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Modelling Prices in Competitive Electricity Markets
John Wiley & SonsCopyright © 2004 John Wiley & Sons, Ltd.
All right reserved.
Chapter OneStructural and Behavioural Foundations of Competitive Electricity Prices
DEREK W. BUNN
London Business School, Regents Park, London NW1 4SA, UK
This chapter provides an introductory background to the fundamental and strategic drivers of price formation in electricity markets. It does not go into detail on the various time-series and econometric models, which are beginning to be applied to electricity data, as a range of these are presented in later chapters. Alternatively, it seeks to provide a basic understanding of why electricity prices are quite different in their behaviour and properties to those in other financial and commodity markets. It is also an introduction to some aspects of power system economics and electricity market liberalisation, for readers coming to electricity with experience of modelling other financial markets.
From a financial and commodity markets perspective, wholesale electricity prices can generally be viewed as the result of investors having created real options upon various underlying primary fuel commodities such as gas, oil or coal. Although a substantial amount of electricity is generated from hydro and nuclear sources in various parts of the world, the dominant production process isstill the thermal conversion of fossil fuels such as gas, oil and coal. This is a very capital intensive process, with surprisingly few workers actually being employed at the power plants. Thus, as electricity is often traded on exchanges close to an hour before it is needed, in this short term, the variable cost of power generation is essentially just the cost of the fuel. Even in power systems with a substantial amount of hydro and nuclear, it is the fossil fuel plant that often sets the market prices.
Depending upon the age and technology of the generating plant, in general, around a half of the energy content of the primary fuel gets converted into electricity. It follows from this, that with knowledge of the spot and futures market prices for primary fuels, and relatively well-known efficiency ratings for individual power plants on the system, the short-run marginal cost of each power plant on the system can be reasonably well estimated as a simple conversion of the fuel price. Of course, the owners of power plants would also like to recover their overheads and produce a return on investment, and so the spread between the market prices for fuel and power, the so-called tolling margin, is the value of owning and operating a power plant. As a real asset, or a contract held by a trader, the tolling margin represents the optionality of converting fuel prices into power prices. From this perspective, the fundamental drivers of power prices should, it seems at first sight, be quite straightforward to understand.
In practice, however, whilst this fundamental concept is valid, its application has many complications. Take the case of gas, for example. This is now becoming the fuel of choice for electricity generation. The investment costs are lower than coal, or oil plant; it is cleaner and, depending upon location, the fuel costs are comparable. But with more and more of the gas resources being used for power generation, in some markets the issue of whether gas drives power prices, or vice versa, is not easily answered. Clearly, with convergence between two markets, they become partially co-determined. Figure 1.1 shows the daily average spot prices in the UK for gas and electricity. Clearly convergence was beginning to happen over this period, but at times, the relationship between the two is rather erratic.
Intuitively, the first reason that comes to mind, for the lack of an apparently better convergence with gas, is that gas may not be the only fuel source influencing prices. At some times it may be coal, oil or other plant that is dominant in setting the market prices. Just as the so-called "spark spread" refers to the spread between power and gas prices, the "dark spread" refers to the power-coal market price. As far as the British market has been concerned, gas has steadily been replacing coal as the dominant fuel since the mid-1990s, and there is evidence even in the few years shown in Figure 1.1 that the convergence with gas is improving. However, that is only part of the story.
Looking at Figure 1.1, the basic nature of the electricity time series does seem to be quite different to gas, even though there is a trend to an underlying convergence. As a time series, it is much more spiky, shows higher volatility and a stronger mean-reverting pattern. These, indeed, are the general stochastic characteristics of power prices, as observed in most markets around the world, and there is a fundamental structural reason for this.
The crucial feature of price formation in electricity spot markets is the instantaneous nature of the product. The physical laws that determine the delivery of power across a transmission grid require a synchronised energy balance between the injection of power at generating points and the off take at demand points (plus some allowance for transmission losses). Across the grid, production and consumption are perfectly synchronised, without any capability for storage. If the two get out of balance, even for a moment, the frequency and voltage of the power fluctuates. Furthermore, end-users treat this product as a service at their convenience. When we go to switch on a light, we do not re-contract with a supplier for the extra energy before doing so. We just do it, and there is a tendency for millions of other people to do likewise whenever they feel like it. Electricity may be produced as a commodity, but it is consumed as a service. The task of the grid operator, therefore, is to be continuously monitoring the demand process and to call on those generators who have the technical capability and the capacity to respond quickly to the fluctuations in demand. Figure 1.2 shows the annual range of daily demand profiles from England and Wales. Through a mixture of good forecasting and scheduling by the grid operator, together with a sufficient stock of flexible generating capacity, instantaneous production also follows these demand profiles.
Most spot markets for electricity are defined on hourly intervals (although the British market is half-hourly), and therefore it is clear that throughout the day and throughout the year, a wide variety of plant will be in action and therefore setting the prices at different times. Furthermore, we would expect a diversity of plant on the system for at least two reasons. The obvious one is obsolescence. With power plant lasting for some 40 years, new technologies will come in and be more efficient. So prices will be fluctuating because of the varying efficiencies of the set of plant being used for generation at any particular moment in time.
The more subtle, and second, reason for diversity is, however, again due to the instantaneous nature of the product. The most efficient plant, with the lowest marginal costs (the "baseload" plant), will operate most of the time, but during some of the peaks in demand, some of the power plants (the "peaking" plant) may only be operating for a few hours. The recovery of capital costs on peaking plant, through market prices, may have to be achieved over a relatively few hours of operation compared to the 8760 hours in a normal year for which a baseload plant, without maintenance breaks, could, in principle, serve. Indeed, if we were optimising our stock of power plant, we would invest in some capital-intensive, low-operating-cost plants to serve the baseload, and some relatively cheap to build, but relatively expensive to run, plant (e.g. small diesel generators) available for the peaks. This is, of course, what does happen in practice, with the consequence that prices are much higher in the peaks. We will go through, in more detail, some of the basic economic aspects of the capacity mix in the next section.
