Cha

pter

4

CO

ST R

EC

OV

ER

Y A

ND

SH

OR

T-R

UN

E

FFIC

IEN

CY

C

laud

e C

ram

pes

Gre

maq

and

Idei

, Uni

vers

ity o

f Tou

lous

e, F

ranc

e

Whe

n de

sign

ing

a ta

riff f

or th

e tra

nspo

rt of

ele

ctric

ity, t

he m

ain

diff

icul

ty

is th

at th

e tra

nspo

rt in

dust

ry a

ppar

ently

incu

rs h

igh

fixed

cos

ts a

nd n

o re

al

varia

ble

cost

. In

eff

ect,

whe

n th

e in

fras

truct

ure

is i

nsta

lled

and

whe

n th

e op

erat

ors

are

at th

eir w

orkp

lace

, the

onl

y in

put w

hich

is n

eces

sary

to d

eliv

er

elec

trici

ty a

t a

give

n w

ithdr

awal

nod

e is

ele

ctric

ity a

t som

e in

ject

ion

node

si

nce

elec

trici

ty is

flow

ing

by it

self.

Con

sequ

ently

, at f

irst s

ight

the

prob

lem

is

just

to a

lloca

te fi

xed

cost

s, m

ainl

y in

fras

truct

ure

mai

nten

ance

cos

ts, w

ages

an

d fin

anci

al c

harg

es, a

mon

g th

e di

ffer

ent t

ypes

of u

sers

of t

he g

rid.

A

s a

mat

ter

of f

act,

the

trans

port

of e

lect

ricity

cre

ates

tw

o si

gnifi

cant

va

riabl

e co

sts.1 O

ne is

an

inte

rnal

cos

t, th

at is

, a c

ost i

n te

rms

of e

lect

ricity

: a

frac

tion

of t

he e

nerg

y w

hich

is

inje

cted

int

o th

e gr

id w

ill b

e lo

st d

urin

g tra

nspo

rt.

It re

sults

that

the

cons

umpt

ion

of 1

MW

h of

ele

ctric

ity r

equi

res

the

gene

ratio

n of

(1+L

) MW

h, a

nd th

is e

xtra

L M

Wh

is a

real

cos

t for

whi

ch

prod

ucer

s m

ust b

e co

mpe

nsat

ed.

Add

ition

ally

, bec

ause

the

lines

and

nod

es

used

fo

r tra

nspo

rt ha

ve

a lim

ited

capa

city

, th

e op

timal

al

loca

tion

of

prod

uctio

n an

d co

nsum

ptio

n is

not

as

effic

ient

as

it w

ould

be,

abs

ent

any

grid

con

stra

int.

And

pric

ing

mus

t in

clud

e th

is e

cono

mic

cos

t du

e to

co

nges

tion.

W

hen

trans

port

pric

es a

re c

ompu

ted

usin

g th

e m

argi

nal v

alue

s of

thes

e tw

o co

sts

(the

so-c

alle

d “n

odal

pric

es”)

, the

y pr

ovid

e a

reve

nue

larg

er th

an

the

loss

es o

f en

ergy

. T

his

surp

lus

can

be u

sed

to p

ay f

or f

ixed

cos

ts o

f tra

nspo

rt bu

t, in

mos

t cas

es, i

t is

not l

arge

eno

ugh

to b

alan

ce th

e bu

dget

of

the

oper

ator

. Th

is e

xpla

ins

why

tran

spor

t tar

iffs

mus

t be

eith

er s

econ

d-be

st

linea

r pric

es (R

amse

y pr

ices

) or n

on li

near

pric

es.

The

chap

ter p

rese

nts t

he n

orm

ativ

e pr

inci

ples

of t

he e

cono

mic

ana

lysi

s of

pric

ing

in e

lect

ricity

tra

nspo

rt.

It is

exc

lusi

vely

ded

icat

ed t

o sh

ort-t

erm

106

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

anal

ysis

, th

at i

s to

the

ope

ratio

n of

a g

iven

ele

ctric

ity n

etw

ork.

Th

e de

velo

pmen

t of t

he tr

ansp

ort i

nfra

stru

ctur

e is

ana

lyse

d in

Cha

pter

5.

In

Sec

tion

1, w

e de

fine

the

varia

ble

cost

of

trans

port

as th

e su

m o

f th

e co

st o

f con

gest

ion

and

the

cost

of o

hmic

loss

es.

In S

ectio

n 2,

we

show

how

no

dal

pric

es c

an b

e us

ed t

o de

sign

tar

iffs

for

trans

port.

Se

ctio

n 3

is

dedi

cate

d to

the

prob

lem

of f

und

risin

g in

ord

er to

bal

ance

the

budg

et o

f the

tra

nspo

rt op

erat

or.

Firs

tly,

we

focu

s on

Ram

sey

pric

es,

whi

ch a

re t

he

seco

nd-b

est

linea

r pr

ices

w

hen

one

tries

to

re

ach

effic

ienc

y w

ithou

t im

pairi

ng t

he b

udge

t eq

uilib

rium

of

the

trans

port

firm

. S

econ

dly,

we

cons

ider

a s

peci

al c

lass

of

non-

linea

r pr

ices

, nam

ely,

tw

o-pa

rt ta

riffs

. W

e co

nclu

de in

Sec

tion

4.

We

do n

ot d

iscu

ss h

ow t

o de

fine

trans

mis

sion

rig

hts

on t

he t

rans

port

infr

astru

ctur

e an

d th

e co

nflic

t bet

wee

n th

e su

ppor

ters

of p

hysi

cal r

ight

s an

d th

e su

ppor

ters

of

finan

cial

rig

hts.2

Nei

ther

do

we

cons

ider

the

ow

ners

hip

and

the

gove

rnan

ce o

f th

e tra

nspo

rt fir

m.

We

supp

ose

that

use

rs f

ace

no

barr

ier

to g

ain

acce

ss to

the

grid

. Th

e re

gula

tion

of th

e tra

nspo

rt op

erat

or

unde

r alte

rnat

ive

hypo

thes

es c

once

rnin

g ve

rtica

l int

egra

tion

and

com

petit

ion

betw

een

grid

use

rs is

scru

tinis

ed in

Cha

pter

6.

Whi

le i

n th

e fo

llow

ing

sect

ions

w

e ha

ve a

dopt

ed a

non

-tech

nica

l pr

esen

tatio

n, th

e re

ader

can

fin

d in

the

appe

ndix

a f

orm

al m

odel

ling

of th

e m

ain

resu

lts.

1.

FIR

ST-B

EST

DIS

PAT

CH

IN A

N E

LE

CT

RIC

ITY

N

ET

WO

RK

1.1

The

tran

spor

t of e

lect

rici

ty

In e

cono

mic

term

s, a

good

is d

efin

ed b

y: (i

) som

e in

trins

ic c

hara

cter

istic

s (w

eigh

t, si

ze, q

ualit

y, e

tc.);

(ii)

the

loca

tion;

(iii

) the

dat

e; a

nd (i

v) th

e st

ate

of n

atur

e w

here

it is

ava

ilabl

e. T

rans

port

is th

e ac

tivity

that

mai

nly

cons

ists

in

mod

ifyin

g at

tribu

te (

ii), e

ven

if, a

s si

de e

ffec

ts, t

he th

ree

othe

r at

tribu

tes

are

also

mod

ified

in

mos

t ca

ses.

It

resu

lts t

hat,

to a

naly

se t

he u

tility

of

trans

porti

ng a

spe

cific

goo

d, w

e ne

ed to

ana

lyse

the

utili

ty a

nd th

e co

st o

f th

at g

ood

at th

e de

partu

re a

nd a

rriv

al lo

catio

ns.

The

diff

eren

ce b

etw

een

the

net u

tility

of t

he g

ood

at th

e ar

rival

loca

tion

and

at th

e de

partu

re lo

catio

n is

th

e gr

oss

utili

ty fr

om tr

ansp

ortin

g it.

Thi

s di

ffer

ence

is to

be

com

pare

d w

ith

the

cost

of t

rans

port

in o

rder

to d

ecid

e if

the

good

is to

be

disp

lace

d or

if it

sh

ould

rem

ain

at th

e in

itial

loca

tion.

Th

is i

s th

e no

rmat

ive

prin

cipl

e th

at w

e ha

ve t

o ap

ply

whe

n an

alys

ing

elec

trici

ty t

rans

port.

Th

e st

artin

g po

int

is t

o de

term

ine

the

quan

titie

s to

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

10

7

gene

rate

and

to c

onsu

me

in o

rder

to m

axim

ise

the

wel

fare

of

all t

he a

gent

s th

at u

se t

he t

rans

port

infr

astru

ctur

e.

In t

he s

hort

run,

the

equ

ipm

ent

for

gene

ratio

n, t

rans

porta

tion

and

dist

ribut

ion

is f

ixed

. T

he p

refe

renc

es o

f co

nsum

ers

also

are

fixe

d. T

he o

ptim

al a

lloca

tion

is li

mite

d to

dec

idin

g ho

w

muc

h to

gen

erat

e at

eac

h no

de a

nd h

ow m

uch

to c

onsu

me

at e

ach

node

, gi

ven

the

rest

rain

ts im

pose

d by

the

topo

logi

cal c

hara

cter

istic

s of t

he n

etw

ork

and

the

tech

nica

l ca

pabi

lity

of e

ach

piec

e of

equ

ipm

ent

(see

Box

4-1

for

de

tails

on

the

obje

ctiv

e to

max

imis

e w

elfa

re u

nder

alte

rnat

ive

sets

of

cons

train

ts).

Box

4-1

: Fir

st-b

est,

seco

nd-b

est,

and

cons

trai

nts t

o m

axim

ise

wel

fare

In

the

shor

t run

, the

who

le g

ener

atio

n an

d tra

nspo

rtatio

n eq

uipm

ents

are

fixe

d, a

s w

ell a

s all

the

need

s.

Th

e “g

rid-f

ree”

firs

t be

st a

lloca

tion

is t

he s

et o

f qu

antit

ies

of e

lect

ricity

ge

nera

ted

and

cons

umed

at e

ach

node

that

max

imis

es th

e ne

t wel

fare

, tha

t is,

the

sum

of

the

diff

eren

ce b

etw

een

the

utili

ty o

f el

ectri

city

for

con

sum

ers

and

the

cost

to g

ener

ate

it, in

a fi

ctiti

ous

situ

atio

n w

here

ene

rgy

can

flow

from

one

nod

e to

oth

ers w

ithou

t any

con

stra

int a

nd w

ithou

t any

loss

.

Th

e “g

rid-c

onst

rain

ed”

first

bes

t allo

catio

n al

so m

axim

ises

the

net w

elfa

re, b

ut

taki

ng in

to a

ccou

nt th

e ph

ysic

al c

hara

cter

istic

s of t

he g

rid.

In th

is c

ase:

(i) s

ome

ener

gy i

s lo

st d

urin

g tra

nspo

rt; a

nd (

ii) b

ecau

se s

ome

lines

and

int

erm

edia

ry

node

s ha

ve l

imite

d ca

paci

ty,

the

“grid

-fre

e” o

ptim

al f

low

s ar

e no

lon

ger

feas

ible

, whi

ch c

reat

es a

“co

nges

tion

cost

”.

In

eco

nom

ic t

heor

y, “

seco

nd-b

est”

mai

nly

refe

rs t

o a

situ

atio

n w

here

the

be

nevo

lent

pla

nner

has

to

bala

nce

the

budg

et o

f th

e pr

oduc

ers

he s

uper

vise

s.

Act

ually

, th

is e

xpre

ssio

n ca

n be

use

d in

any

situ

atio

n w

here

a c

onst

rain

t is

ad

ded

to a

n in

itial

allo

catio

n pr

oble

m.

In t

hat

resp

ect,

the

“grid

-con

stra

ined

” fir

st-b

est i

s a se

cond

-bes

t with

resp

ect t

o th

e “g

rid-f

ree”

firs

t bes

t allo

catio

n.

W

hen

a co

nstra

int

is a

dded

to

a gi

ven

optim

isat

ion

prob

lem

, ei

ther

tha

t co

nstra

int

is n

ot b

indi

ng a

nd t

he i

nitia

l al

loca

tion

does

not

cha

nge,

or

it is

bi

ndin

g an

d it

resu

lts i

n a

decr

ease

of

the

initi

al p

erfo

rman

ce.

The

new

al

loca

tion

can

neve

r gi

ve a

hig

her

perf

orm

ance

sin

ce,

if fe

asib

le n

ow,

it w

as

feas

ible

bef

ore

the

new

con

stra

int i

s ad

ded

and

it w

ould

hav

e be

en c

hose

n. T

he

diff

eren

ce b

etw

een

the

perf

orm

ance

with

out

and

the

perf

orm

ance

with

the

co

nstra

int

is t

he e

cono

mic

cos

t of

the

con

stra

int.

For

exa

mpl

e, t

he e

cono

mic

co

st o

f th

e tra

nspo

rt gr

id is

the

diff

eren

ce b

etw

een

the

grid

-fre

e so

cial

wel

fare

an

d th

e gr

id-c

onst

rain

ed so

cial

wel

fare

.

In

the

sam

e w

ay, o

ne c

an m

easu

re th

e co

st o

f add

ition

al c

onst

rain

ts, s

uch

as:

– th

e ob

ligat

ion

to b

alan

ce b

udge

t;

108

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

– th

e pr

ohib

ition

to d

iscr

imin

ate

on p

rices

; –

rest

rictio

ns o

n ta

riff c

lass

es (l

inea

r, tw

o-pa

rt, e

tc.);

–

the

inab

ility

of t

he o

pera

tor t

o co

llect

info

rmat

ion

on p

refe

renc

es a

nd c

osts

; –

the

univ

ersa

l ser

vice

obl

igat

ion;

–

etc.

Sh

ort-r

un d

ecis

ions

are

con

stra

ined

by

the

inca

paci

ty t

o ad

apt

the

trans

port

infr

astru

ctur

e an

d th

e ge

nera

tion

plan

ts.

For

this

rea

son,

the

shor

t-run

cos

t, in

w

hich

the

re a

re s

igni

fican

t fix

ed c

osts

, is

hig

her

than

the

lon

g-ru

n co

st ex

clus

ivel

y m

ade

of o

ptim

ally

cho

sen

varia

ble

inpu

ts.

To u

nder

stan

d w

hy th

e op

timal

allo

catio

n ca

n be

def

ined

in th

at s

impl

e w

ay,

it is

int

eres

ting

to s

tress

som

e im

porta

nt d

iffer

ence

s be

twee

n th

e tra

nspo

rt of

ele

ctric

ity a

nd o

ther

tran

spor

t act

iviti

es, f

or e

xam

ple

frei

ght o

r pa

ssen

gers

tran

spor

t. F

irstly

, ele

ctric

ity is

hig

hly

stan

dard

ised

, whi

ch m

eans

cl

ose

subs

titut

abili

ty b

etw

een

gene

ratio

n no

des

for

a gi

ven

need

and

, sy

mm

etric

ally

, clo

se s

ubst

ituta

bilit

y be

twee

n co

nsum

ptio

n no

des

for a

giv

en

prod

uctio

n. T

his h

omog

enei

ty p

rope

rty a

llow

s to

pool

qua

ntiti

es.

Seco

ndly

, fo

r el

ectri

city

, the

tim

e at

tribu

te o

f th

e go

od i

s no

t m

odifi

ed b

y tra

nspo

rt.

Pow

er f

low

s in

stan

tane

ousl

y th

roug

h lin

es a

nd i

nter

med

iary

nod

es.

