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Last updated on 2024年11月15日

How can you calculate the power output of a wind turbine?

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Wind turbines are one of the most popular and efficient sources of renewable energy, but how do you know how much power they can produce? In this article, you will learn how to calculate the power output of a wind turbine using some basic formulas and factors. You will also discover how to optimize your electrical design for wind energy systems and avoid common pitfalls.

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Franklin A. Mendoza L.

Electrical Engineer

1 Power formula

The power output of a wind turbine depends on three main factors: the wind speed, the swept area of the rotor blades, and the power coefficient. The power formula is: P = 0.5 * ρ * A * Cp * v^3 where P is the power in watts, ρ is the air density in kilograms per cubic meter, A is the swept area in square meters, Cp is the power coefficient, and v is the wind speed in meters per second. The power coefficient is a dimensionless number that reflects the efficiency of the turbine and varies depending on the design, pitch, and speed of the rotor. The typical range of Cp is between 0.25 and 0.45.

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Franklin A. Mendoza L.

Electrical Engineer
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En este caso la potencia entregada por un aerogenerador de velocidad variable según la velocidad del viento se expresa de la siguiente manera: P(v)={0 si 0≤v≤vci =q(v)=1/2 ρ.A.Cp.V^3 =Pr? si vr≤v≤vco donde P(v) es la potencia eléctrica del aerogenerador, vci es la velocidad de conexión en m/s, vco es la velocidad de desconexión en m/s, vr es la velocidad nominal en m/s, Pr es la potencia nominal del aerogenerador y q(v) es la relación no lineal que existe entre la potencia y el viento

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2 Wind speed

The wind speed is the most critical factor that affects the power output of a wind turbine, as it is raised to the third power in the formula. This means that a small increase in wind speed can result in a significant increase in power output. However, wind speed is also unpredictable and variable, so it is important to measure it accurately and use statistical methods to estimate the average and extreme values. You can use anemometers, wind maps, or historical data to measure and analyze the wind speed at your site.

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Luis Ortiz ????, P.Eng.????, P.E.????, IntPE

Building the next generation of electrical engineers in safety, empowering future leaders, and sharing every lesson learned along the way.
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The relationship between wind speed and power output is cubic, this means a small change in wind speed results in a large change in power output, so wind is essential! If the wind speed doubles, the power output increases by 2^3 which is 8 times. So, speed changes make a substantial impact on the turbine behavior. If a turbine generates 100 kW at 5 m/s, it will generate 800 kW at 10 m/s (if all other factors remain constant). This turbine may shutdown for safety which will limit the benefits of extreme wind conditions. The design will determine the best equipment to use in order to get well use of extreme wind conditions.

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3 Swept area

The swept area is the area covered by the rotor blades as they spin. The larger the swept area, the more wind energy the turbine can capture and convert into power. The swept area is proportional to the square of the rotor diameter, so increasing the diameter by a small amount can also increase the power output by a large amount. However, larger rotors also require stronger and heavier materials, more space, and higher costs, so you need to balance the benefits and drawbacks of different sizes.

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Franklin A. Mendoza L.

Electrical Engineer
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El área A barrida para una hélice, es la superficie total barrida por las palas del rotor, perpendicular a la dirección del viento. Para un rotor de hélice, de eje horizontal, paralelo a la dirección del viento, y diámetro D, el valor de A es: Pi*D^2/4, Para máquinas de eje vertical (viento transversal), con un radio uniforme alrededor del eje de rotación igual a (d/2) y altura h, el área A barrida es: A = Altura x Anchura = h d de aplicación al rotor Savonius y a los rotores Darrieux de palas planas tipo giromill. En un rotor Darrieux, la curva envolvente que conforma el perfil (catenaria) proporciona el área A.. A = 2,67* d*h, siendo d el diámetro máximo de giro y h la altura del aparato

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4 Power coefficient

The power coefficient is a measure of how well the turbine converts the wind energy into power. It depends on the design and performance of the turbine, such as the shape, number, and pitch of the blades, the gearbox, the generator, and the controller. The power coefficient also changes with the tip speed ratio, which is the ratio of the blade tip speed to the wind speed. The optimal tip speed ratio depends on the type of turbine and can be determined by testing or simulation. The maximum theoretical value of Cp is 0.59, also known as the Betz limit, but in reality, it is lower due to losses and inefficiencies.

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5 Electrical design

To optimize your electrical design for wind energy systems, you need to consider several aspects, such as the voltage, frequency, power quality, grid connection, and protection. You need to choose the appropriate generator, converter, transformer, and cable for your turbine and match them with the load and grid requirements. You also need to ensure that your system can handle the fluctuations and disturbances caused by the wind speed variations, faults, and grid events. You need to apply proper control and regulation strategies to maintain the stability and reliability of your system.

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Franklin A. Mendoza L.

Electrical Engineer
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Los circuitos eléctricos de potencia de los aerogenertadores están compuestos de tres elementos principales: el convertidor, responsable del control de diferentes parámetros del lado del generador y de la red, el transformador de potencia, cuyo papel consiste en elevar la tensión de generación, de 690V, a un nivel de media tensión de 20 kV adaptado para el transporte de la energía hasta la subestación, y la celda de media tensión, principal elemento de seguridad contra fallos eléctricos

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How can you calculate the power output of a wind turbine?

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2

3

4

5

6

1 Power formula

2 Wind speed

3 Swept area

4 Power coefficient

5 Electrical design

6 Here’s what else to consider

Electrical Design

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How can you calculate the power output of a wind turbine?

1

2

3

4

5

6

1 Power formula

2 Wind speed

3 Swept area

4 Power coefficient

5 Electrical design

6 Here’s what else to consider

Electrical Design

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