A national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

National Renewable Energy Laboratory 

Innovation for Our Energy Future 

Modeling of Uncertainties 

in Major Drivers in U.S. 

Electricity Markets 

Preprint 

W. Short and T. Ferguson 

National Renewable Energy Laboratory 

M. Leifman 

U.S. Department of Energy

To be presented at the 26th USAEE/IAEE North American 

Conference 

Ann Arbor, Michigan 

September 24–27, 2006 

Conference Paper 

NREL/CP-620-40451 

September 2006 

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 
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Modeling of Uncertainties in Major Drivers in U.S. Electricity 

Markets 

Walter Short (NREL), Tom Ferguson (NREL), and Michael Leifman (DOE) 

Contact Information: 

Walter Short 

Principal Researcher 

National Renewable Energy Laboratory 

1617 Cole Blvd. 

Golden CO 80401 

Phone: (303) 384-7368 

Fax: (303) 384-7499 

Walter_short@nrel.gov 
Introduction and Objective of the Stochastic Energy Deployment Model (SEDS) 

The U.S. Department of Energy (DOE) and the National Renewable Energy Laboratory (NREL) 

are developing a new model, intended to address many of the shortcomings of the current suite 

of energy models. Once fully built, the salient qualities of the Stochastic Energy Deployment 

System model (SEDS) will include full probabilistic treatment of the major uncertainties in 

national energy forecasts; code compactness for desktop application; user-friendly interface for a 

reasonably trained analyst; run-time within limits acceptable for quick-response analysis; choice 

of detailed or aggregate representations; and transparency of design, code, and assumptions. 

Moreover, SEDS development will be increasingly collaborative, as DOE and NREL will be 

coordinating with multiple national laboratories and other institutions, making SEDS nearly an 

“open source” project. The collaboration will utilize the best expertise on specific sectors and 

problems, and also allow constant examination and review of the model. 

Here, we present the rationale for this project and a description of its alpha version, as well as 

some example results. We also describe some of the expected development efforts in SEDS. 

Rationale for SEDS 

Today’s U.S. energy situation can be characterized as complex, uncertain, and even disturbing. 

Oil prices are increasing as worldwide supply tightens and demand increases. Natural gas 

supplies appear to be limited for the near term. Climate change is heavily debated, while 

symptoms abound. Technology options rise to the forefront with acclaimed salvation status and 

recede quietly into the laboratories. Energy security is the topic of the day. Policies are 

proposed to address all the above. 

Despite this turmoil, nearly all of our energy forecasts are purely deterministic, and offer only 

limited insights for policy makers. Indeed, the most prominent energy model, the DOE/EIA 

Annual Energy Outlook 2006 (AEO), points to a business-as-usual energy market with 2025 

crude oil import prices at two-thirds the cost of July 2006, and natural gas prices at 90% of 

today’s cost. Of all the future possibilities, this may be the most likely scenario. But it’s not 

probable – in fact, the authors would maintain there is less than a 50% chance that this forecast is 

exactly right. The EIA AEO report does include other scenarios – high and low economic 

growth, three different world oil price scenarios, various technology improvement scenarios, 

three liquefied natural gas (LNG) supply cases, etc. But, which one is a person to use? Do they 

cover the range of possibilities? What if several things go awry simultaneously? 

The DOE/EIA is not alone in facing such uncertainties, or in using scenarios to address them. 

Probably one of the better known recent scenario exercises came from the United Nation’s Intergovernmental Panel on Climate Change (IPCC), which produced the results shown in Figure 1. 

While useful for many purposes, such multiple scenarios leave a lot for the reader to determine – 

Which ones should I use for planning purposes? What’s most likely? What’s the average? What 

strategies would be most robust across these possibilities? 

This paper describes an alternative to the use of scenarios, as well as a model under development 

to help answer the above questions. 

