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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
                                     monica@ele.puc-rio.br                       5
                                                                                      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.

                                     monica@ele.puc-rio.br                       7                  monica@ele.puc-rio.br     8
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.

                   monica@ele.puc-rio.br     9                                monica@ele.puc-rio.br                            10




PLD – Settlement Price Simulation                 PLD – Settlement Price Simulation
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.

                   monica@ele.puc-rio.br    11                                monica@ele.puc-rio.br                            12
PLD – Settlement Price Simulation                                                                          PLD – Settlement Price Simulation
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.
                                                     monica@ele.puc-rio.br                           13                                                                    monica@ele.puc-rio.br                                      14




PLD – Settlement Price Simulation                                                                          PLD – Settlement Price Simulation
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



                                                     monica@ele.puc-rio.br                           15                                                                    monica@ele.puc-rio.br                                      16
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;
                                                        monica@ele.puc-rio.br                                          17                     monica@ele.puc-rio.br    18




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.
                                                        monica@ele.puc-rio.br                                          19                     monica@ele.puc-rio.br    20
Simulation Model for Energy                    Simulation Model for Energy
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.

               monica@ele.puc-rio.br     21                     monica@ele.puc-rio.br      22




Simulation Model for Energy                    Simulation Model for Energy
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.

               monica@ele.puc-rio.br     23                     monica@ele.puc-rio.br      24
Simulation Model for Energy                                             Simulation Model for Energy
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
                        monica@ele.puc-rio.br                      25                     monica@ele.puc-rio.br                    26




Simulation Model for Energy                                             Simulation Model for Energy
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.

                        monica@ele.puc-rio.br                      27                     monica@ele.puc-rio.br                    28
Simulation Model for Energy                                                                         Simulation Model for Energy
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.
                                         monica@ele.puc-rio.br                                 29                                                     monica@ele.puc-rio.br                              30




Simulation Model for Energy                                                                         Simulation Model for Energy
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



                                         monica@ele.puc-rio.br                                 31                                                     monica@ele.puc-rio.br                              32
Simulation Model for Energy                     Simulation Model for Energy
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.
                monica@ele.puc-rio.br     33                    monica@ele.puc-rio.br    34




Simulation Model for Energy                     Simulation Model for Energy
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.


                monica@ele.puc-rio.br     35                    monica@ele.puc-rio.br    36
Simulation Model for Energy                                                                                    Simulation Model for Energy
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



                                                         monica@ele.puc-rio.br                            37                                       monica@ele.puc-rio.br                      38




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.

                                                         monica@ele.puc-rio.br                            39                                       monica@ele.puc-rio.br                      40
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.

              monica@ele.puc-rio.br   41

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Icord 2007

  • 1. 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
  • 2. 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 monica@ele.puc-rio.br 5 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. monica@ele.puc-rio.br 7 monica@ele.puc-rio.br 8
  • 3. 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. monica@ele.puc-rio.br 9 monica@ele.puc-rio.br 10 PLD – Settlement Price Simulation PLD – Settlement Price Simulation 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. monica@ele.puc-rio.br 11 monica@ele.puc-rio.br 12
  • 4. PLD – Settlement Price Simulation PLD – Settlement Price Simulation 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. monica@ele.puc-rio.br 13 monica@ele.puc-rio.br 14 PLD – Settlement Price Simulation PLD – Settlement Price Simulation 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 monica@ele.puc-rio.br 15 monica@ele.puc-rio.br 16
  • 5. 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; monica@ele.puc-rio.br 17 monica@ele.puc-rio.br 18 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. monica@ele.puc-rio.br 19 monica@ele.puc-rio.br 20
  • 6. Simulation Model for Energy Simulation Model for Energy 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. monica@ele.puc-rio.br 21 monica@ele.puc-rio.br 22 Simulation Model for Energy Simulation Model for Energy 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. monica@ele.puc-rio.br 23 monica@ele.puc-rio.br 24
  • 7. Simulation Model for Energy Simulation Model for Energy 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 monica@ele.puc-rio.br 25 monica@ele.puc-rio.br 26 Simulation Model for Energy Simulation Model for Energy 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. monica@ele.puc-rio.br 27 monica@ele.puc-rio.br 28
  • 8. Simulation Model for Energy Simulation Model for Energy 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. monica@ele.puc-rio.br 29 monica@ele.puc-rio.br 30 Simulation Model for Energy Simulation Model for Energy 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 monica@ele.puc-rio.br 31 monica@ele.puc-rio.br 32
  • 9. Simulation Model for Energy Simulation Model for Energy 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. monica@ele.puc-rio.br 33 monica@ele.puc-rio.br 34 Simulation Model for Energy Simulation Model for Energy 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. monica@ele.puc-rio.br 35 monica@ele.puc-rio.br 36
  • 10. Simulation Model for Energy Simulation Model for Energy 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 monica@ele.puc-rio.br 37 monica@ele.puc-rio.br 38 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. monica@ele.puc-rio.br 39 monica@ele.puc-rio.br 40
  • 11. 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. monica@ele.puc-rio.br 41