TrainingManual English

8/20/2019 TrainingManual English

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Modeling Electricity and Natural Gas Trade with Optimization

of Generation and International Transmission Capacity Expansions

GENERAL TRAINING MANUAL

FOR THE PURDUE LONG-TERMELECTRICITY TRADING MODEL

Edition 2.1July 2003

F.T. SparrowBrian H. BowenShimon K. Modi

PURDUE UNIVERSITY

Power Pool Development GroupInstitute for Interdisciplinary Engineering Studies

500 Central Drive, Suite 270West Lafayette, IN 47907-2022 USA

Fax: 765-494-2351


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GENERAL TRAINING MANUAL FOR THE PURDUE LONG-TERM PLANNING MODELVersion 2.1, July 2003

ii

Table of Contents

Page

Introduction 1

Chapter 1 - Definition of Economic Terms 2

1.1 Economic Cost versus Accounting Cost 21.2 Opportunity Cost 21.3 Fixed and Variable Costs 21.4 Marginal Cost 31.5 Sunk Cost 51.6 Market Price 51.7 Shadow Price 51.8 Capital Recovery Factor (crf) 5

Chapter 2 - Costing and Computing Concepts 6

2.1 Average (“Unit”) Costs 62.2 Marginal Costs 72.3 The Irrelevance of Sunk Cost 82.4 LaGrange Multipliers 102.5 Operations Research 112.6 Introduction to GAMS 132.7 Computing Requirements 15

Chapter 3 - Basic Electricity Modeling Formulation 16

3.1 Model I: Short Run, Power Trade Only 163.2 Model II: Short Run, Power and Reserves Traded 173.3 Model III: Long-Run Model 18

Chapter 4 - The Generic Seven Country Regional Model 21

4.1 Generation, Transmission and Demand 214.2 Demonstration Results from the 7-node Generic Model 26

4.3 Demonstration Outputs from the 7-node Generic Model 274.3.1 Trade 274.3.2 International lines 294.3.3 Cost summary for short-term 304.3.4 Cost summary for long-term 314.3.5 Scenario 3 country1 output file 32


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Chapter 5 - Inputs and Outputs to the Model 40

5.1 Summary of the Files Used in the SAPP Long-Term Model 405.2 Weighting of the Seasons, Days, and Hours 43

Chapter 6 - Electricity Policy Analysis Scenarios 45

6.1 Short-Term and Long-Term Modeling 456.2 Electricity Forecasting Policy 456.3 Electricity Trading Commodities 456.4 Policy for Unmet Reserve and Distributed Generation 466.5 Short-Term Power Trading and Tariff Setting 466.6 Reliability of Power Supplies 476.7 Dependency Policy on International Electricity Trading 47

6.8 Capital Investment Strategies 476.9 Drought Scenario Planning in Hydropower Networks 486.10 Electricity Wheeling Tariffs 486.11 Environmental Policy 49

Appendix 1 - Template Data Collection Sheets 50

Appendix 2 - Modeling Notation 69

Bibliography 76


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Introduction

SUFG (Purdue University’s State Utility Forecasting Group) electricity and natural gas systems planning models have been employed for the past 20 years. Many countries around the worldhave yet to develop the capacity for construction and use of these analytical tools and so

Purdue’s modeling team is being instrumental in promoting programs of collaboration withgovernments, utilities, and universities internationally. These collaborative internationalmodeling activities encourage regional cooperation and provide a substantial quantitative basison which to build improved regional electricity trading policies with potential enormous costsaving options from collective construction and closer regional integration. This introductorytraining manual is intended for general planners who wish to better understand and use theseeconomic models for electricity market assessment and for support in training for data collectionfor the models.

Purdue’s electricity trade models are used in Indiana, USA Mid-West and internationally since1997 (Southern African Power Pool, SAPP). The SAPP work was funded by the USAID with

much interest and general support from the DOE and the World Bank. Following the successfulwork with SAPP the Purdue energy modeling group in now playing a significant role if theinfrastructure building of the West Africa Power Pool (WAPP). The organization of theseinternational projects is administered through Purdue University’s Power Pool DevelopmentGroup (PPDG). Both the SUFG and PPDG are housed at Purdue University’s Institute forInterdisciplinary Engineering Studies (IIES).

SUFG advises and is supported by the Indiana State Government since the early 1980s. SUFG’sforecasting and marketing models provide quantitative analysis of many electricity policyscenarios. All of the interested stakeholders have full and equal access to the SUFG modelformulation and so there is a transparency to the analysis that promotes in-depth study of optionsfor construction of new capacity (generation and transmission), deregulation, and tariff structuresthat face government and the utilities.

The SUFG forecasting and long-term planning models use mathematical programming andoperations research techniques (linear and mixed integer) to combine the many economic andtechnical objectives and constraints into clearly defined algorithms for optimal (costminimization) solutions.

There is a fully detailed description of the SUFG long-term (LT) electricity-planning model inthe “Long-Term Model User Manual,” Edition 7, June 2000. This can be freely downloadedfrom the web page: http://engineering.purdue.edu/IIES/PPDG/

The LT Model User Manual provides a full description of the objective function, load balanceequation, capacity and reliability constraints, and technical operating instructions. It is writtenwith the technical user and operations research specialist in mind. Over the past three years auser-friendly windows interface has been developed that helps all energy planners to easily usethe complex LT model. This current document, the General Training Manual, is for the generalelectricity policy decision maker. It is for the person who is not so involved or interested in the precise line by line description of the program structure and who does not have the time toinvestigate it and to look into all the technical details of the model.


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Chapter 1

Definition of Economic Terms

As we start to look at energy modeling, let’s first be sure of some of our essential economicterms. Let’s first look at some definitions.

1.1 Economic Cost versus Accounting Cost

“An economist thinks of cost differently from an accountant, who is concerned with the firm’sfinancial statements. Accountants tend to take a retrospective look at a firm’s finances becausethey have to keep track of assets and liabilities and evaluate past performance.

Economists take a forward-looking view. They are concerned with what cost is expected to be

in the future, and how the firm might be able to rearrange its resources to lower its cost andimprove its profitability. They must therefore be concerned with opportunity cost, the costassociated with opportunities that are foregone by not putting the firm’s resources to theirhighest value use.” [1]

1.2 Opportunity Cost

The benefit foregone by using a scarce resource for one purpose instead of for its next bestalternative use.

An opportunity cost is incurred because of the use of limited resources, such that the opportunity

to use those resources to monetary advantage in an alternative use is foregone. Thus, it is thecost of the best rejected (i.e., foregone) opportunity and is often hidden or implied.

Example:Suppose that a construction project involves the use of a storage space presently owned by acompany. The cost for that space to the project should be the income or savings that possiblealternative uses of the space may bring to the company. In other words, the opportunity cost forthe space should be the income derived from the best alternative use of it. This may be morethan or less than the average cost of that space obtained from the accounting records of thecompany [3].

1.3 Fixed and Variable Costs

Fixed costs are those unaffected by changes in activity level over a feasible range of operationsfor the capacity or capability available. Typical fixed costs include interest costs on borrowedcapital, insurance and taxes on facilities, general management and administrative salaries, andlicense fees. Of course, any cost is subject to change, but fixed costs tend to remain constantover a specific range of operating conditions. When large changes in usage of resources occur,or when plant expansion or shutdown is involved, fixed costs will be affected.


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Variable costs are those associated with an operation that vary in total with the quantity ofoutput or other measures of activity level. If you were making an engineering economic analysisof a proposed change to an existing operation, the variable costs would be the primary part of the prospective differences between the present and changed operations as long as the range ofactivities is not significantly changed. For example, the costs of material and labor used in a

product or service are variable costs – because they vary in total with the number of output units – even though the costs per unit stay the same.

1.4 Marginal Cost

An incremental or marginal cost is the additional cost, or revenue, that results from increasingthe output of a system by one (or more) units. Marginal cost is often associated with “go/no go”decisions that involve a limited change in output or activity level. For instance, the incrementalcost per mile for driving an automobile may be $0.27, but this cost depends on considerationssuch as total mileage driven during the year (normal operating range), mileage expected for thenext major trip, and the age of the automobile. Also, it is common to read of the “incremental

cost of producing a barrel of oil.” The incremental cost (or revenue) is often quite difficult todetermine in practice.

With electricity generation the marginal cost is a function of how much advance notice is

given for demand . One additional MW in a minutes time horizon is a very different cost to anadditional MW in one month’s time.

The data in Table 1.4 describe a company with a fixed cost of $50. Variable cost increases withoutput, as does total cost. The total cost is the sum of the fixed cost in column (1) and thevariable cost in column (2). The marginal cost of increasing from output from 2 to 3 units is$20, because the variable cost of the firm increases from $78 to $98. Total cost of productionalso increases from $128 to $148. The average total cost of producing at a rate of five units is$36, $180/5. Average cost tells us the per unit cost of production.

