IEEE TransactionS on Power Delivery ,Vol. 6, No. 3. July 1991

RADIO-FREQUENCY ANALYSIS OF CARRIER CHANNELS ON MULTICONDUCTOR DISTRIBUTION CABLE NETWORKS

s. C e l o== I M.C A m o r - e , Feilow lEEE

D e p a r t m e n t of El ectr i cal Engr new- i ng U n i v e r s i t y of R o m e "La S a p i e n z a "

V i a E u d o s s i a n a , 18 Fiome. I t a l y

A b s t r a c t

The f r e q u e n c y - d o m a i n a n a l y s i s o f carr ier c h a n n e l s cin d i . s t r i b u t i o n c a b l e n e t w o r k s is p e r - f o r m e d b y means of a n e f f i c i e n t p r o c e d u r e b a s e d upon t h e n o d a l a p p r o a c h a n d modal t h e o r y . T h e m u l t i c o n d u c t o r s y s t e m may p r e s e n t a n y c o n i i g u r a t i o n w i t h m u l t i p l e d i s c o n t i n u i t y p o i n t s . The u s e o f e q u i v a l e n t t w o - - p o r t PI- c i r c u i t s a l lows t h e n o d a l a d m i t t a n c e matrix t o b e d e f i n e d i n a new f o r m . V e r y a c c u r a t e f r e q u e n c y - d e p e n d e n t a n a l y - t i c a l m o d e l s are d e - v e l o p e d t o s i m u l a t e s y s t e m s o f s i n g l e - c o r e c a b l e s or m u l t i p l e - c o r e p i p e - t y p e c a b l e s , hcrr i - e d or- a b o v e a g r o u n d p l a n e .

The s i m c r i a t i o n a n d p r o p a g a t i o n m o d e l s are u s e d t o c o m p u t e t h e v o l t a g e a t t e n u a t i o n o f car- r ie r c h a n n e l s on u n i f o r m l i n e - s e c t i o n s a n d c l i s - t r i b u t i o n n e t w o r k s o f tree- a n d mesh.-type c c : ) n f i g u r a t i o n s w i t h d i f f e r e n t lumped l o a d s , i n a f r e q u e n c y r a n g e u p t o 2tX) kHz.

1. INTRODUCTION

' E a r l i e r s t u d i e s h a v e shown t h e f e a s i b i l i t y of d i g i t a l s i g n a l t r a n s m i s s i o n o n HV m u l t i - c o n d u c t o r - o v e r h e a d l i n e s j . In t h e f r -equency d o m a i n , a . c c u r a t e s i m u l a t i o n m o d e l s a.nd e f f i - c i e n t p r o p a g a t i o n a l g o r i t h m s were d e v e l o p e d f o r n o n - u n i f o r m carrier s y s t e m s a b o v e a l o s s y g r o u n d p l a n e . A p r o c e d u r e b a s e d o n d i s c r e t e c o n v o l u t i o n w a s p r e s e n t e d t o c o m p u t e carr ier c h a n n e l t r a n s i e n t r e s p o n s e s t o a n y i n p u t d i y i tal s i g n a l . c o d e . The ' e y e d i a g r a m a p p r o a c h w a s c o n s i d e r e d f o r e v a l u a t i o n o f d i g i t a l t r a n s m i s s i o n q u a l i t y . P e r f o r m a n c e s of o p t i m a l c o u p 1 i n g a r r a n g e m e n t s were e v a l u a t e d t a k : i n g iwko a c c o u n t t h e c o r o n a n o i s e a n d t h e electro- m a g n e t i c d i s t u r b a n c e g e n e r a t e d b y d i g i t a l t r a n s m i s s i o n C1-SI.

S c t c c e s s i v e l y , t h e research p r o g r a m h a s a d d r e s s e d t h e r-adio-f reqc tency a n a l y s i s o f d i s t r i b u t i o n l i n e carr ier channel : , , which is t n e s u b j e c t of s e v e r a l r e c e n t s t . i t d i e s C4-83 .

The s i g n a l t r a n s m i s s i o n on p r i m a r y a n d s e c o n d a r y d i s t r i b u t i o n s y s t e m s p o s e s many a ~ f f i c u l t i e s i n t r v i n y t o d e f i n e t h e s imu- l a t i o n m o d e l s a n d i n t r y i n g t o p r e d i c t t h e p r o p a g a t i o n cl iaracterist i cs .

90 St3 462-2 PWRD A paper recommended and approved by the IEEE Power System Communications Committee of the IEEE Power Engineering Society for presentation a t the IEEZ/PES 1990 Summer Meeting, Minneapolis, Minnesota, July 15-19, 1990. 1.ianuscript submitted August 30, 1989; made available for printing June 6 , 1990.

