Stochastics and StatisticsImpact of some parameters on investments in oligopolistic electricity markets☆
Highlights
► The paper solves a competitive stochastic model of Finnish electricity industry. ► It assesses the impact on equilibrium of key model’s parameters. ► It provides insights on robustness of results to parameter changes. ► It compares long-term equilibrium predictions to realizations.
Introduction
Investment decisions in electricity generation capacity have received considerable attention during the last fifty years or so. Till the recent wave of deregulation, the methodological framework to deal with the generation expansion problem (GEP) was optimization (see e.g., Masse and Gilbrat, 1957, Bloom, 1982, Borison et al., 1984, Mo et al., 1991, Hobbs, 1995). This approach was natural given the mandate assigned to the vertically integrated and regulated utility, namely, serving its protected market at the lowest possible cost. Deregulation brought an overnight paradigm change. The new context involves few generators competing for profits and grants strategic values to capacity (see e.g., Newbery, 2000, Stoft, 2002 for descriptions of deregulated electricity markets, and Ventosa et al., 2005 for an overview of decision-support models used in electricity market modelling). More specifically, the GEP is now viewed as a multi-player profit-maximization problem, with its solution derived as an equilibrium of a noncooperative game (Nanduri and Das (2008)).
When setting a model to deal with the capacity expansion problem in an oligopolistic context, one has to make some assumptions related to the structure of the model (e.g., stochastic or deterministic, static or dynamic, number of market segments), the mode of play and the equilibrium concept, the functional forms of production and investment costs and demand functions, as well as assumptions regarding the numerical values of some key parameters. The objective of this paper is to assess the impact on investment prescriptions of some of these choices (assumptions), namely, (i) the depreciation rate of physical capacity (zero vs. positive rate); (ii) the values of short- and long-term price elasticities; (iii) the planning horizon; and (iv) the number and relationship between market segments. Whereas the first three items are akin to sensitivity analysis, the last point involves somehow a change in the model.
To assess the impact of such changes in an empirical setting, we adopt as a starting point the stochastic and dynamic model of the Finnish electricity provided in Pineau and Murto (2003). The rationale for choosing this model is twofold. First, we have access to all modeling and estimation details as well as forecasted investments, and, second, we have the actual realizations, i.e., the investments made by the companies in Finland during the relevant period of time, that is from 1996 to 2006. Therefore, we can interestingly compare the predicted equilibrium investment levels provided by two models (the benchmark and one of its variation) to realizations. Our methodology can be seen as an experimental design with the items (i)–(iv) above being the manipulated factors and the level of investment being the dependent variable. Ultimately, our objective is to assess the robustness of some of the modeling choices involved in the generation expansion capacity model. Although we compare our results to realizations, our goal is not to replicate past investment decisions, but to assess how some modeling choices influence these results.
The rest of the paper is organized as follows. In Section 2, we present a brief description of the electricity industry context, followed by a review of the literature on GEP (Section 3). In Section 4, we introduce the stochastic dynamic model for GEP in general terms. A short description of the model developed by Pineau and Murto is provided in Section 5, with details on its calibration and on implemented modifications. We present our results in Section 6, and conclude in Section 7.
