optimal power contract porfolios por ech may 2008

96. Industry Application—Electric/Utility 321

96. Industry Application—Electric/UtilityOptimal Power Contract Portfolios

File Name: Electric Utility—Electricity Contract Risk

Location: Modeling Toolkit | Industry Application | Electric Utility—ElectricityContract Risk

Brief Description: Modeling electric utility contracts under uncertaintyand performing portfolio optimization to obtain the efficient portfolioallocation

Requirements: Modeling Toolkit, Risk Simulator

Special Credits: This case study was contributed by Elio Cuneo Hervieux,CRM, an electrical civil engineer with an MBA in finance. He is the energysupply contracts manager in an energy generation company in northernChile, an area in which important mining companies are located. Besidesbeing responsible for looking after the correct application of the contrac-tual agreements with clients, he specializes in the analysis and definition ofrisk metrics for each contract and for the company’s portfolio. He can becontacted at [email protected].

Electricity is generated through different production methods, either with hy-dropower (reservoirs and rivers) or thermal methods (where a great variety oftechnologies exists, depending on the type of fuel used). A common characteris-tic of the units that produce electricity at competitive prices is that they are verycapital intensive. In addition, the input used to generate energy may present impor-tant variations in its prices, as in the case with thermal power stations. Anotherpotential source of volatility that should be considered is the hydrology, specifically,the availability of the water resource for hydropower generation.

In Chilean legal contracts of electricity supply, there are two items that comprisethe electricity billing. The first is associated with the power levels, and the second isassociated with the energy levels.

Billings associated with power levels are related to the peak of the client’s demandexpressed in US$/kW-month (U.S. dollars per kilowatt, per month of usage). Theamount is also related to the investments in generation made by the energy producer,developed at the client’s request, or an alternative value is used in accordance withthe unitary price of the power that is traded in the respective markets. The last casecorresponds to the electricity market in Chile.

Billings associated with energy levels are related to the type of fuels used for theenergy generation or according to a future projection of the prices of the spot marketor a mixture of both.

Ecuneo

Resaltado

322 MODELING TOOLKIT AND RISK SIMULATOR APPLICATIONS

Since billings to the client consider these two key variables, to obtain the prospec-tive margins and the associated profitability, it is necessary to assign different weightsto each variable. In practice, there is no consensus in this respect. From the point ofview of obtaining the margin for the electricity sale, the margin can be divided intotwo components with different characteristics in terms of risk: the margin for powerand the margin for energy.

1. Margin for power. Once the rate of power for the client is fixed, the respectivemargin for this variable is determined by the level of the client’s maximumdemand with respect to the cost levels where power is traded in the electricitymarket. If the client maintains a stable level of maximum demand, the marginwill be maintained.

2. Margin for energy. This margin corresponds to the difference between the in-comes associated to energy and the costs incurred during the energy production.As an example, an energy generator using only one type of fuel, the energy ratewould be upgraded according to the price variations experienced by the input. Ifthe producer maintains a generation matrix with units that use diverse types offuels (diversified matrix of fuels), the energy rate would be upgraded consideringa polynomial function that contemplates the variation in the prices of the inputsaccording to certain percentages in that each part participates in the generationportfolio. In terms of risk, this last event presents a particularity, because it isexpected that the polynomial function of upgrading the energy rate representsthe form in which the production costs move, so it is possible to properly coverthe upgraded rate.

In analyzing the risk of the polynomial function of upgrading the energy ratefor a hypothetical company, we assume the use of typical prices of inputs as well asstandard technical aspects for thermal stations of electricity generation.

EFF IC IENT FRONTIER OF GENERATION

According to the theory of efficient portfolios of investment, when a portfolio ofdifferent assets with diverse profitability and risk levels exists, the most efficientinvestment portfolio is obtained when the combination of assets that is selected(given by the percentage of investment allocation of each asset) is located at somepoint along the efficient frontier of all possible feasible combination portfolio sets.In the case of electricity generation, the same output can be generated according todifferent inputs. The associated risks to the generation costs can be analyzed usingthe theory of efficient frontier, where each input represents an asset, the productioncost and profitability, and the risks associated with the volatility of the price ofeach input.

