Electricity Generating Portfolios with Small Modular Reactors

This paper provides a method for estimating the probability distributions of the levelized costs of electricity. These probability distributions can be used to find cost-risk minimizing portfolios of electricity generating assets including Combined-Cycle Gas Turbines (burning natural gas), coalfired power plants with sulfur scrubbers, and Small Modular Reactors, SMRs. Probability densities are proposed for a dozen electricity generation cost drivers, including fuel prices and externalities costs. Given the long time horizons involved in the planning, construction, operation, refurbishment, and post-retirement management of generating assets, price data from the last half century are used to represent long-run price probabilities. This paper shows that SMRs can competitively replace coal units in a portfolio of coal and natural gas generating stations to reduce the levelized cost risk associated with the volatility of natural gas prices and unknown carbon costs. Acknowledgements: US Department of Energy (Office of Nuclear Energy, DOE-NE) directly (ANL Contract #0F−34781) and indirectly through Argonne National Laboratory, ANL. We extend our thanks to M. Crozat, S. Goldberg, F. Lévêque, P. Lyons, H. Maertens, R. Rosner, G. Tolley, R. Vance, and seminar participants at the University of Chicago’s Harris School of Public Policy and the Energy Policy Institute at Chicago for their comments, encouragement, and data. Geoffrey Rothwell is currently working for the Nuclear Energy Agency of the Organization for Economic Cooperation and Development. This paper reflects the views of the authors, and not those of Stanford University, OECD-NEA, ANL, or US DOE. Electricity Generating Portfolios with SMRs v.20 [email protected]; [email protected] 2 Section 1: The Levelized Cost of Electricity In the U.S. from the 1930s through the 1980s, electricity generating plants were built under either (1) some form of government or cooperative ownership, or (2) some form of private ownership with monopoly distribution rights and rate-of-return regulation. To satisfy growing demand, in a rate-of-return regulated utility or state-owned enterprise making the decision regarding what electricity generating technologies came down to the question: “What’s the cheapest?” During the last half century, a single economic metric has been employed to determine the projected costs of generating electricity: the levelized cost of electricity, LCOE. See definition of levelized cost in NEA-IEA (2010). The levelized cost methodology assigns all costs and revenues to years of construction, operation, and dismantling. Each cost in each year is discounted to the start of commercial operation at an appropriately weighted average cost of capital, such as 7.5%. The “levelized cost” is the tariff that equates the present values of investments, expenditures, and revenues, including a rate-of-return on both debt and equity. However, ex ante when the levelized cost of a new technology is calculated, there are unknowns and uncertain variables in the calculation such as construction cost and duration, operating expenses, and fuel costs. Most calculations of levelized cost of electricity assume that each of the variables is represented by a single, best estimate, or a range of reasonable estimates. Unfortunately, given the uncertainty of future projections, a single best estimate for these variables is not likely to be as reliable as knowing a probability distribution for each of the cost drivers. This will allow the LCOE to be shown as a distribution that reflects these uncertainties. Given the lengthy life times of electricity generators, constructing generating assets requires a long-term time horizon, something that is not necessarily built into unregulated electricity markets. As electricity markets deregulated, U.S. electric utilities moved toward natural gas, because during much of the day, natural gas prices set the marginal cost of electricity, hence its price in deregulated markets. If the producer is burning gas, it will at least do as well as the rest of the sellers of electricity from natural gas. But this “dash to gas” also led to volatile electricity prices, following price volatility in the natural gas market. The cost structure of generating electricity from natural gas leaves it particularly susceptible to this volatility because it is the technology with the highest share of its LCOE coming from fuel costs. Consumers must either accept this price risk or look to long-term bulk sales to reduce it. Therefore, given the complexity of complete electricity markets and the lack of a longterm prospective in many of the remaining markets, there is a role for public policy in helping to encourage the building of portfolios of generating assets to (1) minimize total cost and cost risk, (2) minimize carbon dioxide emissions, and (3) maximize energy security for the nation through the diversification of electricity generation. This paper describes how to approximate the probability distributions of levelized cost drivers, how to simulate the levelized cost of electricity, and how to use these probability distributions to construct generating asset portfolios to minimize the cost risk associated with volatile energy prices, volatile weather conditions, volatile international energy markets, and volatile international relations. The analysis relies on modern portfolio theory to provide a framework to investigate the risk-return tradeoffs of a portfolio of electricity generating technologies. Portfolio theory was developed in the 1950s to evaluate different combinations of financial assets (stocks, corporate Electricity Generating Portfolios with SMRs v.20 [email protected]; [email protected] 3 bonds, government bonds, etc.) to assess how the resulting portfolio would be expected to perform both in terms of likely returns, and the