Table 1.4 Short-Run CostsRate ofOutput

Fixed Cost

(FC)(1)

VariableCost(VC)(2)

Total Cost(TC)

(3)

MarginalCost(MC)

(4)

AverageFixed Cost

(AFC)(5)

AverageVariable

Cost (AVC)(6)

AverageTotal Cost

(ATC)(7)

0 50 0 50 - - - -1 50 50 200 50 50 50 100

2 50 78 128 28 25 39 64

3 50 98 148 20 16.7 32.7 49.34 50 112 162 14 12.5 28 40.5

5 50 130 180 18 10 26 366 50 150 200 20 8.3 25 33.37 50 175 225 25 7.1 25 32.1

8 50 204 254 29 6.3 25.5 31.8

9 50 242 292 38 5.6 26.9 32.410 50 300 350 58 5 30 35

11 50 385 435 85 4.5 35 39.5


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Example:A team of four colleagues live in the same geographical area and intend to travel together to aconference (a distance of 400 miles each way). One of the team has a car and agrees to take theother three if they will pay the cost of operating the car for the trip. When they return from the

trip, the owner presents each of them with a bill for $102.40, stating that he has kept carefulrecords of the cost of operating the car and that, based on an annual average of 15,000 miles,their cost per mile is $0.384. The three others felt that the charge is too high and ask to see thecost figures on which it is based. The owner shows them the following list:

Cost Element Cost per MileGasoline $0.120

Oil and lubrication 0.021

Tires 0.027Depreciation 0.150

Insurance and taxes 0.024

Repairs 0.030Garage 0.012

Total $0.384

The three riders, after reflecting on the situation, form the opinion that only the costs forgasoline, oil and lubrication, tires, and repairs are a function of mileage driven (variable costs)and thus could be caused by the trip. Because these four costs total only $0.198 per mile, andthus $158.40 for the 800-mile trip, the share for each person would be $158.40/3 = $52.80.Obviously, the opposing views are substantially different. Which, if either, is correct? What arethe consequences of the two different viewpoints in this matter, and what should the decision-making criterion be?

Solution:

In this instance assume that the owner of the automobile agreed to accept $52.80 per person forthe three riders, based on the variable costs that were purely incremental for the conference tripversus the owner’s average annual mileage. That is, the $52.80 per person is the “with a trip”cost relative to the “without” alternative.

Now, what would the situation be if the team, because of the low cost, returned and proposedanother 800-mile trip the following weekend? And what if there were several more such trips onsubsequent weekends? Quite clearly, what started out to be a small marginal (and temporary)change in operating conditions – from 15,000 miles per year to 15,800 miles – soon would become a normal operating condition of 18,000 or 20,000 miles per year. On this basis, it wouldnot be valid to compute the extra cost per mile as $0.198.

Because the normal operating range would change, the fixed costs would have to be considered.A more valid incremental cost would be obtained by computing the total annual cost if the carwere driven, say, 18,000 miles, then subtracting the total cost for 15,000 miles of operation, andthereby determining the cost of the 3,000 additional miles of operation. From this difference thecost per mile for the additional mileage could be obtained. In this instance, the total cost for15,000 miles of driving per year was 15,000 x $0.384 = $5,760. If the cost of service – due toincreased depreciation, repairs, and so forth – turned out to be $6,570 for 18,000 miles per year,evidently the cost of the additional 3,000 miles would be $810. Then the correspondingincremental cost per mile due to the increase in the operating range would be $0.27. Therefore,


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if several weekend trips were expected to become normal operation, the owner would be onmore reasonable economic ground to quote an incremental cost of $0.27 per mile for even thefirst trip. [3]

1.5 Sunk Cost

A cost incurred in the past that cannot be retrieved as a residual value from an earlier investment.It is not an opportunity cost. In economics the sunk cost is equivalent to fixed cost in short-termdecision making.

A classic example of sunk cost involves the replacement of assets. Suppose that your firm isconsidering the replacement of a piece of equipment. It originally cost $50,000, is presentlyshown on the company records with a value of $20,000, and can be sold for an estimated $5,000.For purposes of replacement analysis, the $50,000 is a sunk cost. However, one view is that thesunk cost should be considered as the difference between the value shown in the companyrecords and the present realizable selling price. According to this viewpoint, the sunk cost is

$20,000 minus $5,000, or $15,000. Neither the $50,000 nor the $15,000, however, should beconsidered in an engineering economic analysis – except for the manner in which the $15,000may affect income taxes.

1.6 Market Price

The market price is the price at which a good or service is actually exchanged for another goodor service (as an in kind payment) or for money (in which case it is a financial price) [2].

Example: The market clearing price of electricity in a power pool is the price at which the most expensive

unit is dispatched to meet demand. The results from the Purdue power pool model gives a pattern of expansions that occur if a tight power pool were to operate a power exchange, whereevery hour, a market clearing price was set.

1.7 Shadow Price

Shadow price technically implies a price that has been derived from a complex mathematicalmodel (for example, from linear programming). See the discussion that follows in Chapter 2.4.

1.8 Capital Recovery Factor (crf)

The annual payment that will repay a loan of 1 currency unit in “n” years with compoundinterest on unpaid balance – permits calculating equal installments necessary to repay (amortize)a loan over a given period at a stated interest rate “i”. Such that: crf = i(1+i)n/[(1+i) n-1]


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Chapter 2

Costing and Computing Concepts

Further to the general definitions, let us now consider more carefully some of these concepts.

2.1 Average (“Unit”) Costs are usually misleading guides to choosingbetween alternatives; what’s important are marginal, or incremental,costs

Total Costs = TC(Q)

IRS DRS

Fixed Costs = TFC

Q

TC(Q) TC(Q) = TFC + TVC

Variable Costs = TVC

Q1 Q 2

IRS = increasing returns to scale; DRS = decreasing returns to scale.

Questions: Why IRS? Why DRS? Why important?

• Average total cost = ATC =TC(Q) TFC TVC

AFC AVCQ Q Q

= + = +

• Marginal, or incremental, cost = MC =dTC(Q) dTVC(Q)

dQ dQ=


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2.2 Marginal Costs are what are critical in decision making, not average

costs

Example: Suppose that a company wishes to select the level of output, Q̂ , which maximizes

profits.

Total profit = TR − TC;Q

ˆmax PQ TC(Q) Q− ⇒ such thatdTC(Q)

PdQ

= , or

Q̂ such that Price = incremental cost.

Note the irrelevance of average anything, except, after the fact, to indicate profit/unit, cost/unit, price/unit.

Example:

Price = $35/unit, Cost = 50,000 + 20.2x + 0.0001x2

50,000

Total CostTotal Revenue

TC TR

Qx1 x̂ x 2

What x maximizes profit? π max → 35 - 20.2 - 0.0002x = 0

→ =14.8

0.0002 = 74,000

Questions: What are x1 and x2?

Is the $50,000 relevant? What if the $50,000 could be avoided?

Question: When can average costs be used in decision-making?

- When AC = MC, i.e., FC = 0, VC linear.


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A common average cost is depreciation. Equipment lasts 10 years, costs $10,000; want to cost iton a yearly basis. Use straight-line depreciation of $1,000/year. While depreciation is importantfor tax purposes, it is irrelevant for decision making, except as it affects after-tax profits.

Example:

Trying to decide which plant should produce a new product.

(a) New Plant: Low out-of-pocket, high depreciation expenses

Annual variable cost $1 x 106

Annual depreciation $2 x 106 $3 x 10

6

(b) Old Plant: High out-of-pocket, low depreciation expenses

Annual variable cost $1.5 x 106

Annual depreciation $1 x 10

6

$2.5 x 106

Choose (b)? No! Choose (a); minimize out-of-pocket costs.

Determining marginal costs frequently a tricky business:-- Long-term contracts (labor, fuel)-- Costs of change (hire/fire)-- Capacity utilization, when capacity additions are “lumpy”

2.3 The Irrelevance of Sunk Cost

Sunk Costs: A cost irretrievably incurred in the past that cannot be altered by any action takenfrom now on.

Examples:• Binding contractual agreement to purchase a specialized piece of equipment with

no salvage value.• I purchased IBM stock @ $130/share; it is now $80/share. Should the fact that I

purchased @ $130 enter into the decision to keep or sell the stock?

Question: What is the relation between fixed and sunk costs?

Fixed Costs: Once incurred, remain invariant for all alternative courses of action underconsideration.

Examples:• Cost of a factory of fixed size prior to decision to construct

• Salaries, cost of machinery, etc., which do not vary as production varies


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Suppose I’m trying to figure out what type of assembly line to build: (A) an expensive, highlyautomated one, or (B) a cheaper, less automated one.

A B

Equipment: 1 x 106 Equipment 0.5 x 10

6

Marginal operating cost/unit: 50¢ Marginal operating cost/unit: $1.00

TC(Q) = 1 x 106 + 0.50Q TC = 0.5 x 10

6 + 1.00Q

Now: Before I choose: both equipment costs and operating costs are variable.

Which to choose depends on expected sales; < 1 x 106, choose B, > 1 x 10

6, choose A.

1

2

3

TC x 10 6

1 2 3 4 5 6Q x 10 6

Plant B

Plant A

After I choose and construct, fixed costs become sunk costs to the extent that I cannot recoverequipment investment, and they become irrelevant for decision-making.

Question: Do all sunk costs arise from fixed costs?Answer: No. Even fuel costs can be sunk costs, if a take or pay contract is signed.


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2.4 LaGrange Multipliers

Demand theory is based on the premise that consumers maximize utility subject to a budgetconstraint. Utility (U, the level of satisfaction that a person gets from consuming a good orundertaking an activity) is assumed to be an increasing function of the quantities of goods

consumed, but marginal utility is assumed to decrease with consumption. The consumer’soptimization problem when there are two goods, X and Y, may then be written as

Maximize U(X,Y) (1)

subject to the constraint that all income is spent on the two goods:

PXX + PYY = I (2)

Here, U( ) is the utility function, X and Y are the quantities of the two goods that the consumer purchases, PX and PY are the prices of the goods, and I is income. (To simplify the mathematics,

we assume that the utility function is continuous (with continuous derivatives) and that goods areinfinitely divisible.) [3]

To determine the individual consumer’s demand for the two goods, we choose those values of Xand Y that maximize Equation (1) subject to Equation (2). When we know the particular form ofthe utility function, we can solve to find the consumer’s demand for X and Y directly. however,even if we write the utility function in its general form U(X,Y), the technique of constrainedoptimization can be used to describe the conditions that must hold if the consumer is maximizingutility.

