Stochastic Optimization Model of Fuel Procurement, Transportation
and Storage for Coal-Fired Thermal Plants in Hydrothermal Systems
A. Dias
1
, R. Kelman
1
, F. Thomé
1
, M. Pereira
1
, S. Binato
1
, E. Faria
2
and G. Ayala
2
1
PSR, Praia de Botafogo 228, 1701-A, Botafogo, Rio de Janeiro, 22250-145, Brazil
2
MPX, Praia do Flamengo 66, 8
th
floor, Rio de Janeiro, 22210-903, Brazil
Keywords: Stochastic Programming, Mixed Integer Optimization, Decision under Uncertainty.
Abstract: This work presents an optimal strategy of coal procurement for thermal plants, including transportation and
storage in order to guarantee continuous supply of the fuel. The stochastic programming model developed
takes into account the uncertainty associated with inflows in a hydrothermal system and other complex
logistics and commercial aspects related to the international coal market. Different study cases are analysed
and the results are presented through comparisons of different strategies applied to different scenarios of
dispatch.
1 INTRODUCTION
Three new coal-fired thermal plants are being built
in the Brazilian system: Porto do Pecém I and II
(720 MW/360 MW) and Porto do Itaqui (360 MW).
Projects were contracted in the energy auction of
2007/2008 “by availability”, i.e. each project will
receive:
(i) a fixed monthly revenue to guarantee the
investment returns;
(ii) a variable payment, proportional to the energy
production, to reimburse operational costs (fuel,
O&M, etc.).
Because the plants were contracted by availability,
an important problem is to guarantee continuous
supply of coal, since severe penalties are applied if
the plant is not able to meet the generation target due
to fuel shortages. This problem is complex because
time lengths comprising coal purchase and
transportation can be up to three months, while the
plant dispatch order by the operator can be placed
with one day in advance. Although considering the
coal storage capacity, the main challenge is
forecasting the medium/long term dispatch, which is
especially difficult in the case of the Brazilian
system, because of its hydro characteristic (high
volatility of energy spot prices).
Furthermore, in the international coal market,
long-term supply contracts are usually signed with
one year duration, pre-established prices and
delivery deadlines. This practice is a result of
unpredictability of coal prices and coal availability,
leading to longer delivery deadlines and long periods
of negotiation between parties.
For these reasons, coal procurement strategies
must be made under uncertainty, and must be
adequate to the storage capacity of thermal plants,
uncertainty of dispatch, and characteristics of both
coal and freight market. Uncertainties in the
forecasts may lead not only to generation outages
due to coal unavailability, but also to a surplus of
coal, that may be stored, used for inflexible
generation, or sold in the international market;
situations that can result in additional costs. Figure 1
illustrates the procurement decision process for coal
supply with respect to the dispatch uncertainties.
Figure 1: Coal procurement decision under uncertainty.
To summarize, the uncertainties of generation
135
Dias A., Kelman R., Thomé F., Pereira M., Binato S., Faria E. and Ayala G..
Stochastic Optimization Model of Fuel Procurement, Transportation and Storage for Coal-Fired Thermal Plants in Hydrothermal Systems.
DOI: 10.5220/0004285102830291
In Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES-2013), pages 283-291
ISBN: 978-989-8565-40-2
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
dispatch and/or energy spot price (SRMC) can drive
decisions to two types of errors: (1) fuel is purchased
but the thermal plant is not dispatched; and (2) fuel
is not purchased but the thermal plant is dispatched.
In this context, it is important to establish a
methodology to determine a coal supply strategy for
all coal-fired thermal plants. The objective is to
minimize costs of procurement decisions under
uncertainties, taking into account the costs caused by
the corrective actions taken in case of errors (1) (2).
The corrective actions to mitigate errors (1) include:
a) Fuel storage for future use – in this case, there is
an opportunity cost of the coal purchased in
advance;
b) Thermal plant inflexible dispatch – the energy is
sold in the spot market with a loss (in this case
the spot price is lower that its variable cost,
unless it is dispatched by the operator); and
c) Resell the coal vessel in the international coal
market.
