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In an era of energy transition, it is crucial to ensure that the design of the short-term electricity market provides sufficient cash flows to producers so as to allow the investment of the right technology at the right location. In this paper, we revisit the question of capacity allocation in zonal markets from a long-term perspective. We model the capacity expansion problem in zonal markets in which inter-zonal transmission capacity allocation is organized through flow-based market coupling, which is an approximation of power flow equations in aggregate networks that is employed in European market design. We demonstrate that the classical result of equivalence between centralized and decentralized formulations in transmission-constrained markets ceases to hold in this case. We propose a model of the decentralized capacity expansion problem with flow-based market coupling as a generalized Nash equilibrium that we formulate as a linear complementarity problem. We then perform simulations of the capacity expansion problem with nodal pricing and three variations of zonal pricing on a realistic instance of the Central Western European network and comment on the impacts of flow-based market coupling on investment.

The energy transition reveals a number of challenges for the planning and operation of electric power systems, many of which are the subject of active research. Among the open issues that relate to market design, one has been the subject of particularly intense debate in Europe since the liberalization: the market-based allocation of transmission capacity. Currently, the European electricity market is organized around the principle of zonal pricing, which is characterized by the delimitation of regions on the power network, that are called zones, inside which the electricity price is the same in the wholesale market. This principle is opposed to nodal pricing, in which the price is differentiated between every location. In this thesis, we present detailed models and algorithms for analyzing the efficiency of zonal pricing. In the first part, we focus on the short-term efficiency and, in particular, on the impacts of the optimization of the grid topology through transmission line switching for improving the efficiency of zonal pricing. The second part of the dissertation investigates the efficiency of zonal pricing in the long run, when investment decisions in generating capacity are accounted for. First, we propose a model of the long-run equilibrium of zonal pricing with flow-based market coupling, which is the current methodology used in practice in Europe for allocating transmission capacity. We show that this methodology introduces new inefficiencies in the context of capacity expansion. Then, we investigate whether additional locational instruments, such as capacity and energy-based signals or market-based re-dispatch, can restore the efficiency of investments in zonal pricing. For each of the three main contributions, we present simulation results of our models on a large-scale instance that represents the Central Western European network and we discuss the implications of our results for the performance of zonal electricity pricing., (FSA - Sciences de l'ingénieur) -- UCL, 2022

We propose a novel framework for modeling zonal electricity markets, based on projecting the constraints of the nodal network onto the space of the zonal aggregation of the network. The framework avoids circular definitions and discretionary parameters, which are recurrent in the implementation and study of zonal markets. Using this framework, we model and analyze two zonal market designs currently present in Europe: flow-based market coupling (FBMC) and available-transfer-capacity market coupling (ATCMC). We develop cutting-plane algorithms for simulating FBMC and ATCMC while accounting for the robustness of imports/exports to single element failures, and we conduct numerical simulations of FBMC and ATCMC on a realistic instance of the Central Western European system under the equivalent of 100 years of operating conditions. We find that FBMC and ATCMC are unable to anticipate the congestion of branches interconnecting zones and branches within zones, and that both zonal designs achieve similar overall cost efficiencies (0.01% difference), while a nodal market design largely outperforms both of them (5.09% better than FBMC). These findings raise the question of whether it is worth for more European countries to switch from ATCMC to FBMC, instead of advancing directly towards a nodal market design.

We present here a characterization of the Clarke subdifferential of the optimal value function of a linear program as a function of matrix coefficients.We generalize the result of Freund(1985)to the cases where derivatives may not be defined because of the existence of multiple primal or dual solutions.

Transitioning from fossil fuel dominated power systems to high penetrations of intermittent renewable generation is affecting classical electricity market designs. Here, a method is proposed to model and assess the absence of co-optimization of energy and reserve that prevails in the European system. Co-optimization is formulated through an optimization problem (COM), and its absence as an equilibrium problem (EQM) built on Karush-Kuhn-Tucker conditions of agents’ optimization and market clearing equations. EQM cannot be reformulated as a single optimization problem. Market distortions are identified by comparing the complementarity conditions of both models. These are then discussed on system with Feed in Premium to wind generation. Parameters in the models allow to represent different market configurations regarding: available wind generation, Feed in Premium to wind, generators’ risk aversion, and required reserve from wind generation.

This case study presents an analysis and quantification of the impact of the lack of co-optimization of energy and reserve in the presence of high penetration of wind energy. The methodology is developed in a companion paper, Part I. Two models, with and without co-optimization are confronted. The modeling of reserve and the incentive to renewable as well as the calibration of the model are inspired by the Spanish market. A sensitivity analysis is performed on configurations that differ by generation capacity, ramping capability, and market parameters (available wind, Feed in Premium to wind, generators risk aversion, and reserve requirement). The models and the case study are purely illustrative but the methodology is general., Comment: 8 pages, 4 tables, 5 figures. Supplementary material for article entitled: Co-optimization of Energy and Reserve with Incentives to Wind Generation

Scenario studies of energy transition generally point to the central role of electricity. This notion is ambiguous as its interpretation can range from an electricity-only policy to portfolios of different energy vectors with a dominance of electricity. This ambiguity adds to the uncertainty that already pervades today’s investment environment. This paper examines the centrality of electricity through a so-called “variational scenario” analysis with policies obtained by a mix of electricity-only and green gas penetration while maintaining constant decarbonization objectives. Electricity is a complex product that can only be further complicated by the high penetration of renewables and its interaction with the production and use of synthetic fuels. The variational scenario analysis is conducted with sufficiently fine (hourly) granularity to produce an adequate representation of these phenomena. It shows that tilting the central role of electricity to a mix of electricity and green gas offers several advantages in terms of efficiency, flexibility of investment strategies, and robustness with respect to major uncertainties. It shows that the variational scenario analysis can be extended to more complex mixes of policies.

