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Stochastic (Probabilistic) Wind Turbine Simulator for Annual Power Output and Capacity Factor

February 4th, 2015 Posted in wind energy and power

Stochastic (Probabilistic) Wind Turbine Simulator for Annual Power Output and Capacity Factor

 Wind Turbine Generator (WTG) is the current darling of the renewable energy power generation industry.

It is clean, generally available, and cost-effective. It’s power output, however, is very variable, ever changing by the hour with time.

Now with the instantaneous wind speed as a function of the average speed +/- the positive and negative deviation multiplied by a random fraction, the probable wind speed and thus the power output can be simulated, and when aggregated in 24 x 365 hours in a year, the annual energy output and annual capacity factor is determined.

And using statistical analysis, the expected value (mean), standard error, median, standard deviation, variance, skewness and Kurtosis are calculated for both the annual energy output and annual capacity factor.

 

Turbine Model and kW rating GE900 900 GE1.5 S 1500 GE1.5 SL 1500
  MWH % CF MWH % CF MWH % CF
1000 2,108 26.74 3,878 29.51 4,408 33.55
Mean 2,126 26.96 3,911 29.76 4,446 33.83
Standard error 0 0.00 0 0.00 0 0.00
Median 2,126 26.97 3,911 29.77 4,446 33.83
Standard deviation 8 0.10 14 0.11 13 0.10
Variance 65 0.01 197 0.01 178 0.01
Skewness 0.0079 0.0079 0.0105 0.0105 0.0123 0.0123
Kurtosis 2.7407 2.7407 2.7155 2.7155 2.7468 2.7468
Expected value = 2,126 26.96 3,911 29.76 4,446 33.83
The standard deviation*1.96 = 16 0.20 27 0.21 26 0.20
95% of all outcomes, max = 2,142 27.16 3,938 29.97 4,472 34.03
95% of all outcomes, min = 2,110 26.76 3,883 29.55 4,420 33.63

 

To enable your technical team to optimize the selection of the equipment manufacturer (cost per kW, fixed and variable O&M, WTG power curve) and site selection (wind velocity profile given location and wind mast elevation), the following sets of excel models would be most helpful in your technical and economic analysis:

I suggest the following options:

 1) Option 1 – CDM WIND MODEL (project finance model with clean development mechanism carbon credits and financial analysis without taxes and using 100% equity, 0% debt)

 2) Option 2 – ADV WIND MODEL (project finance model with advanced features)

 3) Option 3 – Add 50% to the above Option 1 or Option 2 if you want to include MONTE CARLO SIMULATION for equity and project returns (IRR, NPV and PAYBACK), net income after tax discounted at pre-tax WACC, pre-tax WACC, and electricity tariff (feed-in-tariff). A histogram may also be prepared by the MONTE CARLO simulation.

 4) Option 4 – WIND SIMULATOR (hourly simulation of wind speed for a given location using the wind velocity profile from wind resource tools such as 3-TIER or NREL, power curves to calculate wind turbine power output, annual MWH generation, annual capacity factor CF).

Alternatively, a 15-minute simulation may be prepared if the local transmission/grid operator would require a grid impact study (system impact study) to identify the system/grid requirements to be able to handle the variable power output of the wind turbines.

 5) Option 5 – Add 50% to the above Option 4 if you want to include MONTE CARLO SIMULATION of the annual MWH output and average capacity factor CF, which is then used in the project finance model for wind (CDM or ADV model).  A histogram may also be prepared by the MONTE CARLO simulation.

 6) Option 6 – Wind Energy Resource Assessment Tool_Anemometer Measurement (allows you to enter hourly anemometer readings of wind speed vs. time, and use power curves to calculate wind turbine power output, annual MWH generation, and capacity factor CF).

Using the average wind speed as correction factor, hourly wind speed readings of a similar location may be synthesized if a reference location with complete data is known and may be used to extrapolate the anemometer readings of another location with limited wind data with a known average speed.

7) Option 7 – Wind Turbine Price List (the overnight capital cost of a number of known wind turbines to get a feel of the relative costs of the various wind turbine models, and given the power curves, helps you optimize the selection of model size (MW output) and equipment manufacturer (turbine model).

8) Option 8 – Wind Turbine Power Curves with customized MONTE CARLO SIMULATION of wind speed, annual power output and annual capacity factor for the following WTG models:

  • Bergey
  • Bonus
  • Carter
  • Dewind
  • Fuhrlaender
  • Gamesa Eolica
  • GE Wind
  • Jacobs
  • Jacobs-additions
  • Lagerwey
  • NEG Micon
  • Nordex
  • Norwin
  • Repower
  • Suzlon
  • TMA
  • Turbowinds Inland
  • Vestas

For more information and list of other models, please email

energydataexpert@gmail.com

 

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