## Wind turbine physics: factors affecting performance

The efficiency of wind turbines depends on various factors such as location, geographical factors, mechanics, rotor shape/ size, etc. Output can be regulated by a constant or variable rotational speed, as well as adjustable and non-adjustable blades.

Power in the Wind

The importance of accurate wind speed data becomes clear when one understands how the speed affects the power. Consider a disk of area A with an air mass dm flowing through that area. In a time dt the mass will move a distance U.dt, creating a cylinder of volume A U dt, which has a mass dm = A ? U dt, where ? is the density of air. The power contained in the moving mass is the time rate of change in kinetic energy, given by

P = d(KE) / dt = d(1 mU ) dt = U dm / dt = A?U .

Therefore, the power is proportional to the wind speed cubed. It is important to know the wind speed precisely, because any error is magnified when calculating power.

A careful choice of the shape of the blades is crucial for maximum efficiency. Initially, wind turbines used blade shapes, known as airfoils, based on the wings of airplanes. Today’s wind turbines still use airfoils, but they are now specially designed for use on rotors. Airfoils use the concept of lift, as opposed to drag, to harness the wind’s motion. The idea behind lift is that when the edge of the airfoil is angled very slightly out of the direction of the wind, the air moves more quickly on the downstream (upper) side creating a low pressure that essentially lifts the airfoil upward. The amount of lift for a given airfoil depends heavily on the angle that it makes with the direction of the relative wind, known as the angle of attack, ?. With a certain range, an increased angle of attack means increased lift, but also more drag, which detracts from the desired motion.

When the angle of attack gets too large, turbulence develops and drag increases significantly, while lift is lost. The angle of attack on wind turbine blades can be changed either by creating a specific geometry for the blades along the longitudinal axis/ span, also known as pitch control, or by allowing them to rotate around the axis perpendicular to their cross sections (along the span). This movement of turning the wind turbine rotor against the wind is known as the yaw mechanism. The wind turbine is said to have a yaw error, if the rotor is not perpendicular to the wind. Changing the angle of attack is important to maintain a precise amount of lift so the rotor turns at a constant speed.

Aside from optimizing the blade shape and the yaw direction, a vital consideration in the construction of a wind turbine is the lifetime of the machine. Wind turbines are currently designed to last at least 20 years. The blades must be strong enough to withstand all the loads and stresses from gravity, wind, and dynamic interactions. Blades are carefully manufactured and then extensively tested to make sure they can achieve the desired lifespan. As opposed to a car engine and other mechanical devices, an efficient wind turbine runs about 90% of the time for twenty or more years.

Types of loads are static, steady, cyclic, transient, impulsive, stochastic, and resonance induced. Static loads are constant and occur even with a non-moving turbine. These include steady wind and gravity. Steady loads are constant when the turbine is in motion and are caused by a steady wind. Cyclic loads are periodic, usually due to the rotation of the rotor. They occur from gravity, wind shear, yaw motion, and vibration of the structure. Transient loads are time varying with occasional oscillation. Braking by the inner gears and mechanics will cause this type of load.

Impulsive loads are time varying on short scales, such as a blade being shadowed when passing the tower. Stochastic loads are random, usually around a constant mean value, and are primarily caused by turbulence. Resonance-induced loads, which are to be avoided as much as possible, occur when parts of the wind turbine are excited at their natural frequencies and then vibrate and can induce other parts to vibrate also, putting considerable stress on the turbine.

Power control and aerodynamic braking system

As the angle of attack is one of the most important variables in determining the performance of a wind turbine, both in terms of power output and over-speed induced stress protection, it is important to understand the rotor pitch behavior.

An increasing number of larger wind turbines (1 MW and up) are being developed with an active stall power control mechanism. Technically the active stall machines resemble pitch controlled machines, since they have pitchable blades. In order to get a reasonably large torque (turning force) at low wind speeds, the machines will usually be programmed to pitch their blades much like a pitch controlled machine at low wind speeds. On a pitch controlled wind turbine, the turbine’s electronic controller checks the power output of the turbine several times per second. When the power output becomes too high, it sends an order to the blade pitch mechanism which immediately pitches (turns) the rotor blades slightly out of the wind.  This is actually the aerodynamic braking system, which is the primary braking system for most modern wind turbines. This essentially consists of turning the rotor blades about 90 degrees along their longitudinal axis. Conversely, the blades are turned back into the wind whenever the wind drops again. The rotor blades thus have to be able to turn around their longitudinal axis/ span (to pitch).

When an active stall controlled turbine reaches its rated power, however, you will notice an important difference from the pitch controlled turbine: if the generator is about to be overloaded, the machine will pitch its blades in the opposite direction from what a pitch controlled machine does. In other words, it will increase the angle of attack of the rotor blades in order to make the blades go into a deeper stall, thus wasting the excess energy in the wind.

One of the advantages of active stall is that one can control the power output more accurately than with passive stall, so as to avoid overshooting the rated power of the machine at the beginning of a gust of wind. Another advantage is that the machine can be run almost exactly at rated power at all high wind speeds. A normal passive stall controlled wind turbine will usually have a drop in the electrical power output for higher wind speeds, as the rotor blades go into an even deeper stall.