Market Power Evaluation in
Power Systems with Congestion
Tom Overbye, George Gross, Peter Sauer
Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
Urbana, IL
Mark Laufenberg, Jamie Weber
PowerWorld 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 selfinflicted 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
N
HHI = ∑ q
i =1
2
i
• where N is number of participants
• qi is percentage market share
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
100%
Rest of
Electric
System
99.5 MW
Bus A
300.0 MW
200.50 MW
100 MVA limit on line limits
bus A imports to 100 MVA
Models the
remainder
of the
electrical
system
Networked System
Limit = 100 MVA
25.0 MW
100.0 MW
Bus A
175.00 MW
25%
100%
Limit = 100 MVA
300.0 MW
Rest of
Electric
System
Analysis is
substantially
more complex.
Transfer
capability
into bus A
is NOT equal
to sum of
tie-line limits
Three Bus Networked Example
Imports = 74 MW
Bus B
99.6 MW
100%
324.0 MW
25.7 MW
224.4 MW
26%
Bus A
50.0 MW
23%
226.00 MW
300.0 MW
300.0 MW
Bus C
25 MWs of power is wheeling through bus A
In this
example the
allowable
interchange
is less than
limit 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
40 0.0 M W
4 00. 0 M W
A
Pie charts
show
percentage
loading
on lines
30 0.0 MW
B
D
2 50. 0 M W
17%
C
58%
34%
51%
41%
42%
45%
6%
F
G
E
1 50 .0 MW
2 50. 0 M W
250 .0 MW
54%
32%
39%
29%
I
H
200 .0 MW
50 .0 MW
Figure
shows
base case
flows
Each area contains one bus/one 500 MVA generator.
Each line has 200 MVA limits. HHI = 1089
PTDF Values for A to I Direction
A
44%
D
B
10%
30%
C
56%
13%
10%
20%
G
35%
F
2%
E
34%
34%
32%
H
34%
I
Pie charts now show the percentage PTDF
value; arrows show the direction.
PTDF show
the incremental
impact on
line flows, in
this case for
a transfer from
area A to area
I.
PTDF Values for G to F Direction
A
6%
D
B
6%
18%
C
6%
12%
6%
12%
G
61%
F
19%
E
21%
H
20%
21%
Note that
for both the
A to I and
the G to F
directions
almost all
PTDFs are
above 5%
I
Example: For 200 MW transfer from G to F, line
H to I MW flow will increase by 200*21%=42MW
Large Case PTDF Example:
Direction Southern to NYPP
WPS
NEPOOL
NSP
NYPP
24%
SMP
ONT HYDR
OTP
MGE
DPC
21%
ALTE
20%
15%
WEP
32%
DECO
ALTW
14%
CONS
PENELEC
7%
PP&L
9%
MEC
NI
14%
17%
NIPS
38%
JCP&L
METED
AE
BG&E
8%
6%
A
CIN
P
12%
PEPCO
HE
IP
DPL
STJO
19%
OVEC
IMPA
KACY
11%
PECO
24%
CWLP
6% 5%
AEP
IPL
CILCO
16%
11%
6%
5%
DPL
7%
PJM500
DLCO
8%
MPW
PSE&G
5%
FE
5%
5%
INDN
VP
SIPC
KACP
LGEE
MEC
19%
AMRN
SIGE
NPPD
13%
BREC
EKPC
MIPU
9%
6%
EEI
23%
ASEC
7%
SPRM
DOE
YADKIN
EMDE
CPLE
KAMO
15%
GRRD
6%
TVA
DUKE
CPLW
7%
SWPA
45%
22%
HARTWELL
ENTR
MPA
SCPSA
SEPA-RBR
9%
SOUTHERN
9%
SCE&G
SEPA-JST
AEC
SWEP
LEPA
Figure shows the area to area interface PTDFs
Pie
charts
show
percentage
PTDF on
interface
Southern to NYPP Line PTDFs
H A W T H O R N
M A S S
7 6 5
PTDFs
key
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
J A
C L A I R V I L
I N D E P N D
9 C
M I
P I T Z P
P T 1
O S W E G O
S C R I B A
M A R C Y
T 1
V O L N E Y
M I L T O N
E D I C
T R A F A L H 2
C L A Y
T R A F A L H 1
K I N T I 3 4 5
D E W I T T
3
E L B R I D G E
L A F A Y T T E
P A N N E L L 3
B E C K
B
B E C K
A
R O C H
N I A G
R E Y N L D 3
3 4 5
3 4 5
A L P S 3 4 5
N . S C O T 9 9
M I D D 8 0 8 6
S T O L E 3 4 5
G I L B
3 4 5
N A N T I C O K
L E E D S
3
L O N G W O O D
F R A S R 3 4 5
O A K D L 3 4 5
H U R L E Y
3
W A T E R C 3 4 5
P L T V L L E Y
F I S H K I L L
R O S E T O N
C O O P C 3 4 5
I n d i a n
R O C K
P o i n t
T A V
B u c h a n a n
M i l l w o o d
P l e a s a n t v i l l e
E a s t v i e w
R A M A P O
5
S h o r e h a m
P o r t
S p r a i n
J e f f e r s o n
W i l d w o o d
R i v e r h e a d
B r o o k
D u n w o o d i e
N o r t h p o r t
B r o o k h a v e n
E K
l w o o d
N
D v n p t .
H o l b r o o k
G r e e l a w n
H m p .
T r e m o n t
H a r b o r
S y o s s e t
P i l g r i m
H o l t s v i l l e
S U S Q H A N A
S h o r e
R d .
L c s t .
G r v .
B e t h p a g e
R a i n e y
L a k e
W
4 9 t h
S u c c e s s
S t .
R u l a n d
R d .
N e w b r i d g e
E . G . C .
C o r o n a
E
1 5 t h
S t .
