Electricity Transmission in Deregulated Markets: Challenges, Opportunities, and Necessary R&D Agenda
PRICING TRANSMISSION CONGESTION
IN ELECTRIC POWER NETWORKS
Chan S. Park, Jorge Valenzuela, Mark Halpin,
Sevin Sozer, and Pinar Kaymaz
Auburn University
December 15-16, 2004
Outline
I.
Introduction
II.
Approaches to Transmission Congestion
Pricing
III. Pricing Congestion under System
Stability Constraints
IV. Analysis and Economic Interpretations
V.
Conclusion
December 15-16, 2004
2
Introduction
ƒ In the PJM and NYISO markets, the cost of
moving power represents between 6 to 12% of
total electric costs.
ƒ Consider that the power traded in the US
wholesale market was over 800 TW-h in 2000
and rapidly increasing.
ƒ However, relatively little money has been put
into the transmission system.
December 15-16, 2004
3
Congestion Costs Statistics
Total Congestion Cost as a
Percent of the Total Electricity
Cost
$ Million
Total Congestion Costs
2000
2001
2002
2003
700
600
500
400
300
200
100
0
PJM
NYISO
14.0%
12.0%
10.0%
8.0%
6.0%
4.0%
2.0%
0.0%
2000
2001
2002
2003
PJM
CAISO
Sources: PJM State of the Market Report 2003, 2002
NYISO State of the Market Report 2003, 2002
CAISO Annual Report on Market Issues and Performance 2003, 2002
December 15-16, 2004
4
NYISO
CAISO
Research Issues
ƒ Objective: To include system’s stability in the
operation and economics of power systems
ƒ
ƒ
ƒ
How should the system’s stability be included in
the optimal dispatch model?
If modeled as a flowgate constraint, how should
the additional cost created by the flowgate
constraint be allocated?
Which congestion pricing schemes send more
appropriate economics signal for generation and
transmission expansion that will assure system’s
stability?
December 15-16, 2004
5
Modeling System’s Stability
ƒ Dynamic simulations suggest that proximity to
a stability limit may be predicted using
flowgates
ƒ Some companies presently manage system’s
stability using flowgates
ƒ Flowgates can be related to generator outputs
through Power Transfer Distribution Factors
⎞
⎛ N
k
⎜ PTDFi, j * Pk ⎟ ≤ Pflowgate, max
⎟
⎜
⎠
⎝ k =1
∑∑
i, j
December 15-16, 2004
6
Congestion-Pricing Approaches
Flat Rate
Marginal Cost
Market-based
• Uniform price
approach
• Marginal cost pricing
• Market finds its own
equilibrium.
• Used by preliberalized U.S.
Markets
• Used in restructured
U.S. markets
• Requires a wellestablished market
structure
• Based on full cost
recovery and
regulated return on
investment
• Based on optimum
power flow models,
nodal pricing, and
flow-based pricing
• Based on a coordinated
multilateral trading
model
• No proper locational
economic signals
• Appropriate locational
economic signals
• Appropriate locational
economic signals
December 15-16, 2004
7
Security-Stability Constrained OPF:
A Nodal Pricing Model
N
Min z =
∑
Minimize Total Generation Cost
ck g k
k =1
Subject to
Subject to
∑S
k ,ij
× f ij + g k = Lk
(λk )
Node balance equations for k = 1,…,N
ij
f ij − Yij * (θ i − θ j ) = 0
− f ijmax ≤ f ij ≤ f ijmax
Voltage/flow equations on each line i-j
(µ ij )
