Transcript THE USE AND MISUSE OF OPF IN COMPETITIVE MARKET …

THE USES AND MISUSES OF
OPF IN CONGESTION
MANAGEMENT
presentation by
George Gross
University of Illinois at Urbana-Champaign
Seminar “Electric Utilities Restructuring”
Institut d’Electricité Montefiore
Université de Liège
December 8, 1999
© Copyright George Gross, 1999
OUTLINE
 Review of OPF applications in the vertically integrated
utility environment
 Review of congestion management in the two paradigms
of unbundled market structures
Pool based
Bilateral Trading
 OPF application to competitive markets
 Role of the central decision making authority and impacts
on generators
THE BASIC OPF PROBLEM
 Nature: optimization of the static power systems for a
fixed point in time
 Objective: optimization of a specified metric (e.g. loss
minimization,
production
cost
minimization,
ATC
maximization)
 Constraints:
all
physical,
operational
and
policy
limitations for the generation and delivery of electricity
in a bulk power system
 Decision:
optimal policy for selected objective
and
associated sensitivity information with direct economic
interpretation
OPF PROBLEM CHARACTERISTICS
 Nonlinear model of the static power system
 Representation of constraints
 Representation of contingencies
 Incorporation of relevant economic information
 Central decision making authority determines optimal
policy
OPF PROBLEM FORMULATION
min f ( u, x )
s.t. g ( u, x )  0
h( u, x )  0
u = vector of m control variables
x = vector of n state variables
f :  m x  n   is the objective function
g :  m x  n   n is the equality constraints function
h :  m x  n   q is the inequality constraints function
ECONOMIC SIGNALS IN THE OPF SOLUTION
 For
equality
constraints
the
dual
variables
are
interpreted as the nodal real power or nodal reactive
power prices at each bus
 For inequality constraints the dual variables are
interpreted as the sensitivity of the objective function
to a change in the constraint limit
MARKET STRUCTURE PARADIGMS
Pool model
Bilateral model
THE POOL MODEL
 The Pool is the sole buyer and seller of electricity
 The Pool uses the offers of the suppliers and the bids
of the demanders to determine the set of successful
bidders whose offers and bids are accepted
 The Pool determines the “optimum” by solving a
centralized economic dispatch model taking into
account the network constraints
THE POOL MODEL
Seller 1
...
MWh
$
...
Seller i
MWh
Seller M
MWh
$
$
POOL
MWh
MWh
$
$
Buyer 1
...
MWh
Buyer j
...
$
Buyer
Buyer N
N
CONGESTION MANAGEMENT
IN THE POOL MODEL
The Pool model considers explicitly the impacts of the
transmission network constraints
The Pool model assumes implicitly the commitment of
generators which are bidding to supply power
The determination of the economic optimum is done
with the explicit consideration of congestion
THE BILATERAL TRADING MODEL
Players arrange the purchase and sale transactions
among themselves
Each
schedule coordinator (SC) and each power
exchange
(PX)
are
responsible
for
ensuring
supply/demand balance
The independent system operator (ISO) has the role to
facilitate
the
undertaking
of
as
many
of
the
contemplated transactions as possible subject to
ensuring
that
no
system
constraints are violated
security
and
physical
BILATERAL TRADING
ESP
Load
aggregator
End user
D I S T R I B U T I O N (W I R E S)
IGO
Ancillary
Services
Market
Power
Exchange
G
G
G
G
G
G
...
G
G
Scheduling
Coordinator
G
G
G
G
G
G
...
G
G
G
G
G
G
G
G
...