(Se

e B

ox 4

-2 fo

r som

e ill

ustra

tions

of n

etw

ork

topo

logi

es).

Thi

s exp

lain

s why

, in

the

optim

al d

ispa

tch,

inje

ctio

ns a

nd w

ithdr

awal

s ar

e co

ntem

pora

neou

s. F

or

the

sam

e re

ason

, the

dis

patc

her

can

know

for

sur

e th

e st

ate

of n

atur

e at

a

with

draw

al n

ode

whe

n in

ject

ing

pow

er a

t an

othe

r lo

catio

n, w

hich

gre

atly

re

duce

s th

e ra

ndom

ness

of n

et lo

catio

nal u

tiliti

es.

The

third

diff

eren

ce w

ith

mos

t tra

nspo

rt ne

twor

ks is

that

, for

ele

ctric

ity, t

he te

chno

logy

doe

s not

allo

w

to c

ontro

l the

phy

sica

l flo

w o

f en

ergy

thro

ugh

the

grid

(se

e B

ox 4

-2 f

or a

n ill

ustra

tion)

. C

onse

quen

tly, t

he a

ctua

l flo

w o

n ea

ch li

ne c

anno

t be

a co

ntro

l va

riabl

e.

Four

thly

, in

a g

iven

grid

, on

e ca

n pr

edic

t ve

ry p

reci

sely

the

am

ount

of t

rans

port

loss

es b

ecau

se th

ey fo

llow

wel

l kno

wn

phys

ical

law

s.

To s

um u

p, tr

ansp

ortin

g el

ectri

city

con

sist

s in

con

trolli

ng m

odifi

catio

ns

in it

s at

tribu

tes

(ii)

and

(iv)

with

out m

odify

ing

attri

bute

(iii

) an

d pr

ovok

ing

an u

ndes

irabl

e bu

t pr

edic

tabl

e ch

ange

in

attri

bute

(i).

Th

e ph

ysic

al p

ath

follo

wed

bec

ause

of t

he tr

ansf

orm

atio

n in

attr

ibut

e (ii

) can

not b

e co

ntro

lled;

it

resu

lts t

hat

trans

port

betw

een

two

node

s in

a m

eshe

d ne

twor

k cr

eate

s ex

tern

aliti

es o

n al

l lin

es a

nd n

odes

inte

ntio

nally

and

uni

nten

tiona

lly c

ross

ed

by th

e en

ergy

flow

. In

the

optim

al a

lloca

tion

defin

ed b

y a

bene

vole

nt s

ocia

l pla

nner

, at e

ach

node

, mar

gina

l ut

ility

is

equa

l to

mar

gina

l co

st.

If, a

t on

e no

de, m

argi

nal

cost

wer

e hi

gher

than

mar

gina

l util

ity, t

he la

st k

Wh

wou

ld b

e ge

nera

ted

at

loss

and

, sym

met

rical

ly, i

f m

argi

nal c

ost w

ere

less

than

mar

gina

l util

ity, i

t w

ould

mea

n th

at th

e en

tire

pote

ntia

l soc

ial s

urpl

us is

not

cre

ated

. A

t eac

h

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

10

9

node

, th

is e

qual

ity o

f m

argi

nal

cost

and

mar

gina

l ut

ility

will

mos

t lik

ely

requ

ire a

tra

nsfe

r of

ene

rgy.

So

me

node

s w

ill h

ave

to e

xpor

t en

ergy

and

ot

hers

will

be

net i

mpo

rters

, dep

endi

ng o

n th

e co

st s

truct

ure

of g

ener

atio

n an

d gi

ven

the

cons

umer

s' pr

efer

ence

s fo

r el

ectri

city

. W

hen

no p

iece

of

infr

astru

ctur

e ex

hibi

ts c

onge

stio

n, a

nd w

hen

ther

e is

no

ohm

ic l

oss,

the

optim

al a

lloca

tion

is s

uch

that

ene

rgy

has

one

sing

le v

alue

thr

ough

out

the

who

le n

etw

ork,

whi

ch c

an b

e vi

ewed

as

a gi

ant u

niqu

e no

de o

r as

a p

late

. To

see

this

, obs

erve

that

if th

ere

rem

aine

d a

diff

eren

ce b

etw

een

two

node

s, it

wou

ld b

e ea

sy to

incr

ease

the

glob

al s

urpl

us b

y tra

nsfe

rrin

g so

me

kWh

from

th

e no

de w

ith th

e lo

wer

mar

gina

l val

uatio

n to

war

ds th

e no

de w

ith th

e hi

gher

va

luat

ion.

Box

4-2

: Of n

odes

and

line

s

An

elec

tric

grid

can

be

view

ed a

s a

set

of n

odes

, ei

ther

fin

al (

inje

ctio

n an

d w

ithdr

awal

no

des)

or

in

term

edia

ry

(tran

sfor

mer

s, m

eter

s, co

ntro

llers

, et

c.),

inte

rcon

nect

ed b

y lin

es.

The

sim

ples

t ne

twor

k is

mad

e of

one

sin

gle

line

conn

ectin

g tw

o fin

al n

odes

. Th

e “n

orth

-sou

th”

netw

ork

repr

esen

ted

belo

w (s

ee F

igur

e 4-

1) is

a u

sefu

l the

oret

ical

co

nfig

urat

ion

to u

nder

stan

d co

nges

tion

and

loss

es,

but

it al

so g

ives

a r

easo

nabl

y go

od p

ictu

re o

f the

grid

in s

ome

coun

tries

.3 Sin

ce th

ere

exis

ts a

sin

gle

line,

ther

e is

on

e un

ique

pos

sibl

e pa

th f

or t

rans

porti

ng e

lect

ricity

fro

m n

orth

to

sout

h or

fro

m

sout

h to

nor

th.

Abs

ent

any

ener

gy l

oss,

the

phys

ical

equ

ilibr

ium

of

the

elec

tric

indu

stry

impo

ses

gg

ww

ns

ns

qq

qq

, whe

re

g nq (r

espe

ctiv

ely

w nq) s

tand

s for

the

quan

tity

gene

rate

d (r

espe

ctiv

ely

cons

umed

) at t

he n

orth

nod

e an

d g sq (r

espe

ctiv

ely

w sq) s

tand

s fo

r the

qua

ntity

gen

erat

ed (r

espe

ctiv

ely

cons

umed

) at t

he so

uth

node

. C

onse

quen

tly,

the

quan

tity

of e

lect

ricity

flow

ing

on th

e lin

e is

g

ww

gn

ns

sq

qq

q.

But

in m

any

coun

tries

, par

ticul

arly

in c

ontin

enta

l Eur

ope,

ele

ctric

net

wor

ks a

re

mes

hed.

Th

e co

nseq

uenc

e is

that

ther

e is

not

one

uni

que

path

for

ele

ctric

ity to

go

from

one

nod

e to

ano

ther

. Th

is is

illu

stra

ted

in th

e th

ree-

node

net

wor

k he

reaf

ter (

see

Figu

re 4

-2).

Ene

rgy

flow

s fol

low

pat

hs o

f lea

st re

sist

ance

det

erm

ined

by

Kirc

hhof

f's

law

s. S

uppo

se a

gen

erat

ion

node

and

a c

onsu

mpt

ion

node

are

con

nect

ed b

y tw

o lin

es, o

ne w

ith a

res

ista

nce

twic

e th

e ot

her's

. W

hen

gene

rato

rs in

ject

qua

ntity

q a

t on

e no

de a

nd,

assu

min

g no

los

ses,

cons

umer

s w

ithdr

aw t

he s

ame

quan

tity

at t

he

othe

r no

de, t

he f

low

s on

the

low

res

ista

nce

line

and

on th

e hi

gh r

esis

tanc

e lin

e ar

e re

spec

tivel

y 2q

/3 a

nd q

/3.

In a

3-li

ne n

etw

ork

with

the

sam

e re

sist

ance

on

each

line

, lik

e in

Fig

ure

4-2,

if th

ere

are

two

gene

rato

rs in

stal

led

at n

odes

1 a

nd 2

resp

ectiv

ely,

an

d co

nsum

ers

are

loca

ted

at th

e th

ird n

ode,

the

sim

ulta

neou

s in

ject

ion

of

1g q a

nd

2g q w

ill g

ener

ate

a su

perp

ositi

on o

f flo

ws

on t

he l

ines

con

nect

ing

cons

umer

s to

ge

nera

tors

. Fo

r ex

ampl

e, th

e lin

e be

twee

n no

de 1

and

nod

e 3

trans

ports

two

third

s of

the

ener

gy in

ject

ed a

t nod

e 1

plus

one

third

of t

he e

nerg

y in

ject

ed a

t nod

e 2.

By

cont

rast

, on

ly o

ne t

hird

of

the

net

flow

circ

ulat

es o

n th

e lin

e be

twee

n th

e tw

o ge

nera

tors

.

110

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

nort

h

w sqg sq

w nq

sout

h

g nq

Figu

re 4

-1.

One

line

net

wor

k

12

3

gg

qq

node

2

inje

ctio

n 2g q

node

1

inje

ctio

n 1g q

12

23g

gq

q1

22 3

gg

qq

node

3

cons

umpt

ion

31

2w

gg

qq

q

Figu

re 4

-2.

Thre

e-lin

e ne

twor

k B

ut, a

s ex

plai

ned

belo

w, b

ecau

se o

f lo

sses

and

bec

ause

of

som

e sc

arce

ca

paci

ty in

tran

spor

t, tra

nsfe

rs fr

om o

ne n

ode

to a

noth

er c

anno

t be

done

for

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

11

1

free

. It

mea

ns th

at th

e “v

ery-

first

-bes

t” a

lloca

tion

(or “

grid

-fre

e” a

lloca

tion)

is

not

feas

ible

. Th

e di

spat

cher

can

onl

y re

ach

the

“grid

-con

stra

ined

” op

timal

al

loca

tion

and,

con

sequ

ently

, ene

rgy

valu

atio

n re

sulti

ng f

rom

thi

s di

spat

ch

will

diff

er a

mon

g th

e no

des.

1.2

The

cos

t of c

onge

stio

n

Ass

ume

first

tha

t lo

sses

can

be

negl

ecte

d.

At

impo

rting

nod

es,

the

inco

min

g en

ergy

is li

mite

d by

the

capa

city

of

lines

and

tran

sfor

mer

s al

ong

the

phys

ical

pat

h fo

llow

ed b

y en

ergy

. A

s a

resu

lt, e

lect

ricity

is

rela

tivel

y sc

arce

and

it

is m

ore

valu

ed t

han

if th

ere

wer

e no

cap

acity

con

stra

int.

R

ecip

roca

lly,

at e

xpor

ting

node

s, en

ergy

is

rela

tivel

y in

exc

ess

and

low

va

lued

bec

ause

the

outg

oing

ene

rgy

is li

mite

d by

the

capa

city

of

lines

and

tra

nsfo

rmer

s. T

he m

ore

cong

este

d th

e ne

twor

k, th

e hi

gher

the

disc

repa

ncy

betw

een

noda

l val

uatio

ns.

The

limit

case

is th

e au

tark

y ca

se w

here

line

s ar

e cu

t sot

that

eac

h no

de is

isol

ated

from

the

othe

rs.

The

diff

eren

ce b

etw

een

two

noda

l val

uatio

ns o

f ene

rgy,

abs

ent a

ny lo

ss,

is a

n in

dex

of t

he t

ight

ness

of

the

trans

port

cons

train

t. I

t re

flect

s th

e in

capa

city

of

the

oper

ator

to

incr

ease

gen

erat

ion

at l

ow-c

ost

node

s an

d to

de

crea

se

it at

hi

gh-c

ost

node

s as

w

ell

as

its

inca

paci

ty

to

incr

ease

co

nsum

ptio

n at

hig

h-ut

ility

nod

es a

nd t

o de

crea

se i

t at

low

-util

ity n

odes

. Th

e “m

erit

orde

r” c

omm

ands

that

no

gene

rato

r sho

uld

be d

ispa

tche

d if

ther

e re

mai

ns s

ome

avai

labl

e ca

paci

ty w

ith a

low

er c

ost.

It

is n

o lo

nger

im

plem

enta

ble.

In

the

sim

ples

t ca

se o

f B

ox 4

-3,

with

one

sin

gle

line

conn

ectin

g ef

ficie

nt n

orth

ern

gene

rato

rs w

ith a

sou

th n

ode

whe

re th

ere

are

inef

ficie

nt g

ener

ator

s an

d th

e lo

ad, o

ne c

an e

asily

dra

w th

e gr

id-c

onst

rain

ed

optim

al q

uant

ities

and

mea

sure

how

they

dep

art f

rom

the

grid

-fre

e op

timal

qu

antit

ies.

The

diff

eren

ce in

nod

al v

alua

tions

exa

ctly

refle

cts

the

soci

al c

ost

of h

avin

g an

out

-of-

mer

it-or

der d

ispa

tch

beca

use

of th

e lim

ited

capa

city

for

trans

port

betw

een

north

and

sout

h. T

he d

iffer

ence

is th

e sh

adow

val

ue o

f the

tra

nspo

rt lin

e th

at s

igna

ls b

y ho

w m

uch

soci

al w

elfa

re w

ould

be

incr

ease

d if

the

cons

train

t cou

ld b

e re

laxe

d.

In m

eshe

d ne

twor

ks, e

nerg

y flo

ws

alon

g le

ast

resi

stan

ce p

aths

with

out

the

poss

ibili

ty to

con

trol t

hem

.4 As

a re

sult,

any

inje

ctio

n an

d w

ithdr

awal

of

a gi

ven

quan

tity

at t

wo

dist

inct

nod

es w

ill p

rovo

ke a

tra

nsit

of e

lect

ricity

th

roug

h al

l the

line

s of

the

netw

ork.

If

one

line

is c

onge

sted

, all

path

s w

ill

appe

ar c

onge

sted

. C

onse

quen

tly, i

n a

mes

hed

netw

ork,

con

gest

ion

on o

ne

line

is s

uffic

ient

for n

odal

val

ues

to d

iffer

thro

ugho

ut th

e ne

twor

k. B

ecau

se

of th

is “

cont

agio

n ef

fect

”, th

e du

al v

alue

of t

he c

onge

sted

line

is la

rger

than

th

e m

ere

diff

eren

ce b

etw

een

the

mar

gina

l va

lues

at

the

two

ends

of

the

cong

este

d lin

e.5

The

diff

eren

ce b

etw

een

thes

e tw

o va

lues

ref

lect

s th

e

112

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

nega

tive

exte

rnal

ities

in

el

ectri

city

tra

nspo

rt,

that

is

, th

e ad

ditio

nal

cong

estio

n co

st d

ue to

loop

-flo

ws.

Box

4-3

: Out

-of-

mer

it-or

der

optim

al d

ispa

tch

Con

side

r th

e no

rth-s

outh

net

wor

k in

Box

4-2

(see

Fig

ure

4-1)

. A

ssum

e th

at a

ll co

nsum

ers

are

in ‘

sout

h’ a

nd t

heir

mar

gina

l ut

ility

fro

m w

ithdr

awin

g th

e qu

antit

y w sq

of

elec

trici

ty i

s gi

ven

by t

he d

ecre

asin

g fu

nctio

n '(

)10

ww

ss

Uq

q (

see

Figu

re

4-3)

. In

‘nor

th’,

elec

trici

ty c

an b

e ge

nera

ted

at a

con

stan

t mar

gina

l cos

t equ

al to

1¢

and,

in ‘s

outh

’, th

ere

exis

t pla

nts w

ith a

con

stan

t mar

gina

l cos

t equ

al to

4¢.

