General Information
The specification of a 1.5MW wind turbine with active pitch control states that the rated wind speed is 14 m/s and that the rotor dismeter is 77m. The generator is a double-fed induction machine. The turbine range of operation is 11.0 rpm to 20.4 rpm and the gearbox ratio is 90:1. The generator is a four-pole machine and the grid frequency is 50 Hz.

Part 1: The generator operates at a slop of -0.2 at rated output. Determine the rotational speed of the generator (in rpm) under these conditions. Calculate the speed of rotation of the turbine under these conditions. Confirm that this speed is within the turbine's range of operation

Part 2: Assuming that the active power is shared between the stator and rotor circuits in proportion to the slip(s):

Pr = -sPs

Determine the rotor and stator power under rated conditions

Part 3: The wind speed increases to 15m/s but the slip is maintained at a value of s=-0.2. The power output of the turbine remains at 1.5MW.

Calculate the tip-speed ratio under these conditions. Determine the power co-efficient (Cp) required. How is this combination (Tip Speed & Cp) achieved in this turbine.

So here are my attempts/methods, I mainly stuck on part 2 but I want to get part 1 and part 3 checked.

Part 1 Attempt

Generator Speed = \(\frac{Frequency*60}{Pairs of Poles}\)

Generator Speed = \(\frac{50*60}{2}\)

Generator Speed = 1500 rpm

Rotor Speed = Generator Speed-(Slip)(Generator Speed)

Rotor Speed = 1500-(-0.2)(1500)

Rotor Speed = 1800 rpm

Turbine Speed = \(\frac{Rotor Speed}{Gearbox Ratio}\)

Turbine Speed = \(\frac{1800}{90}\)

Turbine Speed = 20 rpm

As the turbine speed is 20 rpm is within the range of operation

Part 2 Attempt

I orginally tried to used the rotor power formula for a turbine which is Pr=0.5*p*A*Cp*U^3 but there is no Cp value provided and in the next part of the question you are asked to find it. It can't be 1.5=1.5*-0.2 ????

Part 3 Attempt

Blade Tip Speed = \(\frac{Turbine Speed*pi*Diameter}{60}\)

Blade Tip Speed = \(\frac{20*pi*77}{60}\)

Blade Tip Speed = 80.64

Tip Speed Ratio = \(\frac{Blade Tip Speed}{Wind Speed}\)

Tip Speed Ratio = \(\frac{80.64}{15}\)

Tip Speed Ratio = 5.376

Coefficient of Performance = \(\frac{Power}{0.5*rho*pi*R^2*U^3}\)

Coefficient of Performance = \(\frac{1500000}{0.5*1.225*pi*38.5^2*15^3}\)

Coefficient of Performance = 0.1559


Part 2 is my main issue but I want to make sure I did part 1 and 3 correctly.

 

Where are these located...

 

part 1 was ok.. part 2 has a missing part of it, i also dunno if the answer in part 3 is usable.. Cp in part 2 is i think a constant value/given value.. then after the answer of part 2, you get a new Cp at part 3..

--hope this helps

 

Hey that is all the information that I have for the question.

part 1 was ok.. part 2 has a missing part of it, i also dunno if the answer in part 3 is usable.. Cp in part 2 is i think a constant value/given value.. then after the answer of part 2, you get a new Cp at part 3..

--hope this helps

That is the only information provided. It would make sense to request the Cp before the question if that formula was the one they wanted to use. I confirmed part 1 and part 3 are correct.


I have the answer for part 2 which is 1.25MW; 0.25MW. However I still don't know the method.

 

Here is a attempt which is a bit of a cheat.

-20 slip = 120% speed

1,500,000,000/120 = 12,500,000.00

There 1% is 12,500,000.00

20% = 250,000,000
100% = 1,250,000,000.00


While this is the correct answer the method is questionable. However it works with the data provided.

 

surely the answer is that Pt = Ps +Pr = 1.5 (theres nowhere else for the power to go)

substitute into the equation for Pr =-sPs
1.5 -(sPs) =Ps
1.5 = (1+s) Ps
Ps = 1.5/1.2 = 1.25 so Pr = 1.5-1.25 =.25

?

 

I was messing around with those formula today. My mistake was putting 1,500,000,000 instead of 1.5.