PROMETHEUS stochastic model - Energy, Economics and Environment Modeling Laboratory
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.. National Technical University
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Polytechniou 9 Str.
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Energy, Economics and
Environment Modeling Laboratory
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PROMETHEUS
stochastic model..
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TABLE OF CONTENTS
General features................................................................................ 3
Using econometric estimation for obtaining stochastic information.... 3
From econometric estimation to Monte -Carlo runs in PROMETHEUS .. 4
PROMETHEUS output........................................................................ 6
PROMETHEUS model characteristics ................................................. 6
The demographic and economic activity sub-model .............................. 9
The fossil fuel supply sub-model .......................................................... 9
The fuel prices sub-model ................................................................. 10
The final energy demand sub-model ................................ .................. 10
The electricity generation sub-model ................................ .................. 11
The hydrogen production sub-model ................................ .................. 12
The hydrogen storage and delivery infrastructure sub-model ............... 12
The climate sub -model ...................................................................... 13
The two factor learning curve sub-model ............................................ 13
2The PROMETHEUS
model
Short description of the PROMETHEUS
model
General features
PROMETHEUS is a tool for the generation of stochastic information for key energy,
environment and technology variables. In this section a short description of the model is given
by presenting its main features.
It is a self-contained energy model consisting of a set of stochastic equations. It contains
relations and/or exogenous variables for all the main quantities, which are of interest in the
context of general energy systems analysis as well as technology dynamics regarding power,
road transport and hydrogen production and use technologies. These include demographic and
economic activity ni dicators, energy consumption by main fuel, fuel resources and prices,
CO2 emissions, greenhouse gases concentrations, temperature change, technology uptake and
two factor learning curves.
All exogenous variables, parameters and error terms in the model are stochastic with explicit
representation of their distribution including in many cases terms of co-variance. It follows
that all endogenous variables as a result are also stochastic.
Using econometric estimation for obtaining stochastic information
In constructing PROMETHEUS extensive use of econometric techniques was made in order
to obtain the detailed stochastic information required for as complete a representation of their
interaction as possible.
The methodology adopted(advantages):
• Provides an element of objectivity.
• Forces the analyst to investigate the nature and extent of stochastic elements
(why past variability occurred).
• Is amenable to the analysis of co-variance both in terms of statistical
dependence of the parameters and in terms of the simultaneous solution of
sets of econometrically estimated equations.
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.. the other hand, the main disadvantage is the excessive reliance on history. However, it is
.not clear whether this reliance leads to exaggeration or under-estimation of variability –
therefore the method does not in itself produce systematic bias.
The derivation of stochastic elements takes into account that:
• The variance of the regression is unknown and hence itself a random
variable (in the process of implementation in PROMETHEUS this has
proved to be a major source of variability especially since the samples used
were relatively small and the distribution of the variance skewed).
• The parameter estimates are stochastic. As these are used in
PROMETHEUS as time independent variables it was found that it was
preferable to specify equations in dynamic form to avoid excessive early
variability and adequately represent accumulation of uncertainty in the
longer term.
• The parameter estimates are not statistically independent (i.e. they co-vary).
This has often proved an element of stability (example: negative covariance
between autonomous efficiency gains and activity elasticities). However
this is not a general rule: a positive (or negative) co-variance between
activity and price elasticities comb ined with decreasing (or increasing)
prices in the course of a Monte-Carlo run will increase variability.
• The residuals of the equations vary with time but are independent and hence
their cumulative effect though it increases, does so at a decreasing rate.
Econometric estimation has been in many cases supplemented with risk assessment provided
by scientific expertise (examples: geological uncertainties concerning fossil fuel resource
endowment, uncertainties associated with knowledge of GHG accumulation and its effects on
climate change).
For some variables recourse had to be made to expert judgment via Delphi methods (example:
future climate policy stances). In all cases where such “exogenous” risk information was
introduced, care was devoted to incorporate a wide range of opinion: in PROMETHEUS a
biased estimate of variability is considered to be a systematic error every bit as serious as bias
on expected values and is equally likely to distort probabilistic statements made on the basis
of model results.
