Mathematical Efficiency of Wind Power

Conversion Efficiency, Capacity Factor, and Overall Efficiency

Contents

1. Introduction

2. Conversion Efficiency

3. Capacity Factor

4. Overall Efficiency

5. Concluding Remarks

6. A ChatGPT Story

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Bitesize Edition

• Efficiency is discussed frequently when it comes to renewables. Type into Google what the typical efficiency of a wind turbine is and you receive a figure of 20-40%. It’s often just assumed when comparing these electricity generation methods that whoever calculated this is correct for every possible environment and scenario on planet Earth.

• I decided I’d test whether these efficiencies were true in scenarios based on the average environment in the UK.

• Conversion efficiency is the ratio between wind energy input and electrical energy output by a wind turbine. Capacity factor is the average power output divided by the theoretical maximum power output and overall efficiency measures account for other losses such as transmission grid loss.

• Together, these metrics help tell a story for the environment I’ve chosen today, the UK. I hope it could set up similar calculations for other nations. All my sources for metrics used are listed at the bottom of the article.

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Introduction

When it comes to the efficiency of wind turbines, there are a few of the metrics from last week's list that we can cast aside. Firstly, heat rate is used to measure the ability of a generator or power plant to convert fuel into heat and then electricity. Thermal efficiency also isn’t a valid measure since wind turbines generate electricity mechanically. Hence, today we'll explore conversion efficiency and overall efficiency.

Photo by Max Bender on Unsplash

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Conversion Efficiency

Conversion Efficiency – The ratio between the useful output of energy and the energy input.

For a wind turbine to be 100% efficient, all wind energy input into the turbine would need to be converted to electrical energy, and this would mean the wind would have to stop completely when it hits the turbine. This isn’t possible since the rotor moves with the wind energy it receives. Most wind turbines are 25-45% efficient but let’s back this up with an example. Typically, turbines produce electricity at between 3 and 25 m/s but aren't economically viable at less than 5m/s. UK wind speeds are typically between 5m/s and 8m/s. Turbines typically have an electrical output power between 2.5 - 3 MW for onshore turbines, and in 2022, the average rotor diameter was over 130m, so the radius would be 65m.

In the example below, we'll assume we have a 2500KW turbine (2.5MW), an air density of 1.225 kilograms per cubic metre, and a wind turbine radius of 65m.