4 5 7 5 1 6 . 9 4 9 2 4 . 4 9 7 0 . 6 5 8 6 0 7 . 8 7 2 , ) 4 1 8 9 5 7 9 4 7 1 8 . 6 3 1 . 0 7 9 . 7 9 2 0 . 5 7 2 6 1 7 . 3 7 4 I I 2,-!40,5~ T a b l e 6 . 2 P r e s e n t v a l u e s o f e x p e n s e s ( l o s s e s ) 6 . 3 E s t i m a t e d c o s t o f r e c o n s t m c t i o n N e x t p r o v e n m e t h o d f o r i n c r e a s i n g t h e l i n e c a p a c i t y i s r e c o n s t r u c t i n g . R a c o o n c o n d u c t o r c a n h e r e p l a c e d b y L y n x c o n d u c t o r . I l c n c c . i t i s r e q u i r e d t o e s t i m a t e c o s t o f r e c o n s t r u c t i n g . R e c o n s t r u c t i n g c o s t h a s b e e n c a l c u l a t e d a s f o l l m v s u s i n g C L B s t a n d a r d r a t e [ 2 1 . • L y n x l i n e c o s t f o r c o n s t r u c t i o n p e r k m L K R . 3 . 1 4 0 . 0 0 0 • R c m m a l c o s t f o r e x i s t i n g l i n e s p e r k m L K R . 7 5 . 0 0 0 • S c r a p c o s t p e r k m ( A s s u m e d a s 1 0 % ) L K R . 2 2 2 . 4 0 0 • T o t a l a c t u a l c o s t o f r e c o n s t r u c t i n g p e r k m L K R . 2 . 9 9 2 . 6 0 0 • R e c o n s t r u c t i n g l i n e l e n g t h 4 . 3 k m • T o t a l c o s t f o r 4 . 3 k m L K R . 1 2 . 8 6 8 . 1 8 0 4 1 6 . 3 . 1 P r e s e n t v a l u e o f s a v i n g s D u e t o t h e e c o n o m i c u n c e r t a i n t i e s . e s t i m a t e d c o s t c a n b e t a k e n C r o m l o a n w i t h i n t e r e s t r a t e 1 5 % a n d l o a n p e r i o d i s 4 y e a r s . T h e n . t o t a l p r e s e n t v a l u e o f i n t e r e s t h a s b e e n c a l c u l a t e d a s f o l l o w s . · - P r o j e c t c o s t 1 3 . 8 2 4 . 5 0 0 L K R I L o a n 1 3 . 8 2 4 . 5 0 0 L K R L o a n p e r i o d 4 Y e a r s ! 1 I n t e r e s t r a t e 1 5 % I Y e a r 1 2 3 - t [ O p e n i n g b a l a n c e 1 2 . 8 6 8 . 1 8 0 9 . 6 5 1 . 1 3 5 6 . 4 3 4 . 0 9 0 3 . 2 1 7 . ( ) 4 5 l I n t e r e s t 1 . 6 8 8 . 9 4 9 1 . 2 0 6 . 3 9 2 7 2 3 . 8 3 5 2 4 1 . 2 7 8 I L o a n r e p a v m e n t 3 . 2 1 7 . 0 4 5 3 . 2 1 7 . ( ) 4 5 3 . 2 1 7 . 0 4 5 3 . 2 1 7 . 0 4 5 f . - - - . \ C l o s i n g b a l a n c e 9 . 6 5 1 . 1 3 5 6 . 4 3 4 . 0 9 0 3 . 2 1 7 . 0 4 5 0 I P V F 0 . 8 7 0 0 . 7 5 6 0 . 6 5 8 0 . 5 7 2 ' T a b l e 6 . 3 P r e s e n t v a l u e o f s a v i n g s 6 . 4 E c o n o m i c v i a b i l i t y o f t h e p r o j e c t C a s e I : U s i n g e x i s t i n g l i n e Y e a r 1 Y e a r 2 Y e a r 3 Y c a r - t E x t r a c o s t o f 6 9 9 . 6 6 1 8 0 2 . 6 7 9 9 2 4 A 9 7 1 . 0 7 9 . 7 9 2 l o s s e s P V o f c o s t 6 0 8 . 4 0 1 6 0 6 . 9 4 0 6 0 7 . 8 7 2 6 1 7 . 3 7 4 I I I I I T o t a l c o s t ( C ) L K R . 