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lil:
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Massachusetts Institute of Technology
Department of Economics
Working Paper Series
Reliability
and Competitive
Electricity
Markets
Paul Joskow
Jean Tirole
I
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
MAY
!
1
3 200^
Working Paper 04-1
LIBRARIES
April 21,
2004
RoomE52-251
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Cambridge,
MA 021 42
This paper can be downloaded without charge from the
Social Science Research Networl< Paper Collection at
http://ssrn.com/abstract=543862
Reliability
and
Competitive Electricity Markets^
Paul Joskow^ and
Jean Tirole^
April 21, 2004
Abstract
Despite
number
all
of the talk about "deregulation" of the electricity sector, a large
of non-market
mechanisms have been imposed on emerging compet-
wholesale and retail markets. These mechanisms include spot market
price caps, operating reserve requirements, non-price rationing protocols, and
administrative protocols for managing system emergencies. Many of these
mechanisms have been carried over from the old regime of regulated monopoly
and continue to be justified as necessary responses to market imperfections of
various kinds and engineering requirements dictated by the special physical
attributes of electric power networks. This paper seeks to bridge the gap between economists focused on designing competitive market mechanisms and
engineers focused on the physical attributes and engineering requirements they
perceive as being needed for operating a reliable electric power system. The
paper starts by deriving the optimal prices and investment program when
there are price-insensitive retail consumers, and their load serving entities
can choose any level of rationing they prefer contingent on real time prices. It
then examines the cissumptions required for a competitive wholesale and retail market to achieve this optimal price and investment program. The paper
analyses the implications of relaxing several of these assumptions. First, it
analyzes the interrelationships between regulator-imposed price caps, capacity obligations, and system operator procurement, dispatch and compensation
arrangements. It goes on to explore the implications of potential network collapses, the concomitant need for operating reserve requirements and whether
market prices will provide incentives for investments consistent with these
reserve requirements.
itive
*We
Crampes, Richard Green, Stephen Holland, Bruno Jullicn, Patrick
IDEI-CEPR conference on "Competition and Coordination in the
Electricity Industry," January 16-17, 2004, Toulouse and the ninth annual POWER conference,
UC Berkeley, March 19, 2004, for helpful discussions and comments.
^Department of Economics, and Center for Energy and Environmental Policy Research, MIT.
tiDEI and GREMAQ (UMR 5604 CNRS), Toulouse, CERAS (URA 2036 CNRS), Paris, and
arc grateful to Claiide
Rey and
MIT.
the participants at the
Introduction
1
Despite
all
of the talk about "deregulation" of the electricity sector, there continue
to be a large
number
of
non-market mechanisms that have been imposed on the
emerging competitive wholesale and
include: wholesale
retail electricity markets.
These mechanisms
market price caps, capacity obligations placed on LSEs, frequency
regulation, operating reserve
and other ancillary
service requirements enforced
by
the system operator, procurement obligations placed on system operators, protocols
for non-price rationing of
demand
protocols for system operators'
to respond to "shortages",
management
of
and administrative
system emergencies.
Many
of these
non-market mechanisms have been carried over from the old regulated regime without
much
consideration of whether and
mechanisms and
if
of the effects they
how they might be
may have on market
replaced with market
behavior and performance
they are not.
In
some
cases the non-market
mechanisms are argued to be
fections in the retail or wholesale markets:
inability of
most
retail
in particular,
justified
by imper-
problems caused by the
customers to see and react to real time prices with legacy
meters, non-price rationing of demand, wholesale market power problems and imperfections in
mechanisms adopted
to mitigate these
market power problems.
Other mechanisms and requirements have been justified by what are perceived to
be special physical characteristics of
in turn lead to
market
electricity
failures that are
and
unique to
electric
power networks which
electricity.
These include the
need to meet specific physical criteria governing network frequency, voltage and
stability that are
thought to have public good attributes, the rapid speed with
which responses to unanticipated
failures of generating
must be accomplished to continue
to
and transmission equipment
meet these physical network attributes and
the possibility that market mechanisms cannot respond fast enough to achieve the
network's physical operating parameters under
Much
and
retail
sider
all
states of nature.
of the economic analysis of the behavior
and performance of wholesale
markets has either ignored these non-market mechanisms or
them
in
failed to con-
a comprehensive fashion. There continues to be a lack of adequate
communication and understanding between economists focused on the design and
evaluation of alternative market mechanisms and network engineers focused on the
physical complexities of electric power networks and the constraints that these physical
requirements
may
place on market mechanisms.
of Joskow-Tirole (2004)
The
is
The purpose
of this paper
and
to start to bridge this gap.
institutional environment in
which our analysis proceeds has competing
load serving entities (LSEs)^ that market electricity to residential, commercial and
industrial ("retail") consumers.
LSEs may be independent
delivery services from unaffiliated transmission
may be
affiliates of
entities that
and distribution
purchase
utilities or
they
these transmission and distribution utilities that compete with
unaffihated LSEs.
Some
retail
consumers served by LSEs respond to
real
time
wholesale market prices, while others are on traditional meters which record only
their total
consumption over some period of time
therefore do not react to the real-time price.
to non-price rationing to balance supply and
market
is
composed
of
for
is
Retail consumers
demand
a quarter), and
may be
sell
subject
The wholesale
in real time.
competing generators who compete to
The wholesale market may be
power. Finally, there
(for instance,
power to LSEs.
perfectly competitive or characterized
an independent system operator (ISO) which
is
by market
responsible
operating the transmission network in real time to support the wholesale and
retail
markets
for power, including
market power mitigation
meeting certain network
reliability
and wholesale
criteria.-^
^ Or in UK parlance "retail suppliers".
^The latter may include enforcing operating reserve and other operating reliability requirements,
enforcing longer term capacity obligations, procuring and dispatching resources to meet these
Section 2
state contingent
LSE
but their
prices. In this
tor,
derives the optimal prices
first
demand,
at least
can choose any
some consumers do not
all
identical, possibly
have the same load
profile.
up
more complex characterizations
We
competition.
when
of
on
real
time
to a proportionality fac-
Wliile the latter significantly
constrains the nature of consumer heterogeneity considered,
existing literature (e.g., Borenstein-Holland, 2003).
is
react to real time prices,
level of rationing it prefers contingent
model consumers are
and therefore
and investment program when there
it is
consistent with the
Joskow-Tirole (2004) analyzes
consumer heterogeneity
in the presence of retail
then derive the competitive equilibrium under these assumptions
there are competing
LSEs that can
sition that extends the standard, welfare
offer
two part
tariffs.
This leads to a propo-
theorem to price-insensitive consumers and
rationing; this proposition serves as an important
benchmark
for evaluating a
num-
ber of non-market obligations and regulatory mechanisms:
The second
best
be implem,ented by
optimum, (given the presence of price-insensitive consumers) can
an equilibrium with
retail
and generation (wholesale) competition
provided that:
(a)
The
real
time wholesale price accurately reflects the social opportunity cost of
generation.
(b) Rationing, if any, is orderly,
(c)
LSEs
retail
(d)
and makes
efficient use of available generation.
face the real time wholesale price for the aggregate consumption of the
customers for
whom
Consumers who can
they are responsible.
react fully to the real time price are not rationed. Further-
more, the LSEs serving consumers who cannot fully react to the real time price can
demand any
(e)
level of rationing they prefer contingent
Consumers have
the
same
on the real-time
load profile (they are identical up to a scale factor).
The assumptions underlying this benchmark proposition
requirement!?,
price.
are obviously very strong:
and managing system emergencies that might lead the network to
collapse.
(a)
market power on the one hand, and regulator-imposed price caps and other policy
interventions on the other
market price and the
hand create
between the
differences
social opportunity cost of generation; (b)
unlike say rolling blackouts, have systemic consequences, in that
eration cannot be used to satisfy load;
their customers
may be
if
(c)
LSEs do not
controllable distribution circuit; and, relatedly,
scaling factor.
and
(b),
time wholesale
network collapses,
some
available gen-
face the real time price for
these customers are load profiled; (d) price sensitive consumers
rationed along with everyone else that
level of rationing
real
they desire;
(e)
is
physically connected to the
LSEs
generally cannot
consumer heterogeneity
is
same
demand any
more complex than a
This paper examines the implications of relaxing assumptions
(a)
while Joskow-Tirole (2004), that focuses on retail competition, investigates
the failure of assumptions
(c), (d),
and
(e).
Section 3 studies the implications of distorted wholesale prices.
the case where there
in the supply of
is
It first
considers
a competitive supply of base load generation, market power
peak load investment and production, and a price cap
is
applied
that constrains the wholesale market price to be lower than the competitive price
during peak periods (section
the long run
when
show that capacity
there
is
3.1).
This creates a shortage of peaking capacity in
market power
supply of peaking capacity.
We
obligations and associated capacity prices have the potential to
restore investment incentives
by compensating generators ex ante
in earnings that that they will incur
states of natrue (and
the
in the
up
to
for the shortfall
due to the price cap. Indeed, with up to three
two states of nature where generators have market power),
Ramsey optimum can be achieved
despite the presence of market power through
a combination of a price cap and capacity obligations provided that
and base load generating capacity are
and receive the associated capacity
eligible to
price,
and
{ii)
:
(i)
both peak
meet LSE capacity obligations
the
demand
of all consumers,
including price-sensitive consumers, counts for determining capacity obligations and
the capacity prices are reflected in the prices paid by
more than three
states of nature, a combination of spot wholesale
and capacity obligations
is
will not achieve the
only a problem during peak
demand
Ramsey optimum
With
consumers.
market price caps
unless market
power
periods. Thus, the regulator faces a tradeoff
between aheviating market power off-peak,
cap,
all retail
if it is
and providing the proper peak investment
a problem, through a strict price
incentives,
and
further unable
is
to provide price-sensitive consumers with the appropriate economic signals.
intuition for this result
power the optimality
instruments
is
that
when more than two
prices are distorted by
of a competitive equilibrium cannot
The
market
be restored with only two
— a price cap and a capacity obligation.
