The California Power Exchange doesn't solicit separate bids for plant start-up, spinning reserve or base load operation. That can make spark spreads a bit misleading
IT SHOULD COME AS NO SURPRICE THAT THE PROSPECT OF electric competition has created a huge demand for price forecasting services. To their credit, the forecasters have obliged, supplying an abundance of tools and techniques. Do the forecasts serve the needs of those who would use them?
Some might wish to use a price forecast to assign a value to assets. They may wish to buy some of the many generating plants that utilities have decided to sell as part of a settlement to allay stranded costs of alleged market power. Ordinarily, a plant's value reflects the income stream it will produce. Forecasting that income requires an estimate of both market price and the plant's production profile. Moreover, any useful forecast must take volatility into account. It has been argued empirically, in fact, that electricity shows more volatility than other markets, including other energy markets.
Unfortunately, however, real market prices are much more complex than the simple supply-and-demand diagrams of elementary economics texts. Yes, supply and demand remains important, but so are the details of market structure. And in the newly evolving electricity markets, structure is still in question. Valuation becomes especially difficult, for example, when the assets in question are the very units that, when bid into the market, actually help set the prevailing price. To know the price requires, at the very least, that we know the market rules.
The problem begins with the separation of prices from costs. Not all models make this separation. Those that do not typically will set a price at the short-run marginal cost, or SRMC, also known as incremental cost. For competitive electric markets, however, SRMC pricing is incorrect. It is not consistent with the economic reality of the steam-fired generators that set electricity prices most of the time. These generators exhibit average costs that typically run higher than incremental cost. In the world of regulation, SRMC pricing was efficient, because someone (usually the ratepayer) would pick up all those other nonvariable operating costs (perhaps in a fuel adjustment clause). Under competition, however, prices must recover those costs since there won't be a fuel adjustment clause. Consider how this problem is addressed in the pricing rules used in the market for England and Wales.
The market operator in England and Wales takes bids from suppliers that include three different cost elements, representing three types of plant operation:
1. Base Load. Reflects incremental operating costs only (SMRC), excluding costs for plant start-up or costs to maintain inefficient production at low output levels during no-lead periods.
2. Peaking Capacity. Reflects start-up costs for immediate dispatch during high-load hours.
3. Spinning Reserve. Reflects both start-up and no-load costs (SUNL) - i.e., including the costs of inefficient production at low output levels.
The operator then runs a standard unit commitment program to determine which bids minimize total costs. Then the operator must mark up the price for base load capacity that operates during the high demand hours (known in England and Wales as the Table A period) to recover the start-up and no-load costs incurred by all accepted bidders (see Figure 1).
Figure 1 illustrates this fundamental point. This figure is taken from the results of a modern production simulation model. It shows the prices that would result for the same dispatch depending upon which costs need to be recovered. Three cases are shown. One is just SRMC. The second series recovers only start-up costs (in high-load hours). The third recovers both start-up and no-load costs, i.e. the costs of inefficient production at low output levels.
Nevertheless, the E&W market rules have not been universally accepted. In both the California Power Exchange and the Australian electricity markets, the burden of bidding prices that recover start-up and no-load costs falls to bidders. The market operator will not do it for them. This rule is called "single-part bidding," to contrast it with the multiple part bids in the E&W market. If we want to forecast prices in markets that employ single-part bidding, our models must take these rules into account.
Forecasting prices is difficult in markets that employ single-part bidding. Even if a model can allow the user to specify a bid that differs from incremental cost, figuring out what the equilibrium bid strategies will be and simulating them is difficult. Most forecasters don't do this very well, even if they try. Our case study will show us why it is so difficult.
The Option Value in Dispatch
Units that serve intermediate loads (or mid-merit in English terminology) are very different from base load units. The latter can be valued largely on the basis of expected prices. For units that are marginal, the majority of value is option value. That means that the money lies in knowing when to exercise the option to operate. The decision to operate, however, depends upon the distribution of prices - not just on the expected, or average, value of the price.
Table 1 shows two different price structures with the same average, or expected, value, namely $20. The price structure difference between Case 1 and Case 2 is that Case 2 shows a lot of variation; half the time the price is above average and half the time it is below average, while the prices in Case 1 are flat. In Cases 1 and 2 the plant operates all the time, as if it were baseload. In both cases we just break-even. In Cases 3 and 4 we still consider the varying price structure, but we now imagine that the plant is flexible and consider how to operate to maximize profit. In Case 3 we assume perfect flexibility. The plant is operated only when it is profitable. Case 4 represents operating flexibility, so we are only able to turn the plant off half the time that it is unprofitable. These simple examples show that exercising the option to operate or shut down is the key to profitability for mid-merit plant, and that profits can be limited by operating constraints.
What's Hidden by the Averages
Now let's turn to some real valuation experiences. Consider the case of gas-fired steam generation operating in a market based on single-part bidding rules. These units typically have incremental heat rates of 8,000 to 9,000 Btu/kWh, but average heat rates of more than 10,000 Btu/kWh. The reason for the high average heat rates is start-up and no-load costs. The customer who wants to value these units goes to a market price forecaster and says, "Give me some forecasts." Figure 2 is representative of the simulations a customer receives.
These prices are expressed in "spark spread" or market heat rate units, i.e., the electricity price divided by the gas price. The figure shows 24 hourly prices for each day of a "typical week" in a month. Market heat rate units are convenient for profitability analysis because they can be directly related to costs for any gas price. For ease of understanding, I have colored the prices in heat rate bands. (I refer to this scheme as the USA Today weather map of prices, a concept that should be familiar to business travelers.)
