Andre Jordaan, Pragma
The prevalence of boreholes used by municipalities has increased significantly during the droughts of the last couple of years, with the expectation that weather and rainfall would become even more erratic. The following scenario was modelled to assist decision-making within this new trend, using life-cycle costing.
If water were to be found 10 km from the closest waterline flowing into the municipal network and two boreholes were sunk in close proximity to each other, should solar power as a technology be considered, when compared to diesel? Wind could not be considered as it is too erratic and the dependence on this waterline too critical in times of drought.
Even though the capital outlay for solar would be ten times more than the diesel generator, the diesel option turned out 85% more expensive than the solar solution.
The diesel option would in fact be over R1,8- million more expensive over a 50 year period, expressed in today’s monetary terms. This is mainly due to the diesel costs involved, compared to the solar option using the sun as free local available energy source. This is despite the short lifespan of the electric batteries for the solar solution, although it is expected that huge technological improvements will come about over the next couple of years.
A sensitivity analysis was conducted and shows that:
- Only at the unlikely event that fuel halves for the entire duration of operations (50 years), would the diesel option beat the solar option.
- Only if the demand drops by 50%, would the diesel option beat the solar option. This was a likely scenario as water might be required throughout the year during times of drought, but only for the dry season during regular weather.
- Interest rates had to climb from 10% to 25%, to give a resultant discount factor of 20%, before the diesel option became competitive; clearly a very unlikely scenario.
It is clear that without the use of life-cycle costing, the decision as to the technology would merely be guesswork and lead to incorrect decisions.
Analysis and physical design
The two boreholes allowed for 4 m3/h water flow and required a head of 140 m. Two different suppliers and each two different pumps were considered, all of them requiring between 3,5 kW and 4 kW. With the total demand of 8 kW, two high level designs were made, so as to facilitate costing and to compare the technologies. It was also assumed that pumping 70% of the time would be sufficient.
Two different capacity generators were considered, from two different manufacturers, but whether a 13,5 kVA FAW generator ran at 60%, or a 25 kVA Cummings ran at 32% to deliver the 8 kW, they both consumed close to 3 ℓ of fuel per hour. The 13,5 kVA FAW generator was costed into the model. The generator would be overhauled after ten years, with a total life expectancy of 20 years. It would also be serviced by the local branch every second month, with refueling every second week (with just over 710 ℓ of fuel each time).
For the solar solution, 100 panels that would stretch up to a 14 m x 14 m continuous area would be required, with 50 lead crystal deep cycle batteries, and two 5 KW invertors. This would bring about a generating capacity of 147 kWh per day and be able to store almost 50% thereof, for use during the night. The panels would be washed every second month, while at the same time the vegetation cleaned up. The panels and inverter have a life expectancy of 20 years, while the batteries only six years.
The cost, life expectancy and maintenance on the pump, the 10 km water pipe, security features and remote control and feedback were not considered, as it would be the same for both scenarios.
Two different mathematical models were used to compare the two proposed solutions, as follows:
Equivalent annual costing (EAC)
The solar panels and inverter are replaced after 20 years, while the batteries needed replacement every six years. Equivalent annual cost (EAC) makes it easier to cater for such components of different lifecycles within a total solution. It also allows very easily for the ten year overall of the diesel generator to be accounted for, compared to the generator itself which is only replaced every 20 years.
For this exercise, the EAC for each of the components were calculated separately and then added, to get the solution’s total EAC.
The use of EAC allows one to look at the solar solution and think of it as costing the municipality R119 000 per year, while looking at the diesel solution and thinking that it costs the municipality R221 000 per year (see Fig. 1).
Each of the solutions were modeled over a 50 year period. To calculate it into perpetuity, one would use the simple calculation:
r = EAC/r
It turned out that the 50 year calculation was 97% compared to that of perpetuity. The method also allows one to see the total quantum of the decision. Over a 50 year period, in today’s monetary terms, the solar solution would cost the municipality R2,119-million and the Diesel option R4,039-million.
Choosing solar would mean a real R1,85-million benefit over the diesel option, even though the initial capital outlay would be over ten times higher than that of the diesel generator.
Cash flow model
An alternative to the EAC model is to once again sum all the cash flows over the total duration of the 50 years. But for this example, the intervals of replacement and refurbishment needs to be shown. Batteries need to be replaced every six years, generators and panels be replaced every 20 years, and generators overhauled every ten years.
In this example, the discount rate was broken up into its two components:
- The future expenses increased using the inflationary (CPIX) rate.
- The future values brought back to present value (PV) terms using the interest rate.
Comparison between the two models
It is interesting to note that the two models are not in full agreement as to the answer. This is to be expected as the EAC method smooths the payment over a longer term and where a solar installation might have been installed in year 41, it would have considerable life left which is not catered for the same between the models.
The financial differences between the models are an accurate representation of their different way of expressing the solution. It is so small that the answers materially remains the same.
Understanding not just the answer to the problem, but how input variables influences it, creates true knowledge. This is essential to understanding the complete landscape.
The influence of three variables that could fluctuate most after the initial investment decision and implementation were investigated to understand their impact:
- The discount rate
- The price of the fuel
- The actual demand
Each of the options were investigated and changed such that the two models became equal. Thus, how much did the variables have to change to have me reconsider the chosen technology?
The discount rate is essentially the difference between the interest rate and the inflation rate. They normally move together, and currently modelled at 5% apart.
It had to change a further 15%, so that the total discount rate be at 20% before the two models drew equal. This is clearly highly unlikely. It would mean an interest rate at for instance 25%, while inflation stays at 5%.
Even though this might be possible for a short period of time, it is unthinkable that this could be the norm over the 50 year period.
The fuel (diesel) price used was R10,35 per litre, which is already slightly below current, but in line with commercial fuel. The fuel price had to half, to have the two draw equal.
Bulk fuel prices have been extremely volatile over the last two years. And indeed more than halved, but to half from where we are as the norm for the next 50 years is once again extremely unlikely. More likely would be that government would rather maintain and increase the fuel levy if the price dropped further, making this scenario once again extremely unlikely.
The current demand is modelled at pumping the two boreholes 70% of the time, throughout the year. The diesel generator might allow for pushing this higher, but the solar option would not allow it as much so, thanks to the restriction in storage.
If the demand were to half, the diesel option would actually become cheaper than the solar option.
This is a very real possibility, as water demand is often more of an issue during the dry season. The wet season normally produces enough water and only during the drought would the pump be needed almost all year round. This meant that more investigation had to be done to understand the demand, as this could very well influence the technology decision.
Contact Andre Jordaan, Pragma, Tel 021 943-3944, firstname.lastname@example.org