Power plants can bid on more than one product. That's why most spark-spread studies miss the mark.

Forward energy prices can make it look easy to place a value on a power plant. Yet something is missing. Plants can sell more than one product. One price may be up while another is down. As Einstein said, a theory should be as simple as possible, but no simpler.

That is why it is worth reexamining the methods commonly used to calculate forward price curves and estimate the expected revenues and profits of generating assets.

First, do the relevant calculations include all products that the asset's revenue will depend upon? Do they meaningfully incorporate those rare events having large price effects over an extended time horizon? These questions go to the heart of whether a method is either appropriate or adaptive to asset valuation in the future electricity market.

When the forward price curve is focused solely on energy, the assumption is made that generators would passively accept whatever price the forward energy market offers, exclusive of other markets. In practice, a generator operator will seek to maximize income by seeking profits and advantage across all available markets. In order to reveal the full earnings potential of the asset, valuation must also include the revenues that operators might earn by participating in the lucrative ancillary service and spot markets. The price risk that characterizes power markets is too considerable to suppose that market participants will not continuously compare the levels of profit potentially available in the various product markets.

Black's Model: Not Practical for Multiple Bids

The most commonly used method to analyze forward prices is relatively simple in concept. To determine the earnings potential of a base-loaded unit like a combined cycle (CC) unit, the NPV (net present value) of the spark spread (the difference between the forward price and the variable operating cost of the unit) is calculated and aggregated over its lifetime. For cycling units like combustion turbines, the calculation is similar to that used for the CC, except that an annual price duration curve is occasionally used to capture the cycling behavior of the unit. The price duration curve allows a quick appraisal of those hours during which a CT can and should profitably operate; a CC is assumed to serve base-load capacity at all hours, less those lost to outages, due to its lower costs. In either case, the method by which the forward price curve is obtained is the key to the investment decision.

In attempts to develop forward price curves, some projections use an analysis based on a type of Black's model, used to value options. That can prove wanting, however.

While the past may be used as a guide to the current behavior of standardized commodity prices, the electricity market is distinguished by its current evolution and its tremendous short-term, intra-hour volatility. Historical methods lack justification in that they do not meet the two conditions put forth earlier - inclusion of potential revenues from multiple products and markets, and incorporation of rare events causing price spikes.

The period in which energy was a monolithic product is past. Recently, the California Independent System Operator (ISO), plus ISO-New England (the former NEPOOL) and PJM Interconnection LLC, have established more clearly than ever before a distinction between energy, ancillary services and reserve capacity products. These new product markets, as well as the spot markets in energy, offer alternative sources of revenue to the forward energy market. Their prices will depend on the energy market, and vice versa, with the exhaustion of arbitrage opportunities acting nominally, at least, to constrain unlimited inter-market basis differences.

By contrast, the historically derived analyses are necessarily based on scant data and are faced with a lack of liquidity in multiple markets. Black's model, to incorporate ancillary services, would require analyzing liquid futures in multiple commodity markets, not just those in energy. Moreover, those commodity prices and quantities that would characterize liquid energy and ancillary services markets would be highly correlated, whereas Black's model is not capable of application across multi-product markets.

Price Spikes: Not Captured

in Most Methods

As concerns price spikes, an historical model can not capture the supply-demand equilibrium in electricity that forms instantaneously yet changes continuously, and so introduces the characteristic volatility of spot or imbalance prices. (Given the variety of factors that affect electricity prices, even the spark spread, or basis difference between prices of gas and electricity, fluctuates with unpredictable frequency and magnitude.) The factors behind price spikes, and the concurrence of extreme, unpredictable events in terms of precise weather, system outage patterns, and/or demand conditions are not likely to follow historical occurrences. Thus, deriving a future dependency through regression is full of uncertainty, and invites the superposition of one source of volatility upon another.

