Question 4 Calculate the following using the wind turbine pa

Question 4

Calculate the following using the wind turbine parameters in Table 2 and wind speed v_w = 8 m/s.

(a) The turbine output power (Hint: use per-unit formula)

(b) The turbine output torque (Hint: use per-unit formula)

(c) The generator mechanical input torque

(d) The mechanical speed of turbine (Hint: use per-unit formula)

(e) The power coefficient of wind turbine using the answer in question-4, part (a).

(f) The optimal tip speed ratio using the answer in question-4, part (d).

(g) The intermittent tip speed ratio using the answer in question-4, part (f).

(h) The turbine constant C7 using the answers in question-4, parts (f) and (g).

I need PART C, G and H and solution for the resto of the parts is here

Turbine output power P = pi r^2 1/2 rho U^3 P = pi 43.36^2 1/2 1.225 times 8^3 P = 1851331.74 Watts = 1.85 MW b) The turbine output toque By using below formula, P = T middot omega T = Torque = P/omega omega = 22.5 times 2 pi/60 = 2.355 T = Torque = 1851331.74/2.335 = 786128.12 N d) The mechanical speed of rotor N_rotor = 2 pi times 0.375 times 60/2 pi = 22.5 RPM e) The power coefficient of wind turbine C_p C_p = P_out/P_in = 3000/1850 = 1.62 f) Optimal tip speed ratio N_rotor = 22.5 RPM = 2.35 rad/s U_tip = 2. 35 times 43. 36 = 101.896 m/s

Solution

C.

P = c x d x (D^2) x (v^3)

P: Power produced (mechanical) (Watts [W])

c: constant

d: density of wind (kilograms per cubic meter [kg/m^3])

D: turbine blade diameter (meter [m])

=0.395*(86.72²)*1.225*12³                 

=6288.0423   KW