To solve the constrained optimization problem given by Equations (1) and (2), we use themethod of Lagrange multipliers, which works as follows. We first write the “LaGrangian” forthe problem. To do this, rewrite the constraint in Equation (2) as: PXX + PYY –I = 0. TheLaGrangian (L) is then:

L = U(X,Y) - λ(PXX + PYY – I) (3)

The parameter λ is called the Lagrange multiplier.

If we choose values of X and Y that satisfy the budget constraint, then the second term in

Equation (3) will be zero, and maximizing Φ will be equivalent to maximizing U(X,Y). Bydifferentiating Φ with respect to X, Y, and λ and then equating the derivatives to zero, we obtainthe necessary conditions for a maximum (these conditions are necessary for an “interior”solution in which the consumer consumes positive amounts of both goods; however, the solutioncould be a “corner” solution in which all of one good and none of the others are consumed):

MUX(X,Y) – λPX = 0MUY(X,Y) – λPY = 0 (4)PXX + PYY – I = 0


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Here, MU is short for marginal utility (i.e., MUX(X,Y) = ∂U(X,Y)/∂X, the change in utility froma small increase in the consumption of good X).

The third condition is the original budget constraint. The first two conditions of Equation (4) tellus that each good will be consumed up to the point at which the marginal utility from

consumption is a multiple of (λ) of the price of the good. To see the implication of this, wecombine the first two conditions to obtain the equal marginal principle:

λ = [MUX(X,Y)/PX] = [MUY(X,Y)/PY] (5)

Note also that ˆ L Iλ = ∂ ∂ ; it can be shown that ˆ Û Iλ = ∂ ∂ ; e.g., the change in the utility

function with a change on the right-hand side of the constraint – thus, the term “shadow price” –it is what you gain by a relaxation of a constraint.

In other words, the marginal utility of each good divided by its price is the same. To beoptimizing, the consumer must be getting the same utility from the last dollar spent by

consuming either X or Y. Were this not the case, consuming more of one good and less of theother would increase utility.

To characterize the individual’s optimum in more detail, we can write the information inEquation (5) to obtain:

MUX(X,Y)/MUY(X,Y) = PX/PY (6)

2.5 Operations Research (OR, Management Science, Decision Analysis)

Operations research is sometimes also called OR, Management Science, or decision analysis. Inthe process of taking major project decisions there will be thousands and probably millions ofoptions available. Consider a few simple examples:

Consider the options available with the unit commitment problem for one coal fired generatingunit during one time period. List the options of when it is switched on and off.

Example:On Off

Condition 1 0 1 Unit is switched off. Condition 2 1 0 Unit is switched on.

Only two options are possible.

Example:Consider the unit commitment problem and the options again but this time there are twogenerating stations, one thermal and one hydropower. The thermal station has two generatingunits and in the hydropower station there is one unit. How many options or combinations ofswitched-on units are available during one time period?


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Option No: 1 2 3 4 5 6 7 8Condition: On/Off On/Off On/Off On/Off On/Off On/Off On/Off On/Off

Unit 1 0/1 1/0 0/1 0/1 1/0 1/0 0/1 1/0Unit 2 0/1 0/1 1/0 0/1 1/0 0/0 1/0 1/0

Unit 3 0/1 0/1 0/1 1/0 0/1 1/0 1/0 1/0

With this simple example, in one time period (say one hour), there are already 8 different optionsavailable.

With 2 conditions and 3 units there are:23 = 8 possible operating options available.

Example:Consider the example above again but this time let there be two time periods called hour 1 andhour 2.

In hour 1 there is option 1 and following in hour 2 there would be 8 options.In hour 1 there is option 2 and following in hour 2 there would be 8 options.In hour 1 there is option 3 and following in hour 2 there would be 8 options.

Etc. etc. . . . . .In hour 1 there is option 8 and following in hour 2 there would be 8 options.

With a second time period being involved there are now 64 possible operating options toconsider. The complexity of the problem increases exponentially.

There are now 23 x 23 = 64 conditions.26 = 64

In one day with 24 one hour time periods the number of operating options available will be equal

to:23 x 24 = 272

272 = 4.722366483 x 1021 2

72 = 4,722,366,483,000,000,000,000

= 4,722 trillion trillion options

Thus a relatively simple problem can quickly involve an unmanageable number of options.

Imagine the size or complexity of the decision process for the unit commitment in an electricityutility or power pool in which there are several or more power generating stations with scores ofunits to be switched on and off over hourly periods for days and weeks.

It can be appreciated that a computer solver for real problems in decision analysis will beindispensable as a manual procedure would be extremely long and prone to mistakes –effectively impossible to do. The GAMS and CPLEX solvers are used for this type of problem(using branch and bound techniques).


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2.6 Introduction to GAMS (General Algebraic Modeling System)

The basic structure of GAMS has the following components:-SETS (indices)PARAMETERS, TABLES, SCALARS (data)

VARIABLESEQUATIONSMODEL & SOLVE statements

These can be best understood with an example. Consider the following:

(Adapted from “GAMS, A User’s Guide”, Anthony Brooke et al, 1988)We are given the supplies at several markets for a single commodity (electricity) at a single pointin time. We are given the unit costs of shipping the commodity from plants to markets. Theeconomic question is how much shipment should there be between each plant and each marketso as to minimize the total shipment cost?

MarketsHarare Lusaka Pretoria Supplies

(MWh) Plants Wheeling Distances

(Thousands of miles)Inga 1.6 1.3 2.2 2100HCB 0.3 0.6 1.0 1600 Demands 700 400 2500(MWh)

SETS - Indicesi = plants, j = markets

PARAMETERS, TABLES, SCALARS - Given DataHi = supply of commodity at plant i (MW)D j = demand for commodity at market j (MW)Cij = cost of MW shipping/wheeling to ship from plant i to market j (MW)

DECISION VARIABLESXij = quantity of commodity to ship from plant i to market j (MW)

Where Xij ≥ 0 for all i,j

EQUATIONS − COST, SUPPLY & DEMAND must be declared.

MODEL Supply limit at plant i Xij j

≤∑ Hi

Satisfy demand at market j Xiji

≥∑ D j

Objective Function

Minimize C Xij ij ji

∑∑


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j Harare j Lusaka j Pretoria

i Inga i HCB

Shipping costs are approximately $2 per MWh per thousand miles.

GAMS FORMAT ( print-out of the gams code):SET I Generation plants / Inga, HCB /;SET J Demand Centers / Harare, Lusaka, Pretoria /;

PARAMETER H(I) Exporting capacity (MWh) of plant I/ Inga 2100

HCB 1600 /;

PARAMETER D(J) Demand (MWh) at Market J/ Harare 700

Lusaka 400Pretoria 2500 /;

TABLE L(I,J) Distance in thousands of miles from I to JHarare Lusaka PretoriaInga 1.6 1.3 2.2HCB 0.3 0.6 1.1 ;

SCALAR W Wheeling charge in $ per thousand miles / 2 /;

PARAMETER C(I,J);C(I,J) = W*L(I,J);

VARIABLE X(I,J) Shipment quantities in MWhVARIABLE Z Total shipment cost in thousands of $

POSITIVE VARIABLE X ;

EQUATION COST Define objective functionEQUATION SUPPLY(I) Observe supply limit at plant IEQUATION DEMAND(J) Satisfy demand at market J ;

COST.. Z =E= SUM((I,J),C(I,J)*X(I,J)) ;SUPPLY(I).. SUM(J,X(I,J)) =L= H(I) ;DEMAND(J).. SUM(I,X(I,J)) =G= D(J) ;

MODEL ELEC / ALL / ;SOLVE ELEC USING LP MINIMIZING Z ;DISPLAY X.L, X.M


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GAMS OUTPUT:

ITERATION COUNT, LIMIT 6 10000Cplex 6.0, GAMS Link 12.0-7, 386/486 DOSOptimal solution found.

Objective : 10480.000000

VAR X Shipment quantities in MWhLOWER LEVEL UPPER MARGINAL

Inga.Harare . . +INF 0.400Inga.Lusaka . 400.000 +INF .Inga.Pretoria . 1600.000 +INF .HCB .Harare . 700.000 +INF .HCB .Lusaka . . +INF 0.800HCB .Pretoria . 900.000 +INF .

The total shipment cost (minimized) for meeting the demand at the three markets amounts to$10480. The optimal shipments are obtained by Inga sending out 400MWh to Lusaka and1600MWh to Pretoria and by HCB sending out 700MWh to Harare and 900MWh to Pretoria.

2.7 Computing Requirements

The computing requirements to run the Purdue power pool models can be met with a new PC(Pentium 3, etc.) or the latest laptop. The speed of the processor is important for an efficient useof the model and it is recommended that at least 500MHz is used. A large memory is also animportant requirement. The Purdue Generic Seven Country Model is free. The regional modelsthat have already been tested by Purdue have confidential data populating them and for this

reason can not be distributed. Two commercial solvers are needed to run the model and theseare GAMS and CPLEX. More details can be obtained from the LT Model User Manual. A totalexpenditure of about $16,000 will be adequate to fully install the system (hardware andsoftware) for the commercial user. Educational institutions are eligible for substantial costreductions with the solvers.


