Andreas Ehrenmann

A Comparison of Electricity Market Designs in Networks

In Europe, two market designs are discussed for electricity trade and transmission. We argue that their performance in the presence of market power can be represented by two models from the literature. In contrast to examples for simple two-node networks, we show that in more complex networks a general ranking of both designs is not possible. Hence, computational models are required to evaluate the designs for realistic parameter assumptions. We extend existing formulations of both models to represent them as equilibrium problems with equilibrium constraints (EPEC) with equivalent representation of demand, fringe generation, and strategic generators. In a numerical simulation for the Northwestern European network, the integrated market design performs better. This difference illustrates the impact of small assumptions on the outcome of strategic models.

Stochastic Equilibrium Models for Generation Capacity Expansion

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.

Manifolds of multi-leader Cournot equilibria

We show that the known uniqueness results for leader-follower Cournot games with multiple but identical leaders hinge on the tacit assumption that identical leaders make identical decisions. We illustrate that without this assumption multi-leader Cournot games may well possess nontrivial manifolds of equilibria and discuss the underlying reasons.

Capacity Expansion in Non-Regulated Electricity Markets

Investment in new generation is not well understood in a deregulated environment. While 20 years of literature focused on capacity expansion in a regulated world it is only since 2001 that researchers examine the gaming aspect of investment in electricity generation. The natural representation of a capacity expansion game has two stages: first to determine the capacity and to choose the production afterwards. In some cases one stage games can be used to replace two stage games. In most cases they can’t.

Modeling Gas Markets with Endogenous Long-Term Contracts

Since its initial development, long-term contracts have been associated with the gas industry in all regions of the world. This was also the case in Europe where natural gas trade was, for a long time, dominated by bilateral long-term agreements between producers and midstreamers. These contracts fixed a minimum volume to be exchanged (take or pay) and indexed the gas price using a price formula that usually referred to oil product prices. These arrangements allowed market risk sharing between the producer (who takes the price risk) and the midstreamer (who takes the volume risk). They also offered risk hedging since oil is considered as a trusted commodity by investors. The fall of the European natural gas demand, combined with the increase of the oil price, favored the emergence of a gas volume bubble that caused significant losses for most of the European midstreamers bound by long-term agreements. As a result, the downstream part of the industry brought forward the idea of indexing contracts on gas sp...

Risk adjusted discounted cash flows in capacity expansion models

This paper addresses a problem that is typical of multi-period capacity expansion equilibrium models: plants or sectors have different risk exposures that may warrant different costs of capital. The paper examines modifications of a capacity expansion model interpreted in equilibrium terms to account for asset-specific costs of capital.

Risk trading in capacity equilibrium models

We present a set of power investment models, the class of risky capacity equilibrium problems, reflecting different assumptions of perfect and imperfect markets. The models are structured in a unified stochastic Nash game framework. Each model is the concatenation of a model of the short-term market operations (perfect competition or Cournot), with a long-term model of investment behavior (risk neutral and risk averse behavior under different assumptions of risk trading). The models can all be formulated as complementarity problems, some of them having an optimization equivalent. We prove existence of solutions and report numerical results to illustrate the relevance of market imperfections on welfare and investment behavior. The models are constructed and discussed as two stage problems but we show that the extension to multistage is achieved by a change of notation and a standard assumption on multistage risk functions. We also treat a large multistage industrial model to illustrate the computational feasibility of the approach.

The prisoner’s dilemma in Cournot models: when endogenizing the level of competition leads to competitive behaviors

In resource based economies, regulating the production and export activities have always been an important challenge. Examples in oil and gas show that different behaviors have been adopted ranging from the export monopoly to the complete opening of the export market. This paper tries to explain this multitude of solutions via strategic interactions. When modeling imperfect competition, players are separated in two categories: those who exert market power and those who are competitive and propose the good at their marginal supply cost. Letting a player freely choose whether it wants to exert market power or not when it optimizes its utility is not discussed in the literature. This paper addresses this issue by letting the players choose the level of competition they want to exert in the market. To do so, we analyze the behavior of two countries competing to supply a market with a homogeneous good in an imperfect competition setting. Each country decides the number of firms it authorizes to sell in the market. The interaction between the firms is of a Nash-Cournot type, where each one exerts market power and is in competition with all other firms allowed to sell, whether they belong to the same country or not. Each country optimizes its utility, that is the sum of the profits of its firms. We have studied four kinds of interaction between the countries. The first calculates the closed loop Nash equilibrium of the game between the countries. The second setup analyzes the cartel when the countries collude. The third focuses on the open loop Nash equilibrium and the fourth models a bi-level Stackelberg interaction where one country plays before the other. We demonstrate that in the closed loop Nash equilibrium, our setting leads to the prisoner’s dilemma: the equilibrium occurs when both countries authorize all their firms to sell in the market. In other words, countries willingly chose not to exert market power. This result is at first sight similar to the Allaz & Vila (1993) result but is driven by a completely different economic reasoning. In the Stackelberg and coordinated solutions, the market is on the contrary very concentrated and the countries strongly reduce the number of firms that enter the market in order to fully exert market power and increase the price. The open loop result lies in between: the countries let all their firms sell but market power remains strong. These results suggest that the prisoner’s dilemma outcome is due to the conjectural inconsistency of the Nash equilibrium. Finally, in the Stackelberg setting, we give countries the choice of being leader or follower and demonstrate that the counter-intuitive competitive outcome is very unlikely to occur in the market.