CAPACITY SUBSCRIPTION AND SECURITY OF
SUPPLY IN DEREGULATED ELECTRICITY MARKETS
Gerard L. Doorman
SINTEF Energy Research
N-7465 Trondheim, Norway
August 2003
Abstract
In a restructured power system, investment in generation capacity is based on commercial
considerations. Because consumers mostly are not exposed to real time prices, this can result in
occasional shortage of supply. This paper proposes Capacity Subscription, based on the
theoretical concepts of Priority Service and Self-Rationing, as a solution to this problem. Some
time before actual consumption, consumers have to procure a certain amount of capacity.
Demand is limited to this subscribed capacity, but only at times when total system demand
exceeds available supply. This is done by way of a Load Limiting Device, which is activated by
the System Operator. With Capacity Subscription, consumers who want high availability will
buy much capacity to avoid having their demand limited. Consumers who accept occasional
limitation of demand can buy less capacity and save money. Based on demand for capacity from
consumers and supply by generators, a capacity market can be created. Demand for capacity,
and therefore also its price, becomes dependent on consumers’ preferences for uninterrupted
supply. Two solutions are presented on the problem of excess load relief, known from the
literature.
1.
INTRODUCTION
One issue on which power system restructuring solutions differ widely is the treatment of reliability. Power system reliability is associated with the system’s ability to provide an adequate
supply of electrical energy under all circumstances. This very broad concept is usually subdivided in system adequacy and security. Adequacy relates to the existence of sufficient facilities
within the system to satisfy the consumer load demand, which includes both generation, transmission and distribution facilities. Adequacy is associated with static conditions. Security relates to the ability of the system to respond to disturbances arising within that system.
In a traditional environment, system adequacy is controlled centrally with the help of welldeveloped engineering methods. These methods were used to ensure that quantities like the Loss
of Load Probability (LOLP) or Expected Energy Not Served (EENS) were kept within certain
agreed limits. This approach has resulted in power systems with very high reliability. However,
in a restructured market, generator owners’ profitability considerations replace traditional centralized planning of generation capacity. In this setting, it is no longer evident if and how system
adequacy can be controlled, and this results in a potential peaking power problem.
Ideally, according to the theory, the market should solve the problem. When supply becomes
scarce, prices increase and this limits demand to available supply as it does in most markets.
However, electricity is special because it cannot be stored economically. This implies that
supply must match demand continually. Moreover, pricing of electricity is special. Because it
cannot be stored, the price varies continually, and in many cases considerably. However, very
few consumers are exposed for these price variations. Instead, due to historical and practical
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reasons, consumers very often pay the same price, without regard to when they use electricity. A
step in the right direction is the Time Of Use (TOU) tariff, where the price of electricity varies,
depending on the kind of day (workday/weekend) and the time of day (day/night). TOU tariffs
give consumers some incentive to use less during peak load, but the tariff is not dynamic in the
sense that is makes sure that the market clears. As a result of the special pricing of electricity,
consumers have no incentive to reduce their own demand during extreme system demand, and a
shortage of supply may result.
A “shortage of supply” means that the market does not clear, and the only short-term solution is
to shed demand involuntary, which is an inefficient and socially unacceptable solution. Worse,
because of this inefficiency and, not at least, media focus in such cases, system operators appear
to be reluctant to use involuntary load shedding. The result of “waiting too long” may be largescale blackouts with potentially disastrous effects.
If one accepts that a market-design with only an energy spot market may not result in an
efficient outcome during extreme peak demand, several measures can be taken, although it is
not proved that such measures actually are more efficient from an economic point of view.
Some well-known examples of such measures are:
•
•
The former UK Pool, which included additional payment for capacity, based on Loss of
Load Probability calculations and the Value of Lost Load (VOLL).