The

re is

no

con

stra

int o

f cap

acity

for g

ener

atio

n an

d th

ere

is n

o en

ergy

loss

on

the

line.

Let

K

den

ote

the

capa

city

of t

he li

ne.

12

3

gg

qq

node

2

inje

ctio

n 2g q

node

1

inje

ctio

n 1g q

12

23g

gq

q1

22 3

gg

qq

node

3

cons

umpt

ion

31

2w

gg

qq

q

Figu

re 4

-3.

Out

-of-

mer

it-or

der o

ptim

al d

ispa

tch

If K

is v

ery

larg

e, th

e op

timal

dis

patc

h co

nsis

ts in

pro

duci

ng n

othi

ng in

‘so

uth’

w

here

gen

erat

ion

is v

ery

cost

ly.

The

who

le e

nerg

y co

mes

fro

m ‘

north

’. T

he

optim

al c

onsu

mpt

ion

is s

uch

that

'(

)1

Uq

¢, th

at is

the

grid

-fre

e op

timal

qua

ntity

w sq

=9.

If

K <

9, t

he c

apac

ity o

f the

line

doe

s no

t allo

w to

impo

rt th

is q

uant

ity o

f ene

rgy

from

‘no

rth’.

The

dis

patc

h fir

st c

onsi

sts

in s

atur

atin

g th

e lin

e to

tran

sfer

as

muc

h en

ergy

as

poss

ible

fro

m ‘

north

’, w

hich

is K

. A

fter t

hat,

ther

e ar

e tw

o po

ssib

ilitie

s:

(i) if

the

mar

gina

l util

ity fr

om c

onsu

min

g K

is s

till h

ighe

r tha

n th

e m

argi

nal c

ost o

f ge

nera

tion

in ‘s

outh

’, us

e th

e so

uth

plan

t up

to th

e po

int w

here

the

mar

gina

l util

ity

of e

lect

ricity

is

equa

l to

the

mar

gina

l co

st o

f ge

nera

tion,

tha

t is

'(

)4

g sU

Kq

¢.

Oth

erw

ise,

do

not d

ispa

tch

the

cost

ly p

lant

. In

the

first

cas

e, th

e gr

id-c

onst

rain

ed

optim

al

allo

catio

n is

g nq

K,

6g sq

K

(as

long

as

6

K)

and

the

tota

l co

nsum

ptio

n is

6

w sq.

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

11

3

In t

he s

econ

d ca

se,

that

is

for

K b

etw

een

6 an

d 9,

the

tot

al o

utpu

t is

the

co

nstra

ined

flo

w c

omin

g fr

om ‘

north

’, g nq

K,

0g sq

. T

hese

qua

ntiti

es a

re

grap

hed

in th

e m

iddl

e pa

nel o

f Fig

ure

4-3

as fu

nctio

ns o

f the

cap

acity

of t

he li

ne K

.

Bec

ause

of

the

inef

ficie

nt d

ispa

tch

crea

ted

by t

he l

imite

d ca

paci

ty o

f th

e lin

e,

wel

fare

can

not b

e as

hig

h as

it w

ould

be

if lo

w-c

ost g

ener

ator

s w

ere

loca

ted

at th

e so

uth

node

with

con

sum

ers.

The

low

er p

anel

of F

igur

e 4-

3 re

pres

ents

the

mar

gina

l va

lue

of th

e ca

paci

ty c

onst

rain

t, w

hich

rep

rese

nts

the

mar

gina

l co

st o

f co

nges

tion

. W

hen

K i

s sm

alle

r th

an 6

, on

e ad

ditio

nal

unit

of c

apac

ity w

ould

allo

w t

o su

bstit

ute

one

north

kW

h to

one

sou

th k

Wh,

that

is to

sav

e =

4¢

- 1¢

= 3¢

for a

n un

chan

ged

tota

l out

put.

Whe

n K

is b

etw

een

6 an

d 9,

one

add

ition

al u

nit o

f cap

acity

al

low

s to

incr

ease

the

cons

umpt

ion

by m

eans

of m

ore

impo

rts fr

om ‘n

orth

’, so

that

its

val

ue is

the

net

mar

gina

l util

ity o

f el

ectri

city

; =

U'(K

) - 1

¢ =

9 - K

. Fi

nally

, w

hen

K is

larg

er th

an 9

, any

dev

elop

men

t wou

ld b

e us

eles

s, w

hich

is s

igna

lled

by

= 0

. A

s sh

own

in C

hapt

er 5

, the

sha

dow

pric

e of

the

lines

is to

be

com

pare

d w

ith th

e re

al p

rice

of o

ne u

nit o

f eq

uipm

ent t

o kn

ow w

heth

er th

e tra

nspo

rt ca

paci

ty i

s to

be

incr

ease

d or

dec

reas

ed.

Whe

n th

e du

al v

alue

of

the

cons

train

t is

hig

her

than

the

cos

t of

one

add

ition

al u

nit

of e

quip

men

t, th

e tra

nspo

rt lin

e sh

ould

be

deve

lope

d.

And

it

shou

ld b

e do

wns

ized

in

the

oppo

site

cas

e. I

n ac

tual

net

wor

ks, t

he in

fras

truct

ure

is a

lmos

t alw

ays

larg

er

than

its

optim

al s

ize.

The

con

sequ

ence

is th

at th

e sh

adow

pric

e of

line

s an

d tra

nsfo

rmer

s is

less

than

thei

r un

it co

st.

And

it is

eve

n eq

ual t

o ze

ro w

hen

ther

e is

no

cong

estio

n at

all.

1.3

The

cos

t of l

osse

s

Supp

ose

now

tha

t th

ere

is n

o co

nges

tion.

Th

e m

ain

cost

of

deliv

erin

g 1

MW

h at

one

nod

e st

artin

g fr

om a

spe

cific

inje

ctio

n no

de r

esul

ts f

rom

the

fact

that

a q

uant

ity L

of t

he e

nerg

y in

ject

ed w

ill b

e lo

st in

tran

spor

t. It

mea

ns

that

1+ L

MW

h ar

e to

be

gene

rate

d. A

s a

resu

lt, in

an

optim

ised

net

wor

k th

e m

argi

nal v

alua

tion

of 1

MW

h w

ill d

iffer

fro

m o

ne n

ode

to th

e ot

her

by th

e va

lue

of th

e lo

st e

nerg

y. N

ote

that

it is

not

a c

ost i

ncur

red

by th

e tra

nspo

rt gr

id it

self.

It i

s a

cost

due

to th

e di

stan

ce b

etw

een

inje

ctio

n an

d w

ithdr

awal

no

des.

It d

irect

ly c

once

rns g

ener

ator

s and

con

sum

ers.

In e

lect

ric n

etw

orks

, los

ses

incr

ease

pro

porti

onal

ly t

o th

e sq

uare

of

the

ener

gy i

njec

ted.

Th

e co

nseq

uenc

e of

thi

s pr

ecis

e fu

nctio

nal

form

is

that

m

argi

nal l

osse

s are

twic

e hi

gher

than

ave

rage

loss

es.6

114

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

1.4

The

shor

t-ru

n m

argi

nal c

ost o

f tra

nspo

rt

To s

um u

p, b

ecau

se m

aint

aini

ng a

nd d

evel

opin

g th

e in

fras

truct

ure

is

cost

ly, i

t is

optim

al to

kee

p so

me

cong

estio

n in

mos

t pie

ces

of th

e tra

nspo

rt gr

id.

As

a re

sult,

the

dis

patc

h th

at w

ould

max

imis

e ne

t so

cial

wel

fare

w

ithou

t any

refe

renc

e to

the

grid

(lik

e if

all g

ener

ator

s an

d co

nsum

ers

wer

e lo

cate

d at

the

sam

e pl

ace)

is n

ot fe

asib

le.

The

actu

al d

ispa

tch

is s

ub-o

ptim

al

as c

ompa

red

with

the

fic

titio

us o

ne-n

ode

indu

stry

. T

he c

ost

due

to

cong

estio

n is

equ

al to

the

diff

eren

ce b

etw

een

the

max

imum

wel

fare

obt

aine

d w

ithou

t tra

nspo

rt co

nstra

ints

and

the

wel

fare

tha

t re

sults

fro

m t

he a

ctua

l di

spat

ch.

In

addi

tion

to c

onge

stio

n co

sts,

only

a f

ract

ion

of t

he q

uant

ity

inje

cted

can

be

cons

umed

. Th

e cu

mul

ativ

e ef

fect

s of

thes

e el

emen

ts is

that

in

a

netw

ork

built

fo

r el

ectri

city

tra

nspo

rt,

the

optim

al

allo

catio

n of

qu

antit

ies

to g

ener

ate

and

to w

ithdr

aw a

t ea

ch n

ode

is s

uch

that

mar

gina

l va

luat

ions

will

be

diff

eren

t fro

m o

ne n

ode

to o

ther

s. T

he n

odal

val

uatio

n of

en

ergy

is a

nat

ural

by-

prod

uct o

f the

opt

imis

atio

n al

gorit

hms

used

by

syst

em

oper

ator

s. W

hen

an I

ndep

ende

nt S

yste

m O

pera

tor

com

pute

s th

e fe

asib

ility

of

a g

iven

dis

patc

h on

the

grid

he

cont

rols

, the

val

ue o

f ene

rgy

at e

ach

node

ca

n be

pub

lishe

d in

stan

tane

ousl

y. T

he d

iffer

ence

bet

wee

n no

dal v

alua

tions

th

at i

nclu

des

a re

al c

ost

(the

valu

e of

los

t en

ergy

) an

d a

shad

ow c

ost

(the

valu

e of

lost

eff

icie

ncy)

, is

to b

e vi

ewed

as

the

shor

t-run

mar

gina

l cos

t of

trans

port.

Y

et,

note

tha

t no

ne o

f th

e tw

o co

mpo

nent

s of

the

sho

rt-ru

n m

argi

nal

cost

ca

n be

di

rect

ly

rela

ted

to

an

econ

omic

or

ac

coun

ting

expe

nditu

re in

curr

ed b

y th

e op

erat

or o

f the

tran

spor

t inf

rast

ruct

ure.

1.5

Tim

e va

riat

ion

The

need

s fo

r el

ectri

city

are

stro

ngly

var

iabl

e in

tim

e.

They

are

bot

h cy

clic

al (

acco

rdin

g to

wel

l kno

wn

daily

, wee

kly

and

year

ly v

aria

tions

) an

d ra

ndom

(for

exa

mpl

e be

caus

e of

cha

nges

in te

mpe

ratu

re).

The

re o

ccur

oth

er

type

s of

tim

e va

riabi

lity

on th

e ge

nera

tion

side

, due

to th

e sc

arci

ty o

f hyd

ro

reso

urce

s, th

e flu

ctua

tions

of

fuel

pric

es a

nd t

he a

vaila

bilit

y of

pla

nts

(mai

nten

ance

and

rep

airin

g).

In

cont

rast

, th

e tra

nspo

rt in

fras

truct

ure

is

alm

ost

fixed

for

the

med

ium

run

. Th

e op

timis

atio

n of

a s

trong

ly v

aria

ble

wel

fare

func

tion

unde

r inv

aria

ble

trans

port

cons

train

ts o

bvio

usly

resu

lts in

a

cont

inuo

usly

var

ying

opt

imal

allo

catio

n an

d, c

onse

quen

tly, a

con

tinuo

usly

va

ryin

g m

argi

nal v

alue

of e

nerg

y at

eac

h no

de.

Dur

ing

low

act

ivity

per

iods

, th

e ca

paci

ty o

f th

e lin

es a

nd t

rans

form

ers

is n

ot b

indi

ng.

The

nod

al

valu

atio

ns d

iffer

onl

y by

the

mar

gina

l val

ue o

f lo

sses

, whi

ch a

re r

athe

r lo

w

sinc

e th

e le

vel o

f con

sum

ptio

n is

low

. In

con

trast

, dur

ing

peak

per

iods

, the

di

ffer

ence

bet

wee

n no

dal v

alua

tions

is v

ery

high

. N

ote

that

the

last

ass

ertio

n is

not

alw

ays

true.

In

som

e ci

rcum

stan

ces,

the

diff

eren

ce b

etw

een

peak

load

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

11

5

and

off-

peak

loa

d ca

n be

larg

er a

t an

exp

ortin

g no

de t

han

at a

n im

porti

ng

node

. In

that

cas

e th

e el

ectri

city

flow

ing

on th

e lin

e at

pea

k pe

riods

can

be

smal

ler

than

at

off-

peak

per

iods

and

the

nod

al d

iffer

ence

in

elec

trici

ty

valu

atio

n ca

n be

hig

her a

t off

-pea

k pe

riods

.

2.

NO

DA

L PR

ICE

S

2.1

Ene

rgy

pric

es

The

first

-bes

t allo

catio

n ca

n be

dec

entra

lised

by

mea

ns o

f pr

ices

whi

ch

refle

ct t

he m

argi

nal

valu

e of

ele

ctric

ity.

It

mea

ns t

hat

the

first

-bes

t ge

nera

tion

leve

ls a

nd c

onsu

mpt

ion

leve

ls w

ould

be

free

ly c

hose

n by

in

divi

dual

gen

erat

ors

and

indi

vidu

al c

onsu

mer

s if

they

wer

e fa

cing

pric

es

equa

l to

the

mar

gina

l va

lue

of e

lect

ricity

in

the

optim

al a

lloca

tion.

A

nd

sinc

e, a

s sh

own

form

erly

, mar

gina

l val

uatio

ns c

hang

e fr

om o

ne n

ode

to th

e ot

her

(and

fro

m ti

me

to ti

me)

, the

dec

entra

lisat

ion

of f

irst-b

est n

eces

sita

tes

noda

l pr

ices

. I

f pe

rfec

t co

mpe

titio

n m

echa

nism

s pr

evai

l at

eac

h no

de

(rou

ghly

sai

d, if

ther

e ex

ists

a la

rge

num

ber o

f sm

all b

uyer

s an

d su

pplie

rs o

f el

ectri

city

at

each

nod

e w

ho b

ehav

e as

pric

e-ta

kers

), th

e eq

uilib

rium

will

na

tura

lly d

eter

min

e en

ergy

pric

es e

qual

to

the

mar

gina

l va

lues

obt

aine

d fo

rmer

ly.

Con

sequ

ently

, or

gani

zing

com

petit

ion

is a

goo

d w

ay t

o re

ach

effic

ienc

y.

How

ever

, eve

n w

hen

the

num

ber

of g

ener

ator

s an

d th

e nu

mbe

r co

nsum

ers

are

reas

onab

ly l

arge

, th

e de

cent

ralis

atio

n of

dec

isio

ns r

equi

res

som

e pu

blic

inte

rven

tion,

for

exa

mpl

e to

org

aniz

e th

e m

atch

ing

of d

eman

d an

d su

pply

in w

hole

sale

mar

kets

. In

con

trast

, if

ther

e is

onl

y a

smal

l nu

mbe

r of

lar

ge s

uppl

iers

and

/or

buye

rs,

the

equi

libriu

m p

rice

wou

ld r

efle

ct t

he m

arke

t po

wer

of

thes

e ag

ents

.7 To

impl

emen

t the

firs

t-bes

t, no

dal p

rices

are

to b

e re

gula

ted

by th

e go

vern

men

t or

, m

ore

prec

isel

y, b

y a

regu

latio

n en

tity

or a

n an

titru

st

auth

ority

.