risks that the holder would have to bear. Portfolio theory has been the basis of financial planning for the last half-century, especially driving home the importance of having diversified portfolios to minimize risk while preserving returns. At the heart of this finding is that having assets that do not move together reduces volatility of the portfolio while preserving its expected long-term value (such as a portfolio of stocks with volatile returns and bonds with more stable returns). This paper applies the models that were developed to assess these financial tradeoffs to electricity generating portfolios. (For an application of real options theory to the choice of new nuclear in Texas, see Rothwell 2006.) Because of the near lack of cost correlation between nuclear power and fossil-fired plants, nuclear power can balance the levelized cost of portfolios of fossil-fired power plants. Small Modular Reactors, SMRs, show promise in replacing coal units while natural gas prices are low and could be built to replace natural gas units as the price of natural gas rises. This paper simulates the levelized costs of SMRs, Combined-Cycle Gas Turbines, CCGTs, burning natural gas, and coal-fired power plants with sulfur scrubbers, COAL (compare with Lévêque, 2013, pp. 48-60). Because the technology for producing energy is fixed during the life of the plant, total construction cost, KC, and hence, levelized capital cost, are fixed at the time of construction completion; capital additions are expensed in the levelized cost model and added to Operations and Maintenance costs, O&M. (Refurbishment costs are not included in this analysis.) Unless otherwise specified, all monetary values are in 2013 dollars. In this context, the levelized cost per megawatt-hour, MWh, can be defined as LCk = [[FCR(r) · KC(OCk, r, ltk)] + FUELk (Fk, pFk) + O&Mk (Lk, pL)] / Ek , (1.1.1) 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] ; (1.1.2)  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: Electricity Generating Portfolios with SMRs v.20 [email protected]; [email protected] 4 Ek = MWk · TT · CFk, (1.1.3) 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. Capacity factors are discussed in Section 2.7 for nuclear power plants and in Section 3 for fossil-fired power plants. (Other operating modes, intermittent renewables, such as wind, will be added in future work.) In Equation (1.1.1) some elements are considered parameters (and are represented in nonItalic fonts) and assigned specific values; the influence of these values is determined with sensitivity analysis. The parameters include (1) the cost of capital, r; (2) the life time of the plant, T; (3) the price of labor, pF ; (4) the size of the plant, MW; and (5) the total number of hours in a year, TT. The remaining elements are variables that can be functions of other parameters and other variables, such as in Equation (1.1.3), where the random variable Ek is a function of the parameters MW and TT and the random variable CFk. Using historic data, random variables are modeled with reasonable probability distributions. The probability distributions for the LCk in Equation (1.1.1) will be determined using a Monte Carlo process and compared with other generation technologies and in portfolios of electricity generators. Section 2 discusses the parameters, variables, and levelized cost of Small Modular (Light Water) Reactors, SMRs, based on the costs of Advanced Light Water Reactors, ALWRs. Section 3 discusses the parameters, variables, and levelized cost of natural gas and coal-fired power plants. Section 4 calculates the expected levelized costs and standard deviations of portfolios of generating assets. Section 5 summarizes the conclusions. Section 2: The Levelized Cost of Electricity of New Nuclear Power This section provides a method for estimating the probability distributions of levelized costs of new nuclear power, in particular, SMRs. Although ALWRs will not be included in the portfolio analysis, SMR costs are derived from the costs of ALWRs, given that many of the SMRs under development are Light Water Reactor technologies. Section 2.1 discusses the appropriate cost of capital under different regulatory programs in the U.S., and how to calculate the accumulation of financing costs during construction. Section 2.2 discusses appropriate contingencies on cost estimates and argues that the cost engineering literature on contingency is compatible with setting the contingency based on the standard deviation of the cost estimate. (The Appendix extends this discussion and introduces the literature on portfolios of financial assets.) Section 2.3 estimates new nuclear’s total construction cost and shows that the estimated overnight cost of a new ALWR unit in the U.S. can be modeled with a probability distribution with a mode of $4,400/kW and a standard deviation of $460/kW. Section 2.4 introduces a “topdown” model of SMR levelized cost. Section 2.5 through Section 2.7, respectively, discuss new nuclear’s power fuel costs, Operations and Maintenance (O&M) costs, and new nuclear’s capacity factor. Section 2.8 presents estimates of the probability distribution of new nuclear’s levelized cost of electricity. Electricity Generating Portfolios with SMRs v.20 [email protected]; [email protected] 5 Section 2.1: The Cost of Capital and Interest During Construction Various public policy instruments have been proposed to lower the cost of capital to investors in new nuclear. To determine the impact of these instruments on the cost of capital, this section discusses the results of a cash flow model to calibrate changes in the WACC, “Weighted Average Cost of Capital,” r, with US Government taxes and policy instruments. (Rothwell, 2011, pp. 88-91, provides a detailed discussion of the cash flow model that was used in MIT, 2003, University of Chicago, 2004, and MIT, 2009.) Based on this literature, in this paper, levelized cost will