solar-lamp

Introduction to Our Problem

I recently went to a grand uncle’s house. Evening hit as we were sitting on the patio, and a string of solar-powered lights lit up. It was a cool idea. Just hang up a bunch of solar lamps where there was sun, and voila! Free light at night.

But it also got me curious: do these solar lamps actually pay for themselves in cost savings? Is the light that they produce really free?

The answer, as always, is “it depends”.

Our Approach

In order to evaluate this question, we have to compare the total costs of setting up and running the solar lamp setup, against a traditional setup.

To do this we will first examine a traditional non-solar setup and its costs. This is a setup where power is drawn from a power mains to power lamps.

Because different setups have different brightness, we then have to work out a method to compare two different setups with each other. To do this we propose a method to make an apples-to-apples comparison between the traditional and the solar setups, using lumens.

We then examine the costs associated with a solar lamp setup.

With the above, we will have the equations we need to derive our breakeven point. This metric decides how long it takes for our solar project to pay for itself.

Traditional Setup

A traditional non-solar outdoor light setup uses an electrical mains to power outdoor lighting. Usually, we pay for power from this mains on a per kWh basis.

Fixed costs: equipment costs

This setup requires the purchase of equipment aside from the light itself, consisting at a bare minimum of wiring that meets waterproofing standards. Other miscellaneous costs can be expected, including integration points with the home electrical grid, and mounting points for the lamp itself. We can summarise the following into a set of equations:

Fixed cost of traditional setup = 
  Cost of lamp 
  + Cost of wiring per unit x units of wiring needed 
  + Other miscellaneous costs

Variable costs: daily cost of operation

In addition to the setup cost, the outdoor light needs to be powered by electrical energy from the grid. And this electrical energy is not free.

Electricity is generally charged by utilities in kilowatt-hours or kWh, while most lamps usually come with a power rating in watts. So we have to convert the power rating of our lamps into kilowatts by dividing by a 1,000.

If we have an estimate of how long our lamp should keep running for after dark every day, we can combine the two factors above to arrive at a daily running cost:

Daily consumption in kWh = Lamp power rating in kW x Hours of operation
Daily cost = Daily consumption x Cost per kWh

Solar-powered Setup

A solar-powered setup uses lamps that are connected to a solar panel. This solar panel charges up a rechargeable battery during the day, which then discharges energy to the lamp at night, keeping it lit for as long as there is energy left in the battery.

Fixed cost of solar setup

The beauty of the solar setup means that the biggest cost we need to actually worry about is just the cost of the lamp itself. The solar panels that recharge the lamp during the day, as well as the battery that stores that charge are usually built into and sold with the lamp together as a whole unit.

Nevertheless, we still need to account for miscellaneous costs like mounting equipment, exactly like in the traditional setup.

As such the cost of a solar setup is basically as follows:

Cost of solar setup = Cost of solar lamp + Other miscellaneous costs

Because this approach is usually so hassle free (some setups don’t even require the installation of mounting points) the convenience of setup and replacement might even be a good enough reason for some to just straight up go with the solar approach.

Variable costs – daily cost of operation

Zilch. Nada. Zero. That’s one of the beauties of the solar lamp. Mount it up, hang it from its desired spot, or stand it wherever has a good amount of sun, and it just works.

Apples-to-apples: Scaling with Lumens

Different lamps have different brightness, which makes comparing between different setups difficult. This is true as well in the comparison between our traditional and solar-powered setups. After all, it isn’t fair to compare a very bright searchlight to a dim lantern, just because both are light sources.

We will need some way to make the comparison on more equal grounds.

Fortunately, physics has a measure for that: the lumen.

The lumen (symbol: lm) is the unit of luminous flux, a measure of the perceived power of visible light emitted by a source

In layman terms, this measures the brightness of a light source.

This gives us a way to compare different setups by scaling the costs of one setup in proportion to how its lumens output compares to the other. Essentially, we apply a lumens-based multiplier to even out the two.

