Power Plant Selection & Economics

Mechanical Engineering DepartmentME 332 Operation and Management of Power Plants

Prof. Osama A El Masry

Power Plant Selection & Economics

Prof. Osama El Masry

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Powerplant SelectionThe following must be taken into consideration:Site Selection: Land price-Close to consumer center-Load Characteristics: Daily, Yearly….Type of Generation and Generation UnitsSize and Number of Units:

◦ Similar Units for less parts◦ Large units have less cost/unit energy◦ Stand-by units should have rating equal to the highest

operating unit◦ Load must be equally distributed between units

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Powerplant SelectionFuel Type, Price and availabilityCooling media and alternativesLabor availability, Experience and Salaries Maintenance facilities and costFuture extension due to increase in population or

activitiesSafety and Environmental measures

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Power System Economic OperationPower System Economic Operation

Power 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.

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Power System Economic OperationPower System Economic Operation

Generation costs can vary widely, with different technologies varying in the:– Investment Cost necessary to build the generator– Running (fuel) 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.

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Cost Calculation

CBA 1

CBA 1

CBA 1

A= Annually calculated Total CostB= Capital Costτ= Life time for the units or the plantC= Running Cost

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Cost Calculation

CBA 1

CBA 1

CBA 1

(B)Capital CostB=B1-B2+B3

B1= B1’+ B1’’+ B1’’’+ B1’’’’+…

B1’= Study, analysis and Design costs

B1’’=Units price delivered at the site

B1’’’=Cost of erection and commissioning

B1’’’’=Civil, Mechanical and electrical work costs

B2=Price for Scrape

B3=Cost for removing scrape7



Cost Calculation

CBA 1

CBA 1

CBA 1

(C) Running Cost C=C1+C2+C3+C4+..C1= land and building rents and maintenanceC2= SalariesC3= City power, water and sewageC4= Taxes and InsuranceC5== Fuel costFuel cost, C6= Spare Parts and consumablesC7= Equipments clothes….

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Time Life Span for Different Components Item Life span

YearsAnnual %

Buildings 50 2Boilers(fire tubes) 10-15 6.5-10

Boilers(water tubes) 20 5Boilers(auxiliaries) 20 5

Condensers 20 5Air preheaters 15 6.5Water heaters 30 3.3

Electrical motors 12-20 5-8.5Air compressors 20-25 4-5

Water pumps 15-20 3.3-5Pipes 15-20 3.3-5

Steam turbines 20-25 4-5Generator 25 4

Feed water heaters 30 3.3Gas Turbines 20 5Diesel Units 25 4

Fuel handling 25-30 3.3-4Electrical transformers 15-20 3.3-5

Electrical switches 15-30 3.3-6.5Electrical wires 15 6.5

Stacks 30-50 2-3.39



COST OF POWER GENERATION SYSTEMSIn order to perform feasibility study or an economic analysis, there is need to know the cost for constructing and operating a system

1.Capital (Investment) CostInvestment cost is also called capital cost or initial cost or first cost. It consists of equipment cost, installation cost, and soft costs. (called also project or engineering and management.)

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Investment Cost

Equipment costs

Installation costs

“Soft” (or project) costs

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Equipment costs◦ Prime mover and generator set. ◦ Heat recovery and rejection system◦ Supplementary firing◦ Exhaust gas system and stack.◦ Fuel supply◦ Control board. ◦ Interconnection with the electric utility◦ Piping. ◦ Ventilation and combustion air systems◦ Shipping charges◦ Taxes

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Installation costs◦ Installation permits,◦ Land acquisition and preparation,◦ Building construction,◦ Installation of equipment,◦ Documentation and as-built drawings

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“Soft” (or project) costs◦ Architectural / engineering design fees.◦ Construction management fees.◦ Environmental studies and permitting costs.◦ Special consultants and inspectors.◦ Legal fees.◦ Letters of credit.

◦ Training.

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Type of cost % of total

Generation unit including heat recovery equipment 55

Instrumentation, regulation and control 15

Auxiliary systems 5

Connection to grid 5

Civil work and/or acoustic enclosure 10

Installation and commissioning 5

Project costs 5

Total 100

Table 1: Breakdown of investment costs for small-scale power station

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2- Running (fuel) costsOperating Costs

These costs include the costs of labor, but they are dominated by the fuel costs necessary to produce electrical energy (MW) from the plant.

The given values reflect only the cost of fuel input to a generation plant; they do not reflect the actual costs of producing electrical energy as output from the plant because substantial losses occur during production. Some power plants have overall efficiencies as low as 35%; in addition, the plant efficiency varies as a function of the generation level Pg. We illustrate this point in what follows. 16



We represent plant efficiency by η. Then η=energy output/energy input. We obtain η as a function of Pg by measuring the energy output of the plant in MWhrs and the energy input to the plant in MBTU.

We could get the energy output by using a wattmeter to obtain Pg over a given period of time, say an hour, and we could get the energy input by measuring the coal tonnage used during the hour and then multiply by the coal energy content in MBTU/ton.

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18



Natural Gas Prices: 1990’s to 2008Natural Gas Prices: 1990’s to 2008

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Egypt (Arab Republic)Proved recoverable reserves

(crude oil and NGLs, million tonnes) 495

Production (crude oil and NGLs, million tonnes, 2005) 33.9

R/P ratio (years) 14.7Year of first commercial

production 1911

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Thermal versus Hydro Generation

The two main types of generating units are thermal and hydro, with wind 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.

