The origin of the LCOE formula

The LCOE stands for Levelized Cost Of Energy and is one of the several economic indexes to compare energy generation alternatives, including energy storage. It is based on the Net Present Value (NPV) criterion, in which all net benefits are taken to an initial moment, made equal to zero.

An NPV equal to zero means that the benefits (BEN) are equivalent to the expenses (EXP) in the lifespan of the energy alternative and, eventually, the net benefit is equal to zero.

Resulting,

In other words, the expenses over the benefits must be equal to one.

The expenses are the sum of the investments (I), maintenance (M), operation (O), and fuel (F) costs during the useful life (n) of the alternative, taken to the present value (t=0), in a given discount rate (r).

Benefits are obtained by selling the generated energy (E) for a given tariff (TE) at the same time t. It must be taken to the present value, using the same discount rate (r).

Therefore, there is:

Although this formulation considers that the energy tariff can change over time, a fulcrum concept defines that this tariff is constant, levelized all over time. This energy tariff is the LCOE that could be deducted from the sum, resulting in:

Rearranging,

Which eventually is the LCOE formula.

Therefore, energy is not corrected with the discount rate, as at first glance might suggest, but the benefits of selling it, and a constant energy tariff is isolated to obtain the LCOE.

You may find more information at:

1. https://www.irena.org/costs
2. https://www.lazard.com/perspective/levelized-cost-of-energy-levelized-cost-of-storage-and-levelized-cost-of-hydrogen/
3. https://en.wikipedia.org/wiki/Levelized_cost_of_energy