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Chapter 3

Basic Electricity Modeling Formulation

3.1 MODEL I: Short Run, Power Trade Only

In the short-run model I the objective is to minimize the total costs that arise from the cost ofoperations (fuel and maintenance), distributed generation costs, and the cost of unserved MW.

t i z

min c(i, z)PG(i, z, t) DG cos tDG(z, t) UM cos tUM(z)+ +∑∑∑

i.e.: Minimizing over all hours, all stations, and all countries, the sum of fuel costs (cost/MWtimes MW) plus demands met by distributed generation plus unsatisfied reserve requirements.

c(i,z) = Fuel Cost/MW at i in z ($)

PG(i,z,t) = Power Generation at i in z during t (MW)

DGcost = Cost/MW of distributed generation demand ($)DG(z,t) = Distributed Generation in z during t (MW)

UMcost = Cost/MW of unmet reserves ($)UM(z) = Unmet reserve requirement in z (MW)

This minimization is subject to the following constraints:

∑ i PG(i,z,t) + ∑ zp PF(zp,z){1-Pfloss(zp,z)} + DG(z,t) = D(z,t) + ∑ zp PF(z,zp)

PF(zp,z) = Power Flow from zp to z (MW)Pfloss(zp,z) = line loss from zp to z (%)D(z,t) = Demand in z during t (MW)

All generation in country z plus all imports from other countries (adjusted for line loss) is equalto the demand in country z plus exports to all countries.

( ) ( )PG i,z,t PGinit i,z≤

PGinit(i,z) = initial capacities (MW)

The generation at station i, in country z, at any time t, is always less than or equal to the initialgenerating capacity of that station i in country z.


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( ) ( )PF z,zp PFinit z,zp≤

PFinit(i, z) = initial capacities (MW)

The power flow from country z to country zp will always be less than or equal to the initial power flow capability along the transmission line connecting country z to country zp.

( )

( )( ) ( )

i

PGinit i,zUM z D z,peak

1 res i,z+ ≥

+∑

res(i,z) = reserve requirement for i in z (%)D(z,peak) = peak demand in z (MW)

The sum of total capacity of all the plants in country z, derated for their reserve margins, plus theunmet MW in country z will always exceed or be equal to the peak demand in country z.

( ) ( ) ( )i

PGinit i,z A z D z,peak ≥∑

A(z) = Autonomy factor for z (%)

The sum total of initial generating capacities from stations i, in country z, will be greater than orequal to the peak demand in country z times the autonomy of country z.

3.2 MODEL II: Short-Run, Power and Reserves Traded

In the short-run models I and II the objective is to minimize the total costs that arise from thecost of operations (fuel and maintenance), distributed generation costs, and the cost of unservedMW.

t i z

min c(i, z)PG(i, z, t) DG cos tDG(z, t) UM cos tUM(z)+ +∑∑∑

This minimization is subject to the following constraints:

∑i PG(i,z,t) + ∑

zp PF(zp,z){1-PFloss(zp,z)} + DG(z,t) = D(z,t) + ∑zp PF(z,zp)

For each hour t, and in each country z, the sum total of generation from all stations, i, plus thesum total of all power flow imports from countries zp into country z ( allowing for thetransmission loss between country z and country zp) plus the distributed generation will be equalto the demand at hour t in country z plus the sum of total exports from country z to all othercountries zp.


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[ ]{ } [ ]{ }i zpzp

PGinit(i, z) 1 res(i, z) Fmax(zp, z) 1 res(i, z)

DG(z) D(z,peak) Fmax(z, zp) (More than or equal to)

+ + + +

> +

∑ ∑

∑

Where Fmax(zp,z) = reserves held by zp for z.

Total generating capacity in country z, derated by the appropriate reserve margins plus reservesin other countries held for country z, derated by import reserve requirements, plus unmet reserve

requirements must be ≥ peak demand plus reserves held by country z for other countries.

As also in Model I :-

∑iPGinit(i,z) > A(z) D(z,peak)

PG(i,z,y)


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The Model II load balance and PF equations with the “y” (yearly) variable added.

PG(i,z,t,y) A(z)D(z,peak,y)

Same as before, except total generating capacity now includes additions up to y.

Implications of Model Structure on Data:

♦

The model is a cash flow model; cash outflows entered into the model in the year in whichthey take place.

♦ No need to collect data on sunk costs (costs of past investments, etc.), only incremental costs.

♦ Model assumes equipment purchases financed by borrowed money – hence equipment purchase cost shows up as an annualized cost, equal to the capital recovery factor times theEngineering, Procurement, and Construction (EPC) cost, in each year subsequent to the purchase date.

♦ Plant operating costs (fuel, variable O&M, water costs) should be average incremental costsfor each plant, not marginal costs which might be lower due to say, take or pay fuelcontracts. Ignore variable heat rates for existing thermal plants – assume heat rate at 100%load.

♦ Plant equipment costs should be EPC costs, not including financing costs.

♦ Fixed O&M ($/kW/yr) should be considered only for new plants; they are sunk costs forexisting plants (unless plants mothballed).


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♦ Reserve margins, autonomy factors, discount rate, crf, unserved energy and reserve costs are policy decisions; get them, if you can but don’t spend a lot of time.

♦ Line losses should be average incremental, not marginal.

♦ Line capacities should be maximum transfer capability, not maximum capacity.

♦ Generation capacities should be net effective (dependable) sent out capacity, not nameplatecapacity.

♦ Demands (D(z,t,y)) should be sent out demands, not received demands.


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Chapter 4

The Generic Seven Country Regional Model

4.1 Generation, Transmission and Demand

The generic seven-country model has been constructed for demonstration and training purposes.

Electricity demand patterns for each time period and for each country are primary datarequirements for populating the regional models. The electricity demand “drives” the model andis further explained in Chapters 5 and 6. Taken into account are the load variations on an hourly,daily, weekly, season, yearly, and national basis. The forecasting of annual growth rates indemand needs special attention during the data collection process.

Table 4.1.1 Existing and Proposed Generation StationsCountry Station

NameDetails of Station

Country1 PG(1A) Existing thermal station, 1200MW. Fuel $68?MWhPG(1B) Existing thermal station, 1600MW (expansion is possible up to

2500MW, costing $0.5m/MW). Fuel $44/MWh

NH(1C) Proposed new hydro station of 900MW with fixed cost $600m for thefirst 300MW and then a variable cost of $0.9m/MW

NH(1D) Proposed new hydro station of 600MW with a fixed cost of $850mGT(1E) Proposed new gas turbine station capable of expansion up to 600MW

with a variable cost of $0.3m/MW. Fuel $6/106BtuCountry2 PG(2A) Existing thermal station, 550MW. Fuel $80/MWh

Country3 PG(3A) Existing thermal station, 260MW. Fuel $25/MWh

GT(3B) Proposed new gas turbine stations capable of expansion up to 600MWwith a variable cost of $0.31m/MW. Fuel $7/106Btu

Country4 PG(4A) Existing thermal station , 500MW. Fuel $59/MWh

PG(4B) Existing combined cycle station, 1200MW, with option of expansion upto 2600MW, with a variable cost of $0.6m/MW. Fuel $30/MWh

CC(4C) Proposed new combined cycle station, 300MW, with fixed cost of$175m and then the option of expansion up to 2100MW with a variablecost of $0.55m/MW. Fuel $3.8/106Btu

GT(4D) Proposed new gas turbine station, 300MW, with a variable cost of$0.325m/MW. Fuel $5.5/106Btu

Country5 PG(5A) Existing combined cycle plant, 2400MW. Fuel $65/MWh

CC(5B) Proposed new combined cycle station, 350MW, with fixed cost $ 405mand then the option of expansion up to 2800MW with a variable cost of

$0.63m/MW. Fuel $3.2/106BtuCountry6 H(6A) Existing hydropower station, 600MW

NH(6B) Proposed new hydropower station, 150MW, with fixed cost of $220mand then the option of expansion up to 900MW with a variable cost of$1.1/MW

Country7 H(7A) Existing hydropower station, 450MW NH(7B) Proposed new hydropower station, 200MW, with fixed cost of $270m,

with the option of expansion up to 600MW at a variable cost of$1.3m/MW


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The existing and proposed new generation and transmission infrastructure within this sevencountry regional model is shown in Figures 4.1 and 4.2. Peak demand in Country1 is 3000MW(Figure 4.1) and this country has an existing thermal generating capacity of 2800MW (station 1Ais 1200MW and station 1B is 1600MW). This country has a generation deficit of 200MW andhas proposed plans to construct a new hydropower station of 900MW (1C), a new hydropower

station of 600MW (1D), and a gas turbine station of 600MW (1E).

Country1 is interconnected with Country2 (Figure 4.2) and can therefore import electricity at peak times. The proposed new generation and transmission project capacities are shown initalics in Figures 4.1 and 4.2. Table 4.1.1 lists the names of the existing thermal generatingstations as PG(1A) and PG(1B) and shows the potentially new hydropower plant called NH(1C). Similarly the existing and proposed international transmission lines from Country1 areshown in Table 4.1.2.