2 , - t 4 0 , 5 8 8 _ _ j T a b l e 6 . - t P r e s e n t v a l u e o f e x t r a c o s t o f l o s s e s 4 2 C a s e 2 : C o n s t r u c t i n g n e w l i n e I S a l v < l Y e a r 1 Y e a r 2 Y e a r 3 I Y e a r . t v a t u C a p i t a l c o s t 3 2 1 7 . 0 4 5 3 . 2 1 7 . 0 4 5 3 . 2 1 7 . 0 4 5 3 . 2 1 7 . 0 4 5 1 1 . 8 3 8 - ~ I n t e r e s t 1 . 6 8 8 . 9 4 9 1 . 2 0 6 . 3 9 2 7 2 3 . 8 3 5 2 4 1 . 2 7 8 T o t a l c o s t 4 . 9 0 5 . 9 9 4 4 . 4 2 3 . 4 3 7 3 . 9 4 0 . 8 8 0 3 . 4 5 8 . 3 2 3 1 1 . 8 3 8 . 7 2 6 ~ -~ P V o f t o t a l c o s t 4 . 2 6 8 . 2 1 4 3 . 3 4 4 . 1 1 8 2 . 5 9 3 . 0 9 9 1 . 9 7 8 . 1 6 1 6 . T i - T o t a l c o s t ( B ) = ( Y e a r l + Y e a r 2 + Y e a r 3 + Y e a r ~-Salvage v a l u e ) = L K R . 5 , - t l ~ ' n ' ' j T a b l e 6 . 5 P r e s e n t v a l u e o f c o n s t r u c t i n g a n e w l i n e I P r e s e n t v a l u e o f P r e s e n t v a l u e o f N e t p r e s e n t v a l u e I L o a d p a t t e r n e x p e n s e s ( C ) L K R . s a v i n g s ( B ) L K R . ( B - C ) L K R . ( C a s e 1 ) ( C a s e 2 ) - - - O m a r a 2 . 4 4 0 . 5 8 8 5 . 4 1 1 . 8 4 1 2 . 9 7 1 . 2 5 3 - - - - 1 R a t m a l w a 1 a 4 . 1 2 5 . 7 5 6 5 . 4 1 1 . 8 4 1 1 . 2 8 6 . 0 8 5 K u d a g a m m a n a 9 5 8 . 8 0 2 5 . 4 1 1 . 8 4 1 4 . 4 5 3 . 0 3 9 - - - - - - " " T a b l e 6 . 6 N e t p r e s e n t v a l u e o f e a c h p r o j e c t I n t h i s c a s e s t u d y . p r e s e n t \ ' a l u e o f e x p e n s e s m e a n s e n e r g y l o s s e s d u e t o 0 \ e r c u r r e n t o r e x i s t i n g l i n e ( C a s e 1 ) , P r e s e n t Y a l u e o f s m i n g s m e a n s c o s t i n c u r r e d i n c o n s t r u c t i n g a n e w l i n e ( C a s e 2 ) _ I t i s o b s e r v e d t h a t p r e s e n t \ a l u e o f s m - i n g s l a r g e r t h a n P r e s e n t v a l u e o f e x p e n s e s f o r a l l l o a d p a t t e r n s _ T h e r c C o r e . c o n s t r u c t i n g a n e \ \ l i n e i s m o r e e x p e n s i v e f o r l o a d p a t t e r n s o r O m a r a . K u d a g a m m a n a a n d R a t m a h \ a l a _ l n o t h e r w o r d s . i m p l e m e n t a t i o n o f a b o v e t h r e e p r o j e c t s i s f i n a n c i a l l y \ i a b l e _ 4 3 C h a p t e r 0 7 C o n c l u s i o n s T h e o b j e c t i v e o f t h i s p r o j e c t i s t o J i : \ . t h e m e r h c a d l i n e p o w e r t r a n s f e r l i m i t s , w i t h e f f e c t i v e w i n d c o o l i n g t h r o u g h t h e p r o b a b i l i s t i c a p p r o a c h . T h e a n a l y s i s c o n s i s t s o f t h e m a x i m u m t e m p e r a t u r e l i m i t o f A C S R R a c o