Lake Discharge Problem

Original models of wind turbines were fixed speed turbines; that is, the rotor speed was a constant for all wind speeds. The tip-speed ratio for a wind turbine is given by the following formula:

$\lambda =\frac{\omega R}{v}$

where $\omega$ is the rotor speed (in radians per second), $R$ is the length of a blade, and $v$ is the wind speed. That is to say, for a fixed-speed wind turbine, the value of the tip-speed ratio changed with the wind speed. In reference to a $C_p$-$\lambda$ graph, which illustrates the relationship between Tip-speed ratio and efficiency, it is evident that only one value of $\lambda$ yields the highest efficiency. That is, the fixed speed wind turbine is not operating at peak efficiency across a range of wind speeds. This was a motivator for the development of variable speed wind turbines.

Background

Cp-λ curves

Below is an illustration of the $C_p-\lambda$ curve for a typical wind turbine.

Maximum efficiency occurs at one tip-speed ratio only. Since tip-speed ratio is given by the aforementioned expression, variable speed wind turbines can operate at maximum efficiency over all wind speeds (ideally).

Gearboxes

A variable speed may or may not have a gearbox, depending on the manufacturer's desires. Wind turbines without gearboxes are called direct-drive wind turbines. An advantage of a gearbox is that generators are typically designed to have the rotor rotating at a high speed within the stator. Direct drive wind turbines do not exhibit this feature. A disadvantage of a gearbox is reliability and failure rates.

An example of a wind turbine without a gearbox is the Enercon E82.

Generators

For variable speed wind turbines, one of two types of generators can be used: a DFIG (Doubly-fed induction generator) or an FRC (fully rated converter).

A DFIG generator draws reactive power from the transmission system; this can increase the vulnerability of a transmission system in the event of a failure. A DFIG configuration will require the generator to be a wound rotor; squirrel cage rotors cannot be used for such a configuration.

A fully rated converter can either be an induction generator or a permanent magnet generator. Unlike the DFIG, the FRC can employ a squirrel cage rotor in the generator; an example of this is the Siemens SWT 3.6-107, which is termed the industry workhorse. An example of a permanent magnet generator is the Siemens SWT-2.3-113. A disadvantage of a permanent magnet generator is the cost of materials that need to be included.

Grid Connections

Consider a variable speed wind turbine with a permanent magnet synchronous generator. The generator produces AC electricity. The frequency of the AC voltage generated by the wind turbine is a function of the speed of the rotor within the generator:

$N=\frac{120f}{P}$

where $N$ is the rotor speed, $P$ is the number of poles in the generator, and $f$ is the frequency of the output Voltage. That is, as the wind speed varies, the rotor speed varies, and so the frequency of the Voltage varies. This form of electricity cannot be directly connected to a transmission system. Instead, it must be corrected such that its frequency is constant. For this, power converters are employed, which results in the de-coupling of the wind turbine from the transmission system. As more wind turbines are included in a national power system, the inertia is decreased. This means that the frequency of the transmission system is more strongly affected by the loss of a single generating unit.

Power converters

As already mentioned, the voltage generated by a variable speed wind turbine is non-grid compliant. In order to supply the transmission network with power from these turbines, the signal must be passed through a power converter, which ensures that the frequency of the voltage of the electricity being generated by the wind turbine is the frequency of the transmission system when it is transferred onto the transmission system. Power converters first convert the signal to DC, and then convert the DC signal to an AC signal. Techniques used include pulse width modulation

References

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