Mathematical Efficiency of Solar Power

Efficiency During A Period of Optimal Performance In The UK

Contents

1. Introduction

2. Conversion Efficiency

3. Capacity Factor

4. Conversion Efficiency Calculation

5. Overall Efficiency

6. Concluding Remarks

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Bitesize Edition

• Last week, we tested the assumption that wind turbines are 20-40% efficient, which is stated all over the internet. This doesn’t consider changing environments, and this has a large effect on hiding true efficiencies.

• This week, I’ll test the same assumptions for solar panels. Two different sources list conversion efficiencies of solar panels typically as between 15-20% or 15-23%. Let’s test these assumptions following the same process we followed for wind turbines.

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Introduction

I enjoyed doing some mathematics on the efficiency of wind turbines last week, and so we’re back with more, this time for solar cells.

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Conversion Efficiency

Conversion efficiency is the ratio of useful output vs the input it consumes. In regard to solar cells, it measures how effectively sunlight is converted into electrical energy.

Last week, with wind turbine efficiency, we were limited by the Betz Limit. This week, the theoretical maximum efficiency of a solar cell is determined by the Shockley-Quiesser limit of 33.7%. These limits are determined by physics and the speed at which solar cells can absorb power.

The solar input power is calculated by:

\(\text{Solar Input Power} = \text{Solar Intensity} * \text{Area of Solar Cell}\)

Before calculating the conversion efficiency, we’ll need the capacity factor.