In a

ny c

ase,

whe

n co

nsum

ers

at n

ode

i can

buy

ele

ctric

ity a

nyw

here

and

pa

y el

ectri

city

com

ing

from

any

nod

e j a

t a p

rice

ip e

qual

to

the

optim

al

mar

gina

l val

uatio

n of

nod

e i,

they

con

sum

e th

e op

timal

qua

ntity

. A

nd w

hen

gene

rato

rs a

t nod

e i a

re a

utho

rised

to s

ell e

lect

ricity

any

whe

re a

nd re

ceiv

e p i

fo

r any

kW

h so

ld to

any

nod

e j,

they

pro

duce

the

optim

al q

uant

ity.8

2.2

Tra

nspo

rt p

rice

s

For

a gi

ven

trans

actio

n, w

hen

the

buye

r an

d th

e se

ller

are

loca

ted

at th

e sa

me

node

i, th

ey tr

ansa

ct a

t the

sam

e pr

ice

p i th

at c

over

s on

ly g

ener

atio

n

116

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

cost

s. If

the

selle

r is

at n

ode

i and

the

buye

r at n

ode

j, th

e fo

rmer

rece

ives

pi

and

the

latte

r pa

ys p

j. T

he p

robl

em i

s to

kno

w w

hat

to d

o w

ith t

he

diff

eren

ce.

To g

ive

an a

nsw

er, n

ote

that

ano

ther

way

to d

ecen

tralis

e th

e fir

st-b

est i

s to

dis

tingu

ish

the

pric

e of

ene

rgy

and

the

pric

e of

tran

spor

t. W

hen

ther

e ar

e tw

o se

para

te b

ills,

the

pric

e fo

r tra

nspo

rting

1 M

Wh

from

nod

e i t

o no

de j

is

to b

e t ij=

pj -

pi.

As

a m

atte

r of

fac

t, th

e co

nsum

er a

t no

de j

mus

t be

in

diff

eren

t bet

wee

n bu

ying

its

ener

gy a

t nod

e j a

t pric

e p j

on

the

one

hand

an

d, o

n th

e ot

her h

and,

buy

ing

it at

nod

e i a

t pric

e p i

and

then

pay

ing

t ij fo

r its

tra

nspo

rt to

nod

e j.

Sim

ilarly

, the

gen

erat

or a

t no

de i

mus

t be

ind

iffer

ent

betw

een

selli

ng it

s en

ergy

at n

ode

i at p

rice

p i o

n on

e ha

nd a

nd, o

n th

e ot

her

hand

, sel

ling

it at

nod

e j a

t pric

e p j

whi

le p

ayin

g t ij

for i

ts tr

ansp

ort t

o no

de j.

C

onse

quen

tly, w

e ca

n co

nclu

de th

at, f

rom

the

poin

t of

view

of

cons

umer

s an

d pr

oduc

ers,

the

diff

eren

ce t i

j= p

j - p

i re

ally

app

ears

as

a tra

nspo

rt fe

e. F

or

this

reas

on, i

t is n

atur

al to

pay

it to

the

oper

ator

of t

he tr

ansp

ort i

nfra

stru

ctur

e ev

en if

the

cost

s cov

ered

are

on

the

user

s' si

de.

N

ote

that

if th

e ne

t flo

w o

f ene

rgy

is fr

om i

(the

expo

rting

nod

e) to

j (th

e im

porti

ng n

ode)

, any

indi

vidu

al tr

ansa

ctio

n fr

om i

to j

incr

ease

s co

nges

tion

and

mus

t be

char

ged

t ij >

0. I

n co

ntra

st, a

ssum

e p j

< p

i so

that

nod

e j i

s a

net

expo

rter

to n

ode

i an

d th

ere

occu

rs a

n in

divi

dual

tra

nsac

tion

betw

een

a ge

nera

tor

loca

ted

at i

and

a co

nsum

er lo

cate

d at

j.

How

can

it b

e po

ssib

le

sinc

e th

e ge

nera

tor

rece

ives

mor

e th

an w

hat

is p

aid

by t

he c

onsu

mer

? B

ecau

se t

he i

ndiv

idua

l tra

nsac

tion

crea

tes

a co

unte

r-flo

w,

it al

levi

ates

the

co

nges

tion

on t

rans

port

lines

. C

onse

quen

tly,

the

trans

port

pric

ing

syst

em

shou

ld p

rom

ote

this

type

of

trans

actio

n by

rew

ardi

ng th

e pa

rties

inst

ead

of

char

ging

them

for t

rans

port.

And

this

act

ually

occ

urs w

ith n

odal

pric

es si

nce

the

trans

port

of 1

MW

h fr

om i

to j

wou

ld th

en b

e ch

arge

d t ij=

pj -

pi <

0. I

n ot

her w

ords

, the

cou

nter

-flo

w tr

ansa

ctio

ns w

ould

be

enco

urag

ed.

The

tota

l val

ue o

f th

e flo

ws

of e

nerg

y us

ing

the

trans

port

pric

es d

eriv

ed

from

nod

al p

rices

is th

e “m

erch

andi

zing

sur

plus

”. E

ven

if co

unte

r-flo

ws

are

to b

e re

war

ded,

the

mer

chan

dizi

ng s

urpl

us i

s ob

viou

sly

posi

tive9 f

or t

he

follo

win

g re

ason

. R

ecal

l th

at n

odal

pric

es r

efle

ct o

ptim

al v

alua

tions

of

ener

gy.

Con

sequ

ently

, the

mer

chan

dizi

ng s

urpl

us is

mad

e of

two

elem

ents

. Th

e fir

st p

iece

is

a ne

t su

rplu

s du

e to

the

spe

cific

fun

ctio

nal

form

of

the

loss

es o

f ene

rgy

and

thei

r cov

erag

e by

a m

argi

nal p

ricin

g ru

le.

Act

ually

, the

ge

nera

tor

mus

t be

paid

for

the

elec

trici

ty h

e pr

oduc

es, e

ven

if it

cann

ot b

e co

nsum

ed.

But

bec

ause

los

ses

incr

ease

with

the

squ

are

of t

he l

oad,

the

ir m

argi

nal

valu

e is

tw

ice

thei

r av

erag

e va

lue.

Con

sequ

ently

, af

ter

com

pens

atin

g th

e ge

nera

tor f

or it

s los

ses,

it re

mai

ns a

n eq

ual s

um th

at c

an b

e us

ed to

pay

for t

rans

port.

The

sec

ond

part

is th

e co

st o

f con

gest

ion,

and

its

over

all v

alue

can

not b

e ne

gativ

e. E

ither

som

e lin

es o

r no

des

are

cong

este

d an

d th

en t

he s

urpl

us i

s po

sitiv

e, o

r th

ere

is n

o co

nges

tion

and

then

the

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

11

7

surp

lus

is z

ero.

B

y its

ver

y de

finiti

on, t

he m

erch

andi

sing

sur

plus

doe

s no

t co

rres

pond

to th

e pa

ymen

t of c

osts

incu

rred

by

the

oper

ator

. Th

e tra

nspo

rt pr

ices

cal

cula

ted

usin

g no

dal p

rices

var

y w

ith th

e da

te, t

he

initi

al n

ode

and

the

term

inal

nod

e of

the

tra

nsac

tion.

A

ll th

e us

ers

who

tra

nsac

t at t

he s

ame

date

, the

sam

e in

itial

nod

e an

d th

e sa

me

term

inal

nod

e sh

ould

pay

(or

sho

uld

be p

aid

for

coun

ter-

flow

s) t

he s

ame

unit

pric

e.

Ther

efor

e, w

e ca

n as

sert

that

the

nod

al p

rice

syst

em i

s ob

ject

ivel

y no

n-di

scrim

inat

ory

(see

Cha

pter

1).

3.

CO

NST

RA

INE

D A

ND

UN

CO

NST

RA

INE

D

PRIC

ING

3.1

Eff

icie

ncy

conc

ern

vs.

fund

-rai

sing

con

cern

Firs

t-bes

t pric

ing

allo

ws

payi

ng fo

r all

the

cost

s of

an

indu

stry

whe

n th

e eq

uipm

ent i

s op

timal

ly d

esig

ned

and

ther

e ar

e no

incr

easi

ng re

turn

s to

sca

le

in th

e lo

ng ru

n. I

n th

is h

ypot

hetic

al s

ituat

ion,

on

the

one

hand

the

shor

t-run

m

argi

nal

cost

and

the

lon

g-ru

n m

argi

nal

cost

are

equ

al a

nd,

on t

he o

ther

ha

nd,

the

long

-run

mar

gina

l co

st i

s at

lea

st e

qual

to

the

long

-run

ave

rage

co

st.

Con

sequ

ently

, a p

rice

equa

l to

mar

gina

l cos

t can

not b

e be

low

the

long

-ru

n av

erag

e co

st.

B

ut th

ese

optim

al c

ondi

tions

are

pra

ctic

ally

impo

ssib

le to

mee

t in

actu

al

netw

orks

, bec

ause

of t

he fo

llow

ing

reas

ons:10

(i)

dis

crep

ancy

bet

wee

n lo

ng-r

un a

nd sh

ort-r

un n

eeds

Th

e op

timal

dyn

amic

exp

ansi

on o

f th

e tra

nspo

rt in

fras

truct

ure

does

not

am

ount

to

the

mer

e co

nnec

tion

of m

any

stat

ic p

lans

. M

ost

netw

ork

faci

litie

s ar

e bu

ilt fo

r 20

or 3

0 ye

ars

and

it is

unl

ikel

y fo

r any

one

of t

he

faci

litie

s to

hav

e ex

actly

the

opt

imal

sta

tic c

apac

ity f

or a

giv

en y

ear.

A

dditi

onal

ly, d

evia

tions

fro

m t

he o

ptim

al p

lan

are

due

to e

rror

s in

the

fo

reca

st o

f dem

and

and

gene

ratio

n co

sts.

(ii) t

echn

ical

non

con

vexi

ties

For

trans

port

faci

litie

s, de

cisi

ons

are

disc

rete

op

tions

ra

ther

th

an

cont

inuo

us v

aria

bles

. Fo

r a g

iven

rein

forc

emen

t, th

e fe

asib

le s

et is

ver

y sm

all,

e.g.

, lin

es o

f 220

kV

or 4

00 k

V.

Con

sequ

ently

, as

com

pare

d w

ith

the

“mar

gina

l opt

imum

”, th

e re

sult

of p

rogr

amm

ing

with

inte

ger n

umbe

r w

ill b

e an

app

aren

tly e

ither

ove

rsiz

ed o

r un

ders

ized

net

wor

k, w

ith a

na

tura

l te

nden

cy

tow

ards

ov

ersi

zing

w

hen

dem

and

is

expe

cted

to

in

crea

se.

118

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

The

tend

ency

tow

ards

ove

r in

vest

men

t is

int

ensi

fied

beca

use

of s

cale

ec

onom

ies:

the

lar

ger

the

capa

city

of

the

inve

stm

ent

the

smal

ler

the

capi

tal c

ost p

er u

nit o

f cap

acity

. (ii

i) ad

ditio

nal c

onst

rain

ts

Net

wor

k ex

pans

ion

plan

ning

is

subj

ect

to r

elia

bilit

y co

nstra

ints

whi

ch

crea

te th

e ne

ed f

or e

xtra

cap

acity

with

res

pect

to th

e op

timal

pla

n un

der

stric

t ec

onom

ic t

erm

s. F

inan

cial

, en

viro

nmen

tal,

tech

nica

l or

eve

n po

litic

al re

stric

tions

are

als

o im

pose

d on

the

expa

nsio

n of

the

netw

ork

in

gene

ral o

r of a

giv

en c

orrid

or.

W

e co

nclu

de t

hat,

beca

use

the

infr

astru

ctur

e is

ove

rsiz

ed a

s co

mpa

red

with

sho

rt-ru

n ne

eds

and

beca

use

ther

e ex

ist

long

-run

eco

nom

ies

of s

cale

, co

nges

tion

rent

s ca

lcul

ated

on

the

basi

s of

sho

rt-ru

n m

argi

nal c

osts

will

be

rath

er lo

w, a

nd th

e re

nts

from

loss

es w

ill n

ot b

e hi

gh e

noug

h to

cov

er a

ll th

e fix

ed c

osts

incu

rred

by

the

grid

ope

rato

r.

3.2

Bud

get c

onst

rain

t

Seve

ral s

olut

ions

are

ava

ilabl

e to

bal

ance

the

budg

et o

f the

tran

spor

t firm

. If

pub

lic s

ubsi

dies

are

allo

wed

, th

ey c

an b

e us

ed t

o pa

y th

e di

ffer

ence

be

twee

n th

e m

erch

andi

sing

sur

plus

and

the

fixed

cos

ts o

f the

infr

astru

ctur

e.

But

the

taxe

s lev

ied

to fu

nd th

e su

bsid

ies c

reat

e ec

onom

ic d

isto

rtion

s and

the

resu

lting

allo

catio

n of

con

sum

ptio

n an

d pr

oduc

tion

cann

ot b

e th

e fir

st-b

est.

B

ecau

se o

f th

e co

st o

f pu

blic

fun

ds,

we

can

only

rea

ch a

sec

ond

best

. A

dditi

onal

ly,

with

in t

he E

urop

ean

liber

alis

ed f

ram

ewor

k, t

he S

tate

-aid

so

lutio

n is

not

aut

horis

ed.

Ther

efor

e, p

rices

are

to b

e ad

just

ed to

cov

er a

ll th

e co

sts.

Whe

n co

nstra

ined

to

bala

nce

the

budg

et o

f th

e tra

nspo

rt op

erat

or,

the

optim

al ta

riffs

will

dep

art f

rom

firs

t-bes

t if s

peci

fic re

stric

tions

are

impo

sed

in th

eir c

ompu

tatio

n. W

hen

any

func

tiona

l for

m c

an b

e im

plem

ente

d, th

at is

w

hen

the

bill

is n

ot n

eces

saril

y pr

opor

tiona

l to

the

quan

tity

of e

nerg

y th

at is

tra

nspo

rted

(non

lin

ear

pric

es),

the

first

-bes

t al

loca

tion

rem

ains

fea

sibl

e.11

A

mon

g no

n-lin

ear

tarif

fs w

e w

ill o

nly

disc

uss

two-

part

pric

es.

On

the

cont

rary

, if p

rices

are

rest

ricte

d to

be

linea

r, th

e be

st o

nes a

re R

amse

y pr

ices

, an

d th

e re

sulti

ng a

lloca

tion

of g

ener

atio

n an

d co

nsum

ptio

n w

ill o

nly

be a

se

cond

bes

t. W

e fir

st c

onsi

der t

he c

ase

whe

re o

nly

linea

r pric

es a

re fe

asib

le.

3.3

Seco

nd-b

est l

inea

r pr

ices

Ram

sey

pric

es a

re th

e be

st li

near

pric

es w

hen

the

bala

ncin

g of

bud

get i

s m

anda

tory

. Th

ey c

over

mar

gina

l cos

t (co

nges

tion

and

loss

es) p

lus

a m

argi

n co

mpu

ted

to p

ay f

or t

he f

ixed

cos

ts.

In

met

hods

for

pric

ing

appl

ied

by

prac

titio

ners

, fix

ed c

osts

are

allo

cate

d ac

cord

ing

to so

me

prop

ortio

nalit

y ru

le

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

11

9

(for

exa

mpl

e th

e co

st s

hare

pai

d by

age

nt i

whe

n co

nsum

ing

the

quan

tity

iq

is:

/i

jj

qq

, or

()/

()

ii

jj

jC

qC

q,

whe

re

()

ii

Cq

is th

e di

rect

cos

t to

prod

uce

iq, o

r an

y ot

her

ratio

12).