This paper investigates different reserve issues inspired by the European situation, focusing on both the moment when reserves are procured and the degree of coordination among Transmission System Operators (TSOs) in that procurement. We present three scheduling models formulated as stochastic programs that represent the day-ahead energy market, the reserve procurement, and the real-time balancing market in a renewable-dominated power system. Two of the proposed models are inspired by reserve procurement mechanisms currently applied in Europe, where reserves are committed either before (Model 1) or after (Model 2) the clearing of the day-ahead energy market. Then, we use as benchmark a third model in which energy and reserve capacity are co-optimized (Model 3). In all models, we consider the procurement of both conventional and upward/downward reserves. We also assess the impact of these organizations on market participants’ remuneration and test the impact of cross-border constraints as those applying in the European power system. The case study is based on the IEEE 24-node RTS, considering the uncertainty in renewable power production and demand. Our results show that Model 1 is the least efficient market design as it leads to a misallocation of the available capacity, while Model 2 becomes as efficient as Model 3 when the TSOs procure reserve in a coordinated way. Finally, a coordinated procurement of reserves reduces the system operating costs in all models.

Uncertainty is a major hindrance to attracting investment for the energy transition. Yet European market design is mainly discussed with a focus on short-term efficiency. Based on computational results from market models for gas and power we derive lessons on the importance of contracts and the implications of incomplete markets. Specifically, we show that short-term efficiency is not sufficient to guarantee a well-functioning long-term market, whether expressed in standard welfare-maximization terms or with respect to the EU criteria (security of supply, sustainability or affordability). The end result can drastically depend on the extent to which one can deal with risk. This result is in line with economic theory.

Government involvement in managing domestic prices of energy and other commodities is a major issue in emerging economies. We examine one aspect of the problem, price controls, when governments set or cap prices. We show how a Mixed Complementarity Problem (MCP) formulation can be used to model and assess the impacts of price controls in multi-sector economic-equilibrium models. Both the gains from deregulation and the consequences of imposing new or altering existing regulations can thus be measured. We present three distinct models that capture different price-control situations: firms have to meet demand and receive an implicit subsidy, demand rationing occurs due to an associated price control constraint, and subsidies limit demand rationing. We present an approach to measuring the effects on the equilibrium in the first case and the levels of disequilibrium induced by price controls in the other cases. We also show how to determine the most efficient allocation program when a government engages in rationing. We illustrate the cases described by these models using markets that have or had price controls.

Renewable energy integration has progressively challenged the operating assumptions of electricity markets, questioning at first the deterministic nature of day-ahead and other forward electricity markets. As the integration of renewable resources became deeper, transmission grids began to experience congestion in unforeseen, dynamic and uncertain patterns, questioning now the management of transmission constraints in electricity markets. This dissertation proposes detailed models and algorithms for analyzing the impacts of uncertain renewable supply on different transmission-constrained electricity market designs, using parallel computing extensively in order to solve large-scale mathematical programs and to carry out simulations under different operating conditions for realistic systems. The contributions of the dissertation are organized in three chapters. Chapter 2 presents an asynchronous distributed algorithm for solving the stochastic unit commitment problem. The algorithm, deployed in parallel, is able to solve realistic instances of stochastic unit commitment within operationally acceptable tolerances and solution times. Chapter 3 proposes a consistent framework for modelling different zonal electricity markets. We develop cutting-plane algorithms to incorporate the N-1 criterion into this framework and we conduct simulations using single-period models for the Central Western European system under 768 000 different operating conditions. In chapter 4, we propose a hierarchy of mathematical programs that model the European zonal electricity market organization in detail in a multi-period setting. We compare the performance of this organization to the performances of a nodal market and the stochastic unit commitment model on the Central Western European system. Numerical results in chapters 3 and 4 indicate that failing to account for the limitations of the transmission grid, in a regime of large-scale renewable energy integration, can undermine system perform, (FSA - Sciences de l'ingénieur) -- UCL, 2018

This paper extends a recent analysis which investigated the impact of scarcity adders produced by operating reserve demand curves on the financial viability of generation units in the Belgian market. Our paper is inspired by practical considerations related to the implementation of the mechanism in European electricity markets. We are specifically interested in: (i) the extent to which the mechanism rewards flexible resources for being available ‘when and where’ needed, as required by European competition law; (ii) the sensitivity of the mechanism to certain parameters that require regulatory judgment; (iii) the interaction of the mechanism with indirect capacity mechanisms; and (iv) the ability of the mechanism to provide long-term investment signals. We find that the restoration of nuclear capacity in the Belgian market would suppress scarcity adders to near-zero values. We show that the increase in value of lost load would have a minor impact on scarcity adders when capacity shortages are negligible. We find that the removal of strategic reserve from the Belgian market would have a significant impact on scarcity adders. We find strong positive correlation in consecutive imbalance increments, and show that this correlation can result in noticeable impact on the computation of scarcity adders. We demonstrate that the back-propagation of scarcity adders is essential for providing a long-term investment signal to flexible resources.

