Yves Smeers

Generation Capacity Expansion in Imperfectly Competitive Restructured Electricity Markets

We consider three models of investments in generation capacity in restructured electricity systems that differ with respect to their underlying economic assumptions. The first model assumes a perfect, competitive equilibrium. It is very similar to the traditional capacity expansion models even if its economic interpretation is different. The second model (open-loop Cournot game) extends the Cournot model to include investments in new generation capacities. This model can be interpreted as describing investments in an oligopolistic market where capacity is simultaneously built and sold in long-term contracts when there is no spot market. The third model (closed-loop Cournot game) separates the investment and sales decision with investment in the first stage and sales in the second stage-that is, a spot market. This two-stage game corresponds to investments in merchant plants where the first-stage equilibrium problem is solved subject to equilibrium constraints. We show that despite some important differences, the open- and closed-loop games share many properties. One of the important results is that the prices and quantities produced in the closed-loop game, when the solution exists, fall between the prices and quantities in the open-loop game and the competitive equilibrium.

Optimal Dimensioning of Pipe Networks with Application to Gas Transmission Networks

We develop an algorithm to solve the problem of the optimal dimensioning of a fluid gas or water transmission network when the topology of the network is known. The pipe diameters must be chosen to minimize the sum of the investment and operating costs. This two stage problem is solved by application of the bundle method for nonsmooth optimization. The validity of the approach is tested on a problem corresponding to a real situation: the optimal design of a reinforcement of the Belgian gas network.

Equilibria in an Oligopolistic Electricity Pool With Stepwise Offer Curves

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 mixed-integer linear conditions can be reformulated as an optimization problem that allows establishing diverse objectives to differentiate among alternative equilibria.

Alternative Models of Restructured Electricity Systems, Part 1: No Market Power

Different equilibrium concepts have been proposed by various authors (Schweppe et al., Hogan et al., Chao and Peck, Wu et al.) to analyse competitive electricity systems. We establish correspondences between these different models through a single framework and provide additional interpretations of these equilibrium concepts. This unifying conceptual view also provides a computationally feasible approach to simulate the market. It also opens the way to the modeling of some imperfect markets.

Stochastic equilibrium programming for dynamic oligopolistic markets

This paper deals with the concept of stochastic equilibrium programming (SEP), which has recently been proposed for the modeling of imperfect competition on uncertain dynamic markets. We show that the equilibria computed via SEP correspond to an information structure, called S-adapted open-loop, which is not common in the dynamic game literature. We compare the single-player case with the many-player case using a simple two-stage dynamical system. An illustration of the use of the approach for the modeling of imperfect dynamic markets is also provided.

Bi-Level Game Approaches for Coordination of Generation and Transmission Expansion Planning Within a Market Environment

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.

On the Impact of Forward Markets on Investments in Oligopolistic Markets with Reference to Electricity

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.

A branch-and-bound method for reversed geometric programming

A general or signomial geometric program is a nonlinear mathematical program involving general polynomials in several variables both in the objective function and the constraints. A branch-and-bound method is proposed for this extensive class of nonconvex optimization programs guaranteeing convergence to the global optimum. The subproblems to be solved are convex but the method can easily be combined with a cutting plane technique to generate subproblems which are linear. A simple example is given to illustrate the technique. The combined method involving linear subproblems has been coded and numerical experience with this code will be reported later.

An age reduction approach for finite horizon optimization of preventive maintenance for single units subject to random failures

We consider a single unit working in a continuous mode of operation characterized by an increasing failure rate. We determine the optimal number of preventive maintenance activities to be scheduled within a time horizon of interest, the required extent of the preventive maintenance by means of an age reduction of the unit and the corresponding optimal value of the expected profit. We assume that any breakdown occuring is minimally repaired, the repair is performed instantaneously, and the repair cost is the same for any repair. On the other hand, the cost associated with a preventive maintenance activity may vary as well as its duration

Towards a common European Electricity market paths in the right direction… still far from an effective design

This paper analyses the future organization of cross border trade in the European electricity market. The draft Regulation “on Conditions for Access to the Network for Cross-Border Exchanges in Electricity” issued in March 2001 by the European Commission together with related documents produced by the European association of Transmission System Operators (ETSO) and the Council of European Electricity Regulators (CEER) until that date constitute the backbone of this analysis. The paper examines whether the economic principles contained in these documents suffice to design a working European electricity market and if not, what is missing. It concludes that these principles need to be completed by harder measures in order to induce the “real integrated single market” of electricity claimed by the Commission. In short, the principles may be necessary, but they are unlikely to be sufficient.