J a m a i c a
F a r r a g u t V e r n o n
C o g e n
T e c h
G o w a n u s
V a l l e y
S t r e a m
B a r r e t t
S U N B U R Y
G r e e n w o o d
G o e t h a l s
F r e s h
K i l l s
F o x
H i l l s
W E S C O V L E
B R A N C H B G
A L B U R T I S
H O S E N S A K
K E Y S T O N E
D E A N S
S M I T H B R G
E L R O Y
J U N I A T A
L I M E R I C K
W H I T P A I N
C O N E M - G H
3
M I L E
I
0 1 Y U K O N
H U N T E R T N
P E A C H B T M
K E E N E Y
C N A S T O N E
B R I G H T O N
W
8 M T
C H A P E L
S T M
0 8 M D W B R K
8 L O U D O N
8 C L I F T O N
B U R C H E S
8 O X
C H A L K 5 0 0
8 P O S S U M
C L V T
C L F
8 M O R R S V L
0 7 M E R O M 5
8 V A L L E Y
8 D O O M S
8 L D Y S M T H
8 N O
8 B A T H
A N N A
C O
8 E L M O N T
8 L E X N G T N
8 M D L T H A N
8 C H C K A H M
8 S U R R Y
8 S E P T A
8 C A R S O N
8 Y A D K I N
8 F E N T R E S
8 C L O V E R
8 A N T I O C H
8 S H A W N E E
8 M A Y O
8 M A R S H A L
1
8 P E R S O N
0 5 N A G E L
8 P H I P P
B
8 S U L L I V A
8 M O N T G O M
8 P A R K W O D
8 P L
G R D N
8 V O L U N T E
8 W A K E
8 W I L S O N
8 B U L L
R U
8 W E A K L E Y
8 R O A N E
8 D A V I D S O
8 J V I L L E
8 M A U R Y
8 M C G U I R E
8 W B N P
1
8 J A C K S O N
8 F R A N K L I
8 C U M B E R L
8 S N P
8 S H E L B Y
8 R I C H M O N
8 R A C C O O N
8 J O C A S S E
8 C O R D O V A
8 B A D
8 W I D
W M - E H V
C R K
C R K
8 O C O N E E
8
8 B N P
1
8 M A D I S O N
8 F R E E P O R
8 B N P
2
8 L I M E S T O
8 B F N P
8 T R I N I T Y
8 U N I O N
8 B O W E N
8 B U L L S L U
8 B I G
S H A
8 N O R C R O S
8 V I L L A
R
8 K L O N D I K
8 U N I O N C T
8 M I L L E R
8 W
P O I N T
8 W A N S L E Y
8 L O W N D E S
8 S .
M C A D A M
B E S S
8 S C H E R E R
8
Color contour of PTDFs on 345 kV and up lines
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
A to I
B to I
C to I
D to I
E to I
F to I
G to I
H to I
PTDF for Line G to F
35%
29%
17%
11%
58%
41%
5%
45%
-1%
54%
-20%
41%
21%
400.0 MW
A
400.0 MW
300.0 MW
B
G
250.0 MW
H
200.0 MW
D
250.0 MW
C
34%
51%
42%
6%
F
E
150.0 MW
250.0 MW
32%
39%
29%
I
50.0 MW
Nine Bus Example
400.0 MW
400.0 MW
A
300.0 MW
B
D
250.0 MW
17%
C
58%
34%
51%
41%