Section 3.2 then examines the effects of two types of behavior by an ISO that
empirical analysis has suggested
The
first
may
distort prices
and investment (Patton 2002).
involves inefficient or "out-of-merit" dispatch of resources procured
by the
ISO. Such dispatch in the short run depresses off-peak prices and in the long term
leads to an inefficient substitution of base load units
by peakers. The second involves
the recovery of the costs of resources acquired by the ISO through an
spread over prices in
the uplift
is
all
demand
states or else in only
socialized (spread over
demand
peak demand
\iplift
states.
charge
Whether
ISO purchases
states) or not, large
discourage the build up of baseload capacity and depresses the peak price. For small
purchases, off-peak capacity decreases under a socialized uplift, and peak capacity
decreases under an uplift that applies
solelj^ to
peak energy consiunption.
Section 4 derives the implications of network collapses and the concomitant need
for
network support
services.
As suggested
above, network collapses differ from other
forms of energ}' shortages and rationing in a fundamental way. While scarcity makes
available generation (extremely) valuable under orderly rationing,
ueless
when the network
^An analogy may
collapses.^ Hence,
it
system collapses, unlike,
makes
it
val-
say, controlled
help understand the distinction between orderly rationing and a collapse:
rolling blackouts that shed load to
match demand with
available capacity, create a
rationale for network support services with public goods characteristics.
We
derive
the optimal level for these network support services, and discuss the implementation
Ramsey
of the
allocation through a combination of operating reserve obligations
and
market mechanisms.
A
2
result
Model^
2.1
There
i is
benchmark decentralization
is
a continuum of states of nature or periods
denoted
/,
(and so
/
—
fidi
1).
Let
E []
i
e [0, 1].
The frequency
of state
denote the expectation operator with
Jo
respect to the density
price-insensitive
We
fi.^
assume that the (unrationed) demand functions of
and price-sensitive consumers, Di and Di, are increasing
Price-insensitive consumers are
gate consumption over
all
on traditional meters that record only
states of nature,
Consumers are homogeneous, up
same load
profile..
[Note that
if
their aggre-
and therefore do not react to the RTP.^
to possibly a scaling factor,
consumers
in i.^
differ in
i.e.,
they have the
the scale of their demand, this
consumption and need not be known by the
social
planner or the LSEs.] Without loss of generality they are offered a two-part
tariff,
scale can be inferred from total
with a fixed
when
fee
A
and a marginal price
a mattress manufacturer
fails,
p.
Their
demand
buyers of mattresses
may
function in the absence
experience delays; competitors
and may even gain from the failure. By contrast, a farmer whose cows have
contracted the mad cow disease maj' spoil the entire market for beef.
^See Turvey and Anderson (1977, Chapter 14) for an analysis of peak period pricing and investment under uncertainty when prices are fixed ex ante and all demand is subject to rationing
with a constant cost of unserved energy when demand exceeds available capacity.
however do not
suffer
°In this paper,
we do not allow intertemporal
only on the price faced by the consimier in state
transfers in
i).
We
demand (demand
in state
i
depends
could allow such transfers, at the cost of
increased notational complexity.
•"As in
Joskow-Tirole (2004), we could also introduce consumers on real-time meters
1 below.
not monitor the real-time price. This would not affect Proposition
who do
of rationing
is
denoted
fraction of their
interrupted
—
(1
Di{'p),
demand
with Dj increasing in
satisfied in state
We
let
Q'j
<
1
denote the
a, decreases, the fraction of load
The alphas may be exogenous
increases.
cij)
As
i.
?'.
(say,
determined by
the system operator); alternatively, one could envision situations in which the
would
affect the
LSEs
alphas either by demanding that their consumers not be served as
the wholesale price reaches a certain level, or conversely by bidding for priority in
situations of rationing.^
state,
and
We let
is
Si
{p, ai)
denote their expected consumption in that
S^ {p, a^) their realized gross surplus,
T),(p,l)
where
Dj
is
= A(p)
and
with
S,{pA)
=
the standard gross surplus function (with
concave in
qjj
on
[0, 1]:
S,{D,{p)),
S'^
=
p).
more severe rationing involves higher
We
assume that
S^
relative deadweight
losses.
In the separable case, the
demand Dj
takes the multiplicative form aiDi (p) and
the surplus takes the separable form $i{Di{p),ai).
consumer may adjust her demand to the prospect
We
will also
assume that
lost opportunities to
More
generally however, the
of being potentially rationed.^
consume do not create value to
the consumer. Namely, the net surplus
Si (p, oti)
is
maximized
Let us
at Qj
now
1,
that
is,
when
discuss specific cases to
and note that the
*The
=
- pVi
it is
latter of course
equal to Sj (D.;(p))
make
social cost of shortages
{p, a,)
this abstract
— pDi{p).
formalism more concrete,
depends on how
fast
demand and supply
assumes that the system operator can discriminate in its dispatch to LSEs
emergency situations that require the system operator to act quickly to
in each state, inchiding in
avoid a cascading blackout.
^A case in point is voltage reduction. When the system operator reduces voltage by, say, 5%,
lights become dimmer, motors run at a slower pace, and so on. A prolonged voltage reduction,
though, triggers a response: consumers turn on more lights, motor speeds are adjusted. Another
example of non-separability
will
be provided below.
^'^
conditions change relative to the reactivity of consumers.
When the timing of the blackout is perfectly anticipated
across geographical areas, then
ctj
and blackouts are roUing
denotes the population percentage of geographical
areas that are not blacked out (and thus getting full surplus Si {Di {p))),
and
1
—
«»
the fraction of consumers living in dark areas (and thus getting no surplus from
electricity).
With
Sj
An
perfectly anticipated blackouts,
(j9, ttj)
=
unexpected blackout
may have worse
the outage
is
D^
makes sense
(p, ai)
=
OfjA
to
assume that
(p)
consequences than a planned cessation
consumer may prefer using the elevator to the
of consumption. For example, a
If
and
OiSi {Di{p))
it
foreseen, then the
consumer takes the
the elevator) and gets zero surplus from the elevator.
obtains a negative surplus from the elevator
if
stairs (does
not "consume"
Bj^ contrast, the
the outage
is
stairs.
consumer
unforeseen. Similarly,
consumers would have planned an activity requiring no use of electricity (going to the
beach rather than using the washing machine, drive their car or ride their bicycle
rather than use the subway)
have planned time
off, etc.
if
they had anticipated the blackout; workers could
More
generally, with adequate
warning consumers can
take advance actions to adapt to the consequences of an interruption in electricity
supphes.
This
is
one reason
planned outages required
for
why
distribution companies notify consumers about
maintenance of distribution equipment.
Opportunity cost example: Suppose that the consumer chooses between an electricity-
consuming activity (taking the
an
electricity-free
latter yields
elevator, using electricity to
approach (taking the
known
surplus
S>
0.
The
stairs,
run an equipment) and
using gas to run the equipment).
The
surplus associated with the former depends
not only on the marginal price p he faces for electricity, but also on the probability 1
10
—
Q'i
of not being served.
This observation
is
made
for
One can
example
in
envision three information structures: (a)
EdF
(1994, 1995).
The consumer knows whether he
be served (the elevator
will
through communication just before the outage); this
case just described, (b)
The consumer knows
is
is
always deactivated
the foreseen rolling blackouts
the state-contingent probability a^ of
being served, but he faces uncertainty about whether the outage will actually occur
(he
more
likely to get stuck in the
The consumer has no information about the
probability of outage and
knows that the period
elevator), (c)
bases his decision on
tions in elevators).
is
E [ai]
a peak one and he
(he just
Letting S^
(p)
is
knows the average occurrence
= max {Si
(D)
— pD}
-
S
of immobiliza-
denote the net surplus in
the absence of rationing; then
Sj {p, a,)
- pT),
=
{p, Q'i)
f
/
a,S"
(p)
+
max {aiS^
(1
(p)
,
ai)
S]
in case (b)
in case (c)
aiSi (p)
E [a,]
(provided that 5f (p)
> S
consumer chooses the
electricity-intensive approach).
The
value of lost load
and, in case
(VOLL)
is
in case (a)
(c),
that
is
high enough so that the
equal to the marginal surplus associated with
a unit increase in supply to these consumers, and
is
here given by
dSi.
^"'
VOLL,
dVi'
dai
since a unit increase in supply allows an increase in a^ equal to 1/ [dVi/dai].
Dj
=
When
aiDi, then
=4?.
VOLLi
Di
For example, with perfectly anticipated blackouts, the value of
the average gross consumer surplus.
for blackouts that give
It is
lost load is
higher for unanticipated blackouts than
consumers time to adapt their behavior
10
equal to
in anticipation of
being curtailed.
Price- sensitive consumers are modeled in exactly the
same assumptions
and react to
it.
RTP
consumers face the
difference
show that
will later
pi (so pi
—
Pi),
it is
we must
is
Dj
[pi,
and
Sj)
that they
their gross surplus
optimal to
let
at this stage allow
the central planner to introduce a wedge between the two prices.
expected consumption
is
Let Pi denote the state-contingent price
chosen by the social planner; although we
price-sensitive
The only
as price-insensitive consumers.
face the real time price
same way and obey the exact
is Sj (pi,
In state
Qj),
i
their
where 3j
is
the rationing / interruptibility factor for price-sensitive consumers.