The Capacity Markets in the Northeastern US. In these markets, the System Operator or the
regulator determine the total need for capacity, which is divided between Load Serving
Entities. This creates an obligation for the LSEs to provide this capacity, which they can
either provide themselves or buy from others. Because there will be both supply of and
demand for capacity, a Capacity Market can be established in such systems.
In neither of these solutions, demand for capacity is based on consumers’ preferences. In the
UK case, the capacity payment is based on VOLL, which results from questionnaires and
theoretical calculations. The Capacity Markets in the US are based on the anticipated need for
capacity, more or less equal to pre-deregulation systems.
As will be shown, with Capacity Subscription demand for capacity is directly based on
consumers’ preferences for uninterrupted supply. Consequently, the part of system reliability
that depends on the availability of generation capacity becomes market determined. In other
words, (this part of) system reliability becomes a private instead of a public good. Section 2 will
explain the principles of Self Rationing. Section 3 will take up some implementational issues of
Capacity Subscription. Conclusions are presented in Section 4.
2.
RATIONING OF EXCESS DEMAND
2.1
Rationing
One solution to the problem is full spot pricing, as described by Schweppe et al (1988). However, it would require a considerable infrastructure of hourly metering and sophisticated consumers to adjust demand continually according to varying spot prices. Moreover, by “spot
prices” in power markets, we normally think of some form of 24-hour ahead prices. To ensure
system security, it would be necessary for consumers to react on real-time prices, e.g. during
line or generation outages or unexpected surges in demand. The transaction costs of continuously following real time prices would be far too high, and as a result demand would not adjust
to varying real time prices. In this context, another problem with spot pricing is the possibility
of hedging. To avoid being exposed to large variations in spot prices, many consumers would
choose some form of fixed-price contract. As soon as they have done this, they are no longer
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exposed to spot price variations. In theory they could sell back the power they bought at a fixed
price when spot prices are high, but it is very doubtful if many consumers would actually do
this.
As an alternative to spot pricing, a specific form for rationing, Priority Service, was proposed by
Chao and Wilson (1987). In their paper, these authors argue that Priority Service can be seen as
a rationing scheme for curtailing excess demand in the case of deficient supply. From this point
of view, the concept of Self-Rationing, first introduced by Panzar and Sibley (1978), can be
seen as an implementation of Priority Service.
While earlier publication have discussed Self-Rationing in a traditionally regulated environment, Self-Rationing might also work as an element in the market organization for a competitive power system. This has two significant implications. Firstly, while Self-Rationing can be a
way to reduce costs in a traditional system (by reducing the need for peak generation capacity),
it can be a solution to solve the problem of potential generation deficiency in a competitive system, thus enabling a market solution without unacceptable supply interruptions. Secondly, in a
traditional context, the utility can set prices at whatever level that covers costs. In a competitive
system, prices are driven down to marginal costs. Unless optimal prices equal marginal costs,
the optimal solution is not reached by the market. This paper will propose two alternative solutions, one of which satisfies the requirement that optimal prices equal marginal costs.
2.2
Self-Rationing
With Self-Rationing each consumer subscribes to a particular level of capacity before actual
consumption. Uncertainty is originally modelled through the stochastic temperature variable t,
where a high temperature implies high demand, but could be interpreted in a more general way.
The consumer pays a capacity charge for the amount he subscribes to, and an energy charge for
actual consumption. If his usage exceeds subscribed capacity, a fuse curtails consumption above
the subscribed level. In a regulated environment, the task of the utility is to find the optimal usage ($/kWh) and fuse ($/kW) prices, and the optimal installed capacity. Panzar and Sibley derive optimal prices equal to marginal costs of production and capacity respectively, and optimal
installed capacity equal to the sum of all fuse sizes. They show that their scheme is ex post optimal under the assumption that the marginal willingness-to-pay function P(q,θ,t) where q is the
quantity consumed, θ customer type and t temperature (i.e. the stochastic variable), is weakly
separable in q and θ, i.e. can be written as P(h(q, θ),t). The behavioral impact of this assumption
is that consumers are similar in the way in which temperature (uncertainty) changes affect their
preferences.
