OFFICIAL MASTER'S DEGREE IN THE ELECTRIC POWER INDUSTRY. Market Equilibrium in Natural Gas Systems: Analysis of the Implementation of a Hub

Transcription

1 UNIVERSIDAD PONTIFICIA COMILLAS ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI) OFFICIAL MASTER'S DEGREE IN THE ELECTRIC POWER INDUSTRY Market Equlbrum n Natural Gas Systems: Analyss of the Implementaton of a Hub Author: Supervsor: Co Supervsor: Aurora del Valle Díez Prof. Dr. Javer Reneses Gullén Dr. Pablo Dueñas Martínez Madrd, July, 2015

2

3 Abstract The ntroducton of competton n the natural gas market, ncreases the nteracton among shppers, changng the scenaro they have to face and therefore ther behavor. Gas demand s expected to be more flexble, manly because of the use of natural gas fred power plants (NGGFPPs) to back up ntermttent generaton. Conversely, most of the contracts are long-term contracts, whch are not sutable for ths flexble demand scenaro and oblge shppers to balance ther poston n the OTC market. Wth the ntroducton of hubs, transactons costs are reduced and addtonal flexblty s acheved. The general objectve of ths master thess s to represent the strategc behavor of agents n a market envronment, n whch they wll try to maxmze ther proft. Each agent maxmzes ts proft facng a ctve demand where t behaves as a monopoly, and nteractng wth the rest of the agents n the hub, n the electrcty market and n foregn markets, holdng dfferent market behavors. The equlbrum s stated as a Mxed Complementarty Problem and the three methodologes whch are used for solvng the problem are descrbed. Fnally, n order to overcome the lmtatons of the Mxed Complementary Problem (MCP) formulaton, an teratve optmzaton problem s proposed. Index Terms Natural Gas Market Equlbrum, Gas Hub, Natural Gas Systems

4 Contents CHAPTER WORLD S NATURAL GAS OUTLOOK NATURAL GAS OUTLOOK IN EUROPE LIBERALIZATION PROCESS SECURITY OF SUPPLY GLOBALIZATION OF GAS MARKETS LONG-TERM CONTRACTS SHALE GAS DEVELOPMENTS LOW CARBON FRAMEWORK THE CONTEXT OF THIS PROJECT RESEARCH IN THE NATURAL GAS SECTOR NASH EQUILIBRIUM MODELING APPROACHES OPTIMIZATION TECHNIQUES EQUILIBRIUM MODELING. COMPLEMENTARITY APPROACH STATE OF THE ART AND MOTIVATION STATE OF THE ART CONTRIBUTION OF THIS RESEARCH MASTER THESIS OBJECTIVES STRUCTURE OF THE DOCUMENT 17 CHAPTER INTRODUCTION REGULATORY FRAMEWORK: POINT-TO-POINT VS. ENTRY-EXIT SYSTEMS MODELING ASSUMPTIONS DEMAND SEGMENTATION INCLUDING A HUB COST FUNCTION 29 CHAPTER 3 31 DOWNSTREAM MARKET REPRESENTATION AND IMPACT OF AGENTS BEHAVIOR IN A GAS HUB ENVIRONMENT INTRODUCTION MARKET REPRESENTATION 34

5 3.3. MODEL DESCRIPTION SOLUTION METHODS EQUILIBRIUM SOLUTION CASE STUDY CASE DESCRIPTION RESULTS CONCLUSIONS GENERAL CONCLUSIONS 43 CHAPTER INTRODUCTION MODEL DESCRIPTION: MCP FORMULATION MODEL DESCRIPTION: ITERATIVE OPTIMIZATION PROBLEM FORMULATION SOLUTION METHODS CASE STUDY CASE DESCRIPTION RESULTS CONCLUSIONS 52 CHAPTER CONCLUSIONS FUTURE RESEARCH 56 REFERENCES 57

6 Lst of Fgures Fgure 1-1 Global gas context. 4 Fgure 1-2 Major trade movements 2014 Trade flows worldwde (bllon cubc meters). Source: BP Statstcal Revew of World Energy June Fgure 2-1 Grhcal representaton of entry-ext systems and pont-to-pont system 21 Fgure 2-2 Monopoly wth a lnear demand curve. 24 Fgure 2-3 Cournot equlbrum. 26 Fgure 2-4 Example of shppers gas portfolo contracted through LT contracts 30 Fgure 3-1 Market equlbrum subject to a set of constrants and all agents proft maxmzaton problem lnked through the electrcty market, foregn market and the hub. 34 Fgure 3-2 Market equlbrum subject to a set of constrants and all agents proft maxmzaton problem lnked through the electrcty market and foregn markets. 35 Fgure 3-3 Mathematcal model representaton of the optmzaton problem for every agent 37 Fgure 4-1 Market equlbrum subject to a set of constrants and all agents proft maxmzaton problem lnked through the hub. 47 Fgure 4-2 Gas market upstream and downstream segments 47 Fgure 4-3 Structure of the proposed teratve optmzaton problem 47 Fgure 4-4 Plot of the prces and quanttes over tme would look lke an nward spral 49 Fgure 4-5 Plot of the prces and quanttes n a unstable case 49