The supply
side
described as a continuum of investment opportunities indexed by
is
the marginal cost of production
Let /(c) denote the investment cost of a plant
c.
producing one unit of electricity at marginal cost
We
denote by G{c)
>
So, the total investment cost
is
to scale for each technology.
function of plants.
'^'-
c.
There are constant returns
the cumulative distribution
/•oo
I{c)dG{c).
/
Jo
The ex post production
cost
is
/oo
/-CX)
cUi{c)dG{c),
/
where
/
Jo
where the
utilisation rate Ui{c) belongs to
Remark: The uncertainty
is
e [0, 1] of
(A)) as in Section 4 below.
^^This distribution
equipments
may be
may
=
Qi.
[0, 1].
demand
here generated on the
availabihty factor A (a fraction A
some cdf Hi
Ui{c)dG{c)
Jo
plants
is
available,
We
could add an
where A
is
given by
This would not alter the conclusions.
not admit a continuous density.
selected at the
side.
optimum.
11
For example, only a discrete set of
2.2
Optimum
A social planner chooses
each state
a,:
and
a marginal price p for price-insensitive consumers, and
marginal prices
i)
% for price-sensitive consmners,
max
<
E
the extents of rationing
and the investment plan (?() so
a^, utilisation rates Ui{-)
$i{p,ai)+%{pi,ai)-
I
-/
Ui{c)cdG{c)
Jo
(for
as to solve:
I{c)dG{c)
^0
J
s.t.
>
u,{c)dG{c)
/
"Di
{p.,
ai)
+
S,
(pi,
3,)
for all
i.
Jo
Letting Pifidi denote the multiplier of the resource constraint in state
i,
the
first-
order conditions yield:
a) Efficient dispatching:
~
Ui{c)
c
for
1
<
Pi
and
Ui{c)
=
for
c
>
pj.
(1)
b) Price-sensitive consumers-}'^
(i)
5,
=
(ii)
S,
=
'^To prove condition
(2),
A(Pi)
l.
apply
(2)
first
the observation that by definition 'Di{pi,a.i)
surplus-maxirnizing quantity for a consumer paying price pi for a given probabihty
served; and second our assumption that lost opportunities don't create value:
Si{Pi,a,)-pi'Di{pi,ai)
<Si(j>i.,ai)-p^T)^(p,,ai)
<5,(5,fe))-KA(pOHence, price sensitive consumers should not be rationed and should face price
12
pi.
is
the net-
q,;
of being
consumers:
c) Price-insensitive
E
(i)
dp
-Pi
0.
dp
dS,
5a,;
-^^ = Pi
Either
(ii)
or
ai
=
1.
(3)
dai
d) Investment:
Either
These
(1)
/(c)
= E max jp, -
says that only plants whose marginal cost
i.
o|
or
dG(c)
=
(4)
can be interpreted in the following way: condition
first-order conditions
dispatched in state
c,
Condition
(2) implies
is
smaller than the dual price pi are
that price-sensitive consumers are never
rationed and that their consumption decisions are guided by the state-contingent
dual price. Condition
(3) yields
the following formula for the price p
that price-insensitive consumers are never rationed {a^
E Up* - pO d[
In case of rationing
(ct,
<
1
for
some
ip*)]
z), its
=
=
— p*
provided
1):
0.
(5)
implications depend on the efficiency
of rationing; condition (3) in the separable case yields the following formula:
E
5A
-
aiPt
For example, for perfectly foreseen outages,
=
D[{p)
it
E[{p-p;)[a.,D[
boils
0.
down
=
to
13
0.
(6)
'^Suppose that the regulator imposes an artificial constraint that retail customers not be voluntarily shut off (one may have in mind a small fraction of such customers, so that the wholesale
prices is not affected). The Ramsey price would then be p*. Under the reasonable assumption that
Qi decreases and [pi — p)\D[\ increases with the state of nature and decreases with p, (6) yields a
corrected Ram.sey price p**:
p'*
<p\
Intuitively, the
impact of p on peak demand
is
reduced by rationing, and so there
keep the marginal price high.
13
is less
reason to
Condition
implies that in
(3ii)
all
cases of rationing
VOLL,= Pi.
That
generators and
is,
LSEs should
Finally, condition (4)
is
all
face the value of lost load.
the standard free-entry condition for investment in gen-
eration.
Competitive equilibrium
2.3
Let us noAv assume that price-sensitive and -insensitive consumers are served by
load serving entities (LSEs), and that
LSEs
face the real time wholesale price for
the aggregate consumption of the retail customers for
The
they are responsible.
following proposition shows that, despite rationing and price-insensitive con-
sumptions,
five
whom
retail
competition
assumptions are
Proposition
1
is
consistent with
Ramsey
optimality provided that
satisfied:
The second-best optimum
(that
is,
the socially optimal allocation
given the existence of price-insensitive retail consumers) can be implemented by an
equilibrium with retail and generation competition provided that:
• the
RTF
reflects the social opportunity cost of generation,
• available generation is
made
• load-serving entities face the
By
use of during rationing periods,
RTF,
contrast, with imperfectly foreseen outages,
as,:
dDi
and
(3) yields
a price above p**.
The
increase in outage cost due to unforeseeability suggests
raising the marginal price to retail consumers in order to suppress
14
demand.
• price-sensitive
consumers are not rationed; furthermore, while price-insensitive
consumers may
be rationed, their load-serving entity
can demand any level of
state-contingent rationing ai (Pi)/^
• consumers are homogeneous (possibly up to a scaling factor).
Proof: Suppose that competing retailers (LSEs) can offer to price-insensitive contracts {A,p, a.}, that
is
two-part
tariffs
state-contingent extent of rationing
of the joint surplus of the retailer
first-order conditions for this
The
rest of the
economy
is
A
and marginal price p cum a
Retail competition induces the maximization
and the consumer:
max E [Si
The
ctj.
with fixed fee
(p, a^)
- p^Vi
{p, a^}]
program are nothing but conditions
(3)
above.
standard, and so the fundamental theorem of welfare
economics applies.
The assumptions underlying Proposition
ket
are very strong: In practice, (a) mar-
power on the one hand, and price caps and other policy interventions on the
other hand create departures of
and
1
(b) available generation
network collapse;
wholesale market
(c)
if
RTFs from
does not serve load during blackouts associated with a
LSEs do not
their
the social opportunity cost of generation;
face the
RTF
for the
power they purchase in the
customers are load profiled; (d) technological constraints in
may be
the distribution network imply that price-sensitive consumers
with everyone
they desire;
The paper
(e)
else; relatedly,
LSEs cannot
consumer heterogeneity
is
generally
more complex than
investigates the consequences of the
Remark: Chao- Wilson (1987)
also
•^Here the state and the price are
first
mapped
two observations.
15
for priority servicing.
More generally, they may not be (the
The proposition still holds as long as LSEs
one-to-one.
a^.
level of rationing
a simple scaling factor.
emphasize the use of bids
state of nat\n-e involves unavailability of plants, say).
can select a state-contingent
demand any
rationed along
Chao and Wilson show that when consumers
are heterogeneous and have unit and
state-independent demands, the first-best (hence rationing free) allocation can be
implemented equivalently through a spot market or an ex ante priority servicing
auction. Proposition
1
by contrast considers homogeneous consumers and introduces
price insensitive consumers; accordingly, markets are here only second-best optimal
and the second-best optimal allocation involves actual
rationing.
Two-state example
2.4
There are two
(/i -f/2
=
1):
states: off-peak
(i
—
and peak
1)
(z
=
price insensitive retail customers have
with frequencies
2),
demands
-Di(p)
1)2 (p),
A
) We assume
/2
5*2
{D2{p)).
(who react to real-time pricing) have demands Di{p) and
with associated gross surpluses
S2 (D2{p)
and
and D2{p) with
associated gross surpluses (in the absence of rationing) ^i (Di(p)) and
Price-sensitive customers
/i
(in
that rationing
unit of baseload capacity costs
the absence of rationing) ^i
may
/i
occur only at peak (oi
and allows production
=
(
1
£>i(p)
,
Q2
j
<
and
1).
at marginal cost Ci
Let Ki denote the baseload capacity. The unit cost of installing peaking capacity
I2.
The marginal operating
cost of the peakers
is
is C2.
Social optimum: Letting p* denote the (constant) price faced by retail consumers,
the (second-best) social optimal solves over <p*,a2 ,Di,lD2f
mso^W = max |/i
Si
(A
(p*))
+
Si
(d^)
-
c^Ki
a'2)
+
52 (^2)
-
C1/-C1
+/2
[§2
{P\
/m
=
Di{p*)
A",
=
- hKi
-
02/^2]
-
/2A'2}
where
+ Di
(7)
T)2{p\a2)-VD2 -
16
Di{p*)
+ Di
(8)
Applying the general analysis yields (provided that the peakers' marginal cost
exceeds the off-peak price pi):
C2 wealcly
Either
S'^
= Pi
A=
or
fi{p*-Pi)D[ +
(2'i)
0,
f2(^-P2^)=0,
dp
dp
(3'i)
and
/i (Pi
-
ci) -f /o {P2
/2 {P2
-
C2)
-
=
ci)
/i
(4'i)
=
Note that the
/2-
investment conditions imply that the peak price exceeds
free entry
the marginal operating cost of peaking capacity in equihbrium.
Proposition 2 Rationing
Proof:
is
desirable
price
/2P2
a2
is
With
is
high.
—h
=
1,
if
p*
!
(a-2.
<
foreseen rolling blackouts, §2 (p*, ^2)
and only
if
Suppose
for
and
pi
~ pi +
— Ci ~
/2
< P2D2
^2 {D2 (p*))
example that
/i
= A+
indeed smaller than ^2-^2
—
/2.