Uncertainty in electricity markets introduces risk for investors. High fixed cost and increased dependency on infrequent and uncertain price spikes characterize investments. The risk-averse behavior of investors might lead to poor decision-making and undermines generation adequacy. Electricity market models rarely treat the interaction of market design and risk aversion. The representation of capacity mechanisms in modeling approaches focusing on risk aversion is limited. Our contribution addresses two problems. First,we propose a stochastic market equilibrium model. Investors are represented as risk-averse agents. The conditional value-at-risk is used as risk measure. Second, we propose an algorithm based on the alternating direction method of multipliers to compute a risk-averse equilibrium. We benchmark our approach with a state-of-the-art solver relying on a mixed complementarity problem reformulation. We show that for larger case studies our proposed approach is preferable. The algorithm converges in all cases while conventional solvers fail to compute a risk-averse equilibrium. The methodology is transferable to other risk-averse equilibrium models. With reference to capacity markets, we conclude that they are more beneficial in a risk-averse market. Capacity markets result in lower total cost, while avoiding expected energy not served. This statement still holds with increased price caps in energy-only markets.

Barring subsidies, investment in the power generation sector has come to an almost complete halt in the restructured European power sector. Market and regulatory failures such as the well known missing money (see Joskow, (2006)) but also normal market features such as risk, possibly also affected by market failures like market incompleteness are mentioned as common causes for the situation. This paper discusses incomplete risk trading and its impact on investment. The analysis applies computable stochastic equilibrium models on a simple market model of the Energy Only type. The paper first compares the cases of complete and fully incomplete markets (full risk trading and no risk trading). It continues by testing the impact of different risk trading contracts on both welfare and investment. We successively consider Contracts for Difference, Reliability Options with and without physical back up that we add to our Energy Only market model. We test the impact of market liquidity on the results. Finally, we compare these methods to a Forward Capacity Market that we also add to the energy only model. We complete the paper by interpretation of these results in terms of hurdle rate implied by these risk-trading situations.

Flexibility is becoming an increasingly important attribute of conventional generators due to the challenges imposed by the unpredictable, highly variable and non-controllable nature of renewable supply. Paradoxically, flexible units are currently being mothballed or retired in Europe due to financial losses. We investigate an energy-only market design, referred to as operating reserve demand curves, that rewards flexibility by adjusting the real-time energy price to a level that reflects the value of capacity under conditions of scarcity. We test the performance of the mechanism by developing a model of the Belgian electricity market, which is validated against the historical outcomes of the market over a study period of 21 months. We verify that (i) based on the observed market outcomes of our study period, none of the existing combined cycle gas turbines of the Belgian market can cover their investment costs, and (ii) the introduction of price adders that reflect the true value of scarce flexible capacity restores economic viability for most combined cycle gas turbines in the Belgian market.

After 50 years of development, building and solving mixed-complementarity problems (MCPs) have become commonplace for policy models that analyze markets. These models are used to develop policies that reshape markets, or introduce markets that replace other organizational forms. In this tutorial, we give some background on building economic equilibrium models, starting with the use of linear programming, and show how MCPs can be used to answer policy questions that require manipulation of the solutions to linear programs of economic sectors. We illustrate the use of MCPs using examples from King Abdullah Petroleum Studies and Research Center projects, including a model of domestic energy markets in Saudi Arabia, which is in the process of changing some of its pricing policies and market regulations.

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The thesis explores price comovements and systemic risk in energy and financial sectors. These sectors, by providing energy and credit to firms and households, are essential for the whole economy. Comovements between the elements of a portfolio or system are expected to increase during a crisis. Ignoring these increasing interdependencies risks lulling decision makers (portfolio manager or policy maker) in a false sense of security. Recent crisis episodes (financial crisis of 2007-2008 and European sovereign debt crisis) are particularly relevant to study because of their negative spillover to the real economy. The risk of the financial sector as a whole being in distress and its spillover to the economy at large is usually referred to as “systemic risk”. The thesis proposes new econometric techniques to address the changing nature of risk in energy and financial sectors, and evaluates the new regulatory approach – macroprudential regulation – adopted by regulators after the financial crisis of 2007-2008 to prevent the costs of the financial sector’s distress spreading to the real economy., (SC - Sciences) -- UCL, 2014

Up to now, the European natural gas trade was dominated by bilateral long-term upstream agreements between producers and midstreamers that fixed a minimum volume to be exchanged (Take Or Pay) and a price formula that was usually indexed on oil products prices. These arrangements were believed to allow: i) market risk sharing between the producer (who takes the price risk) and the midstreamer (who takes the volume risk) as well as ii) risk hedging since oil is considered as a trusted commodity by investors. The fall of the European demand combined with the increase of the oil price favored the emergence of a gas volume bubble that caused net losses for most of the European midstreamers who were bound by long-term agreements. As a result, some energy economists brought forward the idea of indexing contracts on gas spot prices. In this paper, we present an equilibrium model that endogenously captures the contracting behavior of both the producer and the midstreamer who strive to hedge their profit-related risk. The players choose between gas forward and oil-indexed contracts. Using the model we show that i) contracting can reduce the trade risk of both the producer and midstreamer, ii) oil-indexed contracts should be signed only when oil and gas spot prices are well correlated, otherwise, these contracts hold less interest for risk mitigation, iii) contracts are more needed when the upstream cost structure is CAPEX driven and iv) a too risk-averse behavior of the midstreamer might deprive upstream investments and the downstream consumer surplus.

In this paper, we formulate and solve a real life coal blending problem using a Column Generation Approach. The objective of the model is to prescribe optimal mixes of coal to produce coke. The problem is formulated as a mixed integer program. It involves various types of constraints arising from technical considerations of the blending process. The model also incorporates nonlinear constraints. It results in a large-scale problem that cannot be solved by classical operations research methods. Defining three heuristic methods based on column generation techniques, this paper proposes reasonable solutions for the industry.