7 Lst of Tables Table Table 1-2: Gas trade n 2013 and 2014 (bllon cubc meters). Source: BP Statstcal Revew of World Energy June Table 1-3 Man models comparatve Table 2-1 Characterstcs of Entry - ext vs. Pont-to-pont systems Table 2-2 Characterstcs of vrtual hubs vs. physcal hubs Table 3-1 Cost functons from each agent Table 3-2 Maxmum amount of gas from the L.T. contracts Table 3-3 Demand functons faced by each agent Table 3-4 Foregn markets demand functon Table 3-5 Gas consumpton by conventonal demand, used n electrcty sector, sent to foregn market, per agent n MWht Table 3-6 Profts by agent ( ) Table 3-7 Gas consumpton by conventonal demand, used n electrcty sector, sent to foregn market, purchase and sales n the hub per agent n MWht Table 3-8 Profts by agent ( ) Table 4-1 Cost functons for each agent Table 4-2 Maxmum amount of gas from the L.T. contracts Table 4-3 Demand functons faced by each agent Table 4-4 Gas used to supply conventonal demand and purchase and sales n the hub per agent n MWht

8 Notaton The man notaton used n ths master thess s stated below for quck reference. Indexes a e x p Index of agent Ctve demand Electrc demand Foregn market Index of perods Constants c P o Intercept of agents cost functon per perod c Slope of agents cost functon per perod P o Intercept of agents ctve demand functon per perod Slope of agents ctve demand per perod p e P o Intercept of the electrc demand functon per perod p Slope of agents electrc demand per perod p e P Intercept of foregn demand functon per perod x o p x p Slope of foregn demand per perod p c Q Maxmum gas volume contracted per agent k Scalar used to solve the problem as a MILP Varables: q Gas demanded by agent for ts ctve demand q Gas demanded by agent for ts electrc demand e Gas demanded by agent for foregn market q Gas contracted by agent from long term contracts x q p c Agents gas purchase n the hub per perod q q Agents gas sales n the hub per perod Prce n the Hub Dual varable of the upper bound on gas demanded by an agent q q e q x Dual varable of the lower bound on gas demanded by an agent for ts ctve demand Dual varable of the lower bound on gas demanded by an agent for ts electrc demand Dual varable of the lower bound on gas demanded by an agent n foregn markets q Dual varable of the lower bound on gas purchases by an agent n the hub q Dual varable of the lower bound on gas sales by an agent n the hub b _ Bnary varable correspondng to the complementarty between and b _ q q Bnary varable correspondng to the complementarty between and e b _ q q Bnary varable correspondng to the complementarty between e and x b _ q q Bnary varable correspondng to the complementarty between x and c q q e q x q

9 q b _ Bnary varable correspondng to the complementarty between q and q b _ Bnary varable correspondng to the complementarty between q and q q

10 Chter 1 Introducton Dreamng, after all, s a form of plannng. Glora Stenem

11 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub World s Natural gas outlook The Medum-Term Gas Market Report [1], forecasts that global gas demand wll reaccelerate followng a marked slowdown n both 2013 and The global natural gas demand s expected to grow by 1.9% p.a. [2], by Growth s drven by non- OECD demand, whch grows 2.5% p.a. whle OECD demand grows more modestly at 1.1% p.a. [2]. The natural gas sector s facng huge uncertantes, related to technologcal advances, geopoltcal changes, and strategc polcy shfts, that can reshe unexpectedly the gas markets. For nstance, large-scale shale gas developments n Mexco and Argentna, a rd uptake of gas n the transportaton sector, the emergence of the Islamc Republc of Iran as an LNG exporter, the Russan Federaton s shft to the East or the large quanttes of flexble supples from the Unted States that mght be on the way. The most remarkable events and a pcture of the current gas market s gven by the IEA, n [1]. A quck outlook of the world s gas sector s gven below based n [1]. In OECD countres, the crss and the contnued deployment of renewables damped gas demand ncreases whle very hgh mport prces n 2013 and 2014 have undermned gas consumpton growth, especally n the power sector. On the other hand, strong envronmental polces may play a role n enhancng the poston of gas, whch offers flexblty and low carbon emssons. In Asa, the expanson on the use of coal n some countres, the deceleraton n Chna s gas demand growth or Jan nuclear power polcy uncertanty slow Asan demand growth and OECD Asa LNG mports fell for the frst tme snce US gas producton shoot up. US gas producton ncreased by 5.7% n 2014, the fastest growth snce 2011 [1]. Demand growth n Latn Amerca, Afrca, and the Mddle East s constraned by supply avalablty beng that supply shortages a chronc problem. In January 2015, ol prces were below USD 50/bbl. Whle prces have recovered from ther lows, they reman locked n a USD range. As gas s drectly and ndrectly lnked to ol, ths fall n ol prces has result n slower gas producton, because of reductons n ctal expendture programs.

12 4 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub Another consequence of lower ol prces and the fact that the bulk of LNG trade s stll ol-ndexed s that regonal prce dfferentals have narrowed substantally and has brought Asan prces more n lne wth European benchmarks, changng the current gas flows drectons. Fgure 1-1 represents the global gas context and how some of the remarks commented before affect prces, pushng them up or down. Russa-n search of gas markets Shale gas resources and future export plans Europe s gas demand squeeze Gas shortages n MENA and Inda Strong LNG demand across South-East Asan Markets Janese nuclear polcy unclear South Amercan LNG mports ncreasng New emergng gas provnce Massve new LNG projects Factors pushng prces down Factors pushng prces up Fgure 1-1 Global gas context Natural gas outlook n Europe The Natural gas sector has become a focus n Europe n the last decade and even more n the last years, as the supply and demand pcture has become ncreasngly uncertan. A combnaton of factors le behnd: 1) the ongong lberalzaton process started n 1998 wth the frst package (Drectve 98/30/CE); 2) the securty of supply concerns due to the concentraton of supplers most of them comng from countres consdered rsky and Europe s dependency n these mports; 3) the globalzaton of the natural gas markets through the LNG, ts recent convergence n global gas prces and ts sustanablty over tme; 4) the evolvng framework of long-term contracts based on the cost of alternatve fuels (ol prce) and bg take-or-pay commtments to lqud markets wth transparent gas ndex prces; 5) the producton of shale gas n North Amerca, ts 1 Based n the one from Prof. Manfred Hafner, Internatonal and European natural gas markets (supply and demand) and geopoltcs: Developments and Outlook

