Scholarly article on Benzyl alcohol 100-51-6 from

Flowgates, Contingency-

Constrained Dispatch, and

Transmission Rights

There are many reasons to doubt the basic assumption of

a ﬂow-based market; including that there are only a few

commercially signiﬁcant ﬂowgates and these have ﬁxed

capacities and power distribution factors. Perhaps the most

important is that ﬂow constraints arise under multiple

contingencies, not just constraints on actual ﬂows of

physical elements.

Larry E. Ruff holds a Ph.D. in

economics from Stanford University,

and is an internationally recognized

expert on the restructuring of electric

and gas utilities to create competition

and on the operations of the resulting

competitive markets. He has advised

governments and utilities in the United

States, Canada, Europe, the former

Soviet Union, the Indian subcontinent,

the Asia-Paciﬁc region, and Latin

America on competitive restructuring.

He has served as a Senior Vice

Larry E. Ruff

roposals for ﬂow-based elec-

tricity markets are based on the

assumption that there are only a few

commercially signiﬁcant ﬂowgates

equipment (e.g., phase-shifters) spe-

ciﬁcally designed to change PDFs.

But one reason to doubt the basic

assumptions of a ﬂow-based market

is particularly noteworthy, if only

because it is so consistently misun-

derstood and underappreciated:

The actual operations of an electric-

ity system are constrained not only

by the actual ﬂows on individual

network elements, but also by the

ﬂows (and voltages, etc.) that would

appear under any of many contin-

gencies such as sudden loss of a

network element or a critical gen-

erating unit.

P

(CSFs) with ﬁxed capacities and

ﬁxed power distribution factors

(PDFs) that describe how power

ﬂows over individual elements of

the system. These assumptions are

highly suspect for many reasons,

including nonﬂow (e.g., voltage)

constraints that can be more con-

straining than ﬂow limits, nonlinear

physical relationships that cause

PDFs to change with operating con-

ditions, and the widespread use of

President at National Economic

Research Associates and a Managing

Director of Putnam, Hayes & Bartlett

Inc. He has held senior positions in

government, industry, and

nonproﬁt organizations.

34

The Electricity Journal

This article uses a simple example

to illustrate the process of

dilemma: impossible complexity

on one horn of the dilemma, and

unacceptable inefﬁciency and

inequity on the other.

physical CSFs with ﬁxed capacities

and PDFs. But they always hedge

their bets by insisting that the sys-

temoperator/dispatcher—assumed

here to be a regional transmission

organization (RTO)—should social-

ize the costs that will result when

the basic assumptions of a

contingency-constrained dispatch

1

(

CCD), discusses some of the

implications for a ﬂowgate/

The theoretical literature advo-

cating ﬂow-based markets, while

sometimes recognizing the fact of

ﬂowgate rights (FGR) market, and

explains why these same problems

do not arise in a market based on

locational marginal pricing (LMP)

and point-to-point ﬁnancial (or

ﬁrm) transmission rights (FTRs). It

is shown that a ﬂowgate/FGR mar-

ket on any complex system must

have either very many (hundreds

of?) abstract, contingent CSFs or

only many (scores of?) physical

CSFs, but each with many (scores

of?) contingent capacities and

PDFs. The only way to make FGR

trading easy and liquid in such a

situation is for the RTO to deﬁne for

trading purposes an artiﬁcially sim-

pliﬁed and restricted set of CSFs

with ﬁxed capacities and PDFs.

f the RTO creates an artiﬁcial

2

CCD, has not acknowledged the

severity of the dilemma this raises

or proposed plausible resolutions.

One prominent advocate of ﬂow-

based markets has simply

ﬂowgate/FGR market are not true.

CCD does not create the same

sort of problems in an LMP/FTR

market. In such a market, the LMPs

are computed based on actual sys-

tem operations using the full set of

actual and contingency constraints,

and the point-to-point FTRs are

perfect hedges for point-to-point

transactions for any LMPs, i.e., for

any set of binding constraints

asserted that deﬁning a CSF for

Advocates of flowgate/

FGR markets virtually

never acknowledge

and may not even

recognize the

(including nonﬂow constraints).

The RTO deals with the technical

complexity of ﬂow and nonﬂow

constraints to assure that the power

gets from where it is produced to

where it is consumed, and—as

long as the set of FTRs outstanding

is simultaneously feasible on the

grid and the grid is in its standard

dilemma they face.

I

world to make FGR trading

workable, the market solutions

arising from the artiﬁcial forward

trading will often be far from what

is actually feasible or efﬁcient on

the system, requiring the RTO to

incur signiﬁcant costs in real time

to close the gap. If the costs of clos-

ing this gap are paid by the speciﬁc

traders whose infeasible or inefﬁ-

cient forward schedules create

them, the ﬂowgate/FGR market

will not provide price certainty or

good hedges. If these costs are

socialized across system users as a

whole through some sort of uplift,

prices will be distorted and costs

will be shifted, creating both short-

run and long-run inefﬁciencies and

inequities. Thus, a ﬂowgate/FGR

market faces an inescapable

4

each network element/contin-

gency pair—the natural interpre-

tation of the mathematics—is

inconsistent with the theory of

ﬂow-based markets, but has not

dealt with the implication of non-

contingent CSFs with constantly

changing capacities and PDFs.³

Whatever the ﬂowgate theorists

may say, advocates of ﬂowgate/

FGR markets in current policy dis-

cussions virtually never acknowl-

edge and may not even recognize

the dilemma they face. They con-

tinue to say that forward trading in

a ﬂowgate/FGR market would be

easy, intuitive, and highly liquid

because there would be only a few,

condition —can honor all the FTRs

without socializing any costs.

There are very many (thousands

of?) logically possible point-to-

point FTRs, but a single transaction

can be perfectly hedged with pre-

cisely one FTR, and many similar

transactions can be approximately

hedged with one or a few FTRs; the

problem of very many FTRs is fun-

damentally different than the prob-

lem of very many FGRs.

lectricity systems are inher-

E

ently complex, much more so

than the natural gas pipelines that

are often used as analogies. It is

only human to wish that somebody,

somewhere, would invent some-

January/February 2001

thing that would somehow make

electricity simple and more like nat-

ural gas. But a ﬂow-based market is

no more likely to perform this mira-

cle of transubstantiation than is

anything else. Once the many com-

plexities of power ﬂows—including

the reality of many contingent and

nonﬂow dispatch constraints—are

taken into account, a ﬂow-based

electricity market would be any-

thing but simple. The RTO could

try to make it simple and proﬁtable

for traders at the expense of inefﬁ-

cient pricing and operations, large

socialized costs, and an extensive

role in the market for the monopoly

RTO and its regulators, and the

traders who would beneﬁt would

no doubt approve; indeed, they are

actively advocating this in policy

discussions now. But distorting

prices and shifting costs would not

beneﬁt the consumers—probably

small ones—who would pay the

higher costs, and would not pro-

duce the efﬁcient and effective com-

petition that is the objective of elec-

tricity restructuring.

submitted to the RTO are consistent

with the outstanding FGRs and the

PDFs, the scheduled/hedged ﬂows

will meet the constraints on each of

the three lines from GEN to LOAD,

and a market participant whose

operations match its FGR portfolio

will pay no real-time penalties or

congestion charges.

For example, if a generator in

GEN2 sells 10 MW to a buyer at

LOAD, the generator (or the

Figure 1: The Three-Line System

buyer) would need an FGR portfo-

lio consisting of 2.5 MW (0.25ϫ10

MW) of FGRs on Line A, 5 MW of

FGRs on Line B, and 2.5 MW of

FGRs on Line C in order to sched-

gested transmission lines, A, B,

and C, each with a 100 MW line

rating. These lines connect a gener-

ation region GEN with three subre-

gions, GEN1, GEN2, and GEN3 to

a single load center LOAD. The

PDFs indicate how energy gener-

ated in each of the three generation

subregions distributes itself over

the three lines to get to LOAD. For

example, if an additional MW is

generated at GEN1 and consumed

at LOAD, an additional 0.5 MW

will ﬂow on Line A, 0.3 MW on

Line B, and 0.2 MW on Line C.

6

ule or fully hedge the transaction.

If every schedule submitted is

fully covered by FGRs in this way

and the MW quantity of FGRs out-

standing for any line does not

exceed the physical ﬂow limit on

that line, the total scheduled ﬂow

on each line cannot exceed the line

limit. Scheduled operations will be

feasible and efﬁcient.

B. A “Hybrid” Flow-Based/LMP

Market

(Losses are being ignored.)

n simple explanations of ﬂow-

based markets, the system in

The early literature on ﬂow-

based congestion management

implied or assumed that no

markets other than the forward

markets in energy and FGRs

would be required, because the

FGRs would accurately reﬂect the

real constraints and trading would

be efﬁcient, so that the resulting

schedules would be feasible and

efﬁcient. The RTO would have so

little to do in real time that it need

not—indeed, should not—operate

a real-time market, but should just

pay a few generators for a few

ancillary services such as load-

I. Contingency-Constrained

Dispatch in a Hybrid Market

I

Figure 1 would usually be described

as having three potential CSFs, one

for each potentially congested line

This section describes the CCD

process using a simple three-

constrained-line example. It also

discusses the concept of a “hybrid”

market in which forward trading is

based on ﬂowgates and FGRs

while real-time operations and

pricing are based on LMP.