Table 4.1.2 Existing and Proposed International Transmission Lines

From Country

To Country

Interconnector

Name

Details of International Interconnector

1 to 2 OT(1-2) Existing international transmission line with a total loadcarrying capability of 100MW – can be expanded up to2000MW at a cost of $0.2m/MW

2 to 3 OT(2-3) Existing international transmission line with a total loadcarrying capability of 100MW – can be expanded up to2000MW at a cost of $0.25/MW

3 to 4 OT(3-4) Existing international transmission line with a total loadcarrying capability of 150MW – can be expanded up to2000MW at a cost of $0.15/MW

4 to 5 NT(4-5) Proposed new international transmission line with aninitial carrying capability of 350MW having a fixed costof $100m. This line can be further expanded up to2000MW with a variable expansion cost of $0.16m/MW.

5 to 6 NT(5-6) Proposed new international transmission line with aninitial carrying capability of 300MW having a fixed costof $40m This line can be further expanded up to 750MWwith a variable expansion cost of $0.22m/MW.

6 to 2 NT(6-2) Proposed new international transmission line with aninitial carrying capability of 150MW having a fixed costof $88m This line can be further expanded up to 750MWwith a variable expansion cost of $0.15m/MW.

6 to 7 NT(6-7) Proposed new international transmission line with aninitial carrying capability of 300MW having a fixed costof $120m This line can be further expanded up to2000MW with a variable expansion cost of $0.25m/MW

7 to 1 NT(7-1) Proposed new international transmission line with aninitial carrying capability of 300MW having a fixed costof $95m This line can be further expanded up to 2000MWwith a variable expansion cost of $0.2m/MW

Similar to Country 1 the information about the existing and proposed generation stations for eachcountry is summarized in Table 4.1.1. It is noted that there are no existing proposals for newgenerating capacity in Country 2. Countries 4 and 5 both have excess generating capacity withsignificant generation coming from combined cycle stations (using natural gas). Countries 6 and7 are dominant hydropower countries and also have excess capacity but this time it is excess


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hydropower. Both countries 6 and 7 have proposals for the construction of new furtherhydropower generating capacity.

It is possible at present for Country 1 to import up to a maximum of 100MW from Country 2(Figure 4.2). The existing line can have its existing load carrying capability increased up to a

maximum of 2000MW. There is also a proposed totally new international transmission line forconnecting Country 1 with Country 7. The initial capacity of this new line is 300MW. Thecapacities of the existing international lines are shown for between countries 1, 2, 3, and 4, inFigure 4.2. All of the existing and proposed new transmission lines can be expanded up to amaximum load carrying capability of 2000MW.

Table 4.1.3 Supplies of Natural Gas in the Generic Model

CountryExisting Supplies of

Natural Gas(mmscfd – millions of

cubic feet per day)

Proposed MaximumSupplies of

Natural Gas(mmscfd)

Combined CycleGenerating capacity,Existing – Proposed

(MW)

Country 4 200 790 1200 – 4700Country 5 60 470 350 - 2800

Notes: Assuming that 100mmscfd will generate 600MW of combined cycle.Only Countries 4 and 5 have access to natural gas supplies. The other countries have nonatural gas available to them except that a gas pipe-line be built from Country 4 or 5.The generic model in this manual does not provide the option of the expansion of a pipe-line to the other countries.

There are no options to construct natural gas pipe-lines to all parts of the region. Table 4.1.3summarizes the status of existing and proposed maximum supplies of natural gas to the region.

The mix of fuels in the region is broad. Existing old thermal stations (1A, 1B, 2A, 3A and 4A)can be described as either oil or coal fired. The fuel costs and heat rates will reflect the fuelcharacteristics. Old thermal station 4B is the only existing combined cycle station using naturalgas. Station 4B can expand its capacity to use more gas and Country 5 also has the potential forlarge combined cycle generation. The capital costs (fixed and variable) for generation expansionwill determine whether hydro, solid fuels or gas usage is to be further increased. The costs of theinterconnecting transmission lines will determine the ease or difficulty of trade, depending on thecapital fixed and variable costs for increased transmission capacity.


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Figure 4.1 Training Model with Peak Demand (D) & Existing Generation (PG, CC, HCountry

Boundafor pow

Country 1 D = 3000PG(1A) = 1200PG(1B) = 1600-2500(NH(1C) = 300-900 NH(1D) = 600GT(1E) = 800)

Country 2D = 500PG(2A) = 550

Country 3 D = 300PG(3A) = 260(GT(3B) = 600)

Country 4 D = 1000PG(4A) = 500PG(4B) = 1200-2600

(CC(4C) = 300-2100GT(4D) = 300)

Country7D = 400H(7A) = 450(NH(7B) = 200-600)

Country 6 D = 300H(6A) = 600(NH(6B) = 150-900)

Country 5 D = 2000PG(5A) = 2400(CC(5B) = 350-2800)

Key (all values iD = Electricity DPG = Old thermCC= Old CombiH = Old hydropo

(Italicized values are proposed capacity expansions

Adearco


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Figure 4.2 Training Model with Existing International Transmission Lines and Pro

Boundafor pow

Key (all lin

12

4

3

5

67

100100

150

300150

300300

350

Italicized values are proposed new line expansions (MW) All lines can expand up to 2000MW


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4.2 Demonstration Results from the 7-Node Generic Model

Four demonstration electricity policy scenarios are provided:Scenario #1: Static 1 year model. There is no capacity expansion.Scenario #2: Static 1 year model. Minimum expansions and no trade.Scenario #3: Free trade & 10 year planning horizon.Scenario #4: Minimum trade permitted & 10 year planning horizon.

A summary of costs and capacity expansions are shown below in Table 4.2.

Table 4.2 Summary of Projects Selection for the Three Policy Scenarios

Scenario #1

1 year static

Scenario #2

1 year static

Min.Trade

Scenario #3

Free Trade

10 years

4% growth

Scenario #4

No Trade

10 years

4% growth

Total regional cost ($bn) 4.03 4.34 13.32 18.14Operational Costs ($bn) 2.02 2.06 8.59 11.13

Capacity capital costs ($bn) 0 0 3.29 2.42Unserved Energy, MWh ($bn) 0.35 0.37 0.65 1.59

Unmet Reserve Margin, MW ($bn) 1.62 1.88 0.63 2.86

Generation Expansions (MW) Old Thermal (MW) 0 0 955 900

New Combined Cycle (MW) 0 0 3,553 3,111 New Hydropower (MW) 0 0 2,342 1,479 New Gas Turbines (MW) 0 0 0 427

Transmission Expansion (MW)

Old Transmission (MW) 0 0 833 0 New Transmission MW) 0 0 2,031 0

• There is a 23% saving in total regional costs when the countries adopt a free trade policy (4% electricity annual demand growth rates in all countries) .

• Free trade reduces the massive unmet reserve margin penalty costs.

•

Generation capacity increases by 16% for free trade.

• Construction of 3,611MW of load carrying transmission capacity causes enormouscost savings.

•

Net exporters: Countries 4, 5, 6, 7, 8 Net importers: Countries 1, 2, 3

Some of the benefits and projects (generation and transmission) optimally selected underthese three scenarios are summarized in section 4.3. The user-friendly PLTETM windowsinterface facility provides some of the output results.

4.3 Demonstration Outputs from the 7-node Generic Model


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4.3.1 Consequences of trade with County 7 being a major exporter and County 1 being amajor importer. Note the revenues and costs to each country over the 10 year planninghorizon:

Figure 4.3.a Scenario 3 for country7 – A major exporting country

Figure 4.3.b Scenario 3 for country1 – A major importing country


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4.3.2 Construction of key international transmission lines takes place in periods 4 and ?

Figure 4.3.c Scenario 3 Old Transmission Expansion for Period 1 (2004-2005)

Figure 4.3.d Scenario 3 New Transmission Expansion for Period 2 (2006-2007)


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4.3.3 Cost summary of short-term 1 year model: Scenario 1 compared to Scenario 2


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4.3.4 Cost Summary of 10 year long-term model: Scenario 3 compared to Scenario 4


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==================================================================NEW TRANSMISSION EXPANSION

___________________________________________________________________


per2 | country1 and country7 | 499 MW

per5 | country1 and country7 | 47 MW

===================================================================OLD TRANSMISSION EXPANSION

___________________________________________________________________


per1 | country1 and country2 | 102 MWper3 | country1 and country2 | 13 MWper4 | country1 and country2 | 128 MWper5 | country1 and country2 | 108 MW

===================================================================

B) MW RESERVES========================================================================(Generation Capacity + Firm Import Reserve - Firm Export Reserve = PeakDemand)-----------------------------------------------------------------------Year | 2005 | 2007 | 2009 | 2011 | 2013

(a) PEAK DEMAND (MW)(From input files)| 3245 | 3510 | 3796 | 4106 | 4441

(b) PEAK LOAD CARRYING CAPABILITY (MW)(Adjusted by Decay Rate & Reserve Margin)Old Thermal | 3103 | 3097 | 3091 | 3084 | 3078New Hydro | 0 | 1133 | 1133 | 1133 | 1155

Total | 3103 | 4229 | 4223 | 4217 | 4233

(c) FIRM IMPORT RESERVE (MW)(Adjusted by line loss, forced outage rate)Imports From:country2 | 140 | 0 | 0 | 0 | 0country7 | 0 | 0 | 0 | 0 | 206

Total | 140 | 0 | 0 | 0 | 206

(d) FIRM EXPORT RESERVE (MW) NONE

(f) TOTAL MW CAPACITY[ (b) + (c) - (d) = (e) ]

| 3243 | 4229 | 4223 | 4217 | 4439

(g) TOTAL RESERVE MARGIN (%)[(b)(Adjusted only by decay)+(c)(Adjusted only by line loss)-(d)-(a)]/[(a)-(c)+(d)]=(f)Total | 18.9%| 40.5%| 29.7%| 19.7%| 16.5%

