VoxSolaris: The Voice of the Sun |
Simple wind turbines |
Basic principles and terminology Wind turbines work by deflecting the flow of air through the turbine, changing its momentum. This gives rise to a force which causes the turbine to rotate. Momentum is given by the formula mass * velocity . The force is given by the rate of change of momentum . If 1Kg of air is slowed by 1 meter per second every second, a force of 1 newton is produced. Energy is Force * distance and if 1 newton is applied for a distance of 1 meter, this amounts to 1 Joule of energy. Power, which is what we are really interested in, is the energy produced per unit time. 1 watt is 1 joule per second. Power output from a wind turbine is proportional to the cube of the speed so doubling the speed produces 8 times the power. This is because doubling the speed doubles both the mass of air flowing through the turbine and doubles the extent to which the air is slowed, quadrupling the force on the turbine which now covers twice the distance per second. Alas by the same token, halving the speed divides the power by 8. The total wind power in watts (p in the area swept by the wind turbine rotor is given by p = 0.5 * ad * A * V^{3 } where ad is the velocity or wind speed, in meters per second, A is the area in square meters and ad is the air density (about 1.3 Kg/m^{3 }at sea level, less higher up so assume 1.25 to be safe). However it is impossible to extract all the power from the wind because some flow must be maintained through the rotor. So, we need to include some additional terms to get a practical equation for a wind turbine. These are the the efficiencies of the generator, eGen , the gearbox eGear and a horrible thing called the coefficient of performance cp . To understand cp you need to delve deep into aerodynamics but it has a maximum theoretical value of 0.59 (called the Betz limit) and a more typical value of 0.35 for good designs. The overall equation for power output of a wind turbine is thus p = 0.5 * ad * A * V^{3 }* eGen * eGear * cp . So for example, a small household turbine with a 2 meter diameter rotor that sweeps an area of 3m^{2 }, operating at an altitude such that air density is 1.25 Kg/m^{3 }in winds of 5 m/sec (11 mph) having a coefficient of performance of 0.35 and a generator efficiency of 85% and a gearbox efficiency of 95% will have a power output of 0.5 * 1.25 * 3 * 125 * 0.35 * 0.85 * 0.95 or approximately 66 watts. In double the wind speed, 10 m/sec or 22 mph, the same turbine will produce 0.5 * 1.25 * 3 * 1000 * 0.35 * 0.85 * 0.95 or about 528 watts. Power management As we all know, wind speeds vary enormously and can vary very rapidly. And output being proportional to the cube of the wind speed, varies to a much greater extent and certainly much more than the power output of solar electric cells. This variance has an impact on the designs of circuitry used to manage the power from wind turbines and also has implications for the design of the generator. If in the example above our wind turbine experienced a gust to say 40 m/s (90 mph) the power output would soar to a staggering 32KW. Great except that somehow this extra power has to be handled without things melting or catching fire. Up to a point we can build a great deal of tolerance into the system, but always at a price. We could easily put a generator on our household wind turbine capable of handling 32KW but this would weigh far more than the generators one might normally fit to such systems and would require a sturdier tower. Both the larger generator and tower would drive up the cost of the turbine and worse then this, when the turbine was in winds of 5 m/sec, much of the available energy would be lost driving a much bulkier generator armature. What would be the point of capturing a lot of energy once in a blue moon at the expense of loosing what was available most of the time? Likewise with the circuitry. We could build a battery capable of being charged at 32KW or put in heavy duty electronics capable of uploading 32KW to the grid and of course, having an industrial standard grid connection capable of recieving it. Obviously it can be done just as one can use a sledghammer to crack a nut. So we allow the energy in powerful gusts and storms to go to waste. We do this by restricting the amount of kinetic energy that gets converted to electrical energy in the generator. There are a number of ways of doing this. Either the gearbox can select a lower gear meaning the higher turbine speed does not result in a higher generator speed. Or we can reduce the current in the generator's energizer coils, reducing the magnetic field so that a faster armature does not result in too much current in the coils and hence too much heat. Or we can apply a break or just as simple, disconnect the gearbox and generator with a clutch. Noise and low frequency noise The biggest complaint concerning wind turbines is the noise they produce. Some noise is produced by the mechanical components, the generator and the gearbox, but this is not generally significant. The majority of the noise arises from the interaction of vortices from the blades and the tower and from the unsteady aerodynamic forces on the blades, most notably on the blade tips. Low frequency noise arises from the slow speed of the rotors. If the noise is below 20Hz it is infrasonic and cannot be heard although it can be felt. Infrasonic noise can be coincidence with the resonances of nearby structures such as houses which amplify the sound and have harmonics that produce low frequency noise we can hear. With larger wind turbines the answer is to place them at a safe distance from houses. Smaller wind turbines are often mounted on poles that are bolted to the side of the house. The only saving grace then is that they tend to rotate faster and have more blades so that they put out less infrasonic noise and more audiable noise. This is a nussiance but less so because it tends to miss the resonances of the house. Instead of amplifying the sound, the house tends to shild you form it. Overall noise from wind turbines is manageable but definitely something to think about very carefully if you are particularly sensitive to noise or you have neighbors who are. In our experience the biggest problem with wind turbines is they are all to obvious. Anyone with a selective memory will see the turbine being erected and from that moment on, will blame the turbine for sleeplessness that was previously blamed on something else! Costs of wind turbines Costs of wind turbines are roughly comparable per KWHr produced to solar voltaics - providing you have a reasonable availability of wind. In a windy area it can work out cheaper. The 2 meter diameter wind turbine could in the right place, provide enough electricity to power your home. Not bad for an investment of a around $1,000 including the management system needed to integrate it with the grid. But a less windy location could lower these yeilds to only a fraction and in that case you have to forego the turbine and go for solar. |