Market Power Evaluation in Power Systems with Congestion

Tom Overbye, George Gross, Peter SauerDepartment of Electrical and Computer Engineering

University of Illinois at Urbana-ChampaignUrbana, IL

Mark Laufenberg, Jamie WeberPowerWorld Corporation

Urbana, IL

Introduction

• Power industry is rapidly restructuring• Key goal of restructuring is to reap benefits

of competitive marketplaces• Significant concerns benefits could be lost

through development of horizontal market power

Horizontal Market Power

• Market power is antithesis of competition–ability of a particular group of sellers to

maintain prices above competitive levels• An extreme case is a single supplier of a

product, i.e. a monopoly.• In the short run, Price monopolistic

producer can charge depends upon price elasticity of the demand.

Horizontal Market Power

• Market power can sometimes lead to decreased prices in the long run –Accompanying higher prices can result in a

quickening of the entry of new players and technological innovation

• Some market power abuses are actually self-inflicted by consumers by their reluctance to respond to favorable prices offered by new vendors in deregulated markets

Symptoms of Market Power

• Economic theory tells us that in a market with perfect competition, prices should be equal to the marginal cost to supply the product

• Therefore prices above marginal cost can indicate market power

Market Power Analysis

• Market power analysis requires 3 steps–identify relevant product/services–identify relevant geographic market–evaluate market concentration

Relevant Product

• FERC defines at least three distinct products–non-firm energy–short-term capacity (firm energy)–long-term capacity

• Emphasis shifting to short-term energy markets

• Presentation considers short-term• Challenge in electricity markets is demand

varies over time

Relevant Geographic Market

• Most difficult step in electricity market due to impact of transmission system

• Size of market is dependent on–competitive prices of generators–impacts of charges from transporting energy in

transmission network–physical/operational characteristics of transmission

network

Herfindahl-Hirshman Index (HHI)

• HHI is a commonly used methodology for evaluating market concentration

• where N is number of participants• qi is percentage market share

∑=

=N

iiqHHI

1

2

HHI Examples

• For monopoly HHI = 10,000• If N=4, q1=40%, q2=25%, q3=25%, q4=10%,

then HHI = 2950• DOJ/FTC standards, adopted by FERC for

merger analysis–HHI below 1000 is considered to represent an

unconcentrated market–anything above 1800 is considered concentrated

Market Power Without Transmission Considerations

• If transmission system is ignored, market power depends only on concentration of ownership relative to other producers in interconnected system

• Without considering any constraints (using NERC 1997 peak data)–Eastern Interconnect HHI = 170–ERCOT HHI = 2415

Market Power with Transmission Charges

• In determining geographic market, FERC requires that suppliers must be able to reach market–economically

• supplier must be able to deliver to customer at cost no greater than 105% of competitive price to customer

• delivered cost is sum of variable generation cost and transmission/ancillary service charges

–physically

Pricing Transmission Services

• Goal is to move energy from source to sink• A number of different mechanisms exist;

examples include–pancaking of transmission service charges along

contract path–establishment of Independent System Operator

(ISO) with single ISO-wide tariff

Market Power with Transmission Constraints

• Market size can be limited by physical ability to delivery electricity

• Whenever physical or operational constraints become active, system is said to be in state of congestion

• Congestion arises through number of mechanisms–transmission line/transformer thermal limits–bus voltage limits–voltage, transient or oscillatory stability

Radial System with Market Power

Line Limit = 100 MVA

Bus A

300.0 MW

100%

200.50 MW

99.5 MW

Rest ofElectricSystem

100 MVA limit on line limitsbus A imports to 100 MVA

Models theremainderof the electricalsystem

Networked System

Limit = 100 MVA

Limit = 100 MVABus A

300.0 MW

25%

175.00 MW

25.0 MWRest ofElectricSystem100%

100.0 MW

Analysis issubstantiallymore complex.

Transfer capabilityinto bus Ais NOT equalto sum oftie-line limits

Three Bus Networked ExampleImports = 74 MW

Bus B

Bus C

Bus A

300.0 MW

100%

226.00 MW

99.6 MW

26% 25.7 MW

23%

300.0 MW

50.0 MW

224.4 MW

324.0 MW

25 MWs of power is wheeling through bus A

In thisexample theallowableinterchangeis less thanlimit either line

Congestion in Networks

• Need to introduce several definitions concerning network power transfers–source: set of buses increasing their injection of

power into network–sink: set of buses decreasing their injection of

power into network–direction: source/sink pair

• Power transfer is then associated with a particular direction

Congestion in Networks

• To understand impact of congestion in networks, need to consider two interrelated issues–power transfer in a particular direction may impact

line flows in large portion of system• this impact is commonly defined as the power transfer

distribution factor (PTDF)

