61.2 Alternating Current Underground: Line Parameters, Models Standard Voltages. Cables Mo-Shing Chen and K.C. Lai Although the capital costs of an underground power cable are usually several times those of an overhead line ual capacity, installation of undergroun is continuously increasing for reasons of safety, security reliability, aesthetics, or availability of right-of-way. In heavily populated urban areas, underground cable ystems are mostly preferred. Two types of cables are commonly used at the transmission voltage level: pipe-type cables and self-contained oil-filled cables. The selection depends on voltage, power requirements, length, cost, and reliability. In the United States, over 90% of underground cables are pipe-type design. Cable parameters A general formulation of impedance and admittance of single-core coaxial and pipe-type cables was proposed by Prof. Akihiro Ametani of Doshisha University in Kyoto, Japan [Ametani, 1980]. The impedance and adm tance of a cable system are defined in the two matrix equations d(v) =-[Z]·(D) 61.13) d(D)=-y]·(V) 61.14) where(V)and(n) are vectors of the voltages and currents at a distance x along the cable and [z and [y are square matrices of the impedance and admittance. For a pipe-type cable, shown in Fig. 61.4, the impedance and admittance matrices can be written as Eqs. (61. 15)and(61. 16) by assuming: 1. The displacement currents and dielectric losses are negligible. 2. Each conducting medium of a cable has constant permeability. 3. The pipe thickness is greater than the penetration depth of the pipe wall. [Z=[Z]+[zp (61.15) [Y=jo[P]-1 (61.16) [P]=[P]+[P where [P] is a potential coefficient matrix. [Zl= single-core cable internal impedance matrix Za O 0] [Zil (61.17) [O][0 [ZI I impedance mat c 2000 by CRC Press LLC© 2000 by CRC Press LLC 61.2 Alternating Current Underground: Line Parameters, Models, Standard Voltages, Cables Mo-Shing Chen and K.C. Lai Although the capital costs of an underground power cable are usually several times those of an overhead line of equal capacity, installation of underground cable is continuously increasing for reasons of safety, security, reliability, aesthetics, or availability of right-of-way. In heavily populated urban areas, underground cable systems are mostly preferred. Two types of cables are commonly used at the transmission voltage level: pipe-type cables and self-contained oil-filled cables. The selection depends on voltage, power requirements, length, cost, and reliability. In the United States, over 90% of underground cables are pipe-type design. Cable Parameters A general formulation of impedance and admittance of single-core coaxial and pipe-type cables was proposed by Prof. Akihiro Ametani of Doshisha University in Kyoto, Japan [Ametani, 1980]. The impedance and admit￾tance of a cable system are defined in the two matrix equations (61.13) (61.14) where (V) and (I) are vectors of the voltages and currents at a distance x along the cable and [Z] and [Y] are square matrices of the impedance and admittance. For a pipe-type cable, shown in Fig. 61.4, the impedance and admittance matrices can be written as Eqs. (61.15) and (61.16) by assuming: 1. The displacement currents and dielectric losses are negligible. 2. Each conducting medium of a cable has constant permeability. 3. The pipe thickness is greater than the penetration depth of the pipe wall. [Z] = [Zi ] + [Zp] (61.15) [Y] = jw[P]–1 (61.16) [P] = [Pi ] + [Pp] where [P] is a potential coefficient matrix. [Zi ] = single-core cable internal impedance matrix (61.17) [Zp] = pipe internal impedance matrix d V dx Z I ( ) = × –[ ] ( ) d I dx Y V ( ) = × –[ ] ( ) = ××× ××× ××× È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Z Z Z i i in 1 2 0 0 0 0 0 0 M M O M