Ci
consumers
I) of price-insensitive
If
(3'i).
that
is
(p*))
and so rationing
intuitively
when
the peak
demand
is
linear
and D[
=
D'2-,
So p* remains bounded, and S2 {D2
rationing
Intuitively, rationing serves to re-create
O2S2 {D2
be optimal.
small {infrequent peak); then from
furthermore
from
(p*), so
is
/2
(p*),
=
may
is
some
(4')
and
{p*))
optimal.
price sensitivity of the
consumption
of consumers on traditional meters. For example, for infrequent peaks, the
peak price
goes to infinity and so the discrepancy between the true price and the price paid by
retail
consumers
is
too large to
make
it
socially optimal to serve these consumers.
17
ISO
Price distortions: capacity obligations and
3
procurement
3.1
A
Price caps and capacity obligations
capacity obligation requires an
peak demand
(plus a reserve
LSE
margin
to contract for
enough capacity to meet
in a world with uncertain
and demand fluctuations). Capacity obligations may take
requires
to the
by
LSEs
to forward contract with generators to
ISO during peak demand
this capacity-^^ to
make
its
equipment outages
at least
two forms. One
their capacity available
periods, leaving the price for any energy
supphed
be determined ex post in the spot market. Alternatively, the
capacity obligations could require forward contracting for both capacity and the
price of
hours.
any energy
(or
operating reserves) supplied by that capacity during peak
^^
Proposition
1
shows that rationing alone does not create a rationale
obhgations. Rather, there must be
adjust to reflect supply and
demand
some reason why the spot
directions. For this purpose,
and
price does not fully
conditions and differs from the correct economic
Leaving aside procurement by the ISO
signal.
for capacity
for the
like in section 2.4,
moment, we can look
we
specialize the
in three
model
in
most
of this section to two states of nature.
Market "power
The
which
in the wholesale
regulator
may impose
market
a price cap
{p2
< p™^^) on
wholesale power prices,
in turn are reflected directly in retail prices given perfect competition
among
"^Or in a world with uncertain equipment outages and demand fluctuations the prices for operating reserves provided by this capacity as well.
^''Another approach is for the system operator to purchase reliability contracts from generators
on behalf of the load. Vazquez et al (2001) have designed a more sophisticated capacity obhgations
scheme, in which the system operator purchases reliability contracts that are a combination of a
financial call option with a high predetermined strike price and an explicit penalty for non-delivery.
Such capacity obligations are bundled with a hedging instrument, as the consumer purchasing such
a call option receives the difference between the spot price and the strike price whenever the former
exceeds the latter.
18
retailers, in
sale
order to prevent generators from exercising market power in the whole-
market during peak demand periods.
Suppose
that:
• baseload investment and production
• peakload investment
We
competitive (as earher),
and production are supplied by an
Ti-firm
Cournot
oligopoly.
have in mind a relatively short horizon (certainly below 3 years), so that
new peaking investment cannot be
this interpretation, I2
peakers).
make
is
is
built in response to strategic withholding (in
probably best viewed as the cost of maintaining existing
The timing has two
stages: First, firms choose the capacity that they will
available to the market. Second, they supply this capacity in the
We
energy'.
market
for
leave aside rationing for simplicity.
In the absence of a price cap, an oligopolist in the peaking capacity market
make
chooses the amount of capacity to
max
P2
Letting
rj2
<^
[/2 {p2
-
C2)
-
available to the market
D2{p)^-D2{p2)-K,~Y.K2
h]
— — denote the
OP2
elasticity of
demand
+
J
>
D2
nr]2
or.
P2
-"-^
D2(p2)-A(Pi) +p2(p)-A(p)]
1
P2
P2—P2, where
of the price sensitive cus-
V2
tomers, one obtains the following Lerner formula:
C2
so as to solve:
L
dD2 D2
= —— /
P2-
K2
is
the Cournot price.
"^^The other equilibrium conditions are:
i^i=-Di(p)
/iPi
+
/2P2
+ 5i(pi),
= ci + Ji
and
E[{p-p,)D[ip)]=0.
19
{P2)
0,
(9)
As expected, the
and with
markup
oligopolistic relative
the elasticity of
demand
decreases with the
of price-sensitive consumers,
number of firms
and decreases when
price-insensitive consum.ers become price-sensitive}^
A price cap p^^^ = p* =
the
C2-\-{l2/ fi) restores
p™^^ <
a price cap creates a shortage of peakers whenever
Let us
now show
that
(i)
Ramsey optimum.
and
(ii)
if
the price cap
is
set too
with three states of nature, the combination of a price cap and capacity
Ramsey optimum provided
obligations restores the
that the price cap
competitive level in the lowest-demand state in which there
With two
p*^}^
with two states of nature, the Ramsey optimum can
nevertheless be attained through capacity obhgations even
low,
B}^ contrast,
states of nature
and a price cap that
is
is
is
set at the
market power.
set too low, to get the
same
level
of investment and production in the second best as in the competitive equilibrium,
the oligopolists must receive a capacity price
[We assume that, as
and
in
PJM,
pk
satisfying
the firm must supply
so ex post withholding of supplies
is
not an
K2 ex
post
if
requested to do
so,
issue.]
Note that
PK + f2P^^ =
and
/2P2
so
h-PK = f2{p'^^-Cl)+fl{Pl-c{),
^^Through the installation of a communication system,
say.
Because price-sensitivity reduces
the consumption differential between peak and off peak, the numerator on the right-hand side of
(and D2 increases) as some more consumers become price-sensitive.
^^The simple two-state example analyzed here assumes that during peak periods the price cap
has been set below P2 to characterize the more general case in which the price cap is, on average,
lower than the competitive market price. If the price cap were set high enough to ensure that
pHiax _ p* j^ would not lead to shortages of peaking capacity. However, the $1000/MWh (or
lower) price caps that are now used in the U.S. appear to us to be significantly lower than the
(9) decreases
VOLL
in
some high demand
states.
20
so incentives for baseload production are unchanged, provided that off-peak plants
are
made
eligible
There are at
for capacity payments?^
least four potential
may
problems that
result
from a policy of
applying binding price caps to the price of energy sold in the wholesale spot market:
•
The
D2 {p^^^)
The
at peak.
price of capacity
•
customers
price- sensitive
pk
price paid by
in order to restore
The signal for penalizing a
measure of the
consume
then
all retail
Ex
capacity contracts
contracts.
that the
^21
show a
sumption. Oligopolist
-°Note that in
the
same
likely to restrict the
is
the
same
(n) in the capacity
New
i
New York and PJM,
all
capacity and can receive
^^In either case, there are then
LSEs
—
—:
more than two
of these
and assuming
price
cap and
h
p^-^^-^
amount
ante.
per unit of peak conq\ of capacity contracts
generating capacity meeting certain
ICAP
of
and wholesale spot
monopoly power ex
therefore chooses to offer an
ICAP
an
no price cap and no capacity
as that with
consumers must pay
England,
counts as
is
number
number
The outcome with ex post
oligopolists just exploit their
see this, note that
bility criteria
for those
the oligopolists choose the
lets
neutrality result:
ex ante capacity obligation
The
is
longer has a
are short of capacity obligations.^-^
then the oligopolists are
of generators
markets,"^ one can
To
one just
no objective penalty
is
Actually, in the absence of price-insensitive consumers
number
obligation.
If
The ISO no
side.
with a supplier's failure to deliver {jp^^^
demand and
ante monopoly behavior:
consume
proper incentives on the demand
underestimate of this cost). Similarly, there
•
They
much:
consumers must also include the
failure to deliver is lost:
social cost associated
that underpredict their peak
too
relia-
payments.
states or nature (but see below the
remark on
idiosyncratic shocks).
^^The ex ante market might be more competitive than the ex post market, in which capacity
is the view taken for example in Chao- Wilson 2003). If so, how much
more competitive depends on the horizon. Competition in peaking generation may be more intense
.3 years ahead than 6 months ahead, and a fortiori a day ahead.
constraints are binding (this
21
solving
max<^ [f2{p''^'''''-C2)+PK-l2]
D^
ei..--)-.-.-E.]}
PK
same
The
first-order condition is the
The
analysis with price-insensitive consumers
can through the capacity market
consumers and thereby the
as (9), with
is
affect the price
latter's
more complex, because the
p
offered
by LSEs to
oligopolists
price-insensitive
peak consumption, while they took D2{p) as given
in our earher analysis of spot markets.
An
issue involving the nature of the contract supporting the capacity obligation
has become somewhat confused in the policy discussions about capacity obhgations.
If
the contract establishes an ex ante price for the right to
call
on a specified quantity
of generating capacity in the future but the price for the energy to be supplied ex
post
is
not specified in the forward contract, then, as shown above, the contracts
supporting the capacity obligation are unlikely to be effective in mitigating market
power unless the market
If
for
the capacity obligation
is
such contracts
is
more competitive than the spot market.
met with a contract that
specifies
both the capacity price
and the energy supply price ex ante then such forward contracts can mitigate market
power even
It is
ify
well
if
the forward market
is
no more competitive than the spot market.
known that when generators have forward contract
the price at which they are committed to
market power
ample,
if
in the spot
sell electricity their
a generator has contracted forward to
it
sell all
receives
output from the spot market to drive up prices to a
this case withholding
incentives to exercise
market are reduced (Wolak 2000, Green 1999). For ex-
price pf in each hour for the next three years
.
positions that spec-
of its capacity at a fixed
no benefit from withholding
level greater
than pf. Indeed, in
output to drive up prices would reduce the generator's
22
pi"ofit
since
it
would now have to buy enough power to make up
capacity
A
it
more
supphes from the
for the
withheld at an inflated price.
controversial issue
is
whether and under what conditions
(risk
sharing
considerations aside) a generator with market power in the spot market would enter
into forward contracts with
to realize
by not engaging
the spot market. That
an overall price
level lower
in forward contracting
why
is,
than what they could expect
and exercising market power
aren't the benefits of any
in
market power generators
expect to realize in the spot market reflected in the forward contract prices they
would agree to sign voluntarily as well? There has been a considerable amount of
theoretical research that supports the view that except in the
be more competitive than spot markets
markets
will
include
AUaz
monopoly case forward
for electricity.