5

or physical network element. To

establish a ﬂow-based market, the

RTO would simply sell 100 MW of

FGRs on each CSF/line and publish

the nine PDFs. Market participants

would then trade the three types of

FGRs (and energy) freely among

themselves in forward markets to

determine transactions or sched-

ules that are consistent with the

FGRs they hold. If the schedules

A. A Flow-Based Market on a

Three-Constrained-Line System

The example system shown in

Figure 1 has three potentially con-

36

The Electricity Journal

following and reactive power, and

in the rare emergency use command-

and-control methods such as trans-

mission loading relief (TLR).

by Chao et al., the RTO identiﬁes

the CSFs, issues the FGRs, deﬁnes

the PDFs used for trading in for-

ward markets, and then operates a

real-time LMP market that prices

and settles all residual congestion

and imbalances. In settlements,

both spot and scheduled transac-

tions pay congestion charges equal

to the difference in LMPs between

the sink and source locations, and

holders of FGRs are paid the value

of their FGRs, with both LMPs and

Chao et al. accept the standard

ﬂowgate/FGR assumptions and

hence do not discuss what hap-

pens when there is nonCSF con-

gestion or when real-time CSF

capacities and PDFs are not the

same as those used to deﬁne FGRs

and hedging portfolios. But if the

ﬂowgate/FGR assumptions are

correct, there is no reason the RTO

should not use all actually binding

constraints and actual PDFs to

determine the LMPs and FGR

prices used in real-time settle-

ments. This rule would require

traders to pay congestion charges

reﬂecting any nonCSF congestion

and changes in CSF capacities

and PDFs, but these congestion

charges should be commercially

insigniﬁcant—if the ﬂowgate/

FGR assumptions are correct.

ecause the objective here is to

ore recently, ﬂowgate/FGR

M

proponents have recog-

nized that electricity is more difﬁ-

cult than natural gas, and hence for-

ward trading will often produce

schedules that are not fully feasible

or efﬁcient in real time, leaving

more for the RTO to do. Indeed,

most ﬂowgate/FGR advocates now

concede that the RTO should oper-

ate a real-time LMP market to man-

age and price real-time imbalances

and congestion. This LMP market

may be described as a residual mar-

ket that will price and settle only

small amounts of energy, but it will

require most of the processes and

systems required for a full LMP

More recently,

flowgate/FGR

proponents recognized

that electricity is

more difficult than

natural gas.

7

market —although FTRs, which

hedge against real-time LMPs, may

not be needed if FGR trading leaves

little real-time congestion.

B

illustrate the problems cre-

ated when the ﬂowgate/FGR

assumptions are not correct, it will

be assumed that the RTO com-

putes real-time settlement prices

that reﬂect all actual congestion,

not just congestion on CSFs, and

does so using the constraints and

PDFs that apply to the actual dis-

patch. It is worth noting that these

are not the same pricing and settle-

ment rules being proposed in pol-

icy discussions now underway at

MISO and perhaps elsewhere.

MISO is trying to develop a more

complex two-stage settlement

process that would shift residual

congestion costs to the RTO and

then on to system users through

an uplift. But the rules proposed

here would prevent the RTO from

being stuck with—i.e., socializing—

large costs when the assumptions

In current policy discussions in

the Midwest Independent System

Operator (MISO), the Southwest

Power Pool (SPP), and elsewhere,

a system in which forward mar-

kets trade FGRs while the RTO

operates a real-time LMP market is

called a “hybrid” system. There are

many important issues involved in

deﬁning such a hybrid, but these

issues are not the primary focus

here. The objective here is to illus-

trate the CCD process and its

implications for a ﬂowgate/FGR

market. For this purpose, it is easi-

est to assume a hybrid market pro-

cess based on one proposed in The

Electricity Journal by Chao, Peck,

Oren, and Wilson.⁸

FGR prices determined using the

same PDFs. The mathematics of

this process guarantee that, if all

congestion is on CSFs and if the PDFs

used to deﬁne hedging portfolios of

FGRs are the same as the actual PDFs

used for pricing, a transaction

exactly covered by FGRs will

receive FGR payments exactly

equal to its LMP-based congestion

payments, and hence will be per-

fectly hedged against real-time

congestion costs. A transaction

approximately but not exactly cov-

ered by FGRs will receive FGR

payments approximately equal to

its LMP congestion charges, so it is

still approximately hedged.⁹

In the hybrid process proposed

January/February 2001

of the ﬂowgate/FGR market are

not correct, and hence are useful

for discussing the implications of

such a situation.

FGRs, with the PDFs used for dis-

lines, perhaps the assumption that

there are few CSFs with ﬁxed PDFs

is not so bad.

patch—the coefﬁcients of the G in

i

the above constraint equations—

determining the relationship

D. Contingency-Constrained

Dispatch of the Three-Line

System

between the LMPs and the FGR

prices. In settlements, each sched-

uled transaction from GEN to

LOAD will pay a per-unit conges-

tion charge equal to the LMP at

LOAD minus the LMP at the gen-

erator’s location, and will be paid

the value of the FGR portfolio

associated with that transaction.

C. Non-Contingent Dispatch

and Pricing of the Three-Line

System

Unfortunately for the concept of a

ﬂowgate/FGR market, an electric-

ity system cannot be operated on

the assumption that every network

element or critical generator is 100

percent reliable and that the full

capacity of each element can be

used. System dispatchers realize

that there is always some chance

that network elements and critical

generators will fail suddenly, so

they dispatch the system in such a

way that it will continue operating

reliably even if one (or sometimes

In the simplest interpretation of

the three-line system of Figure 1,

forward trading of the three FGRs

will determine a set of planned

transactions or scheduled ﬂows

from each of the three GEN sub-

regions to LOAD. These schedules,

along with incremental/decre-

mental (inc/dec) offers indicating

each generator’s willingness (or

not) to produce more or less at var-

ious prices, will be submitted to

the RTO an hour or so prior to real

time. The RTO will then use these

schedules and inc/dec offers to

determine a dispatch—generation

G at GEN1, G at GEN2, and G at

An electricity system

cannot be operated

on the assumption

that every network more) of these critical elements

fail—the so-called “N–1” (or

“N-more”) contingency criterion.

In terms of the three-line system

element is 100

percent reliable.

1

2

3

GEN3—that meets the net demand

at LOAD at least cost subject to the

three transmission constraints. If

the line capacities and PDFs indi-

cated in Figure 1 are the ones that

actually apply to the real time dis-

patch, the RTO will use the follow-

ing three mathematical constraints

in the dispatch process:

of Figure 1, it is possible to dis-

patch the system so that 300 MW

could ﬂow from GEN to LOAD

A transaction fully covered by its

FGR portfolio will break even in

these settlement calculations—if

the PDFs used to determine the

LMPs and FGR prices are the same

as the PDFs used to deﬁne the FGR

portfolios.

without violating any of the three

line limits. But if anything close to

300 MW were ﬂowing from GEN

to LOAD and then one of the three

lines failed, it would be impossible

to shut down generation in GEN

and increase generation at LOAD

fast enough to prevent the ﬂows

over the remaining two lines from

temporarily surging far above

their individual ratings. If this

were to happen, protective devices

could disconnect or “trip” the

remaining lines, starting a cascad-

ing failure that could shut down

the entire system. To avoid this

possibility, the RTO must assure

that the level and location of gen-

0

.5ϫG ϩ 0.25ϫG ϩ 0.2ϫG Յ 100

1 2 3

he assumption that PDFs are

(the Line A constraint)

T

constant on a system with

given topology may be “close

enough” for some purposes,

.3ϫG ϩ 0.5ϫG ϩ 0.3ϫG Յ 100

1

2

3

(the Line B constraint)

although it is grossly inaccurate if

specialized equipment (e.g., phase

shifters) is used to control ﬂows, a

problem not considered here at all.

If PDFs do not change and only

three FGRs are enough on a system

with three potentially congested

.2ϫG ϩ 0.25ϫG ϩ 0.5ϫG Յ 100

1

2

3

(the Line C constraint)

The dispatch optimization will

automatically determine the LMPs

at each location and the value or

price of each of the three types of

38

The Electricity Journal

eration in GEN are such that a sud-

den failure of any of the three lines

would not cause the ﬂow on either

of the remaining two lines to

exceed their 100 MW limit by more

than, say, 20 percent for as long as

it takes for the RTO to ramp down

generation in GEN and ramp up

reserve generation in LOAD.¹⁰

If the RTO dispatches the three-

line system using an N–1 contin-

gency criterion, the dispatch prob-

lem becomes much more complex

even for the simple three-line sys-

tem of Figure 1. The RTO must now

consider not only the power ﬂows

on lines A, B, and C if the grid stays

fully functional, but also how much

power would ﬂow on lines B and C

if line A failed, on lines A and C if

line B failed, and on lines A and B if

line C failed. And in each of these

four contingencies—counting “no-

failure” as one contingency—the

grid would have a different topol-

ogy and hence a different set of line

capacities and PDFs.

To apply the N–1 criterion, the

RTO must consider each of the

four contingencies and the associ-

ated capacities and PDFs as sepa-

rate but simultaneous constraints

on the actual dispatch. Figure 2

shows the system the RTO would

have to deal with if Contingency

A, deﬁned as failure of line A, were

to occur. In Contingency A, all the

power being generated in GEN

would ﬂow over lines B and C

according to the PDFs indicated in

Figure 2: Contingency A

Figure 3: Contingency B

occurred, the ﬂow over line B

would immediately jump to

0.6ϫG ϩ 0.7ϫG ϩ 0.4ϫG

determined—although some con-

tingencies may be considered

important in some circumstances

1

2

3

11

according to the Contingency A

PDFs in Figure 2. To assure that the

post-contingency ﬂows never vio-

late instantaneous ﬂow limits,

the RTO must dispatch the pre-

contingency system so that post-

contingency ﬂow limits are not

exceeded given the post-contin-

but not in others —but leaves them

there as actual constraints on the

actual dispatch, even though in all

probability none of the contingen-

cies will actually occur. In the rare

event that one of the contingencies

does occur, the RTO adjusts the dis-

patch and the LMPs to reﬂect the

actual situation, perhaps using

some “post-contingency contin-

gency constraints” to protect

gency PDFs, i.e., so that 0.6ϫG ϩ

1

0.7ϫG ϩ 0.4ϫG Յ 120. A similar

2

3

post-Contingency A ﬂow con-

straint would apply to line C, and

similar post-contingency con-

straints would apply in each of

Contingency B and Contingency

C, shown in Figures 3 and 4.

t is critical to understand here

against a new set of contingencies,

and adjusting transmission rights

(or not) depending on the contrac-

tual terms in these rights.