From econometric estimation to Monte-Carlo runs in PROMETHEUS
In practical terms following the performance of regression estimation the following steps are
performed in order to obtain the appropriate parameters to be used in the operational version
of PROMETHEUS.
1. Divide the variance co-variance matrix of the estimated parameters by the
estimated variance.
2. Apply Cholesky decomposition to the matrix resulting in the previous step.
3. Generate a chi squared distributed random value for the variance (with the
estimated mean and the sample requisite degrees of freedom).
44. Multiply the triangular matrix resulting from step 2 by the random variable
generated in 3.
5. Multiply the triangular matrix resulting from step 4 by a vector of standard
normal variates to obtain an experimental trial vector of equation
parameters (they will have the required variance and covariance)
6. Generate residuals for all time periods as normal random variables with
zero mean and the experimental variance obtained in step 3.
7. Repeat the same for all equations in the model and then solve the whole
model (using also experimental values obtained with non-econometric
methods
The above process is repeated for the number of Monte Carlo runs. A major problem
encountered in the procedure described above has been the possibility of values that violate
economic theory or downright common sense.
More specifically, the Standard Least Squares estimation and statistical interpretation, which
is used in the econometric estimation of PROMETHEUS model, is based on the assumption
of normality of error terms. This leads to parameter estimator distributions Student t), which
in theory imply the possibility that a parameter changes sign. While this may not always cause
problems, in most cases economic theory (and commo n sense) stipulate a specific sign for key
parameters.
The problem is aggravated by the fact that many of the PROMETHEUS equations have rather
poor statistics (high variances) for many estimated parameters (in itself a minor problem in
the context of PROMETHEUS), which implies non-negligible probabilities for illegal values.
Clearly such values cannot generally be tolerated and in the context of PROMETHEUS could
prove particularly pernicious as in the course of Monte-Carlo runs they could be combined
with extreme values for some results thus completely perverting the experiment.
Possible solutions to the problem presented above are:
• Assume a different distribution (log normal or some generalized form) for
parameter estimators while attempting to maintain key properties (mean,
variance, co-variance with other parameter estimators)
⇒ The major drawback is the complex specifications in order to
maintain desired properties while at the same time arbitrary
interventions cannot be avoided anyway
• Ignore illegal values (which is equivalent to scaling the distribution)
⇒ The major drawback is the different moments from those implied
by the estimation
⇒ The major advantage is the better respect to the initial “form” of
distributions and naturally simplicity of implementation.
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.. ⇒ However, rejection of an illegal value must be accompanied by
rejection of associated (and probably legal) values for the other
parameters in order to maintain the desired properties of the Monte
Carlo exercise.
PROMETHEUS output
The basic output of PROMETHEUS is a data set of Monte Carlo simulations containing
values for all the variables in the model.
This set can be used as strategically or analytically important information on risks and
probabilities, regarding the variables incorporated in it or any pre-determined function
involving them. Major applications could be in security of supply assessment environmental
risk assessment, investment risk analysis etc.
It can also be used to fit joint Normal or Lognormal distributions for the impact variables to
be used in the ISPA policy exploration tool. Note that the problem of estimating the
covariance is satisfactorily solved by the process itself. Justifications for the co-variances can
also be provided through the data set itself or through inspection of PROMETHEUS relations.
PROMETHEUS model characteristics
The forecasting horizon of the model is the period 2005-2050. However, for 2005 and 2006
real data are used where available from the various data sources.
The model distinguishes 4 main regions:
1. OECD 90 Europe, which includes the EU-15, Norway and Switzerland
2. Other OECD 90, which includes the USA, Canada, Japan, Australia and
New Zealand
3. The NMS-12, the new members of the European Union, joined the union
after 2000, which includes Czech republic, Slovakia, Slovenia, Malta,
Cyprus, Poland, Hungary, Latvia, Lithuania, Estonia, Bulgaria and
Romania.