959

D e s c r i b e d i n t h i s p a p e r are t h e r e s u l t s a c h i e v e d d u r i n g t n e f i r s t p h a s e of t h e r e s e a r c h c o n c e r n i n g t h e s i g n a l p r o p a g a t i o n on m u i t i c o n - d u c t o r d i s t r i b u t i o n s y s t e m s a n d t h e s i m u l a t i o n m o d e l s o f power c a b l e s i n t h e r a d i o - f r e q u e n c y domain .

The p r o p o s e d a n a l y s i s m e t h o d , b a s e d o n t h e n o d a l a p p r o a c h a n d modal t h e o r y [ ' ? I , is v a i i d f o r d i s t r i b u t e d - p a r a m e t e r n e t w o r k s h a v i n g a n y c o n f i g u r a t i o n w i t h m u l t i p l e d i s c o n t i n u i t y p o i n t s a n d impres . sed v o l t a g e or c c t r r e r t t s o u r c e s . Each i i n e - s e c t i o n is r e p r e s e n t e d b y a n e q u i v a l e n t : t w o - p o r t m u l t i c o n d u c t o r P I - c i r c u i t c4,93.

T h e d e v e l o p e d s i m u l a t i o n m o d e l s o f m u l t i c o n d u c t o r c a b l e s y s t e m s are b a s e d on e x i s t i n g a n a i y t i c a 1 .Formulas ClO-122. T h e d e p e n d e n c e of t h e c o n d u c t o r s a n d of t h e g r o u n d s e r i e s - i m p e d a n c e s on f r e q u e n c y is ta1::en i n t o a c c o u n t . M e t h o d s are a p p l i e d t o s u p p r e s s t h e r e l e v a n t d i s c o n t i n c t i t y i n t h e f r e q u e n c y s p e c t r a of t h e core s e r i e s - i m p e d a n c e s , which arises when t h e p e n e t r a t i o n d e p t h o f t h e c u r - r e n t e x c e e d s t h e t h i c k n e s s of t h e o u t s i d e armor.

The s i m u l a t i o n a n d a n a l y s i s m o d e l s are u t i l i z e d i n a f r e q u e n c y r a n g e up t o 2Ot3 l,Hz t o c o m p u t e t h e v o l t a g e a t t e n u a t i o n of carrier c h a n n e l s on m u l t i c o n d u c t o r power c a b l e systems. A u n i f o r m l i n e - s e c t i o n a n d t w o d i s t r i - b u t i o n n e t w o r k s o f tree- a n d m e s h - t y p e c o n - f i y u r i t i o n s are c o n s i d e r e d w i t h d i f f e r e n t l o a d c o n d i t 1 o n s .

2. ANALYSIS OF DISTRIBUTION LINE CARRIER PROPAGATION USING NODAL APPROACH

2.1 U n i f o r m L i n e - S e c t i o n s

L e t us c o n s i d e r 3. u n i f o r m l i n e - s e c t i o n , l e n g t h 1 , w i t h n c o u p l e d c o n d u c t o r s .

The e q u i i-a1 e n t mu]. ,k i c o n d u c t or c i r c u i t i s d e s c r i b e d b y d i s t r i b u t e d p a r s m e t e r s , which c h a r a c t e r i z e t h e nxn matrices of t h e p e r - u n i t l e n g t h s e r i e s - i m p e d a n c e s , CZI, a n d s h u n t a d m i t - t a n c e s , C Y ] .

The column v e c t o r - , 0.f t h e p h a s e v o l t a g e s a n d c u r r e n t s are:

C V l = E V , V I .. v i . . V n l t ( l a )

t i l - C i a Ia .. I * ..In]* ( I b )

w h e r e s u b s c r i p t t d e n o t e s m a t r i x t r a n s p o s i t i o n .

The l i n e - s e c t i o n is r e p r e s e n t e d i n F i g . l a as a t w o - p o r t m u l t i c o n d u c t o r c i r c u i t . The octtpc.tt q u a n t i t i e s are e x p r e s s e d as f u n c t i o n s of t h e i n p u t q u a n t i t i e s :

0885-8977/91/0700-~59$01.~1991 IEEE

960

(b)

Fig.1 - Two-port representation (a) and equivalent PI-circuit (b) of a uniform multiconductor line-section.

w h e r e t h e matrix o p e r a t o r s are:

CAI= CNI Ccosh m 1 1 CNI-" (Sa)

CHI= CHI C s i n h m l l C m l - l CHI-' CZI ( 3 b )

CCI= C Y 1 CMI C m l - 1 C s i n h m 1 1 C H l - 1 (3c)

C D l = [MI Ccosh m 1 1 [MI'-'= CAI, ( 3 d )

