FIGuRE 61.4 A pipe-type cable system FIGURE 61.5 A single-core cable cross section. mll…pl (61.18) Lz21z1…zn The diagonal submatrix in [Z] expresses the self-impedance matrix of a single-core cable. When a single core cable consists of a core and sheath( Fig. 61.5), the self-impedance matrix is given by [Z= where Zssi= sheath self-impedance sheath-outt sheath/pipe-insulation (61.20) Zsi= mutual impedance between the core and sheath 'sheath-mutual (61.21) Zoi= core self-impedance (Zcore Zcorelsheath-insulation Zsheath-in )+ Z-Z 'sheath-mutu (61.2) where pm Io(mr) I1(m)© 2000 by CRC Press LLC (61.18) The diagonal submatrix in [Zi ] expresses the self-impedance matrix of a single-core cable. When a single￾core cable consists of a core and sheath (Fig. 61.5), the self-impedance matrix is given by (61.19) where Zssj = sheath self-impedance = Zsheath-out + Zsheath/pipe-insulation (61.20) Zcsj = mutual impedance between the core and sheath = Zssj – Zsheath-mutual (61.21) Zccj = core self-impedance = (Zcore + Zcore/sheath-insulation + Zsheath-in) + Zcsj – Zsheath-mutual (61.22) where (61.23) (61.24) FIGURE 61.4 A pipe-type cable system. FIGURE 61.5 A single-core cable cross section. = ××× ××× ××× È Î Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Z Z Z Z Z Z Z Z Z p p p n p p p n p n p n pnn 11 12 1 12 22 2 1 2 M M O M [Z ] Z Z Z Z ij ccj csj csj ssj = È Î Í Í ˘ ˚ ˙ ˙ Z m r I mr I mr core = r 2p 1 0 1 1 1 ( ) ( ) Z j r r core/sheath-insulation = wm p 1 2 1 2 ln