–once a line is congested, any new power transfers with a PTDF on the congested line above 5% can not take place

Nine Bus, Nine Area Example

17%

58% 41%

51%

45% 42%

34%

6%

54%

29%

32%

A

G

B

C

D

E

I

F

H

400.0 MW 400.0 MW 300.0 MW

250.0 MW

250.0 MW

200.0 MW

250.0 MW

150.0 MW

50.0 MW

39%

Each area contains one bus/one 500 MVA generator. Each line has 200 MVA limits. HHI = 1089

Pie chartsshow percentageloadingon lines

Figureshows base caseflows

PTDF Values for A to I Direction

I

A B

C

D

F

E

G

H

44%

56%

30%

13%

10%

20%

10%

2%

32%

35%

34% 34%

34%

PTDF showthe incrementalimpact on line flows, inthis case fora transfer fromarea A to areaI.

Pie charts now show the percentage PTDFvalue; arrows show the direction.

PTDF Values for G to F Direction

I

A B

C

D

F

E

G

H

6%

6%

18%

12%

6%

12%

6%

19% 61%

20% 21%

21%

Note thatfor both theA to I andthe G to F directionsalmost all PTDFs are above 5%

Example: For 200 MW transfer from G to F, lineH to I MW flow will increase by 200*21%=42MW

A P

AEC

DPL

JCP&L

AE

KACP

CILCO

DECO

DUKE

LGEE

IP

IPL

PECO

NI

STJO

SWEP

ALTE

NYPP

PSE&G

VP

SOUTHERN

AMRN

TVA

CPLW

CPLE

HE

SWPA

MIPU

SIPC

CIN

OVEC

DLCO

IMPA

PENELEC

PJM500

SCPSA

SCE&G

ENTR

EEI

DOE

NEPOOL

ONT HYDR

NIPS

CWLP

FE

AEP

PP&L

PEPCO

METED

LEPA

MPA

EMDE

SPRM

GRRD

ASEC

KACYINDN

DPL

BG&E

BREC

SIGE

EKPC

CONS

NSP

MEC

SEPA-RBR

SEPA-JST

HARTWELL

YADKIN

WEP

WPS

MGEDPC

MEC

ALTW

KAMO

NPPD

OTP

MPW

SMP

6%

24%

14%

5%

13%

17% 8%

19%

12%

9%

6%

38%

19%

6%

8%

14%

15%

7%

23%

7%

21%

22%

9%

9%

6%

6% 11%

5%

7%

24%

20% 15%

32%

5% 5%

5%

7% 16%

11%

9%

45%

Large Case PTDF Example: Direction Southern to NYPP

Figure shows the area to area interface PTDFs

PiechartsshowpercentagePTDF oninterface

R i v e r h e a dW i l d w o o d

S h o r e h a m

B r o o k h a v e n

P o r t J e f f e r s o n

H o l b r o o k

H o l t s v i l l e

N o r t h p o r t

P i l g r i mS y o s s e t

B e t h p a g e

R u l a n d R d .N e w b r i d g e

L c s t . G r v .