Equilibrium in Economics has been seldom addressed in a situation where some variables are discrete. This work introduces a problem related to lot-sizing with several players, and analyses some strategies which are likely to be found in real world games. An illustration with a simple example is presented, with concerns about the difficulty of the problem and computation possibilities., Comment: 10 pages, Computability in Europe 2010

This paper compares the impact of the Nodal Pricing and European Market Coupling organizations on different economic agents of the power system under two main wind policies. Under the "priority dispatch" policy, Transmission System Operators (TSOs) must accommodate all wind energy produced, which thus has the priority over energy produced by conventional plants; in the "no priority dispatch" policy, TSOs can decide not to inject all potential wind power in the grid in order to limit congestion problems. The effects of these two wind policies are measured by developing simple stochastic programming models that consider cases with different wind penetration levels, existing capacities and endogenous investments, as well as assumptions on the EU-ETS. Our computational experiments show that, when there is "priority dispatch", Nodal Pricing and Market Coupling evolve in a similar way as long as wind penetration is not too high. In contrast, a significant increase of wind penetration causes the collapse of the Market Coupling organization while Nodal Pricing continues to perform well. On the other hand, "no priority dispatch" removes most of the problems resulting from Market Coupling, which still exhibits a slightly lower efficiency than Nodal Pricing. These outcomes do not depend on the contextual assumptions (fixed capacities vs. investment; EU-ETS vs. non EU-ETS) that characterize the several cases analyzed. This suggested that our policy conclusions are robust. Furthermore, our models overestimate the flexibility of conventional plants, which means that these conclusions would likely be reinforced with a more detailed model.

The horizontal integration of the energy market and the organization of transmission services remain two open issues in the restructured European electricity sector. The coupling of the French, Belgian and Dutch electricity markets (the trilateral market) in November 2006 was a real success. The extension of the system to Germany in November 2010 also proceeded smoothly and the intent is to continue with the same market architecture. But Market Coupling is based on a zonal system which has often failed in meshed grids. This may cast doubts on what will happen in the future when electricity demand picks up again and wind develops. The nodal system has generally been more successful than zonal architectures but its implementation is not currently foreseen in the EU. This paper analyzes versions of Market Coupling that differ by the organization of counter-trading. While underplayed in current discussions, counter-trading could become a key element of Market Coupling as its geographic coverage expands and wind penetrates. We simplify matters by assuming away strategic behavior between the energy and counter-trading markets and conduct the analysis on a stylized six node example taken from the literature. We simulate Market Coupling for different assumptions of zonal decomposition and coordination of Transmission System Operators (TSOs). We show that these assumptions matter: even in the absence of strategic behavior, Market Coupling can be quite vulnerable to the particular situation on hand; countertrading can work well or completely fail and it is not clear beforehand what will prevail. Our analysis relies on standard economic notions such as social welfare and Generalized Nash equilibrium, but the use of these notions is probably novel. The nodal organization is the reference first best scenario: different zonal decompositions and degrees of coordination are then studied with respect to this first best solution.

The extreme volatility of electricity prices makes their financial derivatives important instruments for asset managers. Even if the volume of derivative contracts traded on Power Exchanges has been growing since the inception of the restructuring of the sector, electricity remains considerably less liquid than other commodity markets. This paper assesses the effect of limited liquidity in power exchanges using an equilibrium model where agents cannot hedge up to their desired level. Mathematically, the problem is formulated as a two stage stochastic Generalized Nash equilibrium with possibly multiple equilibria. Computing a large panel of solutions, we show how the risk premium and players profits are affected by illiquidity. We also dhow that the illiquidity in the FTR market affects the trades in the electricity futures market.

Regulation EC No714/2009 on “… conditions for access to the network for cross-border exchanges in electricity …” (see European Commission 2009) and the Framework Guidelines on Capacity Allocation and Congestion Management (ACER 2011) formally introduced Transmission Rights in the European Electricity System. None of these documents really explain what these transmission rights should be but the Framework Guidelines are slightly more explicit than the regulation: transmission rights can be physical or financial; physical rights should be options subject to a use it or sell it clause (UIOSI); and financial rights can be options or obligations. Further details will come with the grid codes that Transmission System Operators (TSO) are preparing. The Framework Guidelines do not really elaborate on the market design that must accommodate these rights. They simply mention that “TSO implement capacity allocation in the day-ahead market on the basis of implicit auction … based on the marginal pricing principle”. Both Market Splitting (MS), which is now well established in the Nordic power market and Market coupling (MC), which is emerging as the European reference system outside of the Nordic countries satisfy these conditions. The US experience shows that the transmission rights and market design are closely intertwined and that one cannot discuss the former without referring to the latter. We follow suit and discuss the extent to which Transmission Rights can be meaningfully implemented in Market Coupling. Market Coupling can be seen as a very simplified version of nodal pricing (replacing nodes by zones and hoping that the rest applies). It is thus convenient to discuss transmission rights in Market Coupling keeping the nodal system in background. Chapter 3 of this book (Oren 2012) offers an in depth discussion of transmission rights in the nodal pricing model: we continuously (most often implicitly) refer to this chapter during the discussion. Much of the analysis of con

The main purpose of this paper is to develop methodologies for simultaneous generation and transmission expansion planning problem of power networks while investigating interactions between these two important sections. In the proposed methodologies, a transmission operator (TO) operating under different incentives decides about investment in transmission network while anticipating the outcome of a purely competitive electricity market where several rival generation firms complete with each other to determine operating level of their generators, amount of their sales and amount of their investment in generation capacity. The proposed methodologies rely on bi-level programming models whose upper level model represent the problem of investment in transmission by TO and the lower level problems represent market outcomes obtained from clearing the market. These bi-level models are reduced to mixed-integer linear and nonlinear programming using the duality theory and Karush-Kuhn-Tucker (KKT) optimality conditions. The results of the proposed models are analyzed and compared using two illustrative examples. © 1969-2012 IEEE.