In the case of errors (2), the possible corrective
measures to avoid penalties due to fuel shortage are:
a) Buy energy from a thermal plant not dispatched
in the same week, for example, from an oil-fired
plant; and
b) Use “energy credits” stored in hydro reservoirs
resulted from previous inflexible generation.
An overview of the optimization system for coal
supply procurement is presented in the next section.
2 SYSTEM OVERVIEW
Figure 2 shows a schematic representation of the
coal procurement optimization system for thermal
plants operating in hydro-dominated systems,
composed by two blocks:
a) The first block (blue area) illustrates the module
responsible for the hydrothermal simulation. The
objective is to estimate scenarios of generation
dispatch and SRMC. Generation scenarios of
coal-fired thermal plants are converted into coal
consumption scenarios, which are used by the
procurement optimization module.
b) The second block (grey area) illustrates the coal
procurement optimization model (MOCCA),
which is responsible for evaluating an optimal
strategy for supply procurement and coal
delivery schedule for thermal plants.
Figure 2: Coal procurement optimization system.
As illustrated, besides thermal plants data (such
as heat rate, installed capacity, O&M costs),
MOCCA needs information about coal initial
storage, cargoes in transit, coal availability (prices,
quantities, and delivery conditions), coal price
projections (international market), coal consumption
scenarios and energy spot prices scenarios.
3 PROBLEM FORMULATION
In this section, the mathematical formulation of the
coal procurement optimization model is discussed.
The objective function of the model is given by the
sum of four shares:
1
|
|
∈
(1)
Where
|
|
represents the size of the set , that
represents the set of all hydrothermal dispatch
scenarios. is the number of stages (months or
weeks) of the study horizon. The first share 1/
|
|
∙
represents the expected payments of coal supply
procurement that will be shipped to the thermal plant
∆,
∙
∆
∙
∆,,
∈
∆
(2)
Where
represents the set of dispatch
scenarios in stage Δ that share the same
procurement decision (procurement cluster), Δ is the
required antecedence (in stages) for the supply
procurement;
,
represents the number of
dispatch scenarios in the procurement cluster ;
is the coal supply procurement unitary cost
(including transportation cost) and
∆,,
ICORES2013-InternationalConferenceonOperationsResearchandEnterpriseSystems
136
represents the amount of the coal procured in stage
Δ, cluster , that will be shipped to the thermal
plant using the cargo type .
The second share 1/
|
|
∙ represents the
expected fines which are imposed on the thermal
plant for not meeting the generation target
determined by the system operator:
∙
̃
,
∈
(3)
Where is the penalty value and ̃
,
is the
deficit related to the target in stage and scenario .
The third share 1/
|
|
∙ represents the expected
revenue due to the thermal production for meeting
the generation target, forced generation and energy
exportation:
∙
,
,
∙
,
∙
,
∈
(4)
Where
is the unitary reimbursement of the
thermal plant for meeting the generation target
,
in stage and scenario ;
,
and
,
are
respectively the energy spot price forecast and the
inflexible generation in stage and scenario and;
and
,
represent, respectively, the energy
exportation price and the energy exported amount.
The last share 1/
|
|
∙ represents the expected
revenues from the procured loading resale which is
redirected to the international market:
∆,
∙
∙
∈
∆
(5)
Where
is the forecasted coal resale price in
the international market and
is the redirected
coal amount.
The coal supply procurement optimization
process is subjected to a set of physical or logical
constraints which are briefly and discussed next.
The first constraint represents the energy supply
target set by the system operator, formulated as:
,
̃
,
,
,∀1,…,,1,…,
(6)
It means that the generation target
,
in stage
and scenario , is met by the sum of thermal
generation
,
and energy deficit ̃
,
, penalized in
the objective function.
