ASSESSMENT OF TRANSMISSION CONGESTION PRICE RISK AND HEDGING IN THE
BRAZILIAN ELECTRICITY MARKET
F. PORRUA*
PSR/MERCADOS DE ENERGIA
Brasil
L. A. BARROSO*
G. B. SCHUCH
UFRGS
Brasil
A. STREET
M. JUNQUEIRA
PSR/MERCADOS DE ENERGIA
Brasil
S. GRANVILLE
Summary
The objective of this paper is to provide a methodology for pricing, under a generation company
(Genco) point of view, long-term energy contracts signed across different price zones in a zonal
pricing hydro-based power system where classical Financial Transmission Rights (FTRs) are not
available. The main result is the establishment of the overprice that a Genco must include in the
contract signed in a neighbor zone (where the Genco faces the congestion risk) when compared to the
same contract offered in its own zone (with no congestion risk). All relevant risks (hydrological risk,
congestion risk, etc) are captured for the long-term through the use of scenarios. Based on these
scenarios and on the risk profile of the agent modeled by Utility Functions (UFs), the pricing of crosszones contracts are determined. The approach will be illustrated with practical examples deriving from
the Brazilian electricity market, which is hydro-based, has a zonal-pricing scheme and does not offer
instruments to hedge against congestion risks, such as FTRs.
Keywords
Congestion Risk - Risk Pricing - Transmission Congestion - Utility Functions - Energy Auction.
*
Rua Voluntários da Pátria, 45 – 1507 – CEP 22270-000 – Rio de Janeiro – RJ – BRASIL
fernando@psr-inc.com, luiz@mercados.com.br
2
1 – Introduction
As widely discussed in the literature [1-4], the existence of transmission constraints in electricity
markets based on nodal pricing scheme may create financial risks to market agents in different nodes
of the network. Generators in the exporting bus but with financial contracts in the importing bus are
exposed to the price difference between these nodes. This financial risk is also known as transmissioncongestion price risk.
In order to hedge against this risk, generators may acquire FTRs [1-4]. These are contracts that
exist between market participants — in fact, any individual or organization — and the system or
market operator. FTRs are defined from a source (node) to a destination location. They are
denominated in a MW amount and entitle the holder to receive the contracted amount (MW) times the
spot price difference between the two nodes, thus becoming a perfect hedge against the pricedifference risk. The system operator does not need to take FTRs into account in the system operation
because FTRs are purely financial instruments that can be settled outside of the spot market.
Successful experiences with FTR implementation are observed in many markets, such as PJM,
ISONE, NYISO, Nordic Countries, etc. The existence of FTRs markets allows the increase of
competition in zones or nodes where just a few suppliers are present.
On the other hand, in markets where zonal or nodal pricing schemes are adopted but no FTR
markets are available competition may be reduced in certain zones or nodes. Without an FTR market,
generators have to correctly price the congestion risk (in terms of spot price difference) in order to sell
a cross-zone contract and this is usually translated into an overprice in the corresponding contract. This
is the case of the Brazilian power system, where a zonal pricing system is adopted but there is no
coupled FTR market. Therefore, Gencos usually overprice their financial energy selling contracts
whenever it is settled in another zone than his. The calculation of this overprice is the main focus of
the paper. One possible approach to price the congestion risk is by using the expected value of the
forecasted spot price difference between the corresponding zones during the contract term as a
surcharge. This risk-neutral approach is in fact carried out in some cases.
Because Brazil is hydro-dominated and hydrological regimes in the main basins are highly
diverse, the transfer of huge power blocks among regions is observed (depending on the hydrological
condition) and, as a consequence, the probability distribution of the spot price forecast is extremely
skewed. Therefore, depending on the generator’s risk profile, a higher overprice than the expected
value of the spot price difference can be applied.