2
Figure 1 

IPCC Scenarios 

Background 

One reason scenarios are developed is that often the models behind the scenarios cannot predict, 

with confidence, one or more of the market drivers. Consider the U.S. electric sector. As shown 

in Figure 2, major shifts have occurred in the types of electric capacity installed in the United 

States during the past 60 years. Probably the most distinguishing feature of the graph is the 

dominance of natural gas power plants that came online between 1998 and 2003. Although 

larger, this shift is typical of similar shifts in prior years: ramp-up of nuclear in the 1970s and its 

demise in the late 1980s; dramatic fall in new coal plants in the 1980s; decrease in gas use in the 

late 1970s and its rise in the late 1980s. Similar shifts have occurred in other fuels not shown in 

Figure 2. For example, there have been no significant oil-fired additions to capacity since the 

1970s, and very little hydropower. 

 

At the risk of oversimplifying, Figure 2 also shows the major drivers behind these shifts in the 

type of capacity installed. For our purposes, there are four important features associated with 

most of these drivers. First, many are outside the scope of most of today’s U.S. energy market 

models. Second, most could not have been forecast with economic models as they were driven 

by acts of nature, human error, politics, increasing awareness of environmental impacts, resource 

discoveries, and technological breakthroughs. Third, most of these events were not likely 

enough to have been included in any prior sensitivity analysis conducted for national energy 

planning, even though their impacts were profound. Finally, there are a host of other driving 

events that did not happen that might have been included in any prior comprehensive scenario 

analysis (e.g., nuclear that actually is “too cheap to meter” or U.S. ratification of the Kyoto 

protocol). 

3
The above would suggest that, with our current energy market models, we are at risk of missing 

the real drivers in planning for our national energy future. Today, as in the past, there is a host of 

natural, social, political, and technological drivers outside the scope of our models that are the 

true determinants of the future. And, as in the past, we can’t simply insert them into our 

deterministic models because they are highly uncertain – even unlikely – but still possibilities 

with potentially huge consequences. There are so many of them with such a range of possible 

values, many of which are correlated with each other, that it is also not possible to do a 

comprehensive sensitivity or scenario analysis. And even if one could, no one could make sense 

of them all. We’re left with only one viable option, which is the subject of this paper. 

Annual Electric Generating 

Capacity Additions

0

2

4

6

8

10

12

14

16

18

20

195019601970198019902000

GW

Coal Natural Gas Nuclear

Gas increases

PIFUA changed 

PURPA 

CC efficiency 

Low price 

through 

deregulation 

Coal declines

CAAA 

deregulation 

63 GW 

NG in 

2002 

Gas declines 

PIFUA prohibits 

Nuclear emerges

Technology Available 

Too cheap to meter

Nuclear decline

Interest rates 

3-Mile Island (1979) 

Chernobyl (1986) 

Regulation 

Figure 2 

Major Historical Drivers in the U.S. Electric Sector 

Basic Structure of the SEDS Model 

Although there is no way to remove all the uncertainties associated with the future, there are 

alternatives other than scenarios for analyzing them. We have applied a widely known technique 

(Monte Carlo simulation) to SEDS, a model of U.S. energy markets. When complete, SEDS will 

simulate the evolution of the U.S. energy market from 2005 to 2050. SEDS moves forward 

through time, simulating the U.S. energy market in one 5-year time-step after another. Its 

principal outputs are energy demands, energy capacity stocks, energy/fuel use, energy prices, and 

probability distributions that capture the uncertainty in each of those. 

4
SEDS is being developed with a commercially available software package, Analytica, designed 

to facilitate the development of stochastic models. For more information on Analytica, see 

http://www.lumina.com. 

Sectors, Technologies

As shown in Figure 3, the alpha version of the electric sector in SEDS is complete, and the 

transportation sector is under development. In the electric sector, SEDS estimates the type of 

generation capacity that will be deployed nationally in each 5-year period from now to 2050, and 

the generation from that capacity. To meet future loads, it considers technology, fuel, and 

emission costs in selecting among fossil, nuclear, and renewable electric technologies. 

Figure 3 

SEDS Logic Flow 

Treatment of Uncertainty

SEDS can be operated in either a deterministic mode or a stochastic mode. When operated 

deterministically, SEDS uses a single value instead of the input probability distributions for the 

uncertain parameters. These deterministic SEDS runs can be extremely quick and informative in 

terms of how the model responds to different inputs and assumptions. 