An alternative to the historical approach merits attention, for the strengths it offers in the same areas in which historical projections suffer their most serious weaknesses. A Multi-product, Multi-area Optimal Power Flow (MMOPF) model with real-time dispatch is a structural model that incorporates generation, load and transmission data into a dynamic simulation. Such a structural model is required to simulate the hourly price fluctuations, and to ascertain how the uncertain distribution of the fundamental price drivers affects the price distributions among markets. (A description of such models can be found in "Forecasting Energy and Ancillary Prices and Asset Evaluation," a monograph published by my company, LCG, Los Altos, Calif.) An MMOPF model performs these analyses by its fusion of the technological characteristics of plants, their operational choices and market eligibility, and by incorporating the system constraints that affect the real-time dispatch of generating units. Fuel prices, demand fluctuation and emergency outages are some of the elements that are combined with overall system conditions within a structural model.

As for the introduction of new technologies, valuation with a structural model also can project the actual market participation by a unit, given its relevant characteristics and bid parameters. The range of product markets available to combustion turbines is especially broad, and thus, ancillary services will make up a relatively larger portion of overall revenue than they will for other generators. Even if a plant is only able to provide energy, its valuation needs to take into account the interaction of prices in forward, spot and ancillary services markets. A structural model makes possible volatility analysis, which captures the systematic effects of key driver distributions and interactions. By running multiple scenarios based on Monte Carlo sampling of the distributions of fundamental market drivers, one can obtain the volatility distribution of both energy and ancillary service prices. The drivers' distributions are changeable, given new information or a need to explore scenarios under changed conditions.

Whereas a time-series model will not be able to account for the occurrence of price spikes, a structural model can derive a reasonable estimate of their likelihood, given the coincidence of less likely values among key drivers over multiple scenarios. For a long-term structural simulation, the number, severity and duration of price spikes will all result from the other system conditions encompassed by the model. Indeed, price spikes may provide crucial revenue to enable a plant's profitable operation. In asset valuation, insights into these phenomena can prove decisive.

Most importantly, a structural approach offers the ability not only to capture the prices in the electricity markets based on rational bidding by participants, but incorporates the dynamic interaction of prices in the various markets.

A Case Study:

Simultaneous Bidding in Multiple Markets

Consider an illustration of the impact of earning revenues from multiple product markets. I use an MMOPF-type model to derive the revenues of a CC unit and a simple-cycle CT unit whose characteristics are displayed in Table 1. The study will compare asset valuations based only on the forward price curve of energy against what the units could earn if they are bid simultaneously on other products in the ancillary services and spot markets. The model outputs used are prices for energy, regulation up, regulation down, spinning and non-spinning reserves, replacement reserve and real-time. The prices for these multiple products are displayed in Table 2 and compared graphically in Figure 1 for all the hours in a particular day.

What happens if plants bid only on one product, in the day-ahead market for energy in the power exchange?

ENERGY ONLY. First, the forward curve is used to derive purely forward energy market-based revenues. Note that from Table 1, the marginal cost of the CC is $15.07. In the day-ahead PX market, a bid of $0 will allow the generator to be dispatched in every hour, and obtain revenue over marginal cost in most hours. It is better for the generator to incur a small loss for a few hours than to pay the additional startup cost that would be necessitated after shutting down briefly. According to the overall market-clearing operations, and as indicated in Figure 1, the price of energy will be above the CC's marginal cost for 21 hours. Thus, the CC will earn an income of $181 per megawatt-day, taking into account the different prices in each hour and the possible marginal losses from operating in those few hours when marginal cost exceeds the PX price.

The daily income changes with forward prices. In our case, the total income over the initial and subsequent years adds up to $78,277 per megawatt-year. The NPV of the income generated over the unit's lifetime is $638 per kilowatt. The corresponding numbers for the CT are $94 per megawatt-day, $29,333 per megawatt-year and $177 per kilowatt, respectively. These earnings are based on the expected annual earnings for the unit, taking into consideration the impact of outages, seasonal price volatility and operational costs.

Now what about a strategy that involves multiple bids on multiple products?

