Reduction of the Initial Grid According to
Critical Branches
Workshop “Enhanced
Enhanced pan
pan-European
European Transmission Planning Methodology”
Methodology
May 28th & 29th, 2015
S. Lumbreras, F. Banez-Chicharro, L. Olmos, A. Ramos, M. Rivier and J.M.
L t
Latorre,
COMILLAS
Th need
The
d ffor network
t
k reduction
d ti
 The size and complexity of large-scale power systems make them unmanageable for the purposes of
optimal TEP as proposed.
 It is therefore necessary to reduce the size of the problem
problem.
STEP 1 – ADEQUACY WITHOUT GRID
 Scenario and horizon selection
STEP 2 – DETECTION OF SYSTEM
 Snapshot selection
Yearly
MonteCarlo
simulations
STEP 3 – NETWORK REDUCTION
ACCORDING TO CRITICAL BRANCHES
 Network reduction
 Step1:
Network partition assigns the nodes to zones
STEP 4 – OPTIMAL GRID EXPANSION AT
ZONAL LEVEL FROM TODAY TO 2050
STEP 5 – GRID EXPANSION AT NODAL LEVEL
 Step 2:
Calculation of equivalent network parameters
STEP 6 – ROBUSTNESS OF THE PROPOSED
GRID ARCHITECTURES
Methology proposed in eHighway2050, WP8.
Reduction of the initial grid according to critical branches.
2
S
Summary
description
d
i ti off th
the ttask
k
Input :
- Nodal network
description
- Indices from power flow
simulations/snapshots
p
Identification of critical branches
Several indicators are calculated in order to identify the
lines that have the most critical impact on the operation of
the system
Network partition
Nodes are clustered into zones
Reduced network calculation
Calculation of zonal equivalent network
Output :
- Assignment of nodes
into zones
- Zonal network
description
Reduction of the initial grid according to critical branches.
3
C it i ffor network
Criteria
t
k partition
titi
 Most of the references that deal with network partition use electrical distance to guide the process.
 The electrical distance between a pair of nodes is defined as the equivalent impedance between
them ii.e.,
them,
e the voltage drop between the nodes when a current of 1 A is injected in one and withdrawn
from the other.
 This equivalent impedance is computed using the elements of the inverse of the admittance matrix
(i e Zbus):
(i.e.
Dij = Zbusii +Zbus jj -2Zbusij
Zbus = Ybus -1
(
Ybusij = - Rij +jX ij
Ybusii =
å (R
)
+jX ij
ij
j
-1
) +å jB
-1
ij ,i
j
 Pairs of nodes that are connected by short, low reactance lines present lower distances between
them.
[1] Haixia Wang; Rao Liu; Weidong Li; Caihong Zhao, "Power Flow Tracing with Consideration of the Electrical Distance," Power and Energy Engineering
C f
Conference,
2009 APPEEC 2009.
2009.
2009 Asia-Pacific
A i P ifi , vol.,
l no., pp.1,4,
1 4 27-31
27 31 March
M h 2009
Reduction of the initial grid according to critical branches.
4
C it i ffor network
Criteria
t
k partition
titi (cont’ed)
(
t’ d)
 Several techniques have been applied to network partition in the literature.
 Clustering algorithms such as K-means or K-medoids [2]: efficient, easy to implement.
 Other approaches: MIP (unmanageable), Spectral Clustering [3] (useful in some cases but
difficult to implement)
 If network partition is established solely on the basis of electrical distance, all considerations other
than equivalent impedance are disregarded: system operation, demand and generation, line
capacities and congestion.
 There is no guarantee that frequently congested lines will not belong to the same partition, so
they will not be represented.
 This might lead the planning process to miss potentially important reinforcements.
reinforcements
[2] E. Cotilla-Sanchez, P. D. H. Hines, C. Barrows, S. Blumsack and M. Patel, "Multi-Attribute Partitioning of Power Networks Based on Electrical
Distance," Power Systems, IEEE Transactions on, vol. 28 (4), pp. 4979-4987, 2013.
[3] C. Hamon, E. Shayesteh, M. Amelin and L. Söder, "Two partitioning methods for multi-area studies in large power systems," International Transactions
on Electrical Energy
gy Systems,
y
, 25 ((4),
), 648-660,, April
p 2015
Reduction of the initial grid according to critical branches.
5
C it i ffor network
Criteria
t
k partition
titi (cont’ed)
(
t’ d)
 We propose to build the partitions around transmission lines that are particularly relevant for
the purposes of TEP. We will refer to them as critical branches.
 Frequent congestions
 Power flow control devices (HVDC lines, PSTs).
 We propose a heuristic algorithm that builds an initial partition around the critical branches.
 We propose to base the partition on a composite distance (electrical + geographical) in order to avoid
overlapping partitions
partitions.
Reduction of the initial grid according to critical branches.
6
G
General
l idea
id off th
the ttestt case study
t d
 Number of nodes ൎ 1,000
 400 kV nodes = 548
ൎ 3,715
 Number of circuits ൎ 3 715
 400 kV lines = 981
 PST = 8
Reduction of the initial grid according to critical branches.
7
Id tifi ti off critical
Identification
iti l branches
b
h
 The output of Monte Carlo (MC) simulations is used to calculate a range of indicators that are used
to identify critical branches:
 Average flow
 Proportion of simulations/snapshots where a line is congested
 Congestion severity, calculated as the dual variable of flow constraints (marginal severity) or as
nodal price differences
differences.
 The correlation among these congestion severity indicators is relatively low.