I

that contingency constraints are

not things that come into play only

on the rare occasions when some-

thing actually fails, but that they

must be taken into account and

could affect the dispatch and prices

any time the contingences could

occur—i.e., all the time. The dis-

patcher does not remove the contin-

gency constraints from its dispatch

optimization if all the lines are still

in place when the dispatch is being

Figure 2. With generation G at

1

GEN1, etc., the ﬂow over line B

prior to any contingency would be

0

.3ϫG ϩ 0.5ϫG ϩ 0.3ϫG

1 2 3

according to the three-line PDFs in

Figure 1. But if Contingency A

Figure 4: Contingency C

January/February 2001

The RTO will determine an

optimal dispatch and the associ-

ated LMPs and FGR prices by

minimizing bid-based costs sub-

ject to the instantaneous ﬂow lim-

its and PDFs in all of the contin-

gencies that have been judged to

be worth worrying about—or

that the RTO monitors in dispatch-

ing the three-line system, the three

constraints corresponding to post-

contingency ﬂows on the failed

lines ([4], [8], and [12]) reduce to

“0 Յ 0,” and the three constraints

on actual operations ([1], [2], and

[3]) turn out to be always less strin-

gent than the post-contingency

constraints (see Figure 5), making

only six of the 12 constraints

“monitoring”—for operational

purposes. Even with the simple

three-line system being considered

here, the four contingencies and

three potential line constraints in

each contingency mean that up to

Figure 5: Example Nomograms (“Line C

in B” means the ﬂow constraint on Line C

would be binding in Contingency B)

“interesting.” But there is no way

to know which of the 12 potential

constraints are interesting without

careful analysis of the speciﬁc con-

tingencies even on the same sys-

12 (4ϫ3) separate linear ﬂow con-

them will be binding in any partic-

ular dispatch. For example, with

only three dispatch variables (G₁,

G , and G ) in this case, no more

straints must be monitored in the

contingency-constrained dispatch

12

tem. Changes in the monitored

contingencies have precisely the

same effect on dispatch and pric-

ing as do changes in the physical

system, and can occur even if the

physical system does not change.

Thus, any or all 12 constraints (or

others) could come into play under

different circumstances, even on a

system with only three physical

lines that can be congested.

(CCD) process, with up to 36

(3ϫ12) PDFs as coefﬁcients

(although not all 36 PDFs are

2

3

than three of the six interesting

constraints will actually be bind-

ing at any time (except by coinci-

dence). The problem is that the set

of binding constraints, and hence

the PDFs used for pricing, can vary

widely from one dispatch and one

hour to the next, not because the

PDFs associated with a given grid

topology change—which might or

might not be a relatively minor

problem—but because a different

contingency with a different topol-

ogy becomes a binding constraint.

It is important to note that there

is no difference anywhere in this

process between the constraints on

actually expected ﬂows and the

constraints on contingent ﬂows

that are not really expected to

mathematically independent, e.g.,

each row in the PDF matrices must

sum to 1.0 in this no-loss case). The

12 mathematical equations corre-

sponding to the 12 constraints

potentially needed for this three-

constrained-line system are given

in Table 1.

Given the speciﬁc assumptions

made here about the contingencies

lthough there can be many

A

interesting constraints even

on a simple system, only a few of

Table 1: The Twelve Dispatch Constraints on the Three-Constrained-Line System

[

1] 0.5ϫG ϩ 0.25ϫG ϩ 0.2ϫG Յ 100 (the Line A constraint in Actual Operations)

1 2 3

2] 0.3ϫG ϩ 0.5ϫG ϩ 0.3ϫG Յ 100

(the Line B constraint in Actual Operations)

1

2

3

3] 0.2ϫG ϩ 0.25ϫG ϩ 0.5ϫG Յ 100 (the Line C constraint in Actual Operations)

1

2

3

4] 0.0ϫG ϩ 0.0ϫG ϩ 0.0ϫG Յ 0

(the Line A constraint in Contingency A)

(the Line B constraint in Contingency A)

(the Line C constraint in Contingency A)

(the Line A constraint in Contingency B)

(the Line B constraint in Contingency B)

(the Line C constraint in Contingency B)

(the Line A constraint in Contingency C)

(the Line B constraint in Contingency C)

(the Line C constraint in Contingency C)

1

2

3

5] 0.6ϫG ϩ 0.7ϫG ϩ 0.4ϫG Յ 120

1

2

3

occur. The mathematical equations

above make no distinction

6] 0.4ϫG ϩ 0.3ϫG ϩ 0.6ϫG Յ 120

1

2

3

7] 0.7ϫG ϩ 0.5ϫG ϩ 0.3ϫG Յ 120

1

2

3

between actual and contingent

constraints, suggesting that there

is no logical basis for treating these

differently in a ﬂow-based market

that is supposed to produce sched-

ules or hedging portfolios that

8] 0.0ϫG ϩ 0.0ϫG ϩ 0.0ϫG Յ 0

1

2

3

9] 0.3ϫG ϩ 0.5ϫG ϩ 0.7ϫG Յ 120

1

2

3

[

10] 0.6ϫG ϩ 0.3ϫG ϩ 0.4ϫG Յ 120

1 2 3

11] 0.4ϫG ϩ 0.7ϫG ϩ 0.6ϫG Յ 120

1

2

3

12] 0.0ϫG ϩ 0.0ϫG ϩ 0.0ϫG Յ 0

1

2

3

40

The Electricity Journal

approximate actual operations.

The logical implication is that an

FGR is required for each combina-

tion of a physical network element

and a contingency that is poten-

tially binding in any dispatch.

he effects of contingency con-

be difﬁcult to explain after the fact

why some particular contingencies

were binding. It is not even true

that only a single contingency will

be binding at any time. In Figure 5,

for example, the optimal dispatch

will usually be at a “kink” in the

nomogram, such as point X, where

there are two binding constraints:

Line Ain Contingency B and Line B

in Contingency A. It will be the rare

trader—or even system operator—

who will be able to predict such an

operations just as though it were a

separate constraint on the actual

ﬂow on a network element, the

assumption of a few CSFs with

ﬁxed PDFs becomes untenable.

And this is without considering

nonﬂow constraints or the other

factors that can make CSF capaci-

ties and PDFs vary.

T

straints on the scope and com-

plexity of the feasible dispatches

are illustrated in the two-dimen-

sional nomogram in Figure 5. In

order to get a two-dimensional

nomogram, it is necessary to ﬁx one

of the three generation levels, so it

ot every potentially con-

N

strained network element/

contingency pair will be commer-

cially signiﬁcant at any time, but

for operational purposes the RTO

must include every element/

is assumed in Figure 5 that G in

2

GEN2 is ﬁxed at 50 MW. If the rest

of the system is dispatched ignor-

ing contingency constraints, the

three-line system and PDFs in Fig-

ure 1 apply and any of the dis-

patches within the outer boundary

are feasible, with only two (three,

contingency pair that has any non-

negligible probability of being

binding. On a system of any com-

The problem is that

there is no practical way plexity there will be at least scores

of potentially constrained net-

to predict which combi-

work elements and at least scores

nation of contingent

FGRs is likely to have

value at any time.

of potentially important dispatch

14

when G can vary) relevant ﬂow-

contingencies, implying that

hundreds of network element/

contingency pairs may be at least

operationally and potentially com-

mercially signiﬁcant. Further-

more, these potential CSFs are not

intuitively obvious things or

2

gate constraints. If, however, the

rest of the system is dispatched sub-

ject to contingency constraints—as

any real system always is—the fea-

sible dispatches are limited by the

inner boundary in Figure 5, and

outcome in advance or even pro-

vide an intuitive explanation for it

after the fact.

any of four (six, when G is allowed

places, but abstract combinations

of a network element and a con-

tingency, e.g., “Transformer T

when Line L is out of service.”

This reality has serious implica-

tions for the assertion that trading

in a ﬂowgate/FGR market will be

easy and highly liquid.

2

to vary; nine, if ﬂows on “failed”

lines can be non-zero; 12, if actual

13

ﬂows can also be constraining )

different network element/contin-

gency pairs can be binding.

II. Some Implications for

a Flow-Based Market

Because only a few of the many

possible constraints will be binding

at any time, most of the FGR

The only basis for the claim that

a ﬂowgate/FGR market will result

in easy and liquid trading is the

assertion that there are only a few,

predictable, intuitively obvious

CSFs, and these will have stable,

predictable capacities and PDFs.

But when every possible combina-

tion of a potentially constrained

network element and a dispatch

contingency is treated in system

A. Treating Each Element-

Contingency Pair as a CSF

prices—mathematically, the con-

straint multipliers—will be zero

most of the time and will have a

high value only occasionally. The

problem is that there is no practical

way to predict which combination

of contingent FGRs is likely to have

value at any time, and it can even

The mathematics of the CCD

problem suggest that each combi-

nation of a potentially congested

network element and a contingency

should be treated as a separate

ﬂowgate with its own FGRs, capac-

January/February 2001

ity, and PDF matrix. In principle, a

ﬂowgate/FGR market could oper-

ate this way, at the expense of hav-

ing very many potential CSFs/

FGRs. In the three-line system

being discussed here, there are 12

logically possible line/contingency

combinations, six of which turn out

to be interesting given the speciﬁc

assumptions in the example.

To implement a ﬂowgate/FGR

market in this example, the RTO

could deﬁne six CSFs, issue six dif-

ferent types of FGRs in different

MW quantities, and publish the

three PDFs corresponding to each

type of FGR, or 18 PDFs in all.

Market participants could then

trade the six types of FGRs among

themselves to assemble FGR port-

folios that would hedge their

expected transactions. For exam-

ple, using the PDFs from Figures 2

through 4 above, a trader wanting

to hedge a 1 MW transaction from

GEN1 to LOAD would simply

assemble the following portfolio of

the six FGRs:

in a simple three-constrained-line

example, a system with “only” a

few dozen potentially congested

physical network elements could

easily require scores or hundreds

of contingent FGRs to hedge each

transaction fully. A trader consid-

ering alternative transactions

would have to compare the prices

of different portfolios, each con-

sisting of many FGRs, and then

buy the entire portfolio needed to

very liquid. Even proponents of

ﬂowgate/FGR markets do not

usually argue otherwise. What

they usually say is that there are

ways to simplify trading so that

this nightmare of very large num-

bers of FGRs would not arise. But

what are the possible simpliﬁca-

tions and how well are they likely

to work?

B. Simplifying the System

Assumed for FGR Trading

One way to simplify FGR trad-

ing would be to create a simpliﬁed

model of the real system, use that

simpliﬁed model for trading pur-

poses, and let the RTO deal with

the fact that the trading model

ignores some—perhaps a lot—of

reality. The simpliﬁed system

model might be created by com-

bining several network elements

into compound or proxy ﬂowgates

and building into the capacity

assigned to each compound ﬂow-

gate some of the contingencies that

would otherwise have to be con-

sidered explicitly.

hedge the transaction it chooses.

