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An overview of the Gas Analysis Modeling System (GAMS)
Encry>~ Vol. IO. No. 8, PP. 951-962. Printed in Great Bntain
1985
AN OVERVIEW
0360-5442/X5 $3 00 + .oO Pergamon Pres Ltd.
OF THE GAS ANALYSIS SYSTEM (GAMS)?
MODELING
ANDY S. KYDES, MARK J. MINASI, STEVEN H. WADE, BRADFORD J. WING EnergyEconomy Systems Analysis Division, Brookhaven National Laboratory. Building 475. Upton.
NY 11973. U.S.A.
and BARBARA MARINER-V• LPE and RICHARD P. O’NEILL Office of Oil and Gas, Energy Information Administration. U.S. Department 1000 Independence Ave.. SW., Washington, DC 20585. U.S.A. (Received
of Energ).
30 June 1984)
Abstract-This paper is an overview of the March 1984 version of the Cias Analysis Modeling System (CAMS), the detailed natural gas market model used by the Energy Information Administration (EIA) to analyze the U.S. natural gas markets.
I.
INTRODUCTION
The need for a detailed analysis capability for the complex U.S. natural gas production/ delivery/demand system was an outgrowth of the oil crises in 1973-1974 and the perception that natural gas was a scarce, high quality fuel which had to be restricted in its use through legislation. The Powerplant and Industrial Fuel Use Act (PIFUA. Public Law 95-620) restricted the use of natural gas and the Natural Gas Policy Act of 1978 (NGPA, Public Law 95-62 1) provided an agenda for the phased decontrol of most natural gas prices at the wellhead by 1985. The NGPA specifies formulas for calculating the maximum price of each category of gas and the date of decontrol for most of those categories. Gas in other categories remains subject to price ceilings. The NGPA categories are defined by the physical characteristics of the well, the age of the well and to whom it was sold. The first comprehensive natural gas legislation in the U.S.. the Natural Gas Act (NGA) of 1938, brought natural gas sold in the interstate markets under federal control. The NGA provided statutory limits on the price that interstate pipelines could bid for gas but provided no limits on the bid price that intrastate pipelines could offer for the same gas. It became clear in the early 1970s that federal wellhead price controls were seriously distorting the natural gas market and Congress. after 18 months of debate, passed the first comprehensive natural gas legislation (NGPA) since the Natural Gas Act of 1938. The NGPA was intended to reduce the gas market distortions by bringing the intrastate gas market under federal price control and to gradually eliminate price ceilings on most new gas discoveries. The Gas Analysis Modeling System (GAMS) was developed over a period of three years for the Analysis and Forecasting Branch, Office of Oil and Gas, Energy Information Administration (EIA). This paper provides an overview of the March 1984 version of GAMS used in support of the 1983 Annual Energy Outlook (AEO).’ GAMS models the production, transmission, distribution and consumption of natural gas in the U.S. These four activities are carried out, respectively, by the producers. pipeline companies, distributors and consumers. Gas production capacity is a function of the number of active wells which. in turn, is determined by past and present drilling activity. Drilling activity is divided into exploratory t This paper was prepared DE-ACO2-76CHOOO 16.
as an account
of work sponsored
by the II.% Government
under contract
number
952
A. S. KYDES et al.
and developmental categories. Exploration yields new additions to the stock of known reserves. Development determines the rate of production from the stock of known reserves. Once gas is discovered, producers will offer to develop these reserves under longterm contractual agreements. Since long-term contracts can carry large amounts of risk, general provisions that govern both the price and quantity of gas are usually included. The need to analyze alternative decontrol and pricing options and their impacts on the U.S. natural gas system provided the main incentive for EIA to develop CAMS. GAMS has been used to analyze legislative proposals aimed at changing the regulatory environment of the natural gas market and its results have been used in debates in the U.S. Congress. 1.1. History of GAMS development GAMS was developed under the auspices of the Analysis and Forecasting Branch, Office of Oil and Gas, Energy Information Administration. The EIA, The National Bureau of Standards (NBS), Brookhaven National Laboratory (BNL), as well as several consultants and subcontractors have contributed to the design, implementation and refinement of this model. Model development began in 1981.T Following the completion of the development of GAMS in 1982, modifications and enhancements to GAMS were initiated to improve its projection accuracy, timeliness, flexibility and capabilities for analyzing the complex natural gas market. At the time, the modeling efforts were supplemented by BNL.$ GAMS is maintained and operated at EIA. 2.
GENERAL
DESCRIPTION
OF
GAMS
GAMS produces forecasts of natural gas production, consumption and prices annually through 1995. While the model structure is generally at the state or substate level, detailed reports are available for the 10 Federal (or DOE) regions. GAMS neither requires nor provides much detail on the rest of the U.S. energy-economy system. Several different mathematical structures are incorporated into the GAMS components in order to represent the modelers’ perspectives of how the different groups interact. For example, the producers were perceived to optimize their expected profits when exploring for new reserves or developing new reserves and this led to a linear programming formulation for the supply representation. The reconciliation of production from existing reserves with consumer demand led to an equilibration framework constrained by the institutional structure of the gas market-including the regulatory structure, long-term contracts and other pricing conventions. The interaction of producers with pipeline companies within the natural gas institutional framework was viewed as a constrained equilibration between producers who were assumed to market all of their newly developed reserves and pipeline companies who were assumed to maximize their expected natural gas sales. This led to a dynamic programming formulation for representing pipeline company behavior and an equilibration methodology for the allocation of new reserves. Finally, different levels of regional definition were required by the different GAMS components in order to accurately reflect the natural gas market. Consequently, consumer demand is modeled at the state level by end-use sector to capture differences, for example, in the fuel switching potential, but the supply model (PROLOG) distinguishes six producing regions with their associated transmission costs. The interface between supply and demand is the detailed sales network defined by the Market section. GAMS has been integrated with the Intermediate Future Forecasting System (IFFS)2 to provide a consistent method for analyzing the feedbacks of natural gas markets with the rest of the U.S. energy-economy system. IFFS is an annual, regional, equilibrium model of the U.S. energy-economy system which is also used by the (EIA) to develop projection information for the Annual Energy Outlook (AEO). t The following individuals made significant contributions to this effort: R. P. O’Neill, J. Heinkel, W. Kurator, B. Mariner-Volpe, and W. Trapmann, EIA; P. B. Saunders, C. J. Witzgall, NBS; C. Mylander, U.S. Naval Academy; W. Stewart, College of William and Mary. Additional support to these initial efforts was provided by numerous individuals at EIA and NBS. $ The principal contributors were A. S. Kydes, M. J. Minasi, S. H. Wade, B. J. Wing, R. M. Saltzman, and H. M. Leuterio.
An overview of GAMS
953
The integration of IFFS and GAMS benefits GAMS because of the increased detail for sectoral gas demands, electric utility consumption of gas and oil prices. IFFS benefits from the integration because of the increased gas detail available from GAMS with regard to natural gas production, transmission, distribution and pricing. The 1983 AEO forecasts were developed by the integrated IFFS and GAMS models. The general operating sequence for GAMS in each year is as follows: Step I.
2. 3. 4. 5. 6. 7.
Description
Component
System Update Annual Reserve Demand Bidding these Report
Control Price Market Prolog Market
initialization annual prices for gas by category demand and supply balancing projections for future years projections for future years for new reserves and the allocation of reserves generation and intertemporal operations
Bid and Award Control
The first section is named Control. This section supervises the execution of all other sections of the system. It performs the data initialization for the model and determines how often and in what sequence each of the other sections is executed. One of its tasks is maintenance of the Gas Reserves Supply Table (GRST) which specifies the disposition of known reserves (NGPA category, price, ownership, quantity of reserves, production potential, take-or-pay provisions), Control includes additional reserves in the GRST as provided by the PROLOG module, updates the quantity and price of new reserves awarded to the pipelines with information provided by the Bid and Award section. and subtracts current year production from reserves in the GRST table using information provided by the Market section. The Price section is the first computational section of GAMS executed for each forecast year. Its purpose is to calculate the wellhead price for each of the reserve blocks available for production in the current forecast year and to make this information available to the other sections of GAMS. Price computes the wellhead price of gas based on the type of market for the gas (interstate or intrastate), the NGPA category of the gas, the marginal price for decontrolled gas. the year of the contract between the producer and the pipeline. restrictions on the price according to contract pricing provisions. and the legislation assumed. START 4 CONTROL ---+
RESERVES INFORMATION
Gas Category
Price BID/AWARD
Excess
Deliverability Volumes
Fig.
1. CAMS
system
chart.
954
A.S.KYDES
et al.