5
When operated stochastically, SEDS estimates a number of trajectories 1

 through time, with each 

trajectory beginning in 2005 and extending in 5-year increments out to 2050. In each trajectory, 

the random variables are sampled using a Latin Hypercube approach, which improves on a 

standard Monte Carlo simulation by dividing the range of possible values for that particular 

random variable into bins of equal probability and selecting one sample from each of the equalprobability bins. 

For each period in a trajectory through 

time, electricity demands and costs from 

the different generation options are 

updated, stock is retired, and a market 

share algorithm is employed to 

determine generation from existing and 

new generation capacity. In moving 

from one period to the next within a 

single trajectory, SEDS captures the 

correlation between uncertain variables 

in time (periods t and t+1), first by 

updating the value in t by simulated 

physical drivers; and, second, by adding 

to or multiplying the updated simulated 

value by a random variable that captures 

the uncertainty in the variable’s value 

from one period to the next. For 

example, the price of natural gas from 

period t in a particular trajectory through 

time is first adjusted by a supply 

elasticity to capture resource issues, and 

then multiplied by a random variable 

intended to capture price escalation, 

market uncertainties, and 

interdependencies with other random 

variables (e.g., the price of oil) to yield 

the gas price in period t+1. 

Table 1 identifies those drivers that are 

currently treated stochastically in the electric-sector portion of SEDS. This list will be expanded 

and modified as the SEDS model evolves, and as required by individual studies. We used four 

criteria in developing this preliminary list of uncertain market parameters. Each uncertain 

parameter is: 

TABLE 1 

PRIMARY UNCERTAINTIES in SEDS 

TECHNOLOGY

 Rate of learning-induced improvements 

 Rate and size of R&D improvements 

FUELS

 Oil 

 Domestic resource/price 

 Time to world prod’n peak 

 Impact of peak on price 

Natural gas 

 Domestic resource/price 

 Coal 

 Domestic resource/price 

 Biomass 

 Domestic resource/price 

 Nuclear 

 Will new plants be built? 

MARKETS/POLICY

 Climate change - taxes 

 Macroeconomics 

 Demand growth 

 Discount rate 

 Wind and Geothermal Production Tax Credits 

1) potentially a major driver of future U.S. energy markets 

2) highly uncertain with a range of possible outcomes 

3) outside the normal scope of an energy market model 

4) of particular interest to the development of renewable energy 

 

1

 The user can input the number of trajectories through time, with more trajectories producing a more statistically 

accurate picture. 

6
Many other uncertain drivers could have been included in Table 1. A SEDS user can always 

make any parameter stochastic, with the specification of the appropriate probability distribution 

for that parameter. Any parameters not included in Table 1 are currently treated 

deterministically by SEDS, as in any other model. 

Analytica includes a large selection of probability distributions that can be used to represent 

these uncertain parameters. It is a simple matter to examine the sensitivity of the SEDS results to 

different distributions. For our default distributions, we have generally used triangular 

distributions, which are easily understood and visualized. There are a few examples in Table 2. 

The low, mode, and high columns are the lower bound, mode, and upper bound, respectively, 

which define the triangular distribution. In the case of a Bernoulli distribution, the “High” 

column is used to represent the likelihood of a positive value (0.5 means that the event has a 50% 

chance of happening). 

Table 2 – Sample Probability Distribution Parameters 

Variable name Low Mode High Shape 

Carbon tax start year 2010 2015 2025 Triangular

Carbon tax phase in period (yrs) 5 10 15 Triangular

Carbon tax amount ($/ton C) 25 100 500 Triangular

Carbon Tax Allowed 0.50 Bernoulli 

Coal heatrate period (years) 20 25 30 Triangular 

Coal heatrate % reduction 0 0.027 0.055 Triangular 

Coal cap cost period (years) 5 15 25 Triangular 

Coal cap cost % reduction 0.05 0.10 0.12 Triangular 

Interdependencies: Where the physical relationships between energy variables are well 

understood, SEDS uses explicit formulas to capture those relationships. However when there are 

interdependencies between variables that are outside the scope of SEDS, correlation coefficients 

are used. For example, in SEDS, natural gas prices are assumed to be partly correlated to oil 

prices. 