And each FGR would apply to

an abstract network element/

contingency pair, not some physi-

cal thing or place. This is a far cry

from trading a few, simple, intu-

itively meaningful FGRs.

The problems involved in trad-

ing FGRs, compared to the prob-

lems involved in trading FTRs, are

discussed below. But whatever the

wonders of modern technology, it

is likely that a market in which

each individual transaction may

need a speciﬁc combination of

scores of the potentially hundreds

of ﬁnancial instruments could be

complex, costly, inefﬁcient, and not

Line-B-in-Contingency-A FGRs

or example, the three-line sys-

0

.6 MW

Line-C-in-Contingency-A FGRs

.4 MW

Line-A-in-Contingency-B FGRs

.7 MW

Line-C-in-Contingency-B FGRs

.3 MW

Line-A-in-Contingency-C FGRs

.6 MW

Line-B-in-Contingency-C FGRs

.4 MW

F

tem in Figure 1 could be sim-

pliﬁed for trading purposes into

the one-proxy-ﬂowgate system in

Figure 6. The RTO could deﬁne a

single ﬂowgate, ABC, with a PDF

of 1.0 from anywhere in GEN to

LOAD and sell (say) 220 MW of

tradable FGRs on this ﬂowgate to

account for the contingency that

one of the lines may fail at any time

leaving a maximum of 240 MW of

instantaneous transmission capac-

ity. Market participants could then

trade these FGRs among them-

selves and schedule up to 220 MW

of transactions from anywhere in

0

If six (or perhaps 12, with differ-

ent assumptions) contingent FGRs

are required to hedge a transaction

42

The Electricity Journal

to either curtail some transactions

even though they are covered by

FGRs—i.e., call a TLR—or redis-

patch the system so that all 220

MW of FGRs could be honored,

and recover the redispatch costs

from somewhere.¹⁶

Under other market conditions,

the 220 MW of FGRs could be used

to schedule 220 MW of generation

distributed across the three GEN

subregions in such a way that

none of the lines would be con-

gested in any contingency. To

assure efﬁcient use of the whole

system, the RTO would then have

to sell the unused capacity in the

spot market, implying that some

transactions would not be

element/contingency pairs are

truly commercially signiﬁcant, the

RTO must choose between deﬁn-

ing so many CSFs that trading is

unworkable or so few that large

costs are socialized—or perhaps

some intermediate number that

results in both difﬁcult trading and

inefﬁcient prices. The dilemma cre-

ated by a complex reality does not

go away just because the RTO cre-

ates an artiﬁcially simpliﬁed mar-

ket for trading purposes.

Figure 6: A 1-Flowgate Proxy

C. Forecasting/Guessing the

Binding Contingencies

and PDFs

GEN to LOAD. The RTO would

then deal with the actual system

and its constraints in real-time, and

settle payments using some agreed

set of settlement rules.

Another way to try to make FGR

trading easy even though reality is

complex is to deﬁne noncontingent

CSFs and FGRs for the physical

network elements that are often

constrained, and let market partici-

pants decide how to assemble a

portfolio of these noncontingent

FGRs that will hedge against

prices determined in the CCD pro-

cess. In the three-line system, for

example, the RTO could issue 100

MW (or 90 MW or 80 MW) of non-

contingent FGRs on each of Lines

A, B, and C, perhaps inform

traders about the RTO’s best guess

about which constraints will be

binding, but provide no guaran-

tees. A generator at (say) GEN1

wanting to hedge a transaction to

LOAD could do so by buying a

mix of the three available FGRs

that it expects to have a value in

the CCD process that approxi-

mates the LMP congestion pay-

ments that will be determined in

that same process.

hedged. If the RTO reduced the

underscheduling/hedging prob-

lem by selling more FGRs, it

would ﬁnd itself dealing with

infeasible schedules more often.

n short, if the RTO tries to sim-

The primary problem with sim-

plifying FGR trading in this way is

that the artiﬁcially simpliﬁed mar-

ket could easily result in schedules/

hedges that poorly reﬂect reality

and leave a large gap for the RTO

I

plify FGR trading by creating

15

to close somehow. The actual

capacity of this system to move

power from GEN to LOAD can be

anywhere from 171.4 MW (if any

of G , G , or G ϭ 171.4 MW and

compound or proxy ﬂowgates that

do not reﬂect reality, it will often

have to take action in real time to

reduce the gap between the solu-

tion determined in the simpliﬁed

market and the dispatch that is fea-

sible and efﬁcient given reality. If

the cost of these RTO gap-closing

actions is allocated to the traders

whose unrealistic forward sched-

ules caused the problem—as they

would be if the RTO settled all

transactions using LMPs that

1

2

3

the others are zero) to 240 MW (if

G ϭ G ϭ 120 MW and G ϭ 0).

1

3

2

The assumption that the proxy

ABC ﬂowgate has a capacity of 220

MW might seem a reasonable com-

promise between 171.4 MW and

240 MW. But if a large fraction of

the 220 MW of FGRs were traded

to generators in any subregion and

used to schedule 220 MW of trans-

actions to LOAD—which looks

OK, given the proxy system of Fig-

ure 6—the scheduled ﬂows would

violate several of the actual con-

straints. The RTO would then have

reﬂect all congestion—the FGRs

are poor hedges. If the RTO social-

izes these costs through an uplift,

prices are distorted and costs are

shifted, creating short-term and

long-term inefﬁciencies and ineq-

uities. If very many network

In principle, a trader that knows

which constraints will be binding

January/February 2001

and hence which PDFs will be

used for pricing can use the mathe-

matical relationship between the

LMPs and FGR prices to compute

the combination of the three FGRs

needed for a perfect hedge. But

there would be nothing easy or

intuitive about this process, which

would involve selecting PDFs

from different contingencies

depending on which combination

of constraints was expected to be

binding. More importantly, the

only reason to hedge against con-

gestion prices is that it is not pos-

sible to predict them, i.e., there is

no way to know which constraints

will turn out to be binding. A

trader smart enough to be able to

predict which contingencies will

be binding could make a fortune

without bothering to hedge actual

transactions.

patch, which are not known until

the actual dispatch is known.

costs when different contingencies

turn out to be binding.

Chao and Peck do not acknowl-

edge that this arrangement creates

any commercial problems for

traders; after all, the mathematics

still work. But how are market

participants supposed to know

which PDFs to use for scheduling/

hedging when the relevant PDFs

will not be known until the dis-

patch and prices are known? Even

If the RTO tries to go down the

road of issuing noncontingent

FGRs in an effort to make a ﬂow-

gate market workable, the problem

of unstable and unpredictable

PDFs will quickly arise. The RTO

will then come under strong pres-

sure to tell traders how many of

these FGRs they will need to hedge

a given transaction—i.e., to specify

the PDFs that apply to the FGRs—

and then to socialize the costs of

guaranteeing that anybody fully

hedged based on RTO-provided

information will pay no congestion

charges. In fact, the pressure to

guarantee PDFs and socialize costs

is already arising in MISO and per-

haps elsewhere, where ﬂowgate

proponents are insisting that the

RTO guarantee that anybody

hedged using FGRs and PDFs

issued a month or so in advance

will be protected against real-time

congestion no matter what hap-

pens to binding contingencies,

ﬂowgate capacities, or PDFs

learly, nothing is solved by

C

deﬁning noncontingent FGRs

and telling market participants to

guess which PDFs will be used for

pricing. Nonetheless, this “solu-

tion” is sometimes proposed, at

least implicitly, in the theoretical

literature. For example, at one

point in the Chao and Peck text,¹⁷

FGRs are not indexed by contin-

gencies and hence must be treated

the same in all contingencies, even

though the PDFs used for pricing

and settlements will be those cor-

responding to the actually binding

contingencies. The implication is

that a trader can select an FGR

portfolio based on any PDFs it

chooses, but its transactions will be

hedged against actual congestion

only if (to the extent that) those

PDFs turn out to be (similar to) the

PDFs that apply in the actual dis-

if market participants can guess at

the hedging portfolio that works

for the next hour, a different port-

folio may be required the hour

after that, because different contin-

gencies may be binding in each

hour; an FGR portfolio cannot pro-

vide even a medium-term term

hedge if the binding dispatch con-

tingencies can change often. This

leaves market participants with

only two options: (1) They can

guess at a hedging portfolio and

hence are unlikely to be well

within the month. It is not clear

how or whether this can be done in

any administratively feasible man-

ner, or how it can provide mean-

ingful long-term transmission

rights, but this is clearly the direc-

tion in which MISO is being

pushed now and other RTOs will

be pushed soon.

D. Selecting a Few of the Very

Many Contingent FGRs

Yet another way to try to deal

with very many contingent CSFs

and FGRs is for the RTO to issue

contingent FGRs with associated

PDFs for every signiﬁcant network

hedged, particularly over any

meaningful time period; or (2) they

can pressure the RTO to give them

guaranteed PDFs and socialize the

44

The Electricity Journal

element/contingency pair, and

then let market participants decide

which of the contingent FGRs are

worth buying. The problem with

this “solution” is that no small

number of contingent FGRs will

provide a reasonable hedge for a

speciﬁc transaction. Most FGRs for

speciﬁc element/contingency

pairs will have no value most of

the time, but will occasionally be

very valuable, with no practical

way for anybody to predict just

which contingent FGRs will have

value at any time.

For example, when the optimal

CCD solution is at point X in Fig-

ure 5, above, only two, apparently

unrelated FGRs have any value—

the Line-A-in-Contingency-B FGR

and the Line-B-in-Contingency-A

FGR. Relatively small changes in

the market could make one or both

of these FGRs worthless and make

others valuable. The only way to

get a reasonable hedge is to hold a

portfolio that hedges against many

element/contingency pairs, i.e.,

that contains many contingent

FGRs. Holding only a few of the

very many contingent FGRs can-

not give a good hedge.

the dispatch. If there are ten similar-

price nodes in region A and ten

similar-price nodes in region B,

there are 100 possible (two-way)

point-to-point FTRs between region

A and region B, but all 100 of them

will have approximately the same

value in every hour and hence any

one of them will provide a reason-

able hedge for any A-to-B transac-

tion. It is perfectly logical and rea-

sonable to deﬁne hundreds or

ent in every hour. Even so, this

nonsolution is sometimes pro-

posed in the theoretical literature

advocating ﬂow-based markets.

or example, Chao and Peck

18

F

suggest in a footnote that the

RTO could issue many contingent

FGRs, and—because only a few of

them will have a positive value at

any time—these FGRs can be bun-

dled together somehow to simplify

trading. It is not clear whether the

suggestion is to create bundles of

FGRs for each physical CSF or for

each contingency, but neither of

these approaches would help

much. Every transaction would

need a different bundle of contin-

gent FGRs on each CSF, depending

on the contingent PDFs that apply

19

to that transaction. A small num-

ber of instruments each of which is

a bundle of many contingent FGRs

is still a small number of instru-

ments, and no small number of

instruments can capture the full

complexities of many ﬂowgates,

many contingencies, and many

possible transactions.

thousands of potential FTRs and let

market participants select the few

they need to hedge important

transactions, e.g., from hub to hub.

