MULTI-PERIOD, STOCHASTIC EMISSION COMPLIANCE MODEL … · 2020-05-18 · i introduction i...

I

I Introduction

UNIVERSIDAD PONTIFICIA COMILLAS ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)

MÁSTER OFICIAL EN EL SECTOR ELÉCTRICO

TESIS DE MÁSTER

MULTI-PERIOD, STOCHASTIC EMISSION COMPLIANCE MODEL THROUGH

TRADING UNDER EU ETS

Autor: Muhajir Tadesse Mekonnen

MADRID, August 2010

UNIVERSIDAD PONTIFICIA COMILLAS ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA (ICAI)

MÁSTER OFICIAL EN EL SECTOR ELÉCTRICO

TESIS DE MÁSTER

MULTI-PERIOD, STOCHASTIC EMISSION COMPLIANCE MODEL THROUGH


Tutors Prof. Dr. D. Michel Rivier Abbad ([email protected])

Elena Mateos Bermejo ([email protected])

Author Muhajir Tadesse Mekonnen ([email protected])

Madrid, August 2010

mailto:[email protected]�

mailto:[email protected]�

©Universidad Pontificia Comillas – Escuela Técnica Superior de Ingernieria (ICAI)

Alberto Aguilera, 23, 28015, Madrid

All rights reserved.

Autorizada la entrega de la tesis de máster del alumno/a:

Muhajir Tadesse Mekonnen

EL DIRECTOR

Elena Mateos Bermejo

Fdo.: ________________ Fecha: ______/______/_______

EL TUTOR

Michel Rivier Abbad

Fdo.: ________________ Fecha: ______/______/_______

Vº Bº del Coordinador de Tesis

Michel Rivier Abbad

Fdo.: ________________ Fecha: ______/______/_______

ACKNOWLEDGEMENTS

I am deeply grateful to my supervisor Dr. Michel Rivier, from IIT, whose support, stimulating suggestions, encouragement and confidence in my abilities were a source of constant motivation. This thesis would not have been possible without his guidance and pragmatism. I am also very grateful for Dr. Andres Ramos and Dr. Javier Garcia for their generosity when sharing their immense knowledge on optimization principles.

I owe my deepest gratitude to Elena Mateos, from gas Natural Fenosa, for her continuous mentorship through the period of my thesis. Her continuous feedback and comments have played the most important role in shaping up this work. I also would like to thank the people from gas Natural Fenosa Marta Pla and Angel Rojo for their continuous support and feedback and for sharing their knowledge in the area of emission trading as well as for several helpful discussions throughout my work.

I am indebted to many of my colleagues who support me in advice and by sharing their experiences. Special thanks to my colleague Birhane Hailesilase and my roommate Francesc Torrent for their continuous encouragement and moral support.

I feel profoundly indebted to European Commission for offering me financial assistance during my graduate studies without which I could not have undertaken studies in Europe.

Finally and especially, I would like to give my special thanks to my parents for their patient, love, encouragement and for the many sacrifices they have made over a number of years. This thesis is dedicated to them.

August 2010

Muhajir

I

CONTENTS

1 Introduction .............................................................................................................. 1

2 Problem Analysis ...................................................................................................... 2

2.1 Problem Background ........................................................................................... 2

2.2 Problem description ............................................................................................. 4

2.3 Research Objective .............................................................................................. 5

2.4 Scope of the research ........................................................................................... 6

2.5 Research Methods ............................................................................................... 7

2.5.1 Literature studies .......................................................................................... 7

2.5.2 Modeling ...................................................................................................... 7

2.6 Organization of the thesis .................................................................................... 8

3 EU Emission Trading Scheme ................................................................................... 9

3.1 EU ETS origin and scope .................................................................................... 9

3.2 Characteristics of EU ETS ................................................................................. 10

3.2.1 The cap setting process ................................................................................ 10

3.2.2 Banking and borrowing ............................................................................... 11

3.2.3 Offset rules ................................................................................................. 12

3.2.4 Monitoring, reporting and verification ......................................................... 13

3.2.5 Compliance and enforcement ...................................................................... 13

3.3 What happened so far? ...................................................................................... 13

3.4 Future expectations and uncertainties in EU ETS ............................................... 17

4 Models for emission trading planning ...................................................................... 19

5 A model to develop strategic emission compliance plan through trading under EU ETS

............................................................................................................................... 21

5.1 The modeling process ........................................................................................ 21

5.2 The modeling approach used in this thesis .......................................................... 22

5.3 Mathematical formulation ................................................................................. 24

<Contents II

5.3.1 Time Horizon ............................................................................................. 24

5.3.2 Decision variables ....................................................................................... 24

5.3.3 Parameters ................................................................................................. 27

5.3.4 Constraints ................................................................................................. 28

5.3.5 Objective function ....................................................................................... 31

5.4 Stochastic Modeling .......................................................................................... 35

5.4.1 How to deal with the uncertainties .............................................................. 36

5.4.2 Developing a multi-period stochastic model ................................................. 36

6 Computational results ............................................................................................. 40

6.1 Testing and experimenting with the deterministic model .................................... 40

6.1.1 Quality of data used .................................................................................... 40

6.1.2 Verification and validation .......................................................................... 41

6.1.3 Scenario analysis ........................................................................................ 46

6.1.4 Sensitivity analysis ...................................................................................... 49

6.2 Testing and experimenting with stochastic model ............................................... 55

6.2.1 Verification of the stochastic model ............................................................. 55

6.2.2 Optimal stochastic solution ......................................................................... 57

6.2.3 Stochastic measures .................................................................................... 58

7 Conclusions and Recommendations ........................................................................ 60

7.1 Conclusions ...................................................................................................... 60

7.2 Recommendations ............................................................................................. 61

7.3 Future line of research ....................................................................................... 62

8 Appendix ................................................................................................................ 63

9 Bibliography ........................................................................................................... 72

III

LIST OF FIGURES

Figure 3-1 Price and Volume history of EUAs during the EU ETS Phase I ....................... 14Figure 3-2 EUAs Spot Allowance prices during phase II (in €/ton of CO2) ...................... 16Figure 3-3 Comparison of the price of CER and EUA futures of Dec 2008 maturity ......... 17Figure 5-1 Flow chart of the modeling process ................................................................. 22Figure 5-2 Calculation of NPV of allowance purchasing costs and selling revenues ........... 32Figure 5-3 the decision process of a utility in emission compliance ................................... 37Figure 6-1Results of the Base case ................................................................................... 43Figure 6-2 Base case with high allowance price in phase II (experiment 1) ....................... 44Figure 6-3 Model output with very expensive EUA prices in Phase II (experiment 2) ....... 45Figure 6-4 Optimal strategy for backwardation allowance prices (experiment 3) ............... 46Figure 6-5 EUA spot price scenarios ............................................................................... 46Figure 6-6 Comparison of Strategies developed different scenarios .................................. 47Figure 6-7 Influence of EUA/CER spread on the model results ....................................... 50Figure 6-8 Spread curves used for the sensitivity analysis ................................................. 50Figure 6-9 Euribor variation for sensitivity analysis ......................................................... 51Figure 6-10 The influence of discount rate on model results ............................................. 52Figure 6-11 The variation in the interest rate used for sensitivity analysis ......................... 53Figure 6-12 The influence of interest rate on model results ............................................... 54Figure 6-13 Influence of emission estimates on the optimal strategic decision ................... 55Figure 6-14 Comparison of the stochastic outputs with only one scenario with the deterministic results ........................................................................................................ 57Figure 6-15 Stochastic model output ............................................................................... 58Figure 8-1 Future price and volume history of EUA December 2008 to 2013 expiration ... 63Figure 8-2 Future price and volume history of CERs of December 2008 to Dec 2011 expiration ....................................................................................................................... 63Figure 8-3 Historical EUA/CER Spread ......................................................................... 67Figure 8-4 Scenario tree used for analysis ........................................................................ 68Figure 8-5 Historical interest rates that were used to quote EUA futures from 2009 spot prices ............................................................................................................................. 69Figure 8-6 A-Historical Euribor 12 month average, B- historical and estimated annual average ........................................................................................................................... 70

IV

LIST OF TABLES

Table 5-1 list of indices and their notation used in this paper ............................................ 25Table 5-2 Notations used for Decision variables .............................................................. 26Table 5-3 List of parameters and their notation used in the paper ..................................... 27Table 6-1 Input data used for the Base case scenario ........................................................ 42Table 6-2 Summary of costs of each scenario (in millions) ................................................ 49Table 6-3 The costs of each decision under different scenarios .......................................... 59Table 6-4 The expected regret pay off .............................................................................. 59Table 8-1 Assignations and types of installations ............................................................. 65Table 8-2 Estimated emission levels of each installation ................................................... 66Table 8-3 EUA price forecasts [33] .................................................................................. 66Table 8-4 Price scenarios used for analysis ....................................................................... 67Table 8-5 EUA/CER spreads used for case studies and sensitivity analysis ...................... 68Table 8-6 The interest rates used to quote future prices .................................................... 69Table 8-7 Euribor values used for NPV calculation .......................................................... 70

V

BNX BlueNext

LIST OF ACRONYMS

CAAA Clean Air Act Amendment

CDM Clean Development Mechanism

CERs Certified Emission Reductions

CHP Combined Heat and Power

CITL Community Independent Transaction Log

EC European Commission

ECX European Climate Exchange

ERUs Emission Reduction Units

EU ETS European Union Emission Trading Scheme

EUAs European Union Allowances

GHG Greenhouse gases

HFC Hydro-floro carbon

IET International Emission Trading

IPCC International Panel on Climate Change

JI Joint implementations

NAP National Allocation Plan

UNFCCC United Nations Framework Convention on Climate Change

VII

EXECUTIVE SUMMARY

Global warming has become the most relevant and the hottest issue in the world, now days. The main cause is identified to be the rapidly increasing green house gas (GHG) emissions due to human activities. Since the industrial revolution, the globe’s economy became entirely based on fossil fuels which are the main sources of GHG emissions.

Several policies and strategies have been designed and implemented to address the global warming problem worldwide. Among these policies and strategies, emission trading has become more popular and is proven to be effective when there are uncertainties on the benefit and cost of GHG abatement. It has been in practice in various places since the 1990 SO2 emission trading in USA.

European Union Emission Trading Scheme was started in 2005 and is the largest multi-national emission trading in the world. It covers around 12,000 carbon intensive installations from the energy and industry sector within EU which are responsible for the 40% of the EU’s GHG emission level.

The introduction of EU ETS brought about profound challenges and opportunities to participating companies. Compliance obligations, price dynamics of allowances, regulatory and emission uncertainties and information asymmetry are the main challenges for those companies while, emission trading, investment in allowance production as well as swapping are identified as opportunities that attract those companies.

In order to become more competitive and to win in the market, companies subject to EU ETS have to develop a strategy for their emission compliance portfolio management. This includes strategic schedules on buying, selling, banking as well as surrendering allowances.

This thesis has addressed the problem of developing an optimal CO2 emission compliance strategy through emission trading for a power utility subject to EU ETS obligation. Taking emission estimates as in input, the proposed methodology develops optimal allowance purchasing and surrendering strategies. With the extension of the EU ETS to a long term market and the dominance of thermal generation units subject to EU ETS in the electricity sector, this issue is currently very important in the sector.

The issue of developing optimal emission compliance strategy through emission trading for a company under EU ETS is mainly influenced by legal and regulatory binding rules embedded in the scheme. Extensive survey of EU ETS history, origin and performance has been conducted to identify those rules.

Executive summary VIII

The search for an optimal emission compliance strategy involves allowance purchasing, and surrendering strategies. This requires the evaluation of the expected costs of any candidate strategy. Particularly, estimation of expected costs from both spot and futures market participation is crucial. This requires spot allowance prices and interest rates used to quote the corresponding future prices to be identified explicitly.

Uncertainty with respect to emission price is the key issue in developing emission compliance strategy through emission trading. In this thesis a deterministic model is developed for scenario and uncertainty analysis followed by a stochastic model to include the uncertainty with respect to prices. The uncertainty in the emission estimates and other parameters other than allowance prices is not considered in the stochastic model rather a sensitivity analysis is carried out to study the effect of these uncertain parameters using the deterministic model.

The thesis focuses on the development of annual purchasing and surrendering strategy for the company’s emission. However, this annual strategies can be break down in to monthly or weekly operational decisions. That means the results can be used as a frame work to develop the daily operational decisions.

The validity of the methodology developed is confirmed through experiments with different price scenarios and parameter values performed on a fictitious but representative Spanish power utility owing 20 installation subject to EU ETS.

Finally, the result of the stochastic model is measured in terms of sum of expected regret, which shows that in the case of high uncertainty, the stochastic decision yields the minimum sum of expected regret.

1

1 INTRODUCTION

In the framework of global efforts to reduce emission level of greenhouse gases, beside various pollution abatement strategies, emission trading appears more and more as an effective alternative. Currently there exist emission trading systems in various parts of the world. International emission trading (IET) created as one of Kyoto flexible mechanisms, European emission trading scheme (EU ETS), New Zealand Emission trading Scheme and several voluntary and non-voluntary markets in USA are the major ones.

The introduction of emission trading brought about a profound challenges and opportunities to participating industries. Following the introduction of emission market, participating energy utilities are subjected to compliance obligation. The presence of uncertainty in the price of allowances, emission estimates and regulatory changes on the top of information asymmetry makes compliance decisions difficult for those companies. However, the introduction of emission market also creates a situation where utilities can invest, trade and profit from allowance trading in addition to their energy portfolio.

This thesis aims to develop an original methodology to construct optimal emission allowance compliance strategy through emissions trading for a company subjected to EU ETS.

This paper is organized in six sections. The first section is dedicated to problem analysis. The problem and its background are described, the objective of the thesis is set and the scope of the research is specified, followed by a sub section justifying the proper methodology. The next two sections describe the literature review where a brief description of EU ETS is presented and some relevant works are revised. Section five is devoted to developing multi-period deterministic and stochastic optimization models that used to construct optimal emission allowances compliance strategy. A numerical analysis is carried out to illustrate and evaluate the adequacy of these models in section six using a case of fictitious but representative Spanish power utility subject to EU ETS. Finally, conclusions are drawn and recommendations are suggested from the thesis.

2

2 PROBLEM ANALYSIS

This chapter gives a thorough analysis of the problem. In this chapter, the general background that motivates this thesis is presented (2.1), the problem is briefly described (2.2), the objective of the research is set and questions to be answered in order to achieve this objective are identified (2.3), the scope of the research is specified (2.4) and finally the choice of a methodology to deal with the underline problem is justified (2.5).

This thesis aims to develop an original methodology to construct optimal emission allowance compliance strategy through emission trading for a company subjected to European Union Emission Trading Scheme. The chapter also briefly describes the organization of the thesis to facilitate its reading.

2.1 Problem Background

It is now generally accepted amongst scientists and politicians worldwide that the globe is warming to such an extent that the livelihoods of the world’s habitats are under serious threat. Violent and frequent storms destroy people’s habitats here and there; unpredictable weather drastically changes the usual trend of agriculture especially in developing countries that are still dependent on rain-fed agriculture and causes droughts and floods; ecosystem disruption, rising sea levels and new health threats emerge. The potentially catastrophic effect of global warming for human health, the environment and the economy within the not so distant future is described by Stern [1]. Thus awareness of global warming is increasingly influencing thinking throughout the world.