The next step in the operating sequence for GAMS is accomplished by Market. Market determines, for the current solution year, the consumption volumes and the associated prices by region and end-use sector. It does so by solving for the economic equilibrium, the level of wellhead production such that the cost of producing and transmitting is equal to the price that end-users are willing to pay for that gas. As a result of take-or-pay provisions and the long-term nature of natural gas contracts, gas supply curves can be U-shaped leading to multiple equilibrium points. A bisection algorithm is used to find the highest production equilibrium. The Gas Reserve Supply Table (GRST) is the main interface with the other sections of GAMS. At the beginning of each iteration year, the GRST contains the information necessary to determine supply curves for each pipeline system. At the end of the Market iteration, the GRST information is updated to reflect the draw-down of reserves that has taken place. PROLOG simulates, on an annual basis, the exploration and development of onshore oil and gas reserves in response to expected profitability, capital resources, costs, and the availability of drilling rigs. The projections are based on price expectations that are updated each year based on the current market clearing prices. PROLOG is called once per forecast year and provides, via the GRST, reserve additions by NGPA category and parameters necessary to estimate the production potential of the reserves for each year through the bid model horizon (reserve projections for years beyond the present forecast year are used by the BID model). Some of the calculations in PROLOG are based on information provided by other sections in GAMS such as the latest available decontrol price. Exogenous offshore projections are passed to GRST by PROLOG. Finally, PROLOG adjusts the menu of gas prices associated with the reserves based on the forecast year and the scenario to be modeled. The next step is accomplished by the Bid and Award section. This section establishes the current market clearing price for new reserve additions based on: price of reserves currently dedicated to individual pipeline systems, estimated reserve additions for future years, and an estimated price and quantity of gas that can be marketed over the next several years. Estimates of consumer demands are determined by testing the Market model’s response to a series of prices. The generation of these demand projections is a procedure in Market known as NXTSYS.3 Projections of future reserve additions and demands are required for each model year because the Bid section uses a dynamic programming approach to maximize each pipeline’s expected gas flow over a userspecified planning horizon. (For each iteration year, only the reserve additions for the next year are allocated to the pipelines.) Each pipeline system is treated as an independent supply/demand system. Bid examines the GRST table using both past natural gas reserves already allocated to specific pipeline systems and a forecast of natural gas reserve additions from PROLOG in order to determine a bidding strategy for each pipeline system. Bid assumes that each pipeline system independently seeks to maximize the quantity of gas it expects to market over a 2-6 year time horizon. The length of the time horizon is a user-specified input and a 2 year time horizon was used in the 1983 AEO. The length of the time horizon determines the length of foresight used by pipeline companies for planning purposes. A 6 year time horizon in BID, for example, would imply that each pipeline company uses 6 years of reserve projections (from PROLOG) and demand projections (from Market) to determine this year’s optimal bid. Bid computes a set of price/quantity pairs for each pipeline system (new reserves demand curves) and passes these to the Award module to determine the allocation and pricing for the new reserves. After individual demand curves for new reserves have been established by Bid for each pipeline system, the Award module establishes a national, industry-wide demand for new natural gas reserves. Award then determines the price at which the demand for the new uncommitted reserves equals the supply of new gas reserves (the market clearing price), the decontrolled natural gas price, the price for the new reserve blocks and the allocation of the various gas reserves among the pipelines; this information is entered into the GRST. At this point, the iteration for 1 year is complete. If the requested forecast horizon has not been reached, a few adjustments are made to the GRST and the process is repeated for the following year starting with the Market section.
An overview of CAMS 3. SYSTEM
OVERVIEW
955 OF
CAMS
CAMS consists of three main components or submodels. PROLOG models developmental and exploratory drilling activity. Market models the production, transmission, distribution and consumption of natural gas. Bid and Award models the acquisition of new gas reserves by pipelines. During a model run, each of these three components are run in turn for each successive model year. NLIilII.UI g&v .sll/~plj’ The natural gas supply forecasts used in GAMS are obtained from two submodels: the PRoduction of Onshore Lower-48 Oil and Gas (PROLOG) supply mode1,4.5 and the Outer Continental Shelf (OCS) model.6 PROLOG is embedded within GAMS whereas the OCS model is run alone and the results are fed into GAMS as input. Potential supply from ,4laska to the continental United States can be specified as an exogenous input but was omitted from this analysis: the availability of synthetic and imported gas are exogenous estimates. PROLOG is an annual, linear programming formulation of exploratory and developmental drilling in the continental U.S. It is the section of GAMS that provides the natural gas supply forecasts for each of the six supply regions by NGPA category. PROLOG maximizes the expected present value of profits from exploratory and developmental drilling based on a discounted cash flow analysis, subject to capital availability, engineering constraints and other institutional constraints. Given a sequence of expected annual prices. PROLOG provides the GAMS module with a slate of natural gas reserve additions by year, region and NGPA category. PROLOG also acts as a transfer point for natural gas reserve blocks which have been derived from the OCS model and need to be made available for bidding and production in the rest of GAMS. The NGPA categories employed for exploratory drilling are 102 onshore (new pools discovered after February 1977). 102 offshore. and three classes of 107 gas (deep. tight sands, and Devonian). The expected price path for the first forecast year is provided to PROLOG from exogenous data. .4fter the first year, the expected price path is updated by using the GAMS-derived decontrolled gas price and the market clearing price to generate a new price series. The linear program is formulated so that the discounted present value of profit is maximized. This is subject to: (1) the sum of rotary rigs used does not exceed total rigs available: (2) the change in national drilling expenditures equals a linear combination of this year’s and last year’s change in revenues; (3) the total number of rigs available is a linear function of the last year’s total number of rigs and total expenditure on drilling: (4) this year’s drilling activity is bounded above and below by historically derived parameters and last year’s drilling level. This linear program is solved sequentially for every year of the forecast. The solution provides forecasts of reserves added from exploratory drilling and forecasts of drilling footage and production from all drilling categories. 3.1
3.2. AIur-liCl Market is a regional, annual (or, optionally, semiannual) model of production, transmission, distribution, and consumption of natural gas in the continental United States. Market consists of 17 distinct pipeline systems each of which contains its own supply and demand components. Market’s primary outputs are projections of annual state. regional or national consumption of gas and annually averaged prices paid by end-users within each state from 1980 to 1995. Also included are summaries of the annual operations and transactions of the principal transmission and distribution companies, including sales and take-or-pay defaults (the minimum amount of gas which must be paid for whether or not the gas is desired). The pipeline networks in Market. Each of the 17 pipeline systems is a network of sales relationships between pipeline companies, distribution companies and end-users. These sales relationships are assumed constant throughout a model run. That means for example, that a distribution company will always purchase gas from the same (primary) supplier although the quantity purchased will vary. This assumption is required for the equilibration procedure which is described in detail below.
A. S.
956
KYDES
el ai.
These networks represent actual pipeline systems or aggregations of several pipeline systems as shown in Table 1. The networks themselves are comprised of nodes and arcs. Each node in the network represents either a specific agent (e.g. gas distribution company) or an aggregated group of the same agent type. An arc or link between two nodes represents a sales transaction between two agents. Each network has a tree structure with arcs branching out from a single supply node or root node pipeline to the other pipeline, distributor and end-user nodes which it serves. The supply at the root node pipeline is considered equivalent to the wellhead supply. A tree structured network has the property that there is exactly one path (arc) between any two nodes. Thus each node in a network must have a unique predecessor or supplier. The unique predecessor node is referred to as the primary supplier (or primary arc). Each node’s designated primary supplier was that node’s largest domestic volume supplier in 1980. These primary arcs are illustrated by the solid lines in Fig. 2. A pipeline or distributor may also be served by secondary suppliers which represent transfers of gas between pipeline networks and imports. These secondary arcs are represented by dashed lines in Fig. 2. The distinction between primary and secondary arcs is crucial during the equilibration phase of Market when prices and quantities for a particular year are modeled. Only gas volumes and prices on primary arcs are allowed to vary during this phase. The secondary arc volumes and prices are determined prior to and remain fixed during equilibration. The secondary arc prices and quantities vary only from year to year, not within a year. End-user nodes represent the aggregate demand behavior at a state or substate level. A residential node, for instance, represents all of the residential customers of a particular distributor in a given state. Utility and industrial nodes are further disaggregated between switchers (those with alternate fuel-burning capability) and non-switchers. Thus, a Table
I. The pipeline
Number of agents
Total system flow, 1980 (TBtu)
2 3
91 179 319
1228 598 1030
4
233
910
5 6
98 285
874 1541
229
918
8
143
1088
9
349
863
10
158
784
11
271
815
12
414
1566
I3
130
537
14
42
425
15 16 17
99 62 77
3694 789 1526
System number
systems
in Market.