ANCILLARY SERVICES. A CC plant, when equipped with automatic generation control, or AGC, can participate in the market for "regulation," one of the various ancillary services. If selected for regulation, a unit is paid one price to maintain available capacity; the ISO then dispatches the unit as needed and pays a second price for the hours that the unit actually supplies regulation service. In California's current market, the payments for availability are not withdrawn when a unit is paid a second price for dispatch. Rather, the two payments overlap.

To develop simultaneous bids for these multiple products, the unit operator needs a set of expectations regarding the prices from the energy and ancillary services markets like those in Figure 1. A bidding strategy takes into account the maximum possible profit based on expected prices in various markets within each hour, as given in Figure 2.

Glancing from the profit trend in Figure 2 to Figure 1, one will see that the generator's highest expected profits during the early and late hours of the day lie in the regulation up market. During peak hours, the higher PX energy prices promise the most profit.

In addition to the income from energy and regulation up availability, Figure 2 displays a potential revenue trend called "supplemental real-time income." That term indicates the net income that would result whenever a generator was required to supply energy by the ISO. The hourly income is given by the hourly real-time energy price, which is what the generator receives, less marginal cost. The dispatch revenue is called "supplemental" in this discussion because the ancillary service reserves the unit, but cannot guarantee energy production in terms of capacity or duration of operation. It therefore carries some uncertainty.

If the CC unit in the example were dispatched for real-time energy during the hours when it is supposed to provide ancillary service, a net loss could be incurred during the early hours, while positive net revenue would be earned in the latter part of the day. Since the proportion of the generator's capacity that can be dispatched for ancillary service purposes is a part of (never more than) the total capacity secured through availability payments, the availability payments will have greater magnitude than dispatch income in the overall profit calculation. The percentage of capacity that actually will be dispatched will vary according to the type of service and fluctuation in the need for it.

How should a bidding strategy balance the various simultaneous profit opportunities in multiple product markets?

BALANCING PROFIT POTENTIAL. The operator of this unit needs a bidding strategy that will result in a uniform expected level of profit, whichever market accepts him. The rationale behind this condition is the optimization of income, assuming indifference to the origin of profit. Given the expectations summarized in Figures 1 and 2, the operator develops bids that position the generator as a price-taker in the most profitable market during each hour. Clearly, the priority for an AGC-equipped generator would be to enter the energy market at peak hours, and to be scheduled for regulation availability during off-peak hours. A generator unable to serve regulation would need to consider the next most profitable market after regulation, spinning reserve, if the generator were capable.

In the off-peak hours, the bids into the regulation up market would be the expected energy price less its marginal cost (as regulation carries no marginal cost). His regulation bids are low enough to have a high likelihood of acceptance. Thus, he stands to make no less from regulation than the expected energy market profit.

As explained, the operator should bid to insure the same profit across markets, that is, whatever the most profitable market promises. The corresponding hourly bid into the PX for energy should be the marginal cost of delivery plus the expected regulation profit, which is regulation's expected price.

BIDS AND EARNINGS. Suppose the operator expects the clearing price for regulation availability will be $10.00 per megawatt-hour. The marginal cost of the CC in our example to supply energy is $15.07 per megawatt-hour, so to equalize his profit across markets, he bids $25.07 per megawatt-hour (= $15.07 + $10.00), into the PX. Thus, a minimum profit of $10.00 from energy would result from acceptance, commensurate with the profit expected through regulation.

During peak hours, when energy is expected to offer the highest profit, his bid into the forward energy market is the expected regulation price (also the expected regulation profit) plus the marginal cost of generation ($15.07). The rational bid for regulation is the profit expected from energy, or the anticipated energy price less the marginal cost (again, because regulation carries no marginal cost).

On the basis of its bidding strategy, the AGC-equipped CC in this example is scheduled for dispatch in the energy market for 11 consecutive hours, 9 through 19. For the other 13 hours of the day, it is scheduled for regulation up availability, and will be running at a minimum level, to be dispatched as needed by the ISO. The profit that the unit makes in each market is calculated below.