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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

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These costs include the costs of labor, but they are dominated by the fuel costs necessary to produce electrical energy (MW) from the plant.

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Generator Cost Curves

Generator costs are typically represented by one or other of the following four curves– input/output (I/O) curve– fuel-cost curve– heat-rate curve– incremental cost curve

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

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Fuel-cost CurveThe fuel-cost curve is the I/O curve multiplied by fuel cost.

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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 divided by MW.

Most Efficient Generation Level

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For the heat rate curve the y-axis is inverted to yield MBTU/MWhrs, which is proportional to

1/η

The curve indicates that efficiency is poor for low generation levels and increases with generation, but at some optimum level it

begins to diminish. Most power plants are designed so that the optimum level is close to

the rated output.

Heat-rate Curve

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Example 1

A 500 MW (net) generator is 35% efficient. It is being supplied with coal costing $2.325 per MJ and with heat content 27000kJ/kg. What is the coal usage in kg/hr? What is the cost?

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Example 2

Assume 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 irreplaceable coal has he/she wasted?

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Incremental (Marginal) cost Curve

The cost per hour increases with generation, a feature that one would expect since higher generation levels require greater fuel intake per hour.

The desired $/MWHR characteristic, called the incremental cost curve for the plant, is obtained by differentiating the plot dC/dPg.

Plot of cost per hr (C) vs. generation (Pg)

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

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Mathematical Formulation of CostsMathematical Formulation of Costs

Generator 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 functions– piecewise linear functions

We'll assume a quadratic approximation:

2( ) $/hr (fuel-cost)

( )( ) 2 $/MWh

i Gi i Gi Gi

i Gii Gi Gi

Gi

C P P P

dC PIC P P

dP

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Incremental Cost Example

21 1 1 1

22 2 2 2

1 11 1 1

1

2 22 2 2

2

For a two generator system assume

( ) 1000 20 0.01 $/hr

( ) 400 15 0.03 $/hr

Then

( )( ) 20 0.02 $/MWh

( )( ) 15 0.06 $/MWh

G G G

G G G

GG G

G

GG G

G

C P P P

C P P P

dC PIC P P

dP

dC PIC P P

dP

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Incremental Cost Example

1 2

21

22

1

2

If 250 MW and 150 MW Then

(250) 1000 20 250 0.01 250 $ 6625/hr

(150) 400 15 150 0.03 150 $6025/hr

Then

(250) 20 0.02 250 $ 25/MWh

(150) 15 0.06 150 $ 24/MWh

G GP P

C

C

IC

IC

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Example 3

An 100 MW coal-fired plant uses a type of coal having an energy content of 28,000 kJ/kg. The coal cost is $1.5/MJ. Typical coal usage corresponding to the daily loading schedule for the plant is as follows:

Time of Day

Electric Output (MW)

Coal Used (tons)

12:00am-6:00am

40 105.0

6:00am-10:00am

70 94.5

10:00am-4:00pm

80 156.0

4:00pm-12:00am

100 270.0

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For each of the four load levels, find (a) the efficiency η, (b) the heat rate H (kJ/kWhr) (c) the cost per hour, C ($/hr). Also, for the loading

levels of 40, 70, and 80 MW, use a piecewise linear plot of F vs P to obtain incremental cost IC as a function of unit loading P.

Then plot incremental cost as a function of unit loading.

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SolutionLet T be the number of hours the plant is producing P MW

while using y tons of coal. We need to compute the total energy out of the plant and divide by the total energy into the plant.

(a)

Note that the above expression for efficiency is dimensionless

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(b)The heat rate is the amount of kJ used in the amount of time T divided by the number of kW.hrs output in the amount of time T.

or

Time of Day Electric

Output (MW)Coal Used

(tons)Efficiency

(η)Heat rate

MJ/MW.Hr(H)

12:00am-6:00am

40 105.0 29.4% 12.245

6:00am-10:00am

70 94.5 38.1% 9.448

10:00am-4:00pm

80 156.0 39.6% 9.091

4:00pm-12:00am

100 270.0 38.0% 9.474

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(c) C = RK where R is the rate at which the plant uses fuel and K is fuel cost in $/MJ. Note from units of P and H that

R = PH C = PHK where H is a function of P.

Application of these expressions for each load level yields the following results:

THrs

Electric Output (P)

MW

Heat rate (H)

MJ/MW.Hr

Fuel price (C)

($/hr)6 40 12.245 7354 70 9.448 9926 80 9.091 10918 100 9.474 1421

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To obtain incremental cost , we can plot C vs. P and then get an approximation on the derivative by assuming a piecewise linear model as shown in the following figure

Calculation of Incremental Cost41



The incremental costs are plotted as a function of loading

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The quadratic function is

C(P)=0.0903P2-2.9553P+604.85

The plot obtained from Matlab

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Clearly, the curve is inaccurate for very low values of power (note it is above $605/hr at P=0 and decreases to about $590/hr at P=10). We can get the incremental cost curve by differentiating C(P):

IC(P)=0.1806P-2.9553

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Power Plant Selection & Economics

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