We expand below on how these major uncertainties are currently treated in SEDS. 

Fuel Prices: 

 Oil – Three random variables are used to capture the price of oil. The first is the percent 

change in the price for each year in the period before world oil production peaks. This is 

represented by a triangular distribution that is accessed each year, i.e. the percent change varies 

from one year to the next. In the SEDS base case, the mode of the triangular distribution is set to 

the growth rate between 2001 and 2020 in the Reference Case of the Annual Energy Outlook 

2006. The second random variable is represented by a triangular distribution on the time at 

which world oil production peaks. The third is a distribution on the annual percent change in the 

price that covers the period after world oil production peaks. While oil is not a primary fuel for 

any of the electric-generating technologies in SEDS, it is included because we plan to expand 

SEDS to the transportation and industrial sectors – and because the price of natural gas, which is 

7
used in the electric sector, is assumed to be partly correlated to the price of oil as described in the 

next paragraph. 

 Natural gas – There is a single distribution for the price of natural gas. The price of 

natural gas is assumed to be correlated to the price of oil. The price of natural gas in year t is 

determined from the price of natural gas in period t-1, first, by adjusting it with a supply 

elasticity that is a function of the cumulative demand for gas through period t-1; and second, by 

the random variable for the annual percent change in gas prices, which is represented by a 

triangular probability distribution. The distribution is correlated to the price of oil with mode set 

in the SEDS base case equal to the average annual increase in gas prices from the Reference 

Case of the Annual Energy Outlook 2006. We anticipate that we will eventually significantly 

modify the gas-pricing uncertainties to reflect uncertainties in both LNG availability/price and 

the construction of an arctic pipeline. 

Coal – The change in the price of coal from one year to the next is captured through a 

random variable on the annual percent change in coal prices. The change is slightly correlated to 

the change in oil prices and is captured in the SEDS base case by a triangular distribution with 

mode equal to the average annual increase in coal prices from the Reference Case of the Annual 

Energy Outlook 2006. 

 Nuclear – Nuclear fuel prices are taken directly from the Reference Case of the Annual 

Energy Outlook 2006. A binomial random variable is used to represent the probability that 

nuclear will be allowed to be built in the future. If the random variable ever indicates that 

nuclear can be built, then nuclear can be built in all future years from that point forward. This 

single random variable is used to capture all the potential market uncertainties associated with 

nuclear power – proliferation, waste, accidents, financial risk, and public opinion. 

Technology change: 

Uncertainty in technology improvements through learning currently is captured through a 

triangular probability distribution on the learning parameter used in the learning curve, which is 

applied to a technology’s capital cost. The parameter value is selected once for each technology 

for each trajectory through time. Currently, the following technologies have stochastic learning 

parameters: wind, integrated coal gasification combined cycle (IGCC), advanced combined 

cycle, advanced combined cycle with sequestration, and enhanced geothermal systems (EGS). 

Improvements due to R&D are also uncertain. Each technology’s capital cost and efficiency is 

represented by two random variables – the amount of improvement, and the length of time it 

takes to achieve that improvement. 

Policy: 

SEDS currently includes uncertainty in two major policy drivers – carbon taxes and production 

tax credits (PTCs). Uncertainty as to how or whether restrictions might be imposed on 

greenhouse gas emissions is treated through the imposition of a carbon tax. Four random 

variables are used to impose a carbon tax. First, a binary distribution is used to determine 

whether or not a carbon tax is ever imposed. Second, if a carbon tax is imposed, a triangular 

distribution is used to set the time at which the tax is first imposed. 

