Energy Technology Expert

How to Calculate the Levelized Cost of Energy and Electricity – some updates and developments

The author is re-issuing this article in view of the tremendous interest worldwide on this article.  A number of readers have in fact ordered my technology articles, specifically on the cost of power generation technology (a spreadsheet containing the technology, rated capacity, overnight cost $/kW, capacity factor % of rated capacity, fixed O&M $/kW/year, variable O&M $/kWh, energy conversion efficiency % of fuel energy, fuel cost $/GJ, economic life years, construction lead time years, reliability % of operating hours, availability % of calendar days, and levelized cost $/kWh).

Using the NREL formula and a detailed project finance model, I was able to demonstrate that the results would be the same in calculating the levelized cost of energy or electricity.  The reader is adviced to email me if they would like to get a copy of the spreadsheet showing the two calculations.

With the passage of the Philippine Renewable Energy Act of 2009 (RE Law) and its implementing rules and regulations (IRR), it is imperative that financial models for renewable energy projects be revised accordingly.  This author and our group of experts would assist project proponents and investors in the Philippines develop an updated financial model for evaluating their RE project proposals for endorsement by the Department of Energy (DOE) and for the approval of their feed-in tariffs with the Energy Regulatory Commission (ERC).

Marcial T. Ocampo

Here is the original article that is being re-printed for our new readers.

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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 power 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.

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) * AEPnet * (Price, $/kJ)

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.

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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Please email for the spreadsheet.  You need to order this model via the ENERGY DATA page of my website.

ASSUMPTIONS:

Franchise Tax = 2.0% of revenue

Business Tax = 0.005% of revenue

DOE 1-94 Fee = 0.01 PhP/kWh sold

Corporate Income Tax = 35% of taxable income

Hours Per Year = 24 * 365 = 8,760 hours/year

Equity = 30%

Debt = 70%

Minimum Equity IRR = 15% p.a.

Debt Interest = 12% p.a.

Weighted Average Cost of Capital (WACC) = 30% x 15% p.a. + 70% x 12% p.a. = 12.9% p.a.

Discounting Rate = WACC = 12.9% p.a.

Exchange Rate = 48.46 PhP/US$ (April 21, 2009)

Diesel Price = 25.45 PhP/Liter = 83.51 US$/bbl

(19,650 BTU/lb HHV, 18,453 BTU/lb LHV, 0.820 kg/Liter)

Bunker Price = 17.90 PhP/Liter = 58.72 US$/bbl

(18,400 BTU/lb HHV, 17,449 BTU/lb LHV, 0.92 kg/Liter)

Natural Gas Price = 6.00 US$/MMBTU

(20,754 BTU/lb HHV, 18,798 BTU/lb LHV)

Orimulsion Price = 50% of Bunker

(13,330 BTU/lb HHV, 12,384 BTU/lb LHV)

Coal Price = 85 US$/MT

(11,630 BTU/lb HHV, 11,105 BTU/lb LHV)

Nuclear Fuel Price = (365 fuel + 400 fabrication) = 765 $/kg (3,900 GJ/kg)

CONVERSION FACTORS:

