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Wind turbine power curve
The wind turbine power curve contains the optimal operating points. Notable wind speeds such as cut-in wind speed, rated wind speed, and cut-out wind speed define five operating zones. These zones determine the dynamic behavior of the wind turbine.
Power surface
The power surface contains all possible points where the wind turbine can operate. Figure 1 shows this surface depending on the wind speed (4 – 20 m/s) and the speed of the wind turbine (8 – 20 rpm). By changing the power coefficient (Cp), different power curves can be obtained, where the black highlighted curve is called the optimal power curve. This curve is where the wind turbine will operate throughout its lifetime.
The optimal power curve can be projected on the Mechanical Power (Pm) vs. RPM (Ω) or Mechanical Power (Pm) vs. Wind Speed (Vw) axes. The graph of the projected power curve on the above axes is shown below.
Power Curve (Pm vs. Vw)
This curve is obtained by projecting on the axes of mechanical power and wind speed (P-V curve). Figure 2 shows the P-V curve of a 2 MW wind turbine. This curve is provided by the wind turbine manufacturer.
The following important points can be distinguished in the P-V curve:
Cut-in wind speed (Va): This is the wind speed at which the turbine begins to deliver useful power. It is usually in the range of 3 to 5 m/s.
Rate wind speed (Vn): This is the wind speed at which the nominal power of the wind turbine is reached. It is usually in the range of 10 to 15 m/s and depends on the manufacturer.
Cut-out Wind Speed (Vc): It is the wind speed at which the rotor is stopped by the regulation and control systems in order to avoid the risk of damage that a high wind speed can cause. It is in the range of 20 to 30 m/s.
Wind Turbine Operating Zones
The power-speed curve (Figure 2) shows the five operating zones of a wind turbine. The following is a description of the operating zones:
Zone 1: The wind speed is not strong enough to overcome the internal friction (inertia) of the wind turbine. In this zone, the wind turbine cannot produce useful power because the wind is not able to rotate the turbine blades to the minimum rotational speed. Therefore, it is not possible to extract maximum power from the wind. This is generally found at wind speeds below 3 m/s or 5 m/s (depending on the manufacturer).
Zone 2: This is the operating zone where the Maximum Power Point (MPPT) is tracked. It is also the zone where the wind turbine is most likely to operate. It is generally found between wind speeds of 5 m/s to 12 m/s.
Zone 3 (optional): A zone that occurs in some wind turbine designs when maximum speed is reached but not maximum power is generated. It is a small band of operation before Zone 4, which in some wind turbines is part of Zone 2. The speed must be maintained at the maximum value, even if it is not possible to capture the maximum power from the wind, so it does not operate at the point of maximum power.
Zone 4: This zone begins when the captured power is equal to the rated power. The mechanical power generated and the speed of the wind turbine remain constant at their rated values. To achieve this, the pitch angle is modified when the wind speed varies above the rated wind speed.
Zone 5: This is the zone where the wind speed becomes dangerous for the wind turbine, causing it to rotate at higher than nominal speeds, causing mechanical stress and possible destruction of the wind turbine. The angle is set between 45° and 90° so that the mechanical power extracted from the wind is approximately zero. In addition, the mechanical braking system of the entire drive shaft prevents it from rotating until a wind speed suitable for its operation is detected.
Power Curve (Pm vs. Ω)
This curve is obtained by projecting on the mechanical power and speed axes of the wind turbine (P-Ω curve). Figure 3 shows the P-Ω curve of a 2 MW wind turbine.
Ωmin: Minimum wind turbine speed.
Ω0: Initial speed of the wind turbine where it starts to produce optimal electrical energy.
Ω1: Final speed of the wind turbine, which is very close to the maximum speed.
Ωmax: Maximum speed of the wind turbine.
The operation of a wind turbine depends on the wind speed and the rotational speed. On the power surface is the power curve of the wind turbine at which it operates optimally, limited by the blade angle control. The P-V curve shows what the mechanical power of a wind turbine will be at different average wind speeds. This curve can be used to calculate the energy generated by a wind turbine in a given period of time, usually a year.
Reference
[1] Munteanu, I., Bratcu, A. I., Cutululis, N.-A., & Ceanga, E. (2010). Optimal control of wind energy systems: Towards a global approach. Springer.
[2] Anaya-Lara, O., Jenkins, N., Ekanayake, J. B., Cartwright, P., & Hughes, M. (2011). Wind energy generation: Modelling and control: Modelling and control (1a ed.). John Wiley & Sons.
