Levelized cost of energy

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The levelized cost of energy (LCOE), or levelized cost of electricity, is a measure of the average net present cost of electricity generation for a generating plant over its lifetime. The two commonly used definitions of LCOE are; a first one (denoted as LCOE₁) is calculated as the ratio between all the discounted costs over the lifetime of an electricity generating plant divided by a discounted sum of the actual energy amounts delivered.., and a second one (denoted as LCOE₂) is calculated as the ratio between all the discounted costs over the lifetime of an electricity generating plant divided by a sum of the actual energy amounts delivered.. The LCOE is used to compare different methods of electricity generation on a consistent basis. The LCOE₂ "represents the average revenue per unit of electricity generated that would be required to recover the costs of building and operating a generating plant during an assumed financial life and duty cycle." Inputs to LCOE are chosen by the estimator. They can include cost of capital, decommissioning, "fuel costs, fixed and variable operations and maintenance costs, financing costs, and an assumed utilization rate."

Calculation

The LCOE is calculated as:

$\mathrm {LCOE_{1}} ={\frac {\text{sum of costs over lifetime}}{\text{sum of electrical energy produced over lifetime}}}={\frac {\sum _{t=1}^{n}{\frac {I_{t}+M_{t}+F_{t}}{\left({1+r}\right)^{t}}}}{\sum _{t=1}^{n}{\frac {E_{t}}{\left({1+r}\right)^{t}}}}}$

or

$\mathrm {LCOE_{2}} ={\frac {\sum _{t=1}^{n}{\frac {I_{t}+M_{t}+F_{t}}{\left({1+r}\right)^{t}}}}{\sum _{t=1}^{n}{E_{t}}}}$

It	:	investment expenditures in the year t
Mt	:	operations and maintenance expenditures in the year t
Ft	:	fuel expenditures in the year t
Et	:	electrical energy generated in the year t
r	:	discount rate
n	:	expected lifetime of system or power station

Note: Some caution must be taken when using formulas for the levelized cost, as they often embody unseen assumptions, neglect effects like taxes, and may be specified in real or nominal levelized cost.

Typically the LCOE is calculated over the design lifetime of a plant, which is usually 20 to 40 years, and given in currency per energy unit, for example EUR per kilowatt-hour or AUD per megawatt-hour. However, care should be taken in comparing different LCOE studies and the sources of the information as the LCOE for a given energy source is highly dependent on the assumptions, financing terms and technological deployment analyzed. In particular, assumption of capacity factor has significant impact on the calculation of LCOE. Thus, a key requirement for the analysis is a clear statement of the applicability of the analysis based on justified assumptions.

In particular, for LCOE to be usable for rank-ordering energy-generation alternatives, caution must be taken to calculate it in "real" terms, i.e. including adjustment for expected inflation.

LCOE₁ is an economic paradox

Contrary to common understanding, one can show that the LCOE₁ definition used by many government agencies, all around the world, is mistaken. For example, assuming that I_t+M_t+F_t = C, and E_t = E, where C and E are the real constants, one obtains LCOE₁ = C/E and LCOE₂ = (C/E)D, where D is a mean value of the discount function. The formal proof of this fact follows from the mean value theorem for integrals and shows that LCOE₁ violates the discounting procedure. The another proof is based on the mean costs-revenues equilibrium and characterizes LCOE₁ as an undiscounted quantity Summarizing, the definition LCOE₁ does not have:

• a sound economic base,

• violates the Newtonian physics, and

• induces an economic paradox.

There is no point to use this definition. From the other site, the LCOE₂ definition does have proper economic meaning and should be used in applications. The LCOE₂ is commonly used in the oil industry.

Considerations

There are potential limits to some levelized cost of electricity metrics for comparing energy generating sources. One of the most important potential limitations of LCOE is that it may not control for time effects associated with matching electricity production to demand. This can happen at two levels:

• Dispatchability, the ability of a generating system to come online, go offline, or ramp up or down, quickly as demand swings.
• The extent to which the availability profile matches or conflicts with the market demand profile.

In particular, if matching grid energy storage is not included in models for intermittent renewable energy sources such as solar and wind that are otherwise not dispatchable, they may produce electricity when it is not needed in the grid without storage. The value of this electricity may be lower than if it was produced at another time, or even negative. At the same time, intermittent sources can be competitive if they are available to produce when demand and prices are highest, such as solar during summertime mid-day peaks seen in hot countries where air conditioning is a major consumer. Some dispatchable technologies, such as most coal power plants, are incapable of fast ramping. Excess generation when not needed may force curtailments, thus reducing the revenue of a energy provider.

Another potential limitation of LCOE is that some analyses may not adequately consider indirect costs of generation. These can include environmental externalities or grid upgrades requirements. Intermittent power sources, such as wind and solar, may incur extra costs associated with needing to have storage or backup generation available.

The LCOE of energy efficiency and conservation (EEC) efforts can be calculated, and included alongside LCOE numbers of other options such as generation infrastructure for comparison. If this is omitted or incomplete, LCOE may not give a comprehensive picture of potential options available for meeting energy needs, and of any opportunity costs. Considering the LCOE only for utility scale plants will tend to maximize generation and risks overestimating required generation due to efficiency, thus "lowballing" their LCOE. For solar systems installed at the point of end use, it is more economical to invest in EEC first, then solar. This results in a smaller required solar system than what would be needed without the EEC measures. However, designing a solar system on the basis of its LCOE without considering that of EEC would cause the smaller system LCOE to increase, as the energy generation drops faster than the system cost. Every option should be considered, not just the LCOE of the energy source. LCOE is not as relevant to end-users than other financial considerations such as income, cashflow, mortgage, leases, rent, and electricity bills. Comparing solar investments in relation to these can make it easier for end-users to make a decision, or using cost-benefit calculations "and/or an asset’s capacity value or contribution to peak on a system or circuit level".

Discount rate of low-carbon technologies

Choice of specific parameters in the above equation, especially discount rate, has a critical impact on the outcome. For example, a typical choice of 10% discount rate results in the energy production in 20 years being assigned accounting value of just 15%, which nearly triples the LCOE price. This approach, which is considered prudent from today's private financial investor's perspective, is being criticised as inappropriate for assessment of public infrastructure that mitigates climate change as it ignores social cost of the CO2 emissions for future generations and focuses on short-term investment perspective only. The approach has been criticised equally by proponents of nuclear and renewable technologies, which require high initial investment but then have low operational cost and, most importantly, are low-carbon. According to Social Cost of Carbon methodology, the discount rate for low-carbon technologies should be 1-3%.

Levelized avoided cost of energy

The metric levelized avoided cost of energy (LACE) addresses some of the shortcomings of LCOE by considering the economic value that the source provides to the grid. The economic value takes into account the dispatchability of a resource, as well as the existing energy mix in a region.

Levelized cost of storage

The levelized cost of storage (LCOS) is the analogous of LCOE applied to electricity storage technologies, such as batteries. Distinction between the two metrics can be blurred when the LCOE of systems incorporating both generation and storage are considered.

See also

• Cost of electricity by source

References

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