 

The third carbon tax random variable is represented by a triangular distribution on the size of the 

final carbon tax expressed in $/ton of carbon. And the fourth random variable is again 

represented by a triangular distribution on the length of the implementation period. The tax is 

assumed to grow linearly over the implementation period, starting at the initial date provided by 

8
the second distribution. The carbon tax is simply translated into the cost per kWh generated by a 

technology based on the fuel used and the generator heat rate. 

There is considerable uncertainty as to whether the existing federal production tax credits for 

renewable energy will be renewed at the end of 2007, when they are legislated to expire. This 

uncertainty is explicitly accounted for by including a triangular distribution on the year that the 

PTC will expire. 

Time and regional disaggregation: 

The precision of a model with respect to specificity of results is generally improved by 

disaggregating over time and geography, as far down as can be supported by available input data. 

The tradeoff with detailed disaggregation is that computer run-time and memory requirements 

can be excessive. Another tradeoff that is the subject of active debate and research – and may be 

the subject of SEDS experiments – is the degree to which the added uncertainty, introduced with 

added detail, affects overall prediction accuracy. With respect to time and regions, we discuss 

these tradeoffs in the paragraphs that follow. 

Time: As evidenced in Figure 2 for the U.S. electric sector, significant trends have formed over 

long periods in the type of generation selected: coal additions dominated from 1950 to 1980; 

nuclear penetrated between 1970 and 1990; gas was a major addition in all but the years 1975 to 

1990. These additions would suggest that for the electric sector, SEDS can capture the major 

drivers and trends with periods as long as 5 years. 

While 5-year periods might suffice to capture capacity additions, it is clear that operationally, 

generation changes diurnally – or even second-by-second – as load swings and 

generator/transmission availability dictate changes in the contributions from individual plants. In 

the electric-sector portion of SEDS, we simulate these varying generator-operating levels simply 

by expressing electric demand in terms of annual energy; and base, intermediate, and peak loads, 

i.e. we do not disaggregate over time within a year. 

Regions: Figure 2 showed that in the electric sector, swings in market penetration from one 

technology are tending more and more to occur at the national level. In the 25 years between 

1950 and 1975, we saw a mix of coal, gas, oil, and – in the end – nuclear penetrate the market. 

However, since 1975, new coal additions dominated for 10 years, then 5 years of new nuclear 

builds; then gas ramped up for years in the mid-1990s, before it went off the chart post-2000. 

Today, coal again seems to be the fuel of choice almost nationwide. Certainly there are strong 

regional variations, especially in the use of coal (e.g., emissions restrictions in California have 

largely prohibited new coal plants). However, it is clear from Figure 2, that the major drivers in 

market penetration for conventional technologies are not local drivers, but national factors. In 

the electric sector currently modeled in SEDS, we have taken advantage of this national picture 

to keep the model simple and quick-to-solve by using a single region. Fortunately, Analytica has 

a somewhat unique capability to disaggregate an existing model regionally, should that be 

required in the future for individual studies. 

Our preliminary analysis of the transportation sector suggests that national trends far outweigh 

regional differences, and that we can again avoid regional disaggregation in that sector. When 

9
we develop the buildings and industrial sectors, some level of regional disaggregation will 

probably be required. Tradeoffs will be required between accuracy and model run-time. 

Regional Treatment of Renewable Energy: The cost and performance of many energy 

efficiency/renewable energy (EE/RE) technologies are highly site-specific and cannot be 

captured by a set of average numbers at the national level. In SEDS, we use reduced-form 

supply curves to capture such variation. For example, SEDS assumes the cost of generation 

from wind is the bus-bar costs of a Class 5 resource site. SEDS adds to this an extra-generation 

cost associated with resource quality, site access, transmission, intermittency, and ancillary 

services. This extra-generation cost is presented by a supply curve derived from NREL’s Wind 

Deployment System (WinDS) model (http://www.nrel.gov/analysis/winds/related_pubs.html). 

