Approaches to electricity market modelling

A large number of papers have been devoted to modelling the operation of deregulated power systems. In this section, we draw upon some earlier reviews to compare and contrast the main approaches based upon model attributes. Such attributes can help us to understand the advantages and limitations of each modelling approach.

From a structural viewpoint, the approaches to electricity market modelling reported in the technical literature can be classified according to the scheme shown in Figure 11.3. They fall into three main classes: optimisation, equilibrium, and simulation models. Optimisation models focus on the profit maximisation problem for a single firm competing in the market, while equilibrium models represent the overall market behaviortaking into consideration competition among all participants. Simulation models are regarded increasingly as an alternative to equilibrium models when the problem under consideration is too complex (for example, too nonlinear or dynamic) to be addressed within a traditional equilibrium framework.

Figure 11.3. Some trends in electricity market modelling

Some trends in electricity market modelling

Source: Ventosa et al. 2005

Various assumptions are often made on the objectives, strategies, beliefs and capabilities of market participants. In game theory models, for example, participants are assumed to be rational in the sense that they can obtain and explore all the relevant information in order to deduce the best outcome. As we shall see shortly, some of these rigid assumptions can be relaxed with the help of agent-based simulation, since participants may employ different strategies and be subject to different sets of rules to guide their behaviour. They may have access to different information and possess different computational capabilities. The challenge then is how to assign a particular agent the appropriate set of behavioural rules and computational capabilities.

Previous review articles (Kahn 1998; Day et al. 2002; Ventosa et al. 2005) have focused mostly on the equilibrium models found in game theory. Kahn’s survey was limited to 2 types of equilibrium resulting from firms in oligopolistic competition: Cournot equilibrium , where firms compete on a quantity basis; and Supply Function Equilibrium (SFE), where they compete on both quantity and price. Although both models are based on the Nash equilibrium concept, the Cournot approach is usually regarded as being more flexible and tractable.

Day et al. (2002) conducted a more detailed survey of the modelling literature, listing the strategic interactions that have been, or could be, included in power market models as:

Their conclusion was that the CSF approach to modelling oligopolistic competition is more flexible than the Cournot assumption, and more computationally feasible for larger systems than the standard supply function equilibrium models. We shall discuss the CSF approach further in the next section.

Trends reported in Ventosa et al. (2005) followed similar lines, noting that most models used to evaluate the interaction of agents in wholesale electricity markets have persistently stemmed from game theory’s concept of the Nash equilibrium. For the first time, however, some simulation models were included (albeit briefly). We shall discuss simulation models further in following sections.

Cournot equilibrium models

Previously, we revealed that larger generators in the NEM use quantity offers rather than price offers to improve their market positions, especially in peak periods. In other words, they seem to act like players in Cournot competition. The assumptions underlying a Cournot solution correspond to the Nash equilibrium in game theory. At the solution point, the outputs (quantities dispatched) fall into an intermediate zone between fully competitive and collusive solutions. In effect, a second firm becomes a monopolist over the demand not satisfied by the first firm, a third over the demand not satisfied by the second, and so on.

Since the Cournot solution represents a kind of imperfect collusion technique, we must ask if this equilibrium concept approximates the reality of Australia’s NEM? Although generators are forbidden from changing bid prices in the rebidding process, by shifting quantity commitments up or down between different price bands they can achieve a similar effect to changing prices directly. In reality, therefore, both quantity (directly) and price (indirectly) serve as decision variables. Thus the Cournot assumption may not be appropriate for NEM generators. Furthermore, by expressing generators’ offers in terms of quantities only (instead of offer curves), equilibrium prices are determined by the demand function. This shortcoming tends to reinforce the idea that Supply Function Equilibrium (SFE) approaches may be a better alternative to represent competition in the NEM (Rudkevich et al. 1998).

In an electricity market context, a Cournot solution posits rather shortsighted behaviour on the part of generating agents. It implies that each of them modifies its bids in response to the bids and dispatches of others, without allowing for the fact that others may react in a similar manner. There is no evidence that most NEM generating agents behave in this manner, although small groups of them may do so.

Supply Function Equilibrium Models

In the absence of uncertainty and knowing competitors’ strategic variables, Klemperer and Meyer (1989) showed that each firm has no preference between expressing its decisions in terms of a quantity or a price, because it faces a unique residual demand. When a firm faces a range of possible residual demand curves, however, in general it expects a greater profit in return for exposing its decision tool in the form of a supply function (or offer curve) indicating those prices at which it is willing to offer various quantities to the market. This SFE approach, originally developed by Klemperer and Meyer (1989), has proven to be an attractive line of research for the analysis of equilibrium in wholesale electricity markets.

To calculate an SFE requires solving a set of differential equations , instead of the typical set of algebraic equations that arises in traditional equilibrium models, where strategic variables take the form of quantities or prices. Thus SFE models have considerable limitations concerning their numerical tractability. In particular, they rarely include a detailed representation of the generation system under consideration. Originally developed to address situations in which supplier response to random or highly variable demand conditions is considered, perhaps their attraction nowadays is the possibility of obtaining reasonable medium-term price estimations with the SFE methodology.

Conjectural variations approaches

A recent strategy has been to employ the Conjectural Variations (CV) approach described in traditional microeconomic theory. The CV approach can introduce some variation into Cournot-based models by changing the conjectures that generators may be expected to assume about their competitors’ strategic decisions, in terms of the possibility of future reactions (CV). Day et al. (2002) suggest taking this approach in order to improve Cournot pricing in electricity markets. For example, one could assume that firms make conjectures about their residual demand elasticities or about their rivals’ supply functions (Day et al. 2002). In the context of electricity markets, the latter is called the Conjectured Supply Function (CSF) approach. The CV approach can be viewed as generalising Stackelberg models (in that the conjectured response may not equal the true response). Also, superficially it resembles the SFE method described above.