Actual
pipelines
modeled
or based upon
El Paso N.G. Co. Columbia Gas Transmission Co. Tennessee Gas Pipeline Co.: Tennessee Natural Gas Lines Inc.: Alabama Tennessee Natural Gas Co. Texas Eastern Transmission Corp.; Algonquin Gas Transmission Co.: Consolidated Gas Supply Corp. Natural Gas Pipeline Co. of America Mississippi River Transmission Co.; United Gas; Texas Gas Transmission Corporation Transcontinental Gas Pipeline Corp. Transwestern Pipeline Co.; Cities Service Gas Co.; Arkansas Louisiana Gas Co. Florida Gas Transmission Co.; Southern Natural Gas Co. Michigan Wisconsin Pipeline Co.; Midwestern Gas Transmission Inc./Great Lakes Gas Transmission Co.: Aggregated Midwest Area Agents Northwest Pipeline Corp.: Colorado Interstate Mountain Fuel Supply Co.: Kansas Nebraska Natural Gas Co.; Montana Dakota Utilities: Aggregated Mountain Area Agents Panhandle Eastern Pipeline Co.: Trunkline Gas Co.: Northern Natural Gas Co. National Fuel Gas Supply Corp.; Aggregated Appalachia Area Agents Pacific Gas Transmission Co.: Aggregate Far West Aggregated Texas-New Mexico Area Agents Aggregated Oklahoma-Kansas Area Agents Aggregated Louisiana-Arkansas Area Agents
An overview
Fig. 2. Diagram
of a sample
distribution
of CAMS
network
with two pipeline
systems
distributor may have up to six customer classes, representing the residential, commercial, electric utility and industrial sectors. End-use sector nodes are each served by a single distributor and can have no secondary supplies (arcs). Each pipeline system has its own supply system connected primarily to the root node. Sources of supply include dedicated reserves (offshore and onshore), imports, Alaskan gas, and inter-pipeline sales. Each system has a mapping of reserves and reserve characteristics which define its supply system. This supply system is modeled by entries in the Gas Reserve Supply Table (GRST). Along with NGPA category information, takeor-pay information on reserves is available from the GRST. The volumes that can be produced by a particular reserve block in any year are calculated from exogenously specified production profiles. These profiles express maximum production rates as a function of the maturity of the reserves in question. The pricing of a given annual purchase at the wellhead is a function of the withdrawal strategy. In Market, there are two alternate draw-down strategies, minimum cost take and rateable take. The user selects the strategy for each run. In the minimum cost take strategy, prices are calculated assuming that quantities are sequentially withdrawn from the dedicated reserve blocks in a way that minimizes the average purchase cost from producers subject to the take-or-pay provisions. Under the rateable take strategy. the take is allocated proportionally to the deliverabilities of the dedicated reserve, after the takeor-pay obligations have been satisfied. Given a quantity of required gas and a strategy for ordering contracts to draw from, an average price of gas can be obtained for any given demand quantity. Given the tree structure of the network, wellhead prices and quantities from the root node can be easily translated into prices to the end-user nodes. Beginning at the root node, prices to successive nodes are increased to reflect tariffs (see below) and transmission losses. Quantities are also adjusted for transmission losses. Prices and quantities are also adjusted to reflect any transactions on secondary arcs. In this manner. the wellhead price and quantity are propagated up the network to the end-user nodes. In a similar fashion, quantities from the end-user nodes can be accumulated down the network to the root node accounting for losses and secondary transactions along the way. Pipeline and distributor tat-l% in Market. The term tariffs in Market refers to the charges in addition to purchased gas costs that pipelines and distribution companies are allowed to recover. This use of the term differs from its use in regulatory proceedings
958
A. S. KYDES
et al.
where it denotes the entire rate schedule that recovers both the purchased gas costs and other costs. As normally found in actual rate structures, the tariffs in Market have two components: fixed charges and variable charges. Fixed charges are quantity invariant, that is, they must be paid regardless of the quantity purchased. Variable charges are assessed on a per unit of sales basis and are therefore often referred to as commodity charges. Pipeline tariffs are set by direct exogenous specification for each arc of the base network. The fixed charge is the product of the demand rate and the expected peak day volume. The variable charge is an input constant. Pipeline tariffs remain fixed in constant dollars over the forecast period. A distributor rate model is used to produce tariffs for all distributors with initial (1980) end-user demands in excess of 1000 BBtu (billions of Btus). Roughly one-third of the distributors have loads which meet this criterion. Tariffs for the remaining two-thirds of the distributors are exogenously specified and are fixed in constant dollars at these levels over the forecast period. The distributor rate model consists of a series of equations which define the financial, physical and regulatory environment of the individual distributors. Equations are included for taxes, depreciation, operation and maintenance expenses and utility plant in service. These equations are primarily functions of base year demand and number of customers and the expected growth in demand and number of customers. Once tariffs have been calculated, they are separated into fixed and variable tariff components. The unitized cost of gas to a distributor’s customer consists of the sum of the distributor’s cost of purchased gas, the variable charge and the fixed charge divided by quantity consumed. Modeling price sensitivity of end-user-node demands. GAMS does not have detailed endogenous demand models. The responsiveness of the end-user nodes to changes in gas prices is determined by exogenously specified price elasticities which vary by end-user sector and DOE region. These elasticities are applied to base node demands which are derived from regional projections from the IFFS model. In this way, GAMS can indirectly utilize the detailed sectoral demand models of IFFS. Quantities, prices, and elasticities for the residential, commercial, and industrial end-user sectors and for the 10 DOE regions are taken from the solution file of a prior IFFS run. The utility demand for natural gas is taken from the IFFS utility module solution file and is represented by a set of price/quantity pairs (step function) by federal region and year. A sharing algorithm based on 1980 historical shares converts the regional IFFS demand projections into reference node quantities for the Market end-user nodes. Price sensitivity of the end-user nodes is incorporated as follows. Demand at a node is equal to the reference node quantity modified by a function of the ratio of the gas price (determined by propagating the root node supply price) at the end-user node to the price from the IFFS solution file. The price ratio is exponentiated by the input elasticity which is appropriate for the end-user sector and region. This use of the elasticity is similar to that which would be derived from a log-linear demand function. GAMS may also be run in conjunction with IFFS. In such a run, the elasticities are used only as approximations to the behavior of the IFFS demand models. By iterating between IFFS and GAMS, the price responsiveness of the nodes is determined by the actual price responsiveness of the IFFS demand modules. The equilibration process. Each of the 17 pipeline systems is equilibrated separately. Only the primary arc prices and quantities vary during this process. The results are then summed to yield the state, regional or national totals. Following equilibration on the primary network, the prices and gas flows on the secondary network are adjusted for the next forecast year. The prices of gas on the secondary arcs are exogenously set to grow at a pre-defined percentage rate; the quantities on the secondary arcs for the next forecast year are adjusted to satisfy the requirement that the percentage change in the value of sales for each secondary arc into a node must equal the percentage change in the value of sales to that node on the primary arc. This secondary network can be viewed as a boundary condition on the equilibrium solution for the 17 systems because it determines
An overview
of GAMS
959
the minimum amount of gas that each pipeline system must transport. Separation of the secondary sales network is a network simplification technique used in Market to allow prices and quantities to be uniquely propagated up and down the network during equilibration. By fixing the secondary arc prices and quantities during equilibration, cycling between the primary and secondary networks is eliminated in the network. ‘The equilibration process is the determination of root node (or wellhead) production levels and prices such that the propagation of these prices and quantities to the end-user nodes results in all the gas available to these nodes being sold. This requires a balancing of wellhead supply price sensitivity to quantity against the price sensitivity of the end-user node demands. For a pipeline which withdraws gas from its least expensive reserves first (the minimum cost take strategy), the supply at the wellhead will be U-shaped. Because take-or-pay provisions require a pipeline to pay for a certain percentage of available production whether or not it is actually taken, there is what amounts to a minimum gas expenditure for levels of wellhead demand up to the (aggregate across reserves) take-or-pay limit for each pipeline system each year. As demand at the wellhead increases up to the take-orpay minimum, the average unit price of gas decreases. For wellhead demands above that minimum. the average unit price of gas increases as would normally be expected. The presence of this U-shaped supply curve complicates the equilibration process as there may be multiple equilibration points. Equilibration is. in principle, the solution to pairs of simultaneous supply and demand equations. The simulated process is slightly more complicated in that each demand quantity at the wellhead results from accumulating end-user node demands down through the pipeline system. accounting for transmission and distribution losses, transfers in and out of storage. and secondary purchases and sales along the way. l‘he equilibration procedure checks test price/quantity pairs from the wellhead supply curve for feasibility. The check for feasibility begins by propagating the test price/quantity up the system to the end-user nodes. Then the end-user demands implied by the end-user node prices are accumulated down the network to the root node. Next, the relationship between the initial wellhead supply quantity and the accumulated wellhead demand quantity is checked. If the wellhead demand quantity is equal to or greater than the wellhead supply quantity. the initial test price/quantity point on the wellhead supply curve is considered feasible. If the accumulated demand is actually greater than the supply quantity. an excess demand condition occurs which results in curtailments. If the two quantities arc equal (within some tolerance) an equilibrium condition exists. If the accumulated demands are less than the wellhead supply. excess supply exists and the initial test pair is deemed infeasible. This occurrence is depicted in Fig. 3. In such an event. a new smaller quantity will be tested and a search algorithm to hnd the equilibrium begins. The search algorithm for finding the equilibrium price/quantity pairs involves dividing the quantity interval of the wellhead supply between the maximum feasible production level (as determined by the GRST information) and the minimum required production level (determined by committed flows forced by secondary arc boundary conditions) into IO equal steps. The process begins with the maximum producible quantity and sequentially checks each test price/quantity pair for feasibility. If the maximum supply quantity is not feasible because of excess supply (see Fig. 3) the model tests progressively lower wellhead supply price/quantity pairs until either: (1) no quantity will clear which causes equilibration failure due to continuous excess supply, (2) clearance or equilibration occurs, or (3) the test quantity/price results in excess demand. In this last case. we have found two points on the wellhead supply function, one with excess supply, the other with excess demand. If. as in Fig. 3. both supply and demand are continuous functions. an exact equilibrium condition exists in this subinterval. This subinterval is then successively bisected until the starch interval size is smaller than some user-delined threshold siLe (e.g. 20.000 billion Btus) and equilibration is achieved. The final equilibration price/quantity pair is the point in the search interval with the largest quantity. Once the conditions for equilibration have been met. Market has finished its tasks.
