ELEC 1104 Lecture 6: OhdlidOverhead lines and underground cables Power Syyystem Layout Transmission lines Distribution lines Transmission and Distribution Lines Transmission lines are hung from steel towers through insulator strings, and they may be sin gl e circu i t o r doub l e cir cui t lin es. There are usually one or two earthed wires at the top of tower for lightning protection . Distribution lines are usually supported on iltiinsulator pins mount on wood en or concret e poles. Saggp and Span Earth wire Sag Conductor tower Minimum clearance Span Earth Wires Overhead lines are Earth wire usually protected from lightning by installing one or two overhead earth wires positioned to Line give suitable shielding conductor Shield angle over the line conductors. These earth wires are electrically connected to the earthed towers. Insulators Overhead lines Bare conductors stranded of several wires for greater flexibility and mechanical stre ngt h. Standard number of strands are in either one of the series: (a) 1, 7, 19 …….. (b) 3, 12, 27 ……. Overhead lines Conductors Material Hard drawn Hard drawn Heat treated CiCopper wire Alum in ium Alum in ium wire alloy Specific gravity 8.89 2.7 2.70 Breaking stress 23-30 10-12 19.2 (tons/sq in) Conductivity at 20oC 97.4 61 53.5 (% of ICAS) Resistivity at 20oC 1.774 2.826 3.22 (Ω-m x 10-8) Coefficient of linear 0.000017 0.000023 0.000023 expansion (oC-1) Resistivity of International Annealed Copper Standard (IACS) at 20oC = 1.7241 x 10-8 ohm-meter. Copper vs Aluminium Aluminium is liggyhter but its conductivity is lower. For equal conductivity, aluminium conductor has 1.64 times the cross section of copper, but its weight is only about half of that of the copper conductor. Aluminium has low tensile strength and high coefficient of expansion. Cost of aluminium is lower and more stable. ASCR Aluminium conductors are often reinforced by steel for greater mechanical strength and are known as ACSR (Aluminium Conductor, Steel Reinforced). In ACSR the central strands of the conductor are madflde of galvani idzed steel lf for strength hh whereas th e peripheral strands are made of aluminium for electrical conductivity . 6 aluminium 6 aluminium 1 steel 7 steel Bundle conductors Bundle conductors composed of two, three or four stranded conductors are used for ver y hi gh vol tages. Lower voltage gradient at conductor surface BttBetter h eat tdii dissipati on and dh hence b bttetter current rating. A bundle of 2 A bundle of 3 A bundle of 4 Corona A corona is a luminous ppgartial electrical discharge due to ionization of the air surrounding a conductor. The breakdown stress, i.e. the critical field intensity, of air would depend on the atmospheric conditi ons. For a given voltage, the maximum field intensity occurs attht the con duc tor sur face an ddd decreases as the conductor radius is increased. Corona Corona There is a certain definite loss associated with corona. The ionization current associated with corona flows in pulses only during the voltage peaks and is therefore rich in harmonics. Ozone is produced in corona and would cause deterioration to any organic materials nearby. Audible noise is produced in corona and hence is a source of noise pollution. Electrical Parameters These are distributed parameters by nature: » Series resistance r Ωm » Series inductance l H/m » Shunt capacitance c F/m » Shunt conductance g S/m For overhead lines, shunt conductance represents leakage through insulators or corona loss and is usuallyyg ignored. Transmission Line Model Transmission line as a two-port VS = sending end voltage IS = sending end current VR = receiiiving end volt age IR = receiving end current IS IR VS Line VR Transmission parameters VS = AVR + BIR IS = CVR + DIR IS IR VS A, B, C, D VR Line Model Nominal π representation (Medium line) Z = R + jX IS I IR VS YC/2 YC/2 VR Line Model I = IR + VRY/2 VS = VR + ZI = (()1+ZY/2)VR + ZIR IS = I + VSY/2 = Y(1+ZY/4)VR + (1+ZY/2)IR Hence A = D = (1+ZY/2), B = Z, C = Y(()1+ZY/4) Line Model Nominal T representation (Medium line) (R + jX)/2 (R + jX)/2 IS V IR VS YC VR Line Model V = VR + IR Z/2 I = YV = YVR + IR YZ/2 IS = IR +I+ I = YVR +(1+YZ/2)I+ (1+YZ/2)IR VS = V + ISZ/2 = (1+YZ/2)VR + Z(1+YZ/4)IR Hence A = D = (1+ZY/2), B = Y(1+ZY/4), CYC = Y. Line Model Series impedance (Short line) » VS = VR + ZIR;IS = IR R + jX IS IR VS VR Example Given a 3-phase, 132 kV line 350 km long with parameters r = 0. 108 ohm/km; l = 1. 