A remaining problem is that of “untimely curtailments” when idle capacity exists, exemplified
in Panzar and Sibley (1978) by the “insomniac” blowing his fuse at 4 a.m.)1. Woo (1990) recognizes this problem, and proposes an innovative solution, by letting the utility activate the fuses
only when a capacity shortage occurs. In this context, the word “fuse” becomes confusing, and
it should rather be called a Load Limiting Device (LLD).
Limiting of demand implies comfort reduction or incurred costs for the consumer. The degree of
comfort reduction or the costs naturally depend on the limiting level. For a consumer who does
not buy capacity at all, the LLD, when activated, will limit demand to zero. In other words, the
consumer experiences a complete power interruption when the LLD is activated. Consumers
who accept this can be said to accept a low quality of supply. Other consumers may not be willing to accept interruptions at all. They would buy capacity close to their maximum demand, and
1
Basically the same criticism is given against demand charges in Schweppe et al., 1988 (pp. 69-71),
where it is stated that “Demand charges do not send good price signals”.
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have the maximum attainable quality of supply. It is difficult to know a priori which choice consumers actually would make, but it must be expected that, once they have to pay for it, consumers differ in their preferences for quality of supply. Self-rationing allows consumers to make different choices, based on their preferences.
Although devised for a traditionally regulated environment, the scheme of Woo may be attractive in competitive systems for a number of reasons:
•
Willingness to pay for capacity directly mirrors consumers’ preference for quality of supply.
Consumers with a low preference for quality of supply will obtain little capacity, resulting in
considerable curtailment when there is a capacity shortage. On the other hand, consumers
with a high preference for quality of supply will obtain much capacity, and will not be curtailed when there is a capacity shortage.
•
Capacity installation can be based on consumers’ real preferences, instead of surveys where
consumers answer hypothetical questions.
•
Quality of supply becomes a private good instead of a public good, and demand and supply
can be matched in an optimal way.
•
Introduction of demand for capacity enables the creation of a capacity market, where demand for capacity truly reflects demand for the real function of capacity, i.e. to ensure uninterrupted supply during all circumstances. If demand is high relative to installed capacity,
the price of capacity will become high, and producers can invest in peaking capacity. On the
other hand, if demand is low, e.g. because many consumers are satisfied with being curtailed
during shortage periods, prices will stay low, and no new investments are made.
•
Although definitely more complicated than an energy-only market, the transaction costs of
Self-Rationing as proposed by Woo are probably lower than for full spot pricing because
there is no need for real time metering.
Some comments on Woo’s paper are appropriate. Based on ex ante social welfare optimization
for the multi period case, Woo derives optimal prices equal to marginal cost for energy and capacity respectively, and optimal capacity equal to total capacity demand. The decisive difference compared with earlier contributions is the utility’s opportunity to control the LLDs. Consequently, it will not activate LLDs before demand actually equals capacity. Consumers anticipate this, and obtain capacity according to their expected demand when system demand is at its
maximum. Under the same weak separability assumption as Panzar and Sibley, Woo shows that
the scheme also is optimal ex post.
In spite of its innovative contribution, there are two reasons why inefficiencies remain in Woo’s
model, as pointed out by Doucet and Roland (1993). Firstly, marginal willingness to pay generally differs between consumers at the time of consumption. This means that once limited by
their LLDs, some consumers will be willing to pay more for additional consumption than others
and they would become better off if mutual trade was possible in some way. Secondly, although
the control of LLDs reduces this effect, some consumers will still be limited by their consumption while system demand is less than capacity, because consumers reach their LLD sizes at different temperatures. In Woo’s scheme, this situation is avoided through the property of weak
separability, which entails that all consumers reach the activation temperature tˆ at the same instant. As Doucet and Roland point out, in that case the possibility to control the LLDs is superfluous. However, the assumption of weak separability is unrealistic and consequently too strong.