The efficient frontier of generation (EFG) should be representative of the op-eration of the power stations for a certain period of time; typically, 12 months isappropriate, because it is necessary to consider the period of time where the unitsare out of service for programmed maintenance or forced outage (FOR), and whereit is necessary to buy backup energy from third parties. Usually this energy has riskcharacteristics different from those of the energy generated by a unit that is forcibly


TABLE 96.1 Technical Aspects

Fuel Type Net MW Heat Rate COYM FOR Maintenance

Natural Gas 220 7.50 MMBTU/MWh US$ 2.00/MWh 7% 35 Days/yr.Coal 150 0.41 Ton/MWh US$ 2.00/MWh 8% 40 Days/yr.

TABLE 96.2 Economic Variables

Fuel Type Volatility Fuel Price COYM Variable Cost

Natural Gas 20% US$ 2.00/MMBTU US$ 2.00/MWh US$ 17.00/MWhCoal 30% US$ 60.00/Ton US$ 2.00/MWh US$ 26.60/MWhSpot Market 60% US$ 30.00/MWh

stopped. If we add the fact that the prices of the inputs have their own volatility,besides the changes that the industry is exposed to in the local market, it is clear thatthe EFG results will have dynamic characteristics rather than being stationary. As anexample of obtaining the EFG, let us consider a company that has generating unitsof the characteristics indicated in Tables 96.1 and 96.2.

The EFG for the generation assets are obtained in the example model as well asin Figure 96.1, which summarizes the results.

From Figure 96.1, it is interesting to highlight these points:

� Under normal operating conditions with the two power stations in service, theEFG moves between points A and B. In any contract of electricity supply, therate of updated energy should be over the line that unites points A and B.

F IGURE 96.1 Typical generation portfolio curve with mix natural gas, coal, and marginalcost (CMg)


� The EFG for the assets sustains a change that is represented by the curves thatunite the points A and C, similar to the one that unites points B and C. Thischange originates from the fact that the units must be subject to maintenance(the cost of generation of the unit that goes out of service is replaced by thepurchase of the same energy block in the spot market or a similar block throughcontracts with third parties).

� The EFG curves shown clearly indicate the changes in the position of risk thatthe hypothetical company sustains when units are out of service compared to acontrolled risk condition when the units operate in a normal way.

� For the hypothetical company and considering the previously stated technicaleconomic variables to be the operational points of each curve, we find:

Frontier Average C Volatility

NG - Coal US$ 20.89/MWh 18.63%Coal - CMg US$ 22.27/MWh 27.08%NG - CMg US$ 28.62/MWh 45.99%

� The EFG curves shown in Figure 96.1 represent a static situation of operationsfor the units of the market, which allow you to individualize the aspects thathave to be taken into account at any moment to fix the upgrade scheme of theenergy rate to the risk levels the company may face. The case corresponds to therisk that the hypothetical company faces when maintaining one of the units inprogrammed maintenance. This risk can notably affect the annual margins forenergy.

Since the EFG of the generation assets represent a static situation of operationof the power stations, it is necessary to run stochastic simulations that allow stresstesting of the indexation polynomial function that is considered for the energy ratein order to detect possible scenarios where the originally estimated margin is notreached. If there were such scenarios, a certain probability of obtaining lower marginsthan those originally estimated would exist.

I LLUSTRATIVE EXAMPLE

To illustrate, suppose there are two outlines for energy rates upgrading to a hypo-thetical client whose demand reaches the 370 MW level, with a load factor of about90% per month conditional on the typical demand for electricity in a mining com-pany. To cover this client’s demand, there are two possible outlines of rate upgradesin which each one is associated with the kind of fuel used for the electricity produc-tion and for the generation asset of the hypothetical company. The analysis seeks tocompare two outlines of rate upgrades, determining the impact of each outline in theprospective annual margins as well as its risks. The goal of the analysis is to generaterecommendations regarding which outline the electricity-producing company shouldchoose.


Out l ine 1

This first upgrade outline is typical in the electricity supply based on thermal stationsand considers, as a base for the energy rate upgrade, the variation of the prices of thesupplies with which the electricity is generated. The considered shared percentagescorrespond to the participation of the different inputs used by the electricity producerin the process of generation (e.g., here we consider natural gas and coal).