The objective of this paper is to propose a methodology to price the transmission congestion pricerisk in cross zones long-term energy contracts, considering the Genco’s risk profile which is modeled
by means of UFs. The main idea is to find the contract overprice that leaves the Genco indifferent
between selling a cross-zone contract and selling in its own pricing zone. Two different cases will be
analyzed: (i) first, we analyze the case of a typical bilateral negotiation between a Genco and a
distribution company (Disco), where for a given contracted amount and price offered to the Genco in a
neighbor zone, we determine the overprice that must be added in order to leave him indifferent (in
terms of Expected Utility – EU) between selling in the neighbor zone and in his own zone; and (ii) we
construct a “willingness to contract” curve that, for each contract price (in a neighbor zone) offered,
provides the optimal quantity to be contracted that maximizes the Genco’s EU. This approach can be
used, for example, in auctions for long-term Power Purchase Agreements (PPAs). Practical examples
will be provided with data from the Brazilian system.
2 – The Brazilian Power System
Brazil started its power sector reform in 1996. As in many countries worldwide, the new rules
were designed to encourage competition in generation and retailing [5]. In turn, transmission and
distribution remained regulated activities, with provisions for open access. Other reform ingredients
included the creation of an Independent System Operator (ONS), a short-term electricity market
(CCEE) and a regulatory agency (ANEEL), as well as the privatization of distribution and some
generation companies. The country has an installed capacity of 91 GW (2005), where hydro generation
accounts for 85%, for a peak demand near 54 GW. The hydro system is composed of several large
reservoirs, capable of multi-year regulation (up to five years), organized in a complex topology over
3
several basins. Thermal generation includes nuclear, natural gas, coal and diesel plants. The country is
fully interconnected at the bulk power level by a 80,000 km meshed high-voltage transmission
network (Fig. 1), with voltages ranging from 230 kV to 765 kV A.C., plus two 600 kV D.C. links
connecting the Itaipu power plant (14,000 MW) to the main grid. The main direct international
interconnections are the back-to-back links with Argentina (2,200 MW), plus some smaller
interconnections with Uruguay (70 MW) and Venezuela (200 MW).
Source: ONS, http://www.ons.org.br
Fig. 1 – Brazil – physical system.
Both generation and transmission resources are centrally dispatched on a least-cost basis by the
ONS, that is, there are no price bids from generators or loads. In particular, hydro plants are dispatched
with basis on their expected opportunity costs (“water values”), calculated by a multi-stage stochastic
optimization model that takes into account a detailed representation of hydro plant operation, as well
as inflow uncertainties. The solution algorithm is the Stochastic Dual Dynamic Programming (SDDP),
an extension of the traditional stochastic DP recursion, which can handle hundreds of state variables in
this case, reservoir storage levels (see [6-7]). Bilateral contracts are financial instruments and thus not
considered in the centralized dispatch.
Because system dispatch is cost-based, there are no “real” short-term prices, based on the
equilibrium between supply and demand bids. In addition to the optimal production schedule for each
hydro and thermal plant, the SDDP solution scheme calculates the Short-Run Marginal Cost (SRMC)
– Lagrange multipliers of the stochastic dispatch model – for each network bus, which would then
correspond to the well known Locational Marginal Price (LMP). Given that the energy production of
each generator and the spot price are both determined by a computational model, the market settlement
is an accounting procedure (clearing of net difference between the energy produced and the energy
volumes registered in financial forward contracts).
3 – Congestion Risk in the Brazilian Power System
For the purposes of accounting and clearing at the short-term market, the LMPs are calculated with
a simplified procedure, where the network is divided into “zones”: the transmission limits of all
circuits within a zone are made infinite; only the tie-lines between zones are retained1. The system
today is currently divided into four zones, also called “submarkets”, (roughly) corresponding to the
As discussed in [8], the price in each bus is calculated as the SRMC for a “reference bus” in each zone,
adjusted by a loss factor but the wholesale market considers just the zonal prices for market settlement.
1
4
country’s major geographical regions: South, Southeast/Center-West, Northeast and North2 (see Fig.
2).