A. S. KYDES et al Price +
SupplyQuantity
-Excess
t
i
Fig. 3. Excess supply at the wellhead during equilibration. equilibrium, we first use the GRST information to determine a at (1). We then propagate the supply price to the end-use nodes wellhead demand quantity (2). The difference between Q and
To test if a quantity Qs is the corresponding average supply price and accumulate the corresponding the demand quantity is the excess
supply.
Information on end-user consumption and price is passed along to the report writer. Data on reserve drawdowns at the wellhead are passed to Bid and Award and PROLOG, and data on take-or-pay defaults is also passed to Bid and Award. 3.3. Bid and Award The supply model (PROLOG) specifies the quantity of reserves that has been added and is open for bids in the current model year. In addition, PROLOG produces an estimate of reserve additions for each future year up to five years into the future. The Bid and Award component establishes a price at which all available reserves (current model year) will be bought based on the projected future reserve additions and projected demands for natural gas obtained from the transmission and distribution module in Market. The price established by this process is referred to as the market clearing price, and it is fed back to PROLOG for the next model year to adjust the expected prices for natural gas. This approach is a break from the traditional modeling approach, which views pipelines as purchasers of spot-market production in a given time period. Purchases of produced gas not under long-term contract are very limited. Pipelines and other purchasers generally contract for the receipt of gas volumes over time according to specified contract terms. The long-term nature of such contracts requires the consideration of expectations in the transaction. The Bid and Award module is composed of two parts: the bidding routine, Bid, and the awards routine, Award. Conceptually, Bid develops individual pipeline company demand curves for new reserves based on the assumed behavior that pipeline companies attempt to maximize gas sales. Award develops a pipeline industry demand curve from the individual pipeline demand curves and finds the (one) industry-wide price for which the supply of new reserves equals the industry demand for new reserves (market clearing price). For each pipeline system, Bid determines a quantity of gas reserves desired at each of several potential prices based on: ( 1) the current offering of new reserves (PROLOG), (2) the pipeline’s future market prospects (from Market), (3) its current holdings of reserves and their production prices (from GRST). The bidding takes place independently for each of several series of potential future prices and future reserves. These prices begin with the current average price of all gas reserves. The price/quantity pairs produced for each pipeline by Bid constitute a piecewise linear function, which will be referred to as the bid function, relating desired quantities of gas to potential prices.
An overview
of CAMS
961
A dynamic programming approach’ is used in the bidding routine (Bid) to determine these price/quantity pairs. The amount of gas desired is the decision variable. The quantity of reserves controlled by a pipeline system and the average price for production from the controlled reserves are known and are the state variables. The objective function used in the dynamic program is the maximization of the throughput of the pipeline system (gas purchased and resold) during the planning horizon. The awards module, Award, parcels out the current year’s reserve offerings based on the bid functions of all the pipeline systems. The bidding functions are summed to specify an industry demand function for gas reserves. That function is combined with the (inelastic) supply of new reserves and used to determine a market clearing price for the reserves. At that clearing price, the total demand for new gas reserves of all pipelines equals the quantity of gas reserves available. Gas is awarded to each pipeline company so that each company receives exactly the amount it would desire at the market clearing price. When a particular NGPA category of new reserves is allocated to a pipeline system. the original entry in the GRST table is split into a separate entry for each pipeline system. For each new entry in the GRST, a code is added identifying the pipeline system the reserves are dedicated to, the quantity of gas reserves assigned, and the price that must be paid for production from that block. Bid develops individual pipeline demand curves for new reserves. The bidding algorithm assumes a price for new reserves being offered in the current model year, and it determines through dynamic programming the quantity of the new reserves that a pipeline system should purchase at that price in order to maximize its quantity of gas sales over the horizon. The mathematical formulation of the Bid module is to maximize the total throughput of gas (quantity of gas purchased and resold) for each pipeline from the current period to the end of the planning horizon; the maximization is subject to: (I) expected sales are the minimum of potential (maximum feasible) production from dedicated reserves and expected demand, (2) reserves available next year equal current reserves plus new acquisitions minus sales, (3) contractual requirements (input) are met. Note that contractual requirements/conditions are exogenous and scenario-dependent for forecast years and that conditions are known through time at the beginning of a model run. The throughput maximization in Bid is solved using a backward recursion (as is typical in dynamic programming algorithms). First, end-of-the-planning horizon values have to be assigned to the throughput function for all possible values of reserves at the horizon prices. For the last year of the planning horizon these are simply the values of sales. Since the throughput at the horizon is now known. the previous year throughput can be computed sequentially backwards through time. The value of the decision variable which maximizes the throughput for each potential price is the desired amount of reserves b) the pipeline at that market price. The optimization called for in the throughput maximization is done over a finite set of the possible values of the quantity of new reserves desired (decision variable). An exhaustive search for the optimal value of the throughput is carried out over the finite set of trial values of the bid quantity. Bid passes to Award a demand curve for new gas reserves for each pipeline system. Summing the demand curves of the individual pipeline systems gives an industry demand curve for gas reserves. The intersection of the industry demand curve and the (inelastic) quantity of gas reserves available for allocation gives a price, called the market clearing price. The market clearing price is then used to determine the quantity of new reserves each pipeline system would have sought to acquire at that market clearing price for new reserves. This is done by linear interpolation on the bid quantities. The bid price/quantity pair thus found is then used in allocating the reserves discovered in the current year. Each pipeline system is allocated the quantity of new gas reserves it would demand at the market clearing price. The reserves available in the current year are assigned such that: (I) all the currently available reserves will be allocated. (2) the average price of reserves assigned will be the market clearing price. (3) each pipeline gets quantities of
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reserves it desired at the market clearing price, (4) each pipeline system is assigned same proportion of each of the categories of gas available. (In this way, the per unit cost of the bundle of new gas reserves acquired should be the same for all pipelines in a particular year), (5) controlled gas is assigned at the ceiling price for each category whose ceiling price is below the decontrolled gas price, (6) any reserve categories with a maximum lawful price above the price determined for decontrolled reserves will be treated as a decontrolled category in this procedure for assigning gas reserves to pipeline systems, (7) the price of decontrolled gas is determined so that the average price of all new gas reserves will equal the market clearing price. However, the decontrol price is capped at 130% of the cost of number two fuel oil. Acknowledgements-The
authors are indebted to A. B. Cambel for editorial advice. All errors, as usual, are the sole responsibility of the authors. REFERENCES I. Energy Information Administration, U.S. Department of Energy. “Annual Energy Outlook”, DOE/EIA0383(83), Washington, DC (1984). 2. Energy Information Administration, “Intermediate Future Forecasting System: Executive Summary”, DOE/ EIA-0430, Washington, DC (1983). 3. Energy Information Administration, “Model Documentation of the Gas Analysis Modeling System”, DOE/ EIA-Draft, Washington, DC (1984). 4. Energy Information Administration, U.S. Department of Energy. “Production of Onshore Lower-48 Oil and Gas Model Methodology and Data Description”, DOE/EIA-0345, Washington, DC (1982). 5. W. Trapmann, Energy Information Administration, “Overview of Changes to the Production of Onshore Lower-48 Oil and Gas Mode1 Methodology”, DOE/EIA-0442, Washington, DC (1983). 6. Energy Information Administration, U.S. Department of Energy, “Outercontinental Shelf (OCS) Oil and Gas Supply Model, Vol. I-Model Summary and Methodology Description”, DOE/EIA-0372/l, Washington, DC (1982). 7. G. Nemhauser, Introduction to Dynamic Programming. John Wiley, New York (1966).