The same strategy does not solve

the problem of very many contin-

gent FGRs, because even a single

hub-to-hub transaction could need

scores of contingent FGRs.

Again, it should be obvious that

it solves nothing to tell traders to

pick the few FGRs that will have

value if there is no way to predict

which few will have value. Nor

does this solve the problem of

long-term hedging, because the

few contingent FGRs that will be

valuable in an hour can be differ-

E. Are there Few, Predictable

CSFs with Stable,

Predictable PDFs?

t is worth noting here a critical

I

point that is discussed in more

Although proponents of ﬂow-

based markets assert that there are

few, predictable CSFs with stable,

predictable capacities and PDFs,

they have not deﬁned how many

CSFs are “few,” how CSFs would

be deﬁned, how CSF capacities

and PDFs would be predicted, or

what happens when the predic-

tions turn out to be wrong—other

than saying the RTO will deal with

it somehow. Nor have they pre-

sented any evidence suggesting

detail below: Although point-to-

point FTRs are often criticized

because there are potentially so

many of them, any feasible transac-

tion can be perfectly hedged with a

single FTR, and many similar trans-

actions can be approximately

hedged with one or a few FTRs.

The value of an FTR does not

switch from zero to some large

number depending on which con-

tingency turns out to be binding in

January/February 2001

that there are few, predictable CSFs

with stable PDFs. In fact, their

record at predicting the amount or

location of congestion is very bad.

For example, one study by ﬂow-

gate proponents predicted that

some 28 constraints could capture

most of the congestion in the

expect the number and identity of

CSFs to settle down at some point.

After all, there is only a ﬁnite—

albeit, very large—number of phys-

ical elements that can be congested,

and one would expect a “Top 100”

list of congested physical elements

to stabilize over time. But when

constraints must be deﬁned as net-

work element/contingency pairs,

there is virtually no limit to the

number of pairs that can be com-

son to think that this year’s Top-

100-of-2,500 element-contingency

pairs will be a very good predictor

of next year’s Top 100.

erhaps recognizing that dis-

P

patch contingencies under-

mine the whole notion of a ﬂow-

based market, some ﬂowgate

advocates have said that CSFs

should not be deﬁned as network

element/contingency pairs. For

example, according to Shmuel

Oren, “deﬁning ﬂowgates as pairs

of a monitored element and a con-

tingency element would not allow

deﬁnition of unique ﬂowgate

rights and is not consistent with

the theory of ﬂowgate based con-

Pennsylvania–New Jersey–

Maryland (PJM) Interconnection,

but in the ﬁrst six months of LMP

operations in PJM there were 43

important constraints—not one of

which was on the list of 28 con-

20

straints predicted beforehand.

The best available evidence on

the number and predictability of

CSFs comes from operating experi-

ence to date in PJM. As reported by

22

gestion management.” This

apparently means that CSFs and

FGRs should be deﬁned for spe-

ciﬁc physical elements (or com-

pound elements) without regard

to contingencies. As discussed

above, CSFs and FGRs can be

noncontingent—but only if their

associated capacities and PDFs are

contingent, which invalidates the

fundamental assumption of a

ﬂow-based market: that ﬂowgate

capacities and PDFs are stable and

predictable. A ﬂowgate/FGR

market with a relatively few (but

probably still several score) CSFs,

each with constantly changing

capacities and PDFs, will either

provide very poor hedges against

actual congestion or require the

RTO to play an active role in the

market and socialize large costs—

or both. There is no escape from

the dilemma.

21

Andy Ott of PJM, this experience

suggests that it would take more

than 50 and perhaps as many as

1

8

00 contingent CSFs to capture

0–90 percent of the annual con-

gestion costs in PJM. Perhaps more

importantly, the set of element/

contingency pairs that captured

most of the congestion costs in one

year has so far not been a very good

predictor of the commercially sig-

niﬁcant pairs for the following year.

The limited but rapidly expanding

experience to date suggests that

the number of CSFs in PJM is more

than 100 and still increasing, with

new element/contingency pairs

becoming commercially signiﬁcant

all the time.

mercially signiﬁcant over a period

of time.

Even if the same, say, 50 physical

network elements are congested

every year and the same, say, 50

contingencies are monitored in the

CCD process every year, changes

in the pattern of load and genera-

tion will bring new element/

contingency pairs into play all the

time. With 50ϫ50 ϭ 2,500 possibil-

ities, there could be a totally differ-

ent Top 100 list every year for 25

years. More realistically, an unpre-

dictable 50 CSFs could drop off the

Top 100 list every year and a differ-

ent unpredictable 50 CSFs could

appear. There is certainly little rea-

t should not be surprising that

I

it is so hard to predict how

many or which network element/

contingency pairs will turn out to

be important. If CSFs really could

be deﬁned in terms of physical net-

work elements alone, without

According to Oren, the theory of

ﬂow-based congestion manage-

ment does not even allow CSFs to

be deﬁned in terms of element/

regard to contingencies, one might

46

The Electricity Journal

contingency pairs. But Chao and

Peck do allow for contingent

able difﬁculties of a market that

depends on deﬁning stable paths

through the network.

age restrictions, the inherently

nonlinear character of the net-

work, and the increasing use of

equipment—i.e., phase shifters—

speciﬁcally designed to change

PDFs. As a practical matter, it is

essentially impossible to deﬁne

long-term transmission rights that

depend on the pattern of ﬂows

through the grid—as evidenced by

the fact that the industry has been

searching for such ﬂow-based

methods for years without success.

To avoid the many problems of a

ﬂow-based approach to deﬁning

transmission rights, Hogan devel-

oped the concept of point-to-point

FTRs, which are rights to the LMP

differentials between two deﬁned

points. He noticed that if system

users are given FTRs correspond-

ing to a speciﬁc dispatch, both

individual users and the settle-

ment system as a whole are largely

unaffected ﬁnancially even by

large changes in the pattern of

injections and withdrawals, even

when these changes resulted in

large changes in ﬂows, PDFs, and

LMPs. These observations moti-

vated the development of the

theory of LMPs and FTRs.

LMP/FTR theory was explicitly

designed to avoid the difﬁculties

associated with a ﬂow-based

approach by basing pricing and

transmission rights on the out-

come of the actual dispatch rather

than on speciﬁc network ﬂows

and PDFs that are essentially

unpredictable over any commer-

cially interesting period of time.

The speciﬁc LMPs and LMP differ-

entials that deﬁne congestion

charges depend on which of the

many constraints are actually

CSFs—albeit, only in a footnote,

and without providing a plausible

solution to the resulting problem

of too many CSFs—raising ques-

tions about just what the theory of

ﬂow-based congestion manage-

ment really is. As a mathematical

matter, however, constraints on

contingent ﬂows enter into the

CCD process in precisely the same

way that constraints on scheduled

ﬂows do, so it is unclear why Oren

would not treat them the same

when deﬁning FGRs—unless it is

that doing so would make obvious

the impracticality of the whole

idea of a ﬂow-based market.

A. Development of LMP/FTR

Theory and Practice

The principal developer of

LMP/FTR theory was William

23

Hogan of Harvard. Building on

the work of Fred Schweppe and

24

his colleagues at MIT, the LMP/

FTR approach exploits the concept

III. FTRs and Dispatch

Contingencies

The current proposals for

ﬂow-based markets appear to be

motivated by a desire to ﬁnd

something—maybe anything—as

an alternative to a market based on

LMPs and FTRs, preferably some-

thing in which transmission rights

are “physical” as they are said to

be in natural gas. It is noteworthy

that, as ﬂowgate advocates have

thought more about the problem,

they have come to accept that

FGRs should be ﬁnancial instru-

ments with little or no operational

effect and that the RTO should use

a real-time LMP process to manage

and price physical operations and

to settle FGRs. As they think about

the problem some more, they are

likely to (re)discover the advan-

tages of FTRs—which were, after

all, developed speciﬁcally to avoid

the still apparently insurmount-

that a (approximately) consistent

set of LMPs could be derived from

an (approximately) optimal opera-

25

tional dispatch. This was an

important variation on the

Schweppe idea that LMPs can and

should determine actual opera-

tions, because it allowed (approxi-

mately) efﬁcient prices to be deter-

mined from a dispatch that was

inﬂuenced by the judgment of

human operators.

he complexity of electricity

T

systems goes beyond the con-

tingency issues discussed in this

article, to include the changing

patterns of power ﬂows and trans-

mission limits that arise from volt-

January/February 2001

binding in the dispatch, and hence

are volatile and difﬁcult to predict—

although not nearly as much so as

the individual constraint multipli-

ers/FGR prices. But if a market

participant holds point-to-point

FTRs that exactly cover its point-

to-point transactions, it is per-

fectly hedged against congestion

charges no matter what happens

to LMPs. This allows a market

participant to hedge a transaction

with a single, easy-to-understand

ﬁnancial instrument without wor-

rying about ﬂows, dispatch con-

straints, contingencies, PDFs, con-

straint multipliers/FGR prices, or

any of the other arcane network

details about which market par-

ticipants have little knowledge

and over which they have virtu-

ally no control.

straints, contingencies, or operating

parameters. Market participants can

get good hedges against any feasi-

ble set of transactions—with only

one FTR required to hedge one

transaction—with no risk that the

RTO will have to socialize large

costs when market conditions

and binding dispatch contingen-

cies change.²⁷

incentives to seek cost-effective

trade-offs between congestion

costs and other costs. The only

way to make a ﬂowgate/FGR mar-

ket anywhere near as easy as an

LMP/FTR market is to get the RTO

to deﬁne an artiﬁcially simpliﬁed

set of constraints for trading pur-

poses and then to manage and

socialize the costs of the real con-

gestion outside the market.

