# Measured Power And Power Coefficient

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A common specification is the power output of the wind turbine versus wind speed, a power curve. The power curve generally includes all efficiencies from wind to electrical output, not just the rotor efficiency. Since all wind turbines must control power output at high wind speeds, at some point the efficiency is lower. Control can be implemented by changing blade pitch or by operating fixed-pitch blades at constant angular speed. Operating at fixed pitch is also called stall control. Power curves are obtained by the method of bins, so in reality, a power curve is not a line but a band of values.

The experimental power and power coefficient curves (Figure 6.13) are for a wind turbine that has an induction generator, operation at constant angular speed, and fixed pitch, which means it is stall controlled. Therefore, it reaches maximum power coefficient at only one point, and the decreased aerodynamic efficiency at wind speeds above this point make the power coefficient also decrease. The increased power in the wind and the decreased aerodynamic efficiency combine to give a constant power output above 12 m/s. The high efficiency, which includes drive train and generator, is because this unit has an almost optimal blade; taper, twist, and thickness.

Besides the tip and hub losses of the blades, there will be a further reduction of the power coefficient due to the inefficiencies of the mechanical system (drive train, coupling) and the generator. Under the optimum design conditions, the modern two- or three-bladed rotors at tip speed ratios in the range of approximately 4-10 will have power coefficients of about 0.4 to 0.5 (Figure 6.14). The power coefficients for the farm windmill and the Savonius rotors are essentially the same, with a maximum just over 0.3. The maximum power coefficients for the vertical-axis wind turbines are just over 0.4, which makes them less than those for the horizontal-axis wind turbines. This is one of the reasons that in 2008, vertical-axis wind turbines are not commercially available for wind farms.

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Wind Speed, m/s

FIGURE 6.13 Experimental power and power coefficient for a Carter 25, rated 25 kW, 10 m diameter. Notice at 3 m/s the turbine uses power (energy for the field coils of the induction generator).

 Darrieus, 100 kW "" ™ Farm windmill, Savonius — • Darrieus, 500 kW □ Two blade HAWT *-■ "tteoretical

Tip Speed Ration

FIGURE 6.14 Experimental power coefficients for different rotors compared to the theoretical value: farm windmill [31], Savonius [32], 100 kW Darrieus [33], 500 kW Darrieus [19], horizontal-axis wind turbine, Carter 25 (data from Figure 6.12).

### Tip Speed Ration

FIGURE 6.14 Experimental power coefficients for different rotors compared to the theoretical value: farm windmill [31], Savonius [32], 100 kW Darrieus [33], 500 kW Darrieus [19], horizontal-axis wind turbine, Carter 25 (data from Figure 6.12).

The three methods of regulating output are passive stall, where the wind turbine operates at fixed rotational speed with fixed-pitch blades; active stall, where the wind turbine operates at fixed rotational speed with adjustable pitch; and variable pitch, where the wind turbine operates at variable rotation speed with adjustable pitch blades. The last method is the most efficient aerodynamically, but the method of control chosen is always a trade-off between energy production and cost.

Control of rotor rpm using adjustable pitch includes full-span control, where pitch motors are located in the hub; variable-pitch tips; and ailerons (flaps on airplane wing) to control aerodynamics, even though it is not adjustable pitch. The last two have pitch motors in the blade. Now for large wind turbines, the most common method is full-span control, although wind turbines have been built with the other two control methods. The MOD-2 and MOD-5 had tip control.

Ailerons are moved to the low-pressure side of the blade to reduce lift, in contrast to flaps on planes, which are moved in the opposite direction to increase lift. NASA-Lewis investigated ailerons both theoretically and experimentally for application to medium and large wind turbines [34]. Zond built twelve 500 kW units with aileron control, and they were installed near Fort Davis, Texas, as part of the Utility Wind Turbine Verification Program [35]. However, after 4 years of operation they were dismantled, with one of the reasons being the maintenance problems with the ailerons. Finally, there was the Italian Gamma 60, 1.5 MW, wind turbine with fixed-pitch blades where the control was to yaw the rotor. One problem with that is the difference in lift on the blade on each cycle.

There have been efforts to develop passive pitch control techniques that adjust the blade pitch angle without a need for actuators [36]. One concept is the self-twisting blade in which the blade spar at the hub is flexible, and the thrust and centrifugal forces on the blade cause it to twist to the feathered position. United Technologies Research Center built a 10 m diameter unit with the two blades (constant chord, no twist) attached to a flexbeam (Figure 6.15), which was attached in the middle to the drive shaft. There was enough twist to provide torque for start-up, and pendulum weights outside the plane of rotation moved toward the plane of rotation and provided proper pitch angle for the run position, and also, the weights provided control at high winds by twisting

FIGURE 6.15 Passive control with flexbeam and pendulum weights, unit was constant-rpm operation.

the blades toward stall. One problem was that over time, the flexbeam moved toward a different set twist, which reduced the starting torque. The Proven wind turbine has a flexible hinge near the root of the blade [37]. As rotor rpm increases, the blades are forced outwards, which changes the pitch of the blade toward stall. So even in high winds, the rotor rpm is limited, and it can continue to produce power.