42%
45%
6%
F
G
E
150.0 MW
250.0 MW
250.0 MW
54%
If the line from G to
F were congested,
then area I could
only buy from areas
E, F or I.
32%
39%
29%
I
H
200.0 MW
50.0 MW
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
N
∆Pi = max ∑ sik ∆Pgk
N
such that
k =1
∑ ∆P
k =1
gk
=0
• where Sik is sensitivity of line i MW flow to
change in generation at bus k
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
400.0 MW
400.0 MW
A
300.0 MW
B
D
250.0 MW
22%
C
53%
39%
67%
30%
53%
100%
11%
F
G
E
150.0 MW
430.0 MW
70.0 MW
73%
31%
21%
48%
H
200.0 MW
I
50.0 MW
Generators F and G are deliberately
dispatched to congest line G to F
With G-F
congestion
area I can
only buy
from 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
• The first step to doing this is developing an
•
optimal power flow
Lagrange multipliers then used as spot-prices
Benefits
Costs
max B(d ) - C (s )
x,s,d
s.t.
h(x, s, d) = 0
g(x, s, d) ≤ 0
Maximize “Social Welfare”
Include the
Power Flow Equations
Include Limits such as:
* transmission line limits
* bus voltage limits
Market Simulation Setup: Get
away from “costs” and “benefits”
• Suppliers and Consumers will submit pricedependent generation and load bids
– For given price, submit a generation or load level
∂B
Price = p =
[$/MWhr] ∂d
Price = p = ∂C
[$/MWhr] ∂s
pmax
md
ms
pmin
Supply Bid
[MW]
Demand Bid
[MW]
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]
“k times” the “True”
Marginal Bid
ms
k
ms
pmin k*pmin
“True” Marginal Bid
Supply Bid
[MW]
What does an Individual Want to
do? Maximize its Welfare
• Maximize An Individual’s Welfare
– Individual may control multiple supplies and
multiple demands
f (s,d,λ ) =
∑ [ B ( d ) − λ d ] + ∑ [ −C ( s ) + λ s ]
i =controlled
demands
i
i
i
i
i
i
i i
controlled
supplies
+Benefits
-Costs
-Expenses
+Revenue
– Note: An individual’s welfare is not explicitly a
function of its bid (implicitly through s,d,λ)
Determining a Best Response in
this Market Structure
• A “Nested Optimization Problem”
Individual’s Welfare
max
f (s,d,λ )
s.t.
(s,d,λ ) are determined by
k
B(d, k ) - C (s, k )⎞
⎛ max
x,
s,
d
⎜
⎟
h(x, s, d) = 0 ⎟
⎜
⎜ s.t.