This is a remarkable result that

greatly simpliﬁes both the opera-

B. The Problem of Very

Many FTRs

The efforts to develop a ﬂow-

based alternative to an LMP/FTR

market are motivated largely by

the belief that there are too many

potential point-to-point FTRs to

make FTR trading easy and liquid.

Flowgate/FGR advocates like to

say, for example, that with 100

2

urthermore—and this is the

nodes there are 100 or 10,000 pos-

2

8

F

real key to FTRs—as long as

sible point-to-point FTRs. They

do not say that a ﬂowgate/FGR

market with only 20 potentially

congested physical network ele-

ments and only 20 contingencies

the pattern of injections and with-

drawals implied by the set of FTRs

issued by the RTO would be simul-

26

taneously feasible on the grid, the

LMP-based congestion charges

associated with any optimal dis-

patch on that grid will be at least

enough to cover all the FTR pay-

ments the RTO must make given

that dispatch and LMPs, no matter

which of the many possible actual

or contingent ﬂow constraints (or

nonﬂow constraints, or phase-

shifter settings, or . . .) apply in the

new dispatch. Thus, the RTO can

issue a set of FTRs that fully hedges

any simultaneously feasible set of

transactions without fear that the

RTO’s settlement system will run a

deﬁcit if the market prefers a dif-

ferent set of transactions that cre-

ates a different set of binding con-

2

tional and the commercial prob-

lems of market-based congestion

management. Neither LMP/FTR

theory nor its application is easy in

any absolute sense or even relative

to what is required in most other

markets. But that is because elec-

tricity itself is not easy. LMP/FTR

theory and practice are easy only

relative to the logical alternatives

for market-based congestion man-

agement on a complex electricity

system. In particular, an LMP/FTR

market is easy relative to any ﬂow-

based market that makes a serious

effort to price all congestion in the

market so that market participants

will have good price signals and

could need 20 or 400 contingent

CSFs/FGRs, and even if only 50 of

these contingent CSFs/FGRs are

important and any point-to-point

transaction can be reasonably

hedged with FGRs on only 10 of

these, there are more than 10 bil-

lion possibly interesting point-to-

point FGR portfolios—even with-

out considering variations in the

quantity of each type of FGR.²⁹

Such numbers games prove noth-

ing, but if FGR proponents want to

play them they should be pre-

pared to lose.

The essential characteristic of

real transactions on the grid is that

they are point-to-point: Power is

48

The Electricity Journal

injected somewhere for delivery

somewhere else. The pattern of

ﬂows that results from a speciﬁc

injection and withdrawal depends

on the laws of physics—and, when

such things as phase-shifters are

considered, the actions of system

controllers—not the preferences or

actions of the traders involved in

the transaction. To hedge a speciﬁc

point-to-point transaction against

all possible combinations of ﬂows

it could “cause” under all contin-

gencies that can affect dispatch

could require a portfolio consisting

of a very large number of contin-

gent FGRs.

folios that are analogous to FTRs.

But this brings into play the other

horn of the dilemma facing a

bazaar in which many, competitive

FGR mongers would be making

markets in individual FGRs by

holding inventories and posting

prices, particularly if a use-it-or-

lose-it rule were in place making it

very risky to hold FGR invento-

ﬂowgate/FGR market: How efﬁ-

cient or liquid will a market be if

every point-to-point deal needs a

speciﬁc combination of many of

the very many contingent FGRs?

Some ﬂowgate/FGR proponents

say it will be no problem trading

dozens or maybe even hundreds of

individual FGRs using modern

3

0

ries. So perhaps there would be

a centralized, sophisticated,

multi-round auction process simi-

lar to electromagnetic spectrum

auctions, as suggested by Chao

31

et al. —although this seems

unlikely, given that FGRs would

have to be traded continuously

whereas spectrum auctions are

one-off, multi-day affairs.

he number of FGR portfolios

s these examples show, ﬂow-

T

actually needed to hedge all

A

gate/FGR proponents can-

possible transactions is, of course,

limited by the number of possible

point-to-point transactions. On a

system with 100 nodes there can

not decide whether FGR trading,

which is supposed to be easy,

cheap, and highly liquid, will be a

highly decentralized, simple,

over-the-counter entrepreneurial

affair or a highly sophisticated,

centralized, probably monopo-

lized (and almost surely Securi-

ties and Exchange Commission-

and/or Federal Energy Regula-

tory Commission-regulated)

activity. The most likely outcome

is that FGR trading would evolve

to include one or a few central-

ized exchanges trading a few

standard FGR portfolios that

hedge point-to-point transac-

tions between important hubs,

with specialized brokers assem-

bling FGR portfolios for transac-

tions between the major hubs and

nearby locations. In other words,

FGRs would be traded in port-

folios that are awkward and

2

be no more than 100 ϭ 10,000

interesting portfolios of (one-

way) FGRs—which is precisely

the same as the number of pos-

sible (one-way) point-to-point

FTRs. Not all of these possible

FGR portfolios would be com-

mercially interesting, because

there will not be any transactions

between most point-to-point

pairs, many of the FGR portfolios

could serve as reasonable-if-not-

perfect hedges for all transactions

from one region to another

region, etc. But all of this is just as

true with point-to-point FTRs as

it is with point-to-point FGR port-

folios. There is no difference.

Some advocates of ﬂow-based

markets respond to such observa-

tions by saying that a ﬂowgate/

FGR market will trade individual

FGRs, not point-to-point FGR port-

technology, and even demonstrate

prototype software that allows a

trader to specify a point-to-point

transaction, get an instant quote on

the price of the entire portfolio of

FGRs necessary to hedge this

transaction, and then buy that

portfolio with the push of a button

or click of a mouse. But such elec-

tronic gadgetry begs the commer-

cial question of who will be hold-

ing and pricing hundreds of

different FGRs so that there is

somebody on the other end of the

mouse-click.

It is highly unlikely that a

ﬂowgate/FGR market would func-

tion as some sort of electronic FGR

incomplete versions of FTRs.

If FGR trading is likely to evolve

into a difﬁcult form of FTR trading,

January/February 2001

it would seem preferable to skip

the FGR step entirely and go

straight to FTRs. Conceptually and

mathematically, FTRs are portfo-

lios of all the FGRs needed for a

perfect point-to-point hedge

against all congestion on all net-

work elements in all contingencies

considered for dispatch and

market participants who want to

use such markets for short-term

trading. Such traders say that

LMP/FGR systems such as PJM

make it difﬁcult to get the FTRs

they need to hedge transactions

that change from day-to-day or

even hour-to-hour. Amarket based

on ﬂowgates and FGRs, although

not even deﬁned in concept much

less demonstrated in practice, is

held out as a solution to these

some ﬁnancial instrument or mar-

ket process might lower costs and

risks for somebody if only some-

body else would pay for it is no

proof that such an instrument or

market should exist. Certainly

there is a lot of room for improve-

ment in short-term trading and

hedging arrangements in electric-

ity markets. But one should be real-

istic about how rapidly these can

develop and how far they can go.

The claims that there is little

pricing—plus hedges against all

congestion arising from nonﬂow

constraints and against PDF

changes due to nonlinear effects

and operator actions such as

changing phase-shifter settings.

There are very many possible

point-to-point FTRs, just as there

are very many possible point-to-

point FGR portfolios. But any

point-to-point transaction can be

perfectly hedged with a single

FTR, and many similar trans-

actions can be approximately

hedged with one or a few FTRs.

t is far easier and more natural

liquidity in functioning LMP/

FTR markets such as PJM are at

least overstated, if not ﬂatly

wrong, given that PJM appears by

most measures to have the most

liquid electricity and transmis-

3

2

sion markets in the US. There

may currently be little short-term

trading of the valuable FTRs from

western PJM to eastern PJM, but

that is because there is limited

capacity for west-to-east transfers

and the FTRs on that capacity are

held by entities—the utilities with

load-serving obligations—who

need those FTRs to hedge their

own transactions and/or have

regulatory disincentives to trade

I

to work with FTRs than with

FGRs. The operators of LMP/FTR

systems and the traders using such

systems still have a lot to learn

about how to use FTRs to accom-

plish various legitimate (and per-

haps illegitimate) commercial

objectives. But there is no reason to

think that this learning process

would be any easier or the ulti-

mate results would be any better if

point-to-point FTRs were replaced

with hundreds of contingent FGRs

that must be assembled into thou-

sands of point-to-point portfolios

to work as well.

problems. But it is unreasonable to

blame LMP/FTR markets generi-

cally for the implementation prob-

lems on speciﬁc systems, and unre-

alistic to think the same problems

would not arise for the same rea-

sons in a ﬂowgate/FGR market.

The fact that traders naturally

want a system that allows near-

perfect short-term hedging does

not mean that such a system

should or could exist. In any real

commodity market there are many

logically possible hedging instru-

ments that could exist but do not,

presumably because they are not

worth what they would cost to

develop and use. The fact that

3

them. These speciﬁc transi-

tional and implementation prob-

lems have nothing to do with the

nature of FTRs themselves and

would not be solved by replacing

FTRs with FGRs.

hatever the reality or cause

W

of short-term trading prob-

lems with FTRs in functioning

LMP/FTR markets, there is no

logic or evidence suggesting that

short-term trading would be any

better in a ﬂowgate/LMP market.

The only basis for thinking that

FGR trading would be easy and

C. Short-Term Hedging

and Trading

Much of the current criticism of

LMP/FTR markets comes from

50

The Electricity Journal

liquid is the belief that there would

be few FGRs with stable capacities

and PDFs, a belief that has no

foundation for many reasons,

including the CCD process consid-

ered here. As the RTOs (indepen-

dent system operators) in PJM,

New York, and New England con-

tinue developing short-term FTR

auctions—including the FTR auc-

tion implicit in the day-ahead

energy markets—as traders learn

more about FTRs, and as the tran-

sitional disincentives to trading

fade away, short-term FTR trading

can be expected to become easier

and more liquid in those markets.