In a Computable General Equilibrium (CGE) setting, we show how the cost of a carbon policy for an open economy depends on the assumptions made about future exogenous structural changes. For dynamic CGE models, we propose an analytical framework derived from static CGE models and associate structural changes with the construction of a non-stationary dynamic Social Accounting Matrix (SAM). Such matrices are benchmark scenarios that embed the modelers view on how technologies and preferences should evolve. These benchmark scenarios must be replicable and relevant (by matching what the modeler regards as plausible). To combine these two properties and produce alternative benchmark scenarios, we use partial parameter adjustments and general equilibrium computation. We produce three alternative benchmark scenarios that differ in terms of energy efficiency gains and structural shift in GDP. For each benchmark scenario, we then simulate the GDP deviation induced by a shock on carbon price. We show the dependence of the simulated GDP losses and terms of trade response on the benchmark scenario considered.

We take advantage of the interpretation of stochastic capacity expansion problems as stochastic equilibrium models for assessing the risk exposure of new equipment in a competitive electricity economy. We develop our analysis on a standard multistage generation capacity expansion problem. We focus on the formulation with nonanticipativity constraints and show that their dual variables can be interpreted as the net margin accruing to plants in the different states of the world. We then propose a procedure to estimate the distribution of the Lagrange multipliers of the nonanticipativity constraints associated with first stage decisions; this gives us the distribution of the discounted cash flow of profitable plants in that stage.

This paper outlines a methodology for implementing cost of service regulation in retail market for electricity in India when wholesale market is liberalised and operates through an hourly spot market. As in a developing country context political considerations make tariff levels more important than supply security, satisfying the earmarked level of demand takes a back seat. Retail market regulators are often forced by politicians to keep the retail tariff at suboptimal level. This imposes budget constraint on distribution companies to procure electricity that it requires to meet the earmarked level of demand. This is the way demand response is introduced in the system and has its impact on spot market prices. We model such a situation of not being able to serve the earmarked demand as disutility to the regulator which has to be minimised and we compute associated equilibrium. This results in systematic mechanism for cutting loads. We find that even a small cut in ability of the distribution companies to procure electricity from the spot market has profound impact on the prices in the spot market. © 2012 Elsevier Ltd.

"Market Coupling" is currently seen as the most advanced market design in the restructuring of the European electricity market. Market Coupling, by construction, introduces what is generally referred to as an incomplete market: it leaves several constraints out of the market and hence avoids pricing them. This may or may not have important consequences in practice depending on the case on hand. Quasi-Variational Inequality problems and the associated Generalized Nash Equilibrium can be used for representing incomplete markets. Recent papers propose methods for finding a set of solutions of Quasi-Variational Inequality problems. We apply one of these methods to a subproblem of market coupling namely the coordination of counter-trading. This problem is an illustration of a more general question encountered, for instance, in hierarchical planning in production management. We first discuss the economic interpretation of the Quasi-Variational Inequality problem. We then apply the algorithmic approach to a set of stylized case studies in order to illustrate the impact of different organizations of counter-trading. The paper emphasizes the structuring of the problem. A companion paper considers the full problem of Market Coupling and counter-trading and presents a more extensive numerical analysis. © 2011 Springer Science+Business Media, LLC.

The EU-ETS is the first measure initiated by the EU to contribute to the decarbonization of the European energy sector. It is a cap and trade system that requires industries participating to the program to procure allowances to cover their emissions. Electricity Intensive Industries (EIIs) have complained that the system put their European plants at disadvantage compared to facilities located outside the EU. They have asked for actions to mitigate this effect; one of them is to have access to long term contracts with electricity suppliers, ideally with those operating carbon free plants. This paper presents and illustrates a method for assessing the impact of this measure on EIIs participating to the EU cap and trade system. We model a power market segmented in two consumer groups EIIs and the rest of the market (N-EIIs). These two groups are subject to different price regimes: EIIs purchase electricity from dedicated base-load power plants at average cost price, while N-EIIs are supplied at marginal cost. The French Exeltium and the Belgian Blue Sky consortia are existing examples of this market organization. The expanse of the territories that can be covered by these systems depends on the organization of transmission organization and on national energy position relative to carbon free generation. We examine two different types of long term average cost based contracts that differ by the organization of transmission and study their impact under different national energy policies. We formulate the problem of operations and investment in this market as a spatial equilibrium model where generators can invest in new capacity subject to different regional constraints. Transmission is organized according to a "flow based" approach as foreseen by Regulatory Authorities and Transmission System Operators in Europe. We also examine the impact of nuclear policies. CO 2 emission allowances are auctioned and tradable. We describe the models and discuss their policy

Although there are mechanisms to control market power in the spot market, withholding investments can still increase profits and hamper adequate capacity expansion.We examine the effect on investment of one suggested approach to reducing market power, contracting longer term. We construct a stylized model of an energy only market where two firms, each specializing in one technology, invest in a first stage, contract part of their production in the second stage and sell the rest in the spot market in the third stage. We compare this model to one of an energy-only market having two stages, investment and a spot market. We find cases where the contracts change neither capacity nor peak prices, where the foreclosing effect of one player blocking the other from contracts markets increases investments and reduces prices, and where the opportunity to foreclose the market can incentivize one firm to lower its investment and increase its pricing power to the detriment of consumers. The model relies on the simplest possible assumptions of imperfect competition (subgame perfect equilibria with Cournot agents). We illustrate the different outcomes in a numerical example with two load steps (peak and off-peak) where we change one parameter, the height of the off-peak time segment. We find cases with increased and decreased capacity as well as no change in capacity. Since there is no general characterization of the consequences of contracts in this simple example, there can be no characterization in more complicated models that contain the market structures included here, and regulators or competition authorities cannot rely on contracts to induce sufficient capacity expansion by reducing market power. One other market mechanism that has been proposed to induce investment, a capacity auction with predetermined capacity requirements, is a potential alternative to limit market power that deserves further exploration to determine the extent to which it can provide an adequate incent

