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How to Calculate the Levelized Cost of Energy – a simplified approach

How to Calculate the Levelized Cost of Energy – a simplified approach

Calculating the levelized cost of energy is a fundamental principle in the energy and power industry. It basically allows the comparison of various technologies of unequal life times and capacities without resorting to developing a full-blown project finance model.

This simplified approach is particularly appropriate when doing a rough estimate on the cost of electricity given the various technologies in a country. By applying the formula on each power plant, as if it is continuously replaced to provide incremental power to meet new incremental demand, it provides a good estimate on the cost of electricity had a new plant been constructed to replace the old plant that became obsolete.

The weighted average levelized cost for the country is then estimated by using the electricity generation of each technology as weighing factor. For instance, the effect of injecting a nuclear power plant into the generation mix will be estimated quickly so that the country’s average levelized cost of energy could be compared with its neighboring competitor countries having nuclear power. Applying the same set of formulas and cost factors for each technology will yield a good index on our country’s competitiveness with respect to power costs.

Various Power Generation Technologies

I am sharing with you my own list and classification of the various power generation technologies, both existing and future technologies, that taken as a whole, would supply the ever growing needs of the peoples of our mother earth.

Levelized Cost of Each Power Generation Technology

The only way power generation technologies could be compared with respect to cost is to calculate the levelized cost of energy over its economic life. This involves obtaining data on rated capacity kW, overnigh costs $/kW, fixed Operating & Maintenance cost $/kW/year, variable O&M cost $/kWh, efficiency % or plant heat rate kJ/kWh, economic life years, availability %, load factor % or capacity factor %, fuel cost $/GJ or $/kg or $/L, fuel Gross Heating Value kJ/kg or kJ/L, fuel density kg/L, and construction lead time years.

The levelized cost allows comparison of different power generation technologies of unequal economic life, capital cost, risk and returns, capacity factor, efficiencies or plant heat rate, fuel costs and construction lead times.

The basic formula used is based on the US NREL formula for the levelized cost of energy (net):

Net COE = ICC * CRF / AEPnet + (LLC + O&M + LRC + MOE) – PTC, in US $/kWh

where ICC = Initial Capital Cost (total debt), $

CRF = capital recovery factor, 1/yr = int / (1 – (1 + int)^-Life)

AEPnet = Net Annual Energy Production, kWh/yr (net of plant own use)

= (kW capacity) * (capacity factor) * (hours/year)

LLC = Land Lease Cost, $/kWh

O&M = Levelized Operating & Maintenance Expense, $/kWh

LRC = Levelized Replacement/Overhaul Cost, $/kWh

MOE = Miscellaneous Operating Expense, $/kWh

PTC = US Production Tax Credit, $/kWh

In the case of the Philippines where the effect of income tax and depreciation needs to be considered, the RP MTO formula developed by Engr. Marcial T. Ocampo is shown:

Net COE = Total Cost / ((1 – g) * (1 – t)), in US $/kWh or US cents/kWh

where Total Cost = ( ICC * CRF + (FixO&M + VarO&M + DOE + Fuel) * (1 – t) – t * DEPN ) / AEPnet

ICC = (Capacity, kW) * (Overnight Cost, $/kW)

Overnight Cost = Installed Cost + Interest During Construction

CRF = capital recovery factor, 1/yr = int / (1 – (1 + int)^-Life)

AEPnet = Net Annual Energy Production, kWh/yr (net of plant own use)

= (kW capacity) * (capacity factor) * (hours/year)

FixO&M = (Fixed O&M, $/kW/yr) * (Capacity, kW)

VarO&M = (Variable O&M, $/kWh) * AEPnet

DOE = (PhP 0.10 / kWh) / (Exchange Rate, PhP / US $) * AEPnet

Fuel = (net Heat Rate) * AEPnet * (Price of fuel)

= (3600 / Efficiency, kJ/kWh net) * AEPnet * (Price, $/kJ net)

DEPN = Depreciation, $ / yr = ICC / Life

g = Franchise Tax + Business Tax = 2.5% + 0.005% = 2.005%

t = Income Tax = 35%

int = Interest Rate, %

Life = Economic Life or Project Life, yrs

Please note that when the RP MTO formula of Marcial is simplified by disregarding depreciation, franchise tax & business tax and income tax, the RP MTO formula becomes similar to the US NREL formula:

Net COE = ICC * CRF / APEnet + (FixO&M + VarO&M + DOE + Fuel) / AEPnet

where the last term (FixO&M + VarO&M + DOE + Fuel) / AEPnet are unit costs per kWh.

