Wind EngineeringModule 6.1: Cost and Weight Models

Lakshmi N. Sankarlsankar@ae.gatech.edu

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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)

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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).

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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.

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Cost of EnergySource: NREL /TP-500-40566

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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

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Initial Capital CostSum of turbine system cost for elements listed below + balance of station costs

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Initial capital Cost (Continued..)

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Annual operating Expenses

• Include land lease, operation and maintenance, cost of replacing or overhauling parts.

• Expressed in dollars per KWh.

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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.

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Example: Turbine Capital CostNREL Report

Rating (kWs) 1500 1500

Baseline ProjectedComponent Component

Component Costs $1000 Costs $1000

Rotor 248 248 Blades 148 148 Hub 64 64 Pitch mchnsm & bearings 36 36Drive train,nacelle 563 563

Low speed shaft 20 20 Bearings 12 12 Gearbox 151 151 Mech brake, HS cpling etc 3 3 Generator 98 98 Variable spd electronics 101 101 Yaw drive & bearing 12 12 Main frame 64 64 Electrical connections 60 60 Hydraulic system 7 7 Nacelle cover 36 36

Control, safety system 10 10Tower 101 101

TURBINE CAPITAL COST (TCC) 921 921

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Blade Cost

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Example continued..We compare baseline and projected

Rating (kWs) 1500 1500

Baseline Projected

Component Component

Component Costs $1000 Costs $1000

     

Foundations 49 49

Transportation 51 51

Roads, civil works 79 79

Assembly & installation 51 51

Elect interfc/connect 127 127

Permits, engineering 33 33

BALANCE OF STATION COST (BOS) 388 388

   

Project Uncertainty 162 162

Turbine cost from previous slide   921 921 

Initial capital cost (ICC) 1,472 1,472

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Other costs

 

BaselineIn $1000 

Projectedin

$1000 

LEVELIZED REPLACEMENT COSTS (LRC) ($10.7 per kW) 16 16

O&M $20/kW/Yr (O&M) 30 30

Land ($/year/turbine) 5 5

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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.

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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

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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: 0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 0.2 0.4 0.6 0.8 1 1.2

Eff

icie

ncy

P/P(rated)

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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.

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Annual Energy Production

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tyAvailabili * 8760 * lossesother for correctedEnergy Turbine

• 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

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Cost of Energy

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

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