Section snippets
Brief description of the context
Finland introduces competition in its electricity industry in 1995. The interested reader may consult Pineau and Hämäläinen (2000) for a description of the deregulation of the Finnish electricity market. The country has scarce energy resources. It imports 70% of the primary energy used (oil, coal, natural gas, uranium), with more than half from Russia (Foratom (2009)). This situation pushes electricity producers to develop all generation technologies in order to achieve independence from a
Literature review on GEP
The generation expansion problem (GEP) literature in deregulated markets is of relatively recent vintage. Table 3 gives an overview of some of the papers in this area, classified in terms of the following (often interrelated) five main characteristics:
A stochastic dynamic model
In this section, we introduce, in relatively general terms, a stochastic dynamic model for a deregulated electricity market. Denote by J = {1, … , m} the set of players (producers), by S the set of available technologies (hydro, nuclear, coal, gas-fired turbine, etc.) and by L the set of load periods. In principle one may consider a larger number of load periods but it is typical in this literature to focus on only two, namely base-load (b) and peak-load (p). Time t is discrete, t = 0, … , T, and demand
Benchmark model
We use the model in Pineau and Murto (2003) as the benchmark case modulo one modification, i.e., we relax the assumption that investments in base technology are excluded. In their paper, the authors stated that “nuclear and hydro production units are very costly in terms of new developments and are not open options in Finland, at least in the short term.” Here, we shall allow for such option. With respect to the model of the previous section, Pineau and Murto (PiMu hereafter) make the following
Experiments
As stated in the introduction, and in light of the observed differences between the model’s outputs [predictions] and the realizations, we are interested in assessing the impact of varying four features in the benchmark model on investment strategies. We now briefly discuss these variations.
Depreciation rate: as stated before, Pineau and Murto (2003) set the decay rate equal to zero in the dynamics of capacity (Eq. (3)). We assign a positive value to this rate and assess its impact on
Conclusion
We examine in this paper the implications of some modeling features on equilibrium investments in a deregulated electricity market. We mainly rely on a reference model developed in PiMu. The interest of our study lies in the fact that there are still no empirical assessment of how modeling choices (e.g., market structure, depreciation rate of capacity, demand elasticities, planning horizon, etc.) influence outcomes computed by electricity market models. Further, it has been rarely the case that
References (54)
- et al.
The EU regulation on cross-border trade of electricity: A two-stage equilibrium model
European Journal of Operational Research
(2007) Electricity demand by time of use – an application of the household aids model
Energy Economics
(1995)- et al.
Solving stochastic complementarity problems in energy market modeling using scenario reduction
European Journal of Operational Research
(2009) - et al.
An analysis of capacity and price trajectories for the ontario electricity market using dynamic nash equilibrium under uncertainty
Energy Economics
(2008) - et al.
Dynamic oligopolistic games under uncertainty: A stochastic programming approach
Journal of Economic Dynamics & Control
(2007) Optimization methods for electric utility resource planning
European Journal of Operational Research
(1995)The real-time price elasticity of electricity
Energy Economics
(2007)- et al.
Long-term price and environmental effects in a liberalised electricity market
Energy Economics
(2008) - et al.
A game theoretic model of the northwestern European electricity Market–Market power and the environment
Energy Policy
(2006) - et al.
A survey of stochastic modelling approaches for liberalised electricity markets
European Journal of Operational Research
(2010)
Some initial evidence of Canadian responsiveness to time-of-use electricity rates: Detailed daily and monthly analysis
Resource and Energy Economics
A Perspective on the restructuring of the finnish electricity market
Energy Policy
Minimal adjustment costs, factor demands, and seasonal time-of-use electricity rates
Resources and Energy Economics
A new pricing scheme for a multi-period pool-based electricity auction
European Journal of Operational Research
Electricity market modeling trends
Energy Journal
Oligopoly models for market price of electricity under demand uncertainty and unit reliability
European Journal of Operational Research
Two-settlement electricity markets with price caps and cournot generation firms
European Journal of Operational Research
The response of small and medium size business customers to time-of-use (TOU) electricity rates in Israel
Journal of Applied Econometrics
Dynamic Non-Cooperative Games
Long-range generation planning using decomposition and probabilistic simulation
IEEE Transactions on Power Systems
A state-of-the-world decomposition approach to dynamics and uncertainty in electric utility generation expansion planning
Operations Research
A game-theoretic model for generation expansion planning: problem formulation and numerical comparisons
IEEE Transactions on Power Systems
Differential Games in Economics and Management Science
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We wish to thank the two anonymous reviewers for their very helpful comments and suggestions. Research supported by HEC Montréal and NSERC Canada.