Cross-border trade remains a contentious issue in the restructuring of the European electricity market. This paper analyzes the cross-border trade problem through a set of models that represent different degrees of coordination both between the energy and the transmission markets and among national Transmission System Operators (TSOs). We first present a nodal price-like organization of the system, where Power Exchanges (PXs) and Transmission System Operators are integrated to operate the energy and transmission markets. This system is not implemented in Europe but its success elsewhere makes it the natural reference for the study. We then move to a more realistic representation of the European electricity market based on the so-called market coupling design where energy and transmission are operated separately by PXs and TSOs. We consider different degrees of coordination of the national TSOs' activities to assess the range of inefficiencies that the lack of integration can lead to. The paper supposes price taking agents and hence leaves aside the incentive to game the system induced by zonal systems. Copyright © 2012 by the IAEE.

This paper examines the impact that uncertainty over economic growth may have on global energy transition and CO2 prices. We use a general-equilibrium model derived from MERGE, and define several stochastic scenarios for economic growth. Each scenario is characterized by the likelihood of a rapid global economic recovery. More precisely, during each decade, global economy may - with a given probability - shift from the EIA's (2010) low-economic-growth path to the EIA's (2010) high-economic-growth path. The climate policy considered corresponds in the medium term to the commitments announced after the Copenhagen conference, and in the long term to a reduction of 25% in global energy-related CO2 emissions (with respect to 2005). For the prices of CO2 and electricity, as well as for the implementation of CCS, the branches of the resulting stochastic trajectories appear to be heavily influenced by agents’ initial expectations of future economic growth and by the economic growth actually realized. Thus, in 2040, the global price of CO2 may range from $21 (when an initially-anticipated economic recovery never occurs) to $128 (in case of non-anticipated rapid economic recovery). In addition, we show that within each region, the model internalizes the constraints limiting the expansion of each power-generation technology through the price paid by the power utility for the acquisition of new production capacity. As a result, in China, the curves of endogenous investment costs for onshore and offshore wind are all bubble-shaped centered on 2025, a date which corresponds to the establishment of a global CO2 cap-and-trade market in the model.

This paper considers the general problem of optimal timing of the exchange of the sum of n Ito-diffusions for the sum of m others (e.g., the optimal time to exchange a geometric Brownian motion for a geometric mean reverting process). We first contribute to the literature by providing analytical sufficient conditions and necessary conditions for optimal stopping (i.e. sub- and super- sets of the stopping region) for some sub-cases of the general problem. We then exhibit a connection between the problem of finding sufficient conditions for optimal stopping and linear programming. This connection provides a unified approach which does not only allow to recover previous analytically determinable subsets of the stopping region, but also allows to characterize (more complex) subsets of the stopping region that do not have an analytical expression. In the particular case where all assets are geometric Brownian motions, this connection gives us new insights. In particular, it simplifies the expression of the subset of the stopping region identified by Nishide and Rogers (2011). Our numerical examples finally confirms the good behavior of the candidate investment rule introduced by Gahungu and Smeers (2011) for this particular case, which seems to comfort a conjecture that their rule might be optimal.

This paper proposes a real option capacity expansion model for power generation with several technologies that differ in operation and investment costs. The economy is assumed perfectly competitive and the instantaneous payoff accruing from the generation system is the instantaneous welfare defined as the usual sum of consumer and producer surplus. The computation of this welfare requires the solution of a multi- technology optimization problem and the obtained optimal function value is not additively separable in generation capacities, contrary to what is generally assumed in multi asset real option models to prove the optimality of a myopic behavior. Using the geometric Brownian motion as uncertainty driver we propose two regression models to approximate the instantaneous welfare. A first, additively separable approximation implies the optimality of myopia. The second approximation is non separable and hence forces to take myopic behavior as an assumption. Using myopia as an assumption, we propose a semi-analytic method which combines Monte Carlo simulations (used to compute the value of the marginal capacity) and analytical treatment (to solve an optimal stopping problem on a regression scheme).

The dissertation addresses some important topics arising in restructured electricity markets. A first part is dedicated to the pricing of power contingent claims. Electricity is a derivative product, structurally related to other energy assets: it is mainly produced by fuel fired thermal power stations. For pricing power derivatives, we propose a hybrid model that accounts for these structural relationships and which can be understood as a combination of both the fundamentals of power generation and the classical stochastic framework. It is recognized that financial markets deviate to varying degrees from the perfect paradigm and in particular that electricity markets significantly remain less liquid than other commodity markets. We assess the effect of limited liquidity in power exchanges by using an equilibrium model where illiquid contracts prevent agents from hedging up to their desired level and study the implications of the introduction of such market frictions in the theory of derivatives pricing. In the second part of the thesis we elaborate on investment valuations in stochastic generation capacity expansion models. Designed originally as optimization problems for the regulated monopoly industry, those models can be interpreted as equilibrium models in a competitive environment. We specifically develop a procedure to accurately estimate the distribution of the margin profit in a standard stochastic program. We eventually focus on the risk averse problem using the good-deal risk measure, which can be seen as an extension of the stochastic discount factor constructed from standard corporate finance theories such as the CAPM and the APT., (FSA 3) -- UCL, 2011