1985
AN OVERVIEW
0360-5442/X5 $3 00 + .oO Pergamon Pres Ltd.
OF THE GAS ANALYSIS SYSTEM (GAMS)?
MODELING
ANDY S. KYDES, MARK J. MINASI, STEVEN H. WADE, BRADFORD J. WING EnergyEconomy Systems Analysis Division, Brookhaven National Laboratory. Building 475. Upton.
NY 11973. U.S.A.
and BARBARA MARINER-V• LPE and RICHARD P. O’NEILL Office of Oil and Gas, Energy Information Administration. U.S. Department 1000 Independence Ave.. SW., Washington, DC 20585. U.S.A. (Received
of Energ).
30 June 1984)
Abstract-This paper is an overview of the March 1984 version of the Cias Analysis Modeling System (CAMS), the detailed natural gas market model used by the Energy Information Administration (EIA) to analyze the U.S. natural gas markets.
I.
INTRODUCTION
The need for a detailed analysis capability for the complex U.S. natural gas production/ delivery/demand system was an outgrowth of the oil crises in 1973-1974 and the perception that natural gas was a scarce, high quality fuel which had to be restricted in its use through legislation. The Powerplant and Industrial Fuel Use Act (PIFUA. Public Law 95-620) restricted the use of natural gas and the Natural Gas Policy Act of 1978 (NGPA, Public Law 95-62 1) provided an agenda for the phased decontrol of most natural gas prices at the wellhead by 1985. The NGPA specifies formulas for calculating the maximum price of each category of gas and the date of decontrol for most of those categories. Gas in other categories remains subject to price ceilings. The NGPA categories are defined by the physical characteristics of the well, the age of the well and to whom it was sold. The first comprehensive natural gas legislation in the U.S.. the Natural Gas Act (NGA) of 1938, brought natural gas sold in the interstate markets under federal control. The NGA provided statutory limits on the price that interstate pipelines could bid for gas but provided no limits on the bid price that intrastate pipelines could offer for the same gas. It became clear in the early 1970s that federal wellhead price controls were seriously distorting the natural gas market and Congress. after 18 months of debate, passed the first comprehensive natural gas legislation (NGPA) since the Natural Gas Act of 1938. The NGPA was intended to reduce the gas market distortions by bringing the intrastate gas market under federal price control and to gradually eliminate price ceilings on most new gas discoveries. The Gas Analysis Modeling System (GAMS) was developed over a period of three years for the Analysis and Forecasting Branch, Office of Oil and Gas, Energy Information Administration (EIA). This paper provides an overview of the March 1984 version of GAMS used in support of the 1983 Annual Energy Outlook (AEO).’ GAMS models the production, transmission, distribution and consumption of natural gas in the U.S. These four activities are carried out, respectively, by the producers. pipeline companies, distributors and consumers. Gas production capacity is a function of the number of active wells which. in turn, is determined by past and present drilling activity. Drilling activity is divided into exploratory t This paper was prepared DE-ACO2-76CHOOO 16.
as an account
of work sponsored
by the II.% Government
under contract
number
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A. S. KYDES et al.
and developmental categories. Exploration yields new additions to the stock of known reserves. Development determines the rate of production from the stock of known reserves. Once gas is discovered, producers will offer to develop these reserves under longterm contractual agreements. Since long-term contracts can carry large amounts of risk, general provisions that govern both the price and quantity of gas are usually included. The need to analyze alternative decontrol and pricing options and their impacts on the U.S. natural gas system provided the main incentive for EIA to develop CAMS. GAMS has been used to analyze legislative proposals aimed at changing the regulatory environment of the natural gas market and its results have been used in debates in the U.S. Congress. 1.1. History of GAMS development GAMS was developed under the auspices of the Analysis and Forecasting Branch, Office of Oil and Gas, Energy Information Administration. The EIA, The National Bureau of Standards (NBS), Brookhaven National Laboratory (BNL), as well as several consultants and subcontractors have contributed to the design, implementation and refinement of this model. Model development began in 1981.T Following the completion of the development of GAMS in 1982, modifications and enhancements to GAMS were initiated to improve its projection accuracy, timeliness, flexibility and capabilities for analyzing the complex natural gas market. At the time, the modeling efforts were supplemented by BNL.$ GAMS is maintained and operated at EIA. 2.
GENERAL
DESCRIPTION
OF
GAMS
GAMS produces forecasts of natural gas production, consumption and prices annually through 1995. While the model structure is generally at the state or substate level, detailed reports are available for the 10 Federal (or DOE) regions. GAMS neither requires nor provides much detail on the rest of the U.S. energy-economy system. Several different mathematical structures are incorporated into the GAMS components in order to represent the modelers’ perspectives of how the different groups interact. For example, the producers were perceived to optimize their expected profits when exploring for new reserves or developing new reserves and this led to a linear programming formulation for the supply representation. The reconciliation of production from existing reserves with consumer demand led to an equilibration framework constrained by the institutional structure of the gas market-including the regulatory structure, long-term contracts and other pricing conventions. The interaction of producers with pipeline companies within the natural gas institutional framework was viewed as a constrained equilibration between producers who were assumed to market all of their newly developed reserves and pipeline companies who were assumed to maximize their expected natural gas sales. This led to a dynamic programming formulation for representing pipeline company behavior and an equilibration methodology for the allocation of new reserves. Finally, different levels of regional definition were required by the different GAMS components in order to accurately reflect the natural gas market. Consequently, consumer demand is modeled at the state level by end-use sector to capture differences, for example, in the fuel switching potential, but the supply model (PROLOG) distinguishes six producing regions with their associated transmission costs. The interface between supply and demand is the detailed sales network defined by the Market section. GAMS has been integrated with the Intermediate Future Forecasting System (IFFS)2 to provide a consistent method for analyzing the feedbacks of natural gas markets with the rest of the U.S. energy-economy system. IFFS is an annual, regional, equilibrium model of the U.S. energy-economy system which is also used by the (EIA) to develop projection information for the Annual Energy Outlook (AEO). t The following individuals made significant contributions to this effort: R. P. O’Neill, J. Heinkel, W. Kurator, B. Mariner-Volpe, and W. Trapmann, EIA; P. B. Saunders, C. J. Witzgall, NBS; C. Mylander, U.S. Naval Academy; W. Stewart, College of William and Mary. Additional support to these initial efforts was provided by numerous individuals at EIA and NBS. $ The principal contributors were A. S. Kydes, M. J. Minasi, S. H. Wade, B. J. Wing, R. M. Saltzman, and H. M. Leuterio.
An overview of GAMS
953
The integration of IFFS and GAMS benefits GAMS because of the increased detail for sectoral gas demands, electric utility consumption of gas and oil prices. IFFS benefits from the integration because of the increased gas detail available from GAMS with regard to natural gas production, transmission, distribution and pricing. The 1983 AEO forecasts were developed by the integrated IFFS and GAMS models. The general operating sequence for GAMS in each year is as follows: Step I.
2. 3. 4. 5. 6. 7.
Description
Component
System Update Annual Reserve Demand Bidding these Report
Control Price Market Prolog Market
initialization annual prices for gas by category demand and supply balancing projections for future years projections for future years for new reserves and the allocation of reserves generation and intertemporal operations
Bid and Award Control
The first section is named Control. This section supervises the execution of all other sections of the system. It performs the data initialization for the model and determines how often and in what sequence each of the other sections is executed. One of its tasks is maintenance of the Gas Reserves Supply Table (GRST) which specifies the disposition of known reserves (NGPA category, price, ownership, quantity of reserves, production potential, take-or-pay provisions), Control includes additional reserves in the GRST as provided by the PROLOG module, updates the quantity and price of new reserves awarded to the pipelines with information provided by the Bid and Award section. and subtracts current year production from reserves in the GRST table using information provided by the Market section. The Price section is the first computational section of GAMS executed for each forecast year. Its purpose is to calculate the wellhead price for each of the reserve blocks available for production in the current forecast year and to make this information available to the other sections of GAMS. Price computes the wellhead price of gas based on the type of market for the gas (interstate or intrastate), the NGPA category of the gas, the marginal price for decontrolled gas. the year of the contract between the producer and the pipeline. restrictions on the price according to contract pricing provisions. and the legislation assumed. START 4 CONTROL ---+
RESERVES INFORMATION
Gas Category
Price BID/AWARD
Excess
Deliverability Volumes
Fig.
1. CAMS
system
chart.
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A.S.KYDES
et al.