The energy production in the thermal plant is
limited by its installed capacity, that is:
,
,
,
̅
,∀ 1,…,, 1,…,
(7)
The coal storage of the thermal plant is basically
modeled by two constraints:
Coal storage balance:
,
,
,
,
,
∀1,…,,1,…,
(8)
Coal storage capacity
,
̅
,∀1,…,
(9)
Where
,
represents the stored coal in the
thermal plant;
,
is the coal amount used for
energy production and
,
is the coal amount
delivered in the storage, all values in stage and
scenario .
The first of the two storage constraints is the coal
balance in each stage, which means, the stored coal
at the end of the stage is a function of the stored coal
at the beginning of the stage and the net difference
between the amount of coal used (to produce
energy) and the amount of coal unloaded in the
thermal plant during this stage. The second
constraint represents the coal storage physical limit
in the thermal plant yard.
The next constraint establishes the connection
between the amount of coal delivered
,
in the
plant at stage and scenario , with the amount of
procured coal
, with Δ being the required
antecedence to request the coal amount.
,
∆,
∆,
,
,
∀1,…,,1,…,
(10)
And the last set of constraints represents the
allocation of the procured coal to the ships:
∆,
∆,
,
Κ
∙
∆,
∆,
,
,
(11)
Where Κ
is the capacity of cargo type , and
∆,
∆,
,
is a binary variable that represents that
the cargo is being used to transport the amount of
the coal
∆,
∆,
,
in stage Δ.
4 TEST CASES
The results of the optimization model for coal
supply procurement are illustrated by the following
StochasticOptimizationModelofFuelProcurement,TransportationandStorageforCoal-FiredThermalPlantsin
HydrothermalSystems
137
test cases:
a) Case 1: Stochastic case considering 20 scenarios
of generation dispatch and spot price, obtained
from the studies with the hydrothermal Brazilian
system (considering the horizon from May 2011
to Dec 2015). The coal procurement decisions
for this case study was represented in a
deterministic way, i.e. supply decisions are the
same for all 20 scenarios;
b) Case 2: Case 1, but using a decision tree (instead
of a deterministic decision) to represent supply
procurement decisions.
c) Case 3: Case 2, but considering 200 scenarios
(instead of 20 scenarios) of generation dispatch
and spot price.
The main objective of the proposed studies is to
determine the coal amount to be procured in the long
term by the thermal plant. As mentioned before, the
long-term contracts have greater execution deadlines
(typically one year), but are associated to more
attractive prices than the short-term contracts. It
should be emphasized that the data used in the test
cases of this particular work, associated to thermal
plants, coal supply contracts, and others, have been
created in order to illustrate the optimization model
behavior and may be different from a real case data.
Thermal Plant Data
The model was applied in the procurement strategy
optimization of the Porto do Itaqui thermal plant,
located in the Northern region of the Brazilian
system, assuming the following basic data:
Installed capacity: 360 MW;
Efficiency (coal consumption): 4.84 × 10
-7
MWh/kcal (or 2 066 kcal/kWh);
Coal storage capacity: 210 000 tons
(equivalent to approximately 70 days of the
thermal plant nominal power operation);
O&M cost: 7.5 US$/MWh;
Losses and self-consumption are neglected;
Operational cost: 61.2 US$/MWh.
Scenarios
For the coal resale price scenario, a constant value of
105 US$/ton (FOB-Colombia, i.e. no shipping cost
is considered for the buying market) was adopted.
In order to represent thermal dispatch and spot
price scenarios, the results obtained from the studies
with the hydrothermal Brazilian system (May 2011)
using the SDDP dispatch model (PSR, 2011a, PSR,
2011b) were used.
Candidate Contracts Data
In each one of the test cases, 30 candidate contracts
were considered, where 8 of them are long-term
contracts and the rest are short-term contracts.
Parameters associated to the long-term contracts:
Availability: 500 000 tons;
Procurement cost (FOB): 110 US$/ton;
Shipping cost: 20 US$/ton (Handymax ships);
Antecedence in procurement decision: up to 1
year;
Time interval for boarding the procured amount:
3 months (travel time of 1 month).
The following figure illustrates the eight long-term
contracts, emphasizing the intervals that define their
procurement decision and shipping:
Figure 3: Long-term contract data.
