Generation Adequacy Planning in Multi-Area Power Systems
Abstract
Under
deregulated
environment,
Independent
Power
Producers
(IPPs)
individually invest on generation and transmission line expansion. IPPs and ISOs may
wish to obtain the optimal location that yields a favorable trade off between system
reliability and cost. This helps guide the development of additional generation capacity
that is optimal with respect to cost and reliability. This problem is stochastic due to
random uncertainties in area generations, transmission lines, and area loads. Reliability
is also a big challenge in the problem. This project proposes an optimization mixedinteger stochastic programming approach to the solution of the generation expansion
planning problem. The problem is formulated as two-stage recourse model. Reliability
index used in this problem is expected load loss, i.e. expected power that is not supplied
to load. The objective is to minimize the expansion cost in the first stage and the expected
loss of load cost in the second stage. In this project, the problem will be solved by Lshaped algorithm. A power system with three-area will be tested to see the effectiveness
of the proposed model.
1. Introduction
Electric power systems in the United States are going through a restructuring
process that transforms electric market from integrated utility to privately owned
generation, transmission, and distribution units. The vertical arrangement of generation
and distribution varies in some degrees by state policy. The transmission lines are
accessible by all market participants. Independent System Operator is established to
assure system reliability and provide congestion management.
Previously, state owned utilities projected the generation and transmission
investment concurrently and correlatively in multi-area power systems. Consequently, the
system is well balanced and stabilized. Under the deregulated environment, the state has
no control over the location of prospective generation. Independent Power Producers
(IPPs) can install new generations in any area which may results in imbalances between
1
generation and transmission. Therefore, the need for determining generation in each area
and tie lines requirements, which will improve system reliability, is assuming an
increased importance.
Long term generation adequacy in integrated environment assumes one bus model
where all generating units and loads are connected into a single bus. Only generation
requirement is evaluated since transmission line has already been planned to ensure
energy delivery ahead of time. The analysis is thus simple as the transmission line
constraint is not considered. However, this assumption is no longer valid in the
restructured environment when IPPs individually decide the additional generation
location and transmission line investment and expansion are still under debate [3], [7],
[8], [12], [17].
The additional generation in one area may or may not deliver assistance capacity
to others and, as a result, each area reliability level may not be improved. Hence,
individual generation investment is not an efficient way to improve system reliability
where deficient generation exists in the system. On the other hand, the system with
sufficient generation may experience market power problem. While there are
considerably small numbers of firms in wholesale generation, each firm can exercise
some market power unilaterally by withholding capacity resulting in high marketclearing price [7], [8], [9], [10].
Installed Capacity Market (ICAP) is established to assure long term system
adequacy and prevent market power. Each area generation will be procured as required
and the rest can be paper traded. The system will have adequate power supplies in a long
run and the market will have a proper signal of generation investment in the future.
Moreover, the requirement will prevent the power producers from limiting their power
supplies. Long term adequacy analysis will not only benefit the consumers for affordable,
efficient and reliable electricity but also serves the IPPs as a tool for minimum cost
generation investment.
At present, the generation requirement is calculated by simulation and ad hoc
method. As an example, Independent System Operator--New England (ISO-NE) utilizes
Multi-Area Reliability Simulation Program (MARS) for the calculation [5]. Recent study
of long term generation adequacy in multi-area power system is thoroughly analyzed and
2
reported by Rau and Zeng [5]. An optimization procedure along with MARS is proposed
to determine an excess or deficient amount of generation in each area. One of the
contributions of this paper is to show the relationship between each area risk level and
load changes. The analysis pointed out that an exponential approximation of risk level
[30] in single area system can be applied to multi-area systems. The major drawback of
[5] is that the method requires iterations between optimization and risk calculation which
is obtained from several MARS runs. In a single MARS run, the outage of each
component in the system is simulated chronologically by Monte Carlo sampling which
may demand long history to produce converged results.
An optimization method has also been applied to solve transmission expansion
planning [1], [2], [4], [6], [11], [13], [14], [16], [19], [22]. Even though the applications
are for single area power systems, it can be extended to multi-area power systems by
considering a bus as an area. In addition, transmission lines in single area power systems
can be considered as tie lines in multi-area power systems with some modifications in
maximum forward and backward capacity of each line since tie lines do not necessarily
have the same maximum capacity in both directions.