0 7 M E R O M 5

K E Y S T O N E

0 1 Y U K O N

C O N E M - G H

J U N I A T A

S U N B U R Y

S U S Q H A N A

W E S C O V L E

A L B U R T I S

H O S E N S A K

B R A N C H B G

E L R O Y

W H I T P A I N

L I M E R I C K

D E A N S

S M I T H B R G

3 M I L E I

R A M A P O 5

H U N T E R T N

C N A S T O N E

P E A C H B T M

K E E N E Y

B R I G H T O N

W C H A P E L

C L V T C L F

C H A L K 5 0 0

B U R C H E S

8 P O S S U M

8 O X

8 C L I F T O N

8 L O U D O N

0 8 M D W B R K

8 M O R R S V L

8 M T S T M

8 V A L L E Y

8 D O O M S

8 B A T H C O

8 L E X N G T N

8 N O A N N A

8 L D Y S M T H

8 E L M O N T

8 M D L T H A N

8 C H C K A H M

8 C A R S O N

8 S E P T A

8 Y A D K I N

8 F E N T R E S

8 S U R R Y

8 P E R S O N8 M A Y O 1

8 P A R K W O D

8 W A K E

8 P L G R D N

8 C U M B E R L

8 R I C H M O N

8 M C G U I R E

8 J O C A S S E

8 B A D C R K

8 O C O N E E

8 N O R C R O S

8 B U L L S L U

8 B I G S H A

8 B O W E N

8 K L O N D I K

8 U N I O N C T

8 V I L L A R

8 W A N S L E Y

8 S N P

8 W B N P 1

8 R O A N E

8 B U L L R U

8 V O L U N T E

8 S U L L I V A

8 P H I P P B

0 5 N A G E L

8 W I L S O N

8 M O N T G O M

8 D A V I D S O

8 M A R S H A L

8 S H A W N E E

8 J V I L L E

8 W E A K L E Y

8 J A C K S O N

8 S H E L B Y

8 C O R D O V A

8 F R E E P O R

W M - E H V 8

8 U N I O N

8 T R I N I T Y

8 B F N P8 L I M E S T O

8 B N P 2

8 M A D I S O N8 B N P 1

8 W I D C R K

8 R A C C O O N

8 F R A N K L I

8 M A U R Y

8 M I L L E R

8 L O W N D E S

8 W P O I N T

M C A D A M 8

8 S . B E S S 8 S C H E R E R

8 A N T I O C H

8 C L O V E R

R O C K T A V

C O O P C 3 4 5R O S E T O N

F I S H K I L L

P L T V L L E Y

H U R L E Y 3

L E E D S 3

G I L B 3 4 5

F R A S R 3 4 5

N . S C O T 9 9

A L P S 3 4 5

R E Y N L D 3

E D I C

M A R C Y T 1

M A S S 7 6 5

O A K D L 3 4 5

W A T E R C 3 4 5

S T O L E 3 4 5

L A F A Y T T E

D E W I T T 3

E L B R I D G E

C L A Y

V O L N E Y

S C R I B A

J A P I T Z P9 M I P T 1I N D E P N D C

O S W E G O

P A N N E L L 3

R O C H 3 4 5

K I N T I 3 4 5

N I A G 3 4 5

B E C K A

B E C K B

N A N T I C O K

M I D D 8 0 8 6

M I L T O N

T R A F A L H 1

T R A F A L H 2

C L A I R V I L

H A W T H O R N

E S S A

B R U J B 5 6 1

B R U J B 5 6 9

B R U J B 5 6 2

L O N G W O O D

B a r r e t t

E . G . C .

V a l l e y S t r e a m

L a k e S u c c e s sR a i n e y

J a m a i c a

G r e e n w o o d

F o x H i l l s

F r e s h K i l l s

G o e t h a l s

C o g e n T e c hG o w a n u s

F a r r a g u t

E 1 5 t h S t .

W 4 9 t h S t .

T r e m o n t

S h o r e R d .

D u n w o o d i eS p r a i n B r o o k

E a s t v i e w

P l e a s a n t v i l l e

M i l l w o o d

B u c h a n a n

I n d i a n P o i n t

D v n p t . N K

H m p . H a r b o r

V e r n o n

C o r o n a

G r e e l a w n

E l w o o d

Southern to NYPP Line PTDFs

Color contour of PTDFs on 345 kV and up lines

PTDFskey

PTDF Implications on Market Power

• Once congestion is present on line, any power transfer with PTDF above 5% on congested line, in direction such that line loading would be increased, is not allowed

• Congestion on a single line can constrain many different directions

Nine bus example - Area I buying

• Table : Line G to F PTDF Values• Seller to Buyer PTDF for Line G to F• A to I 35%• B to I 29%• C to I 11%• D to I 5%• E to I -1%• F to I -20%• G to I 41%• H to I 21%

17%

58% 41%

51%

45% 42%

34%

6%

54%

29%

32%

A

G

B

C

D

E

I

F

H

400.0 MW 400.0 MW 300.0 MW

250.0 MW

250.0 MW

200.0 MW

250.0 MW

150.0 MW

50.0 MW

39%

Nine Bus Example

17%

58% 41%

51%

45% 42%

34%

6%

54%

29%

32%

A

G

B

C

D

E

I

F

H

400.0 MW 400.0 MW 300.0 MW

250.0 MW

250.0 MW

200.0 MW

250.0 MW

150.0 MW

50.0 MW

39%

If the line from G to F were congested,then area I could only buy from areas E, F or I.

When congestion is present, area I load only has possibility of buying from three suppliers. If we assume each supplier has 1/3 of the potential market, resultant HHI is 3333.