Various Power Generation Technologies:

Oil – Gas Thermal

Reciprocating / Piston Engine:

Small or High-Speed
Medium Speed
Large or Slow Speed
Combined Cycle – Waste Heat Boiler

Natural Gas – Simple GT:

Aero-Derivative GT
With Recuperation
Humid Air Turbine (HAT)
Cascaded Humid Air Turbine (CHAT)
Heavy Frame GT

Natural Gas – Combined Cycle GT

Coal:

Pulverized
Amospheric CFB
Presurized FBC
IGCC
IGHAT
Direct Coal-Fired Combined Cycle (DCCC)
Supercritical & Ultra-Supercritical Coal Comb.

Nuclear Fission:

Boiling Water Reactor (BWR), advanced
Pressurized Water Reactor (PWR)
Pressurized Heavy Water Reactor (PHWR)
Advanced Gas-Cooled Reactor (AGR):
Candu Reactor
High Temp. Gas-Cooled Reactor (HTGR)
Gas Turbine Modular Helium Reactor (GT-MHR)
Breeder Reactors

Nuclear Fusion

Hydro:

Large:
Pelton Turbine – 50-6,000 ft head
Francis Turbine – 10-2,000 ft head
Propeller Turbine – 10 – 300 ft head:
Kaplan Turbine
Small / Mini
Micro

Energy Storage:

Pumped Hydro
Compressed Air Energy Storage (CAES) – Huntorf:
Large CAES
Small CAES
Above Ground CAES
Flywheel Systems
Utility Scale Batteries (USB):
Lead acid
Advanced
Stored Hydrogen
Superconduction Magnetic Energy Storage (SMES)
Ultracapacitors

Geothermal:

Dry Steam (Vapor)
Flashed Steam (Single, Double)
Binary Cycle
Petrothermal (Hot Dry Rock)
Geothermal Preheat
Fossil Superheat

Wind

Solar PV:

Crystalline silicon
Thin film – Amorphous Silicon
Thin film – Indium Diselenide
Flat Plate
High Efficiency Multi Junction – IHCPV

Solar Thermal:

Trough
Tower
Dish
Salt Pond (power + water)

Fuel Cells:

Alkaline (AFC)
Phosphoric Acid (PAFC)
Proton Exchange Membrane (PEM)
Direct Methanol
Molten Carbonate (MCFC)
Solid Oxide-GT (SOFC-GT)

Biomass:

Direct Combustion
Co-firing with Coal
Biomass Gasification (BIGCC)
Municipal Waste
Pyrolysis
Landfill Gas (40 – 60% CH4)
Anaerobic Digestion (65% CH4)
Sewage Digestion

Ocean Thermal:

Claude (open cycle)
Controlled Flash Evaporation (open)
Anderson (closed cycle)

Ocean Wave:

Oscillating Water Column (OWC)
Hydraulic Accumulator
High Level Reservoir
Float or Pitching Devices
Wave Surge or Focusing (“tapchan”)
Pendulor

Tidal Power:

Single Pool
Modulated Single Pool w/ Pumped Hydro
Two Pool

The reader is encouraged to share his data on each power generation technolology so that the levelized cost of energy could be calculated using the two formulas above (US NREL and RP MTO).

In the next update, I would present a sample calculation to guide the reader.

I would like to invite you and your company to continue supporting this blog thru the DONATE button.  You may order my power generation technology articles and project finance models thru the ENERGY DATA page. Thanks!

Marcial T. Ocampo

(Friendly note: All content written by Engr. Marcial T. Ocampo are copyrighted and may not be redistributed in any way or form.)

71 Responses to “How to Calculate the Levelized Cost of Energy – a simplified approach”

  1. Waste-Technology » Energy Technology Expert » Blog Archive » How to Calculate the ... Says:

    [...] Energy Technology Expert » Blog Archive » How to Calculate the …Various Power Generation Technologies: Oil – Gas Thermal. Reciprocating / Piston Engine: Small or High-Speed Medium Speed Large or Slow Speed Combined Cycle – Waste Heat Boiler. Natural Gas – Simple GT: Aero-Derivative GT … [...]



  2. admin Says:

    Thanks for the question: what are the components of fixed and variable O&M costs.

