Generation Asset Divestment in the England
and Wales Electricity Market:
A Computational Approach to Analysing
Market Power
Christopher J. Day and Derek W. Bunn[*]
April 1999
Decision Technology Centre
London Business School
Sussex Place, Regents Park
London NW1 4SA, UK
Generation Asset Divestment in the England
and Wales Electricity Market:
A Computational Approach to Analysing
Market Power
Abstract
The task of developing an adequate modelling approach to understanding strategic behaviour in competitive electricity markets is a major open research question. Contributions from economic theory based on equilibrium solutions give some comparative insights on market design, but provide an inadequate representation of the observed, dynamic evolution of these typically quite imperfect markets. In this paper, we develop an approach to modelling competition between electricity generating companies based on computational modelling and simulation. In this approach, each company, or agent, is modelled with specific objectives and bounded reasoning abilities. Using the price-setting mechanism found in the England and Wales pool, the interaction of the generating companies is simulated through time. For validation, we compare the computational approach with the theoretical equilibrium in continuous supply functions, for the scenario of symmetric firm sizes. As the computational approach is not constrained by the requirement of symmetry or continuity, we then demonstrate its ability to analyse more general circumstances. We apply the new approach to analysing the second round (1999) of capacity divestment proposals which the government and regulatory authorities in England and Wales required in order to improve the efficiency of the wholesale power market. In this context, we suggest that, for a second time, the level of market power may be underestimated and that although the proposed amount of divestment is substantial, it may still be insufficient to avoid the need for further regulatory controls in the short term.
1. Introduction
With a well re-structured electricity industry, the aspirations of full de-regulation are to create wholesale markets which are perfectly competitive and deliver prices close to short-run marginal costs. Yet many of the re-structuring exercises of the past decade have been cautiously tempered with concerns about security of supply, stranded assets and various other externalities, the result of which has been the creation of power pools with market power on the generation side. The Electricity Pool of England and Wales is a prime example. Under such circumstances, continuous monitoring for the abuse of market power becomes necessary, and the persistent issues of price controls or further re-structuring add considerable regulatory risk to the industry.
With the perception that generating companies in the England and Wales market had indeed been exerting excessive market power, the UK office of electricity regulation previously attempted to mitigate such abuses by requiring plant divestments (OFFER 1994). In accordance with this directive, 17% of the capacity owned by the two major price-setting generators (National Power and PowerGen) was divested in 1996. At that time, an official report on the market power of National Power and PowerGen concluded that with this amount of divestment and the prospect of further new entry, their ability “to affect the level of Pool prices, whether to keep them high or cause them to fluctuate, will be small” (MMC, 1996). However, this did not happen, and by 1998, those two generators were again accused of maintaining high prices (DTI, 1998), So much so, in fact, that the regulatory office was again saying that the “most effective route to increased competition in the short term would seem to be to transfer more of National Power’s and PowerGen’s coal-fired plant into the hands of competitors” (OFFER, 1988).
Just how to decide upon the appropriate level of plant divestment is a formidable and unenviable regulatory task. Clearly, OFFER got it wrong the first time in 1996, but used very little formal analysis other than indices of market share and price-setting. For example, Littlechild (1996) referred to a reduction in the HHI index of market concentration from about 3,600 in 1991 to about 1,600 in 1996 as a measure of success in making the industry more competitive. Green (1996) addressed the divestment issue by applying the approach of supply function equilibria (Klemperer and Meyer, 1989), as an extension of previous analyses for the England and Wales pool (Green and Newbery, 1992; Green, 1996), and similarly to what has been done elsewhere (eg Andersson and Bergman, 1995). In that study, Green (1996) broadly endorsed the level of divestment being undertaken at the time. However, the derivation of such supply function equilibria is analytically difficult, and the published studies have tended to make very strong assumptions to facilitate solutions. The basic framework is to assume that generating companies bid supply functions into the pool, representing the price at which they will make available a range of generation capacity, as happens in the Cal PX and the pools of England and Wales, Spain, Colombia and elsewhere. Demand being revealed later, as a forecast, or via demand-side bidding or in actuality (for ex post markets like Victoria) then clears the market. Analytical evaluation of the equilibrium solution either assumes that these supply functions are continuous (Green 1996), whereas the nature of generating units makes these functions increase with quite distinct steps in practice, or restricts the prospective analysis of various industry ownership structures to symmetric, equally sized firms (Rudkevitch et al, 1998), or both (Green and Newbery, 1992). It could therefore be argued that the underestimation of residual market power after the first round of divestment reflected the inadequacy of the modelling approaches available at the time.
In this paper we present a new method for determining imperfectly competitive outcomes in electricity markets that utilises the approach of computational modelling and simulation. Rather than directly calculating the equilibrium solution, we formulate a computational model of profit maximising behaviour for each generating company and then simulate the interaction of the companies, observing the adaptation of supply functions during the repeated play of the daily game. In principle, this approach can take actual marginal cost data and deal with both discontinuous supply functions and asymmetric market concentrations.
This rest of this paper proceeds as follows. First, we describe the computational framework we have developed for modelling supply function competition and discuss the properties of the dynamic behaviour resulting from simulating the strategic interaction. Then after specifying the demand and marginal cost assumptions of the model, we see how the results of this approach compare with those obtained by calculating a continuous supply function equilibrium, for those simplified circumstances to which the latter can be applied. This provides a calibration and validation of the approach. Then we apply the approach to analysing the second (1999) round of plant divestment, thus demonstrating the applicability of this new approach to modelling competition between asymmetric generating companies with discontinuous supply functions.