The problem is initially formulated as linear programming as the power flows are
continuous variables. Mixed-integer programming and dynamic programming [1], [2],
[6], [11], [16], [19], [22] are then proposed to incorporate the discrete decision of
additional capacity and to obtain the sequence of optimal decision respectively. Power
system networks are characterized by power flow equations (DC flow) [6], [11], [16],
[19] or by capacity flow network [1], [4], [13], [14], [22]. The common constraints are
system capacity constraints and demand constraints. The common objective of all
formulations is to minimize the expansion cost over a certain time period. Various
optimization techniques; such as, Brach and Bound, Bender’s decomposition, heuristic
techniques; such as, Fuzzy logic, greedy adaptive search, genetic algorithm, and tabu
search, and meta-heuristic technique; such as, simulated annealing have been used to
solve the problem.
Reliability aspect is included in the problem either in an objective function with
some penalty cost on unserved energy in [4], [22] or as a constraint in [2] on loss of load
probability where random uncertainties; for example, generations and load are modeled
3
with their probability distribution functions. However, these formulations utilize heuristic
techniques to account for random uncertainties along with optimization schemes; as an
example, mixed-integer programming, and a simulation tool; as an example, Monte Carlo
simulation, to obtain the solution [4], [22].
The explicit formulation accounting random uncertainties in generation capacities
and load has been shown in stochastic programming literature [20]. Power systems are
modeled as a capacity flow network. Stochastic mixed integer programming approach is
proposed to the solution of electric power capacity expansion. The problem is formulated
as two-stage recourse model where the first stage decision variables are the additional
capacity units and the second stage decision variables are network flows. The objective is
only to minimize the expansion cost. Reliability aspect has not been considered in
stochastic programming literature.
In this project, the problem is formulated as two-stage recourse model. The first
stage and second stage variables are the same as [20]; however, reliability is also
included in the second stage objective function. The overall objective is to minimize
expansion cost in the first stage and at the same time to minimize expected loss of load
cost in the second stage. L-shaped algorithm is applied to solve the problem. The
problem is implemented to three area power systems.
2. Problem Statement
Power system network is generally composed of generation, transmission line,
and load. The system is partitioned into several areas geographically where each area
contains various generation units, transmission lines in the area, load and tie lines
between areas. Multi-area power systems are modeled as capacity flow network with area
generation, area load, and tie-line connections between areas. The problem is to
determine the generation capacity requirement in each area with minimum cost and
maximum reliability. In this analysis, it is assumed that tie-line equivalent parameters are
given. The followings present detailed modeling of each unit namely area generation,
area load, and tie lines.
4
Area Generation Model
Generation units in each area will be given forced outage rate, repair time and its
capacity. Discrete probability distribution function is constructed based on each unit
parameters assuming two stages Markov process, up and down states as shown in Fig. 1.
Up
state
Failure rate
Repair rate
Down
state
Fig. 1. Two-stage Markov Process
The distribution function construction utilizes unit addition algorithm approach
[25]. The probability table contains numbers of state capacity including zero and its
corresponding probability.
Let
gi : generation capacity vector of area i
pig : probability vector of generation capacity in area i such that Pr ( g i ) = pig
For computational efficiency, the generation capacity will be rounded off to a
fixed increment so that only minimum capacity state and number of states in each area
are stored. A state with very small probability will be neglected.
Area Load Model
Discrete joint distribution of area load is composed employing hourly load history
data in each area to preserve the correlation between area loads.
Area load is presented in (1)
(
l h = l1h , l2h ,…, lnh
where
l h : load vector for the hour h
lih : load for the hour h in area i
n : number of area in the system
5
)
(1)
Due to numerous numbers of load states, they are grouped together utilizing
clustering algorithm to an appropriate number of states.
Tie Lines Model
Tie-line parameters are its capacity, forced outage rate and repair rate. Discrete
probability distribution of tie-line capacity between areas is constructed based on the
given parameters assuming two stages Markov process, up and down states. Like area
generation model, the distribution function construction utilizes unit addition algorithm
approach [25].
The Tie-line model is represented by (2), which contains the connection areas
(from area, to area), its capacity and its corresponding probability.