The curve presents the costs ($/kW) as a function of the amount of wind installed nationwide, as 

shown by the top curve in Figure 4. The three stacked curves of Figure 4 break the extrageneration cost from wind into that due to additional wind capital cost, transmission cost for 

wind, and the cost of conventional capacity and fuel to firm up wind resource variability. Using 

this curve, SEDS computes the extra-generation costs for wind as a function of installations-todate and adds that cost to the wind bus-bar cost of generation. Whether SEDS’ reduced form 

representations capture the appropriate heterogeneity in the electric sector will be a topic of 

investigation this coming year. 

0

100

200

300

400

500

600

700

800

20 45 70 95 120 145 170 195 220 245 270 295 320 345 370 395 420 445 470

GW Wind Installed

Marginal Capital Cost ($/kW)

Conventional Costs

Wind Transmission 

Wind Capital

Figure 4 

Wind Supply Curve for Extra-Generational Costs 

Electricity demand: 

At the start of each 5-year period, electricity demand is estimated based on the electricity price 

and the growth from the past two periods for the particular trajectory through time. To 

determine the capacity needed to meet the load, the load is divided into the fraction occurring as 

base, intermediate, and peak load. These demands and plant retirements are used to determine 

the additional capacity builds that are required. Once the capacity builds are determined, the 

10
actual load for the period is estimated from the projected value and a random perturbation. The 

current stock of plants is then dispatched to meet the actual load. 

Once SEDS is refined to include an explicit end-use sector representation, energy demand will 

be modeled as a combination of the demand for energy services and the end-use energy needed 

to meet that service demand. The former is driven by macroeconomic conditions, demographics, 

and energy prices; the latter is driven by technological change. Eventually, a macroeconomic 

module will be implemented to provide these macro drivers. 

Capacity Expansion: 

A market-share algorithm is used to allocate the demand in each 5-year period for new electricgenerating capacity to different prime movers from each technology. Separate capacity 

expansion markets are assumed for base, intermediate, and peak loads. Different technologies 

compete in each of these load categories based on their levelized cost of electricity (LCOE). For 

example, coal, nuclear, combined-cycle natural gas, and all the renewable electric technologies 

compete to meet the base-load demands, while only hydro, natural gas combustion turbines, and 

land-fill gas compete in the peak market. The LCOE of each technology is computed based on 

technology costs (capital, O&M, fuel, emissions) and performance (capacity factor, heat rate, 

etc.) Capacity factor is assumed to be the same as that experienced by similar plants in the 

preceding period. The LCOE for wind is incremented by the “extra-generation” cost described 

above. Similarly, there are resource supply curves for biomass and geothermal that increase their 

costs as the best resource sites are built out. 

To capture the efficiency of energy use and the need for new capital stock, SEDS tracks capital 

stock. Retirements are estimated through planned retirements, extrapolations of past trends, and 

economics. Economic retirements are more important than in most models, because SEDS must 

be responsive to events that, though unlikely, might arise in the Monte Carlo simulation, e.g., 

carbon taxes. Economic retirements are calculated on the basis of the present value of “going 

forward” costs for existing plants (fuel and O&M) compared to the full costs of new plants 

(capital, fuel, and O&M). 

Market Share Algorithm:

The cost and performance of all generation technologies vary around the country. To account for 

this variation, SEDS uses a logit market-share model. A single-nomial logit based only on cost 

does not account for the status of each technology’s supply industry. To prevent the growth of 

any particular technology from being stretched too thin, the market share is recalculated with a 

multi-nomial logit that considers not only price, but also the rate of growth of that technology in 

the marketplace. 

In one sense, the use of a logit market-share algorithm is redundant with the explicit treatment of 

uncertainty in SEDS, because the logit implicitly assumes the competing technology attributes 

are random variables with Weibul distributions. Nonetheless, we have elected to use the logit for 

two reasons: 1) it is simple and computationally quick, and 2) the underlying probability 

distribution captured by the logit is assumed to represent primarily the variability in competitors’ 

attributes, as opposed to the uncertainty in those attributes. For example, we might use SEDS’ 

Monte Carlo capabilities to capture the uncertainties in 2020 natural gas prices, while using the 

logit to capture the variability around the country in that 2020 price. 