13 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub 5 global present and future output and possble shale gas developments n Europe; and 6) the role of natural gas n a low carbon Europe. In partcular, the shale gas revoluton n Amerca has put gas-ntensve European ndustral companes at a compettve dsadvantage. At the same tme, the dsplaced coal from the Amercan generaton mx has lowered coal prces n Europe, and worldwde, such that coal-fred generaton s now more proftable than runnng gas-fred power statons. The low emsson allowance prce has also ntensfed ths phenomenon. Furthermore, for a long perod, gas demand had been rsng, whlst on the supply sde, European Unon (EU) producton, whch s located largely n the UK and the Netherlands, s declnng Lberalzaton process The European gas ndustry was hstorcally managed by natonal, vertcally ntegrated companes. Lberalzaton, ntroduced by the Frst Gas Drectve (European Unon, 1998), whch sought to create compettve markets by ensurng access to the network to thrd partes was refned n the Second Gas Drectve, (European Unon, 2003), named the Acceleraton Drectve, whch mandated regulated thrd party access (rtpa) for all exstng nfrastructures 2, commanded legal unbundlng as the mnmum level of unbundlng, and renforced the mportance of the regulator beng the result of a push toward a sngle European compettve gas market by the European nsttutons and the member states. Ths seres of legslatve measures, followed n 2009 by the set of drectves and regulatons known as the Thrd Gas Package (European Unon, 2009), led to the unbundlng of the transmsson assets, to the mplementaton of an entry-ext transport gas system and the creaton of vrtual hubs. Ths successon of changes and adjustments has not come to an end, and the European legslaton wll contnue to adt, n order to complete the vson enclosed n the regularly updated Gas Target Model 3. Ths lberalzaton process has changed the legal and economc framework of the gas ndustry and how agents behave n ths new envronment s the man motvaton of ths 2 Negotated thrd party access s not omtted on purpose as t s ndeed an excepton to regulated thrd party access. Instead of beng mposed by regulatory authortes, the cost recovery framework wll be decded by the nfrastructure owner. Nevertheless, the owner s not totally free to set access rules, whch are normally subject to regulatory authortes proval. 3 In September 2010, the European energy regulators ntated a process to establsh a target model for European gas markets. CEER publshed the Vson for a European Gas Target Model and Conclusons Per on 1 December The revew of ths per was undertaken by ACER n 2014

14 6 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub master thess, more precsely the mpact on agents behavor due to the ncorporaton of vrtual hubs Securty of supply The EU mports more than half of all the energy t consumes. Its mport dependency s partcularly hgh for crude ol (more than 90%) and natural gas (66%) 4. The total mport bll s more than 1 bllon 5 per day. Securty of supply s n the spotlght of the European Commsson, because of: 1. The concentraton of supplers, many countres are heavly relant on a sngle suppler. 2. To a large extent, the supples come from countres that are perceved as rsky, for nstance, Central and Eastern Europe currently suffers from a strong dependency on Russan natural gas exports. Ths dependence leaves Europe vulnerable to supply dsruptons, as for nstance, the 2009 gas dspute between Russa and the transt-country Ukrane, left many EU countres wth severe shortages or n Algera where the state s constantly undermned by slamst rebels (even f t has never been nterrupted due to ths reason). Amng at mprovng supply securty and n response to these concerns, the European Commsson released ts Energy Securty Strategy n May 2014 addressng short- and long-term securty of supply. The Strategy ams to ensure a stable and abundant supply of energy for Europe Globalzaton of gas markets The European market s ncreasngly becomng part of a globalzed natural gas market wth the nterconnecton of the world regons va lquefed natural gas (LNG). Even though, two thrds of gas mports are stll done through ppelnes. The flow by ppelne n 2014 accounted for bllon cubc meters whereas total trade lquefed natural gas n 2014 accounted for bllon cubc meters accordng to [3]. 4 European Comsson 5 European Comsson

15 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub 7 Table 1-1 Table 1-2: Gas trade n 2013 and 2014 (bllon cubc meters). Source: BP Statstcal Revew of World Energy June 2015 The total LNG regasfcaton cacty n OECD Europe represents about 45% of the regon s consumpton [1], wth Span leadng n number wth sx regasfcaton plants. Fgure 1-2 Major trade movements 2014 Trade flows worldwde (bllon cubc meters). Source: BP Statstcal Revew of World Energy June 2015 Inter-regonal gas trade wll expand by 40% between 2014 and 2020, surpassng 780 bllon cubc meters (bcm) by Lquefed natural gas (LNG) wll account for 65% of the ncrease [1].

