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Wind Engineering Module 6.1: Cost and Weight Models

Wind Engineering Module 6.1: Cost and Weight Models. Lakshmi N. Sankar lsankar@ae.gatech.edu. Overview. In this module, we will briefly examine models for estimating the cost of energy (in cents per KWhr) that the operator needs to charge. We will look at two approaches

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Wind Engineering Module 6.1: Cost and Weight Models

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  1. Wind EngineeringModule 6.1: Cost and Weight Models Lakshmi N. Sankar lsankar@ae.gatech.edu

  2. Overview • In this module, we will briefly examine models for estimating the cost of energy (in cents per KWhr) that the operator needs to charge. • We will look at two approaches • Engineering models based on weight and cost (This module 6.1) • Models suitable for hybrid power systems (Module 6.2)

  3. Some Definitions • Debt: Money the operator borrows to finance a wind turbine project • Interest on debt: Interest charged per year by finance institution (expressed in percentage) • Equity: Funds the operator raises by issuing stocks • Return on equity: Return the share-holders expect on their investments (expressed in percentage per $1 invested).

  4. Definitions, continued.. • AWCC: Average weighted cost of capital • Example: • 20% equity • 13% return on equity • 80% loan • 6.94% interest on loan • AWCC for this example is (0.20*13+0.80*6.94) = 8.15%=0.0815 • Inflation-adjusted AWCC = (AWCC-Inflation)/(1+Inflation). • For example if inflation is 3%, the inflation adjusted AWCC is (0.0815-0.03)/(1.03) = 0.05=5% • This is sometimes called discount rate.

  5. Cost of EnergySource: NREL /TP-500-40566

  6. Definition • FCR: fixed charge rate. It includes • AWCC (payment to the bank loan and equity holders) • Depreciation • Income tax • Property tax • Insurance • Other finance fees

  7. Initial Capital Cost Sum of turbine system cost for elements listed below + balance of station costs

  8. Initial capital Cost (Continued..)

  9. Annual operating Expenses • Include land lease, operation and maintenance, cost of replacing or overhauling parts. • Expressed in dollars per KWh.

  10. Net Average Energy Production (AEP)Overview • Units are in KWh • We may view this as power production integrated over time for a whole year. • Here is a very crude description of how this is computed. • Power production depends on how hard wind blows and how often • It is assumed that the wind speed at a particular site has a Weibull distribution. • This distribution gives the probability that the wind is blowing at a given speed • With some knowledge of the wind turbine power characteristics (rated power, peak Cp, tip speed ratio at which peak Cp occurs, etc), power production at different wind speeds is estimated. • This is multiplied by the Weibull probability that wind is blowing at that speed. • Summation is done over all the wind speeds. • The result is multiplied by 365 days x 24 hours/day • Capacity Factor = AEP / (Rated Power x 365 x 24) may also be computed. • See weibull_betz5_lswt_baseline.xls for example calculations.

  11. Example: Turbine Capital CostNREL Report

  12. Blade Cost

  13. Example continued..We compare baseline and projected

  14. Other costs

  15. Example, continued.. • We next compute probability of wind blowing at a particular speed. • Weibull probability function is used. • This depends on a parameter called K factor, and wind speed at the hub.

  16. Weibull Distribution • K: Shape factor • Changing k shifts probability to the left or right. • l : Scale parameter • In our example, k= 2 • l = Wind Speed at the hub

  17. Efficiency of the Turbine • We next compute efficiency of the turbine when it operates at power other than rated power. • If field data is available, it is used. • Otherwise a simple logic is used:

  18. Hub Power • If wind velocity is less than cut-in speed, hub power is zero. • If wind velocity less than rates speed it is found from • At higher than rated speeds, rated power is used. • At greater than cutout speeds, power is zero. • The hub power, when multiplied by Weibull probability and efficiency h, gives turbine energy output at that speed.

  19. Annual Energy Production • Other losses may include electrical system losses • We divide by 4 because the wind speeds are binned (or grouped by • ¼ m/sec increments. • We will find power, for example at 2, 2.25, 2.50, and 2.75 m/sec and take • the average. • 365 x 24 is 8760

  20. Cost of Energy • Once all the information is available, we can find the cost of energy per KWh.

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