4. Rest of the world (less developed countries).
Figure 1 presents a summary flow chart of the PROMETHEUS stochastic model. The model
is triangular and it is logically divided into sub-models, which are interacting using time lags
in their common variables in order to avoid simultaneity in the model equations. The sub-
models are:
• The demographic and economic activity sub-model, which projects
population and GDP.
• The fossil fuel supply sub-model, emphasizing on oil and gas resources.
• The fuel prices sub-model, projecting international and consumer prices,
with the latter being differentiated for each demand sector
6• The final energy demand sub-model, projecting the demand in three main
consumption sectors; industry, transport and residential/services/agriculture
• The electricity generation sub-model, identifying in detail more than 20
power generation technologies.
• The hydrogen production sub-model, identifying in detail more than 10
different hydrogen production options
• The hydrogen storage and delivery infrastructure sub-model
• The climate sub-model, which uses reduced form atmospheric dynamics,
following the IPCC Third Assessment Report in order to calculate the GHG
concentrations and consequently the global average temperature change.
• The two factor learning curve sub-model, which ednogenises as much of the
technical progress as possible through learning by research and learning by
experience.
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.. Figure 1: Summary flow chart of PROMETHEUS specification
8The demographic and economic activity sub-model
This sub-model is autonomous in the sense that it does not depend on the output of the rest of
the PROMETHEUS sub-models. Using reduced forms, it projects the population and the
economic activity in the four PROMETHEUS regions, which constitute main drivers for the
rest of the model variables.
The fossil fuel supply sub-model
PROMETHEUS puts the emphasis on oil and gas resources, while coal is assumed to have
abundant supplies relative to production prospects in the projection time horizon.
High uncertainty surrounds the amount of oil and gas resources that are yet to b e discovered.
This uncertainty has been incorporated into PROMETHEUS. Using studies conducted by the
United States Geological Survey (USGS), stochastic analysis has been carried out in order to
obtain distributions for the yet to be discovered oil and gas at the starting year of simulation.
The two variables are jointly distributed i.e. there is a considerable amount of correlation
between the unknown quantities of gas and oil due to geological factors (uncertainties on
hydrocarbon formation and retention in sedimentary basis). In each Monte Carlo experiment,
PROMETHEUS begins from different world state regarding these variables. The rate of
discovery as well as the rate of recovery are endogenous in PROMETHEUS depending on
fuel prices and subject to their own specific uncertainties. For g as it is also assumed that when
oil is sought, gas is often found.
Figure 2: Scatter graph of the yet to be discovered gas and oil in the starting year of
PROMETHEUS simulations
Yet to be discovered conventional oil in Gbl
3500
3000
2500
2000
1500
1000
500
0
100 200 300 400 500 600 700 800 9001000
Yet to be discovered gas in Gtoe
PROMETHEUS also looks through conventional and non-conventional oil reserves.
Conventional oil reserves are differentiated between Gulf and non-Gulf to allow for
alternative disruption risks, while non-conventional oil is distinguished in Venezuela’s extra
heavy oil and Canada’s tar sands. On the other hand, coal and natural gas reserves are
identified at the global level.
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.. gross addition to reserves of conventional world oil is a function of the yet to be
.discovered oil, the international price of oil and the production of oil. The recovery rates of
non-conventional oil sources are price-dependent and they act as a crucial “backstop”
preventing frequent occurrences of very high world oil prices. The gross additions to the
reserves of gas are a function of the yet to be discovered gas, which is based on the natural
gas endowments, and the gross additions to the world reserves of oil.
The production of oil is based on the world demand for oil, the international price of oil and
oil reserves. Oil production capacity in the Middle East is driven by production trends but it is
also subject to random disruptions determined from historical data. On the other hand, gas and
coal production are assumed to be demand driven.
The fuel prices sub-model
The fuel prices sub-model calculates the consumer price for each energy form used in final
demand. The model differentiates prices for each final consumption sector.