16 8 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub Long-term contracts Gas markets have tradtonally reled on long-term blateral contracts for coverng gas demand. Producers sgned long-term supply contracts wth shppers, n whch producers guarantee the recovery of ther huge nvestments n ctal-ntensve facltes and shppers guarantee a frm supply at prces well-known n advance. Whle long-term contracts may have slowed down the natural gas market lberalzaton process, they have favored the development of long-term, ctal-ntensve supply projects such as ppelnes, and LNG termnals. Realzaton of these projects would not be possble wthout the nsurance provded by long-term contracts. Also consumers, lke ndustres or local authortes on behalf of households, sgned long-term contracts wth shppers for smlar reasons. Nowadays, producers, shppers and consumers stll sgn these longterm contracts. Conversely, gas demand s expected to be more flexble (as, for example, s the case of natural gas fred power plants) n the future and yet current prcng and market structures are not amenable to that outcome. The prce of gas was based on the cost of alternatve fuels (ol prce) and contracts rely on prce revew clauses. The framework s changng and even f long-term contracts stll play a key role, they are becomng more flexble and there s an ongong transton from long-term ol-ndexed contracts to hub based contracts Shale gas developments Shale gas has been n producton for several decades, but started to grow rdly only n the md- 2000s, growng at more than 45% per year between 2005 and Unconventonal gas producton was nearly 60% of total gas producton n the Unted States n 2010 [4].The reasons for ths shale gas boom, as stated n [5], are related to government polcy, prvate entrepreneurshp, technology nnovatons, prvate land and mneral rghts ownershp, hgh natural gas prces n the 2000s, and a number of other factors. Ths remarkable growth of shale gas producton n the Unted States leads to nterest n explorng shale resources n other areas of the world. A number of countres, ncludng Chna, Mexco, Argentna, Poland, Inda, and Australa consdered developng ther own shale gas resources. Currently, globally the outlook s less postve than t was a couple of years ago. Development n Chna, n partcular, has proved slower than expected. In Europe, companes nterest n shale gas s evoratng fast, even n those countres where

17 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub 9 governments have proven supportve, such as Poland and Romana. Dspontng test wells, regulatory constrants, and contnued publc hostlty have added to deteroratng economcs as a result of lower ol and gas prces that have all contrbuted to dmmng the outlook for shale gas.[1]. In the Unted Kngdom, although the government s supportve of the technology, the debate remans due to publc hostlty aganst frackng. In Span, exploraton permts are unlkely to be granted before Germany proved a draft law for the commercal explotaton of shale gas and ol. Poltcal ndecson and publc hostlty aganst European shale gas development leads us to conclude a mnor role for European shale gas producton n the near future Low carbon framework Strong envronmental polces can play a role n enhancng the poston of gas. Natural gas s advertsed as a clean fossl fuel able to cope wth the clmate change and s often seen as an mportant energy carrer on the way to low carbon economy. Compared to other fossls fuels, natural gas has the lowest carbon content per unt of energy and due to the hgh flexblty of natural gas fred power plants (NGGFPPs), they are used as a backup for ntermttent renewable power generaton. The role of natural gas as a transtonal fuel n a Clmate and Energy framework was hghlghted n the EU Energy Roadm "... gas wll play an mportant role, n the short to medum term, n the transformaton of the energy system, snce t represents a relatvely quck and cost-effcent way of reducng relance on other more pollutng fossl fuels;..." " recognses natural gas potental as a flexble back-up for balancng varable renewable energy supply alongsde electrcty storage, nterconnecton and demandresponse; consders affordng greater mportance to gas, partcularly f technologes for carbon cture and storage become more wdely avalable; beleves that the objectve of reducng greenhouse gas emssons must be the core consderaton here, and the prevalng objectve n the energy mx;..." On the other hand, the deployment of renewables leaves lmted space for gas demand ncreases, whch currently could not compete wth ncreasngly compettve renewables. 6

18 10 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub Hgh LNG prces n recent years have nfluenced the vablty of gas. Consumpton growth s been slowed due to competton from coal and renewables The context of ths project research n the natural gas sector The 3rd Gas Drectve (2009/73/EC) proposes the unbundlng of actvtes, the mplementaton of entry-ext access systems and the consttuton of natonal or supranatonal vrtual hubs n order to enlarge the market, reduce the barrers to entry and encourage the degree of competton. The lberalzaton process has changed the legal and economc framework of the gas ndustry, from bg monopoles to olgopoles. The ntroducton of competton n the gas market due to the ongong lberalzaton n Europe, ncreases the nteracton among shppers n downstream gas systems. As the entres and exts from the balancng zones may be uncertan, shppers buy and sell gas to balance ther poston. Shppers usually perform Over the Counter (OTC) blateral operatons n the search of balancng ther entres, exts and nventory varatons daly. Wth the ntroducton of vrtual hubs (balancng electronc platforms, lnked to balancng zones), transactons costs are reduced. The pearance of contnental European gas hubs encouraged by the 3rd Gas Drectve has brought up the followng queston: How do agents behave n the hub snce n many cases there are few frms competng? We are nterested n the equlbrum soluton of such game, lookng for the smultaneous soluton of all players (Nash equlbrum) [6] nstead of each ndvdual proft. The motvaton of ths master thess s twofold. Frst, to represent the strategc behavor of agents n a market envronment, n whch they wll try to maxmze ther proft. Each agent maxmzes ther proft facng a ctve demand where t behaves as a monopoly, nteractng wth the rest of the agents n the hub, n the electrcty market and n foregn markets. Wth ths am, the decson-takng process of the dfferent shppers wll be modeled. Second, the per models and assesses how the ntroducton of a gas hub modfes the behavor of the dfferent agents.