In

Ram

sey

pric

es, o

ne ta

kes i

nto

acco

unt t

he re

actio

n of

the

infr

astru

ctur

e us

ers

whe

n th

ey a

re b

illed

or

paid

. P

ricin

g ab

ove

mar

gina

l co

st i

s in

effic

ient

be

caus

e it

prov

okes

a d

ecre

ase

in c

onsu

mpt

ion.

Sim

ilarly

, whe

n a

prod

ucer

is

pai

d le

ss th

an m

argi

nal u

tility

, he

decr

ease

s his

pro

duct

ion.

Con

sequ

ently

, th

e ai

m o

f sec

ond-

best

pric

ing

is to

lim

it th

is b

ias

in q

uant

ities

pro

duce

d an

d co

nsum

ed.

It is

eas

y to

und

erst

and

that

, if

som

e co

nsum

ers

reac

t to

pric

e in

crea

ses

less

than

oth

ers,

it is

opt

imal

to m

ake

them

pay

mor

e th

an m

ore

reac

tive

cons

umer

s. A

nd s

ymm

etric

ally

, if

som

e ge

nera

tors

dec

reas

e th

eir

outp

ut m

ore

than

oth

er p

rodu

cers

whe

n th

e se

lling

pric

e is

dec

reas

ed, i

t is

optim

al to

mod

ify th

eir s

ellin

g pr

ice

less

. Th

is e

xpla

ins

that

Ram

sey

pric

es

are

inve

rsel

y re

late

d to

the

ela

stic

ity o

f de

man

d an

d to

the

ela

stic

ity o

f su

pply

. A

s a

cons

eque

nce,

the

y ar

e di

scrim

inat

ory:

eac

h se

gmen

t of

use

rs t

hat

can

be is

olat

ed f

rom

the

othe

rs w

ill p

ay o

r w

ill b

e pa

id a

diff

eren

t Ram

sey

noda

l pric

e. I

n th

e si

mpl

e ca

se w

here

, at e

ach

node

, one

can

not d

istin

guis

h be

twee

n di

ffer

ent

type

s of

con

sum

ers

and

betw

een

diff

eren

t ty

pes

of

prod

ucer

s, it

rem

ains

true

that

one

can

dis

tingu

ish

a gr

oup

of c

onsu

mer

s on

on

e si

de a

nd a

gro

up o

f pr

oduc

ers

one

the

othe

r si

de.

Con

sequ

ently

the

R

amse

y de

man

d pr

ice

w ip w

ill b

e di

ffer

ent

from

the

Ram

sey

supp

ly p

rice

g ip:

beca

use

of t

he n

eed

to l

evy

fund

s to

cov

er f

ixed

cos

ts,

we

lose

the

pr

oper

ty o

f pric

e un

ique

ness

at o

ne n

ode.

W

hen

ener

gy a

nd tr

ansp

ort o

f ene

rgy

from

i to

j ar

e bi

lled

sepa

rate

ly, t

he

equi

libriu

m c

ondi

tion

is t

hat

payi

ng

w jp t

o co

nsum

e at

nod

e j

is t

o be

eq

uiva

lent

to b

uyin

g at

pric

e g ip a

t nod

e i a

nd tr

ansp

ortin

g to

war

ds j,

that

is

gw j

iij

pp

t.

It re

sults

that

the

Ram

sey

pric

e fo

r tra

nspo

rt g

wij

ji

tp

p is

th

e w

eigh

ted

sum

of t

wo

elem

ents

: (i)

the

cost

in te

rms

of e

ffic

ienc

y du

e to

en

ergy

loss

es a

nd c

onge

stio

n w

e al

read

y ha

d in

Sec

tion

1; a

nd (i

i) th

e co

st in

te

rms

of e

ffic

ienc

y du

e to

the

bud

get

cons

train

t. T

he f

irst

part

can

be

posi

tive

or n

egat

ive

depe

ndin

g on

the

dire

ctio

n of

indi

vidu

al o

pera

tions

as

com

pare

d w

ith th

e ne

t flo

w b

etw

een

i and

j. T

he s

econ

d pa

rt is

nec

essa

rily

posi

tive:

it

depe

nds

on t

he e

last

icity

of

the

ener

gy s

uppl

y fu

nctio

n at

the

in

ject

ion

node

and

on

the

elas

ticity

of

the

ener

gy d

eman

d fu

nctio

n at

the

w

ithdr

awal

nod

e. T

he s

mal

ler t

hese

ela

stic

ities

, the

hig

her t

he R

amse

y pr

ice

for

trans

port

betw

een

i an

d j,

wha

teve

r th

e co

sts

of o

hmic

los

ses

and

cong

estio

n.

120

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

Not

e th

at R

amse

y pr

icin

g co

mm

ands

a g

loba

l al

loca

tion

of f

ixed

cos

ts

base

d on

dem

and

elas

ticity

, but

tran

spar

ency

and

pol

itica

l arg

umen

ts im

pose

so

me

frag

men

tatio

n of

fix

ed c

osts

. A

ctua

lly, t

he o

blig

atio

n to

bal

ance

the

budg

et c

an b

e so

lved

in m

any

diff

eren

t way

s. O

ne p

ossi

bilit

y is

to im

pose

a

glob

al b

udge

t co

nstra

int

to t

he t

rans

port

oper

ator

. I

n th

is c

ase,

Ram

sey

pric

es a

lloca

te a

ll th

e fix

ed c

osts

of

infr

astru

ctur

e to

all

user

s. L

ines

and

tra

nsfo

rmer

s in

low

vol

tage

are

pai

d by

all

user

s, in

clud

ing

larg

e co

nsum

ers

and

gene

rato

rs w

ho u

se o

nly

high

or

med

ium

vol

tage

equ

ipm

ent.

Ano

ther

so

lutio

n is

to e

xem

pt la

rge

user

s fr

om p

ayin

g fo

r th

e fix

ed c

ost o

f th

e lo

w

volta

ge s

yste

m.

In

this

cas

e, t

he o

ptim

al a

lloca

tion

of c

onsu

mpt

ion

and

gene

ratio

n am

ong

node

s an

d th

e re

sulti

ng f

low

s on

line

s is

to b

e ca

lcul

ated

su

bjec

t to

seve

ral b

udge

t con

stra

ints

. A

s exp

lain

ed in

Box

4-1

, the

larg

er th

e nu

mbe

r of

con

stra

ints

, the

hig

her

the

effic

ienc

y lo

ss.

It m

eans

tha

t, w

hen

pric

e di

scrim

inat

ion

is a

llow

ed, d

isco

mpo

sing

the

cos

t re

cove

ry c

onst

rain

t in

to

seve

ral

user

-targ

eted

co

nstra

ints

ca

nnot

be

ju

stifi

ed

in

term

s of

ef

ficie

ncy.

3.4

Tw

o-pa

rt ta

riff

s

The

draw

back

s of

Ram

sey

pric

es a

re o

bvio

us:

(i) a

lar

ge q

uant

ity o

f in

form

atio

n is

nec

essa

ry t

o co

mpu

te t

he e

last

iciti

es;

(ii) d

iscr

imin

atio

n is

fo

rbid

den

by l

aw, (

iii) t

he r

esul

ting

quan

titie

s de

viat

e fr

om f

irst

best

. Fo

r th

ese

reas

ons,

mul

ti-pa

rt pr

ices

can

be

pref

erre

d.

In th

e si

mpl

e ca

se o

f tw

o-pa

rt pr

ices

, the

con

sum

er p

ays

a fix

ed a

mou

nt

of m

oney

inde

pend

ent o

f the

qua

ntity

of t

rans

port

he w

ill re

quire

and

, the

n,

he p

ays

a “m

argi

nal

pric

e” f

or e

ach

unit

he w

ants

to

trans

port.

Si

nce

the

mar

gina

l pric

e ca

n be

set e

qual

to th

e m

argi

nal c

ost o

f con

gest

ion

and

loss

es,

this

tar

iff a

llow

s im

plem

entin

g th

e fir

st-b

est

allo

catio

n, p

rovi

ded

that

the

fix

ed p

art o

f the

tarif

f doe

s no

t exc

lude

any

use

r with

a m

argi

nal w

illin

gnes

s to

pay

hig

her t

han

the

mar

gina

l cos

t. In

eff

ect,

the

risk

with

one

uni

que

two-

part

pric

e is

tha

t th

e fix

ed f

ee m

ust

be h

igh

enou

gh t

o co

ver

all

the

fixed

co

sts,

so th

at u

sers

with

low

inco

me

will

not

be

able

to p

ay f

or it

. If

thes

e lo

w-in

com

e us

ers

can

be e

asily

ide

ntifi

ed, a

sol

utio

n is

to

prop

ose

them

a

spec

ific

two-

part

pric

e, fo

r ins

tanc

e w

ith a

zer

o fix

ed p

art.

The

flaw

is th

at

we

are

back

to d

iscr

imin

atio

n. E

ven

a si

ngle

two-

part

pric

e is

dis

crim

inat

ory

sinc

e th

e un

it pr

ice

paid

is d

ecre

asin

g w

ith th

e qu

antit

y co

nsum

ed.

Inso

far

as tw

o-pa

rt pr

ices

are

acc

epta

ble

on le

gal g

roun

ds, i

t is

effic

ient

to p

ropo

se

to u

sers

not

one

but

a w

hole

set

of t

wo-

part

pric

es, l

ettin

g ea

ch u

ser c

hoos

e w

ithin

the

men

u th

e ta

riff

he p

refe

rs.

It is

a v

ery

effic

ient

way

to

colle

ct

fund

s fo

r fix

ed c

osts

cov

erin

g.

It is

als

o a

good

way

to o

rgan

ize

“sec

ond

degr

ee p

rice

disc

rimin

atio

n” w

hen

the

pric

e m

aker

lack

s in

form

atio

n ab

out

the

will

ingn

ess t

o pa

y of

use

rs.13

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

12

1

App

lyin

g th

ese

prin

cipl

es to

the

trans

port

of e

nerg

y, th

e ta

riff t

o tra

nspo

rt a

give

n qu

antit

y fo

rm n

ode

i to

node

j sh

ould

hav

e a

first

par

t pro

porti

onal

to

the

quan

tity

(whe

re t

he p

ropo

rtion

ality

coe

ffic

ient

is

the

mar

gina

l co

st o

f co

nges

tion

and

loss

es)

and

a se

cond

par

t, fix

ed,

com

pute

d af

ter

the

fixed

pa

rts o

f th

e en

ergy

tarif

fs f

or c

onsu

mer

s at

nod

e j a

nd g

ener

ator

s at

nod

e i.

Th

e fix

ed p

art o

f the

tarif

fs fo

r ene

rgy

mus

t be

adju

sted

not

onl

y to

pay

for

the

fixed

cos

ts o

f ge

nera

tors

but

als

o to

pay

for

the

fixed

cos

ts o

f th

e gr

id

oper

ator

. B

y de

finiti

on, t

he fi

xed

part

of tw

o-pa

rt ta

riffs

doe

s not

dis

tort

effic

ienc

y.

Ther

efor

e, th

e ta

riff

mak

er h

as s

ome

degr

ees

of f

reed

om to

cal

cula

te th

em.

He

mai

nly

has

to a

void

the

exc

lusi

on o

f so

me

agen

ts,

indi

vidu

ally

or

colle

ctiv

ely.

In

elec

trici

ty

trans

port,

th

e m

ain

conc

ern

is

that

la

rge

cons

umer

s ha

ve a

ltern

ativ

e op

portu

nitie

s to

the

use

of th

e gr

id, f

or e

xam

ple

by i

nsta

lling

gen

erat

ion

plan

ts a

t th

eir

loca

tion.

To

pre

vent

thi

s by

-pas

s, se

vera

l tw

o-pa

rt ta

riffs

mus

t be

prop

osed

. Ea

ch it

em in

the

men

u is

tailo

red

so th

at n

o on

e is

exc

lude

d (p

artic

ipat

ion

cons

train

t) an

d ea

ch a

gent

cho

oses

th

e ta

riff

calc

ulat

ed f

or h

im (

self-

sele

ctio

n co

nstra

int).

W

hen

also

tak

ing

into

acc

ount

the

poss

ibili

ty o

f co

aliti

on b

etw

een

seve

ral p

rodu

cers

or

larg

e co

nsum

ers,

or b

etw

een

a pr

oduc

er a

nd o

ne o

f its

clie

nts

in o

rder

to b

ypas

s th

e tra

nspo

rt in

fras

truct

ure,

it is

nec

essa

ry to

hav

e re

cour

se to

coo

pera

tive-

gam

es th

eory

to o

ptim

ally

des

ign

the

fixed

par

t of t

he ta

riff.14

Fi

nally

, no

te t

hat

devi

ces

able

to

cont

inuo

usly

met

er t

he f

low

of

elec

trici

ty o

n a

line

are

very

exp

ensi

ve a

nd,

in m

any

coun

tries

, th

ey a

re

inst

alle

d on

ly o

n th

e hi

gh v

olta

ge g

rid.

Add

ition

ally

, w

hen

avai

labl

e, i

t w

ould

be

very

cos

tly b

oth

at t

he o

pera

tor

leve

l an

d at

the

use

r le

vel

to

proc

ess

all

the

info

rmat

ion

they

col

lect

. A

s a

resu

lt, i

nste

ad o

f se

ndin

g in

voic

es b

ased

on

the

time

prof

ile o

f th

e de

man

d fo

r tra

nspo

rt, i

n m

ost

coun

tries

one

use

s to

cal

cula

te t

he a

ggre

gate

qua

ntity

tra

nspo

rted

durin

g a

give

n pe

riod

(for

exa

mpl

e, o

ne y

ear)

and

to c

harg

e a

unifo

rm m

argi

nal p

rice

of tr

ansp

ort a

ll th

e ye

ar lo

ng.

The

draw

back

is th

at th

e sa

me

tota

l qua

ntity

of

ener

gy c

an b

e tra

nsfe

rred

with

stro

ng t

ime

regu

larit

y or

with

a h

igh

irreg

ular

ity.

And

the

irreg

ular

load

pro

file

is m

uch

mor

e de

man

ding

in te

rms

of tr

ansp

ort c

apac

ity th

an th

e re

gula

r one

. O

ne s

olut

ion

is to

dis

tingu

ish

an

ener

gy c

ompo

nent

and

a c

apac

ity c

ompo

nent

in

the

dem

and

for

trans

port,

ea

ch w

ith a

spe

cific

con

stan

t mar

gina

l pric

e.

But

it r

emai

ns tr

ue th

at th

ese

two

elem

ents

are

to b

e de

sign

ed to

sen

d ac

cura

te s

igna

ls o

f sca

rcity

to u

sers

. A

fixe

d pa

rt re

mai

ns n

eces

sary

to c

over

the

fixed

cos

ts o

f the

infr

astru

ctur

e w

ithou

t dis

torti

ng th

e de

cisi

on o

f the

use

rs.

122

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

4.

CO

NC

LU

DIN

G C

OM

ME

NT

S

To c

alcu

late

the

tar

iffs

to t

rans

port

elec

trici

ty,

the

trade

-off

bet

wee

n ef

ficie

ncy,

bud

get r

equi

rem

ents

, leg

al c

onst

rain

ts a

nd p

ract

icab

ility

, res

ults

in

a n

on li

near

tarif

f ba

sed

on th

e no

dal p

rices

of

ener

gy a

nd o

n th

e fix

ed

cost

s of t

he in

fras

truct

ure.