The green blocks illustrate, for each candidate
contract, the period in which the procured coal can
be shipped from the origin port (in Colombia), being
the loading available for the thermal plants one
month after boarding (expedition time).
The red blocks illustrate the procurement
decision date of each contract. Note that all long-
term contracts for a specific year should be decided
up to October of the previous year.
Parameters associated to the short-term contracts:
Availability: 500 000 tons;
Procurement cost (FOB): 115 US$/ton;
Shipping cost: 20 US$/ton (Handymax ships);
Antecedence in procurement decision: 3 months:
Time interval for boarding the procured amount:
4 months (travel time of 1 month).
In the same way as the long-term contracts, Figure 4
illustrates the required antecedence for a short-term
contract. Note that, in this case, the antecedence is of
four months, because loading acceptance must be
informed one month in advance regarding long-term
contracts (due to an additional period of
negotiation).
Also, short-term contracts don’t require the
procurement decision to be taken too long in
advance (October of the previous year), which
makes them more attractive from the point of view
of the uncertainties of generation dispatch and spot
Contractname SOND J FMAMJ J A S OND J F MAMJ J A S OND
Q1‐2012
Q2‐2012
Q3‐2012
Q4‐2012
Q1‐2013
Q2‐2013
Q3‐2013
Q4‐2013
2010 2011 2012
ICORES2013-InternationalConferenceonOperationsResearchandEnterpriseSystems
138
prices. However, the coal supply procurement cost is
around 5% greater than the long-term contracts.
Figure 4: Short-term contract data.
General Data
The following execution options were considered:
Stage type: monthly
Horizon: 09/2011 – 12/2012 (+ 1 Year)
Annual discount factor: 12 %
Maximum number of ships unloading coal by
stage (one month): 3 ships
Penalty for not meeting generation target: 382
US$/MWh.
4.1 Case 1: Deterministic Decision
In this case, there has been used a subset of 20
dispatch and spot price scenarios extracted from the
original dispatch case (PMO from May 2011). The
next figure illustrates the variability of generation
dispatch of the thermal plant Porto do Itaqui.
Figure 5: Probability of dispatch of Porto to Itaqui.
From the figure above, one can see that the
average dispatch probability for the first year for the
thermal plant is around 20%. However, it is
interesting to see that in the operating month, (Jan-
2012 – 25% probability) the dispatch scenarios
labeled 2-10-14-16-20 (from the sample of 20
scenarios) are the ones with non-null generation; and
in Jun-2012 the scenarios are 7-12-13-16-19; that
means, although there is a reasonable probability
that the thermal plant will be used in any month of
2012, the probability of continual generation for
several months is much lower. This level of
uncertainty in the dispatch scenarios is typical in the
Brazilian system, because the high dependence of
reservoir inflow conditions.
In order to represent the variability of the SRMC
of the Brazilian system, the next figure shows the
range for the SRMC of the same sample of 20
scenarios used for generation dispatch.
Figure 6: Variability of SRMC.
As one can see, average values for SRMC
(illustrated in red) are closer to the minimum values
(in blue) than to maximum values (in orange),
indicating that the number of low-SRMC scenarios
is greater than the number of high-spot price
scenarios. This high volatility of SRMC is also a
characteristic of the Brazilian system.
The purpose of this first test case is to determine
a coal supply procurement decision which is valid
for all 20 dispatch and spot price scenarios, in other
words, to seek for a single procurement sequence
that optimizes the coal trade results for the thermal
plant. Just for complementary information, the
optimization model for this problem contains 138
600 constraints and 24 065 decision variables, where
4 400 of them are binary variables.