Thermal flow limits for all lines i-j
g kmin ≤ g k ≤ g kmax
Power capacities for each generator
∑
Security Constraint (Angular Stability )
ij∈FG
fij ≤ FG max
December 15-16, 2004
8
Security-Stability Constrained OPF
A Flow-based Pricing Model
N
Min z =
∑c
Minimize Total Generation Cost
k gk
k =1
Subject to
Subject to
N
N
∑ g −∑ L
k =1
k
k
k =1
N
−
f ijmax
≤
∑
=0
(λ )
Total balance equation
(µij )
PTDFijk (g k − Lk ) ≤ f ijmax
Thermal flow limits for all lines i-j
k =1
g kmin ≤ g k ≤ g kmax
N
∑ ∑ PTDF ( g
ij∈FG k =1
k
ij
k
Power capacities for each generator
− Lk ) ≤ FG max
LMPs are calculated by
( µ FG ) Security Constraint (Angular Stability)
LMPk = λ + ∑ ( PTDFijk × µij ) +
ij
December 15-16, 2004
9
∑ ( PTDF
ij∈FG
k
ij
× µ FG )
Congestion Cost Calculation
Nodal Pricing Model
ƒ Total congestion cost
Flow-based Pricing Model
ƒ Total Congestion cost
CR = ∑ ( LMPj − LMPi ) f ij
ij
CR = ∑ ( µij × f ij ) + µij × FG max
ij
ƒ Congestion cost allocated to
line ij
(
CRij = LMPj − LMPi
December 15-16, 2004
)f
ƒ Congestion cost allocated to
line ij
CRij = µij × f ij
ij
CRFG = µij × FG max
10
Nodal vs. Flow-based Model
Nodal Model
Flow-based Model
Generation
Expansion
Incentives
Provides correct incentives.
Provides correct incentives.
Transmission
Expansion
Incentives
Little incentive provided.
Correct signals available for
transmission investment.
Market
Experience
PJM (1998)
NY ISO (1999)
ISO-NE (2003)
CAISO (Zonal)
ERCOT (proposed flowgatezonal)
December 15-16, 2004
11
Numerical Example
55≤ g1≤110
300≤ g5≤600
$10/MWh
Bus 1 $14/MWh
Bus 5
L1 = 425MWh
Bus 2
Bus 4
Bus 3
L3 = 425MWh
December 15-16, 2004
100≤ g4≤200
130≤ g3≤520
$25/MWh
$30/MWh
12
L2 = 425MWh
Effects of the Stability
Constraint Alone
Assuming no flowgate and no thermal limits on the lines:
Bus 1
$30/MWh
Bus 5
$30/MWh
Bus 4
$30/MWh
December 15-16, 2004
Bus 3
$30/MWh
13
Bus 2
$30/MWh
Effects of the Stability
Constraint Alone
Assuming no thermal limits on the lines:
Flowgate Limit 670 MW
$20/MWh
Bus 5
$10/MWh
Bus 4
$10/MWh
December 15-16, 2004
Bus 3
$30/MWh
14
Bus 1
$30/MWh
Bus 2
$30/MWh
Effects of the Stability
Constraint Alone
Without FG
Total Revenue to Gen
$38,250
Total Production Cost $23,490
Net Income to Gen
$14,760
Congestion Cost
$0
Total Cost to Load
$38,250
With FG
$24,850
$24,590
$260
$13,400
$38,250
Redispacth Cost
-$13,400
$1,100
$0
ƒ Revenue to generators decreases significantly.
ƒ Total cost to load remains unchanged.
ƒ Although redispatch cost for the production cost is
$1,100, congestion cost is $13,400.
December 15-16, 2004
15
Allocation of Congestion Costs
Line
12
23
Flow-b. App
Nodal App.
$0
$0
$0
$0
54
43*
$0
$5,300
$0
$0
41*
$0
$2,550
51*
$0
$5,550
FG
$13,400
$0
Note that under the nodal congestion pricing scheme, no
congestion cost is ever assigned directly to the flowgate
constraint.
December 15-16, 2004
16
Effects of the Flowgate
Constraint Alone
Partition of the Total Cost to Load in terms of total generation revenues and
congestion costs when there are no thermal limits on the transmission lines.
$45,000
$40,000
Cong.
