Correlation between power and energy return - Windchallenge
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Knowledge | Sander Mertens | 27 Dec 2016

# Correlation between power and energy return

In our journals we delve deeper into some questions we frequently hear from our followers, potential clients and wind energy enthusiasts. In this journal I explore the correlation between power and energy return. During my many years of research, culminating in the design of the The Windleaf, I have learned a lot about this subject. I hope this experience will allow me to explain a little more about the subject.

The output power of a wind turbine is determined by the wind speed. Generally higher wind speeds result in more power. This applies until generator and converter capacity is reached. Allowing more power at this speed would overload the turbine resulting in a requirement to limit the incoming power. The following defines the relationship between power (P) and wind speed (v).

The nominal power is defined by economics. A turbine with a high nominal power is expensive to design and manufacture while this maximum power is only useful during the rare periods of high wind speed. Experience has shown that a wind turbine should deliver nominal power at least 20% of the time. This is defined by the average wind speeds at a certain location. Only then can the economic investment required for the corresponding maximum capacity be justified. This is called the capacity factor. Wind turbines with a capacity factor far higher or lower than 20% are not suited for the most common wind speeds in that location.

The capacity factor of a well designed wind turbine allows you to make a realistic estimate of the energy return. With the capacity factor, we know the turbine delivers nominal power 20% of the time. This means the energy return in kWh per year can be calculated. For this, we use the formula:

E = Pmax × 0,2 × 365 × 24

The Pmax is in kW, which is the nominal power. Averaged out, The Windleaf will deliver 0.35 kW 20% of the time. Inserting this into the formula gives us:

E = 0,35 × 0,2 × 365 × 24 = 613 kWh

This is a simplified approach to calculate the energy return. In the graphs below the relationship between energy return (E) and average wind speed (v) is shown. As well as the power (Watt) to wind speed (v) ratio.

For greater accuracy, a wind turbine’s energy return should be calculated by multiplying the power by the amount of time the turbine is producing it, according to wind statistics. This information isn’t always readily available leading to regular use of the simplification discussed above. Wind turbines with a high power output during periods of high wind speed give an inflated expected energy return when you calculate it according to  this common simplification. Such a return could only be realized at an unrealistically high average wind speed. Only under those conditions could the capacity factor (20%) be achieved. Realistically, such high average wind speeds rarely occur.

The Windleaf is designed for average local wind speeds between 4 and 6 meters per second, with a corresponding generator and inverter capacity. This gives us a capacity factor that is useful in the real world. In areas with these conditions, even built up areas, The Windleaf is at its best. The design has been optimized for the conditions at our specified installation altitudes.