When adopting a zonal pricing scheme, an important aspect to be analyzed is the real physical
dispatch in the system, when compared to the “zonal” dispatch. Given that the centralized “zonal”
least-cost dispatch does not consider any real transmission constraints within the zones, the so-called
constrained-on and off generation in the real dispatch (when considering all transmission constraints)
may be considerable.
Additional operating costs to compensate those generators that have produced more in the physical
dispatch than in the “zonal” dispatch are paid by the ONS. Otherwise, if the generator produced less in
the physical dispatch than in the “zonal” dispatch it has to compensate the ONS for the corresponding
operating cost. The difference between generation cost in the physical and commercial dispatch is
always greater zero and are charged to the consumers as the System Services Charge, which increases
as the number of zones in the system decreases.
NORTH-NORTHEAST
INTERCONNECTION
S.LUIS
NORTHEAST SYSTEM
NORTH SYSTEM
V. CONDE
SOBRADINHO
IMPERATRIZ
P. AFONSO
L. GONZAGA
XINGÓ
B. ESPERANÇA
TUCURUÍ
MARABÁ
S. J. PIAUÍ
P. DUTRA
750 MWmed
200 MWmed
COLINAS
NORTH-SE
INTERCONNECTION
R. TOCANTINS
MIRACEMA
R. S. FRANCISCO
GURUPI
550 MWmed
S. MESA
SAMAMBAIA
R. PARANAÍBA
ITUMBIARA
T. MARIAS
S. SIMÃO
A. VERMELHA
R. GRANDE
kV
MALHA - 345/440/500
I. SOLTEIRA
JUPIÁ
EL O
me
MW
48 30
R. PARANÁ
SOUTHEAST-CENTER WEST
REGION
IBIUNA
CC
d
T. PRETO
40 30
MW
m ed
ITABERÁ
IVAIPORÃ
MA
4700 MW med
R
0
/2 00
SOUTH-SE
INTERCONNECTION
670 MW med
F. IGUAÇU
AREIA
S.SANTIAGO
ITAIPU
R. IGUAÇU
ITAIPU 60 Hz = 4700 MWmed
ITAIPU 50 Hz = 4830 MWmed
Caption
ITÁ
CAMPOS NOVOS
R. URUGUAI
345 kV
GRAVATAÍ
440 kV
550 kV
750 kV
SOUTH REGION
ONS - 1999 - 0029c
Fig. 2 – Brazilian zones (S: South, SE/MW: Southeast and Center-West, N: North and NE: Northeast).
In case of transmission congestion in the tie lines, Gencos may be financially exposed in their
cross-zones bilateral contracts3, thus facing the “congestion risk”. In the Brazilian system, the
exposure due to cross-market contracting can be extremely high, since in some circumstances
(associated to hydrological events) the price differentials due to congestion can be huge. For example,
during the rationing period in 2001, there was a major congestion in the tie-lines from the South region
(which experienced no drought) to the Southeast region (which was under rationing). For several
months, the energy spot price in the South was about 2 US$/MWh, whereas the Southeast prices
reached the regulated price ceiling, about 300 US$/MWh [7-8]. This created a very serious financial
exposure for generators located in South region, which had supply contracts to loads in the Southeast.
As mentioned before, Brazil has no FTR market available. The so-called “transmission surplus”,
used in some markets for the backing of FTR payments, is collected by the system operator and mainly
used to mitigate congestion risks due to mandatory cross-zones vesting contracts4 and to other special
existing mechanisms5. Therefore, in Brazil Gencos must deal with such risk independently for any new
cross-zone contracts to be settled. This topic will be analyzed next.
The definition of zones boundaries is such that the major “structural” transmission constraints lie on the tie
lines between those zones. Definition of zones in the Brazilian system is analyzed in [7].
3
If there is no transmission congestion in the tie lines, the spot price in two different zones is the same (except
for the loss factors) and thus there is no price-difference risk and the cross-zone contract can be interpreted as
being in the same Genco’s zone.