In Doucet and Roland (1993) it is argued that the inefficiencies in Woo’s model can be reduced
by decreasing the use of LLDs, i.e. shortening the interval of temperatures over which LLDs
constrain demand. This can be obtained by increasing the price below the activation temperature
tˆ . A price above marginal cost will result in a new inefficiency. Prices and tˆ (which in this setting becomes a decision variable) should be chosen such as to minimize the total inefficiencies,
or more generally to maximize social welfare.
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The scheme of Doucet and Roland reduces, but does not eliminate the problem of too much load
relief. Furthermore, it will not work in a competitive market, because in this case it will not be
possible for a utility or a regulator to fix the price above marginal cost below tˆ because of the
effect of competition.
2.3
Excess load relief
The problem of excess load relief can be illustrated with the simple two-consumer case from
Woo (1990):
kW
q1+q2
Q
c1+c2
q2
A2
c2
q1
A1
c1
t1
t
t2
t
Figure 1 Illustration of self-rationing for a two-consumer case.
Figure 1 shows demand as a function of the stochastic variable t for two consumers 1 and 2 with
a subscribed capacity of A1 and A2 respectively. Consumer 1 with demand q1 reaches his limit
A1 at a value of t well below tˆ , the temperature where total demand equals installed capacity Q.
Up to this temperature, he is allowed to increase his demand, but at tˆ his LLD is activated, and
his demand is reduced to his fuse size A1. Demand of consumer 2, q2, is still well below his limit
A2 when t equals tˆ , so consumer 2 is at this point not affected by the activation of the fuses. Because consumer 2 has not yet reached his fuse size, total demand drops with an amount equal to
q1( tˆ )-A1, and there is an excess load relief of A2 - q2( tˆ ). In Woo’s scheme, this situation is
avoided through the property of weak separability (which entails that all consumers reach tˆ at
the same instant), but as already pointed out, this is an unrealistic assumption.
Two strategies to solve this problem are random allocation and optimal allocation according to
willingness to pay. Only a textual description of the strategies and their consequences will be
given. A mathematical derivation of the properties of each method is given in Doorman (2000).
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2.3.1 Random allocation of Excess Capacity
The System Operator’s main task is to control the continuous match between demand and supply (with the help of the real-time market) and to operate the transmission network. With random allocation, the System Operator randomly determines to which consumers empty capacity
is allocated. In practice this could be obtained by not activating all LLDs simultaneously, but
only a certain fraction, depending on the expected evolution of demand in the next hour or so.
Measures should be taken to ensure that allocation is truly (semi)random, to avoid that the same
consumers are limited each time this situation occurs. It is important to realize that the System
Operator does not need any knowledge of individual consumers’ real time demand to use random allocation, only of system demand.
From the System Operator point of view this is a pragmatic solution. It is clearly more efficient
to allocate excessively relieved capacity randomly than to leave it unused, even if it is not allocated to those consumers with highest willingness to pay. It can be shown (Doorman, 2000) that
this method is not economically efficient. Apart from the obvious fact that capacity is allocated
regardless of willingness to pay, optimal prices for this case, that would minimize inefficiencies,
are not equal to marginal costs, and the therefore the optimum will not be reached in a free market solution. However, random allocation may be a workable solution without much loss of efficiency in practice.
2.3.2 Optimal Allocation of Excess Capacity
An alternative to random allocation is to allocate the empty capacity to those consumers with
highest willingness to pay. This would ensure an efficient solution in real time for consumers
with activated LLDs. Of course this would require real time metering for those consumers. Once
this equipment is in place, one might ask why spot pricing should not be used. There are several
good reasons for this:
• Continuous spot pricing (8760, 17520 or even more periods per year) for all consumers necessitates the handling of enormous amounts of data. Spot pricing only when there is a capacity shortage reduces this amount to a fraction. Because of this, cheaper solutions can be
applied.
