Economics of Generating Stations. - Definition - Factors affecting cost of generation - Methods of determining depreciation

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Andrew Harrell
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1 Ecoomics of Geeratig Statios - Defiitio - Factors affectig cost of geeratio - Methods of determiig depreciatio

2 Ecoomics of power geeratig statio is the art of determiig the per-uit cost of electric eergy productio; (Cost of oe kwh) Mai factors affectig cost of geeratio: - Cost of lad - Cost of equipmet - Iterest o capital ivestmet - Depreciatio of equipmet - Cost of fuel, lubricats ad maiteace

3 Cost of geeratio: Fixed cost: Idepedet o maximum demad or geerated uits; icludes Cost of cetral orgaizatio, iterest o capital lad cost & high officials salaries Semi-fixed cost: directly proportioal to maximum demad but idepedet o geerated uits; related to aual iterest ad depreciatio o capital ivestmet of buildig ad equipmet, ad salaries of maagemet ad clerical staff. Ruig cost: depedet oly o umber of geerated uits; icludes cost of fuel, lubricats, maiteace ad repair Total aual cost of Eergy A + B Maximum demad + C Geerated kwh per aum or approximately Total aual cost of Eergy A \ Maximum demad + B \ Geerated kwh per aum

4 Depreciatio of equipmet: Depreciatio is the decrease i the value of the power plat equipmet ad buildig due to costat use. Power statio has a useful life ragig from fifty to sixty years. From the time the power statio is istalled, its equipmet steadily deteriorates due to wear ad tear so that there is a gradual reductio i the value of the plat. The reductio every year is kow as aual depreciatio. Due to depreciatio, the plat has to be replaced after its useful life. Therefore, suitable amout must be set aside every year so that by the time the plat retires, the collected amout stadig for depreciatio equals the cost of replacemet. Accordigly, the cost of productio must iclude aual depreciatio charges. Depreciatio may be determied by either of the followig methods: Straight lie method Dimiishig value method Sikig fud method

5 Straight lie method A costat depreciatio charge is made every year o the basis of total depreciatio ad the useful life of the property. Totaldepreciatio Aualdepreciatio charge Usefullife Iitialor capitalcost of equipmet (P)- Scrap(salvage)value(S) Usefullifei years() Disadvatages: -The assumptio of costat depreciatio charge every year is ot correct. - Does t accout for the iterest which may be draw durig accumulatio.

Dimiishig value method A costat depreciatio rate (χ) is applied every year to the dimiishig value of plat as a basis of determiig this year s depreciatio ad the relevat depreciatio charge.

6 Dimiishig value method A costat depreciatio rate (χ) is applied every year to the dimiishig value of plat as a basis of determiig this year s depreciatio ad the relevat depreciatio charge. Equipmet valueafter a Equipmet valueafter st year Equipmet valueafter d year Equipmet valueafter years Depreciatio rate( Disadvatages: year x) -Low depreciatio charges i late years where maiteace ad repair charges are heavy - Does t accout for the iterest which may be draw durig accumulatio. S P Equipmet valueat start of P( P( x P( P-Px P( Scrap value( S) year- Aualdepreciatio P(

7 Sikig fud method A costat depreciatio charge (q) is made every year o the basis of the cost of replacemet (P-S) ad a assumed costat aual iterest rate (R). Amout q deposited at ed of Amout q deposited at ed of Amout q deposited at ed of st year becomes after ( -) years q( year ( -) becomes after last years q( d year becomes after ( -) years q( Total fud collected with iterest after years q {( + ( ( } Total fud collected with iterest after years q {( } R P S Sikig fud or depreciatio charge q ( R ( P S )

8 Meetig the Load (revisited as example of ecoomic operatio): Itercoectig two power statios(, ) the more efficiet plat (with lower ruig cost) is assiged the base load, while the less efficiet oe (with higher ruig cost) is assiged the peak load. Miimum cost of geeratio for a load supplied by plats χ peak load o statio y kwh geerated by statio P Peak load o system Q Total umber of uits to be supplied Area of load duratio curve Aual cost of A + B χ + C y Load kw Statio area y kwh Statio area(q-y) kwh χ P Aual cost of A + B (P - χ) + C (Q y) Total hours

9 Total cost Cost +Cost A + B χ + C y + A + B (P - χ) + C (Q y) For miimum operatig cost: d( Cost) dx & Q h dy dx B C Zero hours of B C dy dx B C B C operatio of peak statio ( h) - Kowig hours of operatio of peak load statio, its capacity χ ad uits geerated y are foud from curve. - Substitutig capacity χ ad uits geerated y i total cost equatio, the miimum cost is determied

Economic Analysis and Optimization

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