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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.

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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