Pu [ pul [P [Pp12][P2 IP [Pmn [Pp2nl The diagonal submatrix in[Pi expresses the potential coefficient matrix of a single-core cable. When a single core cable consists of a core and sheath(Fig. 61.5), the submatrix is given by IP I Pa Psi In 4 P In (61.36) Eo= absolute permittivity of free space, Es= relative permittivity of insulation outside sheath, and Eg= relative permittivity of insulation outside core. [Prik of [p,] is given by (61.37) Ppit in Eq(61. 37)is the potential coefficient between the jth and kth inner conductors with respect to the pipe inner surface. When j=k, Ppie= Ppipe-in otherwise Ppil is given in Eq (61.39) d EPO d dk cos(ne, Pik where E, is the relative permittivity of insulation inside the pipe; R; is the outer radius of cable i and d, d and© 2000 by CRC Press LLC (61.33) The diagonal submatrix in [Pi ] expresses the potential coefficient matrix of a single-core cable. When a single￾core cable consists of a core and sheath (Fig. 61.5), the submatrix is given by (61.34) where (61.35) (61.36) e0 = absolute permittivity of free space, esj = relative permittivity of insulation outside sheath, and ecj = relative permittivity of insulation outside core. Submatrix [Ppjk] of [Pp] is given by (61.37) Ppjk in Eq. (61.37) is the potential coefficient between the jth and kth inner conductors with respect to the pipe inner surface. When j = k, Ppjk = Ppipe-in; otherwise Ppjk is given in Eq. (61.39). (61.38) (61.39) where ep is the relative permittivity of insulation inside the pipe; Ri is the outer radius of cable i; and di , dj , and dk are the inner radii of cables i, j, and k. [ ] [ ][ ] [ ] [ ][ ] [ ] [ ][ ] [ ] P PP P PP P PP P p p p pn p p pn p n p n pnn = ××× ××× ××× È Î Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ 11 12 1 12 22 2 1 2 M MOM [ ] P P P P P P ij cj sj sj sj sj = È + Î Í Í ˘ ˚ ˙ ˙ P r r sj sj = Ê Ë Á ˆ ¯ ˜ 1 2 0 4 3 pe e ln P r r cj cj = Ê Ë Á ˆ ¯ ˜ 1 2 0 2 1 pe e ln [ ] P P P P P pjk pjk pjk pjk pjk = È Î Í Í ˘ ˚ ˙ ˙ P q R d q i i p pipe-in = Ê Ë Á ˆ ¯ ˜ È Î Í Í ˘ ˚ ˙ ˙ Ï Ì Ô Ó Ô ¸ ˝ Ô ˛ Ô ln –1 2 2 pe e0 p q S d d q n n pjk p jk j k n jk n = Ê Ë Á ˆ ¯ ˜ × È Î Í Í Í ˘ ˚ ˙ ˙ ˙ = • Â 1 2 0 2 1 pe e q ln – cos( )