Cost
G5
$35,000
$30,000
$25,000
$20,000
G4
$15,000
$10,000
G3
$5,000
G1
$0
650 670 700 725 750 775 800 825 850 875 900
Flowgate Limit (MWh)
December 15-16, 2004
17
Effects of the Flowgate
Constraint with Thermal Limits
Flowgate Limit 670MW
Bus 5
Bus 1
Limit 240 MW
Bus 4
December 15-16, 2004
Bus 3
18
Bus 2
Allocating congestion costs
$6,000
1
5
Congestion Cost
$5,000
$4,000
4
3
2
$3,000
$2,000
$1,000
$0
Line
-$1,000
12
23
43*
54
41*
51*
FG
Flow-b. App.
$0.00
$0.00
$0.00
$5,208.5
$0.00
$0.00
$4,205.3
Nodal App.
$97.78 -$444.77 $1,392.0 $3,600.0 $336.57 $4,432.2
December 15-16, 2004
19
$0.00
Allocating Congestion Costs to
Transmission Lines
PTDF-based Allocation
ƒ Assumes equal flow sent from
generators.
ƒ Constant coefficients used every
time.
Flow-based Allocation
ƒ The price of the flowgate is used
to assign values by
CRij = p FG × f ij
(∀ij ∈ FG )
Flow-based Allocation
PTDF-based Allocation
Line
Flow
Cong. Cost
ΣPTDFij
Cong. Cost
43
278.40
$1,747.43
1.1177
$2,350.14
41
137.55
$863.37
0.3382
$711.12
51
254.04
670
$1,594.52
$4,205.32
0.5441
2.0000
$1,144.06
$4,205.32
Total
December 15-16, 2004
20
Comparison of the Congestion
Allocation Schemes
$6,000.00
1
5
$5,000.00
Congestion Cost
$4,000.00
4
3
$3,000.00
2
$2,000.00
$1,000.00
$0.00
-$1,000.00
Line
12
23
43*
54
41*
51*
Flow-b. Alloc.
$0.00
$0.00
$1,747.40
$5,208.51
$863.35
$1,594.51
PTDF-b. Alloc.
$0.00
$0.00
$2,350.14
$5,208.51
$711.12
$1,144.06
Nodal App.
$97.78
-$444.77
$1,392.02
$3,600.00
$336.57
$4,432.23
December 15-16, 2004
21
Comparison of Congestion Cost
Allocation Schemes
ƒ Nodal Approach
ƒ
ƒ
ƒ
Provides little incentive for transmission expansion. Prices can’t
give you which constraints are binding.
Assigns value to uncongested lines.
Does not assign a direct cost to the flowgate
ƒ Flow-based Approach
ƒ
ƒ
ƒ
ƒ
Assigns costs to only congested lines.
Assigns a cost to the flowgate.
Flow-based allocation uses flowgate price to assign congestion
due to stability to the lines.
PTDF-based allocation uses fixed coefficients to assign
congestion to flowgate lines but assumes equal dispatched flows
from generators.
December 15-16, 2004
22
Conclusion
ƒ This paper examined transmission congestion pricing
on power networks with flowgate-based stability
constraints.
ƒ The difference of these pricing models is the
allocation of the total congestion costs to the lines on
the network.
ƒ Effects of the stability constraint on the total cost of
generator dispatch, total cost to load, and total
congestion cost were analyzed.
December 15-16, 2004
23
Thank you!
Corresponding authors:
ƒ Chan S. Park (park@eng.auburn.edu)
ƒ Jorge Valenzuela (jvalenz@eng.auburn.edu)
December 15-16, 2004
24
Congestion Costs Reported
from ISOs
ƒ Transmission congestions and investment have become an emergent
problem.
600
517
500
430
391
400
$ Million
525
310
271
300
200
100
0
132
99 120
107
53
99 00 01 02
42
00 01
00 01 02
PJM
ISO-NE
Source: Lesieutre and Eto 2004
December 15-16, 2004
25
CAISO
00 01 02
NYISO
Optimum Dispatch Without any
Congestion
ƒ Optimum dispatch without the stability constraint
and without transmission thermal limits
No Flowgate limit
1
2
3
4
5
LMP
$30
$30
$30
$30
$30
Generation (MW)
110
0
365
200
600
1275
Total Production Cost
$1,540
$0
$10,950
$5,000
$6,000
$23,490
Total Revenue to Gen
$3,300
$0
$10,950
$6,000
$18,000
$38,250
Net Income to Gen
$1,760
$0
$0
$1,000
$12,000
$14,760
425
425
425
0
0
1275
$12,750
$12,750
$38,250
MW
$0
Gen
Redisp.