This means that if we have to compare fixed costs between both setups, we could do something like this to equalise them:

Cost differential = 
  Cost of traditional setup 
  - Cost of solar setup x (Lumens of traditional setup ÷ Lumens of solar setup)

Pay-off metric: Breakeven point

The metric we use to decide how long it takes for any project to pay itself back is the breakeven point.

In our context, this measures how long it will take our cost savings from not having to pay for electricity to recoup our original investment . The equation we will use is a contextualised variant of the usual breakeven equation:

Breakeven point (units) = 
  Fixed Costs ÷ (Sales price per unit – Variable costs per unit)

In our context, our project is a comparison between two approaches, the traditional and the solar. Hence our Fixed Costs actually consists of the extra money we have to spend for the solar setup rather than the traditional setup, aka the cost differential between our two approaches. This is because we would have had to spend on our traditional lighting solution anyway.

In addition, we are not selling anything in our project. Our project instead seeks to examine cost savings. We are however, able to determine cost savings, by looking at the cost of electricity we avoid consuming because of the solar approach. This allows us to directly replace the (Sales price per unit – Variable costs per unit) component in our breakeven equation.

Hence we end up with:

Breakeven point (in days) = 
  Cost differential ÷ Daily cost

The above will tell us how many days it will take for our solar-powered outdoor lights setup to pay itself back.

Cheatsheet

Let’s pull all our equations together to form an easy reference.

Cost of traditional setup = 
  Cost of lamp 
  + Cost of wiring per unit x units of wiring needed 
  + Other miscellaneous costs
Cost of solar setup = Cost of solar lamp + Other miscellaneous costs
Cost differential = 
  Cost of traditional setup 
  - Cost of solar setup x (Lumens of traditional setup ÷ Lumens of solar setup)

Daily consumption in kWh = Lamp power rating in kW x Hours of operation
Daily cost = Daily consumption x Cost per kWh

Breakeven point (in days) = Cost differential ÷ Daily cost

Example Scenario

Different locations will have different answers to our question of whether solar lamps really pay for themselves.

But we can use a simple scenario to hypothesize. For this scenario let’s use a single-family home example in California, a state in the US with a healthy average number of sunny days.

The numbers

  • Traditional setup

  • Solar setup

  • Hours of operation: 4 hours (most solar lamps seem to last 3-6 hours)

  • Cost of electricity: 28.5c in Feburary 2024 as per the U.S. Bureau of Statistics

Note that we ignore miscellenous costs like mounting point installation and labor; to keep things simple we assume similar costs for both projects in this regard, and that labor is done DIY.

Of course, all numbers will differ depending on where exactly you are, but nonetheless this can act as a good guide.

Applying our numbers

Cost of traditional setup = $39.95 + $0.5/ft x 30ft + 0
Cost of solar setup = $46.99 + 0
Cost differential = $54.95 - $46.99 x (13,000lm ÷ 2,500lm)

Daily consumption in kWh = 0.1 kW x 4 hours
Daily cost = 0.4kWh x $0.285/kWh

Breakeven point (in days) = $244.35 ÷ $0.114
Breakeven point (in days) = 2,143 days
Breakeven point (in years) = 5.9 years

So this setup pays for itself in roughly 6 years.

Not a great result, to be honest. Especially considering the uncertainty surrounding the lifetime of such a setup exposed daily to the elements. But perhaps your numbers might end up different?

Complications

Necessarily, our calculations above are simplistic, and ignore crucial factors such as:

  • Usage hours can vary from day to day, and circumstance to circumstance. The lesser the hours, the less we save by switching to the solar based setup, extending breakeven point.
  • We assume that our setups will last as long as we want them to, but in real life this is not true. Project lifetimes and equipment lifecycles do impact replacement costs, and ultimately our fixed costs.
  • Lighting reliability might be important. In this case, relying on a solar setup that might run out of juice at inconvenient times could be a disqualifier.

Necessarily other factors could be concerns as well, and need to be modelled into your calculations. But for a back-of-the-envelope estimate, our equations are likely sufficient.

Conclusion

With this article, we can see that “it depends” can be modelled into a set of calculations that give us a useful ballpark.