The

sim

ples

t is t

wo-

part.

The

tota

l bill

to b

e pa

id

to th

e tra

nspo

rt fir

m is

mad

e of

an

“eff

icie

ncy-

orie

nted

” pa

rt, v

aria

ble

with

th

e qu

antit

y tra

nspo

rted,

and

a “

cost

-rec

over

y” p

art,

inde

pend

ent

of t

he

quan

tity

trans

porte

d.

The

first

par

t is

aim

ed a

t si

gnal

ling

the

cost

of

phys

ical

los

ses

and

the

cost

of

cong

estio

n.

It sh

ould

var

y w

ith t

ime

and

loca

tion

and

shou

ld b

e in

crea

sing

with

the

quan

tity

of e

nerg

y tra

nspo

rted.

15 P

ract

ical

ly, i

t sho

uld

be

a fu

nctio

n of

the

inje

ctio

n an

d w

ithdr

awal

nod

es (n

ot o

n th

e ph

ysic

al p

ath

of

ener

gy s

ince

it

actu

ally

can

not

be c

ontro

lled)

and

on

the

dire

ctio

n of

the

flo

w.

For

prac

tical

rea

sons

, thi

s fir

st p

art o

f th

e ta

riff

can

be d

isco

mpo

sed

into

an

ener

gy te

rm a

nd a

cap

acity

term

, bot

h lin

ear f

unct

ions

, pro

vide

d th

at

the

scar

city

sig

nals

the

y tra

nsm

itted

are

sim

ilar

to t

he o

nes

that

allo

w a

n ef

ficie

nt u

se o

f the

grid

. Th

e fix

ed p

art o

f the

tarif

f is

aim

ed a

t pay

ing

for t

he in

fras

truct

ure

cost

s.

Bec

ause

its

pur

pose

is

pure

ly b

udge

tary

, it

shou

ld n

ot i

nter

fere

with

the

sc

arci

ty s

igna

ls s

ent b

y th

e va

riabl

e pa

rt(s)

. In

par

ticul

ar, w

hen

the

trans

port

tarif

f dis

tingu

ishe

s bet

wee

n an

ene

rgy

com

pone

nt a

nd a

cap

acity

com

pone

nt,

the

latte

r sho

uld

not b

e vi

ewed

as t

he fi

xed

part

of th

e ta

riff.

In m

ost c

ount

ries,

actu

al tr

ansp

ort t

ariff

s ar

e tw

o-pa

rt bu

t the

way

they

ba

lanc

e th

e va

riabl

e pa

rt(s)

and

the

fixed

par

t is v

ery

hete

roge

neou

s.16

APP

EN

DIX

MO

DEL

SET

TIN

G

Two

node

s, n

(for

nor

th) a

nd s

(for

sout

h), a

re c

onne

cted

by

a lin

e of

cap

acity

K.

The

unit

cost

of

capa

city

is r

. Th

e qu

antit

y of

ele

ctric

ity tr

ansp

orte

d th

roug

h th

e lin

e is

mea

sure

d in

th

e sa

me

unit

as K

. W

e no

te

ii

Uq

the

utili

ty d

eriv

ed fr

om th

e co

nsum

ptio

n of

a q

uant

ity

iq o

f ele

ctric

ity a

t nod

e i a

nd

ii

Cq

the

cost

of g

ener

atin

g iq a

t nod

e i

(,

)i

ns

.

Let

,,

,,

wg

wg

wg

wg

nn

ss

nn

nn

ss

ss

Wq

qq

qK

Uq

Cq

Uq

Cq

rK s

tand

for t

he

wel

fare

func

tion

of th

is in

dust

ry, w

here

sup

ersc

ript w

sta

nds

for “

with

draw

al”

and

supe

rscr

ipt

g st

ands

for

“ge

nera

tion”

. W

e co

nsid

er o

nly

shor

t-run

dec

isio

ns, t

hat i

s, K

is n

ot a

con

trol

varia

ble.

The

opt

imal

allo

catio

n is

the

solu

tion

to:

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

12

3

,

,,

max

,,

,,

wg

wg

nn

ss

gg

ww

nn

ss

qq

qq

Wq

qq

qK

(1

)

s.t.

g

ww

gn

ns

sq

qq

q

(2)

de

f

gw

nsn

nz

qq

K

(3)

Prov

isio

nally

, we

assu

me

ther

e is

no

loss

, whi

ch is

refle

cted

by

(2).

To

sim

plify

not

atio

ns,

we

assu

me

that

pre

fere

nces

and

cos

ts a

re s

uch

that

the

north

nod

e w

ill a

lway

s ex

port

a ne

t flo

w o

f ele

ctric

ity

nszto

war

ds so

uth.

For

this

reas

on,

0nsz

.

THE

SOC

IAL

CO

ST O

F C

ON

GES

TIO

N

Let

den

ote

the

dual

var

iabl

e as

soci

ated

to c

onst

rain

t (3)

. Th

e fir

st-o

rder

con

ditio

ns th

at

char

acte

rise

the

solu

tion

(,

,,

)go

gow

ow

on

sn

sq

qq

qto

the

abov

e pr

oble

m a

re:

'w

ogo

ss

ss

Uq

Cq

(4

) '

wo

gon

nn

nU

qC

q

(5)

ogo

gos

sn

nC

qC

q

(6)

gogo

wo

wo

ns

ns

qq

qq

(7

)

0,,

.0

ogo

wo

ogo

wo

nn

nn

Kq

qK

qq

. (8

)

By

(4)

and

(5),

at e

ach

node

mar

gina

l ut

ility

and

mar

gina

l co

st a

re t

o be

equ

al.

If t

he

capa

city

of t

he li

ne is

ver

y la

rge,

we

obta

in th

e “g

rid-f

ree”

allo

catio

n. I

n th

is c

ase,

o nsz

K

so t

hat

0o

by

the

com

plem

enta

ry s

lack

ness

con

ditio

n (8

). T

hen,

by

(6),

the

mar

gina

l va

luat

ion

of e

lect

ricity

is th

e sa

me

at b

oth

node

s.

The

serie

s of

eq

ualit

ies

''

wo

gow

ogo

ss

ss

nn

nn

Uq

Cq

Uq

Cq

, to

geth

er

with

co

nditi

on (7

), fu

lly d

escr

ibe

the

optim

al a

lloca

tion.

(se

e Fi

gure

4-4

).

impo

rts=

o nsz

expo

rts=

o nsz

' nU

nC

wo

nq

go nq

nq

go sqw

osq

sq

' sU

sC

Nor

th

Sout

h

Figu

re 4

-4.

No

capa

city

con

stra

int,

sam

e va

luat

ion

at b

oth

node

s

124

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

Con

vers

ely,

if K

is s

mal

l, th

e co

nstra

int (

3) is

bin

ding

and

we

obta

in th

e gr

id-c

onst

rain

ed

allo

catio

n.

The

optim

al p

rodu

ctio

n in

‘no

rth’

is g

iven

by

'go

gon

nn

nU

qK

Cq

and

, in

‘sou

th’,

by

'go

gos

ss

sU

qK

Cq

. N

ow,

the

shad

ow

pric

e '

'o

gogo

gogo

ss

nn

ss

nn

Uq

KU

qK

Cq

Cq

is

st

rictly

pos

itive

. It

sign

als

that

a l

arge

r K

wou

ld a

llow

to

gene

rate

mor

e en

ergy

in ‘

north

’ w

here

the

cost

of o

ne a

dditi

onal

uni

t is s

mal

ler t

han

in ‘s

outh

’ and

to c

onsu

me

mor

e in

‘sou

th’

whe

re th

e ut

ility

of t

his a

dditi

onal

uni

t is l

arge

r tha

n in

‘nor

th’ (

see

Figu

re 4

-5).

o

K K

' nU

nC

wo

nq

go nq

nq

go sqw

osq

sq

' sU

sC

Nor

th

Sout

h

Figu

re 4

-5.

Bin

ding

tran

spor

t cap

acity

, nod

al m

argi

nal v

alua

tions

of e

nerg

y di

verg

e

THE

SOC

IAL

CO

ST O

F LO

SSES

A

ssum

e no

w t

hat

a fr

actio

n of

the

ele

ctric

ity i

njec

ted

at t

he n

orth

nod

e is

los

t be

fore

ar

rivin

g at

the

sout

h no

de.

In th

e pr

ogra

m to

obt

ain

the

first

-bes

t allo

catio

n, w

e m

ust r

epla

ce

(2) w

ith:

wg

gw

wg

ss

nn

ss

qq

qq

Lq

q

(9)

sinc

e tra

nsm

issi

on lo

sses

.

L in

crea

se w

ith th

e po

wer

con

sum

ed b

y th

e lo

ad.

The

first

-or

der c

ondi

tions

rem

ain

(4),

(5) a

nd (8

). B

ut (7

) is

repl

aced

by

(9) w

ith th

e co

nseq

uenc

e th

at

(6) i

s rep

lace

d by

:

1o

gogo

ss

nn

Cq

Cq

L

(10)

whe

re L

stan

ds fo

r mar

gina

l los

ses.

In t

he n

o-co

nges

tion

case

her

eafte

r ill

ustra

ted

by F

igur

e 4-

6 (

0o

), w

e se

e th

at t

he

optim

al a

lloca

tion

sets

:

(1)

gogo

gos

sn

nn

Cq

Cq

LC

q.

This

refle

cts t

hat i

t tak

es (1

+L')

MW

h ge

nera

ted

in ‘n

orth

’ to

mat

ch th

e ne

ed fo

r 1 M

Wh

in

‘sou

th’.

As

com

pare

d w

ith t

he c

ase

whe

re

0,L

the

vol

ume

of t

rade

is

redu

ced

and

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

12

5

cons

umpt

ion

in ‘

sout

h’ i

s sm

alle

r. B

ut g

ener

atio

n in

‘no

rth’

can

be l

arge

r in

ord

er t

o co

mpe

nsat

e fo

r the

loss

es.

'(1

)n

LU

(1)

gon

nC

qL

go

ss

Cq

nq

sq

' nU

sC

' sU

(1)

nL

C

nC

gon

nC

q

wo nq

go nq

go sqwo sq

Figu

re 4

-6.

Opt

imal

allo

catio

n w

ith e

nerg

y lo

sses

TIM

E V

AR

IATI

ON

Fo

r a g

iven

tran

spor

t inf

rast

ruct

ure,

the

optim

al d

ispa

tch

is ti

me

depe

nden

t, fo

llow

ing

the

chan

ges

in c

onsu

mer

s pr

efer

ence

s of

and

in

gene

ratio

n pl

ants

ava

ilabi

lity.

Th

e ob

viou

s co

nseq

uenc

e is

that

nod

al v

alua

tions

of e

nerg

y ar

e al

so ti

me-

depe

nden

t. A

ssum

e th

ere

are

no

loss

es a

nd th

e tra

nspo

rt lin

e of

cap

acity

K is

use

d du

ring

two

perio

ds o

f equ

al d

urat

ion:

a p

eak

perio

d (la

belle

d D

for d

ay) a

nd a

n of

f-pe

ak p

erio

d (la

belle

d N

for n

ight

). T

he p

robl

em is

to

max

imis

e:

,

,[

]w

g

ii

ii

DN

in

sU

qC

qrK

,

subj

ect t

o tw

o co

nstra

ints

of

type

(2)

and

tw

o co

nstra

ints

of

type

(3)

, one

pai

r fo

r ea

ch

perio

d.17

Fro

m th

e op

timal

allo

catio

n, w

e de

rive

the

shad

ow p

rice

of th

e lin

e du

ring

the

day

ogo

goD

sDsD

nDnD

Cq

Cq

an

d th

e sh

adow

pr

ice

of

the

line

durin

g th

e ni

ght

ogo

goN

sNsN

nNnN

Cq

Cq

. A

s the

nee

d fo

r tra

nspo

rtatio

n is

hig

her d

urin

g th

e da

y, w

e ha

ve

oo

DN

, w

here

the

equ

ality

hol

ds o

nly

in t

he c

ase

0o

oD

N,

that

is

whe

n th

e lin

e is

pe

rman

ently

non

-bin

ding

(w

hich

sho

uld

neve

r oc

cur

sinc

e th

e un

it co

st o

f ca

paci

ty i

s po

sitiv

e).

Dep

endi

ng o

n th

e di

scre

panc

y be

twee

n th

e ni

ght

and

day

char

acte

ristic

s of

co

nsum

ptio

n an

d ge

nera

tion,

w

e ca

n ha

ve

eith

er

a pe

rman

ently

bi

ndin

g ca

paci

ty

(0

oo

DN

) or c

onge

stio

n on

ly d

urin

g th

e pe

ak p

erio

d (

0o

oD

N).

In

any

cas

e, b

ecau

se th

e sa

me

line

is u

sed

to sa

tisfy

diff

eren

t nee

ds, i

t has

the

feat

ures

of a

“p

ublic

goo

d”:18

thi

s ex

plai

ns w

hy t

he t

est t

o kn

ow w

heth

er t

he c

apac

ity o

f th

e lin

e is

too

la

rge

or to

o sm

all c

onsi

sts n

ow in

com

parin

g th

e un

it co

st o

f cap

ital r

with

the

sum

(o

oD

N).

IMPL

EMEN

TATI

ON

Th

e fir

st-b

est s

olut

ion

can

be d

ecen

tralis

ed b

y m

eans

of

noda

l pric

es.

At t

he s

outh

nod

e an

y tra

nsac

tion

will

cos

t '

wo

gos

ss

ss

pU

qC

q p

er u

nit t

o a

cons

umer

and

will

retu

rn

sp

126

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

to a

pro

duce

r, w

hate

ver t

he lo

catio

n of

the

othe

r sid

e in

the

trans

actio

n. S

imila

rly, a

t the

nor

th

node

'

wo

gon

nn

nn

pU

qC

q w

ill b

e ch

arge

d fo

r any

uni

t of c

onsu

mpt

ion

and

will

be

paid

fo

r any

uni

t of p

rodu

ctio

n.

It is

eas

y to

che

ck th

at c

onsu

mer

s who

solv

e:

max

ii

ii

iq

Uq

pq

will

cho

ose

wo

iq, a

nd p

rodu

cers

who

solv

e:

max

ii

ii

iq

pq

Cq

will

cho

ose

go iq a

t ,

in

s.

Ther

efor

e no

dal

pric

es,

eith

er r

esul

ting

from

com

petit

ive

noda

l mar

kets

or i

mpl

emen

ted

by a

regu

latio

n en

tity,

allo

w to

reac

h th

e fir

st-b

est a

lloca

tion.

W

hen

ener

gy a

nd tr

ansp

ort a

re b

illed

sep

arat

ely,

the

equi

libriu

m p

rice

for

trans

port

from

no

rth to

sou

th m

ust b

e su

ch th

at

sn

nsp

pt

; the

n ns

sn

tp

p.

We

conc

lude

that

, whe

n lo

sses

can

be

negl

ecte

d, fr

om (6

) the

firs

t-bes

t tra

nspo

rt pr

ice

is:

oo

nst

(11)

In w

ords

, ab

sent

any

ohm

ic l

osse

s, tra

nspo

rt sh

ould

be

free

if

and

only

if

ther

e is

no

cong

estio

n. W

here

ther

e is

con

gest

ion,

a p

ositi

ve p

rice

is to

be

char

ged.

Sym

met

rical

ly, t

he

equi

libriu

m p

rice

for

trans

port

from

sou

th t

o no

rth m

ust

be s

uch

that

n

ssn

pp

t.