Strategic Market Power

• Characteristic that congestion can limit market size allows possibility that generator portfolio owner may unilaterally dispatch generator to deliberately induce congestion–this results in market power–allows charging of higher prices

• Ability to induce congestion depends on generator portfolio and transmission system loading

Portfolio Flow Control

• A portfolio of N generators may be redispatched to unilaterally control the flow on a particular line, i, by an amount

• where Sik is sensitivity of line i MW flow to change in generation at bus k

∑∑==

=∆∆=∆N

kgk

N

kgkiki PthatsuchPsP

11

0max

Portfolio Flow Control

• Once a line is congested, any generators with a PTDF to a particular load pocket that would increase loading on the congested line are prevented from selling to that market.

• Likewise affected loads are prevented from buying from the “blocked” generators.

Merged Areas F and G Blocking Line

22%

53% 30%

67%

100% 53%

39%

11%

73%

48%

31%

A

G

B

C

D

E

I

F

H

400.0 MW 400.0 MW 300.0 MW

250.0 MW

430.0 MW

200.0 MW

70.0 MW

150.0 MW

50.0 MW

21%

Generators F and G are deliberatelydispatched to congest line G to F

With G-Fcongestionarea I canonly buyfrom FG,or E

Cost to the Congestors

• Such a strategy of deliberate congestion could certainly involve additional costs to congestors (since they presumably would have to move away from an economic dispatch)

• Congestors need to balance costs versus benefits from higher prices

Integrating Economics into the Analysis

Maximize “Social Welfare”

Include the Power Flow Equations

Include Limits such as: * transmission line limits* bus voltage limits

( ) ( )

0d)s,g(x,0d)s,h(x,

sdds,x,

≤=s.t.

-max CB

• The first step to doing this is developing an optimal power flow

• Lagrange multipliers then used as spot-pricesBenefits Costs

Market Simulation Setup: Get away from “costs” and “benefits”

• Suppliers and Consumers will submit price-dependent generation and load bids–For given price, submit a generation or load level

Price = p[$/MWhr]

Demand Bid[MW]

Price = p[$/MWhr]

Supply Bid[MW]

pmin

pmax

ms

md

=dB∂∂

=sC∂∂

Market Simulation Setup

• Consumers and suppliers submit bid curves.• Using the bids, an OPF with the objective of

maximization of social welfare is solved–This will determine the MW dispatch as well as

Lagrange multipliers which will determine the spot price at each bus.

–The consumers and suppliers are paid a price according to their bid, but their bid will effect the amount at which they are dispatched.

Limit Possible Bids to Linear Functions

• Each supplier chooses some ratio above or below its true marginal cost function

Price = p[$/MWhr]

Supply Bid[MW]pmin

ms

k*pmin

msk

“True” Marginal Bid

“k times” the “True”Marginal Bid

What does an Individual Want to do? Maximize its Welfare

• Maximize An Individual’s Welfare–Individual may control multiple supplies and

multiple demands

–Note: An individual’s welfare is not explicitly a function of its bid (implicitly through s,d,λ)

∑∑ +−+−==

suppliescontrolled

demandscontrolledi

])([])([)λ( iiiiiiii ssCddB,,f λλds

+Benefits-Expenses

-Costs+Revenue

Determining a Best Response in this Market Structure

• A “Nested Optimization Problem”

( ) ( )

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

≤=

0d)s,g(x,0d)s,h(x,

kskdds

ds

ds,x,

k

s.t.

,-,maxby determined are )λ(s.t.

)λ(max

CB,,

,,f

The OPF Problem is a “constraint” now

Individual’s Welfare

s,d,λ are implicitfunctions of k

“OPF Sub-Problem”

Economic Market Equilibriums:The Nash Equilibrium

• Definition of a Nash Equilibrium–An individual looks at what its opponents are

presently doing–The individual’s best response to opponents

behavior is to continue its present behavior–This is true for ALL individuals in the market

• This is a Nash Equilibrium• Nash Equilibrium be found by iteratively

solving to individual welfare maximization

• Ci(si)=bsisi+csisi2 = supplier cost

• Bi(di)=bdidi+cdidi2 = consumer benefit

Example: Use 9-bus system and Assign Cost and Benefit Curves

BusSupplier bsiCoefficient

Supplier csiCoefficient

Consumer bdiCoefficient

Consumer cdiCoefficient

1 (A) 18 0.05 80 -0.102 (B) 18 0.05 80 -0.103 (C) 21 0.07 80 -0.104 (D) 21 0.07 80 -0.105 (E) 21 0.07 80 -0.106 (F) 21 0.07 80 -0.107 (G) 17 0.05 80 -0.108 (H) 0 0.10 440 -0.509 (I) 30 0.07 440 -0.50