Now Figure 2, appears similar to Cases 1 and 2 in Table 1. Both forecasts have the same average value. In Figure 2, the average value is about 8,800 Btu/kWh (see the last cell at the bottom of the "Average" column on the right of each panel). One forecast (Fig. 2, Case 1) exhibits a lot more variance than the other did. I point out this difference to the vendor of the forecasts. He calls me back to say that the "smooth" one is correct (Fig. 2, Case 2) and that the other one is wrong. I thank him for his response. I wonder if he would have bothered to tell me if I hadn't asked.
Next I start to do my valuation. Here I am back to the case depicted in Figure 1, not Table 1. The cost structure of the marginal plants includes the start-up and no load costs (remember average heat rates are higher than incremental rates, a fact that is suppressed in Table 1). I know that the plants that I am valuing really can set the market price sometimes (notice that in the Table 1 examples for Cases 3 and 4 they never set the price). So if I am bidding these plants, and I know I can set the price sometime, I need to get my start-up and no-load costs back or I am losing money. If we were to generalize the Table 1 examples to include start-up and no-load costs, then these would have to be bid in prices. The profits estimated for Cases 3 or 4 would be reduced to account for these costs and the unit would have to bid the start-up, no-load costs in some way vaguely related to Figure 1. The unit probably would end up setting the market price at those bids some of the time.
Now in my real valuation problem, I am starting to get a little uncomfortable. If I have to get the start-up, no-load (SUNL) costs back, so does any other marginal generator. So it doesn't really matter if I actually set the price at a given time, because anybody else bidding a similar plant - and there are many similar plants - has the same problem. I look at my price forecasts again. The one that the vendor tells me is correct never has prices that recover SUNL costs - not for me or for anybody. How can this be correct?
Promising, but Still Unreliable
The forecaster in the example above has failed what economists call the incentive compatibility test. This is just a fancy way of saying that if the price formation process doesn't recover costs, it is not sustainable, i.e., it is not equilibrium. Now we never really know over what period of time profitability must be achieved. But if I have market price forecasts that aren't consistent with profitability of participants over some period, then capacity will be withdrawn and prices will rise.
This example shows what can happen when the supplier of a price forecast has not thought through the consistency of his story. When the forecaster is using a production simulation model, there is nothing that will force him to have a consistent story. The users bear the risk.
This example is not the end of the story, however. Defining an incentive compatible equilibrium in electricity markets is still a challenge. The dynamics of entry and exit play a role. The profitability criteria for staying in the market are difficult to observe. But at a minimum, the vendors need to provide better disclosure to the users regarding what they have assumed about the profitability of marginal plant. Conversely, the users have a responsibility to be sure that they know what the assumptions behind a price forecast are and that they are reasonable for the purpose at hand.
One could ask if there might be another path. If the production simulation models are so treacherous what other options might there be? Table 2 outlines alternatives.
One modern concept of equilibrium, taking both price and quantity into account, is called the supply function equilibrium. In this formulation, agents in a market have a cost function that they turn into a bid or offer function, which satisfies the equilibrium condition, namely it is a best response to the offer functions of everybody else. Sounds good. Too good to be true, unfortunately. Another more classical approach is the Cournot technique, which uses quantity strategies. These concepts are useful theoretical constructs, but they are very difficult to implement numerically. The efforts to date have been academic exercises that reveal interesting conclusions, but not reliable price forecasts.
For certain short-term trading problems, various statistical techniques can prove very useful and powerful (see Table 2). For products priced in connection with the various geographic centers in the current wholesale market (Palo Verde, COB, Mid-Columbia), statistical models can give both reasonable expected values by estimating the co-integration of price movements and taking account of mean reversion in price. More importantly, these pricing models yield the volatility estimates required for option pricing techniques, such as the famous Black-Scholes model or stochastic dynamic programming. This is an exciting area of current research and there are important techniques available.
In the current state of market development, however, statistical techniques have limited application to asset valuation. Forward curves are unreliable for longer periods of time; volatilities and correlations are unstable. For the brave-hearted, or those who are thoroughly disgusted with fundamental valuation methods, the statistical models are an alternative. Over time, as the markets broaden and liquidity deepens, they will get better. But right now, price forecast users in the asset valuation market are probably stuck with production simulation products. For these users, beware.
Edward P. Kahn is a vice president in the San Francisco office of National Economic Research Associates Inc. Over the previous decade he has held positions as senior scientist in the energy and environment division of the Lawrence Berkeley Laboratory, leader of LBL's utility policy and planning group, and co-director of the Program on Workable Energy Regulation (POWER) at the University of California Energy Institute, also located in Berkeley, Calif.
1 See, for example, D. Pilipovic, Energy Risk: Valuing and Managing Energy Derivatives, 1998, for some persuasive evidence.
2 The best modern papers in this genre are: For Cournot, S. Borenstein and J. Bushnell, "An Empirical Analysis of the Potential for Market Power in California's Electricity Industry," University of California working paper, 1996, and J. Bushnell, "Water and Power: Hydroelectric Resources in the Era of Competition in the Western US," 1998; For SFE, R. Green and D. Newbery, "Competition in the British Electricity Spot Market," Journal of Political Economy, 100(5) 929-953, 1992 and R. Green, "Increasing Competition in the British Electricity Spot Market," Journal of Industrial Economics, 44(2) 205-216, 1996.
3 See D. Pilipovic, note 1, M. Hsu, "Spark Spread Options are Hot!" The Electricity Journal, v. 11, no. 2 (1998) 6-18 and V. Kaminski, "The Challenge of Pricing and Risk Managing Electricity Derivatives," The US Power Market, 1997.
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