It may never be easy and liquid

enough to satisfy day-traders; but

it should serve the needs of the

generators and consumers who are

the intended beneﬁciaries of com-

petitive restructuring.

based on LMP, creates the follow-

ing situation:

contingency is added to those con-

34

sidered in the CCD process, the

RTO or grid owner may have to

buy back some FTRs to make the

remaining FTRs simultaneously

feasible on the reduced grid; but G

does not have to sell any of its

FTRs, and if it does not sell any

will automatically continue getting

its 100 MW from GEN to LOAD on

the reduced grid.

• G has 100 MW of transmission

service from GEN to LOAD at no

cost (beyond the cost of the FTR

itself) for the term of the FTR

and—as long as all outstanding

RTO-issued FTRs are simulta-

neously feasible—without the RTO

socializing any costs except per-

haps those due to unexpected

changes in the physical network. If

• If G wants long-term rights for

another (say) 50 MW from GEN to

LOAD, G can pay for one or sev-

eral grid expansion projects

(whether or not they are on CSFs)

that relieve congestion (in all con-

tingencies) enough to support an

additional 50 MW of GEN-to-

LOAD transactions simulta-

neously with the transactions

implied by the existing FTRs. GEN

can then be given 50 MW of addi-

tional GEN-to-LOAD FTRs and

these will fully hedge an addi-

tional 50 MW of transactions in all

contingencies.

D. Long-Term Hedging and

Transmission Investments

One of the principal objectives of

any transmission rights regime is

to reduce long-term congestion

cost risks and to encourage long-

term investment in generation and

transmission. This objective is

underemphasized in current pol-

icy discussions, which are domi-

nated by the concerns of short-term

traders. But providing long-term

transmission rights is a critical

objective of any electricity

market—and one for which FTRs

are ideally suited and FGRs are

virtually worthless.

To see this, consider ﬁrst a gen-

erator G at GEN who holds 100

MW of a single long-term FTR

from GEN to LOAD. This FTR,

along with real-time settlements

ow consider this same gen-

market conditions change so that

the pattern of LMPs changes—

implying that congestion is now

appearing on different network

elements and/or in different con-

tingencies and/or due to nonﬂow

constraints—G continues to get its

100 MW of transmission service at

no cost automatically.

• If the grid is expanded, new

FTRs can be sold or allocated to

other users without affecting G’s

rights and without requiring the

RTO to socialize any costs, as long

as both existing and new FTRs are

simultaneously feasible on the

new grid. If part of the grid is

removed from service or a new

N

erator G in a ﬂowgate/FGR

market in which the RTO deﬁnes

CSFs and FGRs for only a subset

of the possibly congested network

element/contingency pairs in

order to try to make FGR trading

workable, but does not socialize

the costs of guaranteeing the

capacities and PDFs for the entire

term of the FGRs. If G holds the

portfolio of FGRs that perfectly

hedges a 100 MW transaction

from GEN to LOAD given the CSF

capacities and PDFs that exist

today, the situation is as follows:

• G has 100 MW of transmission

service from GEN to LOAD at no

cost (beyond the cost of the FGR

January/February 2001

portfolio itself)—except when non-

CSF congestion arises or PDFs

change, which could happen every

hour. If long-term changes in the

market create persistent conges-

tion on different network element/

contingency pairs, new contingent

CSFs will have to be deﬁned with

their associated capacities and

PDFs, or new capacities and PDFs

will have to be deﬁned for the

existing noncontingent CSFs.

tions G will still need a portfolio of

FGRs on many CSFs, with the

required portfolio changing as

CSFs and PDFs change over time.

The RTO will not be able to assure

G that any set of grid expansions

will provide incremental FGRs

that will hedge an additional 50

MW of GEN-to-LOAD transac-

tions as different contingencies

become binding.

thousands of network element/

contingency pairs that have any

chance of becoming important

over the term of the FGRs, and

these FGRs are made contingent

on other factors that can affect CSF

capacities and PDFs, the portfolio

of FGRs needed to hedge the same

transactions must be expected to

change over time, perhaps often

and signiﬁcantly.

The critical point is that a

These difﬁculties would make it

troublesome to provide reliable

grandfathering for existing long-

term rights, to sell new long-term

rights, or to grant long-term rights

to those who pay for grid expan-

sions. Some ﬂowgate/FGR propo-

nents have recognized this prob-

lem and have begun trying to

think of a solution. In one prelimi-

nary proposal, generator G above

would assemble a portfolio of

long-term FGRs that hedge 100

MW from GEN to LOAD given the

CSFs and PDFs that exist today,

and register that point-to-point

transaction with the RTO. Then,

whenever new market conditions

forced the RTO to add CSFs or

change PDFs, the RTO would

exchange that FGR portfolio for

the new one required to hedge the

registered transaction given the

new CSFs and PDFs.

Either way, G must get a new port-

folio of FGRs to hedge the same

GEN-to-LOAD transaction, imply-

ing that G’s original FGR portfolio

was not worth much as a long-

term transmission right.

•

If the grid is either expanded

or reduced physically, some net-

work element/contingency pairs

may be dropped as CSFs while

others may be designated as new

CSFs. And the new grid conﬁgura-

tion will change most of the PDFs.

So G will need a different set of

FGRs to hedge the same 100 MW

GEN-to-LOAD transaction. It may

be desirable to hold G harmless

against changes in the grid that G

cannot predict or control, but this

would require redeﬁning and real-

locating FGRs whenever a change

in the grid changes CSFs, capaci-

ties, contingencies, and PDFs.

ﬂowgate/FGR system must, as a

practical matter, deal with only a

subset of the potentially congested

network element/contingency

pairs and hence cannot provide

reliable long-term transmission

rights when binding ﬂow (or non-

ﬂow) constraints—or other things,

such as use of phase-shifters—

change. Even if the RTO is pre-

pared to guarantee long-term

FGRs and socialize large costs over

their terms, it is not clear how this

could be done given the difﬁculty

of continually deﬁning new and

reallocating old FGRs. Unless con-

tingent CSFs and FGRs are deﬁned

for every one of the potentially

•

If G wants long-term rights for

uch proposals raise more ques-

another (say) 50 MW from GEN to

LOAD, G can pay for one or sev-

eral grid expansion projects and,

as long as they are on CSFs, can be

given FGRs on those CSFs corre-

sponding to the increase in capac-

ity in each contingency (if FGRs

are contingency-speciﬁc). But in

order to hedge an additional 50

MW of GEN-to-LOAD transac-

S

tions than they answer. What

are the “long-term FGRs” that

would be assembled into point-to-

point portfolios and then regis-

tered to get long-term point-to-

point rights? How does the RTO

guarantee that all the registered

point-to-point transactions will be

feasible in combination with the

still-outstanding long-term FGRs

52

The Electricity Journal

when new CSFs and/or PDFs

must be deﬁned? What about non-

CSF congestion or changes in

capacities and PDFs in between

the times when CSFs, capacities

and PDFs are redeﬁned? What will

be the process for deﬁning new

CSFs and PDFs, when every mar-

ket participant will be affected by

such changes? Or does the RTO

guarantee the long-term FGRs and

registered point-to-point transac-

tions by buying back long-term

rights that become infeasible as

new CSFs and/or associated PDFs

emerge over time and socializing

the costs? Perhaps the most difﬁ-

cult question raised by such pro-

posals is: Why is there so much

effort to ﬁnd unnatural and com-

plex ways to do with FGRs what is

natural and relatively easy to do

with FTRs?

how will it ever provide the kind

of long-term transmission rights

needed in any reasonably efﬁcient

and effective market?

cant value over the term of the

FGR. This implies that scores of

contingent FGRs could be required

for even an approximate hedge

over a “long-term” such as a

month, with perhaps hundreds

required for multi-year transmis-

sion rights.

IV. Conclusions

The basic assumption of a ﬂow-

based market is that there are only

a few CSFs and these have ﬁxed

capacities and PDFs. There are

many reasons to doubt this

he need for very many contin-

T

gent FGRs (or fewer noncon-

tingent FGRs but with contingent

capacities and PDFs) is not some

trick invented by the evil advocates

of FTRs, but is a straightforward

logical implication of contingency-

constrained dispatch on a complex

system. In fact, FTRs were devel-

oped largely to deal with the

implications of this and other com-

plex realities of electricity systems.

The point-to-point nature of FTRs,

which mirrors the point-to-point

reality of electricity transactions,

allows a single FTR to hedge a

transaction perfectly against con-

gestion due to ﬂow limits on every

network element in every contin-

gency, nonﬂow constraints, and

changes in PDFs due to nonlinear

physical relationships and opera-

tor actions. Requiring market par-

ticipants to use FGRs to try to

assemble their own hedges against

so many things that they cannot

predict, understand, or control

would be unnatural, ineffective,

and pointless—although it might

beneﬁt those who stand to gain

from high transactions costs and

market inefﬁciency.

The virtual impossibility of pro-

viding even short-term price cer-

tainty with FGRs is driving

ﬂowgate/FGR advocates in, e.g.,

the MISO discussions, to propose

that the RTO guarantee FGRs and

PDFs for periods as long—or as

short, depending on how one

looks at it—as a month, and social-

ize all the costs of making good on

that guarantee. It is not clear how

or whether this could be adminis-

tratively feasible, but it is reason-

ably clear that a guarantee of FTRs

and PDFs for even a month is

likely to create more cost socializa-

tion than RTOs (or public utility

commissions or FERC) are likely

to ﬁnd acceptable. If a ﬂowgate/

FGR system cannot guarantee

FGRs and PDFs for even a month

without a lot of administrative

complexity and cost socialization,

assumption, but one of the most

important is that modern electric-

ity systems are operated subject to

constraints on the ﬂows that

would arise under multiple contin-

gencies, not just constraints on

actual ﬂows on physical elements.