For fossil fuels, the international prices are calculated prior to end -user prices. The
international price of oil depends on the oil production to capacity ratio in the Middle East, as
well as on the world reserves to production ratio. The oil price is also affected by randomly
generated disruptions in oil supply. A uniform distribution, reproducing the frequency of
historical oil crises, is used to trigger a disruption in oil supply. The international price of gas
depends on the reserves and production of gas and on the international price of oil. Finally, as
coal is assumed to have abundant supplies, its international price is demand driven and is only
weakly linked to the prices of other fuels
The spot prices of heavy fuel oil, gasoline, diesel and light fuel oil, as well as the border gas
price, are linked to international prices. The consumer prices are then derived through simple
econometric relations and they are differentiated by region and consumer. The effective
climate policy, through the carbon value, also affects the consumer prices.
Finally, the electricity and hydrogen prices for different loads and consumers are based on the
average production cost of electricity and hydrogen. In the case of hydrogen, storage and
delivery costs related to the hydrogen infrastructure are also explicitly considered.
The final energy demand sub-model
Economic activity and fuel prices are the main drivers of final energy demand. The final
consumption sectors considered in the model are:
• Industry (non-electric uses)
• Industry (electric uses)
• Transport
• Residential/Commercial/Other (non-electric uses)
• Residential/Commercial/Other (electric uses)
The following fuel/energy forms are considered as options in the final demand sectors:
• Coal
• Oil
10• Biofuels
• Natural Gas
• Electricity
• Hydrogen
The private passenger cars sector is modeled in detail, by distinguishing seven types of
passenger cars:
• Internal combustion engine cars (gasoline, diesel, hydrogen, biofuels )
• Fuel cells (hydrogen and gas reformer)
• Electric cars (pure electric, conventional hybrid, plug-in hybrid)
The electricity generation sub-model
The power generation sector is also described in detail. Twenty six electricity generation
technologies compete to satisfy electricity demand:
• Coal fired technologies (Conventional coal and lignite thermal,
Supercritical coal, Integrated coal gasification)
• Gas fired technologies (Conventional thermal, open cycle turbine,
combined cycle turbine, CHP)
• Oil fired technologies (conventional thermal, open cycle turbine)
• Biomass fired technologies (biomass thermal, biomass gasification)
• Renewable technologies (large and small hydro, wind onshore, wind
offshore, photovoltaic, solar thermal)
• Fuel cells (hydrogen and gas)
• CO2 capture and sequestration (integrated coal gasification, supercritical
coal, gas turbine combined cycle, biomass gasification)
• Nuclear technologies (conventional nuclear, 3d and 4th generation nuclear)
In each year of the simulation horizon, a “gap” in the electricity generation is created, which
arises from the increase in the electricity demand, the retirements of power plants that reach
the end of their lifetime and the pre-mature replacement of power plants with high variable
costs. The electricity production cost of each technology (composed by the capital cost, fixed
O&M cost, variable O&M cost, and fuel cost), adjusted for load factors pertinent to different
markets, determines the share of the technology in the “gap” for a given load.
Finally, average cost pricing is used for the calculation of the consumer electricity price.
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The hydrogen production sub-model
On the supply side 9 technologies compete for the centralized production of H2 . These
include:
• Natural gas steam reforming technologies with and without CO2 capture and
sequestration; a special case is also included, which uses solar energy to
increase the reforming process temperature and consequently reduce the
quantity of gas needed for hydrogen production.
• Coal gasification with and without CO2 capture and sequestration
• Coal partial oxidation with and without CO 2 capture and sequestration
• Biomass gasification with and without CO2 capture and sequestration
• Biomass pyrolysis
• Heavy fuel oil oxidation
• Solar and nuclear high temperature thermochemical cycles
• Electrolysis using power from the grid
• Electrolysis using nuclear dedicated plant
• Electrolysis using wind dedicated plant
On the demand side, hydrogen is introduced in the competitive market of distributed
electricity production (through stationary fuel cells) and in the road transport sector (through
fuel cell cars and the hydrogen internal combustion engine car).
