Invited ReviewA survey of stochastic modelling approaches for liberalised electricity markets
Introduction
Until the mid-nineties, the monopoly of power supply companies was justified by the existence of a public energy supply and with the existence of a natural monopoly (cp. for definition e.g. Berg, 1988) in the field of energy supply. Regional markets have been assigned to utilities with a monopoly status by so-called concessional contracts. Prices for electricity have been approved on the basis of the cost structure of the utilities, the forecasted electricity sales and a reasonable profit margin for energy utilities.
In recent decades, most energy markets have been liberalised and privatised with the aim of obtaining more reliable and cheaper services for electricity consumers. A major step in Europe was the Directive of the European Commission at the end of 1996 (European Commission, 1997), requiring the stepwise opening of electricity markets in the European Union, ending with a fully competitive market in 2010 at the latest. In this new context, several wholesale electricity markets have been established in many places and energy utilities have been unbundled into generation, transmission and distribution companies (for an overview of the unbundling progress in Europe, see European Commission, 2005). With liberalisation and the introduction of energy markets, decision making no longer depends on centralised state- or utility-based procedures, but rather on decentralised decisions of energy utilities whose goals are to maximise their own profits. All firms compete to provide services at a price set by the market, as a result of all of their interactions.
However, energy supply companies are exposed to significantly higher risks than in regulated markets. California is often cited as the outstanding example of the risks and difficulties associated with liberalisation. Above all, generation companies are affected by these changing framework conditions, as they are exposed to the different risks from liberalised energy markets in combination with huge and generally irreversible investments. Uncertainties that generation companies face include the development of product prices for electricity as well as for primary energy carriers (e.g. oil, gas, coal and uranium), technological developments, availability of power plants, the development of regulation and the political context, as well as the behaviour of competitors.
The need for decision support tools in the energy business mainly based on operation research models has therefore significantly increased. Especially to cope with different uncertain parameters, several stochastic modelling approaches have been developed in the last few years for liberalised energy markets. In this context, the present paper aims to give an overview and classification of stochastic models especially dealing with price risks in electricity markets.1 The diversity of these approaches makes it difficult to get a comprehensive overview of the field of stochastic models. Hence this survey should guide the way through the different approaches and describe the state-of-the-art in this research area, especially focusing on price risks in electricity markets. Many stochastic OR models for energy currently deal with fluctuating feed-in of renewable energies. However, we do not attempt to fully cover the stochastic issues in wind and renewable energies, which we only shortly mention in the paper.2 Furthermore, we do not go into detail about coal, gas and oil price modelling, as we focus on general approaches for electricity markets. Thereby the focus is placed on stochastic methods developed in operation research and financial mathematics with practical relevance and applicability.
Electricity markets are characterised by some technical features which will be described in Section 2 and which determine the complexity of such models. Electricity market modelling usually requires the representation of the underlying characteristics and limitations of the production assets. As these models take the technical characteristics of the production system and the fundamental data into account, they are often called fundamental models. Beside these fundamental models, sophisticated financial and economic models can be used for modelling uncertain commodity prices in the short-term. In this survey, the various modelling approaches in the energy business are classified as follows:
- –
stochastic processes for electricity prices, commodity prices (for primary energy carriers) and other uncertain parameters (hydro inflow and wind distributions) (see Section 3);
- –
scenario generation and reduction (see Section 4), which is important for the practical relevance and applicability in energy markets due to the need for a structured handling of large data amounts; as well as
- –
stochastic optimising models for investment decisions, short- and mid-term power production planning and long-term system optimisation (see Section 5).
As the three fields cannot be examined separately from one another, they are illustrated by selected integrated models which represent a complete approach. Thereby the practical relevance of the different methods and their applicability to real markets is of crucial importance. In a conclusive summary, shortcomings of existing approaches and open issues that should be addressed by operation research are critically discussed (see Section 6).
Section snippets
Decision problems in liberalised energy markets
Decision problems of utilities are characterised by special technical features of the commodity electricity and characteristics of the technical plants used to produce it. The product electricity is characterised by the following features (cp. Hensing et al., 1998, Wietschel, 2000, Stoft, 2002):
- –
Transportation of electricity requires a physical link (transmission lines).
- –
Electricity cannot be directly stored on a large scale, which necessitates that supply and demand are equalised at all times.
- –
Modelling uncertainties in the electric power production
The first step of stochastic modelling is the analysis of temporal variation of the uncertain parameters. Whereas forecasting the uncertain load was the main challenge before liberalisation (for load forecasting see Hahn et al., 2009), new uncertain parameters now have to be considered in energy modelling, which are, inter alia, electricity prices, commodity prices (e.g. fuel, -certificates), fluctuant inflow to hydro reservoirs and uncertain wind power generation. These parameters are
Scenario generation and reduction
The different stochastic processes are used to simulate the uncertain parameters and to generate future data for them. The simulations of each uncertain parameter at a time can be combined into a scenario. The generation of a large number of scenarios is a method to capture the uncertainties in energy markets. Thereby, two approaches to scenario generation have been successfully applied in energy market models: the analytical and the simulative.
Applications of optimisation models
The reduced scenario tree or the scenario lattice which are generated with the methods described in Section 4, both form the base of a stochastic optimisation model. In electricity markets, these optimisation models concentrate on determining the optimal investment decision or optimal power production plan for a given time period. Some of these stochastic models even optimise whole energy systems from a long-term perspective (see Göbelt, 2001). Table 2 gives a brief overview of some stochastic
Summary and future research
Many models based on a deterministic approach can be found in energy modelling, which are suitable to cover several characteristics of today’s markets. Stochastic approaches are especially useful for modelling uncertain parameters, and in recent years several approaches have been developed for application in energy markets. This paper presented a survey of stochastic models focusing on electricity market prices and also introduced selected integrated approaches which combine econometric models
Acknowledgements
The paper results from the work of the young investigator group “New methods for energy market modeling”. The young investigator group received financial support by the Concept for the future of Karlsruhe Institute of Technology within the framework of the German Excellence Initiative.
References (66)
Optimization model for the energy sector
Energy Policy
(1974)- et al.
Short-term operation planning on cogeneration systems: A survey
Electric Power Systems Research
(2008) - Agnew, M., Schrattenholzer, L., Voß, A., 1979. A Model for Energy Supply System Alternatives and their General...
- Barreto, L., Kypreos, S., 2004. Emissions trading and technology deployment in an energy-systems “bottom-up” model with...
Natural Monopoly Regulation: Principles and Practices
(1988)- Blyth, W., Bradley, R., Bunn, D.W., Clarke, C., Wilson, T., Yang, M., 2007. Investment risks under uncertain climate...
- Bowden, N., Payne, J.E., 2008. Short-term forecasting of electricity prices for MISO hubs: Evidence from ARIMA-EGARCH...
- et al.
Times Series Analysis: Forecasting and Control
(1994) - et al.
Oligopolistic competition in power networks: A conjectured supply function approach
IEEE Transactions on Power Systems
(2002) - et al.
Maximum likelihood from incomplete data via the EM algorithm
Journal of the Royal Statistical Society
(1977)