Market Power Evaluation in Power Systems with Congestion

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Transcript Market Power Evaluation in Power Systems with Congestion

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%
99.5 MW
Rest of
Electric
System
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%
Rest of
Electric
System
Limit = 100 MVA
300.0 MW
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
400.0 MW
A
400.0 MW
Pie charts
show
percentage
loading
on lines
300.0 MW
B
D
250.0 MW
C
F
G
250.0 MW
250.0 MW
150.0 MW
39%
I
H
200.0 MW
50.0 MW
E
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
44%
A
D
B
10%
30%
56%
C
13%
10%
20%
G
35%
F
2%
E
34%
34%
32%
H
34%
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
6%
A
D
B
6%
18%
6%
C
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%
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
21%
MGE
DPC
ALTE
20%
15%
WEP
ALTW
DECO
14%
CONS
PENELEC
7%
PP&L
9%
MEC
NI
17%
AEP
38%
6%
CWLP
8%
PEPCO
DPL
5%
5%
INDN
VP
SIPC
KACP
LGEE
MEC
19%
AMRN
OPPD
AE
19%
OVEC
IMPA
KACY
JCP&L
METED
12%
CIN
HE
11%
5%
BG&E
IP
STJO
6%
PECO
24%
IPL
CILCO
16%
11%
6%
5%
DPL
7%
PJM500
DLCO
8%
NIPS
PSE&G
5%
FE
14%
MPW
32%
SIGE
NPPD
BREC
13%
EKPC
MIPU
9%
WERE
6%
EEI
23%
ASEC
7%
SPRM
DOE
YADKIN
EMDE
CPLE
KAMO
GRRD
15%
6%
TVA
DUKE
CPLW
7%
SWPA
PSOK
45%
22%
HARTWELL
ENTR
OMPA
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
HAWTHORN
MASS 765
PTDFs
key
ESSA
BRUJB561
BRUJB569
BRUJB562
INDEPNDC
9MI PT1 JA PITZP
CLAIRVIL
OSWEGO
SCRIBA
MARCY T1
VOLNEY
MILTON
EDIC
TRAFALH2
TRAFALH1
CLAY
KINTI345
DEWITT 3
ELBRIDGE
BECK B
LAFAYTTE
PANNELL3
REYNLD3
ROCH 345
NIAG 345
ALPS345
BECK A
N.SCOT99
MIDD8086
STOLE345
GILB 345
NANTICOK
LEEDS 3
LONGWOOD
FRASR345
OAKDL345
HURLEY 3
WATERC345
PLTVLLEY
FISHKILL
ROSETON
COOPC345
ROCK TAV
Indian Point
Buchanan
Millwood
Pleasantville
Eastview
RAMAPO 5
Port Jefferson
Sprain Brook
Northport
Dvnpt. NK
Elwood
Greelawn
Tremont
Hmp. Harbor Syosset
Pilgrim
Shore Rd.Lcst. Grv.
Bethpage
Rainey
Lake Success Newbridge
Ruland Rd.
W 49th St.
Corona E.G.C.
E 15th St.
FarragutVernon Jamaica
Cogen Gowanus
Tech
Valley Stream
Barrett
Greenwood
Dunwoodie
SUSQHANA
SUNBURY
Holbrook
Holtsville
Shoreham
Wildwood
Riverhead
Brookhaven
Goethals
Fresh Kills
Fox Hills
WESCOVLE
BRANCHBG
ALBURTIS
KEYSTONE
HOSENSAK
DEANS
SMITHBRG
ELROY
JUNIATA
LIMERICK
WHITPAIN
CONEM-GH
3 MILE I
01YUKON
HUNTERTN
PEACHBTM
KEENEY
CNASTONE
BRIGHTON
W CHAPEL
8MT STM
08MDWBRK
8LOUDON
8CLIFTON
8OX
8POSSUM
BURCHES
CHALK500
CLVT CLF
8MORRSVL
07MEROM5
8VALLEY
8DOOMS
8NO ANNA
8BATH CO
8LDYSMTH
8ELMONT
8LEXNGTN
8MDLTHAN
8CHCKAHM
8SURRY
8CARSON
8SEPTA
8YADKIN
8CLOVER
8FENTRES
8ANTIOCH
8SHAWNEE
8MARSHAL
8PERSON
05NAGEL
8MAYO 1
8PHIPP B
8SULLIVA
8MONTGOM
8PARKWOD
8PL GRDN
8VOLUNTE
8WILSON
8WEAKLEY
8WAKE
8BULL RU
8ROANE
8JVILLE
8DAVIDSO
8MAURY
8MCGUIRE
8WBNP 1
8JACKSON
8FRANKLI
8CUMBERL
8SNP
8SHELBY
8RICHMON
8RACCOON
8JOCASSE
8CORDOVA
8BAD CRK
8WID CRK
WM-EHV 8
8MADISON
8FREEPOR
8OCONEE
8BNP 1
8BNP 2
8LIMESTO
8BFNP
8TRINITY
8UNION
8BOWEN
8BIG SHA
8BULLSLU
8NORCROS
8VILLA R
8KLONDIK
8UNIONCT
8MILLER
8W POINT
8WANSLEY
8LOWNDES
8S. BESS
8SCHERER
MCADAM 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%
11%
5%
-1%
-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
F
250.0 MW
150.0 MW
39%
I
50.0 MW
E
Nine Bus Example
400.0 MW
A
400.0 MW
300.0 MW
B
D
250.0 MW
C
F
G
250.0 MW
250.0 MW
150.0 MW
E
If the line from G to
F were congested,
then area I could
only buy from areas
E, F or I.
39%
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
A
400.0 MW
300.0 MW
B
D
250.0 MW
C
100%
F
G
430.0 MW
H
200.0 MW
70.0 MW
150.0 MW
21%
I
50.0 MW
Generators F and G are deliberately
dispatched to congest line G to F
E
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
max
x,s,d
s.t.
Costs
Maximize “Social Welfare”
h(x, s,d)  0
g(x, s,d)  0
Include the
Power Flow Equations
Bd  - C s 
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 )  l d ]  [C (s )  l s ]
i
i controlled
demands
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,l)
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 determinedby
k
 max
 x,s,d

 s.t.

Bd, k  - C s, k 

h(x, s,d)  0 
g(x, s,d)  0 
“OPF Sub-Problem”
s,d,l 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
286.4 MW
166.8 MW
286.4 MW
46.64 $/MWh
1
A
166.8 MW
183.2 MW
46.64 $/MWh
2
183.2 MW
B
166.8 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%
F
6 46.64 $/MWh
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
60%
46.64 $/MWh
8
393.4 MW
166.8 MW
63%
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
3-D Plot of Combined Profit
of G and H when A-F,I bid k = 1.0
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