Relevant papers
Green (1999), Newbery (1998), and Chao-
(1992), Allaz-Vila (1993),
Wilson (2003).
•
A
capacity
nature.
payment
is
an insufficient instrum.ent with more than three states of
The capacity payment pk should compensate
tive to the socially optimal price) created
of nature
can
still
and many means
compensate
non-peakers as well
for the
if
for the
by the price cap
revenue shortfall
(rela-
With many
states
at peak.
of production (as in section 2.2), the capacity
payment
expected revenue shortfall for peakers and therefore for
the price cap corrects for market power at peak. However, the
price cap then fails to properly correct
market power just below peak. Conversely,
a price cap can correct for an arbitrary
number
there
is
of periods/ state of nature in
which
market power, provided that the plants be dispatchable in order to qualify
then
for capacity obligations;^^ but,
it
To
[0, 1]
see this, suppose that
i
G
fails
to ensure cost recovery for the peakers.
as earher,
and that there
is
market power
for
^^The dispatching requirement comes from the fact that (with more than thi-ee states) the price
may need to be lower than the marginal cost of some units that are dispatched in the Ramsey
optimum. Also, note that the ISO must be able to rank-order plants by marginal cost in order to
cap
avoid inefEcient dispatching.
23
i
^
io-
The
price cap
must be
set so that:
Cost recovery for plants that in the Ramsey optimum operate
if
and only
if z
>
iq
requires that:
(where Hj
>
j
=
1
if z
>
plant, that should operate
?'o
and
when
i
Pk> E
>
k
>
{p*
than three
at
p*2.
all
states.
Then
/a {p^
io
h>
k
and a capacity payment cannot provide the
states of nature to price-sensitive consumers,
With
three states
- p"^"^) = px
{i
cost
oi;er-recoups its investment as:
- p'-n
Similarly, the combination of a price cap
proper signals in
But then a higher marginal
otherwise).
—
if
there are more
1,2,3), though, the price cap can be set
implies that /s
(j9*
- p'"'^^) +
This reasoning has a standard "instruments vs targets"
two prices are distorted by market power (which,
the case with three states of nature, had
U {pI - V^"'') = Pk-
flavor.
incidentally, also
we assumed
When more
than
would have been
that none of the markets
was competitive), two instruments, namely a price cap and a capacity
price,
cannot
restore optimality of the competitive equilibrium.
We have
Remark:
industrial
A
considered only aggregate uncertainty. However, a price-sensitive
consumer
(or
potential issue then
an undiversified LSE) further faces idiosyncratic uncertainty.
is
that while the capacity payment can supply the consumer
with a proper average incentive to consume during peak
aggregate states),
demand
it
there are two
a "low" price p™"^ at the margin) and underconsumes in high
states of idiosyncratic
stiff).
when
implies that the consumer will overconsume for low idiosyncratic
(as she faces
obUgation are
(say,
demand (provided
that penalties for exceeding the capacity
This problem can however be avoided, provided that consumers
24
regroup to iron out idiosyncratic shocks
a mechanism similar to that of "bubbles"
(in
in emission trading programs, or to the reserve sharing
arrangements that existed
^^
prior to the restructuring of electricity systems).
Proposition 3 Capacity
tives by
obligations have the potential to restore investment incen-
compensating generators ex ante for the shortfall in earnings that they
incur due to the price cap. Suppose that haseload generation
With
(i)
most
at
three states of nature (and hence at
market power), the Ram.sey optimum can
power
is
most two
competitive:
states of nature with
be achieved despite the presence of
through, a combination of price cap
and capacity
• off-peak plants are eligible to satisfy
LSE
will
market
obligations, provided that
capacity obligations and. to receive
capacity payments,
• all
consumers (including price- sensitive ones) are subject
gations,
(ii)
and they pay
to the capacity obli-
the applicable capacity prices.
With more than three states of nature (and more than two
states of nature with
market power), a combination of a price cap and capacity obligations
eral inconsistent with
alleviating
Ramsey
market power
ing peakers;
and
is
economic signals in
off
optimality.
peak through a
is
in gen-
The regulator faces a trade-off between
strict price cap
and not overincentiviz-
further unable to provide price- sensitive consumers with proper
all
states of nature.
Time inconsistency / political economy
(Coming back
to perfect competition
and two states of nature), suppose that the
regulator imposes an unannounced price cap, p"^'^^
A
<
p*,
once K2 has been sunk.
regulatory rule that sets a price cap eciual to the marginal operating cost of the
^^The consumers that regroup within a bubble nmst then design an internal market (with price
P2) hi order to induce an internally efEcient use of their global capacity obligations.
25
peaking unit with the highest marginal cost
an example. Such a rule precludes
is
recovery of the scarcity rents needed to provide appropriate incentives for investment
Then one
in peaking capacity.
Avould want a capacity
payment
to offset insufficient
incentives:
PK =
The second best
/2 [P*
- P'^n
.
then restored subject to the caveats enunciated in the previous
is
subsection (except for the one on ex ante monopoly behavior, which
is
not relevant
here)
The imposition
of a price cap in this case
is
of course a hold-up
on peak-load
investments (peakers).'^^ In practice, what potential investors in peaking capacity
want
effectively a
is
forward contract that commits to capacity payments to cover
their investment costs to ensure that they are not held
fortable that they have a
good
legal case that
up ex
post.
are com-
they can't be forced to produce
the price does not at least cover their variable production costs.
rents" that they are concerned will
They
It is
if
the "scarcity
be extracted by regulators or the ISO's market
monitors.
Absence of clearing price
The
third avenue
much
so
is
to assume a choke price: £>2 {Po)
that no consumer under
RTP
=
(the
peak price goes up
ever wants to consume). Alternatively, one
could consider the very, very short run, for which basically no-one can react (even
D consumers).
the
the price
is
One can
in the
Either way, the supply and
infinite (given
D2
— VOLL
(p*)
>
A'2
under the
We
first
curves are both vertical and
hypothesis).
in order to provide generators
with the right incentives
absence of capacity payment. As Stoft (2002) argues,
VOLL pricing augments
set p2
may occur through other channels than price caps. For example, the ISO
purchase excessive peaking capacity and dispatch it at marginal operating cost during peak.
•^^Regulatory hold-ups
may
demand
take up procurement issues in Section
3.2.
26
But
market power.
again,
it
is
unclear whether market power
is
best addressed
through price caps or through a requirement that LSEs enter into forward contracts
for a large fraction of their
potential issue
is
peak demand or through some other mechanism. Another
that the regulatory
500 times the average energy- price)
VOLL
the
consumer
length.
is
very hard to compute:
commitment
ma}'^
be weak.
VOLL
A
pricing (that
may
third potential issue
As we discussed above, the outage
reach
is
that
cost for the
varies substantially with the degree of anticipation of the outage
and
its
2^
Whatever the
most often
reason, regulatory authorities
way below (any reasonable measure
Hes
to
of)
the
VOLL. As
is
set a price
cap that
well-known and was
discussed earlier, the price cap depresses incentives for investment in peakers. Con-
sumers and LSEs individually have no incentive to compensate
shortfall in earnings to the extent that benefits
by
all (a free
for the peakers'
from capacity investment are reaped
rider problem).
Thus, the analysis
is
qualitatively the
same
as previously; quantitatively, though,
the effects are even more dramatic due to the very large wedge between the price
cap and the socially optimal price during outages.
Procurement by the ISO
3.2
Another potential factor leading to discrepancies between wholesale prices and
scarcity values
for
is
linked to the
social
way system operators purchase, dispatch and charge
energy and reserves (Patton 2002).
practices: out-of-merit dispatching
We
study the implications of two such
and recovery
of
some
of the capital or operating
costs of generation through an uplift charge that allocates these costs to wholesale
prices based
on some administrative costs allocation procedure.
As described by Patton, Van Schaik and
26
EdF
(1994, 1995).
27
Sinclair (2004,
page 44) in their recent
evaluation of the
New England
ISO's real time wholesale energy market,
when
"Out-of-merit dispatching occurs in real time
from
a unit
whose incremental energy bid
[locational marginal price] at its location.
assume the two resources
resource and a $65 per
at $65.
closest to the
MWTi
is
energv^
produced
is
gxeater than the
In a very simple example,
margin are a $60 per
resource, with a
MWli
market clearing price
When a $100 per MWh resource is dispatched
out-of-merit,
be treated by the [dispatch] software as a resource with a $0 [per
offer.
LMP
it
set
will
MWh]
Assuming the energy produced by the $100 resource displaces
of the energy produced
by the $65 resource, the
price will decrease to $60 per
all
[locational marginal]
MWli."
Accordingly, the marginal cost of the most expensive resource dispatched
is
greater than the market clearing price and the associated marginal value placed on
incremental supphes by consumers at
the
ISO
effectively
pays two prices
its
location.
for energy. It
through the market and a second higher price
Note as well that
pays one price
for the resource
merit, while treating the latter in the dispatch stack as
cost) of zero.