Block 1: 59.45%, 220MW of the consumption of the client’s energy with ratesbased on use of natural gas, determined as:

EG(m) = EG0PGm

PG0

Block 2: 40.55%, 150MW of the consumption of the client’s energy, with ratesbased on use of coal, determined as:

EC(m) = EC0PCm

PC0

Out l ine 2

Besides considering the variation in the input prices, this outline deals with the effectsof the lack of generation units being used for programmed maintenance or for forcedoutages of generation units. In practical terms, it considers the EFG associated withthe generation assets of the hypothetical company.

Block 1: 49.60%, 184MW of the consumption of the client’s energy, with ratesbased on use of natural gas, determined as:

EG(m) = EG0PGm

PG0

Block 2: 32.85%, 122MW of the consumption of the client’s energy, with ratesbased on use of coal, determined as:

EC(m) = EC0PCm

PC0

Block 3: 17.55%, 64MW of the consumption of the client’s energy, with ratesbased on use of energy purchased in the spot market, determined as:

ECMg(m) = ECMg0CMgm

CMg0

where we define the variables as:

EG0 = Base value of the energy rate for Block 1 of the client’s consumption andconsidering generation to natural gas, in US$/MWh

EC0 = Base value of the energy rate for Block 2 of the client’s consumption andconsidering generation to coal, in US$/MWh


TABLE 96.3 Resolution of the considered percentages

Unit MW FOR Maint Days Net days MW days %

NG 220 7% 35/yr. 304 66,979 49.60%Coal 150 8% 40/yr. 296 44,370 32.85%Spot days 130 23,701 17.55%

Total 370 135,050 100.00%

ECMg0 = Base value of the energy rate for block 3 of the client’s consumptionand considering purchases in the spot market, in US$/MWh

PG0 = Base value of base natural gas, in US$/MMBTU

PC0 = Base value of coal, base 6000 kcal, in US$/Ton

CMg0 = Base value in the spot market, in US$/MWh

EG(m) = Upgraded value to period m of the rate of energy of Block 1

EC(m) = Upgraded value to period m of the rate of energy of Block 2

ECMg(m) = Upgraded value to period m of the rate of energy of Block 3

PGm = Natural gas price, valid for the period m, in US$/MMBTU

PCm = Coal price, valid for the period m, in US$/Ton

CMgm = Price of the spot market valid for the period m, in US$/MWh

The associated percentages of each input were determined by considering theeffects of the programmed maintenance days to each unit as well as the percentagesof forced outages associated to each unit. Table 96.3 summarizes the resolution ofthe considered percentages.

For the case study, the numerical values listed in Table 96.4 are indicated for thedifferent variables that conform to the polynomial of upgrade of the energy rate.

Risk Simulator was used to generate and run the stochastic risk simulations ofthe impact of the indexation outlined in the portfolio energy margin. The associatedparameters of the different variables that represent risks are set as probability distri-butions, as shown in Table 96.5.

TABLE 96.4 Polynomial upgrade variable values

Variable No. 1 No. 2

Eg0 20.40 20.40Ec0 31.92 31.92ECMg0 36.00PG0 2.00 2.00PC0 60.00 60.00CMg0 30.00


TABLE 96.5 Distributional assumptions for simulation

Items Minimum Mid Maximum Distribution

NG 1.8 2.0 3.0 TriangularFOB Coal 30 45 60 TriangularFreight 10 22.5 35 TriangularBunkers 240 302 360 TriangularDiesel 400 521 650 TriangularMW SEP 2,828 2,900 2,973 Triangular

The results of the margins for energy of the portfolio, expressed in US$/MWh,according to the outline of upgrade of the rate of energy are summarized next.

Table 96.6 shows the statistics so readers can visualize the differences in termsof risk for the hypothetical company, comparing one outline versus another outlineof energy rate upgrade.

The statistics obtained from the simulations for each outline of upgrade pro-vide information regarding the different characteristics of risk that the hypotheticalcompany may face for the energy sale.

� In terms of mid values, Outline 2 offers a better prospective value for the marginof the portfolio compared to Outline 1.

� In terms of risk, Outline 2 is more attractive for the hypothetical company (lowerstandard deviation, coefficient of variation and range).