The next step in the operating sequence for GAMS is accomplished by Market. Market determines, for the current solution year, the consumption volumes and the associated prices by region and end-use sector. It does so by solving for the economic equilibrium, the level of wellhead production such that the cost of producing and transmitting is equal to the price that end-users are willing to pay for that gas. As a result of take-or-pay provisions and the long-term nature of natural gas contracts, gas supply curves can be U-shaped leading to multiple equilibrium points. A bisection algorithm is used to find the highest production equilibrium. The Gas Reserve Supply Table (GRST) is the main interface with the other sections of GAMS. At the beginning of each iteration year, the GRST contains the information necessary to determine supply curves for each pipeline system. At the end of the Market iteration, the GRST information is updated to reflect the draw-down of reserves that has taken place. PROLOG simulates, on an annual basis, the exploration and development of onshore oil and gas reserves in response to expected profitability, capital resources, costs, and the availability of drilling rigs. The projections are based on price expectations that are updated each year based on the current market clearing prices. PROLOG is called once per forecast year and provides, via the GRST, reserve additions by NGPA category and parameters necessary to estimate the production potential of the reserves for each year through the bid model horizon (reserve projections for years beyond the present forecast year are used by the BID model). Some of the calculations in PROLOG are based on information provided by other sections in GAMS such as the latest available decontrol price. Exogenous offshore projections are passed to GRST by PROLOG. Finally, PROLOG adjusts the menu of gas prices associated with the reserves based on the forecast year and the scenario to be modeled. The next step is accomplished by the Bid and Award section. This section establishes the current market clearing price for new reserve additions based on: price of reserves currently dedicated to individual pipeline systems, estimated reserve additions for future years, and an estimated price and quantity of gas that can be marketed over the next several years. Estimates of consumer demands are determined by testing the Market model’s response to a series of prices. The generation of these demand projections is a procedure in Market known as NXTSYS.3 Projections of future reserve additions and demands are required for each model year because the Bid section uses a dynamic programming approach to maximize each pipeline’s expected gas flow over a userspecified planning horizon. (For each iteration year, only the reserve additions for the next year are allocated to the pipelines.) Each pipeline system is treated as an independent supply/demand system. Bid examines the GRST table using both past natural gas reserves already allocated to specific pipeline systems and a forecast of natural gas reserve additions from PROLOG in order to determine a bidding strategy for each pipeline system. Bid assumes that each pipeline system independently seeks to maximize the quantity of gas it expects to market over a 2-6 year time horizon. The length of the time horizon is a user-specified input and a 2 year time horizon was used in the 1983 AEO. The length of the time horizon determines the length of foresight used by pipeline companies for planning purposes. A 6 year time horizon in BID, for example, would imply that each pipeline company uses 6 years of reserve projections (from PROLOG) and demand projections (from Market) to determine this year’s optimal bid. Bid computes a set of price/quantity pairs for each pipeline system (new reserves demand curves) and passes these to the Award module to determine the allocation and pricing for the new reserves. After individual demand curves for new reserves have been established by Bid for each pipeline system, the Award module establishes a national, industry-wide demand for new natural gas reserves. Award then determines the price at which the demand for the new uncommitted reserves equals the supply of new gas reserves (the market clearing price), the decontrolled natural gas price, the price for the new reserve blocks and the allocation of the various gas reserves among the pipelines; this information is entered into the GRST. At this point, the iteration for 1 year is complete. If the requested forecast horizon has not been reached, a few adjustments are made to the GRST and the process is repeated for the following year starting with the Market section.
An overview of CAMS 3. SYSTEM
OVERVIEW
955 OF
CAMS
CAMS consists of three main components or submodels. PROLOG models developmental and exploratory drilling activity. Market models the production, transmission, distribution and consumption of natural gas. Bid and Award models the acquisition of new gas reserves by pipelines. During a model run, each of these three components are run in turn for each successive model year. NLIilII.UI g&v .sll/~plj’ The natural gas supply forecasts used in GAMS are obtained from two submodels: the PRoduction of Onshore Lower-48 Oil and Gas (PROLOG) supply mode1,4.5 and the Outer Continental Shelf (OCS) model.6 PROLOG is embedded within GAMS whereas the OCS model is run alone and the results are fed into GAMS as input. Potential supply from ,4laska to the continental United States can be specified as an exogenous input but was omitted from this analysis: the availability of synthetic and imported gas are exogenous estimates. PROLOG is an annual, linear programming formulation of exploratory and developmental drilling in the continental U.S. It is the section of GAMS that provides the natural gas supply forecasts for each of the six supply regions by NGPA category. PROLOG maximizes the expected present value of profits from exploratory and developmental drilling based on a discounted cash flow analysis, subject to capital availability, engineering constraints and other institutional constraints. Given a sequence of expected annual prices. PROLOG provides the GAMS module with a slate of natural gas reserve additions by year, region and NGPA category. PROLOG also acts as a transfer point for natural gas reserve blocks which have been derived from the OCS model and need to be made available for bidding and production in the rest of GAMS. The NGPA categories employed for exploratory drilling are 102 onshore (new pools discovered after February 1977). 102 offshore. and three classes of 107 gas (deep. tight sands, and Devonian). The expected price path for the first forecast year is provided to PROLOG from exogenous data. .4fter the first year, the expected price path is updated by using the GAMS-derived decontrolled gas price and the market clearing price to generate a new price series. The linear program is formulated so that the discounted present value of profit is maximized. This is subject to: (1) the sum of rotary rigs used does not exceed total rigs available: (2) the change in national drilling expenditures equals a linear combination of this year’s and last year’s change in revenues; (3) the total number of rigs available is a linear function of the last year’s total number of rigs and total expenditure on drilling: (4) this year’s drilling activity is bounded above and below by historically derived parameters and last year’s drilling level. This linear program is solved sequentially for every year of the forecast. The solution provides forecasts of reserves added from exploratory drilling and forecasts of drilling footage and production from all drilling categories. 3.1
3.2. AIur-liCl Market is a regional, annual (or, optionally, semiannual) model of production, transmission, distribution, and consumption of natural gas in the continental United States. Market consists of 17 distinct pipeline systems each of which contains its own supply and demand components. Market’s primary outputs are projections of annual state. regional or national consumption of gas and annually averaged prices paid by end-users within each state from 1980 to 1995. Also included are summaries of the annual operations and transactions of the principal transmission and distribution companies, including sales and take-or-pay defaults (the minimum amount of gas which must be paid for whether or not the gas is desired). The pipeline networks in Market. Each of the 17 pipeline systems is a network of sales relationships between pipeline companies, distribution companies and end-users. These sales relationships are assumed constant throughout a model run. That means for example, that a distribution company will always purchase gas from the same (primary) supplier although the quantity purchased will vary. This assumption is required for the equilibration procedure which is described in detail below.
A. S.
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KYDES
el ai.
These networks represent actual pipeline systems or aggregations of several pipeline systems as shown in Table 1. The networks themselves are comprised of nodes and arcs. Each node in the network represents either a specific agent (e.g. gas distribution company) or an aggregated group of the same agent type. An arc or link between two nodes represents a sales transaction between two agents. Each network has a tree structure with arcs branching out from a single supply node or root node pipeline to the other pipeline, distributor and end-user nodes which it serves. The supply at the root node pipeline is considered equivalent to the wellhead supply. A tree structured network has the property that there is exactly one path (arc) between any two nodes. Thus each node in a network must have a unique predecessor or supplier. The unique predecessor node is referred to as the primary supplier (or primary arc). Each node’s designated primary supplier was that node’s largest domestic volume supplier in 1980. These primary arcs are illustrated by the solid lines in Fig. 2. A pipeline or distributor may also be served by secondary suppliers which represent transfers of gas between pipeline networks and imports. These secondary arcs are represented by dashed lines in Fig. 2. The distinction between primary and secondary arcs is crucial during the equilibration phase of Market when prices and quantities for a particular year are modeled. Only gas volumes and prices on primary arcs are allowed to vary during this phase. The secondary arc volumes and prices are determined prior to and remain fixed during equilibration. The secondary arc prices and quantities vary only from year to year, not within a year. End-user nodes represent the aggregate demand behavior at a state or substate level. A residential node, for instance, represents all of the residential customers of a particular distributor in a given state. Utility and industrial nodes are further disaggregated between switchers (those with alternate fuel-burning capability) and non-switchers. Thus, a Table
I. The pipeline
Number of agents
Total system flow, 1980 (TBtu)
2 3
91 179 319
1228 598 1030
4
233
910
5 6
98 285
874 1541
229
918
8
143
1088
9
349
863
10
158
784
11
271
815
12
414
1566
I3
130
537
14
42
425
15 16 17
99 62 77
3694 789 1526
System number
systems
in Market.
