How we determine the optimal PV installation size
The data and analysis are specific to each city. The main steps are the following.
01
Electricity consumption
We estimate the annual consumption of a standard household, which we assume to be a family with 2 adults and 2 children, with a electricity usage typical of the specific city.
This annual consumption is split across the 8760 hours of the year using default load profiles published by regulatory agencies or utility companies of the region.
02
Solar irradiance
We collect hourly solar radiation and PV performance from tools such as PVGIS. We assume the panels can be mounted in an optimal angle relative to the sun.
03
Economic inputs
We collect data on electricity prices, PV panel prices, interest rates for consumer loans, available Government subsidies, and other economic variables.
We assume the equity cost of capital equals the risk-free rate, as the cash flows from this project are essentially savings on the existing electricity bills.
04
Economic optimization
For a given number of panels, we estimate the electricity generated by the PV system at each hour, and then the amount consumed in the house and the remaining sold back to the grid.
We then search over the number of panels to find the optimal installation size. This is the system size that maximizes the Net Present Value (NPV) of the savings in the electricity bills of the household.
05
Payback period of best system
The front page shows the payback period for the system that maximizes the NPV.
The data page shows other indicators for this optimal system, such as NPV, IRR, and LCOE, as well as details on the effect of Government subsidies.T
Glossary
Net Present Value (NPV)
NPV is the sum of all the cash flows generated by the project (discounted at the appropriate discount rate), minus the initial investment.
NPV is the main rule used in Corporate Finance to decide whether to undertake a project.
Example. Suppose the panels cost 3000 € and that you will save 300 €/year in the electricity bills over the next 25 years. If the discount rate is zero, the NPV is 4500 €. You are indifferent between installing the panels on your roof or receiving 4500 € in your bank account today.
Payback period
The payback period is the time it takes to recover the initial investment.
If the payback is substantially less than the expected life of the panels, the system is probably a good investment.
Example. For the NPV example above, the payback is 10 years. If the panels have a warranty of, say, 25 years, it is a good investment. You will be making a profit from the 10th to the 25th year.
Levelized cost of electricity (LCOE)
LCOE is the selling price of energy (€/kWh) that sets the NPV to zero, assuming all energy generated by the panels is sold to the grid. It can thus be interpreted as the minimum price at which you would have to sell all the energy to recover the initial investment.
Example. Suppose the LCOE is 0.05 €/kWh and that the electricity you buy from the grid costs 0.20 €/kWh. If you are able to use all the energy generated by the panels, then the system is definitely a good investment because you will be saving 0.15 € for every kWh of electricity that you use. On the other hand, if there is nobody home during the day and most of the solar power is injected back to the grid at a price of, say, 0.01 €/kWh, then the panels would be a bad investment.
Internal Rate of Return (IRR)
The IRR is the discount rate that sets the NPV to zero.
You should install the panels if the IRR is higher than the rate of return you could get on an alternative investment with the same risk.