2. Formulation of the Computational Model
We develop a computational approach to modelling the interaction of generating companies who compete using supply functions in an electricity pool with rules similar to those found in the England and Wales market. Generating companies are modelled holding the conjecture that their competitors will submit the same supply functions as they did in the previous day. Given this conjecture, each company is modelled as a daily profit maximiser, optimising the supply function it submits to the market. Using data on observed demand and estimates of short-run marginal costs, we simulate the interactions between the generating companies and analyse the resulting supply functions.
Figure 1: An illustration of the piece-wise linear supply function representation.
We model the supply functions as having both discrete capacity and price ranges. In this market it is natural to have a discrete capacity range as a generator's capacity comprises of individual generating plants, hence cumulative available capacity increases in a discrete manner. Discretizing the price range is not such an obvious transformation as the value a generator prices its plants at can vary almost continuously. We perform this discretisation as a modelling simplification to allow the subsequent application of an optimisation routine to the supply functions.
Formally, for all K generating companies, let each generating plant be a standard size equal to PS and let the price range be discretised into N equal sized price ranges indexed from 1 to N, which we will refer to as price bins. If the price range of each bin is also a standard size and equal to BS, then the price range of bin i is (i-1)*BS to i*BS. Thus, we can define the lower price of bin i as and the upper price as .
In this representation we view generating capacity as being strategically allocated each day to individual price bins and define the capacity that company k has allocated to bin i as (MW) which will be a multiple of PS, the standard size of each generating plant. With this representation, a piece-wise linear supply function can be defined for each company k by forming linear sections of the function between the lower price and the upper price of each bin i using the capacity that company k has allocated to the bins. Figure 1 gives an illustration of this piece-wise linear representation. Having defined the price range ( to ) that each linear section of the supply function exists between, for each company k we can define the starting capacity of each bin i as
and the ending capacity of each bin i as
We can now define the linear section of company k’s supply function (price as a function of quantity ) existing in the prices range to and the cumulative capacity range to as
(1)
As we make the constraint that the price bins are the same uniform size across all companies, the process of generators submitting their supply functions to the market can be simplified to each company notifying the market operator of the number of generating plants (quantity) it wishes to allocate to the different price bins. With the submission of the bids by each generator, a system supply function can be created as the aggregation of all bids and given demand, the market price (known as the system marginal price ) can be calculated as the intersection of the demand function with the system supply function.
This market is a uniform auction, with the same price being paid to all companies who generate in a given period t. Therefore, equation (1) can be inverted to attain the quantity an individual company is required to generate in a given period, such that if the system marginal price lies in the range ( to ), then the quantity company k will generate in period t will be given as
(2)
2.1 Supply Function Optimization
Using this representation of supply functions, we model each company optimising its next day profit, given its conjectures about its competitors by modifying its own supply function. In addition to the profit a company may make from electricity sales in the pool, we also model additional revenue earned from contracts that a generator may engage in with buyers of electricity. Known as two-way contracts for differences (CfDs), these purely financial instruments are used in the industry to hedge price volatility in the pool and take the form of a time period t, a strike price and volume . If during the time period, the market price () is greater than the strike price, then the generator will pay the buyer the difference between the market price and the strike price multiplied by the volume. If the market price is lower than the strike price, then the buyer pays the difference between the strike price and the market price multiplied by the volume under contract. Formally, we define the profit for company k in period t as
(3)
Where is the total cost function of company k. As we have chosen to model the supply functions that are submitted by each generating company remaining constant across the 48 half hour periods of the day[1], this results in the value of the total objective function for each company k being given as
An iterative optimisation routine is used to calculate the best response for each generating company, given the supply function conjecture it holds about its opponents[2].
2.2 Dynamic Behaviour and Bounded Rationality
Simulating the interaction of generating companies using this computational model produces interesting dynamic behaviour. For the demand and marginal cost data that we have analysed, when each generating company is modelled fully optimising its supply function, we do not find convergence to a unique supply function. Instead, repeated cycling is observed in the supply functions in a manner similar to the Edgeworth cycle found in models of capacity constrained price competition. This should not be a surprising result. Although this model is one of supply function competition, we do not model the capacity commitment decision, rather we model pricing of individual plants that have already been committed. Thus, our model is one of price competition among many plants.
From a game-theoretic point of view, the identification of Edgeworth cycles would indicate the lack of pure strategy Nash equilibrium, and this usually leads to the consideration of mixed strategy, Nash equilibria. Apart from being analytically complex and computationally problematic to calculate[3], the idea that strategic interaction of this sort can be thought of in terms of mixed strategies is also intuitively unappealing. To quote Rubinstein (1991, p922) “One of the reasons that mixed strategies are popular in both game theory and economic theory, in spite of being so unintuitive, is that many models do not have an equilibrium with pure strategies. However, the nonexistence of a solution concept in pure strategy does not necessarily mean that we should look for stochastic explanations. … Expanding the model or changing the basic assumptions are alternatives which the modeller should consider at least as favorably as mixed strategies.”
One plausible behavioural assumption is that of bounded reasoning on the part of the generating companies. Rather than assuming they will fully identify the optimal response, or formulate a mixed strategy, either explicitly or otherwise, we have assumed limited optimising behaviour, modelling each generating company seeking to incrementally improve its profitability by changing the price of only one or two of its plants each day. Thus, assuming companies conjecture that their opponents will not modify their supply function, this seems to be quite realistic as only small movements in the supply functions do actually occur from day to day. Thus, the fact that this type of process has been observed in practice over several years indicates that the players are not being so obviously mislead by their conjectures, and indeed this approach is consistent with the basic Cournot conjecture of best response.