(
tij = f ij , bij
)
(2)
where
tij : tie-line capacity vector from area i to area j
f ij : tie-line capacity vector from area i to area j in forward direction
bij : tie line capacity vector from area i to area j in backward direction
pijt : probability vector of tie line capacity from area i to area j such that pijt = Pr (tij )
Model formulation
Multi-area power systems are formulated as a network flow problem where a
node in the network represents an area. Source and sink nodes are artificially introduced
to represent area generations and load as shown in Fig. 2. The overall objective is to
minimize the expansion cost while also maximize system reliability under uncertainty in
area generation, load, and tie-lines. The capacity of every arc in the network is random
variable with its discrete probability distributions.
6
g i (ω )
Power system network
Tie line between areas
…….
…….
s
li (ω )
t ij (ω )
t
Fig. 2 Power System Network
An optimization mixed- integer stochastic programming approach is proposed to
the solution of the generation expansion planning problem in multi-area power systems.
Using expected system load loss as reliability index, the problem is formulated as twostage recourse model. The first stage decision variables are number of generators to be
invested in each area which are made before the realization of randomness in the
problem. The second stage decision variables are an actual flow in the network. The
formulation is given in the following.
Assumption
The additional generators in all area are fully available i.e. the probability of
generating full capacity is one.
Index
I : network nodes {1, 2,…, n}
s : source node
t : sink node
ω : system state (scenario), ω ∈ Ω
Ω : state space (all possible scenarios)
Decision variables
xig : number of additional generators at area i
yij (ω ) : flow from arc i to j
7
Parameters
R : budget
cig : cost of an additional generation unit at area i
cil : cost of load loss at area i
M ig : an additional generation capacity in area i (MW)
gi (ω ) : random capacity of generation in area i (MW)
tij (ω ) : random capacity of tie line between area i and j (MW)
li (ω ) : random load in area i (MW)
Objective function
Min z = ∑ cig xig + Eω~ [ f ( x, ω~ )]
(3)
i∈ I
s.t
∑c
x ≤R
g g
i i
i∈ I
xig , xijt ≥ 0 , integer
(4)
(5)
where the only constraint (4) in the first stage is a restriction on maximum number of
additional generators in the system with respect to budget R. Constraint (5) is an integer
requirement for number of additional generators. The function f ( x, ω~ ) is the second
stage objective value of minimizing cost of load loss under a realization ω of ω~ and is
given as follows:
f ( x, ω ) = Min ∑ cil (li (ω ) − yit (ω ))
(6)
i∈ I
s.t. ysi (ω ) ≤ gi (ω ) + M ig xig ; ∀i ∈ I
(7)
y ji (ω ) − yij (ω ) ≤ tij (ω ) ; ∀i, j ∈ I , i ≠ j
(8)
yit (ω ) ≤ li (ω ) ; ∀i ∈ I
(9)
ysi (ω ) + ∑ y ji (ω ) = ∑ yij (ω ) + yit (ω ) ; ∀i ∈ I
(10)
yij (ω ), ysj (ω ), yit (ω ) ≥ 0 ; ∀i, j ∈ I
(11)
j ∈I
j ≠i
j∈I
j ≠i
where, constraints (7), (8), and (9) are maximum capacity flow in the network under
uncertainty in generation, tie line, and load arc respectively. Constraint (10) constitutes
8
conservation of flow in network. Constraint (11) is non-negativity requirement for actual
flow in the network.
3. Solution Approach
Deterministic equivalent of the problem can be written; however, the number of
total variables will be too large to solve it in timely manner. For more computational
efficiency, L-shaped algorithm is implemented to approximate the objective function in
the second stage. The algorithm is implemented with C++ utilizing basic code provided
in class [24]. Since the problem in the first stage has integer decision variables, the
master problem is solved as integer programming. Step of L-shaped algorithm is as
follow.
Step 0. Initialization
• Find x0 from solving
cT x
min
s.t.
Ax = b
x ≥0
• UB ← ∞ and LB ← −∞
Step 1. Solve sub problem
• Reset α k ← 0 , β k ← 0 , f k ← 0
•
For all ω = 1 to Ω , solve sub problem k, each scenario has probability pω
fωk = min qωT y
s.t. Wω y = rω − Tω x k
y≥0
1.If infeasible
I. Obtain dual extreme ray, µωk
( )
( )
T
T
II. Compute feasibility cut from α k = µωk rω , and β k = µωk Tω
III. Go to step 2.
2.If feasible
I. Obtain dual solution, π ωk
II.