o n c o n d u c t o r t h a t i s s e l e c t e d i n o r d e r t o m i n i m i z e l o s s o f s t r e n g t h , s a g . l i n e l o s s , o r a c o m b i n a t i o n o f t h e a b m c . I n t h e f i r s t p a r t . a l l o \ v a b l e l o s s o f s t r e n g t h o f A l u m i n i u m w a s a n a l y z e d t h r o u g h t h e p r o b a b i l i s t i c a p p r o a c h . L o s s o f s t r e n g t h o f A C S R R a c o o n c o n d u c t o r c a n o c c u r d u e t o \ \ i n d s p e e d b e l o w 1 m / s a n d C C C m o r e t h a n 2 0 2 A . D u r i n g t h e s t u d y . i t i s o b s e n c d t h a t s t r e n g t h o f A l u m i n i u m i s n o t r e d u c e d b c l o \ \ 9 0 < 1 < 1 o f i t s s t r e n g t h d u r i n g t h e l i f e t i m e o f 5 0 y e a r s . T h i s r e d u c t i o n o f s t r e n g t h i s n e g l i g i b l e . T h e r e f o r e . c J T c c t i w ' v \ i n d s p e e d c a n b e t a k e n a s 1 m / s . l n t h e s e c o n d p a r t . s a g \ a r i a t i o n s w e r e a n a l y z e d i n e a c h s p a n w h i c h \ \ a s p r e s e n t l y u s e d i n C F B a g a i n s t m a x i m u m a l h 1 \ \ a b l c t e m p e r a t u r e ( 9 0 ° C ) i n t h e a b s e n c e o f \ \ i n d s p e e d . I t i s o b s c n c d t h a t g r o u n d c l e a r a n c e i s n o t ' v i o l a t e d \ V h c n o p e r a t i n g a t h i g h e r t e m p e r a t u r e s . F i n a l l y . C o s t s a n d b e n e f i t s \ \ e r e c \ a l u a t c d \ \ i t h i n c r e a s e o f l o s s e s b y t h i s m e t h o d a g a i n s t i n w s t m c n t i n c u r r e d i n s t r e n g t h e n i n g o f t h e C F B n e t w o r k . l t i s n o t e d t h a t i n Y e s t m e n t c a n b e p o s t p o n e d a t l e a s t 4 y e a r s \ \ h e n a n n u a l g r o w t h r a t e i s c o n s i d e r e d a s 2 . 5 ° / ( J . N e t p r e s e n t Y a l u e \ v a s a n a l y z e d f r o m p r e s e n t v a l u e o f e x p e n s e s ( d u e t o l o s s i n c r e a s e o f e x i s t i n g s y s t e m ) a n d p r e s e n t \ · a l u c o f s a v i n g ( p o s t p o n e m e n t o f i m e s t m e n t i n c u r r e d i n s t r e n g t h e n i n g o f t h e C T B n e t w o r k ) . N e t p r e s e n t v a l u e i s p o s i t i \ ' C f o r l o a d p a t t e r n o f O m a r a . K u d a g a m m a n a a n d R a t m a l w a l a . T h e r e f o r e p r o j e c t i s f i n a n c i a l l y \ i a b l c . S o m e t i m e s i n u n a v o i d a b l e c i r c u m s t a n c e s . CI~B i s f o r c e d t o d e l a y t h e a u g m e n t a t i o n s . 4 4 T h e r e a s o n s m a y h e a s f o l l o w s . 