1 kg = 2.2046 lb

1 MT = 1,000 kg

1 US gal = 3.7854 Liters

1 bbl = 42 US gal = 42 x 3.7854 = 158.9868 Liters/bbl

1 kWh = 3,600 kJ

1 BTU = 1.05506 kJ

1 MMBTU = 1.05506 GJ

1 GJ = 1,000,000 kJ

SAMPLE DATA FOR CALCULATING LEVELIZED COST

0.00%	1996	1	2009	30%	70%	exchange rate		discounted cash flow rate		kJ/kWh	h/yr
SIMPLIFIED LEVELIZED COST OF ELECTRICITY: Method 1a				15%	12%	P / US $ =	48.46	DCF =	12.90%	3600	8760
Type of Plant	Capacity	Overnight	Capacity	Fixed	Variable	DOE	Franchise	Income	Economic	Thermal	Fuel
and Fuel		Cost	Factor	O&M Cost	O&M Cost	fund	Business tax	Tax	Life	Efficiency	Price
	MW	$/kW	%	$/kw/yr	cents/kWh	P/kWh	%	%	yrs	% LHV net	$/GJ net
Oil Thermal	300	991	75.00%	0.300	0.050	0.010	2.005%	35.00%	25	33.00%	9.89
Orimulsion Thermal	100	1,376	57.69%	0.390	0.065	0.010	2.005%	35.00%	19	38.00%	5.05
Gas Thermal	100	991	75.00%	0.300	0.050	0.010	2.005%	35.00%	25	45.00%	6.28
Reciprocating Engine	50	1,300	75.00%	0.040	0.500	0.010	2.005%	35.00%	20	47.00%	14.92
Orimulsion Reciprocating Engine	50	1,685	57.69%	0.052	0.650	0.010	2.005%	35.00%	15	47.00%	5.05
Simple Gas Turbine Aero Derivative	35	325	75.00%	0.040	0.500	0.010	2.005%	35.00%	25	38.00%	6.28
Recuperated GT	3	400	75.00%	0.040	0.500	0.010	2.005%	35.00%	25	40.50%	6.28
CHAT 11 MW	11	800	75.00%	0.040	0.500	0.010	2.005%	35.00%	25	44.50%	6.28
CHAT 300 MW	300	375	75.00%	0.040	0.500	0.010	2.005%	35.00%	25	54.70%	6.28
Heavy Frame GT	200	560	75.00%	0.040	0.500	0.010	2.005%	35.00%	25	35.00%	6.28
Combined Cycle GT	500	650	82.00%	0.150	0.200	0.010	2.005%	35.00%	25	56.00%	6.28
Pulverized Coal Thermal	600	1,079	75.00%	0.225	0.325	0.010	2.005%	35.00%	30	38.00%	3.29
Atmospheric CFB	350	1,300	80.00%	0.225	0.325	0.010	2.005%	35.00%	35	41.00%	3.29
Pressurized FBC	550	1,200	80.00%	0.242	0.325	0.010	2.005%	35.00%	35	43.00%	3.29
IGCC	250	1,206	80.00%	0.242	0.187	0.010	2.005%	35.00%	35	45.00%	3.29
BWR Advanced Nuclear	1,356	2,521	65.00%	0.550	0.040	0.010	2.005%	35.00%	30	33.00%	0.20
PWR Advanced Nuclear	1,460	1,636	65.00%	0.550	0.040	0.010	2.005%	35.00%	30	33.00%	0.20
PHWR once thru	1,330	1,518	65.00%	0.550	0.040	0.010	2.005%	35.00%	30	33.00%	0.20
AGR Advanced Nuclear	1,100	1,550	65.00%	0.550	0.040	0.010	2.005%	35.00%	30	33.00%	0.20
Large Hydro	200	3,000	70.00%	0.000	0.000	0.010	2.005%	35.00%	60	75.00%	0.00
Small / Mini Hydro	30	1,300	50.00%	0.000	0.000	0.010	2.005%	35.00%	50	75.00%	0.00
Micro Hydro	0.1	2,200	33.00%	0.000	0.000	0.010	2.005%	35.00%	20	75.00%	0.00
Pumped Hydro Storage	1800	920	8.33%	0.000	10.000	0.010	2.005%	35.00%	50	75.00%	0.00
Compressed Air Energy Storage	350	350	8.33%	0.000	1.000	0.010	2.005%	35.00%	10	80.00%	0.00
Flywheel Storage	100	750	8.33%	0.000	300.000	0.010	2.005%	35.00%	10	80.00%	0.00
USB – Lead Acid Storage	10	460	8.33%	0.000	17.000	0.010	2.005%	35.00%	10	90.00%	0.00
USB – Advanced Storage	10	320	8.33%	0.000	100.000	0.010	2.005%	35.00%	10	90.00%	0.00
SMES Storage	100	720	8.33%	0.000	300.000	0.010	2.005%	35.00%	10	90.00%	0.00
Ultracapacitors Storage	1	2,025	8.33%	0.000	3600.000	0.010	2.005%	35.00%	10	90.00%	0.00
Geothermal Flashed Steam	50	2,000	90.00%	0.957	0.015	0.010	2.005%	35.00%	50	28.00%	2.00
Wind Farm	40	857	30.00%	0.256	0.000	0.010	2.005%	35.00%	20	60.00%	0.00
Solar PV	10	3,136	30.00%	0.097	0.000	0.010	2.005%	35.00%	20	10.00%	0.00
Solar Thermal trough	80	2,900	30.00%	1.000	0.000	0.010	2.005%	35.00%	30	18.00%	0.00
Solar Thermal tower	200	2,400	30.00%	0.700	0.000	0.010	2.005%	35.00%	30	18.00%	0.00
Solar Thermal dish + Stirling engine	0.5	2,900	30.00%	2.000	0.000	0.010	2.005%	35.00%	30	35.00%	0.00
Phosphoric Acid Fuel Cell	1	1,500	80.00%	0.144	0.200	0.010	2.005%	35.00%	6	36.00%	5.69
Proton Exchange Membrance FC	0.25	1,000	80.00%	0.144	0.200	0.010	2.005%	35.00%	6	35.00%	5.69
Molten Carbonate FC	20	1,440	80.00%	0.144	0.200	0.010	2.005%	35.00%	6	47.00%	5.69
Solid Oxide FC	3	1,000	80.00%	0.144	0.200	0.010	2.005%	35.00%	6	47.00%	5.69
SOFC + GT hybrid	5	1,200	80.00%	0.144	0.200	0.010	2.005%	35.00%	6	50.00%	5.69
Biomass Direct Combustion	1,000	1,900	75.00%	0.430	0.520	0.010	2.005%	35.00%	30	23.00%	5.47
Co-firing with coal  (20% coal)	150	700	75.00%	0.225	0.325	0.010	2.005%	35.00%	30	38.00%	4.83
Biomass Gasification (BIGCC)	30	1,500	75.00%	0.242	0.187	0.010	2.005%	35.00%	30	35.00%	5.47
Municipal Solid Waste	100	5,000	75.00%	0.000	0.540	0.010	2.005%	35.00%	30	23.00%	5.47
Landfill Gas	3	1,170	75.00%	0.000	0.540	0.010	2.005%	35.00%	30	42.00%	5.47
Sewage Digestion	1	5,600	75.00%	0.000	0.540	0.010	2.005%	35.00%	30	26.00%	5.47
Ocean Wave	0.5	1,510	75.00%	0.000	0.000	0.010	2.005%	35.00%	60	50.00%	0.00
Tidal Power	100	2,150	23.00%	0.000	0.000	0.010	2.005%	35.00%	120	50.00%	0.00