Out-of-merit dispatch
is
for
if it
ramping constraints that are not
prices available to the
ISO
example,
energy dispatched
dispatched out-of-
had a bid (marginal
typically rationalized as being necessary to
deal with reliability constraints or dynamic factors related to
or
in this
fully reflected in the
minimum
run-times
"products" and associated
in its organized public markets.
Uplift refers to a situation in which the
in excess of the revenues the generator
ISO makes a payment
would receive by making
to a generator
sales
through the
ISO's organized wholesale markets. These additional payments are then recovered
by the ISO by placing a surcharge on wholesale energy transactions based on some
administrative cost allocation formula.
The
28
costs of out-of-merit dispatch, the costs
power markets, out-
of voltage support in the absence of a complete set of reactive
of-mai'ket pajanents
available during
made by
the ISO to ensure that specific generating units axe
peak demand periods, and out-of-market payments made by the ISO
to certain customers to allow the
be recovered through
uplift charges.
VanSchaick and
what
In
may be
Sinclair,
demands on short notice may
follows, however,
we
treat the effects
uplift charges separately.
Different
recovered with different allocation procedures (Patton,
page
51.)
Out-of-merit dispatching
3.2.1
we assume
In this subsection,
dispatches
them
price-cost test.
A'l is
to curtail their
and recovery through
of out-of-merit dispatch
sources of uplift costs
ISO
at the
Assume
that the
bottom
ISO contracts
that there are two states: State
used only during peak (investment cost
react to the real-time price.
(resp.
A
Ii,
I2
< h,
fi{Pi-ci)
on peak, with demand i?2(p)
h =
/2 {pl
Supply
=
-
+ f2{p*2-Ci)
C2)
demand:
D.iPl)
= Kl
D2{P*2)
= K* + K* = K*
29
,
wdthout regards to a
off-peak, state 2 peak.
ci), A'2 is
marginal cost
fraction /i (resp.
Free entry conditions:
1 is
marginal cost
Competitive equilibrium (indexed by a "star"):
h =
peak production plants and
of the merit order (at price 0)
baseload capacity (investment cost
demand Di{p)
for
C2
>
peak capacity,
Ci).
Consumers
f^) of periods is off peak, \\dth
>
-Di(p)).
The competitive
equilibrium
is
depicted in figure
1.
prices
installed capacity
Figure 1
ISO procurement
behavior
Suppose that the ISO contracts
them
as
even
at price
ISO purchases
also that
peak.
is
units of capacity
and dispatches
This sounds strange, but more generally, as long
if
the dispatch
is
not economically
one could imagine that state
There would then be an off-peak state
price Po
K^ < K^
are financed externally, perverse effects arising from
decisions arise only
Note
off
for
1 is
efficient as
ISO dispatch
long as A'2
<
i^|.
an intermediate state of demand.
with frequency
/q.
As long
as the off-peak
unaffected, one can easily generalize the analysis below.
In order to clearly separate the effect studied here from that analyzed in the next
subsection,
assume that ISO
practice, there
would be
losses (to
be computed
later) are financed externally (in
injection / withdrawal taxes, that
would
shift
the curves.
Let us thus abstract from such complications).
Short-term impact.
One may have
in
We anatyze the short-term impact assuming a fixed
mind that K2
of the
K2
capacity K2.
units of peaking capacity are purchased
by the ISO. For given investments K^ and K^, the short-term impact
30
of the
ISO
policy
is
depicted in figure
2,
which assumes K^
=
K^:
installed capacity
K\
K\ + Kl
Figure 2
the peak price remains unchanged
the off-peak price faUs to
• there
• the
is
ISO
max
(^2)1
{ci, J9f
"*"
{K^
+ K2)} = pf^,
overproduction off-peak,
loses
f^Ki{c2-pn-
Long-term
effects.
units that
it
Suppose that the ISO buys a quantity iv^
dispatches at zero price.
It is
<
-f^l
o^ peak-period
easily seen that prices
and capacities
adjust in the following way:
• P2 ^
= P*2
P^ = Pi
•
Peak units substitute partly
for off-peak units (production inefficiency):
31
Proposition 4 Suppose
that
ISO purchases K^ < K^
are financed externally
(i.e.,
not through an uplift) and are dispatched out- of-merit.
(i)
The short-term incidence of a purchase
is
entirely
on
off-peak price
and quantity:
Pi decreases, qi increases.
(a)
Proof: To prove part
Next
condition.
but then
A'l
=
if
p2
(ii),
<
In the latter case, pi
K^ + K[^ =
pi,
—
then
that
K=
>
jdo
Ki
-\-
P2
^^
inconsistent with the free-entry
K^ > K*, and
—
P2-
in this section
come
solely
ciency as long as energy
To
if
is
from
dispatched only
when the market
if
K2
if
or
<
pi;
Ki >
0.
one must
price,
is,
there
A'l units
and dispatched
fall
it
efficiently only to
in the short run.
could drive the peak period price
ment strategy would be
inefficient.
down
it
is
no
ineffi-
price exceeds marginal
dispatch
is
inefficient.
units of peaking capacity
the dispatch were
quantity of additional peaking capacity and bid
it
tliis
If it
Specifically
efficient.
additional purchases of peaking capacity to increase
the peak period price would
cost C2
get
That
inefficient dispatching.
the ISO were to purchase more than
made
more than
=
pi
assumes that the ISO purchases no more than
could affect the peak period price even
the ISO
K^ < K2,
2).
Moreover, peak period prices are unaffected even
However,
if
Next either Ki
pi by the free entry condition.
and
so
peaking capacity and finances any revenue shortfalls externally. In this
case inefficiencies
cost.
first
A'* (see figures 1
Remark: The analysis
A'2 units of
note
a contradiction. Hence p2
0,
a substitution of off-peak
is
and off-peak prices are unaffected.
units by peakers; on-
have
< K^
The long-term incidence of a purchase Jl"
its
it
if
ownership to
meet peak period demand,
purchased a large enough
into the
market
to C2. Clearly, such
at its
marginal
an ISO invest-
Moreover, such a strategy would have significant
adverse long run effects on private investment incentives.
Private investment in
peaking capacity would be unprofitable and the incentives to invest
32
in
base load
capacity would also be reduced. In the long run this would lead to a substitution
of peaking capacity for base load capacity
and could potentially lead to a situation
where the ISO had to purchase a large fraction of the capacity required to balance
supply and demand.
Recovery through an
3.2.2
uplift
In practice, ISO purchases are not financed through lump-sum taxation.
some
or
uplift.
all
of the associated costs are often at least partially recovered through an
There
monthly
is
no general rule on how
(often) or annually.
They
uplifts are recovered.
are typically spread across
be allocated to groups of hours
will
work with the polar case assumption that none
(for
purchases are recovered from market revenues, but
may be
They can be recovered
all
kWh, but they can
example peak hours). In
also
costs
Rather
this section,
of the associated costs of
we
recognize that
some
we
ISO
of these
recovered from market revenues rather than uplift charges. There are
several reasons for
why some
of the costs of
ISO purchases
in practice are not fully
recovered from selling the energy in the market and so an uplift
is
needed: existence
of a price cap; absence of a locational price allowing recovery at an expensive node;
and usage
of reserves outside the
market
a) Let us analyze the implications of
the cost recovery
through the
is
place.
an
uplift, starting
spread over peak and off-peak periods (the cost
A'2 units of
and dispatches the corresponding units only on peak
in subsection 3.2.1 does not arise).
A'2,
is
"socialized"
uplift).
Suppose that the system operator purchases
Ki +
with the case in which
peaking energy forward,
(so that the inefficiency studied
Total capacity to meet peak
where
-
K2 = Kl
if
/. (p2
C2)
<
h
K2>KI
if
f2{P2-C2)
=
I2.
33
demand
is
then
The
uplift
t is
given by
t
+ t) + hD^ {P2 + t)] = KV2
[fiD, {p,
Off-peak capacity, K2, and prices are given by:
Di
h
-
{P\
Ci)
=^
Peak capacity
+
-
/2 (P2
E{p)
=
Ci)
= h
E{p*).
satisfies:
D2
And
= R\
+t)
{pi
+
{P2
t)
^ Ki +
K2.
so
t
[A^i
+
f2K2]
=
K'lh.
Figure 3 depicts the equihbrium outcome for Hnear demands {Di
For small purchases if^i production prices (pi,p2) don't
curement.
K2 and
This
is
because the private sector
so peak and off-peak prices
ditions.
of
demand
functions and
uneconomical to invest
is
move
ai
— p)
size of pro-
peaking capacity beyond
is
negatively affected by the uplift, while
(the latter property hinges
on the linearity
not robust). At some point, the private sector finds
in peakers; the only available
procured by the ISO. The peak price
with the
offers
move with the
—
must remain consistent with the free-entry con-
Investment in off-peak capacity
total peaking capacity does not
still
{p)
falls
peaking capacit}^
is
it
then that
and the (before tax) off-peak price gTows
size of purchases.
34
KS
Ki
,
A'a
A'l"
A'"
laxge
purcllases
Figure
The
SociEdized uplift (dotted Hue: uplift levied
solely on peak, consumption)
3:
results generalize to
demand
< D[
D'2 ip2)
condition
(this
is
much
functions such that
(pi)
whenever p2
>
pi
stronger than needed, though).
Last, let us consider the impact of an uplift levied solely in peak periods
b)
The
uplift,
when
f2tD2
The
on peak consumption
levied
ip2
+ t) = Kp2 <=^
only,
f2t
[K,
=
/i.
off-peak conditions are
A(pi) =
A^i
and
/l {P\
or,
-
Cl)
+ J2
{P2
-
C\)
equivalently
E[p]
=
E[p*].
35
+
is
given by:
K2)
=
K%.
