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

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) 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). 3

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. 4

5. Cost of Energy Source: NREL /TP-500-40566 5

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 6

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

8. Initial capital Cost (Continued..) 8

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

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. 10

11. Example: Turbine Capital Cost NREL Report 11

12. Blade Cost 12

13. Example continued.. We compare baseline and projected Rating (kWs)1500 BaselineProjected Component Costs $1000 Foundations49 Transportation51 Roads, civil works79 Assembly & installation51 Elect interfc/connect127 Permits, engineering33 BALANCE OF STATION COST (BOS)388 Project Uncertainty162 Turbine cost from previous slide 921 Initial capital cost (ICC)1,472 13

14. Other costs Baseline In $1000 Projected in $1000 LEVELIZED REPLACEMENT COSTS (LRC) ($10.7 per kW)16 O&M $20/kW/Yr (O&M)30 Land ($/year/turbine)55 14

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. 15

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

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: 17

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 , gives turbine energy output at that speed. 18

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 19

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