11
Dispatch: 

Based on the variable cost of operation of each plant type (fuel, variable O&M, emissions costs), 

a dispatch order is constructed to meet the total load. The plant type with the lowest variable 

cost is first in the dispatch order, and the full capacity available is dispatched. The next plant 

type is then dispatched, continuing until the entire load is met. 

Emissions/environmental factors: 

Emissions are simulated in SEDS with simple coefficients per unit energy consumed, e.g., 

pounds of sulfur dioxide emitted per kWh of generation from an existing coal plant. Policies to 

control emissions can take several forms – emission taxes, performance standards, and emissions 

cap (and trade). Emission taxes are easily imposed by adding the tax to the cost of energy from 

the technology. Performance standards are easily implemented by simply restricting technology 

choices to those that meet the standard at least cost and adding that cost to the LCOE. Emission 

caps are problematic in a model like SEDS, because they require an iterative approach to bring 

the emissions in line with the caps. They can also require detailed modeling of the emissionreduction technology and fuel opportunities. To avoid excessive computer run-time and 

complications, SEDS does not model emission caps. 

Initial Results 

To date, we have developed two principal forms of results – deterministic comparisons with 

other models and uncertainty impact estimates. We show results (below) from SEDS that can be 

compared with results from the DOE Energy Information Administration’s National Energy 

Modeling System (NEMS) (EIA 2006). NEMS is used by DOE/EIA to develop the Annual 

Energy Outlook and by other offices in DOE to substantiate research progress in compliance 

with the Government Performance and Results Act (GPRA). The comparisons are made by 

operating SEDS both in deterministic mode using inputs that parallel those of NEMS as closely 

as possible, and also in stochastic mode to see how large the impact of uncertainty can be. 

We compare results for SEDS and NEMS, published by the Energy Information Administration 

in its Annual Energy Outlook 2006 (AEO06). Figure 5 shows the capacity of renewable, gas, and 

coal-fired generators over time, as projected by the NEMS Reference Case in AEO06 and as 

projected by a deterministic run of SEDS using the same inputs as much as possible. The results 

are somewhat close, because these SEDS runs have used the electricity demands and fuel prices 

that come from the NEMS run. 

12
Figure 5 

Deterministic Comparisons with AEO 

Figure 6 presents the same deterministic capacity results from AEO 2006 for renewables, along 

with the expected values when SEDS is run stochastically. This figure shows the true value of 

SEDS. The greater level of renewables is driven by the uncertainties that we know actually exist 

in the U.S. energy system. It accounts for the fact that we know that carbon taxes MAY be 

imposed in the future; it accounts for the fact that we know that there MAY be breakthroughs in 

technology development of both renewables and conventional generators; it accounts for the fact 

that we know future fuel prices are highly uncertain. As such, it presents a more accurate picture 

of the value of renewable electric technologies. 

13
Figure 6 

Renewable Energy Comparisons 

Figure 7 shows that the expected values of Figure 6 are only part of the picture produced by 

SEDS. Figure 7 shows the probability bands around three variables within the same stochastic 

SEDS run: the capacity expansion of wind power, the generation of electricity from coal, and the 

price of electricity. This allows one to plan, not only based on a hoped-for “business-as-usual” 

scenario, but also for a worse-case “perfect storm” situation where several uncertainties evolve 

simultaneously to a critical value/position. A similar distribution can be produced for any of the 

outputs from SEDS, e.g., natural gas capacity, etc. 

14
Figure 7a 

Figure 7b 

Figure 7c 

Probability Bands 

15
Figure 8 is another way to view how the results change over time; however, it provides a bit 

more insight than just the probability bands. Figure 8 shows the probability density function of 

the capacity of coal plants over time, using a different plot color for each year. One can see that, 

as you progress into the future, the results are more distributed (less certain) – an insight you can 

also glean from the probability bands. However, the probability density also provides the insight 

that these results become bimodal – that is, capacity values will tend toward the extreme high 

and low values. In the case of SEDS, this is due to a Bernoulli distribution on whether there will 

be a carbon tax in the future. 