19 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub Nash equlbrum Economc agents can nteract strategcally n a varety of ways, and many of these have been studed by usng game theory. In game theory, the Nash equlbrum [6] s a soluton concept of a non-cooperatve game nvolvng two or more players, n whch each player s assumed to know the equlbrum strateges of the other players, and no player has anythng to gan by changng unlaterally strategy 7. Let (S,f) be a game wth n players, where S S... 1 S2 Sn S s the set of strateges for each player, f f1 x,..., f n x s the payoff s the set of strateges profles and functon of x S. Let x be a strategy profle of player, and x a strategy profle of all players except for player. When a player 1,...,n chooses strategy x resultng n strategy profle x x,..., 1 xn then player obtans a payoff f x. Then, a strategy * * * * profle x S s a Nash equlbrum f x, S : f x, x f x, x, that s, no player has ncentve to devate from hs strategy gven that the other players do not devate. We therefore have a Nash equlbrum when each agent s makng the optmal choce, gven the other agents choce. It may sometmes pear non-ratonal n a thrd-person perspectve. Ths s because t may hpen that a Nash equlbrum s not Pareto Optmal. The Nash equlbrum can be defned ether as strct or weak, accordng f the bestresponse means strct best response (strctly greater pay-off) or weak best response (as good as any other alternatve) Modelng proaches The followng subsectons summarze the two used technques n ths thess for modelng the natural gas sector markets: optmzaton and equlbrum modelng Optmzaton technques Lnear programmng was developed durng the 40s under the leadershp of G. B. Dantzg. Today, optmzaton s plcable to a large set of problems and plays an mportant role n plannng and forecastng n nearly all types of ndustres. It s frequently used for plcatons n producton processes but many other plcatons exst. 7 Osborne, Martn J., and Arel Rubnsten. A Course n Game Theory. Cambrdge, MA: MIT, 1994.

20 12 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub Lnear and non-lnear programmng (LP and NLP) consst of the maxmzaton or mnmzaton of lnear and non-lnear functons of one or several varables under some lnear equalty and/or nequalty constrants. The complexty of the functon and the constrants can vary from few varables and a lnear structure, to numerous varables and nonlnear problems. The basc setup can be expressed n the followng form: Max f x s.t. g x 0 I (1.1) x Where x denotes the decson varable, f(x) the objectve functon and g(x) the th constrant. The optmzaton technque has been wdely used for modelng operatonal problems n the natural gas sector. For example, [7] solve the gas dstrbuton problem as a cost mnmzaton subject to nonlnear flow-pressure relatons, materal balances, and pressure bounds or GASCOOP model [8] that optmzes the system operaton, mnmzng agent s costs n an entry-ext access system. There exsts a lot of market models usng an optmzaton proach for representng gas markets. However, optmzaton models fals when market power s ncluded n the model, as mperfect market games (e.g., Cournot) are dffcult to model wth optmzaton technques Equlbrum modelng. Complementarty proach. The European natural gas market s not a perfect market; therefore, the cost mnmzaton proach may not be representatve for the European natural gas market and ts mperfect market structure. For the representaton of the equlbra, complementarty structures are used n a general equlbrum framework and n non-cooperatve game settng. By smultaneously solvng the optmzaton problems of several players wthn the complementarty system, ths model type gves the equlbrum soluton to the entre market game. Hence, the equlbrum soluton goes beyond the soluton of the ndvdual optmzaton problem of each player, by gvng the smultaneous soluton to all agents n the game. In many stuatons the ndvdualstc nterests of each player causes the equlbrum soluton not to be Pareto optmal, lke the known example of the Prsoner s Dlemma.

21 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub 13 n n As descrbed n [9], havng a functon F: the pure nonlnear complementarty n problem denoted NCP(F)s to fnd x such that for all : F( x) 0 x 0 x F( x) 0 (1.2) The mxed verson of the complementarty problem (MCP) s closely related but also allows for both equatons wth correspondng free varables and nequaltes wth assocated nonnegatve varables. The general form of the MCP s stated as follows [10]: Fndng a vector x, assumng f() x 0, satsfyng the complementarty condton T f( x) x 0, for each element I of the vector x, ether x or f ( x ) must equal zero: 0 x f ( x) 0, I (1.3) Accordngly the varables x and f ( x ) are called complementary. A general maxmzaton problem becomes: s.t. max f( x ) (1.4) x g ( x) 0, ( ), I (1.5) h ( x) 0, ( ), j J (1.6) j j x 0 (1.7) Where and j are ndexng the nequaltes and equaltes respectvely. The correspondng Karush-Kuhn-Tucker condtons (KKT) are the necessary and suffcent condtons for optmalty of the problem f we have a convex objectve functon and a convex soluton space feasble regon. ( ) ( ) T ( ) T f x g x j hj x 0 (1.8) 0 g ( x) 0 I h ( x) 0, free, jj j j (1.9) (1.10)

22 14 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub Equaton (1.8) makes sure the soluton s statonary, (1.9) guarantees complementarty and (1.10) feasblty. Note that the dual varable of the nequalty has to be greater than or equal to zero, whle the dual of the equalty can take any real number. j Dependng on the character of the constrants of the optmzaton problem, g (x) or h j (x), dfferent types of complementarty problems can be dstngushed: If the constrants are exogenous parameters, the lnear or non-lnear complementarty problem can be expressed as a MCP. Ther common characterstc s the smultaneous soluton to all optmzaton problems n the model. There can be several lnked optmzaton problems n such a model, ether n a game context (lnked va reacton functons) or n any other setup where the lnk s done va physcal balance or market clearng condtons. Market games such as Cournot games can be modeled n the MCP format. More generally, MCP models allow to represent Nash games n pure strateges. If the constrant s tself the result of another equlbrum problem, two types can be dstngush: MPEC (mathematcal program wth equlbrum constrants) f the objectve functon of the program s the optmzaton problem of a sngle player (e.g., Stackelberg game, welfare optmzaton). EPEC (equlbrum program wth equlbrum constrants) f the objectve functon gves the soluton of another equlbrum problem. In general, solvng the resultng system of equatons and provng unqueness and exstence of the soluton hpens to be mathematcally challengng. Ths master thess has used some of the above-mentoned modelng methods, specfcally MCP, for solvng the equlbra descrbed n the followng sectons and lnear programmng (LP) for solvng an teratve optmzaton problem that leads to the same soluton of the equlbra State of the art and motvaton In ths secton, the state of the art s descrbed, payng specal attenton to those models that have been focused on solvng the gas market equlbrum. A g of mprovement has been detected n the representaton of the demands n the downstream market as well as the upcomng necessty of representng and study the mpact of vrtual hubs n ths envronment.