FORMULAS:

a) NREL formula	Net COE = ICC * CRF / AEPnet + (LLC + O&M + LRC + MOE) – PTC,  in US $/kWh or US cents/kWh
	where:	Net COE = Levelized Cost of Energy, $/kWh (constant US $)
		ICC = Initial Capital Cost (total debt), $
		CRF = capital recovery factor, 1/yr = int / (1 – (1 + int)^-Life)
		AEPnet = Net Annual Energy Production, kWh/yr = (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
a) RP formula	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)    and			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 = (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, LHV) * AEPnet * (Price of fuel, LHV) = (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 = 32%
		int = Interest Rate, %
		Life = Economic Life or Project Life, yrs

CALCULATED LEVELIZED COST OF ELECTRICITY

0.00%	franchise	business	DOE fee	income tax	Include DOE	Include tax			0	1
SIMPLIFIED LEVELIZED COST OF ELECTRICITY: Method 1a				2.00%	0.005%	0.01	35.00%	1	1			Levelized Cost
Type of Plant	Annual	Fixed	Variable	DOE	Fuel	Capital	Total	Total	NREL	RP (with
and Fuel	Generation	O&M	O&M	fund	Cost	Cost	Cost	Revenue	formula	DOE & Tax)
	MWh/yr	M$/yr	M$/yr	M$/yr	M$/yr	M$/yr	M$/yr	M$/yr	$ / kWh	$ / kWh
Oil Thermal	1,971,000	0.09	0.99	0.41	212.69	40.29	175.34	275.27	0.0650	0.1397
Orimulsion Thermal	505,385	0.04	0.33	0.10	24.17	19.66	33.17	52.08	0.0576	0.1030
Gas Thermal	657,000	0.03	0.33	0.14	33.00	13.43	33.81	53.09	0.0381	0.0808
Reciprocating Engine	328,500	0.00	1.64	0.07	37.55	9.20	33.58	52.72	0.0916	0.1605
Orimulsion Reciprocating Engine	252,692	0.00	1.64	0.05	9.77	12.86	18.39	28.88	0.0696	0.1143
Simple Gas Turbine Aero Derivative	229,950	0.00	1.15	0.05	13.68	1.54	11.05	17.35	0.0352	0.0755
Recuperated GT	21,024	0.00	0.11	0.00	1.17	0.17	0.99	1.55	0.0350	0.0739
CHAT 11 MW	72,270	0.00	0.36	0.01	3.67	1.19	3.70	5.81	0.0396	0.0804
CHAT 300 MW	1,971,000	0.01	9.86	0.41	81.44	15.25	73.29	115.06	0.0285	0.0584
Heavy Frame GT	1,314,000	0.01	6.57	0.27	84.86	15.18	73.22	114.95	0.0413	0.0875
Combined Cycle GT	3,591,600	0.08	7.18	0.74	144.97	44.05	138.92	218.10	0.0300	0.0607
Pulverized Coal Thermal	3,942,000	0.14	12.81	0.81	122.89	85.77	167.04	262.24	0.0354	0.0665
Atmospheric CFB	2,452,800	0.08	7.97	0.51	70.87	59.55	106.62	167.39	0.0361	0.0682
Pressurized FBC	3,854,400	0.13	12.53	0.80	106.19	86.38	157.54	247.33	0.0340	0.0642
IGCC	1,752,000	0.06	3.28	0.36	46.12	39.46	68.83	108.05	0.0321	0.0617
BWR Advanced Nuclear	7,721,064	0.75	3.09	1.59	16.52	452.87	427.26	670.77	0.0496	0.0869