The results in terms of the delivery schedule in
the thermal plant and the contracts acceptance are
illustrated in the following figures:
Contractname S OND J FMAMJ J A S OND J F MAMJ J A S OND
SPOT‐01‐2012
SPOT‐02‐2012
SPOT‐03‐2012
SPOT‐04‐2012
SPOT‐05‐2012
SPOT‐06‐2012
SPOT‐07‐2012
SPOT‐08‐2012
SPOT‐09‐2012
SPOT‐10‐2012
SPOT‐11‐2012
SPOT‐12‐2012
SPOT‐01‐2013
SPOT‐02‐2013
SPOT‐03‐2013
SPOT‐04‐2013
SPOT‐05‐2013
SPOT‐06‐2013
SPOT‐07‐2013
SPOT‐08
‐2013
SPOT‐09‐2013
SPOT‐10‐2013
SPOT‐11‐2013
SPOT‐12‐2013
2010 2011 2012
StochasticOptimizationModelofFuelProcurement,TransportationandStorageforCoal-FiredThermalPlantsin
HydrothermalSystems
139
Figure 7: Deliveries in Porto do Itaqui (case 1).
Figure 8: Acceptances of candidate contracts (case 1).
The figures above show that the optimal solution
indicates the coal procurement through long-term
contracts only (more economic). The solution is
coherent to the fact that it is not possible to adjust
the procurement decision according to the dispatch
and spot price uncertainties.
The first loading acceptance, approximately 60
thousand tons (Q1-2012), occurs on Feb-2012, and
the associated coal amount is available to be used by
the thermal plant on Mar-2012 (expedition time). In
summary, the result of the supply procurement
optimization model indicates the procurement of
approximately 900 thousand tons in long-term
contracts over a price of almost 100 million dollars.
It is important to emphasize that this procurement
policy is based on negotiating all coal amount at the
beginning of the study horizon – because long-term
contracts must be decided up to October of the
previous year of the delivery date.
As a result of this procurement policy, the coal
average stored volume is shown in red in the
following figure containing the stored coal for all 20
scenarios considered.
It is important to highlight that average volume
illustrated above is not an indication of the optimal
coal storage level of the thermal plant.
Figure 9: Scenarios of storage in Porto do Itaqui (case 1).
The financial result for the coal trade is
illustrated in the following table:
Table 1: Financial result for the coal trade (case 1).
As one can see in the previous table (column
“Penalty”), no fuel shortages were estimated for
meeting the generation target dispatch scenarios, as
a result of the procurement model. Another
observation can be made about the coal resale on the
international market, which hasn’t been
economically attractive (column “Resale” of the
table). A low resale level against a high forced
generation level is explained by the difference
between the resale price and the forced generation
refund value given by the spot prices.
The result of the coal trading operations, as can
be seen, is negative in US$ 24 million dollars, which
was already expected since the single procurement
for all generation and spot price scenarios implies in
significant losses due to the coal acquisition needed
for scenarios with thermal generation and also due to
the coal inefficient usage in forced generation for
scenarios without thermal generation, which may be
required because of storage limitations.
4.2 Case 2: Decision Tree for Coal
Supply Procurement
The objective of this case is to determine a
procurement policy (not deterministic), which means
that the procurement decisions can be adjusted
St a g e
Ca r g o s
acceptance Freight
O&M
costs Penalty
En e rg y
reemb.
Co a l
resell Total
Net
value
01/2012 00-209076.5
02/2012 -6-1-2080-2-1.6
03/2012 -10 -2 -2 0 11 0 -3 -3.1
04/2012 -12 -2 -2 0 10 0 -6 -5.3
05/2012 -12 -2 -2 0 11 0 -5 -4.3
06/2012 -12-2-2090-6-5.4
07/2012 -12 -2 -2 0 10 0 -5 -4.6
08/2012 -8-1-2090-1-1.3
09/2012 -8-1-2090-2-2.0
10/2012 -8-1-2080-2-2.0
11/2012 00-209065.3
12/2012 -11-2-1060-7-6.4
ICORES2013-InternationalConferenceonOperationsResearchandEnterpriseSystems
140
according to the dispatch and spot prices scenario
uncertainties. In order to accomplish that, the
procurement policy has been modeled by a binary
decision tree, with openings in stages 2 (Oct-2010)
and 8 (Apr-2012), as illustrated in the next figure:
Figure 10: Decision tree – coal procurement policy.