    Answer:

    The fixed O&M costs generally includes monthly recurring costs that do not vary with the power plant output: salaries and wages, HO and plant overhead, admin expenses, security, rent/lease, regular maintenance, etc.

    The variable O&M costs generally refers to costs that vary with plant output: operating spares, variable labor, materials and supplies.

    Other expenses and regulatory costs (but preferably separate from O&M costs), property and business interruption insurance, real estate tax (property tax), local and national government permits, fees, licenses.

    Admin – Marcial



  3. Levelized Cost of Energy - sample calculation results | Energy Technology Expert Says:


  4. Levelized Cost of Energy - sample calculation results | Intelligent Utility Says:


  5. home made power generator Says:

    Seems like such a basic idea for free energy but it takes a group of people to discuss the details, thanks, excellent read, ive added a bookmark for your site.



  6. sudhindakumar Says:

    Very useful and tachnically execallant



  7. admin Says:

    Hi Kumar,

    Thanks very much for your wonderful comment. Very encouraging.

    Regards,

    Marcial



  8. SUBHASH SOOD Says:

    I need to understand thoroughly the method of quoting charges for fixed and variable components of generation tariff required in competitive bidding being done by the distribution companies in india as per the guide lines of the government. Also i need to understand the evaluation method of the bids. please suggest what to read and how to gather this information



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    Well conceived, novel take on this subject.



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    This is what I need to know and I have been searching for few days. Thank You.



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  12. engr nasim haider Says:

    I need the cost per kw of hydro power stations ( excluding civilworks ), based on Francis and/orKaplan turbines. Would appreciate your help.

    Reards

    Engr. Nasim Haider



  13. Wale Says:

    Hi,
    Can you tell me how to convert $/t capacity of a coal conversion plant to $/MWth?

    Kind regards



  14. admin Says:

    Hi Wale,

    Follow the following formulas to convert from $/t of coal to $/MWh:

    80 US$/ton x (1 ton / 1000 kg) x (1 kg / 2.2046 lb) x (lb / 10,000 BTU heating value) x [(3600/1.05506 Btu/kWh) / (thermal efficiency)] x (1,000 kWh/MWh)

    (cost per ton) / 1000 / 2.2046 / (gross heating value of fuel) x [plant heat rate, Btu/kWh] x 1000 = $/MWh

    Regards,

    Marcial



  15. George Says:

    The simplified LCOE formula from NREL is not the same as what you have given on your website;

    sLCOE = {(overnight capital cost * capital recovery factor fixed O&M cost )/(8760 * capacity factor)} (fuel cost * heat rate) variable O&M cost.

    Which is given in here – http://www.nrel.gov/analysis/tech_lcoe_documentation.html

    I would like to get the peer-reviewed citing of your work of “IEPR Committee Workshop on the Cost of Electricity Generation – Renewable Energy, Clean Coal and Nuclear” thanks. And a copy of the simplified model which could be used to determine the “Best New Entrant” technology for a given application (demand and fuel/energy resource availability)

    Thanks for your clarification.



  16. Laxman Says:

    The approach of leveliseh cost of energy is very useful and undetandable to management who fall different categories of the discipline.
    Laxman



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  37. ritesh Says:

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    I am little confused, regarding how to incorporate total no. of units generated in a year. If life time is 20 years and plant produces 1000 units per annum. Then units per annum for 20 years is calculated by simple average or using NPV as in case of cost.

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  40. Massimo Says:

    Hi, can you explain me which is the difference in calculating LCOE vs calculating cost of genetaed electricity through the following formula: (NPV (investments operating costs)) / (total produced power during project lifecycle)?

    Thanks

    Massimo



  41. Massimo Says:

    hello,
    could you please explain me the difference in calculating LCOE with the above formula vs calculating cost of electricity thouugh the following formula:
    NPV (Investment operating costs) / total generated power during project life

    Thanks



  42. admin Says:

    Hi Massimo,

    The LCOE = ICC * CRF / AEPnet (LLC O&M LRC MOE) – PTC, in US $/kWh or US cents/kWh

    The initial capital cost is multiplied by the captial recovery factor (CRF) which converts a one-time expense into a series of annuity and by dividing by the annualgeneration, you get the capital cost per kWh. Then add the other O&M costs (fixed & variable), regulatory, etc, to arrive at the total capital and O&M costs per kWh.

    On the other hand, the project finance model calculates the first year tariff that will allow the equity investor to meet its IRR requirements (i.e. NPV = 0). The LCOE or levelized cost of electricity can then calculated from the NPV all expense items in the Profit & Loss (Income) statement divided by the NPV of generated electricity.