The main cause of global warming is the rapidly increasing green house gas (GHG) emissions due to human activities. Burning of fossil fuels which become human’s popular activity since the industrial revolution is the primary and the main cause of GHG emission. Fossil carbon is being taken out of the ground, run through combustion chambers, and transferred to a more active and rapidly circulating carbon pool in the air, oceans, vegetation and soil. Some of this active carbon builds up in the atmosphere in the form of carbon dioxide, trapping more of the sun’s heat, warming the earth and destabilizing the climate.

In its third assessment report in 2001, the International Panel on Climate Change (IPCC) projected that, on current trends, the globally averaged surface temperature would increase by 1.4 and 5.8 degrees centigrade over the period 1990 and 2100 [2]. The report also estimated that restricting the temperature rise to 1.5 to 3.9 °C would require CO2 levels to be stabilized at 450 ppm. Restricting the temperature rise to 2°C or less requires levels of

Problem Analysis 3

GHG stabilized at 400 ppm of CO2 equivalent (350 ppm CO2 plus others1 3) [ ]. That would imply even steeper cuts are required since concentrations already are 385 ppm. This signifies the sense of urgency to reduce global green house gas emissions as any delay would result in a faster reduction of emissions requirement.

In fact, in the last decade, several organizations and policy regulators have been studying and discussing with environmental economists possible strategies to tackle problem of climate change described above.

Economists saw the problem as a problem of externalities: damage (or benefit) caused by one economic agent to another for which the former is not held economically accountable. Therefore as long as agents that have been and are emitting greenhouse gases have no obligation to compensate for their pollution of the environment they will keep emitting without limits. They call this phenomenon as a market failure caused by inefficient allocation of market resources.

Some economists argue that such problems can be solved by assigning an obligation in a form of pricing for the emitting agents. In a competitive market, firms with free access to environmental resources will continue to engage in polluting activities until the marginal return of their production is zero. A price equal to the marginal external cost of their polluting activities needs to be imposed to polluting agents so that they will internalize at the margin the full social costs of their pursuits. Such a price incentives in the form of taxes are called Pigouvian taxes named after the name of the economist first proposed them [4].

Subsidies are also alternative methods of solving the problem. Subsidies per unit of emission reduction could establish the same incentive for abatement activity as a tax of the same magnitude per unit of pollution emitted. However, Kamien [5] identified important asymmetries between the two policy instruments. Subsidies increase profits and give an incentive more firms to inter in the business increasing the supply curve in the long run, while taxes have the reverse effect.

The other solution environmental economists suggest as a solution to reduce green house gas emission is marketable permits which now a day is known as emission trading. This is based on the contribution of Coase [6] who argues that the root of the problem is undefined

1 ‘ton of CO2 equivalent’ means one metric ton of carbon dioxide or an amount of any other greenhouse gases listed in Annex II of the EU directive (2003/87/EC) with an equivalent global-warming potential. These gases are Carbon dioxide (CO2), Methane (CH4), Nitrous Oxide (N2O), Hydroflorocarbons (HFCs), Perfllorocarbons (PFCs) and sulfur Hexaflouride (SF6).

Problem description 4

property rights. He claims that if the ownership rights to clean air for example were clearly defined, then self interested parties would use legal and market mechanisms to bring about a socially acceptable level of externalities. In the absence of transaction costs and strategic behavior it doesn’t matter to whom the property right is allocated, the only difference will be the direction of transfer of wealth between the agents interested in the right.

In the framework of worldwide efforts to reduce emission level of greenhouse gases, beside diverse pollution abatement strategies, emission trading appears more and more as an effective alternative. It is proven to be effective especially when there are uncertainties on the benefit [7]or the cost [8] of abatement.

This makes emission trading a more popular practice Emission trading has been introduced in various parts of the world. SO2 emission trading in USA, European Union Emission Trading Scheme (EU ETS), New Zealand emission trading scheme, international emission market (created as one of Kyoto flexible mechanisms), Australian market as well as voluntary and non voluntary CO2 markets in USA could be identified as the major ones. Although the general background of these markets is similar, this thesis will mainly focus on EU ETS.

2.2 Problem description

European Union Emission Trading Scheme is the largest regional emission trading scheme which is started in 2005 to achieve the EU Kyoto targets. In this scheme, large emitters of carbon dioxide within EU must monitor measure and annually report their emissions and they are obliged to return an amount of emission allowances to the government that is equivalent to their CO2 emission every year. In order to meet their targets more flexibly and efficiently, companies are allowed to trade allowances and /or credits from project offset. EU ETS is discussed in detail in the next Chapter.

Following EU ETS, a price is now created for emission of CO2 and a 3% decrease of emissions from the participants is observed between 2007 and 2008 [9]. The strong commitment of EU nations for the 2020 emission target is expected to keep the emission market more active and liquid.

Companies subject to EU ETS have now CO2 trading in their portfolio which should be managed like other portfolios that those companies have. CO2 trading is subjected to several challenges. The following paragraphs describe those challenges.

Kijima [10] showed that firms trade allowances not only to meet their emission target exclusively but also to take advantage of speculative positions. The different prices of allowances at different markets and different trading periods give an incentive for energy

Problem Analysis 5

intensive firms for speculative trading. This price variation also brought about a significant participation of brokerage firms and financial institutions in the emission market. Although the inclusion of financial institutions and brokerage firms adds more diversity and generates more liquidity to the markets, it creates information asymmetry in the market making it difficult for energy utilities to take strategic trading decisions.

High volatility in the price of allowances is observed since EU ETS was started. Alberola [11] and Chevallier [12] explained the price dynamics of emission allowances during EU ETS Phase I and Phase II respectively. Although there are different explanations for the cause of this price dynamics, regulatory changes, initial allocation problems and the economic crisis can be counted as major ones. In spite of the fact that the current carbon prices show more or less a stable trend, there is still a great regulatory and economic uncertainty which may completely alter the current price trends.

Apart from price and regulatory uncertainty, installations are also subject to uncertainty in their emission estimates. The emission of an installation depends on the type of fuel it uses, the amount of production as well as the price of emission allowances. These factors are also uncertain which makes estimating emissions of companies even more difficult and uncertain.

In order to become more competitive and to win in the market, companies subject to EU ETS have to develop a strategy for their emission compliance portfolio management. This includes strategic schedules on buying, selling, banking as well as investing decisions that may lead to minimize their long term emission compliance cost. Trading to minimize only annual emission costs may be short sited behavior and may result in paying higher costs in the long term. Once strategic schedules are set, long term investment decisions and yearly trading schedules can be planned within the strategic framework.

2.3 Research Objective

The main objective of this research is to develop an original methodology that will be used to develop strategic emission compliance strategy for a company subject to EU ETS through emission trading. Taking estimated emission levels of the company as an input data, the methodology will enable in developing the optimal annual schedules to purchase, sell, bank and surrender allowances under EU ETS regulatory framework.

The research first describes the nature of EU ETS, assesses the performance of the market and identifies the potential risks and possible future uncertainties.

In the second section the research focuses on developing, testing and experimenting with a strategic emission compliance planning model that can be used as a framework for annual

Scope of the research 6

trading of a company under EU ETS. Aiming for minimizing total emission compliance cost, the model assures the fulfillment of EU ETS regulatory obligations.

For the objective of the research to be realized, the following research questions must be answered:

What is the best strategy for a company under EU ETS (subject to price and regulatory uncertainties) to optimize its long term emission compliance costs given its estimated emission?

Sub questions:

What are the lessons learned so far from the past EU ETS?

What future uncertainties are anticipated on EU ETS?

Which are the constraints and decision variables?

Which possible price scenarios exist in the EU ETS?

Which are the best purchasing strategies for a company under EU ETS to minimize its long term emission compliance cost?

2.4 Scope of the research

The scope of this study will be limited to European Emission Trading Scheme. The model will be developed as a case study for a power company under EU ETS. However, this model can be modified in order to be used by other industries or even other emission trading schemes.

There are three periods defined under the EU ETS where emission trading takes place. They are commonly known as EU ETS Phases. Phase I (2005-2007) was started as a trial period. Phase II (2008-2012) is taking place right now, where as European Commission is preparing for phase III (2013-2020). Except for some regulatory changes that are expected to be introduced during Phase III, the extension of EU ETS to Phase III is indubitable. Although the time horizon can be easily extended when more information on EU ETS after 2016 is known, the time span from 2010 to 2016 will be considered for the analysis in this study.

Problem Analysis 7

2.5 Research Methods

2.5.1

By performing not only literature study in journals and scientific papers, but also legal literature, EC directives, national royal decrees, industry and market reports a foundation of the study will be provided.

Literature studies

Although the emission market is in its maturity stage, there are quite enough studies, publications and reports about different aspects of EU ETS and its performance, Price dynamics, implications, effects as well as emission compliance planning.

2.5.2

The problem described above (2.3) involves generating emission compliance strategy aiming at reducing total long term emission compliance cost of the company as much as possible while regulatory obligations are still met. This is obviously an optimization problem.

Modeling

An optimization problem may have three components. It may have objective function (s), which is a quantitative measure of the system to be optimized (minimized or maximized); variables, which are decisions to be taken that will affect the value of the objective function, and constraints, which are relationships that the variables have to satisfy that, naturally, limit the value of the objective function. Optimization, in its components, can be defined as finding the value of the variables, so that the objective function is optimized, satisfying the different constraints.

Various optimization problem programming techniques are available in various literatures. Linear programming involves continuous variables, linear constraints and linear function; quadratic programming involves quadratic objective function; Mixed Integer programming involves continuous variables, integer or binary variables, linear constraints and linear objective function; Non Linear programming involves continuous variables, non linear constraints and linear or non linear objective function; dynamic programming involves taking decisions in several steps.

The problem considered in this thesis one of the forms which involves continuous variables, binary variables, linear constraints and linear objective function. It also involves some uncertain variables and has long term nature. Therefore, multi-period and stochastic mixed integer optimization is used to address the problem.

Organization of the thesis 8

Hence, once the different aspects of the EU ETS are studied and analyzed from literature studies and once the challenges of decision making are pointed out, the problem is formulated as a multi-period, stochastic mixed integer programming problem. The problem is then illustrated and evaluated using a case study and solution strategies are pointed out.

2.6 Organization of the thesis

This paper is organized in six sections. The first section gives a brief introduction of the thesis. Section two is dedicated to analyzing the problem. The problem and its background are described, the objective of the thesis is set and the scope of the research is specified, followed by a sub section justifying the proper methodology.

The next two sections describe the literature review. Section three presents the detailed description of EU ETS. The origin and the scope of EU ETS are illustrated followed by its characteristics, its performance as well as future expectations and some uncertainties. In the fourth section some relevant modeling works are reviewed and the unique features of the methodology in this thesis are outlined.

Section five is dedicated to formulating multi-period deterministic and stochastic optimization problem. The variables, parameters and the constraints involved in the problem are identified and converted to mathematical expressions. The problem is formulated as multi-period stochastic MIP problem.

In section six a numerical analysis of the modeling approaches is carried out in order to illustrate and evaluate the methodology proposed. All the analyses use a case of fictitious power utility operating in Spain under EU ETS. Verification and validation tests are conducted; an analysis of the sensitivity of the base case solution with respect to variation of different relevant input parameters is performed. Deterministic and stochastic solutions of the numerical example are proposed under various price scenarios.

Section seven gives a summary of the analysis, conclusion and recommendation from the research conducted in this thesis.

9

3 EU EMISSION TRADING SCHEME

European Union Emission Trading Scheme is the largest and the first multi-national emission trading system and the major pillar of EU’s climate policy. It was started to help the European Union fulfill its Kyoto commitment cost efficiently.

This section gives a comprehensive description of EU ETS. The history and the origin of EU ETS are described (3.1), its characteristics and differences from ordinary cap-and-trade system are illustrated (3.2), its performance and lessons learned so far are explained (3.3) and finally future implications, potential regulatory changes and uncertainties are identified (3.4).

3.1 EU ETS origin and scope

The history of EU ETS goes back to the Kyoto protocol (1997) of the United Nations Framework Convention on Climate Change (UNFCCC). In this convention, annex-B 2

13

countries (including EU) agreed on a binding rule to reduce the green house gas emission level below 8% of the 1990 emission levels [ ]. The downward trend of GHG emissions that was seen in the 1990s had reversed and EU´s emissions were likely to be above the target set by Kyoto protocol during the first commitment period (2008-2012). In order to keep its Kyoto promises, EU was looking for more aggressive actions. Since emission tax was rejected in the 1990s, a cap-and-trade approach was chosen. This is because it guaranteed a limit on GHG emissions, it was compatible with emission trading provisions of the Kyoto protocol and it was the only other instrument available [14].

The cap-and-trade program was first suggested in 2000 in the European Commission’s green paper [15], following the observed increase in the trend of GHG emission. It was then approved by the Council of ministers. The directive was published and become law in 2003. Finally, two years after approval, it was commenced on the first of January 2005 as a trial period with the name European Union Emission Trading Scheme (EU ETS).

EU ETS is the world´s first and largest multi-country emission trading market and it is the major part in the EU climate policy. It is a downstream system. The point of regulation is the installation releasing the emissions into the atmosphere. EU ETS covers around 12,000 large emitting stationary facilities located in the European Union which are responsible for

2 Annex B countries are industrialized countries and countries with economic in transition. They are explicitly listed in the Annex B of the Kyoto Protocol.

Characteristics of EU ETS 10

the 40% of European Union’s GHG emission level. These facilities include installations with a rated thermal input exceeding 20MW, oil refineries, coke ovens, iron and steel plants and factories making cement, glass, lime, bricks, ceramics, pulp, paper and board.

Currently, EU ETS doesn’t cover the transportation sector. However, its extension to the aviation (flying combustion installations) sector is underway and is likely to be implemented starting from 2013. Although it also doesn’t consider greenhouse gas emission other than carbon dioxide, the EU is in progress to expand its scope to include other greenhouse gases.

3.2 Characteristics of EU ETS

EU ETS is mainly a cap-and-trade system. An absolute quantity limit (or cap) on CO2 emissions has been placed on some 12,000 emitting installations, tradable allowances have been distributed among the installations in an amount equal to the cap and these installations must measure and report their CO2 emissions and subsequently submit allowances equivalent to their emission

In a cap-and-trade system, the cap is the maximum amount of pollutant that can be emitted and this ensures the quantity of total emission to be limited to this amount. The trade gives flexibility and economic incentive to the agents subject to the system to sell whenever they have surplus and to buy whenever they have deficit of allowances.

However, EU ETS is not solely cap-and-trade system. It has some significant design difference from the classic cap-and-trade system. Ellerman [14] describes those design differences in comparison with the SO2 emission market which was US’s experience. The cap setting process, the provision of banking and borrowing and the linking or off-system provisions are the main aspects that differentiate the scheme from ordinary cap-and-trade system.