To determine the dispatch/spot price scenarios
allocation in coal procurement decision clusters a
standard k-means clustering algorithm was used
(Hartigan and Wong, 1979), where the clusterization
criteria used to determine which generation
dispatch/spot price scenarios share the same
procurement decision, was the minimum value
between the spot prices, which varies by scenario,
and the thermal unitary cost.
One of the consequences of representing the
supply procurement by a decision tree is that the
optimization model dimensionality grows with
respect to the problem variables. In this case, the
optimization model has 142 800 constraints and 54
100 variables, where 5 640 of them are binary.
The results in terms of the average procured
amount are illustrated in the next figure:
Figure 11: Deliveries in Porto do Itaqui (case 2).
Figure 12: Acceptances of candidate contracts (case 2).
The first important result to be highlighted is that
the procurement representation by a decision tree
encourages the short-term procurement. As it can be
seen in the figure, the coal supply procurement
solution is a combination of both long- and short-
term contracts. Moreover, the total acquisition
(calculated by the average of the branches of the
procurement decision tree) is approximately half of
the amount indicated in the previous case, that is,
537 thousand tons. However, it should be clear that
this value is the average of the 4 branches of the
tree, which means that for clusters associated to the
series with high generation level, the procurement is
greater and, otherwise, it should be lower. The total
procurement for each branch of the decision tree is
shown in the following table:
Table 2: Total procurement coal for each branch.
Branch Tons
1 229256
2 868926
3 328513
4 897975
It is also observed that approximately half of the
average amount of procured coal (278 thousand
tons) is associated to long-term contracts, which
must be negotiated one year in advance. Therefore,
the total amount that should be immobilized in long-
term contracts is around 32 million dollars (almost
70% less than the amount estimated in the previous
case). The additional amount of coal supply is
associated to the short-term contracts, which are
only negotiated in the future, when there is more
information about the thermal dispatch conditions.
The implementation of the supply procurement
policy leads to a distribution of the stored coal
variable illustrated in the next figure:
StochasticOptimizationModelofFuelProcurement,TransportationandStorageforCoal-FiredThermalPlantsin
HydrothermalSystems
141
Figure 13: Scenarios of storage in Porto do Itaqui.
The financial result for the coal trading
operations is illustrated in the following table:
Table 3: Financial result for the coal trade (case 2).
From this table, it is interesting to highlight that
no outages in the generation target due to fuel
shortages were reported – according to column
“Penalty” of the table. Another interesting result that
can be seen in the column “Coal resell”, is that coal
was redirected for resale in the international market
in June 2012, while no resale was observed in the
previous case. This behavior is also explained by the
procurement strategy formulated as a decision tree,
since the resale price was more attractive than forced
generation refunding for the scenarios that share the
cluster where resale occurred.
Finally, the financial result of the trading
operations, when using a procurement strategy
represented by a decision tree, is positive in almost
10 million dollars.
4.3 Case 3: Stochastic Case
Considering All 200
Dispatch/SRMC Scenarios
The purpose of this test case is to show the results of
the supply procurement model considering the
complete set of generation dispatch and spot price
scenarios, obtained from the simulations of the
operation scheduling case study.
A straightforward consequence of increasing the
number of scenarios is the dimension growth of the
procurement optimization model which happens to
be formulated by a programming problem of 1.4
million constraints and 260 thousand variables,
where 45 thousand of them are binary. This increase
in the number of variables and constraints are also
the result of the binary decision tree adopted for this
problem, which has more openings (branches)
compared to those used in the previous case – the
new decision tree is composed by 16 branches with
openings in stages 2 (Oct-2011), 5 (Jan-2012), 8
(Apr-2012) and 11 (Jul-2012). For the series
allocation in the decision clusters, the same k-means
clustering algorithm of the previous case has been
used.
The results for the coal deliveries (average
values) are illustrated in the following figures:
Figure 14: Delivers in Porto do Itaqui (case 3).
