# Fixed speed wind turbine

EXERCISE: FIXED SPEED WIND TURBINE OF 300KW

Let’s consider a fixed speed wind turbine of 300 kW with the following parameters:

• Blades diameter (2R): 28 m
• Nominal wind speed V: 14 m/s
• Nominal rotational speed of the turbine rotor N turbine: 43 rpm
• Gearbox multiplication ratio: 35;  In addition, the air density is 1.225 kg/m3.
1. What parameters should be taken into account when choosing and installing a wind turbine ?
2. Calculate the value of the wind turbine’s power coefficient Cp at the nominal operating point.
3. Calculate the specific speed λ=R×Ω/V of the wind turbine. Conclude about the wind turbine type (rapid or slow). (Ω: Nominal rotational speed of the turbine rotor in rad/s).
4. What is the rated speed N of the generator rotor?
CORRECTION:

1) The parameters that must be taken into account when choosing and installing a wind turbine are:

• The parameters that must be taken into account when choosing and installing a wind turbine are: Instantaneous wind velocity at the cube in generated power;
• Instantaneous air density, which is also involved in generated power, but at factor 1;
• Rotor area, which also intervenes at factor 1 in generated power.

2) Cp=P/0.5×ρ×S×R2×V3=300×103/0.5×1.225×π× R2×143=0.290  .  Only 92% of wind energy is recovered.

3) Ω=43× 2 π/60=4.5rd/s

λ= R×Ω/V =14×4.5/14 =4.5 > 3; so it is a fast wind turbine.

4) The ratio of the multiplier is 35 and the nominal rotational speed of the rotor used is: 43 rpm.

The nominal speed of the desired generator is thus: N = 35 x 43 = 1505rpm.