Icord 2007

Highlights
We propose an energy demand forecasting
model integrated with ...
DECISION SUPPORT METHODS IN models to
ENERGY AUCTIONS simulate and optimize energy purchasing costs
and
Mônica Barros, D.Sc. reduce the penalties that the government
Marina Figueira de Mello, D.Sc. imposes on the energy retailers.
Reinaldo Castro Souza, PhD.
Bruno Dore Rodrigues, M.Sc. We present a resampling scheme to
evaluate the PLD (Settlement Price), one
Instituto de Energia - PUC-Rio
PUC- of the components of penalties in the
electricity market, which is stochastic and
Fortaleza, 30/08/2007
30/08/2007 heavily influenced by inflows.
monica@ele.puc-rio.br 2

The New Electric Sector Regime The New Electric Sector Regime

In the new regime, the regulator is in These decisions are risky for two
charge of auctioning new and existing
projects to supply the whole captive
main reasons:
market. i) auction prices differ (it has been
Distributors are only required to inform possible to buy energy for half the price
their forecasted demands five years in specific auctions);
ahead. They have to decide: ii) errors in demand forecasts are
First decision: How much to ask in each punished in an asymmetric fashion.
individual auction?
Second decision: How to access future demand
in each of the 60 months ahead?

monica@ele.puc-rio.br 3 monica@ele.puc-rio.br 4

The New Electric Sector Regime The New Electric Sector Regime
Distributors who demand a relatively high
The weighted average of the prices share of their needs in low price auctions
paid by the regulator for the total will have their profits increased.
energy bought from various
generators will be passed-through to Losses will come to those distributors who
prices. concentrate their demand in the high price
auctions.
Distributors will pay for their energy
in proportion to their declared Distributors are not truly free to allocate
demand in each auction. their demand amongst auctions because
the terms of the contracts being auctioned
may be incompatible with theirs needs. 6
monica@ele.puc-rio.br

PLD – Settlement Price Simulation
Demand Model
Model
The structure of the demand model is:
Variable Coefficient Standard Error T Statistic Significance
Hydroelectric energy is generally cheaper
Log(C_TOTAL[-1]) 0,772 0,077 10,085 100,0%
but hydro units are not always fully
dispatched since low water levels mean a
Log(PIB[-1]) 0,367 0,122 3,013 98,9%
Log(PR_ENERGIA) -0,189 0,053 -3,564 99,6%

supply risk.
Log(PR_GAS) 0,053 0,017 3,111 99,1%
RACION -0,132 0,022 -6,105 100,0%

Where:
C_total[-1] = consumption in the previous month
C_total[- The ISO ponders the present benefit of
PIB[-1] = GDP in the previous month
PIB[- cheap water use and the future benefits of
PR_ENERGIA = electricity price high level reservoirs, both measured by
PR_GAS = GLP price their opportunity cost in terms of fuel
RACION = dummy variable – rationing period savings in thermoelectric plants.


PLD – Settlement Price Simulation PLD – Settlement Price Simulation
Model Model
NEWAVE is the software used to optimize PLD – Settlement Prices are CMOs –
dispatch between hydro and thermal units. Marginal Costs of Operation in a limited
It also calculates monthly CMOs – range.
Marginal Costs of Operation, considering Currently in 2007, PLDs are restricted to
hydrological conditions, demand levels, the interval (R$ 17.59, R$ 534.50).
new plants, fuel prices and deficit costs. Penalties for demand over and
Monthly CMOs are further transformed underestimation use a yearly PLD which is
into weekly CMOs through the use of a weighted average of the monthly PLDs
another optimization software, DECOMP. prevailing in the twelve preceding months.


Model Model
In this paper, we simulate yearly PLDs 3. Create 2000 realizations of average PLD
through the following process: series through:
w1CMOrestr1i + w2 CMOrestr2i + .... + w12 CMOrestr12,i
1. Estimation of monthly seasonal factors PLDi =
12
2. Estimation of Southeastern CMOs Where i = 2007, 2008, ..., 2011, and
through NEWAVE for 2007-2011 (we w1 is the seasonal factor for January (constant in all
used CCEE’s Feb. 2007 “deck”). In this years)
w2 is the seasonal February factor (constant in all
step, 2000 CMO series are generated for years)
each one of the 60 months ahead: CMOrestr = CMO restricted to the interval (17.59, (17.
534.50), i.e. each monthly CMO subjected to PLD
534.
Jan/2007, Feb/2007, Mar/2007, ...., restrictions. For simplicity, this interval was admitted
Dec/2011. to be the same until 2011.


Model Model
4. The 2000 PLD series of 2007 (and also Thus, if in one simulation the k-th series is
sorted out from the 2000 CMO series, 2007
2000 of 2008, 2000 of 2009 and so average PLD will be calculated using this
on…) are resampled allowing the PLD series; the average 2008 PLD is also calculated
to be introduced as a random variable from the CMOs of this series and so on until
in the model. 2011.

