Forecasting wholesale electricity prices used to be a straightforward, though laborious, task. It generally concerned medium- and long-term time horizons, and involved matching demand estimates to the supply, obtained by stacking up existing and planned generation units in order of their operating costs.
These production-cost models (PCM) had the capability to forecast prices on an hour-by-hour level. However, they ignored strategic bidding practices, including the execution of market power. They were appropriate for regulated markets with little price uncertainty, a stable structure and no gaming, but are not suitable for competitive electricity markets.
The idea of agent-based modelling was developed as a relatively simple concept in the late 1940’s. Since it requires computation-intensive procedures, it did not become widespread until the 1990’s.
In an excellent review paper by Ventosa in 2005 identify’s three main electricity market modelling trends: optimisation, equilibrium and simulation models. In their classification, optimisation models focus on the profit maximisation problem for one of the firms competing in the market. The equilibrium models discussed below (Nash-Cournot framework, supply function equilibrium) represent the overall market behaviour, taking into consideration competition among all participants. Finally, simulation models are an alternative to equilibrium models when the problem under consideration is too complex to be addressed within a formal equilibrium frame-work.
In the Nash-Cournot framework, electricity is treated as a homogeneous good, and the market equilibrium is determined through the capacity setting decisions of the suppliers. Unfortunately, these models tend to provide prices higher than those observed in reality. Researchers have addressed this problem by introducing the concept of conjectural variations, which aims to represent the fact that rivals react to high electricity prices by producing more.
The Cournot model of oligopoly assumes that rival firms produce a homogeneous product, and each attempts to maximise profits by choosing how much to produce. All firms choose output (quantity) simultaneously. The basic Cournot assumption is that each firm chooses its quantity, taking as given the quantity of its rivals. The resulting equilibrium is a Nash equilibrium in quantities, called a Cournot (Nash) equilibrium.
Although their approach is hybrid in nature, Ruibal and Mazumdar (2008) provide one of the very few applications of this framework to EPF. A fundamental bid-based stochastic model is proposed for predicting electricity hourly prices and average prices in a given period. Two sources of uncertainty are considered: the availability of the gene rating units and demand. The results show that as the number of firms in the market decreases, the expected values of prices increase by a significant amount. They also demonstrated that an accurate temperature forecast can reduce the prediction error of the electricity price forecasts significantly.
Supply function equilibrium
The supply function equilibrium approach (SFE) models the price as the equilibrium of companies bidding with supply curves into the wholesale market. Calculating the supply function equilibrium (SFE) requires a set of differential equations to be solved, rather than the typical set of algebraic equations that arises in the Nash-Cournot framework. Thus, these models have considerable limitations concerning their numerical tractability. To speed up computations, the demand can be aggregated into blocks. This in turn leaves the extreme values out of the analysis, which many are not prepared to accept when focusing on price forecasting or risk management.
The supply function equilibrium provides a game-theoretic model of strategic bidding in oligopolistic wholesale electricity auctions
To assist with decreasing the numerical complexity of general SFE models, linear SFE models have been proposed. In such models, the demand is ‘considerable limitations’ (or, more precisely, ‘affine’) at each moment in time the demand as a function of price has a non-zero intercept and a constant negative slope, marginal costs are linear or affine, and SFE can be obtained in terms of either linear or affine supply functions.
All firms receive the marginal clearing price for their supply. Since the supply functions are non-decreasing and the market clearing price is the same for all players, this market clearing condition maximises the social welfare when there is no transmission congestion. This framework has been used extensively for the analysis of bidding strategies, market power and market design, and congestion management; but electricity price forecasting applications have been very limited.
Strategic production-cost models
A third, less popular static equilibrium approach has been proposed by Batlle as a modification of the traditional production-cost models. Based on the conjectural variation, the strategic PCM (SPCM) takes agents’ bidding strategies into account; each agent tries to maximise its own profits, taking into account its cost structures and the expected behaviours of its competitors.