This dissertation exposes new real options models inspired by power plant investment problems. The starting point of the work is a real options capacity expansion model for a power industry under perfect competition (Chapter 3). We use the equivalence between perfect competition’s equilibrium and the supremum of the social welfare to formulate a stochastic control problem. The industry we set up has a convex cost function and a welfare which is not additively separable in its several production technologies. We investigate whether the optimality of the myopic behavior (i.e., the stochastic control/optimal stopping equivalence) which usually prevails for such type of real options models holds in our case. The subsequent chapters (4, 5 and 6) consider myopic real options models, i.e., optimal stopping problems. Chapters 4 and 5 are devoted to multi-asset optimal stopping problems with linear reward, i.e., optimal exercise of perpetual multi-asset exchange options. We successively consider the cases where (1) all assets are geometric Brownian motions (Chapter 4) and where (2) several types of Ito-diffusions are involved in the exchange (Chapter 5). Chapter 6 presents possible applications of these results to power plant investment. We close this dissertation by a discussion on real options’ ability to dampen boom and bust cycles in power investment., (FSA 3) -- UCL, 2011

We cast models of the generation capacity expansion type formally developed for the monopoly regime into equilibrium models better adapted for a competitive environment. We focus on some of the risks faced today by investors in generation capacity and thus pose the problem as a stochastic equilibrium model. We illustrate the approach on the problem of the incentive to invest. Agents can be risk neutral or risk averse. We model risk aversion through the CVaR of plants' profit. The CVaR induces risk-adjusted probabilities according to which investors value their plants. The model is formulated as a complementarity problem (including the CVaR valuation of investments). An illustration is provided on a small problem that captures several features of today's electricity world: a choice often restricted to coal and gas units, a peakly load curve because of wind penetration, uncertain fuel prices, and an evolving carbon market. We assess the potential of the approach by comparing energy-only and capacity market organizations in this risky environment. Our results can be summarized as follows: a deterministic analysis overlooks some changes of capacity structure induced by risk, whether in the capacity market or energy-only organizations. The risk-neutral analysis also misses a shift towards less capital-intensive technologies that my result from risk aversion. Last, risk aversion also increases the shortage of capacity compared to the risk-neutral view in the energy-only market when the price cap is low. This may have a dramatic impact on the bill to the final consumer. The approach relies on mathematical programming techniques and can be extended to full-size problems. The results are illustrative and my deserve more investigation.

We study the equilibria reached by strategic producers in a pool-based network-constrained electricity market. The behavior of each producer is modeled by a mathematical program with equilibrium constraints (MPEC) whose objective is maximizing profit and whose complementarity constraints describe market clearing. The joint solution of all these MPECs constitutes an equilibrium problem with equilibrium constraints (EPEC). The equilibria associated with the EPEC are analyzed by solving the strong stationarity conditions of all MPECs, which can be linearized without approximation by mixed-integer linear programming (MILP) techniques. The resulting mixeid-integer linear conditions can be reformulated as an optimization problem that allows establishing diverse objectives to differentiate among alternative equilibria.

This paper examines the impact that uncertainty over economic growth may have on global energy transition and CO2 prices. We use a general-equilibrium model derived from MERGE, and define several stochastic scenarios for economic growth. Each scenario is characterized by the likelihood of a rapid global economic recovery. More precisely, during each decade, global economy may - with a given probability - shift from the EIA's (2010) low-economic-growth path to the EIA's (2010) high-economic-growth path. The climate policy considered corresponds in the medium term to the commitments announced after the Copenhagen conference, and in the long term to a reduction of 25% in global energy-related CO2 emissions (with respect to 2005). For the prices of CO2 and electricity, as well as for the implementation of CCS, the branches of the resulting stochastic trajectories appear to be heavily influenced by agents’ initial expectations of future economic growth and by the economic growth actually realized. Thus, in 2040, the global price of CO2 may range from $21 (when an initially-anticipated economic recovery never occurs) to $128 (in case of nonanticipated rapid economic recovery). In addition, we show that within each region, the model internalizes the constraints limiting the expansion of each power-generation technology through the price paid by the power utility for the acquisition of new production capacity. As a result, in China, the curves of endogenous investment costs for onshore and offshore wind are all bubble-shaped centered on 2025, a date which corresponds to the establishment of a global CO2 cap-and-trade market in the model., GDF-Suez

This paper examines the impact that uncertainty over economic growth may have on global energy transition and CO2 prices. We use a general-equilibrium model derived from MERGE, and define several stochastic scenarios for economic growth. Each scenario is characterized by the likelihood of a rapid global economic recovery. More precisely, during each decade, global economy may - with a given probability - shift from the EIA's (2010) low-economic-growth path to the EIA's (2010) high-economic-growth path. The climate policy considered corresponds in the medium term to the commitments announced after the Copenhagen conference, and in the long term to a reduction of 25% in global energy-related CO2 emissions (with respect to 2005). For the prices of CO2 and electricity, as well as for the implementation of CCS, the branches of the resulting stochastic trajectories appear to be heavily influenced by agents’ initial expectations of future economic growth and by the economic growth actually realized. Thus, in 2040, the global price of CO2 may range from $21 (when an initially-anticipated economic recovery never occurs) to $128 (in case of nonanticipated rapid economic recovery). In addition, we show that within each region, the model internalizes the constraints limiting the expansion of each power-generation technology through the price paid by the power utility for the acquisition of new production capacity. As a result, in China, the curves of endogenous investment costs for onshore and offshore wind are all bubble-shaped centered on 2025, a date which corresponds to the establishment of a global CO2 cap-and-trade market in the model., GDF-Suez

Financial derivatives are important hedging tool for asset’s manager. Electricity is by its very nature the most volatile commodity, which creates big incentive to share the risk among the market participants through financial contracts. But, even if volume of derivatives contracts traded on Power Exchanges has been growing since the beginning of the restructuring of the sector, electricity markets continue to be considerably less liquid than other commodities. This paper tries to quantify the effect of this insufficient liquidity on power exchange, by introducing a pricing equilibrium model for power derivatives where agents can not hedge up to their desired level. Mathematically, the problem is a two stage stochastic Generalized Nash Equilibrium and its solution is not unique. Computing a large panel of solutions, we show how the risk premium and player’s profit are affected by the illiquidity.