Figure 15: Acceptances of candidate contracts (case 3).
From the above figures, it can be seen that the
average level of coal supply procurement is lower
(379 thousand tons) than in the case 2, where a
subset of 20 generation dispatch/spot price scenarios
were used. But, as in the case of 20 scenarios, there
is an encouragement for short-term acquisitions
(66% of the total procured amount, that means,
250 thousand tons come from this type of contract),
since this type of contract allows greater flexibility
and, consequently, fits better the uncertainties of
St a g e
Ca r g o s
acceptance Freight
O&M
costs Penalty
En e rg y
reemb.
Co a l
resell Total
Net
value
01/2012 00-208066.1
02/2012 -30-208032.6
03/2012 -8-2-1090-2-1.9
04/2012 -9-2-1090-3-2.4
05/2012 -9-2-2 010 0-2-2.0
06/2012 -11-1-109611.2
07/2012 -5-1-2 010 0 21.7
08/2012 -4-1-108021.7
09/2012 -5-1-107000.3
10/2012 -5-1-107010.8
11/2012 -20-107043.1
12/2012 -5-1-1050-1-1.0
ICORES2013-InternationalConferenceonOperationsResearchandEnterpriseSystems
142
thermal plant dispatch. Regarding long-term
contracts, in the first year there was a procured
amount of 129 thousand tons (33% of the total
amount), which requires an investment of
approximately 14 million dollars.
The next figure illustrates the result of the
procurement model for the variable “stored coal in
the thermal plant” (red curve shows the average
value for the 200 scenarios).
Figure 16: Scenarios of storage in Porto do Itaqui.
Once again a low average level is observed for the
coal stored amount, nevertheless, the average level is
not an indication for the optimal level since it varies
accordingly to each one of the generation
dispatch/spot price scenarios associated to coal
supply procurement decision tree of the thermal
plant.
The financial result for the coal trading operation
is illustrated in the following table:
Table 4: Financial result for the coal trade (case 3).
Regarding the table results, the case with 200
dispatch scenarios presents some supply outages on
the generation target (column “Penalty”). It is also
noted a higher level of coal resale on the
international market, this behavior was already
expected in both because of the increase in the
number of dispatch scenarios as well as because of
the number of branches in the decision tree, which
leads to a greater number of clusters in which the
forced generation refund at energy spot price is less
than coal redirection price to the international
market. As for the final result, a positive value of
almost 14 million dollars is observed for the coal
trading operation.
5 CONCLUSIONS
This paper presents an optimization model for coal
supply procurement strategy of coal-fired thermal
plants operating in the Brazilian system, which is
hydro dominated and characterized to have a high
volatility of its energy spot prices.
The results of three test cases for the coal
procurement model were presented and discussed.
These results showed the efficiency of the model,
especially when coal procurement strategy is
represented by a decision tree, which allows a better
adjustment of the coal procurement decisions to the
uncertainties of generation dispatch and energy spot
prices (variables that present a high volatility in the
Brazilian system because of its hydro dominancy).
ACKNOWLEDGEMENTS
The authors would like to thank UTE Porto do Itaqui
Geração de Energia S/A for sponsoring this project
as part of the Research and Development Program of
ANEEL, the Brazilian Regulatory Agency.
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st
edition.
St a g e
Ca r g o s
acceptance Freight
O&M
costs Penalty
En e rg y
reemb.
Co a l
resell Total
Net
value
01/2012 00-2-18065.8
02/2012 -3-1-107022.1
03/2012 -11-2-2076-2-1.7
04/2012 -4-1-107010.5
05/2012 -5-1-108010.8
06/2012 -12-1-108711.1
07/2012 -4-1-107010.9
08/2012 -5-1-107211.2
09/2012 -10-1-10750-0.3
10/2012 -3-1-107022.2
11/2012 -3-1-107021.6
12/2012 -4-1-1050-1-0.6
StochasticOptimizationModelofFuelProcurement,TransportationandStorageforCoal-FiredThermalPlantsin
HydrothermalSystems
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