Figure 8 

Distributions of SEDS Outputs 

Sensitivity Analyses: In a sense, a stochastic model like SEDS automatically considers many 

sensitivities in its multiple trajectories through time. However, we have also investigated many 

sensitivities explicitly. Of particular interest are the sensitivities to the probability distributions 

themselves. We show (below) some sensitivities to the assumed shape of a probability 

distribution and to the mean of a distribution. 

We have found that the results are not very sensitive to the shape of the input distributions. We 

tested this for most of the uncertain inputs by changing the shape from our default triangular 

distribution to a uniform distribution. One of the largest impacts occurred when we changed the 

symmetric triangular distribution on the annual natural gas price growth rate to a uniform 

distribution with the same mean. However, as you can see in Figure 9, the impact on the total 

consumer bill was still minimal. 

16
Figure 9 

Insensitivity to Probability Distribution Shape 

As expected, results are more sensitive to changes in the mean of a probability distribution. 

Figure 10 shows how the model reacts to a relatively small change in the coal-price growth rate 

input. The only difference in the two runs is outlined in Table 3. 

Table 3 - Coal Price Growth Rate Sensitivity Inputs 

Coal price growth rate (%/year) Low Mode Mean High Shape 

Run with mid = 1.008 .99 1.008 1.008 1.025 Triangular

Run with mid = 1.02 .98 1.02 1.02 1.06 Triangular

This increase in the mean of the annual growth in coal price leads on average to a 50% increase 

in the price of coal by 2050. The model responds to this, on average, by retiring coal plants 

instead of continuing to build them as show in Figure 10. 

Figure 10 

Sensitivity to the Mean of a Probability Distribution 

17
NREL and the National Energy Technology Laboratory (NETL) are examining a wide range of 

additional uncertainties with SEDS. 

Future Development

DOE is working with its national laboratories (NREL, NETL, Lawrence Berkeley National 

Laboratory, Argonne National Laboratory, and Pacific Northwest National Laboratory) and 

others to expand SEDS beyond NREL’s current electric-sector version to a full representation of 

U.S. energy markets and their interaction with the U.S. economy. Through a multiyear 

development effort, the full SEDS will include the transportation, buildings, and industry 

demand sectors; an endogenous treatment of fossil resources; and a macroeconomic module. 

These will be developed with enough detail to estimate the impact of different technologies, 

programs, and policies under the full range of future uncertainties in primary market drivers. For 

example, SEDS should provide new insights into the future role of biomass fuels, hydrogen, 

plug-in hybrid electric vehicles, carbon sequestration, coal-fired IGCC power plants, 

photovoltaics for buildings, advanced lighting technologies, and advanced electric motors under 

a wide range of market and policy possibilities. 

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4. TITLE AND SUBTITLE

Modeling of Uncertainties in Major Drivers in U.S. Electricity 

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W. Short, T. Ferguson, and M. Leifman 

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National Renewable Energy Laboratory 

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This paper presents information on the Stochastic Energy Deployment System (SEDS) model. DOE and NREL are 

developing this new model, intended to address many of the shortcomings of the current suite of energy models. 

Once fully built, the salient qualities of SEDS will include full probabilistic treatment of the major uncertainties in 

national energy forecasts; code compactness for desktop application; user-friendly interface for a reasonably trained 

analyst; run-time within limits acceptable for quick-response analysis; choice of detailed or aggregate 

representations; and transparency of design, code, and assumptions. Moreover, SEDS development will be 

increasingly collaborative, as DOE and NREL will be coordinating with multiple national laboratories and other 

institutions, making SEDS nearly an “open source” project. The collaboration will utilize the best expertise on specific 

sectors and problems, and also allow constant examination and review of the model. This paper outlines the rationale 

for this project and a description of its alpha version, as well as some example results. It also describes some of the 

expected development efforts in SEDS. 

15. SUBJECT TERMS

Stochastic Energy Deployment System Model; SEDS; Annual Energy Outlook; installed capacity; regional 

disaggregation; electric sector; uncertainty; generating capacity; Walter Short; Tom Ferguson; Michael Leifman 

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