1 . D i n i c u l t i e s i n r a i s i n g f u n d s l ' o r t h e a u g m e n t a t i o n s 2 . D e l a y s i n p l a n n i n g a n d d e s i g n i n g 3 . E x p e c t e d m a j o r c h a n g e s t h a t m i g h t t a k e p l a c e i n n e a r f u t u r e . h e n c e t h e p l a n n i n g o r a u g m e n t a t i o n i s d e l a y e d W h a t e v e r t h e r e a s o n . t h i s s t u d y g i n : s a g u i d e t o t h e e x t e n t o r p o s s i b l e m e r l o a d o f t h e l i n e s w i t h o u t \ i o l a t i o n o r t e c h n i c a l l i m i t i n g p a r a m e t e r s a n d t h e c o s t b e n e f i t s / l o s s e s i n s u c h o p e r a t i o n s . F i n a l l y . t h e r e s u l t s s h o v v t h a t i n s o m e c a s e s . p o s t p o n i n g o f i n v e s t m e n t . i n c u r r e d i n s t r e n g t h e n i n g o r n e t Y v o r k i n s t e a d o f r e p l a c i n g c o n d u c t o r s . t o t h e e x t e n t s i n t i m e a n d c u r r e n t l i m i t s a s s t u d i e d . i s e c o n o m i c a l l y v i a b l e a n d b e n e f i c i a l t o C E B . 4 5 R e f e r e n c e s : ] 1 ] C L B S p e c i i i · a t i o n n o . O 1 0 . C c y l o n E l e c t r i c i t y B o a r d . 1 9 9 8 ] 2 ] S t a n d a r d C o 1 s t r u c t i o n C ' o s t s . C e y l o n E l e c t r i c i t y B o a r d . 2 0 0 9 . r 3 J B u d g e t e d O r c r a t i n g S t a t e m e n t . C e y l o n E l e c t r i c i t y B o a r d . 2 0 l 0 r 4 ] C o n s t r u c t i o r S t a n d a r d s f o r M e d i u m V o l t a g e P m : v e r D i s t r i b u t i o n L i n e s . C e y l o n E l e c t r i c i t y B o a r d . S e p t e m b e r 1 9 9 7 ] 5 ] I E I T S t a m i : t r d 7 3 8 - 9 3 . · · 1 1 - : E L S t a n d a r d ! ' o r C a l c u l a t i n g t h e C u r r e n t - T e m p e r a t u n · R e l a t i o n s h i p o r B a r e C o n d u c t o r s " . I H T J u n e 1 9 9 3 [ 6 ] I E F F S t a n d : t r d 7 3 8 1 f \ 1 - 2 0 0 C l . " I F E F S t a n d a r d f o r C a l c u l a t i o n o f B a r e ( ) \ c r h e a d C c n d u c t o r s " . T E E ! . J a n u a r y 2 0 0 7 l 7 l I E C S t a n d m . l 1 5 9 7 . " 0 v e r h e a d e l e c t r i c a l c o n d u c t o r s - C a l c u l a t i o n m e t h o d s f o r s t r a n d e d 1 a r e c o n d u c t o r s . . . 1 9 9 5 l 8 ] F o s s . S . D . a n d M a r a i o . R . A . · · E v a l u a t i o n o r a n o v e r h e a d l i n e f o r e c a s t r a t i n g A l g o r i t h m " . :n~E T r a n s a c t i o n o n P o w e r D e l i v e r y . v o l . 7 . N o . 3 . J u l y 1 9 9 2 . J 9 ] F o s s . S . D . m d M a r a i o . l < . A . " ' D y n a m i c l i n e r a t i n g i n t h e o p e r a t i n g e m i r o n m c n 1 · . I E E E T r a n s a c t i o n o n P m \ c r D e l i v e r y . v o L 5 . N o . 