(i) AUTONOMY FACTOR [Generation Reserve(adjusted for FOR, Decay) /Peak Demand]Actual | 1.036 | 1.307 | 1.207 | 1.114 | 1.034Required | 0.000 | 0.000 | 0.000 | 0.000 | 0.000


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(j) MAXIMUM IMPORTS (MW)[Maximum hourly flow of energy during the year unadjusted]Imports from:country2 | 0 | 183 | 191 | 306 | 401country7 | 0 | 558 | 557 | 556 | 608

(j) MAXIMUM IMPORTS (MW)[Time period from which the maximum import flow come from]Maximum Import time:FRM | YEAR | SEASON | DAY | HOUR | MW

cou | per2 | summer | peak | hr9 | 182.8cou | per2 | summer | peak | hr19 | 182.8cou | per2 | summer | peak | hr20 | 182.8cou | per2 | summer | peak | hr21 | 182.8cou | per2 | summer | peak | avdy | 182.8cou | per2 | summer | average | hr20 | 182.8cou | per2 | winter | peak | hr19 | 182.8cou | per2 | winter | peak | avdy | 182.8cou | per2 | winter | average | hr9 | 182.8

cou | per2 | winter | average | hr19 | 182.8cou | per2 | winter | average | hr20 | 182.8cou | per2 | winter | average | hr21 | 182.8cou | per2 | winter | average | avdy | 182.8cou | per3 | summer | peak | hr19 | 191.0cou | per3 | summer | peak | avdy | 191.0cou | per3 | summer | average | hr9 | 191.0cou | per3 | summer | average | hr20 | 191.0cou | per3 | summer | average | hr21 | 191.0cou | per3 | winter | peak | avnt | 191.0cou | per3 | winter | average | hr9 | 191.0cou | per3 | winter | average | hr19 | 191.0cou | per3 | winter | average | hr20 | 191.0cou | per3 | winter | average | hr21 | 191.0

cou | per3 | winter | average | avdy | 191.0cou | per4 | summer | average | hr9 | 306.5cou | per4 | summer | average | hr19 | 306.5cou | per4 | summer | average | hr20 | 306.5cou | per4 | summer | average | hr21 | 306.5cou | per4 | summer | average | avdy | 306.5cou | per4 | winter | peak | avnt | 306.5cou | per4 | winter | average | hr9 | 306.5cou | per4 | winter | average | hr19 | 306.5cou | per4 | winter | average | hr21 | 306.5cou | per4 | winter | average | avdy | 306.5cou | per5 | summer | peak | avnt | 401.1cou | per5 | summer | average | hr19 | 401.1cou | per5 | summer | average | avdy | 401.1cou | per2 | summer | peak | avnt | 557.9cou | per2 | summer | average | hr9 | 557.9cou | per2 | summer | average | hr19 | 557.9cou | per2 | summer | average | hr20 | 557.9cou | per2 | summer | average | hr21 | 557.9cou | per2 | winter | peak | avnt | 557.9cou | per2 | winter | average | hr9 | 557.9cou | per2 | winter | average | hr19 | 557.9cou | per2 | winter | average | avdy | 557.9cou | per3 | summer | peak | avnt | 556.8cou | per3 | summer | average | hr9 | 556.8


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cou | per3 | summer | average | hr19 | 556.8cou | per3 | summer | average | hr20 | 556.8cou | per3 | summer | average | hr21 | 556.8cou | per3 | summer | average | avdy | 556.8cou | per3 | winter | peak | avnt | 556.8cou | per4 | summer | average | hr9 | 555.7cou | per4 | summer | average | avdy | 555.7

cou | per5 | summer | average | hr19 | 607.6cou | per5 | summer | average | avdy | 607.6

(k) MAXIMUM EXPORTS (MW)[Maximum hourly flow of energy during the year unadjusted]Exports to:country2 | 196 | 192 | 201 | 287 | 165

(j) MAXIMUM EXPORTS (MW)[Time period from which the maximum export flow come from]Maximum Export time:TO | YEAR | SEASON | DAY | HOUR | MW

cou | per1 | summer | offpeak | avnt | 196.3

cou | per1 | summer | peak | hr9 | 196.3cou | per1 | summer | peak | hr19 | 196.3cou | per1 | summer | peak | hr20 | 196.3cou | per1 | summer | peak | hr21 | 196.3cou | per1 | summer | peak | avdy | 196.3cou | per1 | summer | average | hr20 | 196.3cou | per1 | winter | peak | hr9 | 196.3cou | per1 | winter | peak | hr19 | 196.3cou | per1 | winter | peak | hr20 | 196.3cou | per1 | winter | peak | hr21 | 196.3cou | per1 | winter | peak | avdy | 196.3cou | per1 | winter | average | hr9 | 196.3cou | per1 | winter | average | hr19 | 196.3cou | per1 | winter | average | hr20 | 196.3

cou | per1 | winter | average | hr21 | 196.3cou | per1 | winter | average | avdy | 196.3cou | per2 | summer | offpeak | avnt | 192.4cou | per2 | summer | offpeak | hr19 | 192.4cou | per2 | summer | average | avnt | 192.4cou | per2 | winter | offpeak | hr9 | 192.4cou | per2 | winter | offpeak | avnt | 192.4cou | per2 | winter | offpeak | avdy | 192.4cou | per3 | summer | offpeak | hr9 | 201.1cou | per3 | summer | offpeak | avnt | 201.1cou | per3 | summer | offpeak | avdy | 201.1cou | per4 | summer | offpeak | avdy | 286.7cou | per5 | winter | offpeak | avnt | 165.0

========================================================================C) INCREMENTAL AND CUMULATIVE GENERATION CAPACITY

========================================================================

(a) GENERATION CAPACITY (MW) [Unadjusted]IncrementalOld Thermal | 900 | 0 | 0 | 0 | 0New Hydro | 0 | 1246 | 2 | 2 | 27

(b) GENERATION CAPACITY (MW) [Unadjusted]Cumulative


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Old Thermal | 3700 | 3700 | 3700 | 3700 | 3700New Hydro | 0 | 1246 | 1248 | 1251 | 1278

(c) NEW TRANSMISSION CAPACITY (MW) [Unadjusted]Incrementalcountry7 | 0 | 587 | 0 | 0 | 56

(d) NEW TRANSMISSION CAPACITY (MW) [Unadjusted]Cumulativecountry7 | 0 | 587 | 587 | 587 | 643

(e) OLD TRANSMISSION CAPACITY (MW) [Unadjusted]Incrementalcountry2 | 102 | 0 | 13 | 128 | 108

(f) OLD TRANSMISSION CAPACITY (MW) [Unadjusted]Cumulativecountry2 | 202 | 202 | 215 | 343 | 451

========================================================================D) DEMAND/SUPPLY

========================================================================(Energy Demand + Energy Exported + Energy Dumped = Energy Generation +Energy Imported + Energy Unserved)-----------------------------------------------------------------------

(a) ENERGY DEMAND (MWh/Year) [Yearly Total]Local Demand | 1.66E+7 | 1.80E+7 | 1.95E+7 | 2.11E+7 | 2.28E+7Exports | 1072285 | 578376 | 215287 | 207405 | 19594

Total | 1.77E+7 | 1.86E+7 | 1.97E+7 | 2.13E+7 | 2.28E+7

(b) ENERGY SUPPLY (MWh/Year) [Yearly Total]Old Thermal | 1.73E+7 | 3224126 | 4070822 | 4719077 | 5153559New Hydro | 0 | 1.08E+7 | 1.08E+7 | 1.08E+7 | 1.08E+7Imports | 0 | 4559889 | 4772071 | 5600568 | 6534672

Unserved Energy | 418408 | 22000 | 69032 | 173267 | 335391Total | 1.77E+7 | 1.86E+7 | 1.97E+7 | 2.13E+7 | 2.28E+7

(c) SUPPLY, BY STATION TYPE

Old Thermal Generation (MWh) [Yearly, by Station]Station:Stat1 | 1434391 | 327570 | 621260 | 895244 | 979611Stat2 | 1.59E+7 | 2896556 | 3449562 | 3823833 | 4173949

Total | 1.73E+7 | 3224126 | 4070822 | 4719077 | 5153559

Old Thermal Load Factor [Yearly, by Station]Station:Stat1 | 13.71 | 3.14 | 5.96 | 8.61 | 9.44Stat2 | 72.78 | 13.32 | 15.89 | 17.65 | 19.30

New Hydro Generation (MWh) [Yearly, by Station]Station:newh1 | 0 | 7095600 | 7095600 | 7095600 | 7095600newh2 | 0 | 3679200 | 3679200 | 3679200 | 3679200

Total | 0 | 1.08E+7 | 1.08E+7 | 1.08E+7 | 1.08E+7

New Hydro Load Factor [Yearly, by Station]Station:newh1 | 0.00 | 99.00 | 99.00 | 99.00 | 96.10


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newh2 | 0.00 | 99.00 | 99.00 | 99.00 | 99.00

(D) ENERGY IMPORTED (MWh/Year)Imported From:country2 | 0 | 449500 | 872305 | 1850751 | 2543801country7 | 0 | 4110389 | 3899766 | 3749817 | 3990871

Total | 0 | 4559889 | 4772071 | 5600568 | 6534672

(e) ENERGY EXPORTED (MWh/Year)Exported To:country2 | 1072285 | 578376 | 215287 | 207405 | 19594