III.
•
•
•
( )
T
( )
T
Update α k + = pω π ωk rω , and β k + = pω π ωk rω
Update current subproblem objective value f k + = pω fωk
Get cut coefficient and rhs, α k , β k
Update UB = min{UB, cT x k + f k }
If UB changed, update the incumbent solution, xincumbent ← x k
9
Step 2. Solve master problem including cut from step 2
• Optimality cut, add η ≥ α k + β kT x
•
Feasibility cut, add β kT x ≥ α k
•
•
Obtain solution from master problem x k +1 ,η k +1
Update LB = max{LB, cT x k +1 + η k +1}
Step 3. Check convergence
•
•
•
Compute percent gap from % gap = (UB − LB ) or % gap = (UB − LB )
UB
LB
*
incumbent
If % gap ≤ ε , STOP and obtain x ← x
, objective value = UB
Else, k ← k + 1 , return to step 1.
4. Computational Experiment
The test system parameters are shown in appendix A. Three area test system, its
parameters, and the probability table for each area before additional units, are shown in
Fig. A.1, TABLE A.I, A.II, and A.III. The additional unit parameters of three area system are
shown in TABLE A.IV. It is assumed that the budget is $200 million and the additional
generators have capacity of 100 MW each. Test instance generated from these parameters
is called mapsG3 and is shown in appendix B. Due to the structure of joint distribution of
three area load, block structure in the STOCH file is implemented.
Sensitivity analysis on c l , cost of load loss, is carried out. It is assumed that load
in three areas are of the same type i.e. loss of load cost per MW of each area are the
same. In the analysis, cost of load loss is varied from 1 to 2000 $m/MW, complete
solutions are shown in appendix C. The sequence of the next best solution can be found
when reliability cost increases. The solution of the problem with different cost of load
loss can be considered as the best solution at different reliability level. Since the
reliability can not be in the constraint, this analysis can offer another approach to see the
best generation combination with different reliability level subject to expansion cost.
TABLE I shows the best generation location and load loss with different cost of load loss,
c l . When this cost is high, the expected loss of load is small.
10
TABLE I
THREE AREA GENERATION SOLUTIONS
Loss of load cost
Number of units in area i
1
2
3
Expected
Loss of load
(MW)
1-5
0
0
0
26.37080
6-9
1
0
0
15.85525
10-17
2
0
0
9.77574
18-2000
2
0
1
5.13922
l
per MW, c
($m per MW)
This means that if reliability cost is very small, there should be no additional unit
in the system. In addition, the next best location subject to cost is area 1, area 1, and then
area 3. The benefit of additional generation can be quantified from this analysis and is
shown in TABLE II. It should be noted that if the objective of the problem is to maximize
reliability with subject to cost, then cost of load loss should be infinity. TABLE III shows
the total number of iterations, and CPU time with different cost of load loss.
TABLE II
ADDITIONAL AREA GENERATION CONTRIBUTION TO EXPECTED LOSS OF LOAD
Number of units in area i
in sequence
1
2
3
Expected
Loss of load reduction
(MW)
+1
0
0
10.515550
+1
0
0
6.079512
0
0
+1
4.636517
TABLE III
THREE AREA GENERATION SOLUTIONS
Loss of load cost
per MW, c
($m per MW)
#iteration
Time
(sec.)
Expected
Loss of load
(MW)
18
5
17.922
5.139221
19
5
17.75
5.139221
20
5
17.812
5.139221
25
4
14.546
5.139221
50
4
14.484
5.139221
100
4
15.187
5.139221
1000
4
14.438
5.139221
2000
4
14.313
5.139222
l
11
It can be observed from the experiment that when this parameter changes, even if
the solutions are the same, it affects computational efficiency. If the solution is the same,
it would be favorable to have loss of load cost value that will yield smaller number of
iteration and less CPU time.
5. Conclusions and Future Work
A solution to generation adequacy planning problem is proposed. The problem is
formulated as a two stage recourse model with the objective to minimize expansion cost
and maximize reliability subject to total budget. Three area power system test instance is
created. L-shaped algorithm is implemented and applied to solve the problem. For larger
systems with very large number of scenarios, interior sampling can also be applied along
with L-shaped algorithm. Sensitivity analysis on cost of load loss is conducted. The
analysis shows that when the cost is high, the system is more reliable (loss of load is
small). It also provides the quantified information (expected loss of load reduction) of the
next best generation location that improves system reliability subject to budget constraint.
