ECE4762011_Lect7

# ECE4762011_Lect7 - ECE 476 POWER SYSTEM ANALYSIS Lecture7...

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Lecture7 Development of Transmission Line Models Professor Tom Overbye Department of Electrical and Computer Engineering ECE 476 POWER SYSTEM ANALYSIS

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2 Announcements For next two lectures read Chapter 5. HW 2 is 4.10 (positive sequence is the same here as per phase), 4.18, 4.19, 4.23. Use Table A.4 values to determine the Geometric Mean Radius of the wires (i.e., the ninth column). Due September 15 in class. “Energy Tour” opportunity on Oct 1 from 9am to 9pm. Visit a coal power plant, a coal mine, a wind farm and a bio-diesel processing plant. Sponsored by Students for Environmental Concerns. Cost isn’t finalized, but should be between \$10 and \$20. Contact Rebecca Marcotte at for more information or to sign up.
3 SDGE Transmission Grid (From CALISO 2009 Transmission Plan)

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4 Line Conductors Typical transmission lines use multi-strand conductors ACSR (aluminum conductor steel reinforced) conductors are most common. A typical Al. to St. ratio is about 4 to 1.
5 Line Conductors, cont’d Total conductor area is given in circular mils. One circular mil is the area of a circle with a diameter of 0.001 = π × 0.0005 2 square inches Example: what is the the area of a solid, 1” diameter circular wire? Answer: 1000 kcmil (kilo circular mils) Because conductors are stranded, the equivalent radius must be provided by the manufacturer. In tables this value is known as the GMR and is usually expressed in feet.

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6 Line Resistance -8 -8 Line resistance per unit length is given by R = where is the resistivity A Resistivity of Copper = 1.68 10 Ω-m Resistivity of Aluminum = 2.65 10 Ω-m Example: What is the resistance in Ω / mile of a ρ × × -8 2 1" diameter solid aluminum wire (at dc)? 2.65 10 Ω-m 1609 0.084 0.0127m m R mile mile π × = = ×
7 Line Resistance, cont’d Because ac current tends to flow towards the surface of a conductor, the resistance of a line at 60 Hz is slightly higher than at dc. Resistivity and hence line resistance increase as conductor temperature increases (changes is about 8% between 25 ° C and 50 ° C) Because ACSR conductors are stranded, actual resistance, inductance and capacitance needs to be determined from tables.

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8 Variation in Line Resistance Example
9 Review of Electric Fields e A 2 To develop a model for line capacitance we first need to review some electric field concepts. Gauss's law: d = q (integrate over closed surface) where = electric flux density, coulombs/m d = differential D a D a g 2 e area da, with normal to surface A = total closed surface area, m q = total charge in coulombs enclosed

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10 Gauss’s Law Example Similar to Ampere’s Circuital law, Gauss’s Law is most useful for cases with symmetry. Example: Calculate
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ECE4762011_Lect7 - ECE 476 POWER SYSTEM ANALYSIS Lecture7...

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