• Consumers may not be interested in spot pricing, but may value the option of being able to
buy electricity in excess of their ex ante obtained fuse size when a real shortage situation
occurs.
• This form for “contingent spot pricing” may also solve the transaction cost problem of spot
pricing. The cost of installing the additional equipment to buy power on spot conditions during capacity shortage could be borne by those consumers who value this option.
It is shown in Doorman (2000) that for this case, optimal prices for energy and capacity equal
their respective marginal costs. Because of this, capacity subscription with optimal allocation of
excess load relief can in principle result in an optimal solution in a deregulated market structure.
3.
CAPACITY SUBSCRIPTION
We choose to call Self Rationing in a competitive power system Capacity Subscription. This
Section will sketch a framework of a market design that supports Self-Rationing, and discuss
shortly the behaviour of the market participants.
A competitive market structure is envisioned with a number of suppliers, none of who has market power, and a number of consumers. Like in a number of today’s electricity markets, there is
a 24-hour day-ahead spot exchange, where suppliers offer their generation with the help of
price-volume relations, and consumers bid for their demand in a similar fashion, either directly
or through intermediate agents. There will also be a real-time market to ensure the continuous
balance between supply and demand. In addition to the daily spot exchange, there is a market
for capacity. Basically, this market has a longer horizon (season or year), but buying and selling
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of capacity can in principle be done more or less continuously, facilitating the market participants’ changing needs over time. In this market, suppliers bid their anticipated available capacity during system-peak as a price-volume relation, while consumers do the same for their anticipated need for capacity.
In a competitive electricity market, there will be a System Operator, whose main task is to control the continuous match between demand and supply (with the help of the real-time market)
and to operate the transmission network. In a market with Self-Rationing, the System Operator
must know the total amount of capacity sold in the market. There are two principally different
ways to use Self Rationing. The first is related to the 24-hour day-ahead market. When the forecast for the next day indicates that demand will exceed system capacity, the System Operator
announces that fuses will be activated, and demand will be limited to total subscribed capacity.
All parties can then take activation of the LLDs into account in their spot market bids and offers. The second way is when LLD activation is used in connection with the real time market,
when demand threatens to exceed supply on short notice. In this context, Capacity Subscription
can avoid both random rationing and extreme price peaks in the real time market.
Limitation of demand with the LLD as described so far results in a considerable loss of comfort
for the consumer: if demand exceeds subscribed capacity, the LLD-fuse blows, and all demand
is curtailed. The consumer has to reduce demand below the limit, before resetting the LLD.
However, off-the-shelf technology is already available to limit demand below a certain level,
while minimizing loss of comfort. The consumer would have to compare the price of such
equipment with the price of capacity to make an optimal choice. Interestingly, widespread introduction of Capacity Subscription could create considerable demand for this type of equipment, especially if the price of capacity is high.
Conceptually, there are three time horizons for the capacity market: firstly, in the short run
(some hours to some days) available capacity is fixed and consumers’ willingness to pay for capacity determines the capacity price. Secondly, in the medium run (a few days to a few years),
some more capacity can be made available: mothballed plants can be made operational, maintenance can be rescheduled or small size gas turbines or diesel engines can be installed. Within
this time horizon the capacity price is determined both by the supply and demand side. Thirdly,
in the long run, it is possible to build new optimally sized peaking plants, and the cost of these
will determine the capacity price.
If there is excess capacity in the market, the probability of unconstrained demand exceeding
supply is practically zero, and it does not make sense for a consumer to buy capacity, as long as
its price is positive. In this case the capacity price will be zero, which is the rational outcome in
a market with excess capacity. However, if there is a shortage of capacity, the price in the short
and medium term may exceed the long-term balance price, because consumers may be willing
to pay a higher price to avoid being limited in their consumption. This gives a signal to the supply side to provide more capacity in the long run.