4
As part of the transition to a market-based model, all Brazilian Gencos have signed mandatory vesting
contracts, called Initial Contracts. Because some of these contracts are across zones, an “automatic FTR” (a share
of the transmission surplus) was assigned for them.
5
Such as the Energy Reallocation Mechanism (ERM), which is a mandatory mechanism for hydrological risk
sharing among all hydro plants [9].
2
5
4 – Pricing of Congestion Risk through Utility Functions
The main uncertainty parameter associated to the pricing of the congestion risk of a long-term
energy contract is essentially the spot price difference between the involved zones. In this paper, this
uncertainty is modeled by scenarios, in a fundamental (or “structural”) forecasting approach: a
probabilistic modeling is applied to the main source of uncertainty (inflow conditions) and spot prices
are calculated from the solution of a generation dispatch model (production costing tool) [6], with a
similar methodology than used by the ONS for system dispatch. Based on a long-term “supply x
demand” expansion scenario, we project spot prices for the associated zones for the contract horizon.
Therefore, one approach to price the congestion risk is through a risk-neutral approach, where the
expected (present) value of the scenarios for price differences between zones over the study horizon
can be used as the overprice in the contract. However, most of Gencos are in fact risk-averse and their
risk profile must be captured. This is discussed next.
4.1 – Risk Measure
In this paper, risk profile of agents is represented through a UF, which takes into account the
whole range of scenarios by “translating” monetary revenues into “utility units” [10]. The objective is
then to maximize the EU. For example, a risk-indifferent Genco would have a linear UF. This means
that a revenue increase has the same impact as a reduction; as a consequence, the expected utility is
equal to the expected income. A risk-averse investor would have a concave UF, as shown in Fig. 3. In
this case, the loss from a “bad” result is not “compensated” by the gain from a “good” result: for each
value of income (R), the UF (U(R)) attributes a respective utility unit. We see that a decrease in the
income (-d) around a reference value (Ro) results in a variation of the UF (DU-) greater than an
increase of the same amount (+d, which results in DU+). This is the characteristic of risk aversion
profile. Theoretically, agents can be risk-averse, risk neutral or even risk taker, but, in the “real world”,
most agents are risk-averse. Therefore, this aversion profile is considered here.
This paper adopts a piecewise linear representation of utility function (PLUF) [11], which is
flexible (adjustments in the breakpoints slopes define different risk profiles) and avoids the need of
nonlinear curves and algorithms. Any concave non linear UF can be represented through a concave
PLUF, by choosing an adequate number of linear segments (see Fig. 4). The PLUF can be represented
by the following linear programming (LP) problem:
U x   Max 
s.t.
(1)
  a k  x  bk
k 1, ..., K
where K represents the number of linear segments; ak represents the angular coefficient of the k-th
segment; bk represents the linear coefficient of the k-th segment; and  is a scalar (always smaller than
all segments). Figure 4 illustrates a PLUF with four segments, with Qk representing a break point
(point of slope changing) where the “satisfaction growth rate” changes. In the PLUF approach the
agent is locally risk neutral, but, globally risk-averse; and the risk aversion coefficient is represented
by the segment slope variation, around each break point, slightly different from traditional definition
[10].
U(R)
U(Ro+d)
U(Ro)
DU+
U(x)
DU-
x
x
x
U(Ro–d)
a(k=4)
U(xo)
k=2
Ro– d
Ro
Ro+d
R ($)
k=1
Q1
Q2
k=3
xo
k=4
Q3
x
(risk averse profile)
Fig. 3 – Concave UF representing a risk-averse profile.
Fig. 4 – Risk aversion profile through the PLUF.
6
5 – Congestion Risk Pricing: a bilateral contract approach
In this case we assume that the Genco is analyzing a contract proposal to be settled in another
zone. The contract amount and price proposed by the counterpart are also assumed to be known.