The hydrogen and electricity systems are connected and interact in the energy system in two
points: in the hydrogen production through the electricity price in grid electrolysis and in the
demand side through the competition between the decentralized fuel cell electricity
production and the electricity from grid.
The hydrogen storage and delivery infrastructure sub-model
In PROMETHEUS, a stylized configuration is used as a reference hydrogen delivery network,
which represents a situation after a take-off of a hydrogen economy of some short but before
maturity of such economy. The stylized configuration refers to an average EU region supplied
with hydrogen and contains a plant connected to a turnpike pipeline, which is used as storage
medium, load management tool and as emergency supply in cases of production disruption.
The turnpike pipeline crosses the region and is connected with similar turnpike pipelines in
the neighboring regions. Moreover, other pipelines of smaller capacity connect the plant with
the urban and industrial areas of the reference region. The service stations, which absorb more
than half of the plant production, are situated under at least two distinct conditions: rural
stations along the roads crossing the region and urban service stations mostly concentrated on
the outside ring of the urban area. It can be reasonably assumed that all rural stations will be
supplied by truck.
12The climate sub-model
The forecasting horizon of the climate sub-model is extended by 15 years in order to take into
account the “additional warming commitment”. The commitment is necessary because th e
climate system can be recognized as a form of “hysteresis” meaning that the current state of
climate reflects not only the inputs, but also the history of how it got there. According to
IPCC TAR, an increase in forcing implies a “commitment” to future warming even if the
forcing stops increasing and is held at a constant value. At any time, the “additional warming
commitment” is the further increase in temperature, over and above the increase that has
already been experienced, that will occur before the system reaches a new equilibrium with
radiative forcing stabilized at the current value.
The sub-model takes as input economic activity, population and fossil fuels production from
the rest of the PROMETHEUS model, and projects emissions for the following greenhouse
gases: CO2 from fossil fuel combustion and industrial processes, N2O from industrial and land
uses and CH4 from biomass burning, landfills, livestock, rice farms, oil & gas supply and coal
mining.
Based on IPCC TAR reduced form equations of the atmospheric dynamics were estimated,
which take into account the uncertainty underlying the interaction of the main components of
the climate system (atmosphere, hydrosphere, cryosphere, land surface and biosphere). The
anthropogenic emissions constitute the main input to equations enabling the calculation of the
atmospheric concentrations and the estimation of global temperature.
It should be noted that there is a feedback between the climate change and the effective
climate policy. The intensity of the climate policy takes into account the change in global
temperature as it averages in PROMETHEUS simulation.
The two factor learning curve sub-model
The objective of a two factor learning curve is to endogenise as much of the technical
progress as possible through learning by research and learning by experience. In fact the
learning by research is the first and more influential element, since it reduces the technology
cost leading to increased technology uptake and hence to further decrease in cost through
learning by experience. PROMETHEUS includes stabilization mechanisms to ensure some
stability in learning cycles. These mechanisms are constraints to technical possibilities and
they emerge from perspective analysis.
In PROMETHEUS the technology dynamics for 51 technological options for electricity
production, hydrogen production/storage/delivery and passenger cars were estimated. These
include:
• Capital costs parameters for 44 technological options
• Fixed O&M costs for 34 technologies; although they are basically labor
costs, technical progress has been assumed based on the increased
automation, reliability and the economies of scale
• Variable cost parameters for 7 technologies, adjusted for efficiency.
• Efficiency parameters for 20 technologies
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.The
.. sub-model introduces clustering between the technologies, by identifying components
.which are used in more than one technology and incorporating two factor learning curves for
them. In this sense, an improvement in the performance of a particular component will affect
the performance of more than one technology.
It should be noted that the energy related R&D expenditures are not an exogenous assumption
in the model, but they are influenced by the GDP growth, the total energy cost and the
effective climate policy.
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