C M I alld CNI are t h e e i g e n v e c t o r m a t r i c e - , r e s p e c t i v e 1 . y of CZICYI a n d C Y l C Z 3 , which h a v e t h e same e i g e n v a l u e s A s , I , , . . , A,, . . , A m , a n d

Ccosh ml l=diag ,C c o s h m i l 2 ( 3 e )

C s i n h m l I = d i a g ( s i n h m i l > ( 3 f )

C m l = d i a g C mi >. (3y)

w i t h m, = A':

The m u l t i c o n d u c t o r l i n e - s e c t i o n c a n b e r e p r e s e n t e d as t h e e q u i v a l e n t P I - c i r c u i t shown i n F i g . l b , w i t h t h e f o l l o w i n g m a t r i x p a r a - meters :

c Ya 1 = c B 1 --I (4a )

CYbl=CBI-'CDl-CBl-' ( 4 b )

L e t us a s s u m e t h e l i n e b e t e r m i n a t e d i n t h e a d m i t t a n c : e C Y r l a n d d r i v p n b y a c u r r e n t s o u r c e CIS] w i t h a s h u n t - a d m i t t a n c e C Y B J , as shown i n F i g . 2 .

Fig.2 - Schematic configuration of a loaded multiconductor line-section driven by a current source.

The v o l t a g e co lumn v e c t o r of t h e i n - d e p e n d e n t 1 a n d 2 nQdeS

CVnol=:C CV1:I CVZ7 It (Sa)

is t i e d t o t h e co lumn v e c t o r of t h e n o d a l s o u r c e c u r r e n t s

b y t h e n o d a l e q u a t i o n o f 2 n x i o r d e r :

CYnol CVnol=C In01 f b )

i n which t h e n o d a l a d m i t t a n c e matrix is:

C Yno 1 = C Y t . 1 +CY 1 1 (7a)

C Y t l is t h e

CY1:7=

a n d C Y 1 1 is

m a t r i x o f t h e t e r m i n a l a d m i t t a n c e s :

1 C Y s l C O 1

c 0 1 C Y r 3 1

( 7 b )

t h e matrix of t h e l i n e a d m i t t a n c e s :

The matrix c o e f f i c i e n t s o f d e r i v e d f r o m (4a,b):

C Yp I = C Y a I + C Yb I = C B I-" C D 1

C Ym 1 =- C Y a 1 --I C H I - l

or ,from ( 3 b , d ) :

EYpl=CYlCMlCm t g h m l l - 1 [MI-I

( 7 c )

C Y 1 1 a r e

( 7d )

(7e)

C Y m l = - C Y I C M 2 C m s i r r h ml I-l C M l - 1 < t3b )

w h e r e :

C m t g h mll=diag.C m i t.gh m * l 2 ( 8 C )

Cm s i n h m l I = d i a g C mi s i n h m i l 1 ( S d )

T h e unknown v e c t o r CVnol is d e r i v e d f r o m (6).

2.2 Distribution Networks

The nodal equation can be derived f o r a network having any conf igurat ion wi th m independent nodes. Let n be the order of the d i s t r i b u t i o n system's components, which can be made of distributed-parameter uniform l i n e s or shunt- and series-lumped loads. The nodal equation i s i n general of (m.n)xl order and the nodal admittance matrix has dimension (m.n)x fm-n).

Let us consider the networks having the mesh-type and tree-type conf igurat ions of Fig.3 and Fig.4, respect ive ly . The number of each branch i s shown i n each f igure. Lumped loads i n tree-type network are represented by the same admittance C Y r l . The ac t i ve branch inc lud ing CEsl and CZsl i s transformed i n t o the equivalent p a r a l l e l connection of CIsl=CYslCEsl wi th C Y s l .

The order o f the nodal equation i s (4 .n)x l f o r the f i r s t network and ( 1 2 - n ) x l f o r the second network.

The ( 4 - n ) ~ (4 -n) dimensional nodal admittance matrix o f the mesh-type network i s :

CYnol=

i n which:

CY111 C Y m l l CO1 CYm41

C Y m l l CY221 CYm21 CO1

COJ CYm21 CY331 CYm31

CYm41 C O 1 CYm.31 CY441

(9)

c Y 1 1 1 = c Y s l + c Y p l l + c Y p 4 l + c Y p . 5 l

CY223=cYpll+cYp2l

CY33l=CYp2l+CYp3l+CYp4l+CYrl

cY441=cYp31+cYp43

The n-dimensional admittance matrices CYpkl and CYmkl of k-th l ine-sect ion are given by (8a,b).

2

F i g . 3 - Schematgc of a mesh-type network.

branch no.

