Wind Engineering: Estimating Energy and Capital Costs, Slides of Environmental Law and Policy

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Wind Engineering

Module 6.1: Cost and Weight Models

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)

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 (0.2013+0.806.94) =

• 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.

Cost of Energy

Source: NREL /TP-500-

Initial Capital Cost

Sum of turbine system cost for elements listed below + balance of station costs

Initial capital Cost (Continued..)

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.

Example: Turbine Capital Cost

Baseline Projected

 - Rating (kWs) NREL Report - Component Costs $1000 Costs $ Component Component 

• Rotor
  • Blades
  • Hub
  • Pitch mchnsm & bearings
• Drive train,nacelle
  • Low speed shaft
  • Bearings
  • Gearbox
  • Mech brake, HS cpling etc
  • Generator
  • Variable spd electronics
  • Yaw drive & bearing
  • Main frame
  • Electrical connections
  • Hydraulic system
  • Nacelle cover
• Control, safety system
• Tower - TURBINE CAPITAL COST (TCC)

Example continued..

We compare baseline and projected

Rating (kWs) 1500 1500

Baseline Projected

Component Component

Component Costs $1000 Costs $

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,

Other costs

Baseline

In $

Projected

in

LEVELIZED REPLACEMENT COSTS (LRC)

($10.7 per kW) 16 16

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

Land ($/year/turbine) 5 5

Weibull Distribution

• K: Shape factor

• Changing k shifts

probability to the

left or right.

• λ : Scale parameter

• In our example, k= 2

• λ = Wind Speed at

the hub

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.

Efficiency

P/P(rated)

Annual Energy Production

4

TurbineEnergycorrectedforotherlosses* 8760 *Availability

• 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

Cost of Energy

• Once all the

information is

available, we can

find the cost of

energy per KWh.