This is very important to preserve the time
The resampling model described above dependency of CMOs the PLD NEWAVE
uses the SAME NEWAVE series simulation scheme.
throughout the period 2007-2011.
PLDs simulated for the period 2007-2011 are
2007-
highly variable as the next graphs show.

Model Model
Simulated PLD – 2007 Simulated PLD – 2009
D istrib utio n fo r pld_m edio _2007/B 2 Statistics Values D istrib utio n fo r pld_m edio _2009/D 2 Statistics Values
X < = 17 .59
5%
X <= 90 .11
95 %
Minimum 17.59 X < = 23 .0 6
5%
X <= 52 0 .23
9 5%
Minimum 17.59
0 .0 8 5
Maximum 203.7 4 .5 Maximum 534.59
0 .0 7 M e a n = 34 .6 85 13 M e a n = 2 0 9.9 2 31

Mean 34.69
4 Mean 209.92
0 .0 6
Values in 10^ -3
3 .5
Std Dev 155.1
0 .0 5 Std Dev 27.27 3

0 .0 4
2 .5 Percentiles Values
Percentiles Values 2
0 .0 3 5% 23.06
5% 17.59 1 .5
0 .0 2 1 50% 169.37
0 .0 1
50% 22.13 0 .5
0
75% 318.38
0 75% 40.92 0 200 40 0 600 95% 520.23
0 55 11 0 16 5 220
95% 90.11


PLD – Settlement Price Simulation Simulation Model for Energy
Model Purchases
Simulated PLD – 2011 The proposed simulation model for
Distribution for pld_medio_2011/F2
Statistics Values the annual cost of energy purchases
is a function of 7 factors:
X <=31.88 X <=534.59
Minimum 17.59
5% 9 5%
7 Maximum 534.59

Percentage of the estimated load
M e a n = 260.4488 Mean 260.45
1.
6
Std Dev 176.74
Values in 10^ -3

5

4
Percentiles
5%
Values
31.88
purchased in a given year;
3
50% 218.66 2. Load forecast in MWh;
2 75% 437.3
1 95% 534.59 3. Standard deviation of the load forecast
0
0 200 400 600 in MWh;
4. Actual demand in MWh;

Simulation Model for Energy Simulation Model for Energy
Purchases Purchases
5. Reference Value (VR), in R$ per MWh;
MWh; The percentage of the estimated load
6. The distribution company’s energy purchased in each year is what we seek to
purchasing cost, commonly known as the optimize.
company’s “mix”, in R$ per MWh;
MWh; It represents the ideal purchasing amount in
7. The average annual settlement price (PLD), in each year, so that the total cost in the
R$ per MWh.
MWh. specified period is minimum.
In the simulation, this percentage was taken
The simulation model was implemented as a Uniform (0.95, 1.10) random variable.
in Excel using the add-in @Risk by That is, in each year, some value between
Palisade Corporation. Some of the inputs 95% and 110% of the forecasted demand can
of the model are random and others are be purchased.
deterministic.

Purchases Purchases
The demand forecast is the value We propose a left truncated Normal
obtained from the time series model. distribution for this variable, at a point x0
It is considered fixed (deterministic) located below the mean of the original
in the simulation model, as well as its Normal distribution.
standard deviation.
The “actual” demand is a stochastic This forces the simulation to produce
input. In fact, nothing can be said higher values of the “actual” demand than
about it until it is observed (in the those that would be observed by
future). simulation from a (non-truncated) Normal.


Purchases Purchases
Since penalties are asymmetric and The Reference Value is deterministic (R$
utilities are more severely penalized for 84.58/MWh), and fixed by the Brazilian
under-purchasing energy, this procedure regulator 2007.
(keeping all other factors constant) raises
the risks of under-purchasing energy in The company´s energy purchasing cost
any given year. (the “mix”) is also taken as deterministic,
and set at R$ 86.70/MWh.
Here we use as truncation point 95% of The average annual PLD is random and
the mean of the original Normal was simulated as previously described.
distribution.


