Calculate the levelized cost of electricity for the following two cases. Assume
ID: 108046 • Letter: C
Question
Calculate the levelized cost of electricity for the following two cases. Assume a price for CO2 emissions of $5/tonne, escalating at 5%/year; the power plants have capacities as given below, and each has a capacity factor of 80%. Work with a 25-year lifetime and a 7% MARR (discount rate). Emissions factors for CO2 are 56 kg/GJ for natural gas and 95 kg/GJ for coal; assume zero net CO2 emissions for biomass.
1. Natural gas advanced combined cycle; fuel cost initially $3/GJ, escalating at 3%/year
2. Biomass combined cycle @ 18 GJ/tonne; $10/tonne cost for fuel escalating at 3%/year
Be sure to take into account the fixed and variable (non-fuel) costs.
Natural Advanced Variable Nominal overnight capacity Heat rate capital cost Fixed O&M; O&M; cost (MW) Btu/kWh) ($/kW cost ($/kW-yr) ($/MWh) Gas m 515.37 53.27 400 6,430 1,023Explanation / Answer
Currently, the most efficient commercial technologies for power production are supercritical pulverized coal combustion (SCPC) and natural gas combustion with combined cycle (NGCC). Emerging technologies for more efficient power generation from coal include ultra-super-critical pulverized coal (USCPC), advanced ultra-super-critical PC, integrated gasification combined cycle (IGCC), integrated gasification fuel cell combined cycle (IGFC), and direct carbon fuel cell. They each have different capital and operating costs leading to different leveled cost of electricity (LCOE). To forecast each of these competing technologies under various scenarios of electricity demand, fuel cost, and research investment, we created a Power Technology Futures Model (PTFM) based on “learning curves” methodology. Because the technology for producing energy is fixed during the life of the plant, total construction cost, KC, and hence, leveled capital cost, are fixed at the time of construction completion; capital additions are expensed in the leveled cost model and added to Operations and Maintenance costs, O&M.
LCk = [[FCR(r) · KC(OCk, r, ltk)] + FUELk (Fk, pFk) + O&Mk (Lk, pL)] / Ek ,
Where
- k indicates the power generating technology, S for SMR, G for CCGT, or C for coal, etc
- FCR is the Fixed Charge Rate (also known as the Capital Recovery Factor, CFR) is a function of the cost of capital, r, and the plant’s depreciation life, T:
FCR = [r (1 + r)T / [(1 + r)T – 1]
-KC(OCk, r, ltk) is the total construction cost, which is a function of the overnight cost, OCk (which is a function of the size of the plant, MWk), the cost of capital, r, and the lead time of construction, ltk; the product of FCR and KC yield a uniform annual payment to investors
-FUELk (Fk, pFk) is the annual fuel payment and a function of the amount of fuel, Fk, and price of fuel, pFk
-O&Mk (Lk, pL) is the annual Operations and Maintenance expense and a function of the amount of labor, Lk, and the price of labor, pL (which is assumed uniform across the generating industry); and
-Ek is annual energy output:
Ek = MWk · TT · CFk,
where MWk is the size of the power plant in megawatts, TT is the total time in hours in a year, and CFk is the power plant’s annual capacity factor. As we know, 3%, appropriate for self-regulated, state-financed utilities (e.g., TVA, see OMB 1992 on financing government projects); this can be considered the baseline “risk-free” rate (because tariffs or taxes can be raised to pay investment costs); 5%, appropriate for state-regulated utilities with Construction Work in Progress, CWIP, financing with access to loan guarantees and production tax credits; 7.5%, appropriate for state-regulated utilities with Allowance for Funds Used During Construction, AFUDC, financing with access to loan guarantees and production tax credits; and 10%, appropriate for utilities in deregulated markets without access to loan-guaranteed financing or production tax credits. The real weighted average cost of capital, r, will be set equal to each of these rates (3%, 5%, 7.5%, and 10%) for both nuclear and fossil-fired forms of electricity generation. Sensitivity analysis will be performed to determine the influence of the cost of capital on levelized costs. A straightforward calculation if the construction expenditures have a uniform distribution, such that CXt = 1 / lt: total overnight cost divided by construction lead time, lt.
IDC = idc * OC, where idc = [( m / 2) * lt ] + [(m 2 / 6) * lt 2 ]
(1)Therefore for Natural gas advanced combined cycle; fuel cost initially $3/GJ, escalating at 3%/year, the levelized cost would be Preliminary Estimate => 30%/1.28 = 23.4% Standard Deviation.
(2) For Biomass combined cycle @ 18 GJ/tonne; $10/tonne cost for fuel escalating at 3%/year, the levelized cost would be Standard Deviation= 23.4% x $1.5B = $0.35 billion.
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