PWR Advanced Nuclear	8,313,240	0.80	3.33	1.72	17.79	316.43	303.93	477.15	0.0331	0.0574
PHWR once thru	7,573,020	0.73	3.03	1.56	16.21	267.47	257.90	404.89	0.0309	0.0535
AGR Advanced Nuclear	6,263,400	0.61	2.51	1.29	13.40	225.87	217.56	341.55	0.0315	0.0545
Large Hydro	1,226,400	0.00	0.00	0.25	0.00	77.45	74.12	116.36	0.0491	0.0949
Small / Mini Hydro	131,400	0.00	0.00	0.03	0.00	5.04	4.79	7.52	0.0299	0.0572
Micro Hydro	289	0.00	0.00	0.00	0.00	0.03	0.03	0.04	0.0894	0.1484
Pumped Hydro Storage	1,314,000	0.00	131.40	0.27	0.00	214.12	288.11	452.32	0.2271	0.3442
Compressed Air Energy Storage	255,500	0.00	2.56	0.05	0.00	22.49	19.89	31.23	0.0880	0.1222
Flywheel Storage	73,000	0.00	219.00	0.02	0.00	13.77	153.50	240.99	3.1672	3.3012
USB – Lead Acid Storage	7,300	0.00	1.24	0.00	0.00	0.84	1.49	2.34	0.2726	0.3206
USB – Advanced Storage	7,300	0.00	7.30	0.00	0.00	0.59	5.22	8.20	1.0713	1.1229
SMES Storage	73,000	0.00	219.00	0.02	0.00	13.22	153.06	240.29	3.1605	3.2916
Ultracapacitors Storage	730	0.00	26.28	0.00	0.00	0.37	17.38	27.29	36.4515	37.3837
Geothermal Flashed Steam	394,200	0.05	0.06	0.08	10.14	12.93	18.94	29.74	0.0516	0.0754
Wind Farm	105,120	0.01	0.00	0.02	0.00	4.85	4.27	6.71	0.0384	0.0638
Solar PV	26,280	0.00	0.00	0.01	0.00	4.44	3.89	6.11	0.1402	0.2325
Solar Thermal trough	210,240	0.08	0.00	0.04	0.00	30.73	28.11	44.13	0.1174	0.2099
Solar Thermal tower	525,600	0.14	0.00	0.11	0.00	63.59	58.15	91.29	0.0971	0.1737
Solar Thermal dish + Stirling engine	1,314	0.00	0.00	0.00	0.00	0.19	0.18	0.28	0.1178	0.2103
Phosphoric Acid Fuel Cell	7,008	0.00	0.01	0.00	0.40	0.37	0.56	0.87	0.0749	0.1245
Proton Exchange Membrance FC	1,752	0.00	0.00	0.00	0.10	0.06	0.12	0.18	0.0592	0.1048
Molten Carbonate FC	140,160	0.00	0.28	0.03	6.11	7.18	9.68	15.19	0.0673	0.1084
Solid Oxide FC	21,024	0.00	0.04	0.00	0.92	0.75	1.20	1.88	0.0529	0.0895
SOFC + GT hybrid	35,040	0.00	0.07	0.01	1.43	1.50	2.13	3.34	0.0584	0.0954
Biomass Direct Combustion	6,570,000	0.43	34.16	1.36	562.42	251.71	618.48	970.98	0.1215	0.1478
Co-firing with coal  (20% coal)	985,500	0.03	3.20	0.20	45.10	13.91	44.23	69.44	0.0568	0.0705
Biomass Gasification (BIGCC)	197,100	0.01	0.37	0.04	11.09	5.96	12.91	20.27	0.0824	0.1029
Municipal Solid Waste	657,000	0.00	3.55	0.14	56.24	66.24	99.36	155.98	0.1717	0.2374
Landfill Gas	19,710	0.00	0.11	0.00	0.92	0.46	1.10	1.72	0.0712	0.0873
Sewage Digestion	6,570	0.00	0.04	0.00	0.50	0.74	1.02	1.61	0.1715	0.2447
Ocean Wave	3,285	0.00	0.00	0.00	0.00	0.10	0.09	0.15	0.0231	0.0447
Tidal Power	201,480	0.00	0.00	0.04	0.00	27.74	27.13	42.60	0.1067	0.2114