3.2.1 The cap setting process

Most of the operation in EU ETS takes place in a decentralized manner. Cap setting, distribution of allowances, the operation of the registries 3

3 Registries are national databases containing accounts which will hold the allowances. Each member state has its own national registry. These registries interlink with the community independent transaction log (CITL) which will record and check every transaction.

for tracking allowances and emissions as well as the monitoring, reporting and verification are all performed by each member state subject to certain criteria and coordinated by the European Commission. Each

EU Emission Trading Scheme 11

member state will propose a maximum limit on emission of its own country. The cap of EU ETS is therefore the sum of all the caps set by individual member states. The proposed cap should be reviewed and approved by the European commission before being implemented. Once it is approved according to the procedures and criteria specified in the EU emission trading directive, the member state will distribute this cap in terms of European Union Allowances (EUAs)4

The National Allocation Plan of each member state is always subjected to European Commission supervision according to certain criteria. Rules at European level provide for a limit of 5% of the member states total to be auctioned during 2005-2007 trading period and 10% during 2008-2012. In addition no free allocation shall be given to installations not covered by the EU ETS. In practice decentralized NAP resulted in different ways of allocating allowances. Some common practices are to be more restrictive allocations for power plants and more generous for other industrial installations.

to installations covered in the scheme. This is often known as the National Allocation Plan (NAP).

In EU ETS trading takes place in sequence of relatively short sequential multi-year trading periods. These are usually known as EU ETS phases. The first three-year trading period was from 2005-07, often called the pilot or trial phase, followed by a second, five year trading period from 2008-12 that corresponds to the first Kyoto commitment period and is usually known as commitment period or Kyoto period. The third trading phase is set to be eight years long from 2013 through 2020. The cap in phase 1 was around 2.2 billion per year while this figure drops to 2.08 billion per year including two more member states. The cap for phase 3 is set to 1.927 billion per year although it will be revised for new entrants to the scheme and if the commitments are made to increase the 2020 emission reduction from 20% to 30%.

3.2.2 Banking and borrowing

Buying or selling of allowances is not the only alternative to the owners of installations for dealing with the difference between allocation and their emission. They are also free either to bank or borrow allowances. Allowances are issued annually and they are valid for covering emissions in any year within the trading period. Banking of allowances is the phenomenon of saving surplus allowances for the coming trading (compliance) years if the

4 One EUA is equivalent to one ton of Carbon dioxide equivalent. That means it will give the right to emit one ton of carbon dioxide equivalent.

Characteristics of EU ETS 12

operator decides not to sell. Borrowing is the use of allowances from the next year’s allocation whenever the operator is short and decides not to buy.

Borrowing can be made only from the next year’s allocation since each year’s endowment of allowances is placed in installation holding accounts at the end of February in each year, two months before the surrender of allowances for the past year’s emission is required. In EU ETS banking or borrowing of allowances within any given trading period is allowed without any restriction.

However, there are tight rules when it comes to trading between phases. Inter-period banking or borrowing was not allowed between the three-year trial period and the subsequent five-year Kyoto period. This made the first trial period more self contained and it was the major fallout of the period. Following the lessons learned from the trial phase, inter-period banking is allowed without restriction from the second to the third phase.

3.2.3 Offset rules

In order to make emission compliance of committed countries flexible and more efficient, Kyoto Protocol introduces three flexible mechanisms: Clean Development Mechanism (CDM), Joint Implementation (JI) and emission trading. In CDM, tradable carbon credits are awarded to projects to reduce GHG emissions that are hosted in developing countries and complete a formal approval process. These credits are known as certified emissions reductions (CERs). In JI credits are awarded to similar projects, only they are hosted in developed countries or those with economic in transition. These credits are known as Emission reduction units (ERUs).

After adopting the linking directive in 2004, EU ETS allows installations to comply their emission target using credits (Kyoto credits) for emission reductions established outside of EU. However, this is subject to both quantitative and qualitative limitations. On the one hand credits associated with nuclear power and from CO2 sinks cannot be used for compliance. On the other hand the credit import, in phase 2, is limited to 13.5 % of the cap although this percentage differs among different member states.

Since its provision, Kyoto credits also become actively used in the trading and compliance within EU ETS. Companies actively participate in direct trading of allowances already issued by the UN’s CDM executive board. They also participate in the trading of projects in their development stage expecting that the projects will be issued with credits. The former is called secondary credits market while the later is known as primary credits market.

Primary markets are cheaper but are exposed to various risks. They also take long time before the projects are issued with the credits. Utilities have to make some kind of analysis


before directly purchasing those projects. The model developed in this thesis gives an input for such analysis by providing the appropriate years to use Kyoto credits for compliance.

3.2.4 Monitoring, reporting and verification

Each installation covered by EU ETS is obliged to monitor and report its annual emissions. The due date for annual report is March 31 of the year after the compliance year. Emissions should be monitored by calculation or on the basis of measurement. Generally, emissions are not measured directly. The common practice for EU-wide monitoring, however, is based on calculation approach. This calculation is based on specified emission factors, activity data (production rate, fuel consumption etc.) and oxidation factor.

The self report is subject to a third party independent verification just like other financial accounting reports. The verification process addresses the reliability, credibility and accuracy of monitoring systems.

3.2.5 Compliance and enforcement

EU ETS directive obliges utilities to submit, for each of their installation, a number of allowances equivalent to verified emission levels of that installation by April 30 of the year after the compliance year. Failure to surrender sufficient number of allowances leads to a penalty.

The penalty during the trial period was 40€ per each of non-surrendered allowances, the obligation to surrender the missing allowances in the following calendar year and the publication (name and shame) of non-compliant companies. In phase II the penalty increases 100 € per non-surrendered allowances. Payment of the excess emissions penalty doesn’t make the operator free from the obligation to surrender an amount of allowances equal to those excess emissions when surrendering allowances in relation to the following calendar year.

3.3 What happened so far?

EU ETS has been put in to practice since 2005. The first phase expired in 2007 which leaves some important lessons behind. This sub-section describes the performance of EU ETS during the first three-year trading period and during the first half or the second five-year trading period (2008-2010).

Figure 3-1 displays the price and volume evolution of trial period EUA allowances since EU ETS was launched. The two line graph series represent spot EUAs exchanged on the

What happened so far? 14

BlueNext5 (BNX) and future EUAs of December 2007 maturity contracted on European Climate Exchange6

(ECX). Apart from the interest rate that is quoted to calculate the future prices, the two series show a more or less similar trend.

Figure 3-1 Price and Volume history of EUAs during the EU ETS Phase I

Source: BLNX for spot and ECX for futures

As a new commodity market, the EU carbon market needed time to achieve real price discovery. The figure shows the EUA price changes during the first two years. From January to July 2005 the price increased to around 30€. Then the price fluctuated in the range 20€ to 25 € until April 2006 where it reaches its global maximum of around 31€. This price however is collapsed for both phase I and phase II EUAs on the last week of April 2006. In less than a week time prices fell from over 30€ to about 20€ for the second phase EUAs and to 15€ for trial period EUAs. The cause for this sharp price decline was the release of verified emissions data of EU member states for the first time which was significantly less than expected [11].

Price collapse like this during the start of trading is a phenomenon that is found in many cap-and-trade programs. The main reason for that is the wrong expectation about the aggregate emission which determines the actual demand for allowances. This uncertainty on

5 BlueNext is the most liquid platform for spot trading in EU ETS. 72% of the volume of spot contracts are traded on Blue Next. 6 European Climate Exchange (ECX) is the most liquid platform for future and option contracts in EU ETS. 96% of the volume of futures contracts are traded on ECX.

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how many allowances are really demanded is especially large at the beginning of any program because it involves lots of uncertainties. In addition to the underlying uncertainties in carbon price main drivers (economic activity, weather, and energy prices), there is large uncertainty on the amount of abatement that will take place in response to the new price on emission [14].

The first public release of emissions data provided a bench mark to adjust expectations with actual demand and prices as it was the first reliable data released. Once the expectations have been calibrated based on this data, later reports have much less if not any effect on prices. The 2007 release of verified emission for 2006 had no effect on EUA prices.

After the price collapse EUA prices (both Phase I and Phase II) moved to the range 15€ to 20€ until October 2006. From this moment the first period price fell farther to zero because of the relatively short time remaining in the period to work off the unexpected surplus [11]. Conversely, the Phase II EUA prices increased to 20€ mainly due to the European Commission’s affirmation to enforce tighter targets.

EUA prices were higher than expected during the first half of the trial period while they were lower than expected at the end of the period. A cold late winter in early 2005, a dry summer in southern Europe, high natural gas and oil prices that made coal more attractive were the factors cited for high price of EUA in phase I. In addition to those reasons, Ellerman [14] argued the imbalance in the presence of buyers and sellers in the EUA market as the main factor for the phenomenon of high unexpected price of EUA during first half of Phase I and very low price at the end.

Because of the fact that electric utilities had more means of abatement available in the short run (like fuel mix and fuel switching) than did other industries and they did not face international competition with countries outside of the EU, lower EUAs than their business-as-usual emissions were allocated to them. Their short position with their demand to hedge their forward power contracts made them to be active from the very beginning. However, non-power companies which are the potential sellers were largely absent from the market because they took a wait and see attitude as they were long and even if they wanted to sell the registries and other institutions were not yet in place [14].

At the end of the first phase, all the registries were in place and were operating well. Non-power companies came to realize that their needs for the first phase were covered and began to sell their excess allowances as they were not bankable to the second phase. This created oversupply to the market which contributed to the decline of first period EUA spot prices and future prices of maturity December 2007 towards zero [14].

What happened so far? 16

The second phase EUA prices show more or less a stable pattern. The following figure shows the spot EUAs exchanged on the BNX and future EUAs of December 2010 maturity contracted on ECX. Both have been oscillating between 10€ and 20€ per ton of CO2. Demand variation due to industrial production [16] and the economic crisis [12] that happened on all the commodities market were identified as the reason for this oscillation of spot EUAs from around 20€ to 10€.

Figure 3-2 EUAs Spot Allowance prices during phase II (in €/ton of CO2)

Source: BNX and ECX

Future prices of EUAs of December 2008 to December 2009 expiration also show more or less similar trends. Figures showing these future prices can be found in Appendix A. December 2008 futures has been rising above 30€ while its mean value is close to 20€ per ton of CO2. Similarly, the December 2009 futures have been showing similar trend. However, the effect of the financial crisis on the carbon market is reflected as allowances futures fell below €15. December 2010 future prices have been trading in the range of 15€ to 25€ per ton of CO2 which is a relatively stable price pattern compared to phase I prices.

Operators in EU ETS were also observed to actively participate in the trading and importing of Kyoto credits after the linking directive is put into practice. The most liquid Kyoto credit is CER. It has been traded actively since it was allowed to be used in EU ETS as a compliance tool.

The following figure presents the CER futures of December 2008 expiration and EUA futures with Dec 2008 maturity. The CER future price has been very different from the

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EUA future prices of corresponding maturity. Chevalier [12] justifies this as due to the transmission of the financial crisis to global commodity market including carbon market. CER futures showed stronger adjustment to the crisis than that of EUA futures. He indicates that this may be due to the risks embedded with CER prices and the global nature of CERs suggesting that the crisis may have been more sever in other regions compared to Europe.

CER futures of maturity December 2009 show strong adjustment during the end of the year 2008. The price has been stabilizing in 2009 between €10 and €15 per ton of CO2. The figures for the CER futures of 2009-2011 maturity are given in appendix A.

Figure 3-3 Comparison of the price of CER and EUA futures of Dec 2008 maturity

3.4 Future expectations and uncertainties in EU ETS

The EC is constantly reviewing and monitoring the performance of EU ETS to make sure a smooth operation so that the intended objective will be achieved. Some changes are expected to be incorporated for the third EU ETS trading phase which will be operational from 2013 onwards.

Although the exact changes and modifications will be decided in the future there have been some implications by the EC on which issues would be modified. These modifications include: a limited extension of the scope, the possibility to remove some small installations, centralized cap setting process (top- down) with a significantly lower cap, a move towards

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Future expectations and uncertainties in EU ETS 18

more and obligatory auctioning, more harmonized rules for free allocation, continuation of UN project credits subject to qualitative and quantitative limitations and strengthening of monitoring reporting and valuation (MRV) rules.

Some uncertainties also exist that may significantly affect the EU ETS. The European Commission and EU governments agreed on a wide ranging package on climate change which includes the target of cutting greenhouse gases by at least 20% by 2020, compared with 1990 levels. This could rise to 30% if an international agreement is reached committing other developed countries. Although an EU wide agreement is not yet reached some countries have been observed to push EC to raise its target.

Despite of the expectation to continuation of UN project credits (CERs and ERUs) during the third phase there is also high uncertainty in the qualitative and quantitative limitation to be set. In phase II credit import is limited to 13.5 % (which differs from member states to member state) of the free allocation for each installation. Further, HFC-237

In addition to the above regulatory uncertainties, common uncertain elements also exist that affect EU ETS’s day to day operation. These include fuel prices, technological development and weather conditions. Avery hot and most relevant issue of uncertainty right now is the economic crisis. It has a significant influence on fuel prices, emission levels which are the key factors in the day to day carbon price dynamics.

destruction CDM projects have been found to incentivize the increased production of HFC-23. For this reason it is expected that either it will be banned or the credits issued will be reduced.

7 HFC-23 has a 100 year global warming potential of 11,700. That means destroying one tone of HFC-23 generates 11.700 CERs. Out of the CERs issued till July 2010, HFC-23 contributes 52% form only 18 projects [36].

19

4 MODELS FOR EMISSION TRADING

PLANNING

This section presents a survey of related modeling approaches that have been proposed to represent emission trading planning. It gives a summary and characteristics of each of the modeling approaches and justifies the particularity of the model developed in this thesis.

Under the US Clean Air Act Amendment (CAAA) of 1990, Lee et al [17] present a method for coordinating sulfur dioxide (SO2) emission allowances trading with energy and spinning reserve transactions and consumption of take-or-pay fuels in the context of generation dispatch. The SO2 emission allowance compliance (trading) has an annual horizon. They distributed adaptively the yearly targets into short term operational targets, which were, in turn, enforced in the associated unit commitment and dynamic dispatch sub-problems.

Manetsch [18] proposed a method used for determining optimal SO2 compliance options within the context of long run unit commitment and dispatch. The lowest cost compliance options among installing scrubbers, switching to low sulfur coal and taking no physical action but purchasing of allowances to cover all generated sulfur dioxide are computed for each coal burning unit.

Rong and Lahdelma [19] studied the emission trading planning problem of an individual combined Heat and Power (CHP) producer at the operational level. They formulated the CO2 emission trading planning of a CHP producer as a multi-period stochastic optimization problem and proposed a solution approach that optimizes CHP plant operation and CO2 emissions trading in coordination. They optimized, during each trading period, the future CHP production until the end of the planning horizon based on scenarios for heat demand, power price and allowance price. Based on the optimized production plans, they estimate CO2 emissions during the obligation period to determine how much allowances should be traded (bought or sold). They explicitly consider the risk attitude of the decision maker.

The first two papers emphasize the production planning of the power systems under the constraints of emissions control. These papers were developed for SO2 trading under the U.S. Clean Air Act Amendments of 1990 which is basically a classic cap-and-trade system. EU ETS, however, has some significant design differences form the classic cap-and-trade system as explained in 3.2. In addition, both papers focus on developing short term operational decisions rather than strategic long term plans.

Future expectations and uncertainties in EU ETS 20

The third paper, although it is studied under the EU ETS, it doesn’t explicitly include the regulatory issues introduced in to the scheme such as the inclusion of Kyoto credits and borrowing. Moreover, the paper focused in the operational level.

Most other published papers that deal with CO2 emission trading are from the view point of policy planning ( [20], [21] and [22]) or allowance price modeling ( [23], [24]; [25]; [26] and [27]). They do not address the emission trading problem itself.

