SimulationBased Design Study Modeling a Wind Turbine Chris Gloss, Andrew Lincoln, Matthew Mustard, John Semmens, & Shereef Shehab Introduction 2 Scope To develop a model of a wind turbine that will provide its expected utility using the Dymola and Model Center software. • Goals o Develop a fully functional model of a 1.5 MW wind turbine based on industry standards o Utilize available wind data for Atlanta’s Airport o Determine the feasibility of installing a wind turbine in Atlanta • Design Variables o Rotor Radius o Tower Height Wind Turbine Modeling 3 Influence Diagram Wind Turbine Modeling 4 Blades • NACA 4412 Airfoil • Triangular planform. • Assumed to be made of fiberglass and hollow. • Moment of inertia of the blade about the base was calculated. Wind Turbine Modeling 5 Dymola Model: Overview Wind Turbine Modeling 6 Implementation of a PID Controller Wind Turbine Modeling 7 Role of Uncertainty • The central composite experiment showed which uncertain variables have the greatest effect. Wind Turbine Modeling 8 Wind Turbine Modeling Cost of Electricity ($/kWh) >1.36 1.28-1.36 1.20-1.28 1.12-1.20 1.04-1.12 0.96-1.04 0.88-0.96 0.80-0.88 0.72-0.80 0.64-0.72 0.56-0.64 0.48-0.56 0.40-0.48 0.32-0.40 0.24-0.32 0.16-0.24 0.08-0.16 0-0.08 Frequency Monte Carlo Analysis Monte Carlo Results Histogram 3000 2500 2000 1500 Frequency 1000 500 0 9 Dymola Model: Cost Wind Turbine Modeling 10 Total Turbine System Cost* AEP (kW-h) Year Rand# Years of Operation Cost of Capital Rand# Cost of Capital Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Wind Turbine Modeling 29 30 $1,770,000.00 3,950,000 1.00 24 0.55 0.13 Triangular Distributions Minimum Most Likely Maximum Years of Operation 10 20 Utility Rate $0.01 $0.07 Cost of Capital 0.01 0.15 Demand (kW-h) 1,316,667 2,633,333 Utility Rand# Utility Rate 0.55 0.66 0.99 0.29 0.33 0.64 0.55 0.98 0.85 0.40 0.05 0.52 0.10 0.55 0.93 0.95 0.55 0.68 0.08 0.34 0.18 0.07 0.12 0.21 $0.09 $0.10 $0.16 $0.07 $0.07 $0.10 $0.09 $0.16 $0.13 $0.07 $0.03 $0.09 $0.05 $0.09 $0.14 $0.15 $0.09 $0.10 $0.05 $0.07 $0.06 $0.04 $0.05 $0.06 Demand Rand# 0.87 0.39 0.70 0.78 0.51 0.34 0.99 0.52 0.92 0.18 0.37 0.79 0.84 0.32 0.61 0.28 0.91 0.09 0.61 0.45 0.66 0.66 0.87 0.04 Demand 3,058,387 2,481,096 2,869,197 2,963,799 2,640,777 2,403,537 3,171,980 2,654,834 3,104,736 2,111,968 2,453,465 2,973,503 3,027,528 2,368,422 2,773,283 2,295,123 3,091,594 1,888,677 2,774,641 2,566,567 2,829,171 2,830,131 3,056,485 1,678,043 Revenue $269,164.88 $246,009.48 $473,286.18 $194,610.79 $182,951.26 $234,506.45 $279,190.64 $422,195.86 $390,259.24 $157,331.60 $80,821.08 $255,100.96 $159,312.26 $208,321.29 $391,709.26 $334,891.83 $272,301.31 $193,291.30 $140,909.47 $178,922.10 $163,737.63 $106,234.38 $163,450.74 $101,118.69 NPV Model 30 $0.17 0.2 3,950,000 Discounted Cash Flow ($1,770,000.00) $237,293.33 $191,199.22 $324,283.78 $117,553.47 $97,425.15 $110,092.47 $115,550.23 $154,046.22 $125,532.86 $44,615.66 $20,205.20 $56,223.48 $30,954.37 $35,684.00 $59,152.20 $44,583.97 $31,958.84 $19,999.57 $12,853.33 $14,388.21 $11,608.02 $6,639.60 $9,005.98 $4,911.82 11 @Risk – Monte Carlo within Excel AEP = 3,950,000 kW-hr Left: Cost = $1,880,000 Right: Cost = $1,770,000 Wind Turbine Modeling 12 Determination of r • NPV Maximum = $3,856,616.88 • NPV Minimum = ($1,173,934.14) At what dollar amount are we indifferent between the NPV maximum and minimum? • Chosen value = $200,000 • Using a Matlab script the risk aversion coefficient is 4.2438x10-7 1 ( 4.243810 7 ) NPV u 1 e 7 4.24 10 Wind Turbine Modeling 13 Full Factorial Exploration Wind Turbine Modeling 14 Deterministic Optimization Wind Turbine Modeling 15 Optimization with Uncertainty Results Optimum Rotor Radius 43.65 m Optimum Hub Height Maximum Expected Utility Wind Turbine Modeling 85 m -$14,205.40 Statistic Expected Utility ($) Minimum -1,917,290 Maximum 950,206 Mean -14,205.40 Median 53,432.20 Lower 25% -134,740 Upper 25% 265,559 Standard Deviation 521,651 16 Thank You Does any one have any questions? Wind Turbine Modeling 17