2 . J u l ) 1 9 9 2 . l l O ] D o u g l a s s . L . A . M o t l i s . Y . . a n d S c p p a . T O . . " ' I U T " s A p p r o a c h C o r i n c r e a s i n g t r : m s m i s s i o n l i n e r a t i n g i n N o r t h A m e r i c a . . . l l l l M o r g a n . V . : . : · R a t i n g o f b a r e O \ c r h e a d c o n d u c t o r s f o r c o n t i n u o u s c u r r e n t " " . I E ! · E . v o L 1 4 . n o . 1 0 . O c t 1 9 6 7 . 4 6 [ 1 2 \ W a n , l L C\~lery, D . l ' v \ c . a 1 1 d V i n a L V . , " I n c r e a s i n g t h e r m a l r a t i n g b y r i s k a n a l y s i s " . I I ;~[Transaction o n P m v e r S y s t e m s . \ · o l . 1 - + . N o . 3 , J u l y 1 9 9 9 . ] 1 3 ] D m i s . M . \ \ , " A n e w t h e r m a l r a t i n g a p p r o a c h : t h e r e a l t i m e t h e r m a l r a t i n g s y s t e m f o r s r a t e g i c o v e r h e a d c o n d u c t o r t r a n s m i s s i o n l i n e s . P a r t I I . " I E E E T r a n s a c t i o n , o n P o w e r A p p : 1 r a t u s a n d S y s t e m s . v o l . P A S 9 7 , p p . 8 1 0 - 8 2 5 , M a r . I A p r . 1 ( 7 8 . ] 1 4 ] A B B R e p o r N o . 2 0 0 5 - 1 0 9 7 7 - 3 R 2 . " D a k t ) t a s W i n d T r a n s m i s s i o n S t u d y T a s k 2 " . A u , u s t 2 0 0 5 . [ 1 5 ] S . P . Ciupth~t " S t a t i s t i c a l M d h o d s " , R e v i s e d E d i t i o n . p p . E - 7 ' 7 0 - F - 7 ' 7 8 , 1 9 9 5 . ] 1 6 ] h t t p : / / e n . \ v i k p c d i a . o r g , w i k i i ! Z a y l c i g h d i s t r i b u t i o n [ 1 7 J h t t p : / / e n . w i L p e d i a . o r g / \ \ i k i C u m u l a t i v e i l T q u e n c y [ 1 8 ] C h e r h e a d A ; 1 m i n i u m H a r e C o n d u c t o r s , A C L C a b l e s P L C D e c e m b e r 2 0 0 8 . 4 7 A n n e x A T h e f o l l o v v i n g c o m p u t e r p r o g r a m i s u s e d t o c a l c u l a t e t h e r m a l r a t i n g o f b a r e o v e r h e a d c o n d u c t o r s . A n n e x A o f I E E E s t a m L r d 7 3 8 - 1 9 9 3 L i s t i n g o f t h e " R A T E L : E E " p r o g r a m f o r s t e a d y - s t a t e a n d t r a n s i e n t c a l c u l a t i o n s o f t e m p e r a t u r e a n d t h e r m : d r a t i n g f o r b a r e o v e r h e a d c o n d u c t o r s . 4 8 A n n e x B T h i r d o r d e r e q u a t i o n f o t calculatin~ T 1 V I S T t ( d a N ) . 