The peak conditions
are, as earlier:
= K^
if
/2(p2-C2)</2
K2>K^
if
/2 (P2
D2
=
^l
K2
-
C2)
=
/2,
and
+
{P2
+ ^2-
Hence:
(10)
^^("^^mItT^I^^^'^^'^We
assume that the equation
in
K
an arbitrary ^2)
(for
B.|p. +
A'?/,
^l=if
K and that this solution
admits a single solution
is
decreasing in /C". 27
For small purchases, as in the case of a socialized
complemented by private sector
offering
{K2
>
a small purchase 7^°
uplift,
-^2) ^^^^ ^o P2
= ^2-
average price must be the same as for the free entry equilibrium, pi
is
Given that the
is
then equal to
Pi-
Hence, for
K2
K2
Pi
=
pI
Ki
=
K*.
small,
and
decreases as
P2
K2
= p2
increases
ISO
investment in peakers by
:
There
—
C2)
<
full
crowding out of private
purchases.
For larger purchases at some point K2
disappears (/2 (p2
more than
is
h)- But (10)
=
still
A'2
and private investment
holds.
in
peakers
Suppose that when iv^ increases,
P2 increases; then pi decreases (as the average price
must remain constant) and so
^^One has
« = |^«;.
Because, in this range, I2
of
=
/2 (P2
demand —D'2Pi/D2 be equal
—
C2),
a sufficient condition for this
to or less than one.
is
that the peak elasticity
(and so does K). For a given K, the left-hand side of (10) decreases as
i^i increases
P2 and
K2
Hence p2
increase.
So to restore equahty
increases.
Proposition 5 Suppose
and
(i)
K must decrease, a contradiction.
in (10),
an
that
uplift is levied in
order to finance
ISO
purchases,
that the latter are dispatched in merit.
If the uplift
is
socialized, off-peak capacity is reduced,
peak capacity
may
increase
or decrease, and prices are unaffected for small purchases. For larger purchases, the
off-peak price increases while the off-peak capacity decreases; the peak price decreases
while the peaking capacity increases with the size of the purchases.
increase, private investment in peakers becomes unprofitable at
only available peaking capacity
is
is
by
the
some point and
the
procured by the ISO.
(a) If the uplift applies solely to peak energy consumption,
affected
As ISO purchases
only peak capacity
is
(downward) for small purchases. For larger purchases, the characterization
same
as for a socialized uplift.
ISO purchases and
as
There
ISO purchases
is
more than full crowding out of peakers
increase a point
reached were private
is
investment in peakers disappears.
4
Network support
services
and blackouts
This section relaxes another key assumption underlying our benchmark proposition
(Proposition
1).
There, we assumed that, while there
makes use
and rationing,
this rationing
assumption
a decent approximation
is
may be
of all available generation resources.
for, say,
controlled rolling blackouts
the system operator sheds load sequentially to ensure that
ceed available generating capacity.
in
insufficient resources
It is
This
where
demand does not
ex-
not for system collapses where deviations
network frequency or voltage lead to both generators and load tripping out by
automatic protection equipment whose operation
bances on the network. For example, the August
37
is
triggered by physical distur-
14,
2003 blackout in the Eastern
United States and Ontario led to the
New
the networks in
in a
demand within
up to 48 hours.
The September
2003).
entire country
of the generating capacity
under the control of the
tripped out despite the fact that there was a surplus of generating
capacity to meet
of service took
as
MW of generating capacity was knocked out of service
Most
few minutes time.
New York ISO
power to over 50 million consumers
York, Ontario, Northern Ohio, Michigan and portions of other
Over 60,000
states collapsed.
loss of
28,
the
New York
ISO's control area. Full restoration
(U.S.-Canada Power System Outage Task Force,
2003 blackout in Italy led to a
and suddenly knocked out over 20,000
loss of
power across the
MW of generating capacity.
Restoration of power supplies to consumers was completed about 20 hours after the
blackout began
(UCTE,
Conceptually, there
2003).
is
a key difference between rolling blackouts in which the
system operator sequentially sheds relatively small fractions of total demand to
match
available supphes in a controlled fashion
and a
both demand and generation shuts down over a large area
Under a
value
is
rolling blackout, available generation
VOLL). By
collapses.
To put
it
is
system collapse in which
total
in
an uncontrolled fashion.
extremely valuable
contrast, available plants are almost valueless
differently, there
is
(actuall}^, its
when the system
then an externality imposed by generating
plants (or transmission lines) that initiate the collapse sequence on the other plants
that trip out of service as the blackout cascades through the system, that does not
exist in
It is
an orderly, rolling blackout.
useful here to relate this
economic argument to standard engineering consid-
erations concerning operating reserves (OpRes). In addition to dispatching generators to supply energy to
match demand, system operators schedule additional gener-
ating capacity to provide operating reserves (OpRes). Operating reserves typically
consist of "spinning reserves"
which can be
fully
ramped up
of electric energy production in less than 10 minutes
38
to supply a specified rate
and "non-spinning reserves"
which can be
in
some
ramped up
fully
places)
.
to supply energy in
up
to 30 minutes (60 minutes
Operating reserves are used to respond to sudden outages of gen-
erating plants or transmission lines that are providing supplies of energy to meet
demand
bility
in real
time sufficiently quickly to maintain the frequency, voltage and sta-
parameters of the network within acceptable ranges. Additional generation
is
also scheduled to provide continuous frequency regulation (or automatic generation
control) to stabilize network frequency in response to small instantaneous variations
in
demand and
generation. These ancillary network support services require schedul-
ing additional generating capacity equal to roughly 10-12% of electricity
any point
demand
at
in time. In the U.S., regional reliability councils specify the requirements
for frequency regulation
and operating
reserves, as well as other ancillary services
such as reactive power supplies and blackstart capabilities, that system operators
are expected to maintain.
Pending U.S.
would make these and other
legislation
rehability standards mandator}^ for system operators.
Let us use a simple model of
To keep modeling
is
modeled
details to a
as inelastic:
Similarly,
minimum without
is
diV,
on the supplj^
involves investment cost
order to analyze the various issues at stake.
KI
altering insights, the
demand
In state ie [0,1],
the consumers' gross surplus
lost load).
OpRes in
where v
is
cost
c,
Di.
If di
the value per
side, there is
and marginal
is
demand
< Di
kWh
is
side
served,
(the value of
a single technology: capacity
which we normalize at
K
in order
to simplify accounting.
The key innovation
is
not fully
known
relative to the
at the
scheduled to meet the
benchmark model
is
that the extent of scarcity
time that generating units with uncertain availability are
demand dispatched by
the system operator.
uncertainty as an uncertain capacity availability factor Ae
1
—A
of the capacity
K will break down.
The
39
[0, 1].
We formalize this
That
distribution Hi (A) (with
is,
a fraction
i^j (0)
=
and
Hi{l)
A
=
=
1)
1 (full availability),
We make
—
hi (A).^^
the following weak assumption:
-
H^
(a sufficient condition for this
[1
in the distribution at
but the distribution has otherwise a smooth density
[1
hi/
may be an atom
can be state-contingent.^*^ There
Hi]
is
'^-^^^-^-g-^
(A)]
is
the standard assumption that the hazard rate
increasing in A, which
is
satisfied for
most commonly used continuous
probability distributions.)
The timing
the
SSO
demand
goes as in Figure
chooses
how much
of this
Given nominal capacity
4:
demand
More
to curtail, and a reserve margin.
system operator can curtail an amount Di
coefiicient r^, so that a capacity (1
Then, the capacity
availability Aj
the network collapses:
If A^ [(1
is
+
to dispatch
<
formally, once load
K
D^
is
how much
realized, the
also chooses a reserve
must be ready to be dispatched.
revealed and the
d^,
and demand Di,
or alternatively
— di>Ooi load. He
r^) di
+ r,) di] <
,
K
demand
di
<
Di
is
served or
the system collapses, and no energy
is
produced or consumed.
Long-term
Load D,
choice of
state
capacity
z
in
Choice of
Availability A, realized
^ dispatched load
^
if
realized.
7f.
^^
k'
,
i/
AJl +
r,)
>
1,
load
d, is satisfiedr
^ ^^
reserves ridi.
'
'
if
X, (1
I
system
+
7-;)
<
1,
li
collapses.
Figure 4
We
mand
assume that scheduling generation to be
costs
.s
per unit
^®For example,
if
(s
(potentially) available to serve de-
can be either a monetary cost of keeping the plant ready
plant unavailability comes from the breakdown of a transmission line connecting
may be more likely to break down under extreme
weather conditions, for which load Di is also large.
^^We assume a continuous distribution solely for tractability purposes. In practice, system
operators fear foremost the breakdown of large plants or transmission lines and therefore adopt
reliability criteria of the type "n — 1" or "n — 2". This introduces "integer problems", but no
fundamental difference in analysis.
the plant and the load, the transmission line
40
to be dispatched or an opportunity cost of not being able to perform maintenance
at an appropriate time).
a) Social
optimum
A Ramsey
social planner
max
<
E
would
solve:
1
1-H,
i
{K,d.,r.}
such that, for
all
states
i
6
-
V
+n
s{l
+
r,)
di-KI
[0, 1]:
di< Di
.
(1
where
(/i,)
+ rO di<K,
Hi
and
Ui
(ui)
are the
shadow
prices of the constraints.
For conciseness, we analyze only the case where
reserves in each state.
The
first-order conditions
it
is
optimal to accumulate
with respect to
r^, di
and
K
are,
respectively:
hi
:V
—
S
=
(i+^y
[1
—
Hi] V
—
s {1
+ ri) >
iJ-i
+
{I
+
r,:)
(11)
Ui,
with equality unless
Ui,
di
=
Di
(12)
and
E[u,]
=
I.