If the budget constraint is relaxed or the loss of load cost in each area is different,
the next best generation location will also change. Therefore, sensitivity analysis on these
parameters should also be investigated in future study. The problem can be formulated to
minimize cost with subject to reliability constraint where reliability index can be obtained
from different budget value. If reliability index (expected loss of load) is above the limit,
budget will be increased. The algorithm has to be repeated until system reliability is
below the limit.
In this analysis, the big assumption is that the additional generators are fully
available. However, these additional units usually have their probabilities of failure
which are caused by either scheduled maintenance or random failure. Future study should
be made when the additional generators (decision variables) have their probabilities of
failure which will affect the outcomes (scenarios) and their probabilities.
In addition, different reliability index can be used; for example, loss of load
probability. However, the objective function will be of different form. To calculate loss
of load probability, number of loss of load state has to be obtained. Therefore,
minimizing loss of load probability is the same as minimizing number of loss of load
12
state. At each scenario, a state is loss of load state when any area suffers from loss of
load. The second stage objective function should be as in (12).
f ( x, ω ) = Max (li (ω ) − yit (ω ),0 )
(12)
i∈I
The analysis should be made to verify that this function is convex on decision
variables, x. Another option would be to incorporate binary decision variables in the
second stage to access information of loss of load in each scenario. However, the problem
will have discrete decision variables in both stages, and other algorithms should be
implemented.
6. Appendix
A. Test System
Area
1
Area
2
Area
3
Fig. A.1. Three Area Test System
TABLE A.I
THREE AREA GENERATION PARAMETERS
Cap
(MW)
500
400
300
200
100
0
Area 1
Probability
0.32768
0.40960
0.20480
0.05120
0.00640
0.00032
Cap
(MW)
600
500
400
300
200
100
0
Area 2
Probability
0.262144
0.393216
0.245760
0.081920
0.015360
0.001536
0.000064
13
Cap
(MW)
500
400
300
200
100
0
Area 3
Probability
0.32768
0.40960
0.20480
0.05120
0.00640
0.00032
TABLE A.II
THREE AREA TIE-LINE PARAMETERS
Cap
(MW)
100
0
1-1
Probability
0.9
0.1
Tie-line
1-2
Cap
Probability
(MW)
100
0.9
0
0.1
Cap
(MW)
100
0
1-3
Probability
0.9
0.1
TABLE A.III
THREE AREA LOAD PARAMETERS
Area 1
(MW)
100
200
300
400
500
Area 2
(MW)
200
300
400
500
600
Area 3
(MW)
100
200
300
400
500
Probability
0.05
0.1
0.7
0.1
0.05
TABLE A.IV
THREE AREA ADDITIONAL UNIT PARAMETERS
Area j
c gj ($m)
1
2
3
60
100
80
B. Test Instance
TABLE B.I shows test statistics for three area power systems.
TABLE B.I
THREE AREA SYSTEM TEST STATISTICS
Number of integer variables
Number of continuous variables
Number of constraints
Number of scenarios
mapsG3.cor
NAME
ROWS
N OBJ_R
L R0001
L R0002
L R0003
L R0004
L R0005
L R0006
L R0007
L R0008
L R0009
L R0010
L R0011
L R0012
L R0013
E R0014
E R0015
E R0016
COLUMNS