This paper presents an original method to develop an optimal strategic emission compliance planning through trading under EU ETS. In this thesis the regulatory aspects of the EU ETS (banking, borrowing and the possibility of using Kyoto credits), the participation in future and spot allowance markets as well as the presence of different allowances (European allowances and Kyoto credits) are explicitly considered.

Emission estimates are taken as exogenous variables. Based on the estimated emissions and allowance price scenarios, a long term emission trading strategy will be generated that will minimize the overall compliance cost. With this method the amount and kind of allowances that should be bought, sold, borrowed or banked will be determined. The most important outputs of the proposed methodology in this thesis are the purchasing strategy and surrendering strategy. Purchasing strategy plans how many allowances to buy or sell during the course of the strategic planning horizon to minimize total purchasing cost. Surrendering strategy determines the best way of using the different allowances to comply with the emission level of each installation.

21

5 A MODEL TO DEVELOP STRATEGIC

EMISSION COMPLIANCE PLAN THROUGH


This section presents the conceptual core of this thesis. It describes in detail the formulation proposed to represent the problem faced by a utility subject to EU ETS.

An original methodology is suggested based on the theory of multi stage stochastic programming to model the strategic emission compliance plan of a utility through trading under EU ETS. In the EU ETS, utilities are subject to compliance obligations and are allowed to buy and sell allowances in order to achieve their obligation cost efficiently. Strategic and long term trading plan allows those utilities to avoid short sighted behavior and to minimize their overall compliance cost. Stochasticity is due to the fact that allowance prices are not known in advance.

In this section the modeling process is described (5.1), a deterministic model is developed (5.2) and the deterministic model is hen extended to stochastic one in order to include the uncertainties involved (5.3).

5.1 The modeling process

It takes a process of several stages before a decision problem faced in the real world is turned into an optimization model. Communication with the problem owners is the important stage through which an understanding about the problem to be solved is reached. It is impossible to quantify all the issues happening in the real world. Therefore, in order to describe the components of a mathematical model which is also tractable, it is often necessary to simplify and also limit the problem somewhat, and to quantify any remaining qualitative statements.

To fully describe the problem in terms of mathematical model, the optimization problem has to be supplied with appropriate data. These include model constants, parameters in functions describing the objective function and some of the constants. Once the model is formulated mathematically, an optimization algorithm should be used to yield a result in the form of an optimal value and optimal solution if it exists. This result is then interpreted and evaluated, which may lead to alterations of the model, and certainly to questions regarding the applicability of the optimal solution

The modeling approach used in this thesis 22

The above process is repeated until the final problem comes at a stage where the interpretation of the result makes sense to the problem owner. At this point, it must be possible to transfer the solution back into the real world where the problem came from. The following figure illustrates the stages in the modeling process [28].

Figure 5-1 Flow chart of the modeling process

The premise of decision making is that there are several different ways to address a problem and that the best way may not be obvious or necessarily unique. The process of finding the best (optimal) way is called optimization. Most analysts break a decision-making process down in to steps of problem identification, problem definition, mathematical model formulation, Model solution, testing, evaluation and sensitivity analysis and finally implementation [29]. A more or less similar step is followed in this thesis.

5.2 The modeling approach used in this thesis

A utility owing a certain number of installations covered by EU ETS has to surrender an amount of allowances equivalent to its annual emission, for each of the installations. During phase II of EU ETS, each of those installations is given a certain number of allowances (cap) for free according to the NAP. The operator of the installations can participate in buying and/or selling of allowances to deal with the difference between its emission and free allocation (cap). There is no such thing as free allocation after the end of Phase II for power utilities (which are considered in this paper). That means power utilities have to purchase allowances to cover their emissions. This thesis does not deal with speculative trading, buying and selling of allowances to benefit from the price difference in subsequent years. It is assumed that utilities participate in buying and selling only to cover their emissions or to deal with the difference between their free allowances and their emissions.

A model to develop strategic emission compliance plan through trading under EU ETS 23

The emission level of the installations is considered in this thesis as an exogenous variable. Depending on the strategic production plans and historical production information of the utility, annual emission levels of the installations can be more or less estimated. These estimates are then used as an input to the model in order to plan emission allowance purchasing and surrendering strategies.

The main objective that must guide a utility when designing its trading strategy is its overall compliance cost. This cost is mainly allowance purchasing cost and may include revenues from selling excess allowances and possible transaction costs. However, transaction costs are not significant in EU ETS [30]. Therefore, total compliance cost is considered as the sum of costs from purchasing allowances and revenues from selling excess allowances. Strategies developed by the utility should foster a minimum total compliance cost.

Although a continuous daily allowance buying and selling platforms exist, allowance submission is a yearly phenomenon. Therefore, annual time horizon is selected for developing the strategic plan. The annual allowance purchasing costs and/or allowance selling revenues are then discounted to calculate their present values.

Forecasted allowance prices are used to calculate the allowance purchasing cost and selling revenue. Since the model can see future allowance prices, there is a tendency to buy and sell allowances in large quantities in consecutive trading periods. Series of constraints are introduced to avoid such arbitrage behavior allowing only excess allocations that are assigned for free to be sold.

According to the linking directive, it is possible to use Kyoto credits as a compliance tool in EU ETS. However, this is restricted to a certain quantity-percentage of annual cap. Optimal surrendering strategy involves finding the best period of time to use this allowed credits since these credits are relatively cheaper than EU allowances. A constraint has been developed include this limit on Kyoto credits.

The possibility to bank and borrow allowances is also another issue that has to be included in the model. The regulatory differenced that exist between different trading periods (EU ETS phases) are represented by different expression for the same constraints.

The above modeling approach is then modified in section 5.4 to include uncertainties in the allowance price.

Mathematical formulation 24

5.3 Mathematical formulation

Mathematical formulation involves identifying its components. Mathematical models consist of three major components: decision variables (unknowns of the model), an objective function (which needs to be optimized) and constraints (restrictions or limitations of the model). The following sub-sections are dedicated to specifying time horizon and identification of these components.

5.3.1 Time Horizon

Although a continuous daily allowance buying and selling platforms exist, this thesis aims for a long term strategic emission compliance plan through trading. Therefore yearly trading periods are considered in this paper. That means the outcomes of the optimization model will be annual decisions. These decisions, however, can be easily made operational by spreading into daily, weekly or monthly trading targets.

The trading period in EU ETS is divided into a series of sequential years which are known as EU ETS phases. There exist slight regulatory modifications from one phase to another. Some of those modifications are already included in the EU directive while others are still on discussion. Since the time horizon that is considered in this model includes both EU ETS Phase II and Phase III, the same issues may have to be formulated with two different constraints one for each phase in order to include the regulatory differences between the two phases.

5.3.2 Decision variables

Decision variables in an optimization problem are decisions that will be taken and affect the objective function. A utility subject to EU ETS can decide the number of allowances to purchase, sell or bank in order to optimize its total compliance cost. Therefore, the number of allowances to buy, the number of allowances to sell and the number of allowances to bank or borrow are identified as important decision variables. These decisions are made in annual basis.

Buying and selling of allowances could be done in various markets. Although the thesis doesn’t consider options, spot and future contracts are explicitly considered. Therefore allowance buying or selling year and actual delivery year should be separately identified for variables involving future contracts.

As EU ETS provides utilities with the opportunity to use Kyoto credits up to a certain limit, they can decide to use those credits or to bank (accumulate) them for later years. Thus, the amount of Kyoto credits using capacity can be identified as another variable


This thesis explicitly considers the different allowances that are allowed to be used as a compliance tool in EU ETS (EU allowances and Kyoto credits). In addition the thesis considers a long term planning while trading and compliance is done every year. Some of the decisions even should be made at installation level. This makes the total number of variables in the model to be equal to the product of number of years considered, number of installations and number of allowance types. It is difficult if not impossible to list all the variables. Therefore, the use of indices is vital to avoid such a bulky representation.

The following table shows the indices used in this thesis

Notation Index

𝑖 The set of installations

𝑗 The set of emission allowances {AS8, EUA, Non-eligible CER9, eligible CER, ERU}

𝑡 The set of decision/compliance periods (years)

𝑃2𝑡 The set of years in Phase II [2010 to 2012]

𝑛𝑒𝑙𝑗 The set of allowances not eligible to be used for phase III {Non-eligible CER, ERU10}

𝑛𝑒𝑢𝑎𝑗 The set of non EUA allowances{AS, ERU, eligible CER, Non-eligible CER}

𝑒𝑙2𝑗 The set of allowances eligible for phase III {eligible CER, EUA}

𝐴𝑆𝑗 The set of allowances allocated for free {As}

Table 5-1 list of indices and their notation used in this paper

In addition to the aforementioned decision variables, the utility can also decide the kind of allowances that should be submitted to cover the emission caused by its individual

8 AS stands for assignations. These are EUAs that are allocated free of charge for each installation during EU ETS Phase II. It is necessary to treat them differently than purchased EUAs. 9 CERs are of two types. One type is those which are eligible to be used for Phase III of EU ETS while there is another type of CERs which will be expired at the end of phase II and will not be applicable after wards. The former refers to eligible CER while the later refers to Non-eligible CERs. 10 ERUs are not also eligible for phase III unless there is a new regulatory rule.


installations. For that reason, ‘allowances to be surrendered’ is defined as another important variable.

The following table shows the notations and the units that will be used to refer to the variables identified in the above paragraphs.

Symbol Variable Unit

𝑥𝑠𝑗,𝑡 The number of emission allowance j to be Purchased in spot market during year t [tCO2]

𝑥𝑓𝑗,𝑡𝑝,𝑡 The number of emission allowance j to be purchased in future contracts market during year tp to be received in year t [tCO2]

𝑠𝑠𝑗,𝑡 The number of emission allowance j to be sold in spot market during year t [tCO2]

𝑠𝑓𝑗,𝑡𝑝,𝑡 The number of emission allowance j to be sold in future contracts market during year tp to be delivered in year t [tCO2]

𝑦𝑗,𝑡 The number of emission allowance j to be banked at the end of year t [tCO2]

𝑒𝑗,𝑖,𝑡 Emission allowance j submitted during year t, to cover emission [tCO2]

𝑈𝑛 𝑖,𝑡 Capacity of Kyoto credits that are left unused until the end of year t [tCO2]

𝑙𝑡 Binary variable indicating the decision to sell assigned allowances in year t {0,1}

m𝑡 Binary variable indicating the decision to bank assigned allowances in year t {0,1}

𝑧𝑡 Binary variable indicating the decision to surrender EUAs in year t {0,1}

Table 5-2 Notations used for Decision variables


5.3.3 Parameters

Parameters are model constants that describe the objective function and some constraints. They are usually used as coefficients in the objective function and constraint equations. Some parameters are estimated values and are therefore subject to uncertainty. Sensitivity analysis is usually used to see the effect of small percentage change in those variables on the results of the model. However, some parameters are stochastic which require a more careful approach like scenario analysis and stochastic programming.

Initial values of the variables, percentages fixed by the national government and hardly subject to change, free allowances allocated for certain years according to NAP, estimated emission level, financial rates as well as spot and future prices of allowances are the parameters identified in the model considered in this thesis.

The following table presents the notation of the parameters that will be used throughout the mathematical formulation.

Notation Parameter Unit

Ei,t The estimated emission level of allowance i for year t [tCO2]

Aj,i,t The assignation for year t ; ACER,t = 0 (assignations are purely EUAs) [tCO2]

Psj,t Average spot price of emission allowance j during year t [€/tCO2]

Pfj,tp,t Future price of emission allowance j during year tp for year t delivery [€/tCO2]

βt Annual discount rate [%]

X0j,t Initially purchased amount of allowance j for year t delivery [tCO2]

Un0i Initial available capacity for using Kyoto credits for installation I [tCO2]

y0j Initially banked allowances [tCO2]

K Ratio of maximum allowed eligible Kyoto credits for any year to assignation of that year (for phase II) which is 42% for the Spanish case [%]

K3 Ratio of maximum allowed eligible Kyoto credits for any year to emission of that year (for phase III) [%]

M1 a large cost [€]

M2 a large quantity [tCO2]

Table 5-3 List of parameters and their notation used in the paper


5.3.4 Constraints

Constraints are the relationships that the variables have to satisfy. These are known as restrictions or limitations of the problem. A constraint usually has a function and a constant as its components, related by either equality or inequality sign. Most model developers and optimization software products adhere to the convention of having the variable expression on the left-hand side of the constraint equation and a constant on the equation’s right hand side [29]. This convention is also followed in this paper.

Most of the constraints identified in this thesis are regulatory constraints. These are rules that have been declared in the EU directive and member states royal decrees. Compliance obligation, banking and borrowing provision and the limit on the use of Kyoto credits are identified as the main constraints of a utility subject to EU ETS.

5.3.4.1 Compliance constraint

Utilities subject to EU ETS are obliged to measure, report and verify their emission from each of their installation every year. And they have to submit an amount of allowance equal to their verified annual emission every year. This obligation is stated in Article 12/3 of EU directive 2003/87/EC as:

‘Member states shall ensure that, by April each year at the latest, the operator of each installation surrenders a number of allowances equal to the total emissions from that installation during the preceding calendar year as verified in accordance with Article 15, and that are subsequently cancelled.’ [31].

Utilities that don’t fulfill the compliance obligation will be penalized. The penalty will be €100 for each ton of CO2 equivalent emitted by that installation for which the operator has not surrendered allowances and the obligation of surrendering the allowances for the CO2 not covered that year remains for the next compliance year. In addition, the name (shame name) of the utility will be published [31].

The shame naming penalty is difficult to quantify but can be conceived as a very high cost that may affect the reputation of the utility. For this reason, this constraint is considered as a hard constraint (which should be always fulfilled).

Every year, the sum of allowances submitted for an installation should be equal to the emission of that installation during that year. However, not all kinds of allowances can be submitted for both phases. Therefore, the constraint can be formulated in two different equations to distinct each phase.


Total allowances submitted = total emission (for each installation & period)

∑ ej,i,p2tj∈J − Ei,p2t = 0 ⊥ µi,p2t,E ;∀ i, p2t (1)

∑ eel2,i,tj∈J − Ei,t = 0 ⊥ µi,tE ; ∀ i, t ≠ p2t (2)

5.3.4.2 Kyoto credit limit

Not all allowances can be equally used for abatement. Every year utilities are allowed to use, for each of their installations, Kyoto credits up to k percent of the installation’s free allocation (cap) for compliance. However, utilities are also free to bank their Kyoto credit using capacity for the coming years. Therefore, at any year t, the utility’s maximum ability to submit Kyoto credit for its installation’s emission will be the sum of the banked capacity and the capacity of that year.

Kyoto credits submitted +cumulative unused capacity at the end of the period= k* assignation +cumulative unused capacity at the end of previous period (for each installation and period in phase II)

∑ ej,i,p2t + Uni,p2tj∈(neua\ASj) − �k ∗ ∑ Aj,i,p2tj∈J + Uni,p2t−1� = 0 ⊥ µi,p2t,Un ;∀ i,p2t (3)

Since there will be no free allocation in phase III, the above equation is only valid for phase II. There is, however, an expectation that the use of Kyoto credits will continue in Phase III. To include this constraint, it is assumed that the use of those credits will be limited to k3 percent of installation’s emission. The mathematical formulation of the constraint for phase III will be:

Kyoto credits submitted +cumulative unused capacity at the end of the period= k3* Emission +cumulative unused capacity at the end of previous period (for each installation and period in Phase III)

∑ ej,i,t + Uni,tj∈((neua \ASj)∩ el2) − �k3 ∗ Ei,t + Uni,t−1� = 0 ⊥ µi,tUn ;∀ i,t≠p2t (4)

5.3.4.3 Banking and Borrowing

If utilities have extra allowances after their compliance, they are allowed to save them so that they can use them for the next compliance years. This phenomenon is called banking. On the contrary, since submission of allowances is made on 30 of April of the year next to compliance year, while assigned allowances are distributed in February, utilities may decide


to use those assigned allowances for complying the previous year’s emission. This is what is called borrowing.