$0
FGR Price
$12,750
Tot FG
Cong.
Cong. Cost
$0
0
$0
$0
$0
Load (MW)
Total Cost to Load
December 15-16, 2004
26
Total
Optimum Dispatch with Stability
Constraint
ƒ Optimum dispatch with the stability constraint and
without transmission thermal limits
Flowgate limit 670
1
2
3
4
5
LMP
$30
$30
$30
$10
Generation (MW)
110
0
495
$10
(1)
100
570
1275
Total Production Cost
$1,540
$0
$14,850
$2,500
$5,700
$24,590
Total Revenue to Gen
$3,300
$0
$14,850
$5,700
$24,850
Net Income to Gen
$1,760
$0
$0
$1,000
(1)
-$1,500
$0
$260
425
425
425
0
0
1275
$12,750
$12,750
$38,250
MW
$0
Gen
Redisp.
$0
FGR Price
$12,750
Tot FG
Cong.
Cong. Cost
$20
670
$13,400
$1,100
$13,400
Load (MW)
Total Cost to Load
(1)
Minimum generation for generator 4 is 100MW.
December 15-16, 2004
27
Total
Allocating congestion costs due
to stability constraint
Allocation of congestion costs under flow-based and nodal approaches in the
case of optimum dispatch with thermal limit on line 54 (= 240MW) and with
flowgate limit (= 670MW)
Flow-based Approach
Nodal Approach
Line
Flow
FGR
12
76.60
$0.00
$0.00
$1.28
$97.78
23
-348.40
$0.00
$0.00
$1.28
-$444.77
*
278.40
$0.00
$0.00
$5.00
$1,392.02
240.00
$21.70
$5,208.51
$15.00
$3,600.00
*
137.55
$0.00
$0.00
$2.45
$336.57
*
254.04
$0.00
$0.00
$17.45
$4,432.23
670.00
$6.28
$4,205.32
$0.00
$0.00
43
54
41
51
FG
Total
Cong. CostLMPj-LMP Cong. Cost
$9,413.83
$9,413.83
Significant differences exist in allocating the congestion costs.
December 15-16, 2004
28
Total Production Cost
$27,000
Total Generation Cost
$26,500
$26,000
$25,500
$25,000
$24,500
$24,000
$23,500
$23,000
650
700
750
800
850
Flowgate (M W)
No limit
December 15-16, 2004
Limit on 54
Limit on 51
29
Limit on 12
900
Total Congestion Cost
$16,000
$14,000
Congestion Cost
$12,000
$10,000
$8,000
$6,000
$4,000
$2,000
$0
650
700
Nolimit
December 15-16, 2004
750
800
Flowgate (M W)
Limit on 54
Limit on 51
30
850
Limit on12
900
Total Dispatch Cost
$40,000
$38,000
Total Dispatch Cost
$36,000
$34,000
$32,000
$30,000
$28,000
$26,000
$24,000
$22,000
650
700
750
800
850
Flowgate Limit (MW)
Nolimit
December 15-16, 2004
Limit on 54
31
Limit on 51
Limit on 12
900
Changes in LMPs with Different
Transmission Thermal Limits
Limit on 54
No limit
$35
LMP
LMP
$35
$25
$15
$5
Node 1
2
3
4
$25
$15
$5
Node 1
5
Limit on 51
LMP
LMP
4
5
4
5
$35
$25
$15
2
3
4
$25
$15
$5
Node 1
5
Flowgate Limit 670MW
December 15-16, 2004
3
Limit on 12
$35
$5
Node 1
2
32
2
3