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ECE4762011_Lect16

# ECE4762011_Lect16 - ECE 476 POWER SYSTEM ANALYSIS Lecture...

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Lecture 16 Economic Dispatch Professor Tom Overbye Department of Electrical and Computer Engineering ECE 476 POWER SYSTEM ANALYSIS

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2 Announcements Be reading Chapter 12.4 and 12.5 for lectures 15 and 16 HW 6 is 6.50, 6.52, 6.59, 12.20; due October 20 in class (for Problem 6.52 the case new is Example6_52) Office hours are changed for today only to 2 to 3 pm.
3 Generator Cost Curves Generator costs are typically represented by up to four different curves input/output (I/O) curve fuel-cost curve heat-rate curve incremental cost curve For reference - 1 Btu (British thermal unit) = 1054 J - 1 MBtu = 1x10 6 Btu - 1 MBtu = 0.293 MWh - 3.41 Mbtu = 1 MWh

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4 I/O Curve The IO curve plots fuel input (in MBtu/hr) versus net MW output.
5 Fuel-cost Curve The fuel-cost curve is the I/O curve scaled by fuel cost. Coal prices vary; around \$1/Mbtu to \$2/Mbtu

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6 Heat-rate Curve Plots the average number of MBtu/hr of fuel input needed per MW of output. Heat-rate curve is the I/O curve scaled by MW Best for most efficient coal units is around 9.0
7 Incremental (Marginal) cost Curve Plots the incremental \$/MWh as a function of MW. Found by differentiating the cost curve

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8 Mathematical Formulation of Costs Generator cost curves are usually not smooth. However the curves can usually be adequately approximated using piece-wise smooth, functions. Two representations predominate quadratic or cubic functions piecewise linear functions In 476 we'll assume a quadratic presentation 2 ( ) \$/hr (fuel-cost) ( ) ( ) 2 \$/MWh i Gi i Gi Gi i Gi i Gi Gi Gi C P P P dC P IC P P dP α β γ = + + = = +
9 Coal Four Types of Coal Anthracite (15,000 Btu/lb), Eastern Pennsylvania; used mostly for heating because of its high value and cost Bituminous (10,500 to 15,000 Btu/lb), most plentiful in US, used extensively in electric power industry; mined in Eastern US including Southern Illinois. Subbitunminous (8300 to 11,500 Btu/lb), most plentiful in Western US (Power River Basin in Wyoming); used in electric power industry Lignite or brown coal (4000 to 8300 Btu/lb), used in electric power industry Coals differ in impurities such as sulfur content

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Coal Prices Source: US EIA At \$50 per ton and 11,800 Btu/lb, Illinois coal costs \$2.12/Mbtu. Transportation by rail is around \$0.03/ton/mile

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ECE4762011_Lect16 - ECE 476 POWER SYSTEM ANALYSIS Lecture...

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