At any year t, the total position of a utility is the sum of free allocations, banked (borrowed) allowances from the year t-1, purchased allowances (both in spot and future market). Therefore, the amount of allowances that can be banked at the end of any year t will be equal to the difference between the total position and the utility’s emission of that year.

This thesis assumes a utility that comply its emissions through emission trading. In order to prevent the speculative nature of the optimization model, selling is restricted to excess free allocations. The banking constraint can be expressed using two mathematical expressions one for assigned allowances (free allocations) and other for purchased allowances.

Banked allowances = assignation +Banked allowances at the end of the previous period ± allowances bought/Sold in spot mkt ± allowances bought/sold in futures mkt +allowances initially purchased in future mkt – allowances submitted (for each allowance and period)

yj,t − ∑ Aj,i,ti∈I − yj,t−1 − xsj,t − ∑ xfj,tp,t − x0j,ttp≤t + ∑ ej,i,t ≤ 0 ⊥ µj,ty ;∀i∈I J ≠ Asj, t (5)

yj,t − ∑ Aj,i,ti∈I − yj,t−1 + ssj,t + ∑ sfj,tp,ttp≤t + ∑ ej,i,t ≤ 0 ⊥ µj,ty ;∀i∈I Asj, t (6)

Some allowances are not eligible to be used for phase III. Thus, either they should be used for compliance or they should be sold. The sum of those allowances that are acquired through buying or initial banking should be equal to the sum of non-eligible allowances that are surrendered or sold.

Allowances initially purchased + allowances initially banked ± phase II cumulative allowances bought/sold in spot ± phase II cumulative allowances bought/sold in futures = Phase II cumulative allowances submitted (for each allowances not eligible for phase III)

∑ xsj,tt∈p2 + ∑ ∑ xfj,tp,ttp≤t + X0j,t + y0jt∈p2 − ∑ ∑ ej,i,tt∈p2i∈I = 0 ⊥ µjnel ;∀j ∈ nel (7)

Since utilities are allowed to borrow, they can have a maximum negative banking value equal to the sum of the assigned allowances of the next year. Mathematically,

yj,t + ∑ Aj,i,t+1i ≥ 0 ⊥ µj,tB ;∀j, t (8)


5.3.4.4 Hedging constraint

For a given price projection, the optimization model looks the future prices. As a result the model may imply buying in large quantities in a single year to bank them for the future compliance years. However, in reality this decision is subject to a lot of uncertainties and investing huge amount of money in purchasing these allowances may be highly risky.

In order to avoid these situations the maximum amount of allowances that can be purchased at any year t should be restricted. This restriction depends on the maximum budget the utility is willing to invest in emission allowances. For this particular case, assuming a power company, this restriction is considered to be equal to the sum of the emission level of the next three trading years including that year.

Allowances purchased in spot mkt + allowances purchased in future mkt = sum of Emissions of the next three trading periods (for each purchasing year)

∑ xsj,tpj + ∑ xf

j,tp,ttp≤t − (∑ Ei,tp + ∑ Ei,tp+1 +i∈I ∑ Ei,tp+2) i∈Ii∈I ⊥ µtH ;∀t (9)

When future markets are concerned the model, looking the future prices, may result in selling in the future what is not in stock aiming to deliver from the next year’s assigned allowance. However, this creates a negative position in the utility’s account. The following constraint has been introduced to avoid such negative position.

Sum of allowances sold in future markets in year t ≤ sum of allowances available in stock in that year (for each allowance and year)

∑ ∑ sfj,tp,tt>𝑡𝑡tp≤tt − yj,tt ≤ 0 ⊥ µtH2 ;∀j, tp, t (10)

5.3.4.5 Non-negativity

xfj,tp,t , sfj,tp,t ,xsj,t, ssj,t ej,i,t ≥ 0 (11)

5.3.5 Objective function

Objective function represents the goal of the problem in terms of decision variables. The objective function that must guide a utility when designing its emission compliance strategy through trading is its overall compliance cost. This cost, actually, is the cost of purchasing of allowances, revenues from selling excess assigned allowances and relates transaction costs. However, a study by Jaraite shows that trading transaction costs are not significant in EU


ETS [30]. Therefore only purchasing costs and selling revenues are considered in the objective function.

Figure 5-2 Calculation of NPV of allowance purchasing costs and selling revenues

Both future and spot allowance markets are mature and the utility can easily participate in over the counter market or over organized exchanges. Future and spot purchasing costs are explicitly considered to include the utility’s participation in those markets.

In order to allow inter-temporal banking, instead of optimizing for each year, the net present value of the annual compliance costs of the whole time horizon will be used as an objective function. This annual cost is discounted to calculate its present value.

Compliance cost =Net present value of ± allowances bought/sold in spot * spot buying/Selling price ± allowances bought/sold in future * buying/ Selling future price

(12)

Another issue is to restrict the model to use all the allowances assigned for free before using purchased EUAs. That means assigned allowances which are given for free shouldn’t be either sold or banked while at the same year EUAs that are purchased from the market are surrendered. As far as a utility that is hedging its emission is assumed, purchased allowances should be surrendered only if the freely assigned allowances cannot cover the emission level.

This doesn’t include the use of Kyoto credits. It is ok for the utility to use those credits and sell its excess assigned allowances. This is usually called the swapping market. That means, the restriction should apply for any year t when the model decides to use EUAs.

The decision to sell assigned allowances at any year will be represented by a binary variable 𝑙t. If at any year t the utility decides to sell excess assigned allowances, then 𝑙t = 0.

In other case, 𝑙t = 1. The utility’s objective function will be modified to:


NPV = �∑ βt−1t∈T �∑ �xsj,t ∗ psj,t + ∑ xfj,tp,t ∗ pfj,tp,t tp≤t �j∈J∖ASj � − �∑ �ssj,t ∗ psj,t + ∑ sfj,tp,t ∗tp≤tASj

pfj,tp,t �� ∗ lt� (13)

It should be noted that there is no need to enforce the value of the binary variable 𝑙𝑡.The optimization procedure will decide the right value when minimizing the company’s total compliance cost.

The term − �∑ �ssj,t ∗ ps

j,t + ∑ sfj,tp,t ∗ pf

j,tp,t tp≤t �ASj � ∗ lt is non-linear (𝑙𝑡 is a variable and so are

𝑠𝑠𝑗,𝑡 and 𝑠𝑓𝑗,𝑡𝑝,𝑡 ). An equivalent mixed linear-integer expression must be derived if the state

of the art MIP optimizers are to be used to solve this problem. For that purpose the term is

modified to �1− �∑ �ssj,t ∗ psj,t + ∑ sfj,tp,t ∗ pfj,tp,t tp≤t �ASj �� ∗ lt adding 1 which is not

significant as we are dealing with revenue of thousands if not millions of Euros. A new

variable, 𝒉𝒐𝒕 , is then introduced such that hot = min �1, �∑ �ssj,t ∗ ps

j,t + ∑ sfj,tp,t ∗tp≤tASj

pfj,tp,t ��. The new mixed-integer expression for the company’s total compliance cost is:

NPV = �∑ βt−1t∈T �∑ �xsj,t ∗ psj,t + ∑ xfj,tp,t ∗ pfj,tp,t tp≤t �j∈J∖ASj � + �hot − �∑ �ssj,t ∗ psj,t +ASj

∑ sfj,tp,t ∗ pfj,tp,t tp≤t �� (14)

To guarantee that hot = min �1, �∑ �ssj,t ∗ psj,t + ∑ sfj,tp,t ∗ pfj,tp,t tp≤t �ASj �� , the following

constraints must be introduced:

∑ �ssj,t ∗ psj,t + ∑ sfj,tp,t ∗ pfj,tp,t tp≤t � −ASj hot ≤ M1 ∗ lt ⊥ µts ;∀t (15)

1 − hot ≤ M1 ∗ (1 − lt) ⊥ µt s2 ;∀t (16)

𝑙𝑡 ∈ {0,1} ,

where M1 is a large cost. To illustrate how this formulation works, let us assume that 𝒍𝒕 = 𝟎.

In that case the constraints 15 and 16 reduce to:

∑ �ssj,t ∗ psj,t + ∑ sfj,tp,t ∗ pfj,tp,t tp≤t � –ASj 𝐡𝐨t ≤ 𝟎 1 − ℎ𝑜𝑡 ≤ 𝑀1

Given the company’s objective is minimizing of its compliance cost; the variable 𝒉𝒐𝒕will

take the minimum possible value, which in this case is∑ �ssj,t ∗ psj,t +∑ sfj,tp,t ∗ pfj,tp,t tp≤t �ASj .


Therefore,𝒍𝒕 = 𝟎 implies that 𝒉𝒐𝒕 = ∑ �𝒔𝒔𝒋,𝒕 ∗ 𝒑𝒔𝒋,𝒕 + ∑ 𝒔𝒇𝒋,𝒕𝒑,𝒕 ∗ 𝒑𝒇𝒋,𝒕𝒑,𝒕 𝒕𝒑≤𝒕 �𝑨𝑺𝒋 and the result is

the company will not sell its assigned allowances. Conversely, if 𝒍𝒕 = 𝟏 the constraints 15 and 16 reduce to:

∑ �ssj,t ∗ psj,t + ∑ sfj,tp,t ∗ pfj,tp,t tp≤t � –ASj 𝐡𝐨t ≤ 𝐌𝟏

𝟏 − 𝐡𝐨t ≤ 𝟎

In this case the minimum value for 𝒉𝒐𝒕 is 1. Hence, the company will sell its assigned allowances.

The decision to use EUAs will be represented by another binary variable 𝒁𝒕. If at any year t the company decides to use EUAs for compliance, then. 𝒁𝒕 = 𝟏. In other cases, 𝒁𝒕 = 𝟎 .The following constraints can be introduced to make the decision to use EUAs and the decision to sell assigned allocation exclusive.

∑ ∑ 𝐞𝐢,j,t𝐄𝐔𝐀𝐢 ≤ 𝐌𝟐 ∗ 𝐙t ⊥ µtz ;∀t (17)

𝐙t + 𝐥t ≤ 𝟏 (18)

where M2 is a large quantity. To illustrate how this formulation works, let us assume 𝒁𝒕 = 𝟎.

In that case constraint 17 and 18 reduce to

∑ ∑ ei,j,tEUAi ≤ 0 lt ≤ 1

Given that the variable 𝒆𝒊,𝑗,𝑡 is positive variable ∑ ∑ 𝒆𝒊,𝑗,𝑡𝑬𝑼𝑨𝒊 will take a value of 0, whereas

𝒍𝑡can take a value of 0 or1 depending on which is optimal for the company. Conversely, if 𝒁𝒕 = 𝟏 constraints (17) and (18) reduce to:

∑ ∑ ei,j,tEUAi ≤ M2 lt ≤ 0

In this case the value of ∑ ∑ 𝒆𝒊,𝑗,𝑡𝑬𝑼𝑨𝒊 is different from zero. Given M2 is a very large

number; it will take its optimal value. The value of 𝒍𝑡 will be 0 ensuring that the model will not decide selling of assigned allowances and using purchased EUAs at the same time.

The decision to bank assigned allowances will be represented by another binary variable 𝒎𝒕. If at any year t the company decides to bank its excess assigned allowances, then. 𝒎𝒕 = 𝟏. In other cases, 𝒎𝒕 = 𝟎 .The following constraints can be introduced to make the decision to bank assigned allowances and the decision use EUAs exclusive.


∑ 𝐲j,t𝐀𝐒𝐣 ≤ 𝐌𝟐 ∗ 𝐦t ⊥ µtm ;∀t (19)

𝐙t +𝐦t ≤ 𝟏 (20)

where M2 is a large quantity. To illustrate how this formulation works, let us assume 𝒎𝒕 = 𝟎.

In that case constraint 19 and 20 reduce to

∑ yj,tASj ≤ 0 zt ≤ 1

The maximum value that can ∑ yj,tASj take is 0, whereas 𝒛𝑡 can take a value of 0 or1

depending on which is optimal for the company. Conversely, if 𝒎𝒕 = 𝟏 constraints 19 and 20 reduce to:

∑ yj,tASj ≤ M2 zt ≤ 0

In this case the value of ∑ 𝐲j,t𝐀𝐒𝐣 can take positive value. Given M2 is a very large number; it

will take its optimal value. The value of 𝑧𝑡 will be 0 ensuring that the model will not decide Banking of assigned allowances and using purchased EUAs at the same time.

5.4 Stochastic Modeling

The above model reflects a deterministic approach where all the variables are assumed to be known. However, in reality, lots of uncertainties are involved in the EU ETS. Decisions on how many allowances to purchase (to sell) or to bank will be made each year. The decision made during one year should take into account all possible future realizations as there is no opportunity to adapt decisions later on.

Two sources of uncertainty are identified for an agent hedging its emissions by allowance trading. On one hand, the agent doesn’t know the actual amount of its annual emissions that it has to hedge, which depends on the agent’s actual future production and kind of fuel used for production. On the other hand the spot as well as future price of emission allowances are also unknown. Due to time constraint, only spot and future price uncertainties are considered in this thesis. However, sensitivity analysis carried out to study the effect of emission estimate deviation on the utility’s compliance strategy.

Stochastic Modeling 36

5.4.1 How to deal with the uncertainties

The emission uncertainty can be analyzed by making sensitivity analysis. This involves analyzing the effect that a small change in the emission estimate has on the output of the model.

Representation of allowance price uncertainty is not an easy task. It will not be a good idea to use historical data as the best representation of allowance price uncertainty. This is because of a couple of reasons. First of all, EU ETS is started only recently (in 2005) leaving not enough historical annual data for analysis. Secondly, there have been significant regulatory changes from first to second trading period and still some changes are expected which will of course lead to a completely different price trend than what has been seen so far. Thirdly, the financial crisis which occurred at the beginning of Phase II completely distorted the market and will be inherited if the historical data is used directly as a representation of price trend.

For this reason, for the case study in this model spot EUA price forecasts from different banks are taken as best representative scenarios. However, due to regulatory uncertainties, since decisions about EU ETS phase III are not still finalized, those price forecasts are not even stable at the moment. Different banks change their forecasts depending on available of anticipated information each time.

Since in this model different allowances are treated explicitly, Kyoto credit price forecast related to the EUA price forecasts of the banks was also required as an input data. A relevant forecast was not available for the price of Kyoto credits-CERs and ERUs. Therefore, the price of CERs is estimate from the forecasted EUA prices and the historical CER/EUA spread data form BLNXT. ERUs are not considered in the case studies due to their illiquidity.

5.4.2 Developing a multi-period stochastic model

A utility decides its annual purchasing and surrendering strategies for each year. In each year, the company has the possibility of taking recourse actions to correct any undesired results obtained in previous compliance years. Figure 5-3 illustrates the decision process, which obviously has the structure of multi-period stochastic program with recourse. Given the structure shown in the figure, a multi-period stochastic programming framework can be adopted in order to address the problem of deciding optimal emission compliance strategies under trading through EU ETS.


