Hellmann's power law
Wind speed π£Wind at any height can be determined approximately based on a measured wind speed at a reference height of 10 m
alpha=1,6 at Neutral air above flat open coast
Wind Energy Development in Germany
30.243 Wind Turbines (1/1/2024)
77.6 GW total installed power (January 2026)
β Onshore (88 %) and offshore (12 %)
Levelized cost of electricity (LCOE) for various power generation technologies in Germany
Ground-mounted PV systems (4.1 - 14.4 β¬cents/kWh)
and onshore wind turbines (4.3 - 9.2 β¬cents/kWh) are
the most cost-effective technologies in Germany
Theoretical Wind Power
Ideal Coefficient of Power β Betz Law
The wind speed before the wind turbine is larger than after. Because the mass flow must be continuous ( αΆπ = π β π΄ β π£ = ππππ π‘. ), the area A3 after the wind turbine is bigger than the area A1 before.
= 59%
Real wind turbines achieve a πΆP,max of 45 to 52 %
Classifications of Wind Turbines
βͺ Position of rotor axis (horizontal, vertical)
βͺ Rotor speed (slow-, fast-running)
βͺ Rotor speed (constant, variable)
βͺ Possibility of influencing power (stall, pitch controlled)
βͺ Possibility of storm protection (switching off, fixing)
βͺ Generator type (asynchronous, synchronous, permanent magnet)
βͺ Network coupling (direct, indirect)
Onshore Dominating System:
Geared Doubly-Fed Induction Generator
Direct Grid Coupling
generator speed must be constant
Advantages
β Simple construction
β A converter is not required
β Low investment costs and less maintenance
Disadvantages
β Only IG feasible
β Stronger fluctuations in wind speed are fed to grid
β High mechanical stresses on the wind turbine
β Operation at optimum operating point not always possible β lower Cp
Indirect Grid Coupling
Generator speed may vary
A Converter is used: Inverter generates the fixed grid frequency and grid voltage
Typically used in high power plants
β The system is very flexible with regard to wind fluctuations
β’ SG gearless and with permanent magnets possible
β System can always be operated at the optimum operating point
β Less mechanical stress on wind turbine (stall and pitch control)
β More complex and expensive construction
β Efficiency of the converter lowers overall system efficiency
Pitch Control, Active Stall Control and Passive Stall
(stall = strΓΆmungsabriss)
Passive Stall
The blades of the wind turbine are designed in such a way that, when the wind is too strong, turbulences occure and cause a stall. This causes the wind turbine to be braked in a passive way.
Active Stall
When wind speed is too high, the wind turbine blade is turned against the wind in order to achieve a stall.
Pitch
If the wind speed exceeds the maximum allowed value, the blades of the wind turbine are actively turned by servo drive systems into the wind. The rotor blades are positioned as close to the wind as necessary to avoid overloading.
Active stall control is specifically about stalling the blades to reduce power, whereas pitch control is about finetuning the blade angles to optimize power output and protect the turbine.
Last changed11 days ago