1 1 5 T c ( d a N ) $ B $ 5 Y o u n g · s m o d : : I u s ( d a N / m m 2 ) $ 8 $ 6 t h e r m a l e x J X l l : , , i o n $ 8 $ 7 c o e f f i c i e n t (/l~·.:g c ) K I S t e m p e r a t u r e < t i n i t i a l c o n d i t i o n . C 1 ( d e g c ) L 1 5 e v e r y d a y t e m p e r a t u r e . C : ( d e g c ) T 1 5 · . r e s u l t a n t w i m : a n d w e i g h t f o r c e a t l 1 c o n d i t i o n ( d a N / m ) I I 1 5 - e q u i \ a l e n t s p : : 1 S 1 5 c . r e s u l t a n t \ V i n t : a n d w e i g h t f o r c e a t l 1 c o n d i t i o n ( d a N / m ) S o l v e r ( T 1 ) POWI~R(V, 5 . 3 ) - J 1 5 - S B $ Y ' £ B $ 6 * $ B $ 7 * ( K 1 5 - I . 1 5 ) - $ B $ 7 * $ B $ 5 * P O W E R ( ! 1 5 . 2 ) * P O \ \ E R ( I I 1 5 . 2 ) / 2 4 * P O W L R ( . I I 5 . 2 l ) * P O W E R ( V 1 5 . 2 ) - $ B $ 7 * $ B $ 5 * P O W E R ( S 1 5 . 2 ) * P O W E R ( I I 1 5 . 2 ) / 2 4 T h i r d o r d e r e q u a t i o n f o r c a l c u l a t i n g T r X I 5 . C . T 1 ( d a N ) M 1 5 = t e m p e r a t u r e a t f i n a l c o n d i t i o n . C 1 ( d e g c ) L 1 5 ~c e v e r y d a y t e m ] .~rature. C ( d e g ' : ) U 1 5 · . · · . r e s u l t a n t \ V i n d m d w e i g h t f o r C l : a t f i n a l c o n d i t i o n ( d a N i m ) I I 1 5 ~·· e q u i \ a l e n t S J X : ; S o l v e r ( T r ) P O W E R ( X 1 1 . 3 ) - ( J I V £ 1 3 $ 5 * $ B $ 6 * $ B $ 7 * ( M 1 5 - I . 1 5 ) - $ B $ 7 * $ B $ 5 * P O W E R C I 1 5 . 2 ) * P O \ \ ' E R ( l I 1 5 . 2 ) / ( 2 4 * P O ' f i ' E R ( J 1 5 . 2 ) ) ) * P O W E R ( X 1 5 . 2 ) - $ B $ 7 * $ B $ 5 * P O W E R ( l . I 5 . 2 ) * P O \ \ ' E R ( I I 1 5 . 2 ) / 2 4 4 9 $ 8 $ 3 · · G r a v i t a t i o n a l ; ( J r c c ( m / s l s ) E q u i v a l e n t s a g a t T 1 ( m l - ( V I 5 * I 0 1 ( S I:~ : · I 0 ) ) * ( C C ) S 1 - 1 ( S 1 5 * I 0 * 1 1 1 5 / ( 2 • : • V 1 5 * $ 1 3 $ 3 ) ) - 1 ) E q u i v a l e n t s a g a t T e ( m · · ( J 1 5 * I 0 1 ( T l : ' I O ) ) * ( C O S I I ( ' I 1 5 * I O * H 1 5 1 ( 2 * . 1 1 5 * $ B $ 3 ) ) - 1 ) E q u i v a l e n t s a g a t T 1 ( 1 1 1 , ~·· ( X I 5 ' ' ' I 0 I ( U I : · I 0 ) ) * ( C C S I I ( l J I 5 * I 0 * I l l 5 I ( 2 ' ' ' X I 5 * $ 1 3 $ 3 ) ) - I ) $ 7 $ 1 5 C 1 6 ( $ 1 - 1 $ 1 5 I n i t i a l s a g ( m ) $ A A $ 1 5 cquiv~: , ; n t s a g a t i 1 ( m l S p a n ( . 1 ) e q u i v : J : _ : n t s p a n · S / S I S * P O W I : R ( C 1 6 . 2 ) , P O W L R ( $ H $ 1 5 . 2 ) c q u i v < l : _ : n t s a g a t l c ( m ) l . . _ v c r y d a y s a g ( m ) · · . $ : \ . \ $ 1 5 ' ' P O \ V E R ( C 1 6 . 2 ) / P O W L R ( $ 1 1 $ 1 5 . 2 ) $ A B $ 1 5 F i n a l s a g ( m ) A C 1 6 $ N $ 1 5 $ S $ 1 5 c q u i v a : . : n t s a g a t T c ( 1 1 1 ) ·~· $ i \ ~~$15 ' ' P O W E R ( C 1 6 . 2 ) / P O W L R ( $ 1 - ! $ 1 5 . 