    The other approach of calculating the NPV of all costs divided by the NPV of all generated electricity will also result in the 3 having the same results if each O&M cost item is constant and do not vary over time.



  43. Massimo Says:

    Thanks for the reply. However I am not sure why I should make the NPV of generated electricity since this is not a cash flow but a given amount of power. Let’s assume a 10MW plant with:
    - 20 years life
    - $10M initial investment
    - $100k constant opex
    - WACC at 5%
    - 8500 hours per year (or 97%)

    LCOE gives me back = 1.06$/kWh

    The other method give me back = 0.007$/kWh

    Thanks for your help



  44. Electric Fence Malaysia Says:

    Calculating cost this way is very difficult for me as i don’t have much idea of different units of electricity and then the other issue is that i have only experience of installing electric fence where we don’t need to do any calculation



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  46. admin Says:

    Thanks Dheeraj, appreciate your kind and thoughtful remarks. Great. Marcial



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    Ashok



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  63. Muniruddin Says:

    I have been told by an expert the formula of calculating fuel as under:

    rate of fuel per ton x gross plant heat rate x annual gross energy / calorific value of coal.
    Is this formula correct.

    further one expert has defined gross plant heat rate as under:
    gross plant heat rate is gross electricity produced by a power plant per unit fuel energy consumed. Is this definition correct.



  64. Muniruddin Says:

    I shall be very thankful if you very kindly guide me in above mentioned two questions as soon as possible.
    Your site is really very useful for the people.
    thanks



  65. admin Says:

    Fuel Consumption (lb/yr) = (gross plant heat rate, Btu/kWh) x (annual generation, kWh/yr) / (gross calorific value, Btu/lb)

    Fuel Consumption (mt/yr) = (lb/hr) x (kg/2.2046 lb) x (mt/1000 kg)

    Gross plant heat rate (Btu/kWh) = (3600 / 1.05506, Btu/kWh at 100% efficiency) / (GCV thermal efficiency, %)

    = (GCV of fuel, Btu/lb) x (2.2046 lb/kg) x (1000 kg/mt) x (fuel consumed, mt/yr) / (annual generation, kWh/yr)

    = (Btu/yr) / (kWh/yr) = Btu/kWh = Gross plant heat rate



  66. admin Says:

    Corrections please:

    Fuel Consumption (lb/yr) = (gross plant heat rate, Btu/kWh) x (annual generation, kWh/yr) / (gross calorific value, Btu/lb)

    Fuel Consumption (mt/yr) = (lb/yr) x (kg/2.2046 lb) x (mt/1000 kg)

    Gross plant heat rate (Btu/kWh) = (3600 / 1.05506, Btu/kWh at 100% efficiency) / (GCV thermal efficiency, %)

    = (GCV of fuel, Btu/lb) x (2.2046 lb/kg) x (1000 kg/mt) x (fuel consumed, mt/yr) / (annual generation, kWh/yr)

    = (Btu/yr) / (kWh/yr) = Btu/kWh = Gross plant heat rate



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  68. Muniruddin Says:

    I am really grateful for early and to the point guidance. Because I am not very well conversant with this kind of knowledge, I need some more guidance as under:

    What would be the gross plant heat rate of a coal fired power plant of capacity 50 megawatt with net output 44 megawatt, calorific value of coal 2422 Kcal/kg, gross efficiency 30.98%, net efficiency 27.26%, annual gross energy 350 Giga watt hours and annual net energy 308 giga watt hours. capacity factor is 80%. Boiler’s efficiency is 83%. can we calculate gross plant heat rate with above data. Some expert has told me that in the above case, the gross plant heat rate would be 2781.7 Kcal/kwh and net plant heat rate would be 3161 Kcal/kwh. Is it correct?

    It is a really a helpful sight. I have searched the net and did not find answer to may questions except your site. Thanks



  69. Muniruddin Says:

    If the expert says that the gross plant heat rate is 3781.7 K cal /kWh and net plant heat rate is 3161 k cal/kWh. can we verify this figure with the help of above mentioned information.

    further can the GPHR and Net PHR be verified with the help of international certification software’s calculations. Would you please like to guide me about this international certification software.How does it work? Thanks



  70. Muniruddin Says:

    Dear sir,
    I have received and email reply but I feel that I need a detailed reply specifically with reference to my above mentioned questions.Would you kindly like to help me?



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