The constraints on contingent

ﬂows have precisely the same

effects on operations, congestion,

and pricing as the constraints on

actual ﬂows. If forward FGR trad-

ing is to produce schedules or

hedges that are close to operational

reality, there must be a different

FGR for every network element/

contingency pair that has any sig-

niﬁcant chance of having signiﬁ-

The proponents of ﬂow-based

markets have not explicitly

acknowledged their dilemma of

either very many CSFs or ever-

changing CSF capacities and PDFs,

but they must realize the dilemma

January/February 2001

is there. If they really believed that

a ﬂowgate/FGR market could cap-

ture all commercially signiﬁcant

congestion with a few CSFs with

ﬁxed capacities and PDFs, they

would not object to requiring

traders to pay LMP-based conges-

tion charges on all actual congestion

not hedged by a few FGRs with

ﬁxed capacities and PDFs, because

the unhedged congestion costs

would not be commercially signiﬁ-

cant. The fact that proponents of

ﬂowgate/FGR markets are so ada-

mant that the RTO must guarantee

a few CSFs with ﬁxed capacities

and PDFs and socialize the costs of

delivering on that guarantee

5. In principle, each of the three line con-

straints implied by Figure 1 could be

interpreted as either an actual or a con-

tingent constraint. But virtually nobody

draws such a simple diagram and then

says that each constrained line in that

diagram actually represents an abstract

Transmission Rights and Congestion Man-

agement, Elec. J., Oct. 2000, at 38.

9. Mathematically, if P

is the price of

f

ﬂowgate f and PDF is the PDF from

gf

location g to the “hub” H over ﬂowgate

f, the LMP at location g is LMP ϭ

g

LMP ϩ ⌺P ϫPDF , where the sum is

H

f

gf

“element/contingency pair.” A “line”

over all ﬂowgates f. The congestion

charge from any location g to any other

location k is then LMP Ϫ LMP ϭ ⌺P ϫ

almost always represents a physical

network element.

k

g

f

6. Whether FGRs are needed for schedul-

(

PDF Ϫ PDF ). A 1 MW transaction

kf gf

ing or only to hedge transactions

depends on whether an FGR is regarded

as a “physical” right or a “ﬁnancial”

from g to h that is covered by (PDF Ϫ

kf

PDF ) FGRs on all ﬂowgates f will be

gf

paid for its FGRs exactly what it pays in

congestion charges and hence will be

perfectly hedged. Approximate coverage

on ﬂowgates with “signiﬁcant” prices

will result in an approximate hedge.

10. This is not just a hypothetical situa-

tion, but arises all the time on real sys-

tems. For example, operation of the New

York system is often constrained by the

risk that one of several cables into Man-

hattan and Long Island might fail and

the ﬂows over the remaining cables

would surge above line limits.

strongly suggests that they know

these costs would not be commer-

cially insigniﬁcant and would prob-

ably be very large. In this, at least,

they are almost surely correct. ᭿

11. For example, the RTO may impose

more stringent—e.g., N–2—contingency

constraints when thunderstorms are in

the area, on the grounds that lightning

strikes may disable several transformers

simultaneously. Who bears the costs

when such changes in dispatch contin-

gencies or actual grid conditions reduce

grid capacity is an important issue that is

essentially the same with either FGRs or

FTRs, and hence is not discussed here.

Endnotes:

1. The term “security-constrained dis-

patch” (SCD) is more commonly applied

to this process, but the term CCD is used

here to emphasize the role of dispatch

contingencies.

right. Although FGRs are still sometimes

called physical rights, it is now generally

accepted that FGRs should not be

required for scheduling, but are prima-

rily ﬁnancial hedges. It is assumed here

that FGRs are ﬁnancial instruments but

that market participants seek FGR port-

folios that reﬂect their expected physical

operations.

2. Hung-Po Chao and Stephen Peck, A

Market Mechanism for Electric Power Trans-

mission, 10 J. Reg. Econ., 1996, at 25–59.

As discussed below, Chao and Peck pro-

pose two, mutually inconsistent ways to

deal with CCD in a ﬂowgate/FGR mar-

ket, neither of which resolve the dilemma.

12. For example, in this case if a line

could fail partially it would be necessary

to consider post-contingency ﬂows on

the failed line in each contingency; and

larger post-contingency instantaneous

ﬂow limits on failed lines—e.g., 150 per-

cent of steady-state limits—could make

the constraints on actual ﬂows binding

in some dispatches.

7. Even if market participants must sub-

3. Shmuel Oren in an e-mail to Andrew

mit balanced schedules covered by

FGRs, the RTO will have to use a full

LMP process to determine the incremen-

tal dispatch and the associated prices.

Energy traded under balanced schedules

covered by FGRs will not be priced or

settled in this process, but will affect

actual transmission congestion and

prices and hence must be an input to the

LMP process.

Ott of the Pennsylvania–New Jersey–

Maryland Interconnection (and a large cc

list), Sept. 20, 2000. See discussion below.

4

. The dispatch is constrained by con-

13. If the limits on instantaneous, post-

tingencies even when the grid is in its

standard condition, i.e., when none of

the contingencies has actually occurred.

The issue of who should bear the costs

when the grid is not in its standard con-

dition is an important issue but is not

considered here.

contingency ﬂows were higher, the inner

boundary in Figure 5 would expand out-

ward, and at some point the two bound-

aries would overlap.

8. Hung-Po Chao, Stephen Peck, Shmuel

Oren, and Robert Wilson, Flow-Based

14. PJM dispatchers reportedly monitor

approximately 50 contingencies.

54

The Electricity Journal

1

5. A secondary problem is that it is

he gave it up as hopeless (personal com-

munication to author).

ally never correct (e.g., PDFs are simply

not constant).

very difﬁcult even to deﬁne a set of set-

tlement rules that make sense here. The

difﬁculty of deﬁning a sensible settle-

ment process is creating difﬁculties for

the efforts to develop a workable hybrid

at MISO and perhaps elsewhere, but is

not discussed here.

24. F.C. Schweppe, M.C. Caramanis,

28. Actually, this is true only if an FTR is

a one-way option, so that an A-to-B FTR

and a B-to-A FTR are different. With

N nodes, there are Nϫ(N–1)/2 differ-

ent point-to-point pairs if A-to-B is

the same as B-to-A. Thus, with 100

nodes there could be “only” 4,950 bi-

directional FTRs.

R.D. Tabors, and R.E. Bohn, Spot Pric-

ing of Electricity (Norwell, MA: Klu-

wer, 1988).

25. William W. Hogan, E. Grant Read,

and Brendan J. Ring, Using Mathematical

Programming for Electricity Spot Pricing,

in Energy Models for Policy and

Planning, International Transactions of

Operational Research, Vol. 3, No. 3/4,

16. In this simple case, redispatch would

require paying some scheduled/hedged

generation in GEN not to run and pay-

ing some unscheduled/unhedged gen-

eration at LOAD to run out-of-merit.

29. If a portfolio of n FGRs can include

any of N Ͼ n different FGRs, there can be

N!/[n!ϫ(N Ϫ n)!] qualitatively different

portfolios. If N ϭ 50 and n ϭ 10, the

resulting number is 10,272,278,170.

1996.

17. Supra note 2, at 44–46. As discussed

below, Chao and Peck suggest a different

nonsolution to the problem of too many

FGRs in a footnote within their article.

30. Under a use-it-or-lose-it rule, any-

body holding an inventory of FGRs must

ﬁnd a buyer for all of its FGRs or be left

with nothing of value in real time. But

buyers could always wait to buy trans-

mission in the spot market by paying

real-time congestion charges. It is hard to

imagine how anybody could afford to

make a market in such FGRs. An FGR

bazaar might be more plausible without

a use-it-or-lose-it rule, but even so a

small market maker would be at a tre-

mendous disadvantage. It seems inevita-

ble that FGR trading would become a

centralized, monopoly activity.

1

8. Supra note 2, at note 18. As discussed

above, Chao and Peck suggest a different

nonsolution in the text of their article.

19. There is no FGR portfolio that per-

fectly hedges congestion on ﬂowgate A

in every contingency for all transactions,

because different PDFs will apply to

each different point-to-point transaction.

For the same reason, there is no FGR

portfolio that perfectly hedges conges-

tion on all ﬂowgates in contingency X for

all transactions. In principle it is possible

to create an FGR portfolio that perfectly

hedges against congestion on all ﬂow-

gates in all contingencies for a speciﬁed

point-to-point transaction. These are

called FTRs.

31. Supra note 8.

3

2. See PJM Market News, Vol. 1, No. 1,

2

6. A dispatch or set of FTRs is said to be

Oct. 2000, for information on the vol-

ume of energy and FTRs traded in PJM

markets.

simultaneously feasible if it satisﬁes all

of the actual and contingent constraints

used for dispatch. To be explicit about

what should be obvious but is some-

times confusing, a simultaneously feasi-

ble dispatch does not have to be feasible

even if all contingencies were to occur

simultaneously. No dispatch could meet

these conditions.

20. William Hogan, Flowgate Rights and

Wrongs, working paper, John F. Kennedy

School of Government, Harvard Univer-

sity, Aug. 20, 2000, at 20.

33. If something is valuable to its current

owners one would not expect it to be

offered for sale unless the prospective

buyers are willing to offer high prices for

it. And if the current owners fear that

they will not be allowed to keep any

trading proﬁts but will be stuck with any

trading losses—a dilemma commonly

created by regulation—they will be

reluctant to sell even when they

21. Andrew L. Ott, Can Flowgates Really

Work? An Analysis of Transmission Con-

gestion in the PJM Market from April 1,

1998–April 30, 2000, PJM Interconnec-

tion, Sept. 15, 2000.

27. Given the nonconvex nature of elec-

tricity systems—economies of scale,

integer choices, etc.—such sweeping

assertions require some technical quali-

ﬁcations, and it is possible to create

counterexamples using unrealistic

numerical examples. But the important

assumptions of LMP/FTR theory

appear to be valid over wide ranges of

actual conditions on real systems, in

sharp contrast to the assumptions of

ﬂowgate/FGR theory, which are virtu-

22. Supra note 3.

23. William W. Hogan, Contract Networks

“should” according to normal commer-

for Electric Power Transmission, 4 J. Reg.

Econ., 1992, at 211–42. Grant Read of

Canterbury University in New Zealand

was an early collaborator with Hogan.

Read spent some time in the late 1980s

and early 1990s developing a link-based

approach to transmission pricing and

congestion management, but says that

cial and economic criteria.

34. For example, the regional reliability

process may decide that the RTO should

replace an N–1 standard with an N–2

standard on some elements. This would

reduce the usable capacity of the grid

just as a grid outage would.

January/February 2001

Article Doi

DOI: 10.1016/S1040-6190(00)00174-3

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Article abstract of DOI:10.1016/S1040-6190(00)00174-3

Full text of DOI:10.1016/S1040-6190(00)00174-3

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