G
G
BILATERAL TRADING
CONGESTION MANAGEMENT
If all contemplated transactions can be undertaken
without causing any limit violations under postulated
contingencies, the system is judged to be capable of
accommodating these transactions and no CM is
needed
On the other hand, the presence of any violation
causes transmission congestion and steps must be
taken by the IGO to re-dispatch the system to remove
the congestion
BILATERAL TRADING MODEL
CONGESTION MANAGEMENT
 Objective function: re-dispatch costs
 Decision variables are incremental / decremental
adjustments to the generator outputs and decremental
adjustments to the loads
 Constraints
 transmission constraints
 maximum/minimum incremental/decremental
amounts bid
OPF solution: optimal re-dispatch in generation/load
increment/decrement at participating buses
ROLE OF OPF IN THE OLD REGIME
 The OPF was originally developed for the vertically
integrated utility (VIU) structure
 In the VIU, the central decision maker is the utility that
operates and controls the generation and transmission
plants and has the obligation to serve load
 The OPF solution makes sense in the VIU environment
KEY DIFFERENCES IN THE ROLE OF OPF IN
THE POOL MODEL
 The decision maker and the players are no longer the
same entity
 The cost is the price that the Pool has to pay to
competitive supply resources
 The demand at each bus may be a decision variable
and as such is not fixed
 The demand is expressed in the terms of willingness
to pay
 The objective is maximize benefits minus costs
OPF STRUCTURAL CHARACTERISTICS
 The “flatness” of solution
x1
x2
 f(x1 ) - f(x2 )  < 
 there exists a continuum of “optimum”
solutions which results in effectively the same
cost within a specified  tolerance
 the choice of an optimum solution has a great
degree of arbitrariness
OPF STRUCTURAL CHARACTERISTICS
 Different solution approaches can lead to different optima
 Sensitivity of the solution to the initial point point:
different initial points can lead to solutions that are
equally “good”
 Solution may be proved to be unique only if the objective
function is convex; in case of multiple minimum solutions
OPF can fail in finding the “true” solution
 Solution may not exist
IMPLICATIONS UNDER DIFFERENT MARKET
STRUCTURE
 In VIU one may favor one generating unit or another
but all units are owned by the same entity and so it is
purely an internal problem
 In competitive markets bias for or against a given
generator may result in the generator’s success or
failure
IMPLICATIONS
 Different optima correspond to different dual variables
nodal prices may be widely different even when the
“optimal’ solutions are close
market signals may not be reliable
DISCRETION OF CENTRAL AUTHORITY
 The central decision-making authority has many
degrees of freedom in specifying the OPF model
 The definition of the model has a deep impact on
the optimum and on the dual variables.
 The major areas under the discretion of the
central authority include:
the inclusion/exclusion of specific constraints
the definition of the set of contingency to be
applied
algorithm choice and parameters
DISCRETION OF CENTRAL AUTHORITY
dual
variables
hconstraint
n
set
yes
IGO
contingency
set
OPF
solution
feasible
algorithmic
details
no
NUMERICAL RESULTS OF OPF
APPLICATIONS TO POOL MODEL
 The objective is to maximize benefits minus costs
the loads are assumed to have fixed benefits
each generator submits a different price offer curve
in effect, the objective is to minimize generation
costs incurred by the Pool operator
 Numerical studies are used to study anomalous results
with OPF and the impacts of the discretion of the Pool
operator
ANOMALIES IN OPF RESULTS
 Power flows from a node with higher nodal price to a
node with a lower nodal price
 Nodal price differences between buses at ends of lines
without limit violations
IEEE 30-BUS TEST SYSTEM
8.20 MW
2.50 MVAR
21.70 MW
12.70 MVAR
2
1
30.00 MW 3
30.00 MVAR
2.40 MW
1.20 MVAR 7.60 MW
1.60 MVAR
15
6.20 MW
1.60 MVAR
14
18
3.20 MW
0.90 MVAR
19
9.50 MW
3.40 MVAR
4
28
8
7
6
9
11
3.50 MW
2.30 MVAR
11.20 MW
7.50 MVAR
22.80 MW
10.90 MVAR
27
3.50 MW
1.80 MVAR
10
20
5.80 MW
2.00 MVAR
22
8.70 MW
6.70 MVAR
21
17.50 MW
11.20 MVAR
29
2.40 MW
0.90 MVAR
24
2.20 MW