23 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub State of the art Because European natural gas sector has been descrbed as a Cournot olgopoly [11], most of the models proposed n the lterature for solvng the equlbrum are Mxed Complementary Problems (MCP), Mathematcal Program wth Equlbrum Constrants (MPEC) or Equlbrum Program wth Equlbrum Constrant (EPEC) [9]. Some of the models that represent gas markets wth detal are descrbed below. The evaluated models are focused on the European natural gas market. MCP models have been the preferred format of the European natural gas sector, because of the mperfect character of the market. Another common characterstc of the current lterature s that, most of the models are focused n the long to medum term. GASTALE [13] s used to analyze the European natural gas market and focuses prmarly on the role of the downstream tradng companes and ther nteracton wth gas producers. Producers of natural gas are assumed to form an olgopoly meanwhle, downstream wthn-country traders of gas are represented n dfferent versons of the model as local olgopoles or perfect compettors. The model therefore has a two-level structure, n whch producers engage n competton a la Cournot, and each producer s a Stackelberg leader wth respect to traders, who may be Cournot olgopoles or perfect compettors. The model s formulated as a complementarty problem, and s solved by nonlnear programmng. NATGAS: The NATural GAS [14] model s an ntegrated model of the European wholesale gas market provdng long-run projectons of supply, transport, storage and consumpton patterns n the model regon, aggregated n 5-year perods, dstngushng two seasons (wnter and summer). GASMOD [15] s a model of the European natural gas supply, whch s structured as a two-stage game of successve natural gas exports to Europe (upstream market) and wholesale trade wthn Europe (downstream market), and whch explctly ncludes nfrastructure cactes. It allows the representaton of dfferent markets scenaros n both markets (Cournot competton or Perfect competton) concludng that Cournot competton on both markets s the most realstc representaton of today's European natural gas market. GASCOOP [8] s a market model whch cture accurately the performance of a gas market based on an entry-ext access system through cost mnmzaton, provdng relable outcomes, not only for academc purposes, but also for any stakeholder, such as a market partcpant, a regulatory authorty or a faclty operator. It contans a detaled

24 16 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub representaton of nfrastructure operaton, optmzng operaton and cacty contractng decsons consderng the nfluence of long-term supply contracts and LNG carrers movements Contrbuton of ths research Whle large-scale gas models have been developed and used extensvely, GASTALE model by [13], NATGAS model by [14], and GASMOD model by [15]; EUGAS model by [16], the model presented n ths master thess dffers from earler models n ts representaton of demands and the representaton of the hub. Market Representaton Operaton detals Demand representaton (Hobbs et al., 2003) GASTALE LT (Zwart et al., 2006) NATGAS LT (Holz et al., 2009) GASMOD LT (Dueñas et al., 2013) OMEGA LT/MT OBJECTIVE ST Table 1-3 Man models comparatve Table 1-3 contans the results of the evaluaton, n whch a whte crcle ponts out that a shortcomng s not addressed at all and a black crcle ndcates that a shortcomng s fully addressed. We have detected a relevant and generalzed lack of models regardng the operaton n the short term wth a detaled analyss of the dfferent downstream gas demands. Ths g s studed and modeled n our model. The model also addresses establshng an organzed market (Hub), as a balancng market, where shppers trade to balance ther poston. Ths market s represented as a perfect market. One lmtaton of our model s that we do not cture antcompettve behavor n the hub, whch may actually occur n mmature and mperfect gas markets.

25 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub Master thess objectves The general objectve of ths master thess s to represent the strategc behavor of gas agents n a market envronment, n whch they wll try to maxmze ther proft. Each agent maxmzes ther proft facng a ctve demand where t behaves as a monopoly, and nteractng wth the rest of the agents n the hub, n the electrcty market and n foregn markets, holdng dfferent market behavors. Wth ths am, the decson-takng process of the dfferent shppers wll be smulated. Along the lnes of the prevous objectve, the EU Thrd Energy Package ncludes the socalled Gas Target Model, whch defnes the consttuton of natonal or supra-natonal vrtual hubs. In ths new envronment, we want to answer: How do agents act n the hub snce n many cases there are few frms competng? For ths purpose, we model and assess how the ntroducton of a gas hub modfes the behavor of the dfferent agents. Aware of the ntrnsc lmtatons of MCP formulaton, we propose an teratve optmzaton problem. The strengths and weaknesses of each formulaton wll be explaned as well as the lmtatons of the proach are noted, as the complexty of the model s not enough yet to draw conclusons Structure of the document In Chter 1, an overvew of the natural gas sector was gven for ntroducng afterward the problem context. Next, the Nash equlbrum and the dfferent modelng proaches used n ths master thess has been explaned. Fnally, the master thess objectves are set. The rest of the document s organzed as follows: In Chter 2, the dfferent regulatory frameworks (entry-ext and pont-to-pont) and the modelng assumptons are descrbed. Specal attenton has been pad to the demand segmentaton. In Chter 3, the equlbrum model, n whch the strategc behavor of agents n a market envronment s represented, s explaned. Two cases have been set out: Frst, the behavor of the agents have been represented wthout consderng the hub. Afterwards, a vrtual hub s ntroduced n the problem and how agents behave under ths new framework s studed. A small case study s presented, where the obtaned results consderng and not consderng the hub are explaned. Fnally, conclusons are drawn.

26 18 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub In Chter 4, an teratve optmzaton problem s proposed to solve the equlbrum problem. A small case study s presented and conclusons are drawn. Chter 5 gathers the conclusons reached n the prevous two chters and proposes next steps and future research..