1st year’s compliance strategy

2nd year’s compliance strategy

tth year’s compliance strategy

tth year’s compliance strategy (Scenario ꙍ)

tth year’s compliance strategy (scenario ꙍ')

Scenarios

Node 0Node 1

Node k

Figure 5-3 The decision process of a utility in emission compliance

The deterministic model developed in the previous section could be modified to incorporate the price uncertainties. When considering strategic planning at the beginning of trading horizon, the future price uncertainties are approximated by a set of scenarios with a certain probability of occurrence. Each scenario represents a set of prices (both future and spot) at each trading period (year) in the future. Those uncertainties are assumed to reflect both the uncertainty of prices and the dependency of information between consecutive years.

Due to the aforementioned sequential decision making process, two different price scenarios ꙍ and ꙍ', may be undistinguishable during the first t years. As shown in Figure 5-3, the information that is available in scenarios ꙍ and ꙍ' is the same. Hence, the decisions taken for both scenarios until year t should be the same (non-anticipativity). A set of constraints that force these decisions to be equal should be introduced or the problem should be formulated in terms of the nodes of the scenario tree to guarantee equal decisions until year t. The probability of each node is the sum of the probabilities of the scenarios sharing that node. The later approach is used in this paper.

To formulate the stochastic problem, the deterministic model is modified by inserting a scenario index, ꙍ, as a superscript for the stochastic parameters and variables. For

Stochastic Modeling 38

example,𝑥𝜔,𝑓𝑗,𝑡𝑝,𝑡, represents the quantity of allowance j that must be purchased in the year

tp to be delivered in year t if price scenario ꙍ is realized. If the probability of scenario ꙍ is denoted by 𝜋𝜔 the objective function to minimize the expected compliance cost becomes:

(21)

The constraints for scenario w generated in period t become:

Compliance

∑ eωj,i,p2j∈J − Ei,p2 = 0 ⊥ µω,i,p2E ;∀ω, i, p2 (22)

∑ eωel2,i,tj∈J − Ei,t = 0 ⊥ µω,i,tE ;∀ω, i, t ≠ p2 (23)

Kyoto credit limit

∑ eωj,i,p2t + Unωi,p2tj∈(neua\ASj) − k ∗ ∑ Aj,i,p2tj∈J + Unωi,p2t−1 = 0 ⊥ µω,i,p2tun ;∀ ω,i,p2t (24)

∑ eωj,i,t + Unωi,tj∈((neua\ASj )∩ el2) − �k3 ∗ Ei,t + Unωi,t−1� = 𝟎 ⊥ µω,i,tun ;∀ω, i, t ≠ p2 (25)

Banking and Borrowing

yωj,t − ∑ Aj,i,ti∈I − yωj,t−1 − xω,sj,t − ∑ xω,f

j,tp,t − x0j,t + ∑ eωj,i,ti∈Itp≤t ≤ 0

⊥ µω,i,ty ;∀ω, j ≠ ASj,t (26)

yωj,t − ∑ Aj,i,ti∈I − yωj,t−1 + sω,sj,t + ∑ sω,f

j,tp,t + ∑ eωj,i,ti∈Itp≤t ≤ 0

⊥ µω,i,ty ;∀ω, ASj,t (27)

∑ xω,sj,tt∈p2 + ∑ ∑ xω,f

j,tp,ttp≤t + X0j,t + y0jt∈p2 − ∑ ∑ eωj,i,tt∈p2i∈I = 0 ⊥ µω,jnel ;∀ω, j ∈ nel

(28)

yωj,t + ∑ Aj,i,t+1 ≥ 0 i ⊥ µω,j,tB ;∀ω, j, t (29)

Hedging constraints

∑ xω,sj,tpj + ∑ xω,f

j,tp,ttp≤t − (∑ Ei,tp + ∑ Ei,tp+1 +i∈I ∑ Ei,tp+2) i∈Ii∈I ⊥ µω,tH ;∀ω, t (30)

∑ ∑ sω,fj,tp,tt>𝑡𝑡tp≤tt − yωj,tt ≤ 0 ⊥ µt

H2 ;∀j, tp, t

∑ �sω,sj,t ∗ pω,s

j,t + ∑ sω,fj,tp,t ∗ pω,fj,tp,t tp≤t � −ASj hoωt ≤ M1 ∗ lωt ⊥ 𝜇𝑡

𝜔,𝑠 ;∀𝜔, 𝑡 (31)

1 − hoωt ≤ M1 ∗ (1 − lωt) ⊥ 𝜇𝑡 𝜔,𝑠2 ;∀𝜔, 𝑡 (32)

∑ ∑ eωi,j,tEUAi ≤ M2 ∗ Zωt ⊥ 𝜇𝑡𝜔,𝑧 ;∀𝜔, 𝑡 (33)

Zωt + lωt ≤ 1 (34)


∑ yωj,tASj ≤ M2 ∗ mωt ⊥ 𝜇𝑡

𝜔,𝑚 ;∀𝜔, 𝑡 (35)

Zωt + mωt ≤ 1 (36)

Non-negativity

𝑠𝜔,𝑓𝑗,𝑡𝑝,𝑡,𝑥𝜔,𝑓

𝑗,𝑡𝑝,𝑡, 𝑠𝜔,𝑠

𝑗,𝑡, 𝑥𝜔,𝑠𝑗,𝑡 , 𝑒𝜔

𝑗,𝑖,𝑡≥ 0 (37)

40

6 COMPUTATIONAL RESULTS

This session presents numerical examples in order to illustrate and evaluate the adequacy of the methodology proposed in this thesis. All the examples consider the case of a fictitious but representative Spanish power utility with 20 installations covered by EU ETS.

For this section, the mathematical model formulated in the previous chapter is formulated in the algebraic modeling language GAMS for analysis. The problem is a mixed integer problem. Therefore, the commercial CPLEX solver is found suitable and used for this work.

The section is organized in two main parts. The first one is oriented to testing and experimenting of the deterministic model (6.1) while the second part is dedicated to testing and analysis of the stochastic model (6.2).

6.1 Testing and experimenting with the deterministic model

In this section model verification and validation tests are carried out followed by scenario analysis. Sensitivity analysis of some parameters and scenario analysis is also performed. All the experiments are based on the fictitious Spanish power utility. The input data and the estimated parameters used for this section can be found in Appendix B.

6.1.1 Quality of data used

As mentioned above, a fictitious Spanish power utility with its 20 installation subject to EU ETS obligations is considered for performing validation tests, verification tests and numerical analysis. In order to carry out the correct analysis and draw relevant conclusions and recommendation, it is important that the input data more or less reflects the reality.

Installations are randomly chosen from the published 2009 verified emission data which is available in the European Commission website. Their corresponding allocation is taken from the Community Independent Transaction Log 11

11 CITL records the issuance, transfer, cancellation, retirement and banking of allowances that take place in the registry. It is mandatory for each Member states to have a national registry which will ensure the accurate accounting of all units under Kyoto protocol plus the accurate accounting of allowances under the community scheme for green house gas emission allowance trading.

(CITL) website according to the Spanish National Allocation Plan. The allocation for phase II (2008-12) was publicly available in the website.

Computational results 41

Future emission levels of each of the installations, for the study period 2010-20, are estimated based on their 2008-09 public verified emissions. This is, however, subject to high uncertainty for which the model’s sensitivity for different estimates is analyzed in section 6.1.4.4.

All the initial parameters are assumed to be null throughout the analysis. The use of Kyoto credits as a compliance option for phase III is not yet made clear by the EC. Therefore, it is assumed that no new Kyoto credits will be used during phase III though banking the potential to use the capacity is considered.

Spot EUA price forecasts available from different banks are taken as best representative scenarios. However, due to regulatory uncertainties, as decisions about EU ETS phase III are not still finalized, those price forecasts are not even stable at the moment. Different banks change their forecasts depending on available of anticipated information each time.

This model treats different allowances explicitly. Thus, a Kyoto credit price forecast related to the above forecast is required. As the only available forecasts were EUA prices, the CER/EUA spread is estimated based on historical data form BNX. ERUs are not considered in the case studies due to their illiquidity.

Additional parameters, the interest rate to quote future prices and the discount rate to calculate the NPV of annual purchasing costs are estimated based on historical data. More information about the assumptions and estimation of these and some other parameters can be found in Appendix B.

6.1.2 Verification and validation

Verification, in the process of modeling, is conducted to check if the model accurately and consistently represents the conceptual description provided in the formulation. In optimization modeling this involves making sure that all the indices, variables, parameters are properly declared and more importantly all the constraint equations and the objective function are correctly defined.

GAMS software provides equation listings and column listings which are very useful debugging tools in the verification process. The equation listing explicitly lists all the equations. It shows all the variables that appear in each equation. Column listing gives a list of the individual coefficients sorted by column. These two features are useful, especially, in order to make sure the constraints specified for the two different trading periods (phases) incorporate the appropriate regulatory changes.

Testing and experimenting with the deterministic model 42

The reduced MIP problem of the base case model has 235 equations, 5880 variables and 1594 non-zero elements which make it difficult and cumbersome to go through the whole list of equations and variables. However, this can be made easier by checking the first few listings of each block of equations and variables just to see the equations for Phase II and Phase III are according to the intended mathematical formulation.

The model has been verified by walking through the first few listings of equations (for both phase II and Phase III) and variables listed in the equation and column listing. An example of the equation column listing for the model can be found in Appendix C.

Validation is another important phase in modeling. It is conducted to make sure the model gives reasonable outcome for reasonable input data. To validate an optimization model one can simplify the model up to the extent that could be solved by hand and compare the results of both the analytical and simulation outcomes. Another approach would be to check the model behavior for extreme input data values. The later approach has been conducted for the deterministic model.

6.1.2.1 The base case scenario

This study case is presented with the aim of providing a basis for model validation and scenario analysis. It is a problem based on the first price scenario and the following input data. The rest of the scenarios to be considered and all the assumptions for the estimated parameters are given in Appendix B.

2010 2011 2012 2013 2014 2015 2016 Scenario 1 €14,50 €16,00 €18,00 €23,00 €25,00 €27,00 €30,00

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Table 6-1 Input data used for the Base case scenario

The following figure depicts the results of the model for the base case scenario. The model was run for the years from 2010 to 2016 using the data in the above table.

12 Euribor is the rate used to calculate the discount rate for the NPV calculation


Figure 6-1Results of the Base case

Figure 6-1 presents the strategies developed by the model to minimize the overall purchasing cost. The model suggests purchasing many EUAs in 2010 spot and 2011 futures for 201313

6.1.2.2 Validation experiments

delivery and to bank them for later years. It is also suggested to use Kyoto credit capacity for 2012 compliance. This is because it is cheaper to use those allowances and sell the excess assignations afterwards. In other words, swapping is economically justified between CERs bought in 2010 and EUAs. With this strategy the NPV of the total annual costs is €1.73 billion.

In order to minimize the overall cost, purchasing in expensive years should be avoided; the use of Kyoto credits during any year should be economical and selling assignations should be done in the most expensive years during phase II. To check the model reflects these hypotheses, three experiments are carried out varying the EUA and CER prices at different years. The following Figures (Figure 6-2and Figure 6-3) show the results of these experiments.

13 Future markets have two time components, the time of purchasing and the time of delivery. The horizontal axis in purchasing strategy graphs throughout this thesis refers to the year allowances will be delivered.

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Figure 6-2 Base case with high allowance price in phase II (experiment 1)

Figure 6-2 shows the results of the first experiment. Expensive prices (30€, 34€ and 36€) have been introduced for allowances at the beginning of the trading period (2010 to 2012). When it is expensive to buy many EUAs at the beginning of the trading period, only few EUAs enough to cover the deficit of those years will be purchased. Using almost all the Kyoto capacity at the beginning was economical in order to leave some assignation and sell them in 2012 when their price is very high. The best strategy to buy EUAs for Phase III compliance was to buy them in 2013 spot and 2013future for 2014 and 2015 delivery and in 2014 future for 2016 delivery.

In the second experiment slightly higher prices are introduced (40€, 41€ and 42€). The results are shown in the following figure. It is suggested that the optimal purchasing strategy is to buy enough EUAs for phase II in 2010 spot market and the rest EUAs in the 2013 spot and futures market where the prices is lower. Since the prices of EUAs are so high in phase II, all the assignations should be used for compliance rather than swapping. The optimal surrendering strategy will then be to use all the allocated allowances every year and eligible-CERs in 2013 to save the EUAs for late r years in phase II

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In the third experiment, backwardation in EUA prices is assumed. With decreasing allowance prices, there is no need to participate in the future prices as well as to bank allowances. Therefore, the cheapest strategy is to purchase allowances equal to annual emission deficits in the spot markets every year

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The above experiments confirm the validity of the modeling approach. The behaviors of its results under different circumstances are justifiable. Indeed, all the results are based on allowance prices that are used as an input data. The model can now be used to develop strategic decisions minimizing the total emission compliance cost under different price scenarios.

6.1.3 Scenario analysis

Once the model has been checked to be free from errors and is proven to be trust worthy in the previous section, the results of different scenarios are analyzed in this section.

The results of the base case scenario (scenario 1) were already explained in 6.1.2.1. Five more scenarios are considered and their analysis is given in this section. The scenarios are based on the price forecasts by different banks. The following figure shows the price curves used for different scenarios analyzed.

Figure 6-5 EUA spot price scenarios

The following figure (Figure 6-6) shows the optimum compliance (purchasing and surrendering) strategies under the various scenarios considered. First column graph shows the annual costs and the NPV under each scenario. The second graph shows the strategic purchasing decision in future market each year for each scenario. The third and the fourth graphs show surrendering strategy and purchasing (future and spot) strategy respectively. The purchasing strategy shows the amount of allowances that should be purchased (either in future or spot market) to be delivered in the year shown in the abscissa of the graph.

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Figure 6-6 Comparison of Strategies developed different scenarios

For the first four prices scenarios, the model results recommend a similar purchasing and surrendering strategy. It is suggested that all the required EU allowances should be purchased in 2010 spot and 2011 future market for 2013 delivery. This is because the EUA prices will be very high in later compliance years. Since all the four scenarios consider an increasing price trend and banking of allowances doesn’t have any cost, purchasing as many allowances as possible during the first cheaper years yields the minimum cost. In order to avoid unrealistic excessive purchasing of allowances at the beginning, the maximum amount of allowances that can be purchased in a year is limited to the emission level of three consecutive years including the purchasing year. As long as increasing price curves are considered, later prices have very low if not no effect on the overall price for this strategy.

Furthermore, the model implies to use all the CER capacity in 2012 to swap with EUAs. The price difference between the non-eligible CERs in 2010 and EUA prices in 2012, makes

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swapping more economical than saving CER capacity for Phase II. Few eligible CERs should also be purchased in 2011 future market for 2013 delivery.

Not only a similar purchasing strategy, but also a similar surrendering strategy is suggested by the model under the four scenarios. For the first two years all the assignations should be used for compliance. The remaining emission deficit should be covered by EUAs and non-eligible CERs that are purchased in the spot market. Most of the emission in the third year (2012) should be covered by non-eligible CERs in order to save the assigned allowances for swapping. Compliance in Phase III is mainly by EUAs and few eligible CERs purchased in the future market.