Specializing the m,odel to the case in which Hi
lyze the optimal dispatching, as described
is
depicted in Figure
^'^We will
state
i.
still
by
(11)
(13)
is
state-independent,'^^ let us ana-
and
(12).
The Ramsey optimum
5.
use state-denoting subscripts, though, so as to indicate the value taken for
For example. Hi
=
H (1/ (1 + r^)).
41
H
in
A Dispatched
load
(
ct,
i
I
i
load curtailed
i
1
!
<
i
!
!
;
\
/
>
A
\
i
i
yAy
45°
Reserve
ratio
!
!
i
i
_"r!rtr::=->^
!
!
1
A
!
K
off-peak
(price:
(1
+
ra)
Figure 5
1
s
=
0.
load shedding
J^
reduction
+rH
j
(price:
_(_ y-
v/il
)
when
(prices indicated in parentheses are prices paid
Off-peak [Di small), there
^:
resenie
Hence from
(11)
and
is
excess capacity,
all
+
rrj
served)
by consumers)
demand
is
served
{di
=
Di),
and
(12)
^rn
r
Avhere
1
h
1
(1
We
of course
assume that
off-peak region
is
rff
V
=
s.
+ ^i/)^
for this value,
it is
1
l-H
The
+
V
l
+
TH,
(1
+
t-h)
worth dispatching load
>
s(l
+
Th)
(/ij
>
satisfied:
di
=
or
.
defined by:
Di
< K.
Peaking time can be decomposed into two regions. As D, grows, load
being
0),
Di, and reserves
become
42
first
keep
leaner (and so the probability of a
blackout increases as load grows):
Load
starts being shed
when
=
//j
0,
or
1
hi
-H,]
[1
+n
1
which from our assumptions has a unique solution:
The optimal investment
policy
is
then given by:
/oo
h,.
V
K
:i
1+TH
The
first
—
s
(1
+ rX-
H,)
fidi.
:i+^-l)
l+'-L
term on the right-hand side of
in reserve reduction states:
-
An
this equation represents the quasi-rents
extra unit of capacity
and thereby reduce the probability of network
used to increase reserves
is
collapse, 1
—
Hi (Di/K), then saving
value of lost load vDi] to this term must be subtracted the cost s of scheduling
generation.
An
(1
And
the second term represents the quasi-rents in load shedding states:
extra unit of capacity allows a reduction in load shedding, which has value
—
Hi) v/
(1
+
ri)
minus the cost
s of scheduling generation.
b) Implementation
First, note that the possibility of
public good. Network users take
system collapses make operating reserves a
its reliability
as exogenous to their
atom
of the
H
(•)
Thus, the market solution leads to an insufficient level of
obtain a proper level of
their
LSE)
^^ There is
reliability,
to purchase a fraction
r^
policy and
The market-determined
thus are unwilling to voluntarily contribute to reserves.
level of reliability is therefore the size of the
own
distribution at
reliability.
A
=
1.
In order to
the system operator must force consuihers (or
of reserves for each unit of
no point further asking generators to hold
43
reserves.
load.'^-^
Does
this
market mechanism cum regulation of reserve ratios generate enough
< K/
quasi-rents to induce the optimal investment policy? Off-peak {Di
the price paid by consumers for reserves
When
load
is
> K/
curtailed (D,
(1
is
+
{1
+
ru)
s,
r//)),
and there are no quasi-rents.
then consumers must pay v/
tl)),
+
(1
conditionally on being actually served (which has probability
1
—
(1
+
r^,)
Hi). Thus, gener-
ators obtain, as they should, quasi-rent:
(1
-
H,)
-^
+
s
rx
l
in this region.
The intermediate
region
is
more complex
to implement through an auction-type
mechanism. In the absence of price-responsive load, the supply curve and the
tal
demand curve
(energy plus reserves) are vertical and identical.
to-
Hence a small
mistake in the choice of reserve ratio creates wild swings in the market price (from
(1 -h
r-j)
.s
to v/ (1 -H Ti) conditionally
operator can bring price
down
on being served).
system
In particular, the
to marginal cost without hardly affecting reliability.
This has potentially significant implications for investment incentives.
The
"knife edge"
lot of discretion in
problem has been recognized by system operators.
It
puts a
the hands of the system operator to affect prices and investment
incentives as small deviations in this range can have very big effects on prices.
the end, determining
when
operating reserve deficiency)
pends
way
in part
in the
on attributes
there
may
of the
rough requirements
is
an operating reserve deficiency
necessarily involve
some
(or a forecast
discretion because
network topology that are not reflected
for
operating reserves
minutes). So, for example, stored hydro
is
(e.g.
ramp up
In
in
in less
it
de-
a refined
than 10
generally thought to be a superior source
of operating reserves than fossil plants because the former can be
instantly rather than in 9 minutes. If there
is
ramped up almost
a lot of hydro in the
OpRes
portfolio
the system operator will be less likely to be concerned about a small shortfall in
44
operating reserves.
compute the marginal
Alternatively, the system operator can
h'Y^
(Av),
)
social benefit,
of the reduction in the probability of collapse brought
by an additional unit
about
of investment. This regulated price for reserves (and thus for
energy) then yields the appropriate quasi-rent:
hi
[i
V
—
s
+ nf
to generators in this region. Accurately computing the regulated prices in this region
also involves substantial discretion, however.
Proposition 6 Suppose
the time of generator
(i)
The
•
that the extent of scarcity is not
Off peak: the entire load
is
dispatched,
Load shedding: Load
The
(a)
and operating reserves are
the entire load is dispatched,
reduced as generation capacity
mum
demand grows,
three regimes:
set at a fixed,
percentage of load.
• Reserve shedding:
•
certainty at
and load dispatch.
socially optimal policy involves, as the forecasted
maximum
known with
is
is curtailed,
and operating reserves are
binding.
and operating reserves
satisfy a fixed, mini-
ratio relative to load.
possibility of
system collapses makes operating reserves a public good. As
a result, investments in operating reserves do not emerge spontaneously as a
market
outcome. The load should be forced to pay for a pre- determined quantity of operating
reserves (e.g. as a proportion of their
• a price set at
VOLL
demand)
:
(divided by one phis the reserve ratio, conditionally on
being served) in the load shedding region,
•
a market clearing price given the ratio requirement off peak,
45
• a price growing
from marginal
cost to the load-shedding-region price in the
reserve-shedding region. Decentralization through an operating reserves market
together with a m,andatory reserve ratio
as the price of reserves is
is delicate
extremely sensitive to small mistakes or discretionary actions by the system
operator.
Conclusion
5
We derived the
an
(second-best) optimal
electricity sector in
program
for prices,
output and investment for
which non-price sensitive consumers
may have
to be rationed
under some contingencies. This allocation provides a benchmark against which the
actual performance of electricity sectors, and the effects of the imposition of various
regulatory and non-market mechanisms and constraints, can be compared.
on to show that competitive wholesale and
best
"Ramsey"
markets
will
support this second-
allocation under a particular set of assumptions.
The assumptions underpinning
gram
retail
We went
these results are very strong.
Our
research pro-
seeks to evaluate the effects of departures from the assumptions needed to
support the benchmark allocation.
sumptions
(a)
of generation
In this paper
we focused on
relaxing the as-
that wholesale electricity prices reflect the social opportunity cost
and
(b) that rationing, if any,
is
orderly and
makes
efficient
use of
available generation.
To examine the
effects of relaxing the first
assumption, we analyzed the effects
of regulator-imposed prices caps motivated either
in the real time
by concerns about market power
market or by regulatory opportunism. While price caps can
signifi-
cantly reduce the scarcity rents required to cover the costs of investment in peaking
capacity, lead to underinvestment,
at
most three
obligations
states of nature (and
and
up
distort the prices seen
to two states with
and associated capacity payments can
46
by consumers, with
market power), capacity
restore investment incentives
if
all
generating capacity
payments, and
is eligible
to
meet capacity obligations and receive capacity
consumer demand
all
to examine the effects of
is
subject to capacity obligations.
ISO procurement
We
go on
strategies that involve either inefficient
generator dispatch or the recovery of some generation costs through an uplift. These
ISO procurement
strategies can distort prices
and investment decisions in various
ways.
Our
analysis then proceeded to examine the effects of relaxation of the second
We
assumption underpinning the benchmark allocation.
demand and operating
in rationing of
demand stands
known with
reserves to analyse the effects of network collapses that result
demand
idle.
used a model of uncertain
while generation that
is
potentially available to
Unlike the benchmark model, the extent of scarcity
certainty at the time of generator dispatch.
reserves are a public
meet
In this
is
this
not
model operating
good and without mandatory operating reserve requirements
there would be under investment in operating reserves and lower reliability than
is
optimal. Moreover, under certain contingencies the market price, and the associated
scarcity rents available to support investments in generating capacity, are extremely
sensitive to small mistakes or discretionary actions
"knife edge"
problem and options
for dealing
with
by the system operator. This
it
requires further analysis
and
attention in the development of the rules and incentive arrangements governing
system operators.
In Joskow-Tirole (2004)
we examine relaxation
of the other key assumptions that
underpin the benchmark model, focusing on the impacts of load
tioning of
demand
for
profiling, zonal ra-
both price sensitive and price insensitive consumers, and
more general characterizations
of
consumer heterogeneity.
Taken together, these
results suggest that the combination of the unusual physical attributes of electricity
and
electric
on metering
power networks and associated
of real time
reliability considerations, limitations
consumer demand and responsiveness to
47
real
time prices,
restrictions
on the
ability to ration individual
system operators, makes achieving an
itive
consumers, discretionary behavior by
efficient allocation of
resources with compet-
wholesale and retail market mechanisms a very challenging task.
48
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51
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