Production costing models have been extensively used to analyse traditional power systems for decades. These tools are based on the costs of production, but in oligopolistic electricity markets market prices can not be explained attending just to marginal costs but instead bid prices have to be considered, since market participants seize their dominant position in the market looking for higher profits.
When simulating the supply curve building process, the SPCM assumes that the firm just knows its costs and its conjecture about the derivative of its residual demand function. As no iterations are made, firms do not have the chance to refine their bids and take into account rivals’ reactions (as in SFE models). Compared with the Nash-Cournot and SFE models, the main advantage of the SPCM is its computational speed, which makes it suitable for real-time analysis.
Agent-based simulation models
The static equilibrium models discussed so far are based on a formal definition of equilibrium, expressed in the form of a system of algebraic or differential equations.
Even if the set of equations has a solution, it is often very hard to find, and the modeller has to resort to heuristics to ‘solve’ the problem. Moreover, such modelling approaches have limitations in the way in which the competition between participants can be represented. On the other hand, agent-based simulation models do not have these limitations, while being not much harder to ‘solve’. Over the last two decades, agent-based computational economics (ACE) has become a widely accepted approach to solving both theoretical and practical problems in energy economics.
An agent–based model is one of a class of computational models for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organisations or groups) with a view to assessing their effects on the system as a whole.
The basic tool of ACE is a class of computational structures and rules for simulating the actions and interactions of autonomous agents (whether individuals or collective entities, such as organisations or groups), with the ultimate objective being to assess their effects on the system as a whole.
One of the first applications of ACE to modelling the strategic behaviour observed in electricity markets was described in the paper by Bower and Bunn (2000), who test a number of market designs which are relevant for the changes that have taken place in the England and Wales market. They conclude that daily bidding, together with uniform pricing, yields the lowest prices, while hourly bidding under the pay-as-bid system yields the highest prices. In a similar context, Day and Bunn (2001) propose a simulation model for analysing the potential for market power. This agent-free simulation approach is similar to the SFE scheme, but it provides a more flexible framework that allows for a consideration of actual marginal cost data and asymmetric firms.
In a review article, Koritarov (2004) argues that the purpose of agent-based modelling is not necessarily to predict the outcome of a system, but rather to reveal and explain the complex and aggregate system behaviours that emerge from the interactions of the agents. Currently, agent based models are typically mere elements of more complex hybrid electricity price forecasting systems, rather than being the source of price forecasts themselves.
Strengths and weaknesses
On the one hand, multi-agent models – and agent-based models in particular – are a class of extremely flexible tools for the analysis of strategic behaviour in electricity markets. On the other hand, this freedom is also a weakness, as it requires the assumptions embedded in the simulation to be justified, both theoretically and empirically. A number of components have to be defined: the players, their potential strategies, the ways in which they interact, and the set of payoffs. Obviously, a substantial modelling risk is present.
While in classical power pools the sellers are generators, and their characteristics are identifiable through their assets directly, in power exchanges every type of market participant can be a seller. For instance, a distribution company that has over-contracted in the bilateral market can be a seller in the power exchange’s spot market. Thus, the problem of identifying the relevant market players and their strategies becomes highly nontrivial.
Moreover, multi-agent models generally focus on qualitative issues rather than quantitative results. They may provide insights as to whether or not prices will be above marginal costs, and how this might influence the players’ outcomes. However, they pose problems if more quantitative conclusions have to be drawn, particularly if electricity prices have to be predicted with a high level of precision.If you’ve found this blog helpful and would like other topics covered, please feel free to drop me an email with suggestions. You’re welcome to subscribe using ‘Subscribe to Blog via Email’ section and this will get you the latest posts straight to your inbox before they’re available anywhere else
- Electricity price forecasting: A review of the state-of-the-art with a look into the future – International Journal of Forecasting (Weron)