Actual
pipelines
modeled
or based upon
El Paso N.G. Co. Columbia Gas Transmission Co. Tennessee Gas Pipeline Co.: Tennessee Natural Gas Lines Inc.: Alabama Tennessee Natural Gas Co. Texas Eastern Transmission Corp.; Algonquin Gas Transmission Co.: Consolidated Gas Supply Corp. Natural Gas Pipeline Co. of America Mississippi River Transmission Co.; United Gas; Texas Gas Transmission Corporation Transcontinental Gas Pipeline Corp. Transwestern Pipeline Co.; Cities Service Gas Co.; Arkansas Louisiana Gas Co. Florida Gas Transmission Co.; Southern Natural Gas Co. Michigan Wisconsin Pipeline Co.; Midwestern Gas Transmission Inc./Great Lakes Gas Transmission Co.: Aggregated Midwest Area Agents Northwest Pipeline Corp.: Colorado Interstate Mountain Fuel Supply Co.: Kansas Nebraska Natural Gas Co.; Montana Dakota Utilities: Aggregated Mountain Area Agents Panhandle Eastern Pipeline Co.: Trunkline Gas Co.: Northern Natural Gas Co. National Fuel Gas Supply Corp.; Aggregated Appalachia Area Agents Pacific Gas Transmission Co.: Aggregate Far West Aggregated Texas-New Mexico Area Agents Aggregated Oklahoma-Kansas Area Agents Aggregated Louisiana-Arkansas Area Agents
An overview
Fig. 2. Diagram
of a sample
distribution
of CAMS
network
with two pipeline
systems
distributor may have up to six customer classes, representing the residential, commercial, electric utility and industrial sectors. End-use sector nodes are each served by a single distributor and can have no secondary supplies (arcs). Each pipeline system has its own supply system connected primarily to the root node. Sources of supply include dedicated reserves (offshore and onshore), imports, Alaskan gas, and inter-pipeline sales. Each system has a mapping of reserves and reserve characteristics which define its supply system. This supply system is modeled by entries in the Gas Reserve Supply Table (GRST). Along with NGPA category information, takeor-pay information on reserves is available from the GRST. The volumes that can be produced by a particular reserve block in any year are calculated from exogenously specified production profiles. These profiles express maximum production rates as a function of the maturity of the reserves in question. The pricing of a given annual purchase at the wellhead is a function of the withdrawal strategy. In Market, there are two alternate draw-down strategies, minimum cost take and rateable take. The user selects the strategy for each run. In the minimum cost take strategy, prices are calculated assuming that quantities are sequentially withdrawn from the dedicated reserve blocks in a way that minimizes the average purchase cost from producers subject to the take-or-pay provisions. Under the rateable take strategy. the take is allocated proportionally to the deliverabilities of the dedicated reserve, after the takeor-pay obligations have been satisfied. Given a quantity of required gas and a strategy for ordering contracts to draw from, an average price of gas can be obtained for any given demand quantity. Given the tree structure of the network, wellhead prices and quantities from the root node can be easily translated into prices to the end-user nodes. Beginning at the root node, prices to successive nodes are increased to reflect tariffs (see below) and transmission losses. Quantities are also adjusted for transmission losses. Prices and quantities are also adjusted to reflect any transactions on secondary arcs. In this manner. the wellhead price and quantity are propagated up the network to the end-user nodes. In a similar fashion, quantities from the end-user nodes can be accumulated down the network to the root node accounting for losses and secondary transactions along the way. Pipeline and distributor tat-l% in Market. The term tariffs in Market refers to the charges in addition to purchased gas costs that pipelines and distribution companies are allowed to recover. This use of the term differs from its use in regulatory proceedings
958
A. S. KYDES
et al.
where it denotes the entire rate schedule that recovers both the purchased gas costs and other costs. As normally found in actual rate structures, the tariffs in Market have two components: fixed charges and variable charges. Fixed charges are quantity invariant, that is, they must be paid regardless of the quantity purchased. Variable charges are assessed on a per unit of sales basis and are therefore often referred to as commodity charges. Pipeline tariffs are set by direct exogenous specification for each arc of the base network. The fixed charge is the product of the demand rate and the expected peak day volume. The variable charge is an input constant. Pipeline tariffs remain fixed in constant dollars over the forecast period. A distributor rate model is used to produce tariffs for all distributors with initial (1980) end-user demands in excess of 1000 BBtu (billions of Btus). Roughly one-third of the distributors have loads which meet this criterion. Tariffs for the remaining two-thirds of the distributors are exogenously specified and are fixed in constant dollars at these levels over the forecast period. The distributor rate model consists of a series of equations which define the financial, physical and regulatory environment of the individual distributors. Equations are included for taxes, depreciation, operation and maintenance expenses and utility plant in service. These equations are primarily functions of base year demand and number of customers and the expected growth in demand and number of customers. Once tariffs have been calculated, they are separated into fixed and variable tariff components. The unitized cost of gas to a distributor’s customer consists of the sum of the distributor’s cost of purchased gas, the variable charge and the fixed charge divided by quantity consumed. Modeling price sensitivity of end-user-node demands. GAMS does not have detailed endogenous demand models. The responsiveness of the end-user nodes to changes in gas prices is determined by exogenously specified price elasticities which vary by end-user sector and DOE region. These elasticities are applied to base node demands which are derived from regional projections from the IFFS model. In this way, GAMS can indirectly utilize the detailed sectoral demand models of IFFS. Quantities, prices, and elasticities for the residential, commercial, and industrial end-user sectors and for the 10 DOE regions are taken from the solution file of a prior IFFS run. The utility demand for natural gas is taken from the IFFS utility module solution file and is represented by a set of price/quantity pairs (step function) by federal region and year. A sharing algorithm based on 1980 historical shares converts the regional IFFS demand projections into reference node quantities for the Market end-user nodes. Price sensitivity of the end-user nodes is incorporated as follows. Demand at a node is equal to the reference node quantity modified by a function of the ratio of the gas price (determined by propagating the root node supply price) at the end-user node to the price from the IFFS solution file. The price ratio is exponentiated by the input elasticity which is appropriate for the end-user sector and region. This use of the elasticity is similar to that which would be derived from a log-linear demand function. GAMS may also be run in conjunction with IFFS. In such a run, the elasticities are used only as approximations to the behavior of the IFFS demand models. By iterating between IFFS and GAMS, the price responsiveness of the nodes is determined by the actual price responsiveness of the IFFS demand modules. The equilibration process. Each of the 17 pipeline systems is equilibrated separately. Only the primary arc prices and quantities vary during this process. The results are then summed to yield the state, regional or national totals. Following equilibration on the primary network, the prices and gas flows on the secondary network are adjusted for the next forecast year. The prices of gas on the secondary arcs are exogenously set to grow at a pre-defined percentage rate; the quantities on the secondary arcs for the next forecast year are adjusted to satisfy the requirement that the percentage change in the value of sales for each secondary arc into a node must equal the percentage change in the value of sales to that node on the primary arc. This secondary network can be viewed as a boundary condition on the equilibrium solution for the 17 systems because it determines
An overview
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the minimum amount of gas that each pipeline system must transport. Separation of the secondary sales network is a network simplification technique used in Market to allow prices and quantities to be uniquely propagated up and down the network during equilibration. By fixing the secondary arc prices and quantities during equilibration, cycling between the primary and secondary networks is eliminated in the network. ‘The equilibration process is the determination of root node (or wellhead) production levels and prices such that the propagation of these prices and quantities to the end-user nodes results in all the gas available to these nodes being sold. This requires a balancing of wellhead supply price sensitivity to quantity against the price sensitivity of the end-user node demands. For a pipeline which withdraws gas from its least expensive reserves first (the minimum cost take strategy), the supply at the wellhead will be U-shaped. Because take-or-pay provisions require a pipeline to pay for a certain percentage of available production whether or not it is actually taken, there is what amounts to a minimum gas expenditure for levels of wellhead demand up to the (aggregate across reserves) take-or-pay limit for each pipeline system each year. As demand at the wellhead increases up to the take-orpay minimum, the average unit price of gas decreases. For wellhead demands above that minimum. the average unit price of gas increases as would normally be expected. The presence of this U-shaped supply curve complicates the equilibration process as there may be multiple equilibration points. Equilibration is. in principle, the solution to pairs of simultaneous supply and demand equations. The simulated process is slightly more complicated in that each demand quantity at the wellhead results from accumulating end-user node demands down through the pipeline system. accounting for transmission and distribution losses, transfers in and out of storage. and secondary purchases and sales along the way. l‘he equilibration procedure checks test price/quantity pairs from the wellhead supply curve for feasibility. The check for feasibility begins by propagating the test price/quantity up the system to the end-user nodes. Then the end-user demands implied by the end-user node prices are accumulated down the network to the root node. Next, the relationship between the initial wellhead supply quantity and the accumulated wellhead demand quantity is checked. If the wellhead demand quantity is equal to or greater than the wellhead supply quantity. the initial test price/quantity point on the wellhead supply curve is considered feasible. If the accumulated demand is actually greater than the supply quantity. an excess demand condition occurs which results in curtailments. If the two quantities arc equal (within some tolerance) an equilibrium condition exists. If the accumulated demands are less than the wellhead supply. excess supply exists and the initial test pair is deemed infeasible. This occurrence is depicted in Fig. 3. In such an event. a new smaller quantity will be tested and a search algorithm to hnd the equilibrium begins. The search algorithm for finding the equilibrium price/quantity pairs involves dividing the quantity interval of the wellhead supply between the maximum feasible production level (as determined by the GRST information) and the minimum required production level (determined by committed flows forced by secondary arc boundary conditions) into IO equal steps. The process begins with the maximum producible quantity and sequentially checks each test price/quantity pair for feasibility. If the maximum supply quantity is not feasible because of excess supply (see Fig. 3) the model tests progressively lower wellhead supply price/quantity pairs until either: (1) no quantity will clear which causes equilibration failure due to continuous excess supply, (2) clearance or equilibration occurs, or (3) the test quantity/price results in excess demand. In this last case. we have found two points on the wellhead supply function, one with excess supply, the other with excess demand. If. as in Fig. 3. both supply and demand are continuous functions. an exact equilibrium condition exists in this subinterval. This subinterval is then successively bisected until the starch interval size is smaller than some user-delined threshold siLe (e.g. 20.000 billion Btus) and equilibration is achieved. The final equilibration price/quantity pair is the point in the search interval with the largest quantity. Once the conditions for equilibration have been met. Market has finished its tasks.