Therefore, we determine the overprice that must be added to the contract in order to leave the Genco
indifferent (in terms of the average net present value ( NPV ) of its expected utility) between settling
the contract in a neighbor zone and in its own zone. That is, we are searching for the overprice Op
($/MWh) that makes:
v

 
NPV E U R PCv  Op

  NPV EU RP 
u
u
C
where R PCv  Op represents the Genco’s total cash flow if the contract is in another zone (labeled
“v”) with price PCv  Op (where PCv is the given contract price and Op is the overprice (decision
 
variable)). The expression R PCu is the Genco’s cash flow if the contract were settled by a price PC in
its own zone (labeled “u”). In this scheme, we are modeling the risk profile of the Genco by its utility
function. A risk-neutral approach (linear UF) would be equivalent as to working with the average
values.
5.1 – Case study
9.0
8.0
Overprice required at Northeast
(R$/MWh)
Overprice Required at Northeast (R$/MWh)
This section provides the result of a case study for a thermal Genco in the Brazilian system, with
450 MW of available installed capacity and 50% of this capacity available for contracting (the
remaining 50% is already contracted). The Genco is physically located in the Brazilian Southeast zone
and the candidate contract is in the Northeast zone (typically an importing zone and the risky one in
this case). It is assumed a contract with 8 years of duration (from 2009 to 2016). A concave utility
function was defined for this Genco, thus trying to capture a risk-averse profile. A sample of 100 spot
prices of the relevant zones, as the Genco’s physical dispatch scenarios, were obtained usind a SDDP
tool [6-7]. We have then calculated the overprices for several pairs of contracting amounts and prices
offered in the neighbor zone. Figures 5 and 6 illustrate the results for the minimum contract overprice
in both situations: a risk neutral approach and the risk-averse case. We observe that in the risk neutral
case the overprice is constant, only depending on the spot price difference between the zones. On the
other hand, when risk aversion is considered, we observe that the minimum overprice required
decreases as the candidate contract price (contract price in the Genco’s zone) increases. All overprices
are higher than those obtained with a risk neutral approach, thus highlighting that this can be a risky
approach to price the contracts. We finally observe that overprices required for cross-zone contracting
depend on both the candidate contract price and the total amount contracted, as shown in Fig. 6.
7.0
6.0
5.0
4.0
3.0
2.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
50
55
60
65
70
75
80
85
90
95
100
Contract = 45MW
3.6
3.5
3.4
3.3
3.3
3.1
3.1
3.1
3.1
3.0
3.0
Contract = 90MW
5.4
5.1
4.9
4.8
4.6
4.4
4.2
4.1
4.0
3.8
3.7
Contract = 135MW
6.7
6.4
6.2
5.9
5.6
5.3
5.0
4.8
4.5
4.3
4.1
Contract = 180MW
8.0
7.5
7.1
6.8
6.3
5.9
5.6
5.2
4.9
4.6
4.4
Contract = 225MW
8.9
8.4
7.9
7.5
7.0
6.6
6.1
5.7
5.3
4.9
4.6
1.0
0.0
50
55
60
65
70
75
80
85
90
95
100
Proposed
6.7
6.4
6.2
5.9
5.6
5.3
5.0
4.8
4.5
4.3
4.1
Traditional
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
Candidate Contract Price at Southeast (R$/MWh)
Fig. 5 – Risk neutral and risk-averse results.
Candidate contract price at Southeast (R$/MWh)
Fig. 6 – “Iso-quantity” curves.
6 – Congestion Risk Pricing: a supply curve scheme
While in the previous section the decision variable for the Genco was the overprice (contracted
amounts were fixed), in this section we leave the contracting quantities to be decision variables for the
Genco. In other words, we construct a “willingness to contract” curve such that, for each candidate
7
contract price offered, the optimal quantity to be contracted that maximizes the Genco’s EU is
determined as the solution of the following LP problem:
E C PC   arg Max EC 1
S  s t
s. t.