Scenario 5 assumes a slight decrease in EUA prices in 2011 before the increasing trend after wards. Since there is a future price decrease, the model implies to purchase few EUAs enough to cover the deficit of 2010 in 2010 spot. With this scenario the optimum strategy developed by the model is to purchase most of the allowances in 2011 and 2012 future markets for later years compliance. Purchasing non-eligible CERs is better done in 2011 futures.

The strategy to surrender allowances is the same as the previous four scenarios. Swapping EUAs with CERs is also suggested in this scenario since the price difference between EUAs and CERs is attractive.

Scenario 6 considers a small slope of increment in the consecutive allowance prices. The purchasing and surrendering strategies developed for this scenario are completely different from the model outputs for the above five scenarios.

It is suggested for this scenario that eligible-CERs should be used at the end of the planning period (2015 and 2016). Swapping is not economically justified; therefore, all the assigned allowances should be used for compliance.

Purchasing EUAs in the 2012 future market for 2013, 2015 and 2016 delivery is suggested for this scenario. CERs are cheaper to purchase in the 2016 spot markets since the spread is wide in that year.

The total cost of each scenario varies in relation to the price considered. Generally, the cost increase is proportional to the price of the first two years (2010 and 2011). This is because with increasing price trend, purchasing is cheaper to be made at the beginning years. The following table presents the summary of the annual costs of each of the above scenarios.


NPV 2010 2011 2012 2013 2014 2015 2016 Sc01 1.749,48 1.009,69 0,00 -174,87 992,96 0,00 0,00 0,00 Sc02 1.816,38 1.009,69 0,00 -223,49 1.117,16 0,00 0,00 0,00 Sc03 1.816,38 1.009,69 0,00 -223,49 1.117,16 0,00 0,00 0,00 Sc04 1.871,04 1.009,69 0,00 -237,08 1.191,22 0,00 0,00 0,00 Sc05 1.592,18 117,38 111,65 81,20 699,74 0,00 395,22 426,50 Sc06 1.678,98 419,87 0,00 0,00 686,11 3,49 412,00 383,49

Table 6-2 Summary of costs of each scenario (in millions)

6.1.4 Sensitivity analysis

Some of the parameters used to construct the numerical examples are estimated or assumed. Estimations or assumptions are usually subject to some margin of errors. Thus, it is important to know the effect of a slight variation in those parameters on the model results. This effect is analyzed in this section by making a small percentage increase and decrease in those parameters. All the analyses are carried out in comparison to the base model.

6.1.4.1 The effect of EUA/CER Spread

One of the most relevant elements of the input data used for the numerical examples is the EUA/CER spread. It is the parameter that is used to estimate CER prices from EUAs. The variation of this parameter results in the variation of estimated CER prices. This intern affects the model output because the decision either to use CER capacity either at the beginning compliance years or to bank it for the later years depends on this price.

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Figure 6-7 Influence of EUA/CER spread on the model results

The figure above illustrates the effect of the spread on the strategic decisions developed by the model. When the spreads are higher at the end of the trading period, the CER prices will be much lower. This makes reasonable to buy and use CERs in those years (Spreads 3and 4). However, if those spreads are lower at the end of the period, using all the CER capacity at the beginning will be the optimal decisions (Spread 1 and 2). A spread ranging from 2€ to 8€ is considered in phase III for the sensitivity analysis. Figure 6-7 shows that these values have no significant effect on the strategies developed under the base case prices scenario. The following figure shows the spread curves used for the sensitivity analysis.

Figure 6-8 Spread curves used for the sensitivity analysis

6.1.4.2 The effect of discount rates

Another important parameter used as an input data to the model is the discount rate used to calculate the NPV of the annual costs. Since the strategic decisions are more like long term

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investments (especially when it is economical to purchase quite a number of allowances during the first years), knowing the sensitivity of this parameter is crucial. The discount rate is calculated from Euribor as it may be seen in Appendix B. Therefore, sensitivity of the model to the discount rate can indirectly be conducted by analyzing the sensitivity of the Euribor.

The following figure shows the variation in the Euribor that is used to conduct this sensitivity analysis. A variation by ± 10%, ± 20%, ±30% and +50% on the initial value of the Euribor that was used to calculate the base case has been introduced.

Figure 6-9 Euribor variation for sensitivity analysis

Figure 6-10 shows model results when the above Euribor variations are introduced. It can be seen from the figure that the parameter doesn’t have any significant effect on the surrendering strategy of the company except on the contribution of non-eligible CERs for the first two years compliance. Its effect is rather reflected on the purchasing strategy.

Generally, lower Euribor rates foster buying most of the allowances during the first two years while higher rates promote distributing purchasing throughout the years. The figure also shows the corresponding changes in the annual costs and the NPV for each Euribor value.

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Figure 6-10 The influence of discount rate on model results

6.1.4.3 The effect of interest rate

The interest rates used to quote future allowance prices are also relevant factors that have an influence on the utility’s participation in future markets. The effect of these rates on the strategic planning developed by the model is studied by changing their value by ±10%, ± 20%, ±25%, +30% from their base value. The following figure shows the variations used for the sensitivity analysis of this parameter.

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Figure 6-11 The variation in the interest rate used for sensitivity analysis

Figure 6-12 depicts the results of the model when the above interest rates are introduced in the model. The variation in the interest rates doesn’t have significant effect in the allowance surrender or Kyoto credit using capacity. In almost all the cases, the use of CER capacity in phase II is suggested except a little variation on the share of non-eligible CERs for compliance among the first two years. With higher interest rates, more non-eligible CERs should be surrendered in 2011 than 2010.

The variation in the interest rate has rather a significant effect in the utility’s purchasing strategy, especially, in its future market participation. With lower interest rates, participation in the future market is recommended by the model. While with high interest rates the model tends to suggesting purchase most of the allowances needed for the period at the beginning in spot markets. This is because the future prices will be expensive when quoted with high interest rates.

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Figure 6-12 The influence of interest rate on model results

6.1.4.4 The effect of emission estimate

One of the uncertainties involved for a utility hedging its emission through emission trading is the estimation of its emission itself. This is an influential parameter used as an input for the model. Therefore, knowing its effect on the optimal strategic decision is very important.

The sensitivity of the model to emission estimates is analyzed by considering a linear increasing and decreasing annual emission estimates from the base case. The analysis is to study how the optimal strategy changes if the utility achieves a 10%, 20%, and 25% increase (decrease) on its emissions in the long term assuming this will be achieved through a linear yearly increase (decrease).

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Figure 6-13 Influence of emission estimates on the optimal strategic decision

Figure 6-13 shows the results of the sensitivity analysis. It shows that the model is not sensitive to the emission variation. Both purchasing and surrendering strategies remain the same in all the variation considered for analysis. Although the amount varies with the emission level considered, all the decisions: participation in future markets, the compliance proportions by each of the allowances are the same in all the cases.

6.2 Testing and experimenting with stochastic model

In this section verification and validation tests are carried out. The benefit of using the stochastic model over the deterministic one is also measured. All the data used in this section is the same as the one used for the analysis of the deterministic model. The scenario tree assumed and the probability of the scenarios is given in detail in Appendix B.

6.2.1 Verification of the stochastic model

A simple and easy way to verify the stochastic model is to run it with only one scenario at a time and compare the results with each of the deterministic outcomes. The results should be the same if the probability of the other scenarios is set to zero.

The following figures show the comparison of stochastic model output with only one scenario at a time with each of the deterministic scenario results. The comparison is carried out only for three scenarios out of the six, and is given in the following figure. It can be seen from the figures that the results are the same, which verifies the stochastic model.

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Testing and experimenting with stochastic model 56

Results of the stochastic model with one scenario at a time

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Figure 6-14 Comparison of the stochastic outputs with only one scenario with the deterministic results

6.2.2 Optimal stochastic solution

Once the model is verified, it can now be used to generate a stochastic strategic plan under the scenarios considered.

The scenarios are assumed to follow a simple scenario tree structure for the analysis of the stochastic model. In addition, equal probability is assumed for each of the six scenarios considered. Each scenario also takes into account the information dependence relationship between the subsequent years.

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Testing and experimenting with stochastic model 58

Figure 6-15 Stochastic model output

Figure 6-15 shows the results of the stochastic model and the scenario tree used. Decision is taken at each node. There is only one node during the first year. Therefore there will be only one decision at the beginning year taking into account all the possible scenarios of the next year. Later, depending on which scenario happened, the decision will vary for each node in the same year.

Except the last two scenarios, the strategic decision suggested by the other scenarios is the same. All the scenarios but scenario 5 consider an increasing price trend from the very beginning. The last scenario (scenario 6) considers very small prices and a slow increase in those prices while the others consider higher prices with a steep increasing slope especially from phase II to Phase III. This explains the similar strategies proposed under these scenarios.

6.2.3 Stochastic measures

Stochastic linear programs have been rarely used in practical situation largely because of their complexity. In order to prove weather using stochastic models rather than pure deterministic model is justified or not, some measures are conducted.

An important measure of the stochastic outputs is called the sum of expected regrets. Regret is the difference between the actual payoff and the payoff that would have been obtained if a different course of action had been chosen. The following table shows the costs of each of the best decision under each scenario if the other scenarios would have happened. Decisions 1 to 6 are the best decisions under scenarios 1 to 6 in the deterministic model while decision 7 is the best decision under the stochastic model.

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Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 Decision 1 1.749.478.900 1.816.384.592 1.816.384.592 1.871.038.196 1.651.818.377 1.715.713.660 Decision 2 1.749.478.900 1.816.384.592 1.816.384.592 1.871.038.196 1.651.818.377 1.715.713.660 Decision 3 1.749.478.900 1.816.384.592 1.816.384.592 1.871.038.196 1.651.818.377 1.715.713.660 Decision 4 1.749.478.900 1.816.384.592 1.816.384.592 1.871.038.196 1.651.818.377 1.715.713.660 Decision 5 1.869.120.469 2.192.954.914 2.192.954.914 2.327.926.568 1.592.175.003 1.707.053.916 Decision 6 2.001.255.011 2.374.810.455 2.470.614.676 2.504.657.345 1.741.138.491 1678981844 Decision 7 1.750.213.511 1.816.928.883 1.816.928.883 1.871.750.954 1.652.711.812 1.679.681.408

Table 6-3 The costs of each decision under different scenarios

The yellow shaded costs in the diagonal of the above table are the best decisions under each scenario. That means they are the minimum costs under each column.

The following table shows the expected regret pay off. The difference between the costs in each column in the above table and the minimum cost under each column is calculated. It is basically the additional cost of taking different decisions under the same scenario. And this value is multiplied by the probability of each scenario.

Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 Sum regrets

Decision 1 0 0 0 0 9.940.562 6.121.969 16.062.532

Decision 2 0 0 0 0 9.940.562 6.121.969 16.062.532

Decision 3 0 0 0 0 9.940.562 6.121.969 16.062.532

Decision 4 0 0 0 0 9.940.562 6.121.969 16.062.532

Decision 5 19.940.261 62.761.720 62.761.720 76.148.062 0 4.678.679 226.290.443

Decision 6 41.962.685 93.070.977 109.038.347 105.603.191 24.827.248 0 374.502.449

Decision 7 122.435 90.715 90.715 118.793 10.089.468 116.594 10.628.721

Table 6-4 The expected regret pay off

The last column in table 6-4 shows the sum of the expected regrets. It can be shown that decision 7 yields the lowest value. This decision is the decision suggested by the stochastic model considering all the scenarios with equal probability. From the table it can be concluded that taking the stochastic decision will yield the minimum value of the sum of expected regrets.

60

7 CONCLUSIONS AND RECOMMENDATIONS

This last chapter is dedicated to evaluating the conclusions that result from the research conducted in this thesis. A brief summary of the analysis, developments and findings that were conducted in the thesis are included and relevant recommendations are proposed.

7.1 Conclusions

This thesis has addressed the problem of developing an optimal CO2 emission compliance strategy through emission trading for a power utility subject to EU ETS obligation. Taking emission estimates as in input, the proposed methodology develops optimal allowance purchasing and surrendering strategies. With the extension of the EU ETS to a long term market and the dominance of thermal generation units subject to EU ETS in the electricity sector, this issue is currently very important in the sector.

The issue of developing optimal emission compliance strategy through emission trading for a company under EU ETS is mainly influenced by legal and regulatory binding rules embedded in the scheme. Extensive survey of EU ETS history, origin and performance has been conducted to identify those rules.

The search for an optimal emission compliance strategy involves allowance purchasing, and surrendering strategies. This requires the evaluation of the expected costs of any candidate strategy. Particularly, estimation of expected costs from both spot and futures market participation is crucial. This requires spot allowance prices and interest rates used to quote the corresponding future prices to be identified explicitly.

Uncertainty with respect to emission price is the key issue in developing emission compliance strategy through emission trading. In this thesis a stochastic model has been developed to include this uncertainty. Sensitivity analysis is carried out to study the effect of the other uncertain parameters such as emission estimates.

The thesis focuses on the development of annual purchasing and surrendering strategy for the company’s emission. However, this annual strategies can be break down in to monthly or weekly operational decisions. That means the results can be used as a framework to develop the daily operational decisions.

The validity of the methodology developed is confirmed through experiments with different price scenarios and parameter values performed on a fictitious but representative Spanish power utility owing 20 installation subject to EU ETS.

Conclusions and Recommendations 61

The following conclusions can be drawn from the research conducted in this thesis.

• The problem of developing optimal CO2 compliance strategy through emission trading can be formulated as a multi-period stochastic MIP problem.

• Given the fictitious company considered, most of the scenarios undertaken suggest a similar strategy. This strategy is to purchase as much EUAs as possible at the beginning and to bank them for the later years.

• Swapping EUAs with no-eligible CER is recommended under most of the scenarios. • The CER/EUA price spread is an important factor that determines either to utilize

the potential to use CERs at the beginning or at the end of the planning period. • When increasing price trends are considered, similar compliance strategies of buying

allowances in the beginning period, swapping EUAs with CERs and banking most allowances for later years are suggested as an optimal strategy.

• Stochastic modeling results are preferred over deterministic ones as they result in a less sum of expected regret.

7.2 Recommendations

A method has been described which makes possible determination of optimal CO2 compliance strategy through emission trading. As would be expected, optimal compliance strategies through trading depend strongly up on the future price of allowances. The method described enables planners to quickly examine a wide range of assumptions regarding these and other relevant factors. Use of the deterministic methods by the utilities would likely involve a careful projection of best case scenarios for a particular set of assumptions introduced.

The methodology includes a lot of constraints in order to limit the speculation nature of the optimization model. By modifying and removing those constraints the method can be also applicable for speculative traders.

Last but not least, the method can be also used by the regulating authorities in order to simulate the behaviors of utilities covered under the EU ETS under different price and regulatory scenarios. In that way the model will help the regulator to consider relevant regulatory practices to keep the trading scheme smooth and stable so that the intended objective may be achieved.

Future line of research 62

7.3 Future line of research

The developments of this thesis lead to two main future lines of research whose exploration is likely to yield interesting results. Because of the short time frame given to complete this thesis it was not possible to incorporate these issues in this work.

As has been in indicated, the methodology developed in this thesis only considers the uncertainty in allowance prices. However, emission estimates are also subject to high uncertainty. They may even be dependent on the price of allowances themselves. It would be interesting to incorporate the emission stochasticity and its dependency on allowance prices.

This thesis considers spot and future contract markets as well as the different allowances in EU ETS explicitly. However, the participation of the utility in an options market is not considered. In addition, the utility can also participate in EUA/CER spread market where the spread is purchased and sold. It would be interesting to include these features and see the results in the proposed methodology.