⎟
g(x,
s,
d)
≤
0
⎝
⎠
“OPF Sub-Problem”
s,d,λ are implicit
functions of k
The OPF Problem is
a “constraint” now
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
Example: Use 9-bus system and
Assign Cost and Benefit Curves
• Ci(si)=bsisi+csisi2 = supplier cost
• Bi(di)=bdidi+cdidi2 = consumer benefit
Bus
1 (A)
2 (B)
3 (C)
4 (D)
5 (E)
6 (F)
7 (G)
8 (H)
9 (I)
Supplier bsi
Coefficient
18
18
21
21
21
21
17
0
30
Supplier csi
Coefficient
0.05
0.05
0.07
0.07
0.07
0.07
0.05
0.10
0.07
Consumer bdi
Coefficient
80
80
80
80
80
80
80
440
440
Consumer cdi
Coefficient
-0.10
-0.10
-0.10
-0.10
-0.10
-0.10
-0.10
-0.50
-0.50
Solution for All True Marginal
Cost Bids
166.8 MW
286.4 MW
286.4 MW
46.64 $/MWh
1
A
166.8 MW
46.64 $/MWh
2
183.2 MW
B
166.8 MW
183.2 MW
46.64 $/MWh
4
D
166.8 MW
14%
46.64 $/MWh
3
C
46%
42%
32%
22%
36%
49%
46.64 $/MWh
7
G
3%
6 46.64 $/MWh
F
46.64 $/MWh
5
E
166.8 MW
296.4 MW
183.2 MW
166.8 MW
95%
H
233.2 MW
183.2 MW
63%
60%
46.64 $/MWh
8
393.4 MW
166.8 MW
14%
I
118.9 MW
46.64 $/MWh
9
393.4 MW
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
• Combined profit for G and H of $10,638 $/hr
Bus
Price
Supplier
Supplier
Consumer
[$/MWhr] Output [MW] Profit [$/hr] Demand [MW]
A
48.51
275.8
4,612.36
157.4
B
48.51
275.8
4,612.36
157.4
C
48.51
183.0
2,690.69
157.4
D
48.51
183.0
2,690.69
157.4
E
48.51
183.0
2,690.69
157.4
F
48.51
183.0
2,690.69
157.4
G
48.51
262.1
157.4
4,824.89
H
48.51
216.1
391.5
5,813.56
I
48.51
123.1
1,218.26
391.5
Totals
1885.0
31,844.19
1885.0
Consumer
Welfare [$/hr]
2,478.55
2,478.55
2,478.55
2,478.55
2,478.55
2,478.55
2,478.55
76,630.97
76,630.97
170,611.81
Nash Equilibrium Found G and H
try to Game the Constraint
• Combined profit for G and H of $12,082 $/hr
Bus
Price
Supplier
Supplier
Consumer
[$/MWhr] Output [MW] Profit [$/hr] Demand [MW]
A
47.08
241.9
4,108.89
164.6
B
47.80
257.5
4,357.63
161.0
C
49.95
192.4
2,978.58
150.3
D
50.67
196.1
3,125.79
146.7
E
51.38
198.3
3,272.70
143.1
F
50.67
196.1
3,126.40
146.7
G
46.36
295.9
168.2
4,310.76
H
60.73
183.3
379.3
7,771.83
I
54.29
84.0
1,546.03
385.7
Totals
1845.4
34,598.62
1845.4
Consumer
Welfare [$/hr]
2,709.01
2,592.32
2,257.62
2,151.16
2,047.09
2,150.68
2,828.57
71,921.82
74,387.47
163,045.74
Contour Plot of Combined Profit
of G and H when A-F,I bid k = 1.0
1.8
Contour Plot of Combined Profit of Supplier G and H
1.7
Global Max at (0.990, 1.644)
Variation of Supply Bid H
1.6
1.5
1.4
1.3
Constraint Boundary
1.2
Local Max at (1.119, 1.119)
1.1
1.0
0.8
0.9
1.0
1.1
1.2
Variation of Supply Bid G
1.3
1.4
1.5
3-D Plot of Combined Profit
of G and H when A-F,I bid k = 1.0
Combined Profit of Supplier G and H
10600
Global Max of $10,456 at (0.990, 1.644)
10400
10200
Local Max of $10,018
at (1.119, 1.119)
10000
9800
Constraint Boundary
9600
9400
9200
9000
8800
1.8
1.7
1.6
1.5
1.4
1.3
1.2
Variation of Supply Bid H
1.1
1
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Variation of Supply Bid G
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