The resultant energy earnings are the summation of the difference between the market-clearing PX energy price and the marginal cost for the 11 hours just stated, times 400 megawatts (the unit's capacity). The earnings for regulation up availability are given by the summation of the market-clearing regulation up prices in hours 1 through 8, and 20 through 24, times 400 MW of capacity accepted. Dispatch by the ISO for regulation will supplement the income. For the revenue calculation in this example, 40 MW is needed during all 13 hours of regulation, and the real-time energy price is paid per megawatt-hour. Thus, the revenue from real-time dispatch for regulation can be calculated as the summation of differences between the real-time energy prices and marginal cost for the 13 stated hours of dispatch, times 40 MW.

The income the unit has achieved after bidding into the PX and ancillary services markets is $310 per megawatt-day. These results are summarized in Table 3. The daily and annual earnings and the NPV over the lifetime of the unit are given in Table 4.

In the case of the combustion turbine, the bid for energy is marginal cost plus the clearing price of non-spinning reserve prices. From Table 3, one can see that the unit participates for 10 hours in the energy market and for 14 hours in the non-spinning reserve market. The daily and annual net incomes are illustrated in Table 4. The net present value represents the summation of these values over the lifetime of the asset. Note that the unit earns $246 per kilowatt, rather than the $177 per kilowatt shown in the case of conventional analyses.

A comparison of the two units' valuations, the first based on energy alone and the other on multiple product bidding (shown in Table 4), suggests the sort of error that one invites with historical projections based on energy. These examples show that with a rational, profit-optimizing approach such as that outlined, a generator can gain access to greater overall revenues. The simplistic assumption that, over its lifetime, a unit will participate in the energy market and may even receive some capacity charges may underestimate its potential income. In California, New England, New York, PJM and Ontario, there is a definite advantage to participating in ancillary service and spot markets, where active ancillary services and real-time imbalance bidding is in place.

Regional Markets: All Equally Friendly?

The task of asset valuation requires attention to the type and structure of ancillary service markets in the relevant region. For instance, ECAR does not have a bidding system for distinct ancillary service products, but is divided between energy and capacity payments. Even in California, the operation of ancillary services markets thus far has seen fewer bids than are necessary to meet ISO requirements for ancillary services, and has removed some supply-side incentive to broader participation through the imposition of price caps. Despite the progress that lies ahead in the emergence of liquid ancillary services markets, generators' operational characteristics and their competitive positioning in providing various products require attention, as the price of energy is insufficient to provide an estimate of a generator's worth. If it alone is used in revenue forecasts, such forecasts are likely to make generators with different technologies appear more similarly profitable than they actually may prove to be. As operators gain insight concerning the prices prevalent in a particular market, their minimum requirements for return from other markets inevitably will cause dynamic price changes. For different generator technologies, the various price fluctuations will affect the temporal bidding profile they adopt.

While the forward price curve of electricity may have been appropriate for an environment dominated by regulatory price determination for a single product, it needs to be augmented in order to conduct strategic planning in the emerging competitive environment. The model based on single-commodity pricing necessarily ignores the possibility for generators' strategic, multiple product bids and the timing of units' dispatch opportunities, linked to startup costs and minimum run duration. In sum, the old approach leaves the income from ancillary services and supply imbalances out of the resultant valuation entirely. Hence, a structural model with the ability to capture price volatility and dynamic interaction for all products is needed to provide an internally consistent set of price curves, and base the earnings from respective sources on the dispatch. In this way, we now can provide a comprehensive assessment of generator value that properly incorporates multiple products and markets.

Dr. Rajat Deb is president of LCG Consulting, which conducted the first restructuring study commissioned by the California Energy Commission, using UPLAN, a multi-commodity, multi-area structural model with optimal power flow. Based in Los Altos, Calif., he can be contacted at deb@energyonline.com or 650-962-9670.

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