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Over the last decades, the United States and other countries have begun a transition from the provision of energy by vertically integrated utilities toward the competitive provision of energy by "unregulated" generation entities that deliver their energy on transmission and distribution systems that have remained regulated or state owned. Serious problems have occurred in restructuring, as readers in California and elsewhere will attest. Nevertheless, the general principle of separating the generation of energy by competing "GenCos" from its delivery by transmission and distribution companies is a minimum requirement for avoiding the inherent conflict of interest between vertically integrated utilities and competing generators. (I should point out that even this minimum requirement has not been achieved in many restructured electricity markets, "Chinese-walls" and "affiliate rules" notwithstanding.)

However, this minimum requirement is still insufficient in a number of dimensions. For example, energy is not the only "commodity" in the electricity system. In addition to energy-related commodities such as reserves, all power engineers know that reactive power is an essential part of production and delivery of real power.

In the balance of this article, I will focus on the planning for and operation of reactive power resources in restructured electricity markets. Again quoting the Task Force, "[m]arket mechanisms should be used where possible." A threshold question to address, therefore, is whether market mechanisms should be used not only for real power but also for the procurement of reactive power.

As shown by Hogan, when there are limitations on the availability of reactive power in the network, the resulting constraints on dispatch options can drive up the price of real power. That is, the value of reactive power can sometimes be very high and limits on production of reactive power can produce high market prices for energy.

Turning, however, to the cost of providing reactive power, we must recognize an important distinction, articulated in both the technical literature, such as Nedwick et al. (see "For Further Reading"), and at least in principle in the Federal Energy Regulatory Commission's open access tariff provisions in Order 888. Reactive power is provided, on the one hand, by capacitors, which have low purchase costs, typically provide relatively coarse control of steady-state reactive power production, and have nearly zero operating costs. On the other hand, reactive power is also produced by generators and static VAr compensators, which are much more capital intensive, have fine control of reactive power production, can respond dynamically to contingencies, and that have some operating costs due to losses.

Based, in part, on these distinctions, Nedwick, Mistr, and Croasdale of Virginia Power advocated in the mid-1990s a philosophy of installing enough reactive support so that distribution feeders have a net unity power factor or are even slightly leading at low loads and so that transmission system steady-state reactive power is essentially all provided by transmission system capacitors. While reactive compensation is used extensively by most utilities, this philosophy goes further by coordinating generators and nearby transmission system capacitors to ensure that generator power factor is close to unity under normal conditions, with voltage profiles maintained fairly flat across the system and despite varying load conditions.

In summary, under this philosophy, generator reactive power is used to "fine-tune" voltage profiles and dynamic response is used to provide reactive reserves. Capacitors nearby to generators are switched to maintain generator power factor close to unity under normal conditions. This philosophy is consistent with the Outage Task Force recommendations.

There are several excellent reasons behind this philosophy, both operational and in support of market operation. The reasons include better response to contingencies, better utilization of generation and transmission equipment, and better conformity to "commercial models" of the transmission system. I will outline these reasons in the following paragraphs.

Consider a generator operating at 0.9 power factor to produce both real and reactive power in steady-state. For each kW of real power it produces, it also produces about 0.48 kVAr of reactive power. Consider the construction cost of capacitors to provide this reactive power. The installed cost of switched capacitors is on the order of $10/kVAr, so 0.48 kVAr would cost about $4.80. Assuming, very roughly, a power station construction cost of $500/kW, the steady-state reactive support provided by the generator could be provided by capacitors at a cost of about 1% of the cost of the generator.

Since there are limits on the joint production of real and reactive power, the construction cost ratio between capacitors and power stations strongly suggests that it is likely to be cheaper on average to provide steady-state reactive power by installing capacitors than by installing a new generation plant. This is because operating a generator away from unity power factor is likely to limit its real power output, at least at peak, decreasing the overall capacity factor for the generator. For example, for a generator operating at 0.9 power factor and at its stator thermal limit, each extra kVAr of reactive power it produced would decrease the amount of real power it could produce by about half a kilowatt.

Moreover, a double problem occurs under contingency of a generator providing both real and reactive power. First, real power provided by spinning reserves will typically increase the loading and reactive losses on the lines. And, just as the reactive demand in the system increases due to increased line loading, the reactive power production from the outaged generator falls. Using a generator to provide steady-state reactive support means that other generators must be available to provide reserves if that generator trips. Joint production of energy and steady-state reactive power by a generator imposes a much greater contingency burden on the system than a generator operated at unity power factor.

Given the relatively low construction cost of capacitors compared to power stations, a reasonable rule of thumb is that generators should not provide significant reactive power in steady-state even at peak conditions. It is well known that reactive compensation can improve the loadability of transmission lines. The above example also shows that the real power generation capacity of generators can be better utilized when the reactive burden is lower. Anecdotally, merchant generation owners in the United States often complain that they are unfairly burdened in the production of steady-state reactive power. The above example suggests that capacitors are likely to be a cheaper way to provide steady-state reactive power.

