Efraim Centeno

Generation Capacity Expansion in Liberalized Electricity Markets: A Stochastic MPEC Approach

This paper proposes a bilevel model to assist a generation company in making its long-term generation capacity investment decisions considering uncertainty regarding the investments of the other generation companies. The bilevel formulation allows for the uncoupling of investment and generation decisions, as investment decisions of the single investing generation company are taken in the upper level with the objective to maximize expected profits and generation decisions by all companies are considered in the lower level. The lower level represents the oligopolistic market equilibrium via a conjectured-price response formulation, which can capture various degrees of strategic market behavior like perfect competition, the Cournot oligopoly, and intermediate cases.

Capacity Expansion Equilibria in Liberalized Electricity Markets: An EPEC Approach

This paper presents a novel way to model the generation capacity expansion problem in a liberalized framework via a multi-year bilevel equilibrium model. In the upper level the competing generation companies maximize their individual profits, while the lower level represents the market using a conjectured-price response approach, which allows us to vary the strategic spot market behavior, to see how much the reigning competitive behavior impacts investment decisions. The bilevel equilibrium model is formulated as an equilibrium problem with equilibrium constraints, transformed into a mixed integer linear program and solved as such using diagonalization in order to verify equilibria. We present a case study to apply this new modeling approach and to demonstrate that the proposed equilibrium problem with equilibrium constraints can have multiple solutions whose respective investments can vary.

Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition

We consider two game-theoretic models of the generation capacity expansion problem in liberalized electricity markets. The first is an open loop equilibrium model, where generation companies simultaneously choose capacities and quantities to maximize their individual profit. The second is a closed loop model, in which companies first choose capacities maximizing their profit anticipating the market equilibrium outcomes in the second stage. The latter problem is an equilibrium problem with equilibrium constraints. In both models, the intensity of competition among producers in the energy market is frequently represented using conjectural variations. Considering one load period, we show that for any choice of conjectural variations ranging from perfect competition to Cournot, the closed loop equilibrium coincides with the Cournot open loop equilibrium, thereby obtaining a ‘Kreps and Scheinkman’-like result and extending it to arbitrary strategic behavior. When expanding the model framework to multiple load periods, the closed loop equilibria for different conjectural variations can diverge from each other and from open loop equilibria. We also present and analyze alternative conjectured price response models with switching conjectures. Surprisingly, the rank ordering of the closed loop equilibria in terms of consumer surplus and market efficiency (as measured by total social welfare) is ambiguous. Thus, regulatory approaches that force marginal cost-based bidding in spot markets may diminish market efficiency and consumer welfare by dampening incentives for investment. We also show that the closed loop capacity yielded by a conjectured price response second stage competition can be less or equal to the closed loop Cournot capacity, and that the former capacity cannot exceed the latter when there are symmetric agents and two load periods.

Coordination between medium-term generation planning and short-term operation in electricity markets

This paper analyzes the coordination between medium-term generation planning and short-term operation in electricity markets. This coordination is particularly important from a practical point of view in order to guarantee that certain aspects of the operation that arise in the medium-term level are explicitly taken into account: limited-energy resources and obligatory-use resources. Three different approaches are proposed in order to guarantee that short-term decisions made by a generation company are consistent with its operation objectives formulated from a medium-term perspective. These approaches make use of technical and economic signals to coordinate both time scopes: primal information, dual information, and resource-valuation functions. This paper presents the main advantages and drawbacks of the three approaches and applies them to a case study that uses a conjectural-variation-based representation of the market.

Stochastic Market Equilibrium Model For Generation Planning

It is widely accepted that medium-term generation planning can be advantageously modeled through market equilibrium representation. There exist several methods to define and solve this kind of equilibrium in a deterministic way. Medium-term planning is strongly affected by uncertainty in market and system conditions, thus extensions of these models are commonly required. The main variables that should be considered as subject to uncertainty include hydro conditions, demand, generating units failures and fuel prices. This paper presents a model to represent medium-term operation of electrical market that introduces this uncertainty in the formulation in a natural and practical way. Utilities are explicitly considered to be intending to maximize their expected profits and biddings are represented by means of a conjectural variation. Market equilibrium conditions are introduced by means of the optimality conditions of a problem, which has a structure that strongly resembles classical optimization of hydrothermal coordination. A tree-based representation to include stochastic variables and a model based on it are introduced. This approach for market representation provides three main advantages: robust decisions are obtained; technical constraints are included in the problem in a natural way, additionally obtaining dual information; and big size problems representing real systems in detail can be addressed.