We

dedu

ce t

hat

reve

rse

flow

s sh

ould

be

char

ged

0o

osn

ns

tp

p.

Ind

eed,

as

long

as

0g

ww

gns

nn

ss

zq

qq

q, i

ndiv

idua

l tra

nsac

tions

from

sou

th to

nor

th s

houl

d be

rew

arde

d si

nce

they

redu

ce th

e co

nges

tion

of th

e lin

e.

Sim

ilarly

, ta

king

los

ses

into

acc

ount

, fr

om (1

0) w

e ob

tain

'

'0

oo

nsn

tL

C a

nd

'(

')

0o

osn

nt

LC

. Th

e la

tter i

s on

ce m

ore

just

ified

bec

ause

any

net

inje

ctio

n in

‘sou

th’

decr

ease

s th

e qu

antit

y of

ene

rgy

that

mus

t be

inje

cted

at t

he n

orth

nod

e an

d, c

onse

quen

tly,

decr

ease

s bot

h th

e lo

sses

of e

nerg

y an

d th

e co

nges

tion

on th

e lin

e.

BA

LAN

CIN

G T

HE

BU

DG

ET O

F TH

E TR

AN

SPO

RT

OPE

RA

TOR

Is

thi

s fir

st-b

est

sust

aina

ble

on f

inan

cial

gro

unds

? O

n th

e ge

nera

tor’

s si

de,

if th

ere

are

incr

easi

ng re

turn

s to

scal

e, m

argi

nal-c

ost p

ricin

g is

not

suff

icie

nt to

bre

ak e

ven.

But

sinc

e th

is

repo

rt is

ded

icat

ed to

tran

spor

t, w

e as

sum

e th

at g

ener

ator

s do

not l

ose

mon

ey w

hen

gene

ratio

n is

val

ued

at fi

rst b

est19

.

Wha

t abo

ut th

e re

sour

ces

of th

e gr

id o

pera

tor?

The

mar

ket e

quili

briu

m u

nder

nod

al p

rices

cr

eate

s a “

mer

chan

disi

ng su

rplu

s”:

wo

wo

gogo

ss

nn

ss

nn

MS

pq

pq

pq

pq

.o

n

LC

LK

K

if th

e co

nstra

int i

s bin

ding

'

.o

nns

o nsLC

Lz

z

othe

rwis

e.

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

12

7

This

surp

lus i

s pos

itive

for t

wo

reas

ons:

be

caus

e of

the

cong

estio

n re

nt

oK

whe

n th

e lin

e is

con

gest

ed,

beca

use

loss

es a

re in

crea

sing

with

the

squa

re o

f the

ene

rgy

inje

cted

. It

resu

lts th

at:

2o nsL

Lz

,

so th

at th

e su

rplu

s due

to lo

sses

is

.n

CL

In

sum

mar

y, u

nder

nod

al p

ricin

g th

e di

ffer

ence

MS

betw

een

the

expe

nditu

res o

f cus

tom

ers

and

the

gain

s of

pro

duce

rs i

s po

sitiv

e an

d it

can

be u

sed

to c

over

the

cos

t of

the

tra

nspo

rt op

erat

or.

But

is it

true

that

MS

rK?

If t

he s

ize

of t

he l

ine

coul

d be

opt

imal

ly a

djus

ted

to t

rans

port

need

s, w

e w

ould

hav

e o

r a

nd th

e M

S w

ould

leav

e th

e op

erat

or w

ith a

net

pro

fit e

qual

to th

e va

lue

of lo

sses

(p

rovi

ded

ther

e ar

e no

-incr

easi

ng re

turn

s to

scal

e).

But

for t

echn

ical

, eco

nom

ical

and

pol

itica

l re

ason

s, in

mos

t tra

nspo

rt ne

twor

ks, t

here

is e

xces

s cap

acity

so th

at

or

, and

eve

n 0

o

for a

bsol

ute

exce

ss c

apac

ity.

In m

ost t

rans

port

infr

astru

ctur

e, it

resu

lts th

at th

e m

erch

andi

sing

su

rplu

s doe

s not

cov

er th

e fix

ed c

osts

.

We

succ

essi

vely

con

side

r sec

ond-

best

line

ar p

rices

and

non

line

ar p

rices

.

RA

MSE

Y N

OD

AL

PRIC

ES

To s

impl

ify o

ur a

naly

sis,

we

com

e ba

ck to

the

hypo

thes

is o

f no

loss

es.

Then

, the

pro

blem

is

to

max

imiz

e (1

) w

ith r

espe

ct t

o pr

ices

(,

,,

)w

wg

gn

sn

sp

pp

p s

ubje

ct t

o (2

) an

d (3

), pl

us t

he

addi

tiona

l obl

igat

ion

to b

alan

ce th

e bu

dget

of t

he tr

ansp

ort f

irm, t

hat i

s:

0w

ww

wg

gg

gn

ns

sn

ns

sp

qp

qp

qp

qrK

, (1

2)

know

ing

that

pric

e-ta

king

con

sum

ers

beha

ve o

ptim

ally

'

ww

ii

iU

qp

and

pric

e-ta

king

ge

nera

tors

beh

ave

optim

ally

g

gi

ii

Cq

p a

t eac

h no

de i=

n,s.

D

enot

ing

by

the

mul

tiplie

r as

soci

ated

with

the

bud

get

cons

train

t (1

2),

by

the

m

ultip

lier a

ssoc

iate

d w

ith th

e flo

w c

onst

rain

t (2)

and

by

the

mul

tiplie

r ass

ocia

ted

with

the

capa

city

con

stra

int

(3),

from

the

firs

t-ord

er c

ondi

tions

, it

is s

traig

htfo

rwar

d to

writ

e th

e se

cond

-bes

t pric

es a

s:20

11

1

wg

nn

wg

nn

wg

nn

pp

pp

in

‘nor

th’

11

1

wg

ss

wg

ss

wg

ss

pp

pp

in

‘sou

th’.

Whe

re:

128

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

/ /

def

ww

ii

w iw

wi

i

qq

pp

is th

e pr

ice

elas

ticity

of d

eman

d an

d

/ /

def

gg

ii

g ig

gi

i

qq

pp

is th

e pr

ice

elas

ticity

of s

uppl

y at

nod

e i.

Bot

h co

nsum

ers

and

gene

rato

rs a

t eac

h no

de h

ave

to c

ontri

bute

to c

over

the

fixed

cos

t of

trans

port.

At n

ode

i we

obse

rve

that

:

()

1

wg

ii

wg

ii

wg

ii

pp

pp

.

It is

no

long

er tr

ue th

at th

ere

exis

ts o

ne u

niqu

e pr

ice

at e

ach

node

. Th

e di

ffer

ence

bet

wee

n de

man

d pr

ice

and

supp

ly p

rice

incr

ease

s w

ith th

e va

lue

of th

e fix

ed c

ost o

f tra

nspo

rt to

be

paid

(w

hich

app

ears

in

wg

ii

pp

thr

ough

the

dua

l va

riabl

e )

and

it de

crea

ses

whe

n th

e de

man

d an

d su

pply

ela

stic

ities

incr

ease

.

RA

MSE

Y T

RA

NSP

OR

T PR

ICES

It

obvi

ousl

y re

mai

ns t

rue

that

the

equ

ilibr

ium

tra

nspo

rtatio

n ch

arge

s ap

plie

d to

the

do

min

ant f

low

(fr

om n

orth

to s

outh

) ar

e su

ch th

at

wg

sn

nsp

pt

. U

sing

the

Ram

sey

noda

l pr

ices

, we

obta

in:

wg

nss

nt

pp

11

wg

sn

wg

sn

pp

(1

3)

As c

ompa

red

with

(11)

, we

obse

rve

two

dist

ortio

ns:

—

first

, to

the

mar

gina

l co

st o

f co

nges

tion21

we

have

to

add

the

cont

ribut

ion

to t

he

reco

very

of t

he tr

ansp

ort f

ixed

cos

ts;

—

seco

nd, t

he m

argi

nal c

ost o

f con

gest

ion

is it

self

dist

orte

d.

An

incr

ease

in

K b

oth

incr

ease

s f

or f

inan

cial

rea

sons

and

dec

reas

es

for

tec

hnic

al

reas

ons.

It

conf

irms

that

the

pric

ing

of t

rans

port

mai

nly

appe

ars

as t

he c

over

age

of f

ixed

co

sts,

exce

pt w

hen

the

capa

city

is v

ery

smal

l.

Fina

lly, n

ote

that

for r

ever

se tr

ansa

ctio

ns (f

rom

sout

h to

nor

th) t

he R

amse

y pr

ice

shal

l be:

wg

snn

st

pp

11

wg

ns

wg

ns

pp

(1

4)

It m

eans

that

the

rew

ard

for a

llevi

atin

g lo

sses

and

con

gest

ion

will

pro

babl

y be

mor

e th

an

com

pens

ated

by

the

part

of t

he t

ariff

tha

t pa

rtici

pate

s to

the

cov

erag

e of

fix

ed c

osts

. I

f de

man

d is

muc

h m

ore

elas

tic i

n ‘s

outh

’ th

an i

n ‘n

orth

’ an

d su

pply

muc

h m

ore

elas

tic i

n ‘n

orth

’ th

an in

‘so

uth’

, it c

an e

ven

be th

e ca

se th

at

snns

tt

, des

pite

the

coun

ter-

flow

eff

ect.

Th

is is

bec

ause

fina

ncia

l con

cern

s app

ear a

s dom

inan

t as c

ompa

red

with

eff

icie

ncy

conc

erns

. In

any

cas

e, c

ompa

ring

(13)

and

(14

), w

e ob

serv

e th

at

nssn

tt

onl

y by

coi

ncid

ence

. A

ctua

lly, s

econ

d-be

st p

rices

are

dire

ctio

nal b

oth

for t

echn

ical

and

fina

ncia

l rea

sons

. A

lso,

it

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

12

9

mus

t be

reca

lled

that

in (

13) a

nd (

14)

the

dual

var

iabl

es, t

he n

odal

pric

es a

nd th

e el

astic

ities

ar

e al

l tim

e de

pend

ent.

We

conc

lude

that

Ram

sey

trans

port

pric

es m

ust b

e tim

e de

pend

ent.

TWO

-PA

RT

TAR

IFFS

W

e co

nsid

er n

ow t

he c

ase

whe

re p

rices

are

not

con

stra

ined

to

be l

inea

r. W

e lim

it th

e an

alys

is to

the

two-

part

tarif

f w

here

(

)w

wi

iT

q =

w

ww

ii

ia

qb

is th

e ex

pend

iture

for

con

sum

ing

w iq a

t nod

e i a

nd

()

gg

ii

Tq

=

gg

gi

ii

aq

b is

the

reve

nue

whe

n ge

nera

ting

g iq a

t nod

e i.

The

ob

ligat

ion

to b

alan

ce th

e bu

dget

of t

he tr

ansp

orta

tion

firm

read

s:

()

0w

ww

wg

gg

gw

wg

gn

ns

sn

ns

sn

sn

sa

qa

qa

qa

qb

bb

brK

(1

5)

By

fixin

g '

'(

)(

)w

wo

ggo

ii

ii

ii

aU

qa

Cq

at e

ach

node

, we

obvi

ousl

y im

plem

ent t

he f

irst-

best

allo

catio

n of

con

sum

ptio

n an

d ge

nera

tion

at e

ach

node

. G

iven

thes

e pr

ices

and

giv

en th

e flo

w c

onst

rain

t (2

) (a

ssum

ing

L=0)

, (15

) re

ads

()

()

0w

wg

go

ns

ns

bb

bb

rK

. O

ne

obta

ins a

n in

finite

set o

f sol

utio

ns fo

r the

fixe

d pa

rt of

the

loca

tiona

l ene

rgy

tarif

fs, e

ven

whe

n ta

king

int

o ac

coun

t th

e pa

rtici

patio

n co

nstra

ints

of

cons

umer

s (

)(

)w

ww

wi

ii

ii

Uq

Tq

u a

nd

gene

rato

rs

()

()

gg

gg

ii

ii

iT

qC

qg

, w

here

iu (

resp

ectiv

ely

ig)

stan

ds f

or t

he r

eser

vatio

n va

lue

of c

onsu

mer

s (r

espe

ctiv

ely,

gen

erat

ors)

at n

ode

i. A

ny ru

le to

sha

re (

)o

rK

am

ong

the

agen

ts b

y m

eans

of

the

fixed

par

t of

the

tar

iffs

that

sat

isfie

s th

e ab

ove

parti

cipa

tion

cons

train

ts,

plus

add

ition

al c

onst

rain

ts d

ue t

o th

e in

form

atio

nal

disa

dvan

tage

of

the

pric

e m

aker

22, i

s per

mitt

ed.

Whe

n th

e bu

yer a

nd th

e se

ller o

f a v

olum

e q

are

loca

ted

at th

e sa

me

node

i, th

ey c

reat

e a

surp

lus:

()

()

wg

ww

gg

ii

ii

ii

Tq

Tq

aq

ba

qb

=

wg

ii

bb

(1

6)

To p

reve

nt a

ny a

rbitr

age

betw

een

the

two

node

s, th

e tra

de o

f a q

uant

ity q

of e

nerg

y fr

om

north

to so

uth

is to

be

bille

d (

)(

)(

)w

gw

wg

gns

sn

ss

nn

Tq

Tq

Tq

aq

ba

qb

. Th

eref

ore:

()

ow

gns

sn

Tq

qb

b

(17)

Sym

met

rical

ly, a

n in

divi

dual

reve

rse

trans

actio

n sh

ould

be

bille

d:

()

()

()

wg

ow

gsn

ns

ns

Tq

Tq

Tq

qb

b

(18)

For t

he sa

ke o

f tra

nspa

renc

y, o

ne c

an p

refe

r a u

nifo

rm

w b fo

r all

cons

umer

s and

a u

nifo

rm

g b f

or a

ll ge

nera

tors

wha

teve

r th

eir

loca

tion,

but

the

ris

k of

exc

lusi

on (

parti

cipa

tion

cons

train

ts th

at w

ould

not

be

satis

fied)

shou

ld n

ot b

e ne

glec

ted.

Fo

r th

e sa

me

reas

ons

as th

e on

es m

entio

ned

form

erly

, bot

h th

e m

argi

nal p

rice

a an

d th

e fix

ed fe

e b

shou

ld b

e tim

e de

pend

ent.

As l

ong

as p

artic

ipat

ion

cons

train

ts a

re n

ot b

indi

ng, t

he

varia

tion

of b

with

the

dat

e is

sup

erflu

ous.

In

cont

rast

, th

e va

riabl

e pa

rt of

the

tar

iff f

or

ener

gy a

and

, con

sequ

ently

, the

var

iabl

e pa

rt of

the

tar

iff f

or t

rans

port

o s

houl

d be

tim

e de

pend

ent i

n or

der t

o se

nd g

ood

scar

city

sign

als t

o us

ers.

MU

LTIP

RO

DU

CT

TWO

-PA

RT

TAR

IFFS

A

s al

read

y m

entio

ned,

ene

rgy

pric

es a

nd c

onse

quen

tly tr

ansp

ort p

rices

sho

uld

be v

aryi

ng

with

tim

e. F

or e

xam

ple,

the

hour

ly tw

o-pa

rt ta

riff d

efin

ed in

(17)

shou

ld re

ad:

130

Tran

spor

t pri

cing

of e

lect

rici

ty n

etw

orks

(,

())

()

()

()

nsns

nsns

nsT

qA

qB

(1

8)

and

the

tota

l exp

endi

ture

s pa

id to

the

trans

port

oper

ator

by

an a

gent

tran

sfer

ring

ener

gy

from

nor

th to

sout

h, le

t us s

ay d

urin

g on

e ye

ar, w

ould

be:

8760 1

()

()

()

nsns

nsns

TA

qB

.