7 : 7-18, 8 : 7-8, 9 : 8-9, l 0 : 6-11, 11 : 11-12 1 : 1-28 2 : 2-31 3 : 2-48 4 : 4-51 5 : 5-6, 6 : 6-71

Fig.4 - Schematic of a tree-type network.

The (12-n)x (12-n) dimensional nodal admittance matrix o f the tree-type network has the fo l low ing form:

CYIII CY~II COI .. 'COI

C Y m l l CY223 CYm21 .. CO1 I CO1 CYm21 CY333 .. CO1 CVnol=

I - .. .. I - 1 C O 3 CO1 CO1 .. CY12,121

i n which:

cY11l=cYsl+cYpll

CY2Zl=CYpl l+CYpZl+CYp.3 l+CYr l

CY33l=CYp2l+CYrl

CY12,12l=CYplll+CYrl

For large networks, the high-order

(10)

nodal equation, inc lud ing CYnol, which-is genera l ly a symmetrical sparse matrix, can be solved by the use of i t e r a t i v e procedures which minimize the computer run-time C181.

3. SIMULATION MODELS OF POWER CABLES AT CARRIER FREQUENCIES

The per-unit- length series-impedance and shunt-admittance matrices of power cables, e i t he r bur ied or above a ground plane, are defined i n a frequency range i n t o the megahertz band.

I t i s necessary t o determine the geometrical parameters and the e l e c t r i c a l spec i f i c quant i t ies of the mater ia ls forming the cable, and the ground e l e c t r i c a l character is t ics . I t i s assumed tha t the inner conductors have a c i r c u l a r cross-section and are not provided wi th a ferromagnetic sheath.

962

4. PERFORMANCE EVALUATION OF CARRIER CHANNELS ON CABLE NETWORKS

4.1 Uniform Line-Sections

1 C

C IZR

!b)

Fig.5 - Coupling arrangement (a) on a uniform line-section with a buried system of three single-core cables (b) . (rl=9.3mm,r2=15.5mm,r3=17mm,r4=19.5mm, ue=3. 3 - 107S/m , t~-=4.7 - 10eS/m , Er I =3.2 , €,,=2.1 ,D=SOmm).

%3

4.2 Distribution Networks 1 C 2

r

C

C

a

iai c: core, a: armor

-1. ......................... ....

ib)

Fig.6- Coupling arrangement (a) on a uniform line-section with a buried triple- core cable (b). (r1=29.5 mm, r2=31.5 mm, r3=35 mm).

A bur ied t r ip le -core pipe-type cable, 1C1i:i ill long, spaced at C i . 5 tn from the sar th p iane , hav: ng a sector-shaped ct"oss-%ix t i an fL s consi I-- e r e z i i n the carr1.w channel canfigC.;.:".~t3.On of F:!.dS,5 wit!, terminai impedance equal t o 32 9. ;-is . ~ . ~ ' E E I oi e.s>:ki sec:tor i s ezL!.a! t i i 150 i i i m t :

ciie eqctivaienk c i r c u l a r section has a rad ius of t. 7 mm.

-. 4.. -

The cable s imulat ion model i s o f the 4th o r d e r - and the nodal equation ha.z dimensions 8:t 1 .

T h e computed frequency spectrum o f the c a r r i e r channel v o l t a g e ii'! tencrat i on i:= r e p o r t e d

(2 r a 1.1 n d

"5 I O Irn i FREaENCY [ L H i I

Fig.7 - Frequency spectra of carrier channel voltage attenuation on uniform line- sections with a system of three single-core cables (1) and a triple- core cable (2).

Table I - Characteristics of the mesh-type (a) and tree-type (b) networks. Ctriple-core cable cross-section type 3x150 mmp ( & I , 3 x 2 4 0 mm=(B) 3 .

964 5 I CONCLUS IONS

t' I I I

60 too IW 203 0 F-Y M-kl

Fig .8 - Frequency spectra of c a r r i e r channel voltage amplitudes a t four nodes of t h e mesh-type network.

7 10 la, FREouENcl rMZ1

<a!

3

F i g . 9 - Frequency spectra of c a r r i e r channel voltage a t tenuat ion a t nodes 2,7,12 of t h e tree-type network, f o r a load impedance o f 1O+j5 R (a ) and of 32 8, 30 P (b).

REFERENCES

F'. Burra;cano , S . C r i st i na, M. D ' Ainoi-e, 3. Sa-

Fnwer Lirle Carr ier Channels: an Introduct ion", IEEE Trar>?i. on ?owel- De: ivery-, V c > l . Plr;RD-L', No. I , January 1987.

;, ~? - i; , '< ?-. ~ ~ g i .: tal S i g n a i Trainsmizsioi? iiri