27 Chter 2 Model descrpton Teach thy tongue to say, I do not know, and thous shalt progress. Mamondes

28 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub Introducton In ths secton, all necessary assumptons to buld the proposed model are ntroduced Regulatory framework: Pont-to-pont vs. Entry-ext systems The lberalzaton process of the gas sector has end up wth the defnton of two man dfferent regulaton frameworks for the network servces lke contractng and operatng rules and a cost recovery framework for the regulated nfrastructure 8. However, the way to coordnate such network servces s stll under debate. On the one hand, pont-to-pont systems establsh two prces at both ppelne extremes. The dfference between both prces reflects transportaton costs and scarce cacty valuaton when transportaton constrants pear. On the other hand, entry-ext systems fragment the market by defnng balancng zones where the network s embedded and establsh entry and ext tarffs. Balancng zones dsregard transportaton and dstrbuton network characterstcs, except at entry and ext ponts [16]. Fgure 2-1 contans a grhcal representaton of the entry exst systems and the pontto-pont. Fgure 2-1 Grhcal representaton of entry-ext systems and pont-to-pont system 8 Negotated thrd party access s not omtted on purpose as t s ndeed an excepton to regulated thrd party access. Instead of beng mposed by regulatory authortes, the cost recovery framework wll be decded by the nfrastructure owner. Nevertheless, the owner s not totally free to set access rules, whch are normally subject to regulatory authortes proval.

29 22 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub Entry-Ext Pont-to-Pont Prmary allocaton of cacty for ntroducng and removng gas n the pont defned as "Entry Ponts" or "Ext Ponts". - Assocated to Vrtual Hubs Flexblty n the allocaton of cacty Promotes lqudty Imbalances need penaltes Cost assocated wth flexblty Cacty allocaton assocated wth an ext pont and a path or route of transport determned. You cannot hre separate nput and output. - Assocated to Physcal Hub Effcent use of transport nfrastructure Tarffs are cost reflectve Hgh barrers to entry It requres a mature market Europe Unted States Table 2-1 Characterstcs of Entry - ext vs. Pont-to-pont systems Ths master thess s focused on the entry-ext access systems whch are beng mplemented n the EU n lne wth the Thrd Energy Package to consttute an nternal gas market Modelng Assumptons Demand Segmentaton The dfferent types of demands suppled by a gas company have been categorzed nto: households, electrcty markets and foregn markets Households The Second legslatve package n 2003, (Drectve 2003/55 / EC) allowed the entry of new supplers of gas n the Member States, and opened the possblty that consumers could choose freely ther gas suppler. Nonetheless, the downstream gas market stll

30 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub 23 reles on monopolstc structures at some pont and, for example, households changng from ther supplers, s even today not so common 9. For ths reason, households have been represented as a ctve demand of each agent, not consderng the consumers swtchng rate among companes. As gas has substtute goods, lke ol or electrcty, consumers wll look for other alternatves, beng the demand elastc, although not much due to the complexty of changng from one fuel to another n the short term (except for the ndustral demand, whch has been omtted n ths research). It s assumed that each gas agent supples ts own market, actng as a monopoly, n whch the demand s a lnear functon of the prce. A monopoly would recognze ts nfluence over the market prce and choose that level of prce and output whch maxmzes ts overall profts. Of course, t cannot choose prce and output ndependently; for any gven prce, the monopoly wll be able to sell only what the market wll bear. It can be seen as the monopoly choosng the quantty and lettng the consumers decde what prce they wll pay for the quantty. The demand behavor of the consumers wll constran the monopolst s choce of prce and quantty [18]. The monopolst s proft-maxmzaton problem then takes the followng form: Let p(y) denote the market nverse demand curve and c(y) to denote the cost functon, then ry () py () ys the revenue functon of the monopolst. max ry () cy () y (2.1) The optmalty condton for ths problem s where the margnal revenues (MR) equals the margnal cost (MC) r c y y (2.2) If margnal revenues were less than margnal costs t would force the frm to decrease outputs, snce the savngs n costs would be more than the resultng loss n revenues. If the margnal revenues were greater than the margnal costs, t would force the frm to 9 In Span, the swtchng rate n 2014 was of 10% accordng to Informe anual de supervson de los cambos de comercalzador Año CNMC

31 24 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub ncrease outputs. The only pont where the frm has no ncentve to change outputs s where margnal revenues equal margnal costs. Expressng the margnal revenue n terms of the elastcty ( y ) optmalty condton margnal revenue equals margnal cost :, and rewrtng the 1 MR() y p()1 y MC() y () y (2.3) If the monopolst faces a household s lnear demand curve py ( ) a b y, the revenue functon s ry () py () yay by 2 (2.4) And the margnal revenue functon s MR() y a 2by (2.5) The margnal revenue functon has the same vertcal ntercept a, as the demand curve, but t s twce as steep. Fgure 2-2 represents a monopoly wth a lnear demand curve and shows that the monopolst s proft-maxmzng output occurs where margnal revenue equals margnal cost. Fgure 2-2 Monopoly wth a lnear demand curve.

