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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.)

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  13. 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:
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  15. 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



  16. 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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