Purchases Purchases
The annual purchasing cost is This penalty occurs because the amount of
energy necessary to supply the actual load
comprised of four components: one is has to be purchased at price PLD.
the energy cost itself, and the other If the PLD is high, the acquisition cost
three are direct or indirect penalties. cannot be passed through to consumers,
The penalty due to non recovery of and the utility should be penalized with
this additional cost.
costs while under-purchasing energy
By construction, this penalty (F1) is always
is given by: qsub = amount underpurchased
nonnegative and implies an increased cost
(gap below 100% of actual
F = { PLD − min ( PLD, VR )}. ( qsub ) demand)
1
for the distributor.
PLD = settlement price
VR = reference value

Purchases Purchases
The penalty for under-purchasing energy This is not a penalty in the literal sense,
is defined as: but an additional cost that cannot be
F2 = max ( PLD, VR ) . ( qsub ) passed to consumer’s tariffs.
Similarly to F1, F2 is also nonnegative and qover = amount of energy

F3 = (qover )(MIX − PLD )
purchased above 103% of the
always leads to increased costs to the . actual demand
distributors. MIX = utility’s average energy
purchasing cost
A third penalty occurs when the utility has
over-purchased energy above a level A cost reduction will happen whenever
considered “acceptable” by the regulator PLD exceeds the company’s average
(103% of the actual demand). purchasing cost.


Purchases Purchases
F3 indicates a clear possibility of profits In the scenarios generated from the official data
instead of losses when a utility chooses to of February 2007, when a shortage is quite
probable in the coming years, these profit
over-purchase energy (above the 103% opportunities arise.
limit).
The total energy purchasing cost is:
Profits will occur in case PLD is high, C = F1 + F2 + F3 + MIX .q
which happens when energy shortages are In the simulation model, the quantity purchased
foreseen. is defined as: q = p.( D _ Actual )
This result may be considered to be rare,
since PLD historically remained at very low Where p is the percentage of energy purchased,
levels. supposed Uniform in the interval (0.95, 1.10) and
D_Actual is the “actual” demand, a truncated
actual”
Normal random variable.
variable.

Purchases Purchases
Total Acquisition Cost – 2007 Total Acquisition Cost – 2009
Distribution for Custo 2007/M5 Distribution for Custo 2009/M7
X <=89 383596 8 X <=103 9363136 X <=9 40 16 60 16 X <=12 19 8 80 44 8
5% 95% 5% 9 5%
1.4 9
8 M ea n =
1.2 M e an = 1.06 54 03 E+0 9

Values in 10^ -9
9.5143 37E+08 7
6
Values in 10^ -8

1
5
0.8
4
0.6 3
2
0.4 1
0.2 0
0.7 0.95 1.2 1.45 1.7
0
0.85 0.95 1.05 1.15 Values in Billions
Values in Billions


Purchases Purchases
A sensitivity analysis on the inputs reveals This tends to alter a company’s purchasing
that the percentage of the estimated load strategy – when forecasting very high
purchased in 2009 is the most important levels for the PLDs, it is cheaper to over-
factor to determine the total cost for that purchase energy than to risk any level of
year. under-contracting.
The higher the amount of energy The results for 2010 and 2011 are quite
purchased, the lower the cost. similar to those for 2009, but there is an
This is due to the substantial increase in even more marked tendency to cost
the Settlement Prices observed in 2009. increases, reflecting higher Settlement
Prices.

Purchases Purchases
This sensitivity analysis suggests a One could also examine the penalty
possible cost minimization strategy: costs separately.
Keep percentages of energy purchases Let F be the total penalty incurred by
high in 2010 and 2011 and, to a lesser a distributor, that is, F= F1 + F2 + F3 .
extent, in 2009.
Components F1 and F2 always
Keep the energy purchase amounts well
adjusted in 2007 and 2008 to avoid represent a loss for the utility, while
unnecessary costs. F3 may bring profits.


Purchases Purchases
Excessive cost due to over- Excessive cost due to over-
purchasing energy – 2007 purchasing energy – 2011
Distribution for F3 (2007)/L5 Almost all values 3.000
Quite often, the
represent a penalty, component F3 represents
1.200
Mean=8850298 Mean =-3.710148E+07
Mean=-3.710148E+07
2.500
1.000
i.e, an added cost profit, not penalty. This
Values in 10^ -7

(when F3 > 0). happens when its value is
0.800 2.000

0.600 1.500
negative.
0.400 1.000

0.200 0.500

0.000 0.000
-80 -60 -40 -20 0 20 40 60 -450 -312.5 -175 -37.5 100
Values in Millions
5% 90% 5% 5% 90% 5%
0 40.7846 -241.8353 12.1127


Conclusions Conclusions

One might think the new regulatory The new regulatory model tries to
model practically eliminated encourage a relatively high
distribution companies risk because purchasing level by means of
their responsibilities were asymetric penalties.
considerably reduced.
Now distributors are only required to
inform their demand forecasts. When companies under purchase,
But they are punished in case these correction possibilities are fewer
forecasts prove wrong. than when the opposite occurs.


Conclusions

The sophisticated regulatory model
implemented is fragile because:
the same acquisition strategy in the
auctions may prove profitable or not
depending on variables that are not
under the control of distribution
companies.
The Settlement Price - PLD is highly
volatile and this increases the
possibilities of punishment.


Icord 2007

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Icord 2007