37 mH/km; g = 0 siemens/km; c = 0.0085 μF/km. Load: 50 MVA at 0.8 power factor lagging. To determine sending-end voltage, current and power factor. Example Z = ((j0.108+j2π×50×1.37×10-3) × 350 =155.27∠75.91o Ω Y = (j2π×50×0.0085×10-6) × 350 = 934.6 ×10-6∠90o Siemens VR = 132/√3 = 76.21 kV (phase) 3 IR = 50×10 /√3×132 = 218. 7 A θ = cos-1 0.8 = 36.87o (lagging) Example Using short line representation o IS = IR = 218.7∠-36.87 A VS = VR + ZIR = 76.21+155.27∠75.91o × 0.2187∠-36.87o kV = 76.21+33.96 ∠39.04o = 104.8 ∠11.78o kV Input power factor = cos (11.78o + 36.87o ) = 0.66 (lagging) Example Using nominal -π representation A = D =1+YZ/2 = 1 + 0. 0726∠165. 91o = 0.9297+j0.0176 = 0.9298 ∠1.08o B = Z = 155 .27 ∠75. 91o Ω C = Y(1+YZ/4) = j 934 .6 ×10-6(1 + 0. 0263∠165. 91o) = 910.8 ×10-6 ∠90.38o Example VS = AVR + BIR = 0.9298 ∠1.08o × 76.21 ∠0o + 155.27∠75.91o × 0.2187∠-36.87o kV = 99. 95 ∠13. 15o kV IS = CVR + DIR = 910. 8 ×10-6 ∠90. 38o × 76210 ∠0o + 0.9298 ∠1.08o × 218.7∠-36.87o = 171. 78∠-16.75 o A Input power factor = cos (13. 15o + 16.75o )086(li)) = 0.867 (lagging) Underground Cables Cables contain one or more conductors within a protective sheath. The conductors are separated from each other and from the sheath by solid insulating material. The protective sheath is an impervious coveriiltidillfing over insulation and is usually of lead. Its main function is to prevent the ingress of moisture to the ins ulation . Underground Cables They may be single-core cables with one cable per phase or three-core cables with one co mmo n lead s heat h. In single-core cables the stranded conductor is always of round cross-section. In multi-core cables so-called sector shaped stran ds are a lso used t o b ett er utili ze th e space within the sheath. Cable Insulations Common insulating materials used in cables are: Oil-impregnated paper Vulcanised rubber synthetic polymeric dielectrics such as » polyethylene (PE), » propylene (PP), » polyvinyl chloride (PVC) Solid Cables Single Core Three core Hessian fillers servings Lead sheaths Paper insulation Stranded Fabraic conductors Belt tapes insulation Solid Cables Single Conductor, paper -insulated power cable. Solid Cables Three-conductor, belted, compact -sector, paper-insulated cable. Solid Cables Three-conductor, shielded (H -type), compact-sector , paper-insulated cable. Solid Cables Three-conductor solid-type cable with protective steel armour. Cable Parameters Cables have the same distributed electrical parameters as the overhead lines but » Capacitance is much higher due to closer proximity of the conductors. » Shu nt loss i s n o l on ger n egli gi bl e. th e sh unt loss in the dielectric include – leakage – dielectric hysteresis Dielectric loss angle The dielectric loss is usually measured by the dielectric power factor dielectric p .f . = cos φ I The dielectric loss angle is δ = 90 – power flfactor angle φ δ Since δ is small φ δ≈sin δ = cos φ = dielectric p.f. V Cable Ratings The current rating of a cable is limited by the maximum permissible temperature of its insulat io ns. Depending on the expected loading, we have the following ratings: » Continuous rating » Short time rating » Cyclic rating Cable Rating The steady loading that results in a final temperature equal to the maximum permissible value is know n as t he cont inuous rating. temp T current max T Continuous rating I time Cable Rating If the loading is applied for a short duration only, say 1 hour, then the loading without the maximu m te mpe ratu re be ing e xceeded is known as the (1 hour) short-time rating. temp T current max Short-time rating I T time Cable Rating For a given cyclic pattern, the maximum load that can be supplied without the maximum tempe ratu re be ing e xceeded is know n as t he cyclic rating. temp T current max T cyclic rating I time Thermal equation Heat Balance Equation Heat generated = heat dissipated +h+ hea t ab sorb ed . Heat generated depends on power loss P in the cable (I2RlR loss an ddild dielect tiric l oss) Heat dissipated depends on the surface area, method of cooling and temperature difference . Heat absorbed results in temperature increase depending on the specific heat . Thermal equation Let P = power loss in cable λ = emissivity (watt/m 2/oC) A = surface area for heat dissipation (m2) θ = temperature rise above ambient ( oC) M = mass (kg) o Cp = specific heat (joule/kg/ C) Thermal equation Then with temperature rise d θ in the time period dt, Heat generated =Pdt= P dt Heat dissipated = λAθ dt Heat absorbed = MCp dθ Hence MCp dθ + λAθ dt = P dt Thermal equation This can be written in the form τ(dθ/dt) + θ = θ∞ where τ = MCp/λA is the heating time constant.