EE 369

POWER SYSTEM ANALYSISLecture 15 Economic DispatchTom Overbye and Ross Baldick*

AnnouncementsRead Chapter 12, concentrating on sections 12.4 and 12.5.Read Chapter 7.Homework 12 is 6.43, 6.48, 6.59, 6.61, 12.19, 12.22, 12.20, 12.24, 12.26, 12.28, 12.29; due Tuesday Nov. 25.Homework 13 is 12.21, 12.25, 12.27, 7.1, 7.3, 7.4, 7.5, 7.6, 7.9, 7.12, 7.16; due Thursday, December 4.

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Retail Electricity PricesThere are many fixed and variable costs associated with power systems, which ultimately contribute to determining retail electricity prices.The major variable operating cost is associated with generation, primarily due to fuel costs:Roughly half of retail costs.*

Aside: Levelized Cost of Generation,operating costs plus paying off capital.Source: California Energy Commission: http://energyalmanac.ca.gov/electricity/levelized_costs.htmlKeep in mind these numbers involve LOTs of assumptions that can drastically affect the value, and that many technology costs are site dependent.*

Technology$/MWh (2007 Dollars) (IOU)Advanced Nuclear104Wind Class 5 67Solar Photovoltaic686Solar Concentrating434Solar Parabolic Trough281Ocean Wave (Pilot)838Small Scale Hydro118Geothermal63

Power System Economic OperationDifferent generation technologies vary in the:capital costs necessary to build the generatorfuel costs to actually produce electric power For example:nuclear and hydro have high capital costs and low operating costs. Natural gas generators have low capital costs, and higher operating costs.*

Power System Economic OperationFuel cost to generate a MWh can vary widely from technology to technology.For some types of units, such as hydro, fuel costs are zero but the limit on total available water gives it an implicit value.For thermal units it is much easier to characterize costs. We will focus on minimizing the variable operating costs (primarily fuel costs) to meet demand. *

Power System Economic OperationPower system loads are cyclical. Therefore the installed generation capacity is usually much greater than the current load. This means that there are typically many ways we could meet the current load.Since different states have different mixes of generation, we will consider how generally to minimize the variable operating costs given an arbitrary, specified portfolio of generators.*

Thermal versus Hydro GenerationThe two main types of generating units are thermal and hydro, with wind and solar rapidly growing.For hydro the fuel (water) is free but there may be many constraints on operation:fixed amounts of water available,reservoir levels must be managed and coordinated,downstream flow rates for fish and navigation.Hydro optimization is typically longer term (many months or years).We will concentrate on thermal units and some wind, looking at short-term optimization.*

Generator typesTraditionally utilities have had three broad groups of generators:Baseload units: large coal/nuclear; almost always on at max.Midload, intermediate, or cycling units: smaller coal or gas that cycle on/off daily or weekly.Peaker units: combustion turbines used only for several hours. during periods of high demand

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Block Diagram of Thermal UnitTo optimize generation costs we need to develop cost relationships between net power out and operating costs. Between 2-10% of power is used within the generating plant; this is known as the auxiliary power.*

Thermal generator Cost CurvesThermal generator costs are typically represented by one or other of the following four curvesinput/output (I/O) curvefuel-cost curveheat-rate curveincremental cost curveFor reference1 Btu (British thermal unit) = 1054 J1 MBtu = 1x106 Btu1 MBtu = 0.29 MWh*

I/O CurveThe IO curve plots fuel input (in MBtu/hr) versus net MW output. *

Fuel-cost CurveThe fuel-cost curve is the I/O curve multiplied by fuel cost. A typical cost for coal is $ 1.70/MBtu.*

Heat-rate CurvePlots the average number of MBtu/hr of fuel input needed per MW of output.Heat-rate curve is the I/O curve divided by MW.Best heat-rate for most efficient coal units is around 9.0*

Incremental (Marginal) cost CurvePlots the incremental $/MWh as a function of MW.Found by differentiating the cost curve.*

Mathematical Formulation of CostsGenerator cost curves are usually not smooth. However the curves can usually be adequately approximated using piece-wise smooth, functions.Two approximations predominate:quadratic or cubic functionspiecewise linear functionsWe'll assume a quadratic approximation:

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Coal Usage ExampleA 500 MW (net) generator is 35% efficient. It is being supplied with coal costing $1.70 per MBtu and with heat content 9000 Btu per pound. What is the coal usage in lbs/hr? What is the cost?*

Wasting Coal ExampleAssume a 100W lamp is left on by mistake for 8 hours, and that the electricity is supplied by the previous coal plant and that transmission/distribution losses are 20%. How much coal has he/she wasted?*

Incremental Cost Example*

Incremental Cost Example, cont'd*

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