0.70 MVAR
23
3.20 MW
1.60 MVAR
10.60 MW
1.90 MVAR
30
13
9.00 MW
5.80 MVAR
17
16
26
25
12
5
EXAMPLES: OPF APPLICATION
 IEEE 30-bus system
 All line MVA limits are enforced
 Additional 8 MVA limit on line joining buses 15 and 23
 Unexpected results of OPF solution
power flows from higher to lower priced nodes
flows on lines without limit violation
OPF POWER FLOWS
l1=3.668
l2=3.694
1
l15=4.135
2
18
14
l 3=3.768
l28=4.542
15
3
l6=3.770
28
8
11
13
12
l10=3.938
l25=4.466
25
20
l24=3.961
l22=3.870
22
17
16
10
26
l19=4.106
l4=3.786
5
7
6
9
4
19
l 18=4.129
21
l21=3.988
23
24
27
29
30
congested lines
power flows from lower to higher nodal prices
power flows from higher to lower nodal prices
IEEE 30-bus system
with the standard line
flow limits and an 8
MVA flow limit on line
15-23
EXAMPLE: OPF APPLICATION
 Real power losses on lines are neglected
 Key focus: line flows on lines without limit violations
LINE FLOWS ON LINES WITHOUT LIMIT
VIOLATIONS
l2=3.489
2
1
15
18
14
l3=3.541 3
4
19
l4=3.550
28
8
7
6
9
5
11
l10=4.501
13
12
10
20
l22=3.975
26
25
22
17
16
23
21 l21=5.046
24
IEEE 30-bus system with
27
29
30
standard line flow limits
and an 8 MVA flow limit
congested lines
on line 15-23; real losses
power flows from lower to higher nodal prices neglected
power flows from higher to lower nodal prices
IMPACTS OF DISCRETION OF CENTRAL
AUTHORITY
 Nature of discretion
consideration of line flows limits
specification of different voltage profiles
 Illustration of the volatility of dual variables
impacts of nodal prices
allocation of generation levels among suppliers
EXAMPLE: LINE FLOWS LIMITS
 Base case: no line limits considered
 Case C1: limits of 20, 15 and 10 MVA on lines 1-2,
12-13 and 25-27, respectively
 Case C2: limits of 20, 20 and 8 MVA on lines 1-3,
21-22 and 27-28 , respectively
 Case C3: limits of 15, 15 and 10 MVA on lines 3-4,
12-13 and 15-23, respectively
EXAMPLE: LINE FLOW LIMITS
bus voltage
BC
C1
C2
C3
1.06
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95
0.94
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930
bus
OPTIMUM AND NODAL PRICE IMPACTS
C1
C2
C3
5.5
5
4.5
4
3.5
3
2.5
2
1.5
% change in objective
nodal prices [$/MWh]
BC
0.45
0.40
0.35
0.30
0.25
0.20
0.15
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930
0.10
0.05
0.00
bus
C1
C2
C3
generator at bus no.
generator
bus
GENERATION LEVEL IMPACTS
27
27
23
23
C3
22
22
C3
13
13
2
2
1
1
10
15
40
55
-350 -30 5-25 -20
-15
-10 20-5 25
0 530 10 35
15 20
254530 50
35 40
45 6050 65
55
generator real power [MW]
generator level variation [%]
C2
C1
C2
BC
C1
EXAMPLE: VOLTAGE PROFILE
SPECIFICATION
 No line power flow limits
 Base case: 0.95  Vi  1.05 p.u. for each bus i
 Case A: fixed voltage equal to 1.0 p.u. at buses 3,4 and
10, and 0.95  Vi  1.05 p.u. for all other buses
 Case B: 0.98  Vi  1.02 p.u. for each bus i
 Case C: 0.98  Vj  0.99 p.u. for j = 10,11,14,20 and 26,
and 0.95  Vi  1.05 p.u. for all other buses
 case D: fixed voltages at 0.98 at buses 9, 19 and 21, and
0.95  Vi  1.05 p.u. for all other buses
VOLTAGE PROFILE CASES
bus voltage
BC
A
B
C
D
1.06
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95
0.94
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930
bus
OPTIMUM AND NODAL PRICE IMPACTS
A
B
C
D
52
12
10
8
6
4
2
0
% change in objective
nodal prices [$/MW hr]
BC
2.50
2.00
1.50
1.00
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930
0.50
0.00
bus
A
B
C
case
D
GENERATION LEVEL IMPACTS
27
D
23
generator at bus no.
generator bus
27
23
22
D
22
C
B
13
A
13
2
1
C
BC
2
1
-4020-25 -10
-85 0-70 -55
10
30
B
A
540 20
35
50
65 70 80
50
60
generator
real power
[MW]
[%]
variation
level
generation
125
95 110
90
80
CONCLUDING REMARKS
 The OPF tool is applicable in a central decision making
environment
 The discretion of the central decision making authority
in OPF applications in unbundled electricity markets has
broad economic impacts, which are especially
significant for generators
 The flat nature of the objective function, particularly in
the neighborhood of the optimum, implies a great
degree of arbitrariness in the choice of the optimum
 An improved understanding of the anomalous results
and more effective application of OPF in unbundled
markets are necessary for the OPF to gain acceptance