MARK0000
C0001
mapsG3
'MARKER'
OBJ_R
60
'INTORG'
R0001
60
14
3
12
16
10080
C0001
C0002
C0002
C0003
C0003
MARK0001
C0004
C0005
C0006
C0007
C0007
C0008
C0008
C0009
C0009
C0010
C0010
C0011
C0011
C0012
C0012
C0013
C0013
C0014
C0014
C0015
C0015
R0002
OBJ_R
R0003
OBJ_R
R0004
'MARKER'
R0002
R0003
R0004
R0005
R0014
R0006
R0014
OBJ_R
R0014
R0005
R0014
R0008
R0015
OBJ_R
R0015
R0006
R0014
R0008
R0015
OBJ_R
R0016
-100
100
-100
80
-100
1
1
1
1
-1
1
-1
-1
-1
-1
1
1
-1
-1
-1
-1
1
-1
1
-1
-1
R0001
100
R0001
80
'INTEND'
R0014
R0015
R0016
R0007
R0015
R0009
R0016
R0011
1
1
1
-1
1
-1
1
1
R0007
R0015
R0010
R0016
R0012
1
-1
-1
1
1
R0009
R0016
R0010
R0016
R0013
1
-1
1
-1
1
R0002
R0004
R0006
R0008
R0010
R0012
500
500
100
100
100
400
RHS
rhs
rhs
rhs
rhs
rhs
rhs
rhs
BOUNDS
LI bnd
LI bnd
LI bnd
ENDATA
R0001
R0003
R0005
R0007
R0009
R0011
R0013
200
600
100
100
100
300
300
C0001
C0002
C0003
0
0
0
mapsG3.tim
TIME
mapsG3
PERIODS
C0001
R0001
C0004
R0002
ENDATA
TIME1
TIME2
mapsG3.sto
STOCH
INDEP
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
RHS
BLOCKS
BL
BL
BL
BL
BL
BL
mapsG3
DISCRETE
R0002
0
R0002
100
R0002
200
R0002
300
R0002
400
R0002
500
R0003
0
R0003
100
R0003
200
R0003
300
R0003
400
R0003
500
R0003
600
R0004
0
R0004
100
R0004
200
R0004
300
R0004
400
R0004
500
DISCRETE
TLINE12
TIME2
RHS R0005
0
RHS R0007
0
TLINE12
TIME2
RHS R0005
100
RHS R0007
100
TLINE13
TIME2
RHS R0006
0
RHS R0009
0
TLINE13
TIME2
RHS R0006
100
RHS R0009
100
TLINE23
TIME2
RHS R0008
0
RHS R0010
0
TLINE23
TIME2
RHS R0008
100
RHS R0010
100
0.00032
0.00640
0.05120
0.20480
0.40960
0.32768
0.000064
0.001536
0.015360
0.081920
0.245760
0.393216
0.262144
0.00032
0.00640
0.05120
0.20480
0.40960
0.32768
0.1
0.9
0.1
0.9
0.1
0.9
15
BL
AREALOAD
RHS R0011
RHS R0012
RHS R0013
BL AREALOAD
RHS R0011
RHS R0012
RHS R0013
BL AREALOAD
RHS R0011
RHS R0012
RHS R0013
BL AREALOAD
RHS R0011
RHS R0012
RHS R0013
BL AREALOAD
RHS R0011
RHS R0012
RHS R0013
ENDATA
TIME2
100
200
100
TIME2
200
300
200
TIME2
300
400
300
TIME2
400
500
400
TIME2
500
600
500
0.05
0.1
0.7
0.1
0.05
C. Complete computational results
Loss of load cost
per MW, c
($m per MW)
Total cost
($m)
1
Number of units in area i
Cost ($m)
1
2
3
Expansion
Loss of load
#iteration
Time
(sec.)
Expected
Loss of load
(MW)
26.3708
0
0
0
0
26.3708
1
3.641
26.3708
5
131.8604
0
0
0
0
131.8604
1
3.672
26.3721
6
155.1315
1
0
0
60
95.1315
3
11.735
15.8553
7
170.9867
1
0
0
60
110.9867
3
10.969
15.8552
8
186.8420
1
0
0
60
126.8420
4
14.328
15.8553
9
202.6972
1
0
0
60
142.6972
5
11.922
15.8553
10
217.7574
2
0
0
120
97.75738
4
14.141
9.7757
15
266.6361
2
0
0
120
146.6361
4
15.031
9.7757
16
276.4118
2
0
0
120
156.4118
4
14.375
9.7757
17
286.1875
2
0
0
120
166.1875
4
14.515
9.7757
18
292.5060
2
0
1
200
92.5060
5
17.922
5.1392
19
297.6452
2
0
1
200
97.6452
5
17.750
5.1392
20
302.7844
2
0
1
200
102.7844
5
17.812
5.1392
25
328.4805
2
0
1
200
128.4805
4
14.546
5.1392
l
50
456.9611
2
0
1
200
256.9611
4
14.484
5.1392
100
713.9221
2
0
1
200
513.9221
4
15.187
5.1392
1000
5339.2210
2
0
1
200
5139.2210
4
14.438
5.1392
2000
10478.4400
2
0
1
200
10278.4400
4
14.313
5.1392
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17