SGO: management information system for strategic bidding in electrical markets

This paper describes SGO, a management information system for bidding in deregulated electricity markets, developed for the Spanish case. SGO has a client-server architecture and consists of a set of integrated cooperative and flexible software tools for assisting the users during the whole bidding process: resources identification, bids generation, market performance characterisation, bidding strategy analysis and optimisation, generation of markets results reports and automatic performance monitoring for suggesting on-line corrective actions.

Long-term market equilibrium modeling for generation expansion planning

This paper introduces a methodology to assist generation companies to deal with planning decisions in a competitive framework. It is based on a two-stage representation of market equilibrium. A first level computes an approximate continuous Cournot equilibrium for the entire model horizon. The second one discretises this solution separately for each year. Some aspects of its practical implantation are discussed.

Generation Capacity Expansion Analysis: Open Loop Approximation of Closed Loop Equilibria

In this paper we propose a methodology to approximate closed loop capacity equilibria using only open loop capacity equilibrium models. In the closed loop model, generation companies choose capacities that maximize their individual profit in the first stage while the second stage represents the conjectured-price-response market equilibrium. In the open loop model, firms simultaneously choose capacities and quantities to maximize their individual profit, while each firm conjectures a price response to its output decisions. The closed loop equilibrium model is an equilibrium problem with equilibrium constraints, which belongs to a class of problems that is very hard to solve. The open loop equilibrium model is much easier to solve; however, it is also less realistic. With the approximation scheme proposed in this paper, we are able to solve the closed loop model reasonably well when market behavior is closer to oligopoly than to perfect competition by smartly employing open loop models which reduces the computational time by two orders of magnitude. We achieve this by transforming the open loop equilibrium problem into an equivalent convex quadratic optimization problem which can be solved efficiently. Finally, a case study is presented in order to validate the proposed approximation scheme.

Dynamics in Forward and Spot Electricity Markets

This paper provides new results that cast doubt on the conventional assumption that introducing voluntary forward markets will mitigate the market power of electricity generating companies by encouraging them to contract forward. We provide complementary insights by developing an agent-based simulation model of an actual system. This facilitates understanding the strategy selection of heterogeneous companies through computational learning. We use a detailed model of the Spanish system, where companies trade through a uniform price, pool-based spot market. We model market power in this pool through agents offering to generate with conjectured price responses estimated from supply function equilibrium assumptions. We envisage the introduction of a forward market, with price formation following the conventional financial perspective of expected spot plus a risk premium. We find, in general, that larger companies prefer to exercise market power in the spot market, while smaller companies prefer to contract forward, but strategy selection itself can be quite a delicate, situation specific process.

An optimization-based conjectured supply function equilibrium model for network constrained electricity markets

This paper proposes a model to compute nodal prices in oligopolistic markets. The model generalizes a previous model aimed at solving the single-bus problem by applying an optimization procedure. Both models can be classified as conjectured supply function models. The conjectured supply functions are assumed to be linear with constant slopes. The conjectured price responses (price sensitivity as seen for each generating unit), however, are assumed to be dependent on the system lines status (congested or not congested). The consideration of such a dependence is one of the main contributions of this paper. Market equilibrium is defined in this framework. A procedure based on solving an optimization problem is proposed. It only requires convexity of cost functions. Existence of equilibrium, however, is not guaranteed in this multi-nodal situation and an iterative search is required to find it if it exists. A two-area multi-period case study is analysed. The model reaches equilibrium for some cases, mainly depending on the number of periods considered and on the value of conjectured supply function slopes. Some oscillation patterns are observed that can be interpreted as quasi-equilibria. This methodology can be applied to the study of the future Iberian electricity market.