Cross-border trade remains a contentious issue in the restructuring of the European electricity market. Difficulties stem from the lack of a common market design, the separation between energy and transmission markets and the insufficient coordination between Transmission System Operators (TSOs). This paper analyzes the cross-border trade problem through a set of models that represent different degrees of coordination both between the energy and transmission markets and among national TSOs. We first present the optimal organisation, not implemented in Europe, where energy and transmission are integrated according to the nodal price paradigm and Power Exchanges (PXs) and TSOs are integrated. This is our reference case. We then move to a more realistic representation of the European electricity market based on the so-called market-coupling design where energy and transmission are operated separately by PXs and TSOs. When considering different degrees of coordination of the national TSOs’ activities, we unexpectedly find that some arrangements are more efficient than the lack of coordination might suggest. Specifically we find that even without a formal coordination of the TSOs’ counter-trading operations, non discriminatory access to common counter-trading resources for all TSOs may lead to a partial implicit coordination of these TSOs. In other words, an internal market of counter-trading resources partially substitutes the lack of integration of the TSOs. While a full access to counter-trading resources is a weaker requirement than the horizontal integration of the TSO, it is still quite demanding. We show that quantitative limitations to the access of these resources decrease the efficiency of counter-trading. The paper supposes price taking agents and hence leaves aside the incentive to game the system induced by zonal systems.

Capacity expansion models in the power sector were among the first applications of operations research to the industry. The models lost some of their appeal at the inception of restructuring even though they still offer a lot of possibilities and are in many respect irreplaceable provided they are adapted to the new environment. We introduce stochastic equilibrium versions of these models that we believe provide a relevant context for looking at the current very risky market where the power industry invests and operates. We then take up different questions raised by the new environment. Some are due to developments of the industry like demand side management: an optimization framework has difficulties accommodating them but the more general equilibrium paradigm offers additional possibilities. We then look at the insertion of risk related investment practices that developed with the new environment and may not be easy to accommodate in an optimization context. Specifically we consider the use of plant specific discount rates that we derive by including stochastic discount rates in the equilibrium model. Linear discount factors only price systematic risk. We therefore complete the discussion by inserting different risk functions (for different agents) in order to account for additional unpriced idiosyncratic risk in investments. These different models can be cast in a single mathematical representation but they do not have the same mathematical properties. We illustrate the impact of these phenomena on a small but realistic example.

“Market Coupling” is currently seen as the most advanced market design in the restructuring of the European electricity market. Market coupling, by construction, introduces what is generally referred to as an incomplete market: it leaves several constraints out of the market and hence avoids pricing them. This may or may not have important consequences in practice depending on the case on hand. Quasi-Variational Inequality problems and the associated Generalized Nash Equilibrium can be used for representing incomplete markets. Recent papers propose methods for finding a set of solutions of Quasi-Variational Inequality problems. We apply one of these methods to a subproblem of market coupling namely the coordination of counter-trading. This problem is an illustration of a more general question encountered for instance in hierarchical planning in production management. We first discuss the economic interpretation of the Quasi-Variational Inequality problem. We then apply the algorithmic approach to a set of stylized case studies in order to illustrate the impact of different organizations of counter-trading. The paper emphazises the structuring of the problem. A companion paper considers the full problem of market coupling and counter-trading and presents a more extensive numerical analysis.

Allaz and Vila made the seminal contribution that forward contracts mitigate market power on the spot market. This result is widely quoted and elaborated in studies of restructured power markets, where generators can potentially exploit the special characteristics of this industry in order to extract higher prices. Allaz-Vila established their result under/the assumption that the production capacities of the players are infinite. We show that the Allaz-Vila result does not hold when capacities are endogenous and constraining generation. Specifically, a forward market can enhance or mitigate market power when capacities are endogenous and demand is unknown at the time of investment. We also show that forward markets do not mitigate market power when capacities are endogenous and demand is known at the time of investment. Our results complement other work that shows that forward markets systematically enhance market power in some symmetric capacity-constrained markets.

Although there are mechanisms to control market power in the spot market, withholding investments can still increase profits and hence hamper adequate capacity expansion. We examine the effect on investment of one suggested approach to reducing market power, contracting longer term. We construct a stylized model of an energy only market where two firms, each specializing in one technology, invest in a first stage, contract part of their production in the second stage and sell the rest in the spot market in the third stage. We compare this model to one of an energy only market having two stages, investment and a spot market. We find cases where the contracts change neither capacity nor prices, where the foreclosing effect of one player blocking the other from contracts markets increases investments and reduces prices, and where the opportunity to foreclose the market can incentivize one firm to lower its investment and increase its pricing power to the detriment of consumers. The model relies on the simplest possible assumptions of imperfect competition (subgame perfect equilibria with Cournot agents). We illustrate the different outcomes in a numerical example with two load steps (peak and off-peak) where we change one parameter, the height of the off-peak time segment. We find that varying this parameter leads to outcomes with increased and decreased capacity as well as no change in capacity. Since there is no general characterization of the consequences of contracts in this simple example, regulators or competition authorities cannot rely on contracts to induce sufficient capacity expansion. One other market mechanism that has been proposed to induce investment, a capacity auction with predetermined capacity requirements is a potential alternative to limit market power that deserves further exploration to determine the extent to which it can provide the adequate incentive to invest in the presence of market power.