For t

he re

ason

exp

lain

ed fo

rmer

ly, t

he fi

xed

part

of th

e ta

riff c

an b

e ch

osen

qui

te e

asily

23,

for

exam

ple

it ca

n be

a c

onst

ant.

The

diff

icul

ty is

that

(18

) re

quire

s to

met

er a

nd to

bill

the

flow

s fr

om n

orth

to s

outh

alm

ost c

ontin

uous

ly.

Bec

ause

the

trans

actio

n co

sts

wou

ld b

e ve

ry

high

, the

ope

rato

r w

ill in

stal

l sim

ple

met

erin

g an

d bi

lling

dev

ices

that

do

not d

istin

guis

h th

e da

te o

f ea

ch f

low

. T

his

mea

ns t

hat

the

mar

gina

l pr

ice

()

nsA w

ill n

ot b

e a

cont

inuo

us

func

tion

of ti

me.

In

mos

t cas

es, i

t will

be

a pi

ecew

ise

func

tion

with

two

seas

onal

(su

mm

er

and

win

ter)

and

two

daily

(da

y an

d ni

ght)

valu

es.

At w

orst

it w

ill b

e un

iform

all

the

year

lo

ng.

Ass

ume

the

latte

r.

In th

is c

ase

()

nsns

AA

so th

at:

8760 1

(,

())

()

()

ens

nsns

nsns

nsns

nsT

qA

qB

Aq

B,

whe

re

8760 1

()

e nsns

qq

is th

e to

tal e

nerg

y co

nsum

ed a

ll th

e ye

ar lo

ng.

The

obvi

ous

draw

back

of

this

tw

o-pa

rt pr

icin

g is

tha

t it

does

not

allo

w t

o di

scrim

inat

e be

twee

n re

gula

r use

rs w

ho c

an b

e sa

tisfie

d w

ith a

“m

ediu

m s

ize”

grid

on

one

side

and

, on

the

othe

r si

de, i

rreg

ular

use

rs w

ho n

eed

larg

e ca

paci

ty o

f tra

nspo

rt fo

r sh

ort p

erio

ds o

f tim

e.

A

solu

tion

is t

o co

mbi

ne t

he t

rans

port

dem

and

for

ener

gy

e nsq a

nd a

pro

xy f

or t

he t

rans

port

dem

and

for c

apac

ity, f

or e

xam

ple

max

()

K nsns

qq

, and

to b

ill th

em se

para

tely

in a

way

that

ap

prox

imat

es th

e op

timal

tim

e-de

pend

ent t

wo-

part

tarif

f. W

e ob

tain

a m

ulti-

prod

uct t

wo-

part

tarif

f:

ee

KK

nsns

nsns

nsns

TA

qA

qB

(1

9)

LOO

P FL

OW

S C

onsi

der

the

thre

e-no

de n

etw

ork

of B

ox 4

-2 a

nd s

uppo

se t

hat

the

line

betw

een

the

two

inje

ctio

n no

des

is t

he o

nly

one

with

a l

imiti

ng c

apac

ity K

. N

egle

ctin

g lo

sses

, the

opt

imal

di

spat

ch is

the

solu

tion

to:

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

13

1

3

11

22

12

3,

,m

axw

gg

gg

wq

qq

Uq

Cq

Cq

rK

s.t.

3

12

wg

gq

qq

1

2

3

gg

qq

K.

Whe

n th

e ca

paci

ty c

onst

rain

t on

this

line

is b

indi

ng, e

ach

gene

rato

r cre

ates

a c

ount

er-f

low

th

at a

llevi

ates

the

load

pro

voke

d by

the

inje

ctio

n of

pow

er fr

om th

e ot

her p

lant

. B

ecau

se o

f th

is p

ositi

ve e

xter

nalit

y, t

he o

ptim

al d

ispa

tch

can

com

man

d th

at a

hig

h-co

st p

lant

sho

uld

gene

rate

pow

er d

espi

te th

e ex

iste

nce

of a

vaila

ble

gene

ratio

n ca

paci

ty a

t low

cos

t som

ewhe

re

else

in th

e ne

twor

k.

The

leve

l of

the

ther

mal

con

stra

int o

n th

e lin

e be

twee

n no

des

1 an

d 2

affe

cts

all

noda

l pr

ices

. If

pla

nt 1

is

mor

e ef

ficie

nt t

han

plan

t 2,

i.e

, if

''

12

Cq

Cq

, pr

ices

:

'2

22

3'

3

def

og

wp

Cq

Uq

>

33

'de

f

wp

Uq

>

'1

11

3'

3

def

og

wp

Cq

Uq

allo

w to

enc

oura

ge (d

isco

urag

e) g

ener

atio

n at

nod

e 2

(nod

e 1)

.

If e

nerg

y an

d tra

nspo

rt ha

ve t

o be

inv

oice

d se

para

tely

, fro

m t

he e

quili

briu

m c

ondi

tions

j

iij

pp

t, w

e ob

tain

the

set o

f lin

ear t

ariff

s for

tran

spor

t:

13/3

ot

, 23

/3o

t,

122

/3o

t.

They

exp

licitl

y en

cour

age

cons

umer

s to

tran

sact

with

exp

ensi

ve g

ener

ator

s (n

ode

2) a

nd

they

dis

suad

e th

em t

o tra

nsac

t w

ith l

ow-c

ost

gene

rato

rs (

node

1).

The

se p

rices

sen

d th

e ac

cura

te s

igna

ls to

pre

vent

jeop

ardi

sing

the

safe

ty o

f the

grid

, nam

ely

the

ohm

ic c

onst

rain

t on

the

line

betw

een

node

s 1 a

nd 2

. N

ote

that

, in

cont

rast

to th

e on

e-lin

e m

odel

, in

a m

eshe

d ne

twor

k th

e sh

adow

cos

t of

the

ther

mal

con

stra

int

on t

he l

ine

betw

een

two

node

s is

no

long

er e

qual

to

the

diff

eren

ce i

n m

argi

nal v

alua

tions

at t

he n

odes

. In

our

illu

stra

tion,

'

'2

21

13

2g

go

Cq

Cq

. Th

is is

be

caus

e al

l con

nect

ed li

nes a

re a

ffec

ted

by a

bila

tera

l tra

nsac

tion.

Con

sequ

ently

, the

mar

gina

l va

lue

of c

onge

stio

n re

flect

s al

l th

e ne

gativ

e ex

tern

aliti

es c

reat

ed t

hrou

gh t

he g

rid b

y th

e lim

ited

capa

city

of e

ach

piec

e of

equ

ipm

ent.

RE

FER

EN

CE

S

Cha

o, H

.P.

and

S.Pe

ck (

1996

), “A

Mar

ket

Mec

hani

sm f

or E

lect

ric P

ower

Tra

nsm

issi

on”,

Jo

urna

l of R

egul

ator

y Ec

onom

ics,

vol 1

0, p

p 25

-60.

C

hao,

H.P

., S.

Peck

, S.

Ore

n an

d R

.Wils

on (

2000

), “F

low

-Bas

ed T

rans

mis

sion

Rig

hts

and

Con

gest

ion

Man

agem

ent”

, Ele

ctric

ity J

ourn

al, O

ctob

er, p

p 38

-58.

C

ram

pes

C.

and

J.J.L

affo

nt (

2001

) “T

rans

port

Pric

ing

in t

he E

lect

ricity

Ind

ustry

” O

xfor

d Re

view

of E

cono

mic

Pol

icy,

Aut

umn,

vol

17,

no

3, p

p 31

3-32

8.

Cre

mer

, H

. an

d J.J

.Laf

font

(20

02),

“Com

petit

ion

in G

as M

arke

ts”,

Eur

opea

n Ec

onom

ic

Revi

ew, v

ol 4

6, n

o 4-

5, p

p 92

8-93

5.

132

Tran

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t pri

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lect

rici

ty n

etw

orks

Hog

an, W

.W. (

1992

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ontra

ct N

etw

orks

for

Ele

ctric

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ower

Tra

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rt”,

Jour

nal

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lato

ry E

cono

mic

s vol

4, p

p 21

1-24

2.

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an, W

.W. (

1998

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odes

an

d Zo

nes

in

Elec

trici

ty

Mar

kets

: Se

ekin

g Si

mpl

ified

C

onge

stio

n Pr

icin

g”, i

n H

ung-

Po C

hao

and

H.G

. Hun

tingt

on (E

ds.)

Des

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ng C

ompe

titiv

e El

ectr

icity

Mar

kets

, Klu

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Aca

dem

ic P

ublis

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, Lon

don,

pp

33-6

2.

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, M. (

1997

) “A

n In

trodu

ctio

n to

the

Pric

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of E

lect

ric P

ower

Tra

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Util

ities

Po

licy,

vol

6, n

o 3,

pp

257-

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skow

, P.L

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J.T

irole

(200

0) “

Tran

smis

sion

Rig

hts

and

Mar

ket P

ower

on

Elec

tric

Pow

er

Net

wor

ks”,

RAN

D J

ourn

al o

f Eco

nom

ics,

vol 3

1, n

o 3,

Aut

umn,

pp

450-

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rez-

Arr

iaga

I.J.

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ín (

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on

Pow

er

Syst

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o 1,

Feb

ruar

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Schw

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aram

anis

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d R

.Boh

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988)

Spo

t pric

ing

for

elec

tric

ty, K

luw

er

Aca

dem

ic P

ublis

hers

. St

oft S

. (2

002)

Pow

er S

yste

m E

cono

mic

s, IE

EE/W

iley.

W

u, F

., P.

Var

aiya

, P.

Spill

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nd S

.Ore

n (1

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, “F

olk

Theo

rem

s on

Tra

nsm

issi

on O

pen

Acc

ess:

Pro

ofs a

nd C

ount

er e

xam

ples

”, J

ourn

al o

f Reg

ulat

ory

Econ

omic

s, pp

5-2

3.

NO

TE

S

1 Th

is is

a g

ood

illus

tratio

n of

the

diff

icul

ty to

giv

e a

prec

ise,

obj

ectiv

e de

finiti

on o

f cos

ts,

as e

xpla

ined

in C

hapt

er 2

. 2

As

show

n in

Cha

o an

d Pe

ck (

1996

), ph

ysic

al r

ight

s an

d fin

anci

al r

ight

s ar

e eq

uiva

lent

w

hen

the

ener

gy m

arke

ts a

nd th

e rig

hts

mar

kets

are

per

fect

ly c

ompe

titiv

e.

Josk

ow a

nd

Tiro

le (2

000)

pro

vide

an

anal

ysis

of v

ario

us n

on-c

ompe

titiv

e co

nfig

urat

ions

. 3

See

Josk

ow a

nd T

irole

(200

0), p

. 45

2.

4 Fo

r an

illus

tratio

n se

e B

ox 4

-2.

For m

ore

deta

ils, s

ee fo

r exa

mpl

e H

su (1

997)

. 5

Schw

eppe

et a

l. (1

988)

. 6

See

for e

xam

ple

Stof

t (20

02),

p. 4

17.

7 St

udie

s of

mar

ket

pow

er a

re b

ased

on

calib

rate

d si

mul

atio

n m

odel

s. S

ee r

efer

ence

s in

C

ram

pes a

nd L

affo

nt (2

001)

. 8

We

do n

ot c

onsi

der t

he is

sue

of n

odal

-pric

e ra

ndom

ness

. To

hed

ge a

gain

st p

rice

vola

tility

, us

ers c

an si

gn fi

nanc

ial c

ontra

cts.

See

Hog

an (1

992)

and

Cha

pter

5 in

fra.

9

See

Ore

n et

al.

(199

6).

10

See

Pére

z A

rria

ga e

t al.

(199

5).

11

Prov

ided

the

auth

ority

in c

harg

e of

pric

ing

is n

ot c

onst

rain

ed b

y a

lack

of i

nfor

mat

ion

on

the

will

ingn

ess t

o pa

y of

the

user

s. F

or a

n ill

ustra

tion,

see

Cha

pter

6.

12

Se

e C

hapt

er 3

. 13

Fo

r det

ails

on

econ

omic

and

lega

l pric

e di

scrim

inat

ions

, the

read

er is

refe

rred

to C

hapt

er 1

. 14

O

n th

e pr

inci

ples

of c

oope

rativ

e-ga

mes

theo

ry, s

ee C

hapt

er 3

. 15

In

the

tw

o-pa

rt ca

se, t

he v

aria

ble

part

is i

ncre

asin

g lin

early

with

the

qua

ntity

of

ener

gy

trans

porte

d.

In m

ulti-

part

tarif

fs,

the

varia

ble

part

is a

pie

cew

ise

linea

r in

crea

sing

fu

nctio

n.

16

Det

ails

on

actu

al ta

riffs

are

pre

sent

ed in

Cha

pter

8.

17

We

do n

ot d

iscu

ss t

he a

dditi

onal

int

erte

mpo

ral

cons

train

ts d

ue t

o th

e m

anag

emen

t of

hy

drop

lant

s or t

o th

e ob

ligat

ion

to sa

tisfy

hea

ting

cond

ition

s in

ther

mal

pla

nts.

Cos

t rec

over

y an

d sh

ort-r

un e

ffici

ency

13

3

18

A

ctua

lly, D

and

N a

re s

ucce

ssiv

e, b

ut th

e ar

gum

ent i

s th

e sa

me

as if

ther

e w

ere

seve

ral

non-

rival

sim

ulta

neou

s ne

eds

to s

atis

fy w

ith th

e sa

me

equi

pmen

t: it

is th

e w

illin

gnes

s to

pa

y of

all

user

s tha

t mus

t be

take

n in

to c

onsi

dera

tion.

19

Th

is i

s tru

e w

hen

the

long

run

mar

gina

l co

st o

f ge

nera

tion

is n

on d

ecre

asin

g an

d ge

nera

tors

hav

e op

timiz

ed th

e si

ze o

f the

ir pl

ants

. 20

Se

e C

rem

er a

nd L

affo

nt 2

001.

21

To

whi

ch th

e m

argi

nal c

ost o

f los

ses s

houl

d be

add

ed.

22

Self-

sele

ctio

n co

nstra

ints

are

to

be a

dded

to

desi

gn t

he m

enu

of t

ariff

s w

hen

the

pric

e m

aker

can

not o

bser

ve s

ome

indi

vidu

al c

hara

cter

istic

s of

the

pric

e ta

kers

, for

exa

mpl

e th

e co

nsum

ers'

will

ingn

ess

to p

ay o

r th

e ge

nera

tion

cost

of

prod

ucer

s. T

he p

robl

em i

s to

pr

even

t an

opp

ortu

nist

ic s

witc

h of

som

e us

ers

tow

ards

tar

iffs

that

are

des

igne

d fo

r so

meb

ody

else

. C

hapt

er 6

pro

vide

s an

illu

stra

tion

of th

e de

sign

of

cont

rol m

echa

nism

s un

der i

nfor

mat

ion

asym

met

ry.

23

Exce

pt w

hen

ther

e is

a se

rious

info

rmat

iona

l gap

that

impo

ses f

ine

tuni

ng to

resp

ect a

ll th

e pa

rtici

patio

n an

d se

lf se

lect

ion

cons

train

ts.