U ts  a k Rt s   bk
U ts 1  r 
t
(2)
 s, t , k
Rts PC , E C   g   u  E C  PC  E C   u OR v
E C  EC  EC
k  1, ..., K
s  1, ..., S
t  1, ..., T
Where:
 EC – quantity to be contracted (decision variable) (MWh);
 PC – candidate contract price ($/MWh);
 Rts – Genco’s cash flow, in scenario “s” and period “t” ($);
 g – Genco’s physical generation (MWh);
 u – spot price in the Genco’s zone “u” ($/MWh);
 u OR v – spot price in the Genco’s zone “u” or the neighbor zone “v”, depending on where the
quantity EC is contracted ($/MWh);
 E C , E C – minimum and maximum available quantity to be contracted (MWh);

r – discount rate (%).
In other words, for a given contract price (either in its own or neighbor zone), the optimal quantity
to be contracted is determined taking into account the agent’s risk profile, captured by the piecewise
linear representation of UF as described in section 4.
6.1 Case study
This section provides an application of the previous approach for a candidate contract in the
Southeast and Northeast zones. The same Genco from the previous example is considered. We
selected a discrete contract price range and, for each contract price, we calculated the optimal amount
to be contracted (solution of problem (2)). Figure 7 shows for the optimal contracting for the two
relevant situations: when the contract is offered in the Genco’s zone (SE) and in another zone (NE).
Optimum bidding curve (MW)
450.0
400.0
350.0
300.0
250.0
200.0
50
55
60
65
70
75
80
85
90
95
100
NE auction 225.0 225.0 225.0 225.0 253.5 285.1 321.7 425.9 450.0 450.0 450.0
SE auction 225.0 225.0 225.0 229.9 289.4 354.4 450.0 450.0 450.0 450.0 450.0
Candidate Contract Price at Northeast (R$/MWh)
Fig. 7 – Optimum bidding curve for a cross-zone
contract.
We see that since the NE is the risky contracting zone, the Genco contracts smaller amounts
between R$65,00/MWh and R$85,00/MWh candidate prices than in the SE zone.
7 – Overprices Comparison
In section 5.1 we have shown the minimum overprice required for cross-zone contracting, such
that the Genco was indifferent between contracting in the SE and NE zones. In section 6.1, as a
subproduct of the “willingness to contract” curve, one can also find a minimum required overprice in
Fig. 7 as Op E C  PCNE E C  PCSE E C .
 
 
 
8
These overprices (from section 5.1 and 6.1) can be compared, as shown in Fig. 8.
10.0
9.0
8.0
7.0
6.0
Overprices (R$/MWh)
5.0
4.0
3.0
2.0
1.0
0.0
Bilateral contract
Willingness curve
70
71
72
73
74
75
76
77
78
79
3.9
4.2
4.6
5.0
4.9
5.2
5.7
6.3
6.3
6.2
6.4
6.2
8.0
8.0
7.3
8.0
7.7
9.2
8.5
7.6
Candidate Contract Price (R$/MWh)
Fig. 8 – Overprices comparison.
We can see from Fig. 8 that overprices obtained in section 5.1 are smaller than those found in
section 6.1. This is not a surprisingly result, given that the approach of section 5 is to find the lowest
overprice that leaves the Genco indifferent between selling in its own zone and in the risky one, while
the approach of section 6 seeks for the optimal amount of energy that must be sold, that maximizes the
agents profits for a given price. Therefore, the reduction in quantities found in section 6 are translated
in higher overprices when the same (price; quantity) points are observed in the analysis of section 5.
8 – Conclusions
This paper presented a methodology for congestion risk pricing for Gencos in cross zones bilateral
contracts settled in electricity markets with zonal pricing scheme but without FTR markets available.
In these markets, the adequate pricing of the congestion risk should be taken into account in order to
sell a cross-zone contract. Because the risk profile of the Genco needs to be captured, the methodology
is developed based on the expected utility theory. The approach is illustrated with practical examples
for the Brazilian system and the results show the importance of considering the agent’s risk profile
when compared to the risk-neutral approach. Although the core of the methodology was developed
considering a zonal pricing system, it can be extended for any LMP-based system with centralized
market for clearing purposes.
9 – Bibliography
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[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
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