� Outline 2 has improved statistics because the risks associated with periodic unitmaintenance as well as no programmed outages are attenuated when consideringthe upgrade of the energy rate, a percentage of the energy bought at the spotmarket should also be reflected under the operating conditions of the powerstations.

TABLE 96.6 Risk simulation forecast statistics and results

Outline 1 Outline 2

Mean 4.038 6.289Median 4.324 6.264Standard Deviation 1.515 1.458Variance 2.295 2.125Average Deviation 1.110 1.112Coef. of Variation 0.375 0.232Maximum 7.485 11.284Minimum −6.051 −0.718Range 13.537 12.002Skewness −1.446 −0.312Kurtosis 3.620 1.40825% Percentile 3.424 5.42975% Percentile 5.027 7.178


F IGURE 96.2 Gross Margin, percentile curve, Outline No. 1 and No. 2

An alternative way to evaluate the outlines of the energy rate upgrading is inconsidering the percentiles associated with the margins that are obtained after run-ning the stochastic simulations. For example, if the hypothetical company determinesthat the margin of its interest on an annual basis is US$4/MWh, which is the moreattractive strategy? Figure 96.2 illustrates the two strategies graphically.

If a minimum annual margin of US$4/MWh is required in commercial terms,upgrade No. 2 is more convenient because the results would indicate that it has aprobability equal to or above 95% that the required margin is exceeded, whereasoutline No. 1 has an associated probability of only 60%.

The comparison is a method contracts of these type can be analyzed. If a portfolioof N commercial agreements exist, based on the methods discussed in this chapter,it is possible to determine the associated probabilities that the margins originallyestimated at contract signing can be exceeded.

CONCLUSION

Based on our analysis, we can conclude:

� The efficient frontier of generation, EFG, is the only way to obtain analyticallyvalid and correct results in the determination of the outline of rate upgrade tomore efficient energy for the hypothetical company.

� A valid analysis of risk in the determination of the impact in the margins forelectric power sale of an industry in a world of highly volatile inputs market canonly be determined with simulation and optimization techniques.

� Even when examples are based on the analysis of the company’s portfolio,analyses should include studies of risks associated with each contract in order to

97. Industry Application—IT—Information Security Intrusion Risk Management 329

recognize the contribution of each to the total risk of the margins of energy ofthe company and the requirements of taking corrective actions. It is advisable todevelop these analyses in a permanent form for risk administration, analyzingexisting contracts as well as future client contracts. The effects of the existingcontracts to the portfolio can be determined using a similar approach.

� Even when the developed example allows us to compare two outlines of rateupgrades on a projection of twelve months, similar analyses can be developed tovisualize the impact in the VAN of the company, considering a long horizon withother risk factors (for example, FOR variable rate, days of maintenance differentto those originally estimated, changes of the market of the inputs, unavailabilityof input supply as in the case of Chile, etc).

97. IndustryApplication—IT—Information

Security Intrusion Risk Management

File Name: Industry Application—IT Risk Management Investment Decision

Locations: Modeling Toolkit | Industry Application | IT Risk ManagementInvestment Decision

Brief Description: The case study and model illustrated in this chapter looksat information systems security attack profile as well as provide decisionanalysis and support on the required optimal investment

Requirements: Modeling Toolkit, Risk Simulator

Special Credits: This model was contributed by Mark A. Benyovszky, managingdirector of Zero Delta Center for Enterprise Alignment. Zero Delta CfEAis a research and development organization that specializes in helpingcompanies to align their strategic and tactical efforts. Mr. Benyovszkymay be reached at [email protected] or +1.312.235.2390. Additionalinformation about Zero Delta can be found at www.zerodelta.org.

Organizations of all sizes rely upon technology to support a wide-range of busi-ness processes that span the spectrum from “back-office” finance and accounting to“mid-office” manufacturing, distribution, and other operational support functions,to “front-office” sales, marketing, and customer support functions. As a generalrule of thumb, larger organizations have more complex system environments andsignificantly greater volumes of data along with a wide range of different types ofinformation.

If you were to look across industries, there are different degrees of sensitivityof both the systems and information that are employed. For example, financial and

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