63

8 APPENDIX

A. Appendix I EU ETS performance

More figures showing the future prices of allowances from 2008 December expiration are given in this appendix. Both EUA and CER future prices histories as well as volumes traded can be shown from the two figures below.

Figure 8-1 Future price and volume history of EUA December 2008 to 2013 expiration

Figure 8-2 Future price and volume history of CERs of December 2008 to Dec 2011 expiration

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Input data for the study cases 64

B. Input data for the study cases

In this thesis a number of numerical examples are solved in order to test the model as well as to illustrate the methodology proposed to address the problem of developing optimal emission trading strategy for a utility under EU ETS. These examples consider the case of a fictitious but representative Spanish electricity generation company. This subsection provides the general overview of the input data used in these numerical examples.

All the numerical examples included in this thesis refer to the same generation utility. It is a large hypothetical utility owing 20 installations subjected to EU ETS of which 11 are coal units, 14 combined cycle units and 3 fuel units.

For the three-year period beginning January 2005 (phase I) and for five-year period beginning January 2008 (Phase II), EU allowances were allocated for each installation free of charge according to member states’ NAP. These allowances are referred in this thesis as assignations or assigned allowances. Table 8-1 shows the assignations of each installation considered in the case examples of this thesis. From 2013 onwards, the EU directive states that allowances are no more allocated for free; there would rather be an auctioning to distribute them among different installations.

B-1 Allocation

Installations are randomly chosen from the published 2009 verified emission data that is available in the European Commission website. Once installations are randomly chosen, their assignation for 2010 to 2012 was available in the CITL website [32].The following table shows the assignations of the installations that are used in the analysis throughout this thesis.

Installation Type Allocation

2010 2011 2012 Inst_1 Coal 4.012.840 3.995.211 3.995.211 Inst_2 Coal 3.366.047 3.330.929 3.330.929 Inst_3 Coal 1.648.343 1.631.146 1.631.146 Inst_4 Coal 1.084.179 1.042.306 1.011.956 Inst_5 Coal 1.047.660 1.036.730 1.036.730 Inst_6 Coal 551.524 527.272 511.919 Inst_7 Coal 298.923 282.823 274.587 Inst_8 Combined cycle 618.818 618.818 618.818 Inst_9 Combined cycle 604.693 604.693 604.693 Inst_10 Combined cycle 604.017 604.017 604.017 Inst_11 Combined cycle 318.771 318.771 318.771 Inst_12 Combined cycle 310.363 310.363 310.363 Inst_13 Combined cycle 306.091 306.091 306.091

Appendix 65

Inst_14 Combined cycle 302.518 302.518 302.518 Inst_15 Combined cycle 297.645 297.645 297.645 Inst_16 Combined cycle 241.515 247.468 247.373 Inst_17 Combined cycle 304.084 304.084 304.084 Inst_18 Fuel 0 0 0 Inst_19 Fuel 0 0 0 Inst_20 Fuel 0 0 0

Total 15.480.673 15.320.698 15.274.900

Table 8-1 Assignations and types of installations

B-2 Emission estimates

Estimating emission for each installation is difficult. Although the historical emission level of each of the installations varies from phase I to phase II and from year to year with in each phase, the emission level of 2008 was taken as a base case for estimation. This is because of two reasons. First, the over allocation of allowances in EU ETS phase I was reported to increase emission levels more than their normal value. This does not make Phase I emission data representative emission level when allowances are short in the market.

The other reason is that 2009 emission data shows a significant decrease in the total emission level. This can be explained by the effect of the economic crisis. This also doesn’t make this year’s data a good representative when normal conditions are assumed.

Table 8-2 shows the estimated emission levels of each installation used in the case examples. Generally, coal units emit more CO2 than combined cycle or fuel units.

Installation Emissions

2010 2011 2012 2013 2014 2015 2016 Inst_1 4.707.027 4.707.027 4.707.027 4.707.027 4.707.027 4.707.027 4.707.027

Inst_2 4.995.507 4.995.507 4.995.507 4.995.507 4.995.507 4.995.507 4.995.507

Inst_3 1.821.493 1.821.493 1.821.493 1.821.493 1.821.493 1.821.493 1.821.493

Inst_4 2.020.466 2.020.466 2.020.466 2.020.466 2.020.466 2.020.466 2.020.466

Inst_5 879.507 879.507 879.507 879.507 879.507 879.507 879.507

Inst_6 265.478 265.478 265.478 265.478 265.478 265.478 265.478

Inst_7 100.334 100.334 100.334 100.334 100.334 100.334 100.334

Inst_8 1.499.132 1.499.132 1.499.132 1.499.132 1.499.132 1.499.132 1.499.132

Inst_9 1.131.891 1.131.891 1.131.891 1.131.891 1.131.891 1.131.891 1.131.891

Inst_10 1.710.775 1.710.775 1.710.775 1.710.775 1.710.775 1.710.775 1.710.775

Inst_11 929.145 929.145 929.145 929.145 929.145 929.145 929.145

Inst_12 856.565 856.565 856.565 856.565 856.565 856.565 856.565

Inst_13 405.099 405.099 405.099 405.099 405.099 405.099 405.099


Inst_14 888.044 888.044 888.044 888.044 888.044 888.044 888.044

Inst_15 723.359 723.359 723.359 723.359 723.359 723.359 723.359

Inst_16 618.914 618.914 618.914 618.914 618.914 618.914 618.914

Inst_17 722.777 468.557 468.557 480.271 489.877 499.674 509.668

Inst_18 0 0 0 0 0 0 0

Inst_19 119.600 119.600 119.600 119.600 119.600 119.600 119.600

Inst_20 0 0 0 0 0 0 0

Total 23.880.312 23.880.312 23.880.312 23.880.312 23.880.312 23.880.312 23.880.312

Table 8-2 Estimated emission levels of each installation

B-3 Price forecasts

EU ETS is launched in 2005 leaving only five years of historical data. After the end of the first phase (2007) significant regulatory changes have been introduced. This completely changed the price trends. The beginning of the second phase was accompanied with a worldwide economic crisis, which had and still has a significant effect on the global economy including emission trading. As the entire available historical price data is distorted due to these factors, using those data for developing a strategic plan is not a good idea. Therefore, forecasted price data is used for all practical examples conducted in this thesis.

The following table shows the EUA spot price forecasts. Those prices were forecasted by different banks. The prices of 2010 to 2012 are explicitly forecasted for each year while the price for Phase III is given as a total average. This requires splitting the average value into yearly values to be used as an input by the model.

EUA PRICE ESTIMATES ASD 2010 2011 2012 P2 P3 BarCap 14.0 18.0 24.0 18.4 40.0

COER2 Commodities 18.0 24.0 30-32 21.8 N/A Daiwa 13.3 13.9 14.4 15.5 20.0

Deutsche Bank (1) 15.0 +CC +CC 20.0 40-42

Nomisma Energy 14.0 N/A 19.0 17.1 N/A

Point Carbon 18.0 22.0 23.0 19.8 37.0 Sagacarbon 15.5 18.0 23.0 18.5 N/A

SocGen/orbeo 16.1 19.0 23.0 18.8 30.1

UBS N/A N/A 35.0 N/A N/A

UniCredit N/A N/A 27.0 N/A N/A AVERAGE 15.5 19.2 24.4 18.7 33.6

Table 8-3 EUA price forecasts [33]

These price forecasts are not constant even for duration of a small period. Depending on new information disclosed, the banks vary their forecasts from month to month. Therefore,

Appendix 67

rather than using the forecasts directly, six price scenarios are developed using the above forecasts as a bench mark for the illustrative examples and the case studies conducted in this thesis. The following table gives these price scenarios.

2010 2011 2012 2013 2014 2015 2016 Scenario 1 €14,50 €16,00 €18,00 €23,00 €25,00 €27,00 €30,00 Scenario 2 €14,50 €18,00 €23,00 €28,00 €30,00 €31,50 €32,50 Scenario 3nrio 3 €14,50 €18,00 €23,00 €30,50 €33,00 €37,50 €39,00 Scenario 4 €14,50 €19,20 €24,40 €29,00 €32,00 €33,50 €35,00 Scenario 5cenar €14,50 €13,00 €14,00 €20,00 €22,00 €25,00 €27,00 Scenario 6ario 6 €14,50 €15,00 €15,50 €18,00 €18,50 €19,00 €19,30

Table 8-4 Price scenarios used for analysis

All the prices are in €per one ton of CO2 emission

B-4 EUA/CER Spread

A related forecast for CER spot prices was not found in literatures and reports. Therefore, it is estimated from the EUA forecast using historical EUA/CER spread. The following figure shows historical the EUA/CER spread since CER is permitted in EU ETS. The spread was very high at the beginning even though this didn’t last long. It dropped below 2€ right away. Mostly it has been between 2€ and 1€.

Figure 8-3 Historical EUA/CER Spread

Source: Blunext

€0.00€1.00€2.00€3.00€4.00€5.00€6.00

12/0

8/20

0812

/09/

2008

14/1

0/20

0813

/11/

2008

15/1

2/20

0819

/01/

2009

18/0

2/20

0920

/03/

2009

23/0

4/20

0926

/05/

2009

25/0

6/20

0927

/07/

2009

26/0

8/20

0925

/09/

2009

27/1

0/20

0926

/11/

2009

29/1

2/20

0901

/02/

2010

03/0

3/20

1006

/04/

2010

06/0

5/20

1007

/06/

2010

07/0

7/20

10EUA/CER Spread


A spread between 3€ and 1€ is assumed for phase II. Since the use of CERs is expected to be restricted in EU ETS phase III, a higher spread is assumed after 2012. The spread values used in the thesis are given in the following table. Only the values in the first row are used to conduct all the illustrative examples. A sensitivity analysis has been conducted to see the effect of changing the spread on the model outcomes. The values in the rest of the rows are those that are used for this sensitivity analysis.

2010 2011 2012 2013 2014 2015 2016 Spread 1 (Base case)

1,35 1,45 1,5 3,5 3,8 4,0 4,12

Spread 2 1,45 1,61 1,85 4,5 5,8 7,00 8,00 Spread 3 1,2 1,4 1,4 1,3 1,4 1,5 1,7 Spread 4 1,4 1,6 1,8 3,8 4,0 4,8 5

Table 8-5 EUA/CER spreads used for case studies and sensitivity analysis

B-5 Scenario tree

The forecasted data is assumed to follow a simple scenario trees structure for the analysis of the stochastic model. Equal probability is assumed for each of the six scenarios. In addition each scenario also takes in to account the information dependence relationship between the subsequent years.

Figure 8-4 Scenario tree used for analysis

2010 2011 2012 2013 2014 2015 2016

Scenario 1, prob. 0,167

Scenario 2, Prob. 0,167





Appendix 69

B-6 Interest rates

The interest rate used to quote the future prices from the spot price forecasts are also estimated based on historical data. The set of daily interest rates that were used to quote future prices of Dec-2010, Dec-2011, Dec-2012, Dec-2013 and Dec-2014 expiration from 2009 and 2010 spot prices are calculated from a historical data that is publicly available on the ECX website. Since the model considers yearly trading decisions, only one set of interest rates is required to quote the average future prices from each forecasted spot price.

Figure 8-5 Historical interest rates that were used to quote EUA futures from 2009 spot prices

When futures approach their maturity, the interest rates used to quote them decreases. For example as it can be shown in the figure above, the interest rate for the 2010 future gradually decreases and becomes close to zero after July, to match with the corresponding spot prices at the end. Similarly the interest rate used to quote 2011 decreases and finally takes a value equal to the interest rate that was used to quote the 2010 future at the beginning of the year. Assuming more liquidity at the end of each compliance year, the averages of the interest rates of the last four months are taken as a best approximation to be used by the model. Table 8-6 gives those interest rates used in this thesis.

2010 2011 2012 2013 2014 2015 2016 Interest rate

0,12% 2,27% 6,38% 3,05% 3,25% 3,92% 4,82%

Table 8-6 The interest rates used to quote future prices

0%

10%

20%

30%

40%

50%

60%

3/8/09 4/27/09 6/16/09 8/5/09 9/24/09

Dec-9 Dec-10 Dec-11 Dec-12 Dec-13 Dec-14


B-7 Discount rate

The NPV calculation from the annual purchasing costs requires the use of discount rate, 𝛽. A relevant discount rate used in mortgages and other investment valuation is calculated from Euribor14

.

Figure 8-6 A-Historical Euribor 12 month average, B- historical and estimated annual average

Since the Euribor is also distorted by the financial crisis (see Figure 8-6), future recovery is assumed in the estimation. Sensitivity analysis has been carried out to see the effect of different Euribor estimates on the results of the model. The Euribor used in this thesis for calculating the scenarios is given in the following table.

2010 2011 2012 2013 2014 2015 2016 Annual (12m) Euriobor

1,3 1,6 2,15 3,05 3,25 3,92 4,82

Table 8-7 Euribor values used for NPV calculation

14Euribor is the rate at which Euro interbank term deposits are offered by one prime bank to another prime bank within the EMU zone, and is published at 11:00 a.m. (CET) for spot value (T+2).

0.001.002.003.004.005.006.00

JAN

-06

MAY

-06

SEP-

06JA

N-0

7M

AY-0

7SE

P-07

JAN

-08

MAY

-08

SEP-

08JA

N-0

9M

AY-0

9SE

P-09

JAN

-10

MAY

-10

Euribor 12m Average

0.001.002.003.004.005.006.00

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

Annual average

estimate Euribor Annual average

Appendix 71

C. Equation and column listings

The following lines show a sample GAMS equation listing for the compliance constraint. Equation listing has been the main feature of GAMS language that is used to verify the model for errors in this thesis.

---- E_COMPLIANCE1 =E= Compliance to emission Phase II E_COMPLIANCE1(Installaion_1,Yr2010).. e(Installaion_1,EUA,Yr2010) + e(Installaion_1,Elig_CER,Yr2010) + e(Installaion_1,NoneligCER,Yr2010) =E= 161534 ; (LHS = 0, INFES = 161534 ****) E_COMPLIANCE1(Installaion_1,Yr2011).. e(Installaion_1,EUA,Yr2011) + e(Installaion_1,Elig_CER,Yr2011) + e(Installaion_1,NoneligCER,Yr2011) =E= 161534 ; (LHS = 0, INFES = 161534 ****) E_COMPLIANCE1(Installaion_1,Yr2012).. e(Installaion_1,EUA,Yr2012) + e(Installaion_1,Elig_CER,Yr2012) + e(Installaion_1,NoneligCER,Yr2012) =E= 161534 ; (LHS = 0, INFES = 161534 ****) ---- E_COMPLIANCE2 =E= Compliance to emission Phase III E_COMPLIANCE2(Installaion_1,Yr2013).. e(Installaion_1,EUA,Yr2013) + e(Installaion_1,Elig_CER,Yr2013) =E= 161534 ; (LHS = 0, INFES = 161534 ****) E_COMPLIANCE2(Installaion_1,Yr2014).. e(Installaion_1,EUA,Yr2014) + e(Installaion_1,Elig_CER,Yr2014) =E= 161534 ; (LHS = 0, INFES = 161534 ****) E_COMPLIANCE2(Installaion_1,Yr2015).. e(Installaion_1,EUA,Yr2015) + e(Installaion_1,Elig_CER,Yr2015) =E= 161534 ; (LHS = 0, INFES = 161534 ****)

72

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