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Problem 2 Consulting company OptiWind is developing a wind farm layout for a wind developer. Knowing that, for any one year, the average wind speed

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Problem 2 Consulting company OptiWind is developing a wind farm layout for a wind developer. Knowing that, for any one year, the average wind speed for the site of consideration is 15 m/s, the standard air density is 1.225 kg/m3, the wake decay constant k is 0.1 and the thrust coefficient is 0.85. Two wind turbine sizes and two layout options are considered, as follows. Wind turbine A1: rotor diameter is 70m, power coefficient is 0.28 Wind turbine A2: rotor diameter is 60m, power coefficient is 0.35 Option 1: Front row: 12 WT of size A1, Second row: 560m behind the first one, 12 WT of size A1. Option 2: Front row: 17 WT of size A2; Second row: 500 m behind the first one, 12 WT of size A1. 1) What are the power production for each row and the total power and energy production for both options? 2) If the developer's income from the sale of energy is $35/MWh, what is the income for a year for each of the options? 3) Based on the income, which option should the developer pursue? Present the results in Table 1 Table 1 # turbines Ux/U. Wind WT power, Total P, W Total energy, speed, m/s w MWh Option 1 Row 1 Row 2 Row 1 Row 2 Problem 2 Consulting company OptiWind is developing a wind farm layout for a wind developer. Knowing that, for any one year, the average wind speed for the site of consideration is 15 m/s, the standard air density is 1.225 kg/m3, the wake decay constant k is 0.1 and the thrust coefficient is 0.85. Two wind turbine sizes and two layout options are considered, as follows. Wind turbine A1: rotor diameter is 70m, power coefficient is 0.28 Wind turbine A2: rotor diameter is 60m, power coefficient is 0.35 Option 1: Front row: 12 WT of size A1, Second row: 560m behind the first one, 12 WT of size A1. Option 2: Front row: 17 WT of size A2; Second row: 500 m behind the first one, 12 WT of size A1. 1) What are the power production for each row and the total power and energy production for both options? 2) If the developer's income from the sale of energy is $35/MWh, what is the income for a year for each of the options? 3) Based on the income, which option should the developer pursue? Present the results in Table 1 Table 1 # turbines Ux/U. Wind WT power, Total P, W Total energy, speed, m/s w MWh Option 1 Row 1 Row 2 Row 1 Row 2

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