2 ) I n i t i a l 1 g ( m ) w e i g h : o r c o n d u c t u r ( c L l N i m ) r e s u l t c : ; : t w i n d a n d wci~'ht f o r c e a t T 1 c o n d i t i o n ( d a N / m ) V e r t i c a l s a g a l i n i t i a l C l ' d i t i o n ( m ) A C 1 6 * $ N $ 1 5 1 $ S $ 1 5 5 0 c v c r y c : ) s a g ( m ) ; \ [ ) 1 6 $ T $ 1 5 R e s u l t 1 t w i n d a n d \ v c i : ; h t f o r c e a t ever~ d a ) c o n d i t i o n ( d a N ; m ) V e r t i c a l s a g a t c v e r y d a : . c o n d i t i o n ( m ) A D 1 6 * $ ! \ S 1 S t £ I $ 1 5 t i n a ! s : > . ! . ( m ) ; \ [ 1 6 $ U $ 1 5 result~· t \ \ i n d a n d \ \ C i ! c ' h t f o r c e a t f i n a l c o n d i t i o n ( d a N / m ) V e r t i c a l s a g a t ! i n a ! cot~ . i t i o n ( m ) A E 1 6 * $ N S 1 5 / $ U $ 1 5 5 1 A n n e x C D e f i n i t i o n f o r E c o n o m i c s E v a l u a t i o n C . l I n t e r e s t R a t e a n d D i s c o u n t R a t e I n t e r e s t R a t e T h e p e r c e n t a g e i n c r e a s 1 . : 1 1 1 t h e v a l u e o r m o n e y o v e r a pe~iod o f o n e y e a r . I n a d d i t i o n t o t h e t i m e v a l u e o r m o n e \ . i n t e r e s t r a t e i n c I u d e s t h e e f f e c t o r i n f l a t i o n a n d e s c a l a t i o n . D i s c o u n t R a t e T h e t i m e v a l u e o f m o m : ) . a s p e r c e i v e d b y a n i n v e s t o r . U s u a l l y e x p r e s s e d i n p e r c e n t a g e p e r y e a r . S a l v a g e V a l u e A s s u m e t h a t s a l v a g e v a l u e i s r e m a i n i n g l i f e t i m e v a l u e a s f o l l o \ \ s . S a l v a g e v a l u e C a p i t a l c o s t x 4 6 / 5 0 W h e r e 5 0 i s l i f e t i m e a m ! ~t6 i s r e m a i n i n g l i t e . P r e s e n t V a l u e D i s c o u n t R a t e r % P V F a c t o r - · Y e a r I \ " : d u e 1 0 I V o I + - - ( 1 + r ) l 1 ( 1 + r } ' 1 - ' ·~ . ' v l 2 I V ; c 1 " J ( 1 + r } i ! I i T 1 I - ~ I P r e s e n t V a l u e V o ( 1 + r ) O V 1 ( 1 + r ) l V z ( l + r ) Z v l ( 1 + r ) 3 c \ - : - 1 _ . . ~ V g - - - i . . . . 9 ( 1 + r ) 9 1 V 1 o 1 0 V 1 o ( 1 + r ) 1 0 ( 1 + r ) 1 0 5 2 C o s t - B e n e f i t A n a J y s i ; , 0 ~ _'"'~ ~Benefit I 1 t - - - + c-_e-l~- ~:~ 1-~J 1 - - ~-- c , , -~-n J L " - - I B o C o I B o I 1 3 1 c : 1 I 1 3 1 I --~ ------~ 1 3 2 C : z B z - 1 3 : 1 c l I B : J ~--- \ . . . . . . . . . . . . . . . . . . . . . . . . . . B n - 1 C : n - 1 B n - 1 e n C : n 1 3 n - ~---P~·csent V a l u e . t - - - C o s t I B e n e f i t j Y e a r C = " n C = ' \ ' n - r i ) > L . t = 1 I L i = 1 ( C I ) I l l , : 1 l ~ - _ ! _ _ B = " . B i = r . , r i ) L . t = l i = 1 ' . ( C 2 ) N e t P r e s e n t Value(NP\'~· = 8 - C ( C 3 ) P r o j e c t A c c e p t e d I f N P \ 0 .~ . ~\ < ' > 5 3