Total | 1072285 | 578376 | 215287 | 207405 | 19594

========================================================================E) COST & REVENUES

========================================================================(a) FUEL COSTS ($/Year)UndiscountedOld Thermal | 8.12E+8 | 1.53E+8 | 1.98E+8 | 2.34E+8 | 2.55E+8

Total Discounted Fuel Cost for Horizon = $2403593687

FUEL COSTS ($/MWh) [Yearly fuel costs/yearly MWh generation]UndiscountedOld Thermal | 46.91 | 47.37 | 48.62 | 49.53 | 49.54

(b) O & M COSTS ($/Year)UndiscountedOld Thermal | 1.12E+7 | 2201690 | 3153679 | 3970978 | 4340079New Hydro | 0 | 1.04E+7 | 1.04E+7 | 1.04E+7 | 1.05E+7

Total Discounted O & M Cost for Horizon = $83319607

(c) WATER COSTS ($/Year)Undiscounted

New Hydro | 0 | 5387400 | 5387400 | 5387400 | 5387400

Total Discounted Water Cost for Horizon = $24846678

(d) CAPITAL COSTS

levelized(t) = (construction cost)(crf) in all t following construction

Year | 2005 | 2007 | 2009 | 2011 | 2013 | Total

NEW HYDRO STATIONSStation Undiscounted Levelized Dollarsnewh1 | 0 | 6.6E+7 | 6.6E+7 | 6.6E+7 | 6.8E+7 | 2.7E+8newh2 | 0 | 7.2E+7 | 7.2E+7 | 7.3E+7 | 7.3E+7 | 2.9E+8Station Discounted Levelized Dollarsnewh1 | 0 | 4.9E+7 | 4.1E+7 | 3.4E+7 | 2.9E+7 | 1.5E+8newh2 | 0 | 5.4E+7 | 4.5E+7 | 3.7E+7 | 3.1E+7 | 1.7E+8

Total Discounted Cost for Horizon = $639526545

NEW HYDRO STATION EXPASIONSStation Undiscounted Levelized Dollarsnewh1 | 0 | 5.9E+7 | 5.9E+7 | 5.9E+7 | 6.1E+7 | 2.4E+8Station Discounted Levelized Dollarsnewh1 | 0 | 4.4E+7 | 3.7E+7 | 3.0E+7 | 2.6E+7 | 1.4E+8


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OLD TRANS. EXPANSIONSStation Undiscounted Levelized Dollarscountr|21.2E+6 | 1.2E+6 | 1.4E+6 | 2.9E+6 | 4.2E+6 | 1.1E+7Station Discounted Levelized Dollars

countr|21.1E+6 | 920767 | 856016 | 1.5E+6 | 1.8E+6 | 6.2E+6


========================================================================F) GAINS FROM TRADE

========================================================================

Year | 2005 | 2007 | 2009 | 2011 | 2013REVENUE FROM EXPORTSEXPORTED TO:country2 | 96035195| 29876495| 15647596| 14181512| 1078256

PAYMENTS FOR IMPORTS

IMPORTED FROM:country2 | 0| 24034729| 34845549| 62453087| 73599463country7 | 0| 184720834| 158120258| 141298266| 131843635

REVENUE FROM RESERVESEXPORTED TO:

PAYMENTS FOR RESERVESIMPORTED FROM:country2 | 18285242| 0| 0| 0| 0country7 | 0| 0| 0| 0| 8

Year | 2005 | 2007 | 2009 | 2011 | 2013

Average Buying Price Present Value| 0.00 | 22.89 | 20.22 | 18.19 | 15.72Average Selling Price Present Value

| 47.14 | 27.19 | 38.25 | 35.99 | 28.96Average Buying Price Real Dollars

| 0.00 | 30.51 | 32.61 | 35.50 | 37.12Average Selling Price Real Dollars

| 51.93 | 36.24 | 61.70 | 70.24 | 68.40

Year | 2005 | 2007 | 2009 | 2011 | 2013Average Buying Price Present Value

| 65183| 0| 0| 0| 0Average Selling Price Present Value

| 0| 0| 0| 0| 0Average Buying Price Real Dollars

| 71810| 0| 0| 0| 0Average Selling Price Real Dollars

| 0| 0| 0| 0| 0

========================================================================G) OBJECTIVE FUNCTION BREAKDOWN (Present Value)

========================================================================


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Year | 2005 | 2007 | 2009 | 2011 | 2013FIXED COSTS(a) Capital CostsOT | 98033328| 81019279| 66958082| 55337258| 45733271LC | 0| 0| 0| 0| 0CC | 0| 0| 0| 0| 0CT | 0| 0| 0| 0| 0

SC | 0| 0| 0| 0| 0Old H | 0| 0| 0| 0| 0New H | 0| 295607305| 244791921| 202710978| 171048648Pumped H | 0| 0| 0| 0| 0New Line | 0| 11491288| 9496932| 7848704| 7103356Old Line | 2228255| 1841533| 1712032| 2990355| 3570158(b) Unserved MegaWattsUM | 0| 0| 0| 0| 0(c) Fixed O&MLC | 0| 0| 0| 0| 0CC | 0| 0| 0| 0| 0CT | 0| 0| 0| 0| 0SC | 0| 0| 0| 0| 0New H | 0| 7476804| 6191529| 5127175| 4329596

Pumped H | 0| 0| 0| 0| 0VARIABLE COSTS(d) Fuel CostsOld T | 1.4733E+9| 229153561| 245421630| 239518781| 216214731LC | 0| 0| 0| 0| 0CC | 0| 0| 0| 0| 0CT | 0| 0| 0| 0| 0SC | 0| 0| 0| 0| 0(e) Unserved EnergyUn En | 106342797| 4621011| 11983610| 24858143| 39766516(f) Water CostsNew H | 0| 8083023| 6680185| 5520814| 4562656Old H | 0| 0| 0| 0| 0(g) Variable O&M

Old T | 20389071| 3303321| 3910450| 4069316| 3675666LC | 0| 0| 0| 0| 0CC | 0| 0| 0| 0| 0CT | 0| 0| 0| 0| 0SC | 0| 0| 0| 0| 0New H | 0| 8083023| 6680185| 5520814| 4562656Old H | 0| 0| 0| 0| 0Old PH | 0| 0| 0| 0| 0New PH | 0| 0| 0| 0| 0

Total | 1.7003E+9| 650680150| 603826555| 553502337| 500567254

TOTAL COST FOR HORIZON = 4008854730.34

MWh Exp | -96035195| -29876495| -15647596| -14181512| -1078256MWh Imp | 0| 208755563| 192965807| 203751354| 205443098

Res Exp | 0| 0| 0| 0| 0Res Imp | 18285242| 0| 0| 0| 8

Total | 1.6225E+9| 829559217| 781144766| 743072179| 704932104

TOTAL COST FOR HORIZON WITH REVENUE AND PAYMENTS = 4681236746.80


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Chapter 5

Inputs and Outputs to the Model

From the perspective of the general user of the long-term planning model the actual modelwith its formulation and coding can be treated with a “black box”. The general policy useris to be concerned only with the data inputs and the resulting outputs (Figure 5.1). Detaileddescriptions of results from the Southern Africa are available [4-6].

Figure 5.1 General Users Approach to the Long-Term Model

Inputs LT Model Outputs

The long-term model has been tested extensively with the input data supplied by theSouthern African Power Pool (SAPP) and Figure 5.2 shows the input and output file names

as they were organized in June 2000. With each world region or power pool that ismodeled then the names of the output files will of course also change in order to report theresults for each new country that is in the model. The structure and number of the input fileswill not change so significantly. One significant addition since June 2000 is the inclusion ofa natural gas sub-model to the LT electricity trading and expansion model.

A brief description of the functions of the input and output files follows. It is recommendedthat the windows interface is used by the general user. This interface is described at the endof the User Manual together with illustrations of the windows options that are available.The use of the interface makes the model very user friendly and prevents the introduction oferrors from inexperienced editors of the basic model coding.

5.1 Summary of the Files Used in the SAPP Long-Term Model

The input and output files are briefly described here:


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(1) June21.gms - Main program, contains all optimization constraints, optimizes model, nochanges will be made to this file.

Figure 5.2 The Files that Comprise the Southern African Long-Term - Model June 21 2000

Outputs

Prices.out

June21.gms

Therm_exp.out

Data.inc

Hydro.inc

Lines_sapp.inc

Reserve.inc

Uncertain.inc

Sixhr.inc

Thermo.inc

Trade.out

Projects.out

Trans_exp.out

Hyd_exp.out

Angola.out

Botswana.out

Lesotho.out

Malawi.out

NMoz.out

SMoz.out

Namibia.out

NSA.out

SSA.out

Swaziland.out

Tanzania.out

DRC.out

Zambia.out

Zimbabwe.out

June21.1st Projects.out

Inputs

Output.inc SAPP.out

Flows.out


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Data Files:

(2) Thermop.inc – Contains data on the cost to expand new thermal stations, data on existingcapacities, maximum expansion of existing capacities, and the capital recovery factor on the

thermal stations.

(3) Lines_sapp.inc – Contains cost of expanding new lines and cost of new lines. Loss ofenergy due to resistance in old lines, loss of energy due to resistance in new lines, initialcapacity of new lines, capital recovery of new lines, and cost of additional capacity on newlines.

(4) Hydro.inc – Contains data on the cost to expand new hydro stations, data on existingcapacities, maximum expansion of existing capacities, and the capital recovery factor on thehydro stations.