be calculated for real weighted average costs of capital, WACC, of 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. To understand the relationship between the cost of capital, construction lead time, and compounding Interest During Construction, IDC, consider capital construction expenditures, discounted to the beginning of commercial operation, i.e., when sales and revenues start: IDC =  CXt · OC [(1 + m) –t – 1], t = – lt, . . ., 0 (2.1.1) where (1) the CXt are construction expenditure percentages of overnight cost, OC, in month t, and (2) m the monthly weighted average cost of capital during construction, (1 + m) = (1 + r) 1/12 . In addition, the IDC factor, idc, is the percentage add-on for financing charges. Because IDC depends on the construction expenditure rate (how much is spent in each month), Equation (2.1.1) can be complicated because the expenditure rate is not the same over the construction period with smaller amounts being spent early to prepare the site, larger amounts being spent on equipment in the middle of the project, and smaller amounts being spent at the end on instrumentation, training, and fuel loading. For probability analysis, what is required is to calculate the percentage increase in the overnight cost due to project financing, equal to the IDC factor, as a transparent function of construction lead time and the cost of capital. Equation (2.1.1) becomes 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. Then Equation (2.1.1) can be approximated (Rothwell, 2011, p. 35) as Electricity Generating Portfolios with SMRs v.20 [email protected]; [email protected] 6 IDC  idc  OC, where (2.1.2) idc = [( m / 2)  lt ] + [(m 2 / 6)  lt 2 ] (2.1.3) The idc factor is a function of a parameter, m, and a random variable, lead time, lt. The random variable, lt, is modeled by fitting construction lead time data for recently completed units from IAEA (2013). Because it is unlikely that the distribution of lead times for new nuclear plants is symmetric, the exponential distribution is more suitable to mimic lead time probabilities: Exponential density: expo(b) = [exp( – x / b )] / b , (2.1.4a) Exponential distribution: EXPO(b) = 1 – exp( – x / b ) , (2.1.4b) where b and x must be greater than 0 (thus avoiding negative lead times in simulation), and b is equal to the mean and the standard deviation. Figure 2.1.1 presents construction lead time data in months fit to an exponential distribution. Because there is only one parameter in this distribution, a shift parameter is introduced to move the origin away from 0 months, this shift is added to b, yielding an expected mean of 59.26 months (= 11.75 + 47.51) or almost 5 years. Using this distribution implies that the construction lead time cannot be less than about 4 years, but could be greater than 10 years: there is no upper limit on construction lead time. (In the figures, blue represents input data, red represents probability densities, and purple represents both.) It is assumed that the construction lead time for an SMR (Section 2.4) is one-half to twothirds of that of an ALWR, i.e., an exponential distribution with a mean between 30 and 40 months with a standard deviation of 8 months. The Interest During Construction, idc, factor is simulated as in Equation (2.1.3). (Lead time only influences the idc factor in the model; overnight cost does not depend on the lead time, although Rothwell, 1986, found that construction cost was positively correlated with the construction lead time.) Figure 2.1.1: ALWR Construction Lead Time in Months, Fitted to Exponential Density Exponential[ 11.8 , Shift( 47.5)], Mean = 59 m, SDev = 10 m, Mode = 52 m 50 m 79 m 5.0% 19.1% 90.0% 74.0% 5.0% 6.9% 3 6 4 8 6 0 7 2 8 4 9 6 1 0 8 min = Source: IAEA (2013) http://www-pub.iaea.org/MTCD/Publications/PDF/rds2-33_web.pdf Electricity Generating Portfolios with SMRs v.20 [email protected]; [email protected] 7 Section 2.2: New Nuclear Power Plant Construction Cost Contingency Traditionally, cost contingency estimation relied heavily on expert judgment based on various cost-engineering standards. Lorance and Wendling (1999, p. 7) discuss expected accuracy ranges for cost estimates: “The estimate meets the specified quality requirements if the expected accuracy ranges are achieved. This can be determined by selecting the values at the 10% and 90% points of the distribution.” With symmetric distributions, this infers that 80% of the cost estimate’s probability distribution is between the bounds of the accuracy range:  X%. To better understand confidence intervals and accuracy ranges, consider the normal (“bell-shaped”) probability distribution in Figure 2.2.1. The normal distribution can be described by its mean (the expected cost) represented mathematically as E(cost), and its standard deviation, a measure of the cost estimate uncertainty. The normal distribution is symmetric, i.e., it is equally likely that the final cost will be above or below the expected cost, so the mean equals the median (half the probability is above the median and half is below) and the mean equals the mode (the most likely cost). The normal density is normal( , ) = (2   2 ) 1⁄2 · exp{ (1/2) · ( x   ) 2 /  2 }, (2.2.1) where  is the mean (arithmetic average),  2 is the variance, and  is the standard deviation. Figure 2.2.1 shows the normal density of a cost estimate with a mean, median, and mode of $1.5 billion and a standard deviation of 23.4%: 10% of the distribution is below $1.05B and 10% is above $1.95B, yielding an 80% confidence level. Figure 2.2.1: A Generic Cost Estimate as a Normal Density Normal ($1.5 B, $0.35 B), Mean = $1.5 B, SDev = 23.4% = $350 M $0.50 $0.75 $1.00 $1.25 $1.50 $1.75 $2.00 $2.25 $2.50 in billions of $ 10% 10% 80% of the distribution is between $1.05 and $1.95 B = 1.5-(1.5 x 30%) to 1.5+(1.5 x 30%) Preliminary Estimate => 30%/1.28 = 23.4% Standard Deviation Standard Deviation= 23.4% x $1.5B = $0.35 billion