So, whilst the fundamental nature of fuel price convergence has a mean-reverting implication, the instantaneous production process of following a highly variable demand profile, with a diversity of plant costs, creates the high spot price volatility. Other factors also come into play in the short term. There may be technical failures with plant, causing more expensive standby generators to come online. The transmission system may become congested so that rather expensive, but locally necessary plant gets called upon. And, of course, there may be unexpected fluctuations in demand. All of these events show up in spot prices. Average forward prices, would, in contrast, be expected to be rather more attenuated than the spot prices. Figure 1.3 shows average month-ahead prices, and compared with Figure 1.1, the fundamental convergence with gas is indeed rather more stable.
There is one further important characteristic of electricity markets, with major implications for price behaviour, and that is their imperfect nature. Most power markets are characterised by a few dominant players, and even in those less common situations where there may appear to be sufficient competitors to achieve efficient prices, at particular times and in special locations, individual companies may have the ability to influence prices. Of the academic research on liberalised electricity markets, by far the bulk of work that has been published has been done on the analysis of, and strategies for the mitigation of, the abuse of market power by the generating companies. As a result of the presence of this market power, prices are generally much higher, and even more volatile, than the fundamentals suggest. In the third section of this chapter, we look at the strategic consequences on prices of imperfect market designs.
1.2 MARKET FUNDAMENTALS
An electricity system essentially provides capacity for immediate consumption, and we, as users, have acquired a call option, to exercise at our convenience, essentially unconstrained in volume up to the limit of our fuse-box. The total utilisation of this capacity by all customers on the system is referred to as the "load", and the basic unit of load is the "watt".
In terms of analysing capacity, and the reasons for possible diversity in its composition, a basic construct is the load duration curve. Figure 1.4 shows an annual load profile of average daily demands, and it is clear that the average daily demand seems to lie within the range 24-43 GW. In Figure 1.5, this same data series, expressed now in hourly intervals, is re-sequenced according to decreasing daily loads, to produce the load duration curve. This load duration curve displays the number of days of the year for which the daily average load is greater than a particular level. Within-day variation would of course display an even greater range of demand on an hourly basis. In Figure 1.6, this same data series, expressed now in hourly intervals, thus displays the hourly load duration curve (note the points on the horizontal axis are now re-expressed as a percentage of the 8760 hours in the year).
For example, it is apparent that for 5% of the year the hourly loads are greater than 43 GW. In other words, if you owned a peaking plant, the running costs of which were so inferior that there was 43 GW of capacity on the system that could be offered more cheaply to the market, then you would only expect to run 5% of the time, which is to say that the "load factor" of this plant is only 5%. Obviously, it is only worth keeping this as an investment if you can gain a substantial margin over the running costs. So, it is easy to see why, in an imperfect market, prices become spiky at the peaks.
In order to fix our understanding of the fundamental economics of the capacity mix, we proceed with a simple example. In Table 1.1, we have assumed a simple set of costs for four technologies, and let us presume an idealised situation where we can design the optimal capacity mix from these four alternatives in order to serve the above-mentioned load duration curve. We would expect nuclear to be baseload, and the open cycle gas turbines (OCGTs) to be peaking; coal and combined cycle gas turbines (CCGTs) will be somewhere in between ("mid-merit"); but how much of each we need is not obvious.
A simple concept is to look at the annual costs of owning and operating a unit (e.g. 1 kW) of each technology. The initial investment cost can be spread over the life of the plant by converting it into an annual annuity using the usual discounting formula, with an assumed cost of capital. This annual annuity value can then be considered the fixed cost of ownership per year. In other words, if you had to lease the plant from an owner, this is the annual rent that would just recover the owner's investment at its cost of capital.
The annual operating cost is the fuel cost multiplied by the number of hours the plant operates in the year. Thus, at a 5% cost of capital (which was the case for pre-liberalised, public sector utilities), for two technologies, we get the annual break-even functions shown in Figure 1.7. We can see from this break-even chart that, under the assumptions of Table 1.1, a coal plant needs to run for more than 4000 hours per year to be a better investment than a CCGT. So, if we were just using these two technologies, how much of each do we install?
In Figure 1.8, we see how this break-even analysis can be projected onto the load duration curve to give the amount of each technology in the cost-minimising capacity mix. With just coal and CCGT, coal would be the baseload, to the extent of about 34GW. With all four technologies, we get the break-even analysis of Figure 1.9. Thus, nuclear provides the baseload in an era of public ownership and access to low costs of capital (but if we went up to a "market" rate of 11%, there would be no nuclear or coal in the optimal mix, just gas CCGT and OCGT, as the higher cost of capital penalises the capital-intensive alternatives). However, staying with these 5% cost of capital results, for the purpose of illustration, after projecting these onto the load duration curve as above, we get a capacity mix of 65%, 4%, 16% and 15%, for the nuclear, coal, CCGT and OCGT technologies.
Figure 1.10 displays this capacity mix in terms of the stack of marginal costs, i.e. the supply function, which this simple system provides. The shape of the supply function is one of the most important fundamentals in understanding the behaviour of electricity prices. It displays the marginal cost of supplying power at a particular level of demand. Evidently, to the extent that market prices are efficient and reflect short-run marginal costs, this is a nonlinear driver of prices, depending upon demand in a particular hourly period.
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