Mathematical Efficiency of Solar Power – The Atacama Desert

A Good Environment For Solar?

Contents

1. Introduction

2. Conversion Efficiency

3. Capacity Factor

4. Conversion Efficiency Calculation

5. Comparison To UK Solar Cells

6. Testing Assumptions

7. Concluding Remarks

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Bitesize Edition

• If given the choice between a solar panel in the UK, and a solar panel in Chile, which would you choose?

• In our energy transition, to avoid an energy crisis, we need to consider what technologies our environments are best suited to. I live in the UK, and it’s cold and dark for a large proportion of the year. The Atacama Desert in Chile receives the same levels of sunlight as the planet Venus, which is 30% closer to the Sun than we are. Without diving into the mathematics, it would make sense that this solar cell in Chile would be taking better advantage of its environment.

• However, let’s not leave it to assumption. Let’s dive into the mathematics of efficiency, specifically during the optimal performance of these solar cells. We did the same for the UK last week, and so will compare the two environments in today’s piece.

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Introduction

The company Sonnedix started operations in Chile in 2015 with a 0.6MW solar plant. After this came a 3.63MW plant in April 2016 and a  3.25MW plant in July 2016. The construction of the Sonnedix Atacama Solar Plant started in 2019, and finished in 2020, and is a 170MW solar plant. It has been providing energy to the Chilean grid since January 2021.

After last week where we calculated the efficiency for solar panels in the UK, we’ll today go through the same process for a solar panel in the Atacama Desert in Chile. From what I’ve heard, it gets slightly more sunlight than the UK. Let’s find out how much difference this makes.

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Conversion Efficiency

Remember, conversion efficiency is the ratio between useful output, in this case electricity, to the solar energy input. To flashback to the equations we’ll need for today’s piece, as we’ve used over the previous few weeks, look here:

\(\text{Conversion Efficiency} = \frac{\text{Average Power Output}}{\text{Solar Input Power}}\)

\(\text{Average Power Output} = \text{Total Power of Cell} * \text{Capacity Factor}\)

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

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Capacity Factor

In my source, we have different capacity factors for tracking and non-tracking solar arrays. For fair comparison to the UK, we’ll use the non-tracking capacity factor. This means the panel can’t follow the sun’s movements whereas tracking panels can.

For non-tracking solar panels in Chile, the capacity factor provided is 20%, and this is referred to as a minimum. We’ll use 20% going forward. Remember,  the UK’s capacity factor for solar was 10.8%.

Photo by Bailey Hall on Unsplash

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Conversion Efficiency Calculation

In our UK calculation, we took solar cells of 1.6m^2 and 2m^2.

We also calculated for 250W and 400W solar cells.

What will differ in Chile is the solar intensity. They receive 9-10kWh/m^2 per day. This is equal to 9000-10000wH/m^2 per day.

They receive an average of 6.26 hours of direct sunlight per day. Hence the total power output of our 250W and 400W cells will be 1565wH and 2504wH respectively. Let’s get calculating.