Solution for All True Marginal Cost Bids

14%

46% 32%

42%

49% 36%

22%

3%

95% 14%

63%

A

G

B

C

D

E

I

F

H

286.4 MW 286.4 MW 183.2 MW

183.2 MW

296.4 MW

233.2 MW

183.2 MW 183.2 MW

118.9 MW

60%

1 2

3

7 65

8 9

393.4 MW

166.8 MW166.8 MW

393.4 MW

166.8 MW

166.8 MW

166.8 MW

166.8 MW166.8 MW

46.64 $/MWh 46.64 $/MWh

46.64 $/MWh 46.64 $/MWh 46.64 $/MWh

46.64 $/MWh

46.64 $/MWh

46.64 $/MWh 46.64 $/MWh4

Market Behavior

• Assume all consumers always submit bids corresponding to true marginal benefit (k=1)

• Assume supplier A-F and I all act alone to maximize their profit

• Assume suppliers G and H collude (or merge) together–G and H now make bid decisions together

What are General Strategies for G and H?

• G and H could act to raise their prices hoping to increase profit

• Also could act to take advantage of the transmission constraint between them–G lowers price hoping that overload on the line

between G-H will result in increased profit by H• Nash Equilibria are found for each of these

two general strategies by iteratively solving the individual welfare maximum

Nash Equilibrium Found When Both G and H raise prices

Bus Price[$/MWhr]

SupplierOutput [MW]

SupplierProfit [$/hr]

ConsumerDemand [MW]

ConsumerWelfare [$/hr]

A 48.51 275.8 4,612.36 157.4 2,478.55B 48.51 275.8 4,612.36 157.4 2,478.55C 48.51 183.0 2,690.69 157.4 2,478.55D 48.51 183.0 2,690.69 157.4 2,478.55E 48.51 183.0 2,690.69 157.4 2,478.55F 48.51 183.0 2,690.69 157.4 2,478.55G 48.51 262.1 4,824.89 157.4 2,478.55H 48.51 216.1 5,813.56 391.5 76,630.97I 48.51 123.1 1,218.26 391.5 76,630.97

Totals 1885.0 31,844.19 1885.0 170,611.81

• Combined profit for G and H of $10,638 $/hr

Nash Equilibrium Found G and H try to Game the Constraint

Bus Price[$/MWhr]

SupplierOutput [MW]

SupplierProfit [$/hr]

ConsumerDemand [MW]

ConsumerWelfare [$/hr]

A 47.08 241.9 4,108.89 164.6 2,709.01B 47.80 257.5 4,357.63 161.0 2,592.32C 49.95 192.4 2,978.58 150.3 2,257.62D 50.67 196.1 3,125.79 146.7 2,151.16E 51.38 198.3 3,272.70 143.1 2,047.09F 50.67 196.1 3,126.40 146.7 2,150.68G 46.36 295.9 4,310.76 168.2 2,828.57H 60.73 183.3 7,771.83 379.3 71,921.82I 54.29 84.0 1,546.03 385.7 74,387.47

Totals 1845.4 34,598.62 1845.4 163,045.74

• Combined profit for G and H of $12,082 $/hr

Contour Plot of Combined Profit of G and H when A-F,I bid k = 1.0

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.51.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Variation of Supply Bid G

Var

iatio

n of

Sup

ply

Bid

H

Contour Plot of Combined Profit of Supplier G and H

Local Max at (1.119, 1.119)

Global Max at (0.990, 1.644)

Constraint Boundary

3-D Plot of Combined Profitof G and H when A-F,I bid k = 1.0

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

11.11.21.31.41.51.61.71.88800

9000

9200

9400

9600

9800

10000

10200

10400

10600

Variation of Supply Bid G

Local Max of $10,018at (1.119, 1.119)

Global Max of $10,456 at (0.990, 1.644)

Variation of Supply Bid H

Com

bine

d P

rofit

of S

uppl

ier G

and

H

Constraint Boundary

Results

• G and H acting together can increase their profit by gaming around the transmission constraint

• Transmission Analysis MUST be included in Market Power Analysis

• Engineering Analysis and Economic Analysis can be integrated together

Conclusions

• Market power abuses in a large power system need to be assessed.

• Regulators need to be cognizant of ability of market participants to act strategically

• Portfolio owners need to be cognizant of their own, and their competitors potential for strategic behavior

Conclusions

• Rules of the game can make it more difficult to act strategically, but it would be difficult to eliminate possibility completely.

• Load’s ability to respond to market power is an important consideration.

• Slides and free 12 bus version of the PowerWorld Simulator software are available at www.powerworld.com