(5) Sixhr.inc – Peak demand for each region: highest demand for one hour for current year.

(6) Uncertain.inc – Contains: data on uncertainties (i.e. expected rainfall).

(7) Reserve.inc – Contains: Autonomy factor – self reliance of each country, reserve marginfor each country, forced outage rate for both transmission lines and for all plant types incountry, unforced outage rate for all plant types in country, and largest generator station foreach country.

(8) Data.inc – Contains data on the demand growth, and domestic growth, which can bechanged by user.

(9) Output.inc – Generates the output files which contain the necessary data used foranalysis.

Output Files:

(10) June21.lst – Generic output file created by gams.

(11) Therm_exp.out – Thermal expansion plans from running the model.

(12) Hyd_exp.out – Hydropower expansion plans from running the model.

(13) Trade.out – Trade quantities from running the model.

(14) Trans_exp.out - Transmission expansion plans from running the model.

(15) Projects.out – All of the chosen projects are defined in this file.

(16) Country.out – The expansion results as they pertain for each country, and SAPP as awhole. (Angola.out, Botswana.out, etc.)


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(17) SAPP.out – Regional output reports.

(18) Prices.out – Trade pricing analysis.

(19) Flows.out – Export/Import flows

5.2 Weighting of the Seasons, Days, and Hours

Consider how do we change the number of day types in each year? We do not actuallychange the number of day types but we can change the weightings. The model has threeday types – peak day, off-peak day, and average day. The total number of days must alwaysadd up to 365. Weightings for the days are shown in Table 5.1.

The SAPP model uses a 25:75 weighting for the winter and summer seasons. There arethree types of days; peak day, average day, and off-peak day. There are12 average nighthours and 12 day hours; 8 average hours, and 4 peak hours.


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Table 5.1 Weighting of Seasons, Days and HoursWeights

Type Season Day Hour Season Day Hour Total Hours Percent Cumm.

1 Summer Average Avdy 0.75 260 12 2340 26.79% 26.79%

2 Summer Average Avnt 0.75 260 8 1560 17.86% 44.64%

3 Winter Average Avdy 0.25 260 12 780 8.93% 53.57%

4 Winter Average Avnt 0.25 260 8 520 5.95% 59.52%

5 Summer Peak Avdy 0.75 52 12 468 5.36% 64.88%6 Summer OffPeak Avdy 0.75 52 12 468 5.36% 70.24%

7 Summer Peak Avnt 0.75 52 8 312 3.57% 73.81%

8 Summer OffPeak Avnt 0.75 52 8 312 3.57% 77.38%

9 Summer Average Hr9 0.75 260 1 195 2.23% 79.61%




13 Winter Peak Avdy 0.25 52 12 156 1.79% 88.10%

14 Winter OffPeak Avdy 0.25 52 12 156 1.79% 89.88%

15 Winter Peak Avnt 0.25 52 8 104 1.19% 91.07%

16 Winter OffPeak Avnt 0.25 52 8 104 1.19% 92.26%

17 Winter Average Hr9 0.25 260 1 65 0.74% 93.01%18 Winter Average Hr19 0.25 260 1 65 0.74% 93.75%

19 Winter Average Hr20 0.25 260 1 65 0.74% 94.49%

20 Winter Average Hr21 0.25 260 1 65 0.74% 95.24%

21 Summer Peak Hr9 0.75 52 1 39 0.45% 95.68%

22 Summer Peak Hr19 0.75 52 1 39 0.45% 96.13%

23 Summer Peak Hr20 0.75 52 1 39 0.45% 96.58%

24 Summer Peak Hr21 0.75 52 1 39 0.45% 97.02%

25 Summer OffPeak Hr9 0.75 52 1 39 0.45% 97.47%




29 Winter Peak Hr9 0.25 52 1 13 0.15% 98.96%30 Winter Peak Hr19 0.25 52 1 13 0.15% 99.11%

31 Winter Peak Hr20 0.25 52 1 13 0.15% 99.26%

32 Winter Peak Hr21 0.25 52 1 13 0.15% 99.40%

33 Winter OffPeak Hr9 0.25 52 1 13 0.15% 99.55%




8736 100.00%

Season

SAPP Winter 0.25 SAPP Winter makes up 1/4 of the year.

SAPP Summer 0.75 SAPP Summer makes up 3/4 of the year.

Day

Peak 52 52 days a year are classified as Peak days.

Average 260 260 days a year are classified as Average days.

Offpeak 52 52 days a year are classified as OffPeak days.

Hour

Avnt 8 8 hours a day are classified as Average Night hours

Hr9 1 Hr9 corresponds to the 9th hour of the day.

Avdy 12 12 hours a day are classified as Average Night hours

Hr19 1 Hr19 corresponds to the 9th hour of the day.

Hr20 1 Hr20 corresponds to the 9th hour of the day.Hr21 1 Hr21 corresponds to the 9th hour of the day.


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Chapter 6

Electricity Policy Analysis Scenarios

6.1 Short-Term and Long-Term Modeling

Short-term (ST) modeling can be for almost any length of time less than 12 months. It can be a period of hours, days, weeks, or months. Long-term (LT) modeling is normallyreferring to several years. LT models are typically anywhere between 5 years and 20 years.

6.2 Electricity Forecasting Policy

The state Governments’ creation of Purdue’s State Utility Forecasting Group (SUFG) was toensure that the State of Indiana had a dependable, accurate, and impartial assessment of thedemand for electricity in Indiana and the Mid-West USA (1985, Senate Bill 29). Theseforecast figures for growth in electricity demand are vitally important for any utility or state.Across the United States and in the industrialized national generally a growth rate of about2% is typical. In the developing economies the growth rates are often quoted as beingdouble or triple this 2% growth rate and even more. A policy of needing to accuratelyforecast the growth rate is especially important for the electricity market modeling work.Very different long-term consequences occur when a 4% increase to growth is made insteadof a 3%. It can be appreciated therefore what the consequences might be when an 8% or12% value is given.

Over a 20 year planning horizon, with a constant growth rate of 2% per year, there is acompounded total increase in growth of 48%. Note the enormous differences in totalexpected growth for a 20 year planning horizon when rates of 4%, 8%, and 12% are used:

1.0220 = 1.48, 1.0420 = 2.19, 1.0820 = 4.66, 1.1220 = 9.64

6.3 Electricity Trading Commodities

The Purdue long-term electricity trade model (PLTETM) trades in two commodities:

(a)

Megawatt reserve power (MW)(b) Megawatt hour energy (MWh)

During each hour modeled the amounts of energy or reserve power traded will vary. Thistakes place for each hour over the total planning horizon (typically this can be 10 years).Most utilities will be interested in trading MW but in situations where a utility cannot meetits production demand, or where much cheaper supplies are available (hydropower etc) thenMWh are traded.

6.4 Policy for Unmet Reserve and Distributed Generation


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In many situations, especially in the developing economies, the power supply, in a certainhour might not be able to meet the demand. Should there be some policy regarding “unmetreserve MW” (UM) such as a penalty charge for not being able to meet demand? In theindustrialized counties there is normally a legal requirement that reserve margins must

always be securely maintained. Power shortage can be very costly to an economy and so thePLTETM places a penalty charge of $2 million per MW if a country fails to meet its daily peak MW demand.

The policy towards distributed generation (DG) is also represented in the PLTETM. If thedaily production level of electricity (for each hour of each day) cannot be met then it isassumed that small stand-by generators (DG) will be available. This is particularly relevantfor rural areas with intermittent supplies and in developing economies when there is a shortfall. The estimated cost for purchasing and operating these small generators has beenestimated at 14 cents per kWh ($140 per MWh). This is the cost given in the model forunserved energy (UE).

6.5 Short-Term Power Trading and Tariff Setting

The PLTETM can be used as a short-term model by limiting the length of the planninghorizon. Typically it is used as a 10 year model (5 time periods with each period being 2years long or 10 periods with each period being 1 year long). If however only a 1 year planning horizon is specified then there will be no capacity expansions taking place and themodel will effectively become a short-term or dispatch model only. The amount of tradingtaking place (using a cost minimization objective) will be subject to a demand constraint:

Such that over time: Generation + Imports + DG = Demand – Exports

{ ie: Total cost = Operational costs + Penalty Costs of unmet demand/power } (Fuel & maintenance)

The cost of trade is initially met by the supply generator in the model but in the finalanalysis the model will also allocate the gains from trade, between the exporting andimporting country, on a equal basis (50% - 50%). The exporting country therefore obtainsrevenues (post optimality) for the exports and the importing country makes costs savingsfrom not generating with its’ own more expensive generators. The present defaultarrangement with the PLTETM is such that a trade tariff of 6 cents/kWh will take place

when the marginal cost of the exporting country is 2 cents/kWh and the marginal cost of theimporting country is 10 cents/kWh.

Trade Tariff = Marginal cost {(Exporter cost + Importer cost)/2}


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6.6 Reliability of Power Supplies

The reliability policy for supplies in electricity is incorporated into the model with two parameters which specify:

•

A reserve margin for thermal power generation

• A reserve margin for hydropower generation

Each country reserve parameter may be given a specific value depending upon the level ofreliability required in that country or utility. In coordinated centrally controlled power poolsthe reliability of supplies can be much more cost effective than with several isolated utilities.With economies of scale and centralized coordination a single reserve unit can provideservice to several utilities. Reliability policy can therefore be significantly proved to bemuch cheaper within a coordinated power pool. Typically a reserve margin value of 10% isused in hydropower generation and a value of 19% is used in thermal generation.

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