32 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub Electrcty sector demand The share of gas demand used for power generaton over the total gas consumpton has augmented durng these years, reachng globally around 40% n 2012 [19]. Besdes, the worldwde share of gas used n the electrc power sector, whch s produced by natural gas fred power plants NGFPPs, has doubled (from 10% to nearly 22.2% [20]. In ths master thess, agents partcpate n the electrcty market wth ther own natural gas fred power plants (NGFPPs), but there are not so many agents as to regard each of them as havng a neglgble effect on prce. Ths s the stuaton known as olgopoly. The electrcty sector s not represented n ths artcle, assumng each agent owns some gas-fred power plants whch request a gas demand. Ths gas demand, s represented by a prce-quantty affne functon for all agents, where the nfluence of each agent n the market s represented by the value of the slope for each agent. Ths market has been represented as a Cournot, where each agent chooses a proftmaxmzng output for tself. e Assume that there are only two agents and agent 1 expects that agent 2 wll produce y 2 unts of output. (The e stands for expected output.) If frm 1 decdes to produce y unts 1 e of output, t expects that the total output produced wll be Y y1 y and the output wll 2 e yeld a market prce of p( Y ) p( y1 y2 ). The proft-maxmzaton problem of agent 1 s then [18]: e max p y y y c y (2.6) y 1 e For any gven belef about the output of agent 2, y 2, there wll be some optmal choce of output for agent 1, y 1. The reacton functon gves one frm s optmal choce as a functon of ts belefs about the other agent s choce. e y f ( y ) y e f ( y ) (2.7) Then, the optmal output combnaton s such that the output of choces y, y * * 1 2 satsfes: y y f ( y ) * * f ( y ) * * (2.8)

33 26 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub Such a combnaton of output levels s known as Cournot equlbrum. For example, n case of the lnear demand functon and zero margnal costs the reacton functon for both agents takes the form y e e aby1 aby2 ; y 2b 2b (2.9) Delveres to foregn markets Fgure 2-3 Cournot equlbrum. The world s nterconnected va lquefed natural gas (LNG), favorng the globalzaton of the natural gas sector and creatng an nternatonal gas market. In ths scenaro, t becomes necessary to account for the foregn gas market. As a global market, the nfluence of each agent on ts prce s reduced; hence, the market s qute elastc,.e., the prce mantans almost constant whle gas s delvered. Ths market could be represented as a perfectly compettve market, assumng that the goods beng offered for sale are all the same and that the buyers and sellers are so numerous that no sngle buyer or seller can nfluence n the market prce. Each agent assumes that the market prce s ndependent of ts own level of output and that ts decson s how much output t wants to produce, beng prce takers. By defnton a compettve agent gnores ts nfluence on the market prce. Thus the maxmzaton problem facng a compettve agent s maxmzng ts profts (revenue mnus cost) [18].

34 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub 27 max pyc y (2.10) y The agent wll operate n the pont where margnal revenue equals margnal cost, that s, when the extra revenue ganed by one more unt of output just equals the extra cost, of producng another unt. p MC() y (2.11) Thus, a compettve frm wll choose a level of output y where the margnal cost (MC(y)) that t faces s equal to the market prce (p). In ths master thess, foregn markets have been represented through an elastc demand functon as sales are consdered to have slght nfluence on prces n any case Includng a Hub A wholesale gas market s a market where the partcpants such as producers, regulated and unregulated utltes, and traders buy and sell natural gas. A gas hub s a place where gas wholesale tradng s facltated. Organzed markets have been often seen as a prerequste for gas prcng through gas-to-gas competton. One key queston n the desgn of a wholesale gas market s the way n whch the hub desgn deals wth the gas network. Two types of organzed gas markets dependng on the aforementoned regulatory framework (pont-to-pont transportaton n the US or entry-ext access n the EU) can be found: physcal hubs and vrtual hubs [8]. Physcal hubs are lnked to a specfc gas faclty where the shpper trade wth gas at a prce at the locaton, usually ppelnes junctons where a sgnfcant amount of gas sales and purchases takes place, and where storage servces can be also traded. On the other hand, vrtual hubs are balancng electronc platforms, assocated wth a standard set of delvery ponts. Therefore, vrtual hubs are not lnked to a specfc gas faclty or any physcal juncton of ppelnes, but to the gas facltes embedded n a balancng zone. US wholesale gas markets are fundamentally based on blateral contracts among producers and marketers (referred as shppers n ths document), wthout the need for any mandatory organzed market to trade. Nonetheless, gas supply and demand patterns are hghly volatle, so the agents solve ther mbalances n the short term at the

35 28 Market equlbrum n natural gas systems: Analyss of the mplementaton of a hub physcal hub, where the delvery of the commodty takes place. The Henry Hub, located n Lousana, s the ntersecton of more than a dozen nterstate ppelnes and t s the most lqud tradng hub n North Amerca and the most mportant physcal hub worldwde. The prce coordnaton between long- and short-term decsons s done through fnancal contracts n organzed fnancal markets New York Mercantle Exchange (NYMEX), where the underlyng asset s usually the delvered gas n the hub [16]. EU gas markets dd not go so far nto the network detals and favor organzng gas transactons around a vrtual hub, whch s not a physcal representaton of ppelnes, but nstead a regulated set of delvery ponts wth a very smplfed representaton of the actual physcal characterstcs of the network [21]. The fundamental logc for vrtual hubs s to ncrease the market lqudty assocated wth the smplfcaton of the network. Several natonal vrtual hubs have been consttuted snce the md 90`s. The most lqud are NBP n the UK (1996) and TTF (2003) n the Netherlands. The NBP works as the prcng pont for the Intercontnental Exchange (ICE) market, and t s the most lqud tradng pont n Europe. Physcal and vrtual hubs may offer smlar servces. The most mportant dfference s the operaton of the network assets. In a vrtual hub, whose man characterstc s embeddng transmsson and dstrbuton networks n balancng zones, the gas transmsson system operator offers a set of network servces calculated from the operaton of the network and s commonly n charge of montorng shppers entres, exts, and nventory varatons wthn the balancng zone. In a physcal hub, t exsts the possblty of trackng the flow of gas wthn the ppelnes and network servces are offered by a company (whch may be a ppelne owner or not), usng a specfc set of physcal assets.