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Fig. 3. Excess supply at the wellhead during equilibration. equilibrium, we first use the GRST information to determine a at (1). We then propagate the supply price to the end-use nodes wellhead demand quantity (2). The difference between Q and
To test if a quantity Qs is the corresponding average supply price and accumulate the corresponding the demand quantity is the excess
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Information on end-user consumption and price is passed along to the report writer. Data on reserve drawdowns at the wellhead are passed to Bid and Award and PROLOG, and data on take-or-pay defaults is also passed to Bid and Award. 3.3. Bid and Award The supply model (PROLOG) specifies the quantity of reserves that has been added and is open for bids in the current model year. In addition, PROLOG produces an estimate of reserve additions for each future year up to five years into the future. The Bid and Award component establishes a price at which all available reserves (current model year) will be bought based on the projected future reserve additions and projected demands for natural gas obtained from the transmission and distribution module in Market. The price established by this process is referred to as the market clearing price, and it is fed back to PROLOG for the next model year to adjust the expected prices for natural gas. This approach is a break from the traditional modeling approach, which views pipelines as purchasers of spot-market production in a given time period. Purchases of produced gas not under long-term contract are very limited. Pipelines and other purchasers generally contract for the receipt of gas volumes over time according to specified contract terms. The long-term nature of such contracts requires the consideration of expectations in the transaction. The Bid and Award module is composed of two parts: the bidding routine, Bid, and the awards routine, Award. Conceptually, Bid develops individual pipeline company demand curves for new reserves based on the assumed behavior that pipeline companies attempt to maximize gas sales. Award develops a pipeline industry demand curve from the individual pipeline demand curves and finds the (one) industry-wide price for which the supply of new reserves equals the industry demand for new reserves (market clearing price). For each pipeline system, Bid determines a quantity of gas reserves desired at each of several potential prices based on: ( 1) the current offering of new reserves (PROLOG), (2) the pipeline’s future market prospects (from Market), (3) its current holdings of reserves and their production prices (from GRST). The bidding takes place independently for each of several series of potential future prices and future reserves. These prices begin with the current average price of all gas reserves. The price/quantity pairs produced for each pipeline by Bid constitute a piecewise linear function, which will be referred to as the bid function, relating desired quantities of gas to potential prices.
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A dynamic programming approach’ is used in the bidding routine (Bid) to determine these price/quantity pairs. The amount of gas desired is the decision variable. The quantity of reserves controlled by a pipeline system and the average price for production from the controlled reserves are known and are the state variables. The objective function used in the dynamic program is the maximization of the throughput of the pipeline system (gas purchased and resold) during the planning horizon. The awards module, Award, parcels out the current year’s reserve offerings based on the bid functions of all the pipeline systems. The bidding functions are summed to specify an industry demand function for gas reserves. That function is combined with the (inelastic) supply of new reserves and used to determine a market clearing price for the reserves. At that clearing price, the total demand for new gas reserves of all pipelines equals the quantity of gas reserves available. Gas is awarded to each pipeline company so that each company receives exactly the amount it would desire at the market clearing price. When a particular NGPA category of new reserves is allocated to a pipeline system. the original entry in the GRST table is split into a separate entry for each pipeline system. For each new entry in the GRST, a code is added identifying the pipeline system the reserves are dedicated to, the quantity of gas reserves assigned, and the price that must be paid for production from that block. Bid develops individual pipeline demand curves for new reserves. The bidding algorithm assumes a price for new reserves being offered in the current model year, and it determines through dynamic programming the quantity of the new reserves that a pipeline system should purchase at that price in order to maximize its quantity of gas sales over the horizon. The mathematical formulation of the Bid module is to maximize the total throughput of gas (quantity of gas purchased and resold) for each pipeline from the current period to the end of the planning horizon; the maximization is subject to: (I) expected sales are the minimum of potential (maximum feasible) production from dedicated reserves and expected demand, (2) reserves available next year equal current reserves plus new acquisitions minus sales, (3) contractual requirements (input) are met. Note that contractual requirements/conditions are exogenous and scenario-dependent for forecast years and that conditions are known through time at the beginning of a model run. The throughput maximization in Bid is solved using a backward recursion (as is typical in dynamic programming algorithms). First, end-of-the-planning horizon values have to be assigned to the throughput function for all possible values of reserves at the horizon prices. For the last year of the planning horizon these are simply the values of sales. Since the throughput at the horizon is now known. the previous year throughput can be computed sequentially backwards through time. The value of the decision variable which maximizes the throughput for each potential price is the desired amount of reserves b) the pipeline at that market price. The optimization called for in the throughput maximization is done over a finite set of the possible values of the quantity of new reserves desired (decision variable). An exhaustive search for the optimal value of the throughput is carried out over the finite set of trial values of the bid quantity. Bid passes to Award a demand curve for new gas reserves for each pipeline system. Summing the demand curves of the individual pipeline systems gives an industry demand curve for gas reserves. The intersection of the industry demand curve and the (inelastic) quantity of gas reserves available for allocation gives a price, called the market clearing price. The market clearing price is then used to determine the quantity of new reserves each pipeline system would have sought to acquire at that market clearing price for new reserves. This is done by linear interpolation on the bid quantities. The bid price/quantity pair thus found is then used in allocating the reserves discovered in the current year. Each pipeline system is allocated the quantity of new gas reserves it would demand at the market clearing price. The reserves available in the current year are assigned such that: (I) all the currently available reserves will be allocated. (2) the average price of reserves assigned will be the market clearing price. (3) each pipeline gets quantities of
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reserves it desired at the market clearing price, (4) each pipeline system is assigned same proportion of each of the categories of gas available. (In this way, the per unit cost of the bundle of new gas reserves acquired should be the same for all pipelines in a particular year), (5) controlled gas is assigned at the ceiling price for each category whose ceiling price is below the decontrolled gas price, (6) any reserve categories with a maximum lawful price above the price determined for decontrolled reserves will be treated as a decontrolled category in this procedure for assigning gas reserves to pipeline systems, (7) the price of decontrolled gas is determined so that the average price of all new gas reserves will equal the market clearing price. However, the decontrol price is capped at 130% of the cost of number two fuel oil. Acknowledgements-The
authors are indebted to A. B. Cambel for editorial advice. All errors, as usual, are the sole responsibility of the authors. REFERENCES I. Energy Information Administration, U.S. Department of Energy. “Annual Energy Outlook”, DOE/EIA0383(83), Washington, DC (1984). 2. Energy Information Administration, “Intermediate Future Forecasting System: Executive Summary”, DOE/ EIA-0430, Washington, DC (1983). 3. Energy Information Administration, “Model Documentation of the Gas Analysis Modeling System”, DOE/ EIA-Draft, Washington, DC (1984). 4. Energy Information Administration, U.S. Department of Energy. “Production of Onshore Lower-48 Oil and Gas Model Methodology and Data Description”, DOE/EIA-0345, Washington, DC (1982). 5. W. Trapmann, Energy Information Administration, “Overview of Changes to the Production of Onshore Lower-48 Oil and Gas Mode1 Methodology”, DOE/EIA-0442, Washington, DC (1983). 6. Energy Information Administration, U.S. Department of Energy, “Outercontinental Shelf (OCS) Oil and Gas Supply Model, Vol. I-Model Summary and Methodology Description”, DOE/EIA-0372/l, Washington, DC (1982). 7. G. Nemhauser, Introduction to Dynamic Programming. John Wiley, New York (1966).