In the case of optimal allocation of excess capacity a consumer can choose not to buy a fuse, but
to purchase a real time meter and buy energy at the spot price when LLDs are activated. Subscribing to a certain amount of capacity can be viewed as a forward contract that allows the
holder to purchase energy up to subscribed capacity at an agreed price. In this way, Capacity
Subscription combines the advantage of spot pricing, in this context price rationing of excess
demand, with the advantage of tariffs, predictability.
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4.
CONCLUSIONS
Capacity Subscription creates product differentiation and enables the creation of a true capacity
market, where “capacity during system-peak conditions” is bought and sold. The essential feature of the solution is a centrally controlled Load Limiting Device, enabling the system operator
to limit demand to subscribed capacity when generation capacity is insufficient to serve unconstrained demand. Based on their preferences for uninterrupted supply and the price of capacity,
consumers buy their preferred amount of capacity, while generators can sell their available capacity. The interesting feature of this solution is, that it guarantees that there always will be
“enough” generating capacity, avoiding random rationing and thus solving one of the major
problems of competitive power markets.
As argued by Chao and Wilson, a Priority Service solution offers several advantages over spot
pricing. One is that it yields important information about consumers’ preferences, which results
in a more efficient level of generation capacity. A second advantage is that it offers consumers
more certainty about their future bill. A third, major point is that spot pricing may not be feasible. Due to transaction costs, the best one can hope for is that consumers adjust demand to
prices based on a day-ahead spot market. This does not take into account short-term variations
in real time that also may result in a generation deficiency. Finally, a Priority Service solution
can be a less costly form for market organization, because it does not require hourly metering.
Because not all consumers will reach their subscribed capacity at the instant when the fuses are
activated, there will be some idle capacity after activation, representing an economic inefficiency. Two methods have been analyzed to avoid this inefficiency: random allocation and optimal (price based) allocation of idle capacity. With random allocation, optimal prices are generally not equal to marginal prices and an optimal solution will not be reached. However, by using a “rolling allocation” routine, the System Operator can divide the excess capacity between
all consumers. With price-based allocation, optimal prices are equal to marginal costs for energy
and capacity, and the solution is feasible in a competitive market.
Price based allocation of idle capacity requires real-time metering. It can be left to the market
participants to obtain such metering devices. Consumers that put a high value on the possibility
of being able to buy electricity in excess of their subscribed capacity during system-peaks, may
invest in such devices as an alternative to buying more capacity. Typically, this will be more
interesting for large consumers than for smaller ones. In addition to this feature, Capacity Subscription requires a less expensive infrastructure than full spot pricing: the LLD and the communication technology that allows the system operator to control the device. It can be left to the
market to develop solutions to control demand efficiently at the consumer’s place. If capacity
prices are high, there will be a motivation to develop devices that control demand with minimal
loss of comfort, allowing consumers to buy smaller “fuses”. On the other hand, if there is excess
capacity, prices will be low, and consumers will prefer to subscribe on higher levels of capacity.
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REFERENCES
Chao, H.-P., R. Wilson, 1987, Priority Service: Pricing, Investment, and Market Organization,
The American Economic Review, Vol. 77, No. 5, 899-916.
Doorman, G. L., 2000, Peaking Capacity in Restructured Power Systems, PhD Thesis, Norwegian University of Science and Technology.
Doucet, J. A. and M. Roland, 1993, Efficient Self-Rationing of Electricity Revisited, Journal of
Regulatory Economics, Vol. 5, 91-100.
Panzar, J.C. and D.S. Sibley, 1978, Public Utility Pricing under Risk: the case of self-rationing,
The American Economic Review, Vol. 68, No. 5, 888-895.
Schweppe, F. C., M. C. Caramanis, R. D. Tabors, R. E. Bohn, 1988, Spot Pricing of Electricity,
Kluwer Academic Publishers.
Woo, C.-K., 1990, Efficient Electricity Pricing with Self-Rationing, Journal of Regulatory Economics, Vol. 2, 69-81.
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