In advocating that generators provide reactive reserves but not significant steady-state reactive power, I recognize that this might still require them to forego some opportunities for sales of energy under normal conditions. This is analogous to the way in which providing energy reserves also limits the amount of energy that can be sold. However, the particular characteristics of reactive generation enable a finessing of this issue. In particular, if there is sufficient switched capacitive support available, there will only be a short-term need for large reactive production from a generator in response to a contingency.

Significant reactive production by a generator in response to a contingency entails increased rotor and stator losses, potentially necessitating increased coolant pressures. If these increased losses are required only over a short period, however, then suitable "emergency" ratings could be used. That is, a generator with some short-term overload capacity can be operating at close to its steady-state real power capability under normal conditions. It can also stand ready to generate both real and reactive power to respond to a contingency, if switched capacitors are available to quickly restore the generator to close to unity power factor. To summarize, from a technical perspective the low cost and coarse control of capacitors complements the high cost, fine control, responsiveness, and overload capabilities of generator reactive production.

A fundamental question is how to incent generators to provide reactive power in a market setting. Given the potential gap between the value of reactive power and the cost of providing better reactive support, there could be a significant opportunity cost from reactive power constraints. Ideally, we would like to provide incentives for efficient investment in reactive power support. There are several proposals for reactive power markets, including Baughman et al. and Hogan in the "For Further Reading Section," fundamental difficulty with reactive power markets, however, is that because reactive power does not "travel" far, there would be extreme local geographical market power in the provision of reactive power. The local market power in reactive power could be much worse than the market power in real power markets today.

The exercise of such market power in reactive power markets and its effect on energy prices can be interpreted in one of the examples in Hogan's article, where a generator withholding reactive power at its bus forces the price for its real power to be extremely high. Provision of reactive power at the generator bus reduces the prices significantly. However, using a market mechanism to acquire the reactive power from the generator would require strong market power mitigation, since limiting reactive power production enhances its market power in the energy market.

This example is couched in terms of steady-state reactive power production. However, as argued above, the steady-state reactive production can be very cheaply provided by capacitors. Moreover, given that capacitors are likely to be bought and maintained by the regulated transmission provider, a market for steady-state reactive power would be fraught with conflicts of interest between transmission providers and generators.

On the other hand, reactive reserve can be the limiting constraint. Again, for the same reasons as applied to steady-state reactive power, reactive reserve markets would be problematic. A workable alternative may be interconnection standards with, for example, regulated cost-of-service remuneration for provision of reactive power reserves.

Finally, I will turn to commercial models. Most commercial models in electricity markets in the United States rely on the "DC powerflow" approximation, which assumes that reactive support is sufficient to keep voltages at one per unit. Under the assumptions of constant voltages and moderate loading, the real power flows on lines in a network are well approximated by superposition of power flows. This linearity allows a convenient representation of transmission constraints that facilitates market clearing mechanisms. To summarize, voltage support enables linear models to be used for market clearing in commercial models for real power markets.

When the voltage support is insufficient or for other reasons the linear approximations fail, or when market forces have insufficient time to respond, we should expect that normal commercial operations of the market will not be effective. Such conditions could be used to help to define when normal market operations based on linear approximations are to be suspended and when independent system operators resort to command and control, rather than market forces.

Putting the reactive power philosophy of Nedwick, Mistr, and Croasdale of the mid-1990s together with the energy markets of the mid-2000s requires transmission and distribution providers to install sufficient capacitive compensation and to coordinate switching of capacitors to maintain unity power factor from generators and unity power factor loading from distribution feeders. NERC planning standards should support this policy. Interconnection standards should recognize the value of reactive reserves from generators and avoid leaning on them for steady-state reactive power. Finally, achieving a flat voltage profile allows the commercial model to work effectively. Reactive power deserves careful policy attention in the ongoing process of restructuring electricity markets.

Acknowledgment

For Further Reading

M.L. Baughman and S.N. Siddiqi, "Real-time pricing of reactive power: Theory and case study results," IEEE Trans. Power Syst., vol. 6, no. 1, pp. 23-29, Feb. 1991.

W.W. Hogan, "Markets in real electric networks require reactive prices," Energy J., vol. 14, no. 3, pp. 171-200, 1993.

E. Kahn and R. Baldick, "Reactive power is a cheap constraint," Energy J., vol. 15. no. 4, pp. 191-201, 1994.

P. Nedwick, A. Mistr, and E. Croasdale, "Reactive management: A key to survival in the 1990s," IEEE Trans. Power Syst., vol. 10, no. 2, pp. 1036-1043, May 1995.

U.S.-Canada Power System Outage Task Force, "Final report on the August 14, 2003 blackout in the United States and Canada: Causes and recommendations," Apr. 2004.

United States of America Federal Energy Regulatory Commission, "Order number 888 final rule," 75 FERC 61,080, Docket Number RM95-8-000 and Docket Number RM94-7-001, Apr. 1996.

A.J. Wood and B.F. Wollenberg, Power Generation, Operation, and Control, 2nd ed. New York: Wiley, 1996.