Relationship among indicators in the test case study (average flow (pu), congested
snapshots
(h),among
marginal
severity
(€/MW)
nodal
price Severity,
difference
)
Relationship
the indicators
(Average
Flow,
Congestion,
Price(€/MW)
Diff)
1
0.5
0
6000
4000
2000
0
2000
1000
Congestion severity indicators
(marginal severity and nodal price
difference) are the only highly
correlated indicators.
0
2000
1000
0
(based on 3714 lines, 8760h)
0
0.5
1
0 200040006000 0
1000 2000
0
1000 2000
Reduction of the initial grid according to critical branches.
8
Id tifi ti off critical
Identification
iti l branches
b
h ((cont’ed)
t’ d)
 However, independently of the specific indicator choice, critical branches tend to appear in the
same areas.
areas
Impact of the selection criterion on the identification of
critical branches (in blue) in the test case study
Critical branches
according to average
flow
Critical branches
according to congestion
Average
Flow
Congestion
x 10
6
6
x 10
2.8
2.8
2.6
2.6
2.4
2.4
2.2
2.2
2
2
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
1
1
-4
-2
0
2
4
6
8
10
12
14
-4
-2
0
2
4
6
8
10
12
5
x 10
Marginal severity
6
Nodal price difference
6
Critical branches according to marginal severity
x 10
Critical branches according to price differences
x 10
2.8
2.8
2.6
2.6
2.4
2.4
2.2
2.2
2
2
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
1
14
5
x 10
1
-4
-2
0
2
4
6
8
10
12
14
-4
5
x 10
-2
0
2
4
6
8
10
12
14
5
x 10
Reduction of the initial grid according to critical branches.
9
N t
Network
k partition
titi
 Aggregates the nodes of the network into areas.
 Several considerations are taken into account:
 Electrical distance
 Geographical distance
Electrical distance (y-axis, in ohm pu)
0.06 vs. geographical distance (x-axis, in m)
Distribution of electrical distance in
theDistribution
test ofcase
study
electrical distance
1800
0.05
1600
1400
0.04
1200
0.03
0
03
1000
800
0.02
600
400
0.01
200
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10
Electrical and geographical distances
are relatively well correlated in the
test case study.
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Outliers in this distribution represent nodes that are
relatively isolated from the rest of the network. They are
eliminated from the network partitioning process in
order to avoid the definition of single-node
single node zones.
zones
Reduction of the initial grid according to critical branches.
10
N t
Network
k partition
titi (cont’ed)
(
t’ d)
 A heuristic has been developed to generate a relatively good starting partition
partition.
 For each critical branch, if both extremes of the line belong to the same area, then the area
is split in two and nodes are reassigned to the two new partitions based on distance.
 A purpose-built clustering algorithm, based on K-medoids, takes into account critical branches at
every step of the algorithm:
 The algorithm works iteratively to find a local optimal clustering solution (there is no
guarantee of global optimality):
1.
2.
Nodes are assigned to the closest medoid.
Medoids are recalculated for each area as the existing node that presents the least
average distance to the nodes of that area.
 Nodes that belong to the extremes of a critical branch can never be clustered together.
Reduction of the initial grid according to critical branches.
11
N t
Network
k partition
titi (cont’ed)
(
t’ d)
 Network partition has been performed for several definitions of aggregate distance:
 50% Geographical / 50% electrical distance
 In order to use electrical distance, only HV nodes (400kV) can be considered, once
relatively isolated substations have been removed (the remaining nodes will be assigned
according to the nearest 400kV node to which they have some connectivity).
 The incorporation of geographical distance avoids the definition of geographically overlapping
partitions.
 The representative node in each partition can be selected as the most central one (lowest
average distance to the remaining nodes in the zone) or as the most connected node, which
leads to selecting the most significant nodes in the network (large power plants or substations).
 Several clustering algorithms have been tested:
 Purpose-built version of K-Medoids that uses the developed initial partition as a starting
solution
l ti and
d checks
h k every node
d assignation
i
ti tto ensure th
thatt critical
iti l b
branches
h are respected.
t d
 K-means and fuzzy C-means that are heuristically modified to incorporate critical branches.
 The solutions are relatively
y similar for all the approaches
pp
tested.
Reduction of the initial grid according to critical branches.
12
T t results
Test
lt
 Initial partition found by the heuristic
 24 zones are needed to respect the critical branches
6
x 10
2.6
2.4
2.2
2
1.8
1.6
1.4
4
1.2
1
-4
4
-2
2
0
2
4
6
8
10
5
x 10
Reduction of the initial grid according to critical branches.
13
T t results
Test
lt (cont’ed)
(
t’ d)
 Network partition based on 100% electrical distance (50 partitions)
 Some partitions have a geographical overlap
6
x 10
2.6
2.4
2.2
2
1.8
1.6
1.4
4
1.2
1
-4
4
-2
2
0
2
4
6
8
10
5
x 10
Reduction of the initial grid according to critical branches.
14
T t results
Test
lt (cont’ed)
(
t’ d)
 Network partition based on 50% electrical / 50% geographical distance (50 partitions)
 Geographically overlapping partitions are avoided
6
x 10
2.6
2.4
2.2
2
1.8
1.6
1.4
4
1.2
1
-4
4
-2
2
0
2
4
6
8
10
5
x 10
Reduction of the initial grid according to critical branches.
15
T t results
Test
lt (cont’ed)
(
t’ d)
 If the most central nodes are selected as medoids,
medoids the representative nodes of each zone are
not necessarily nodes that are representative of the network.
6
x 10
2.8
Medoids map
Medoids selected by centrality (low
distance)
2.6
2.4
2.2
2
1.8
1.6
14
1.4
1.2
1
-4
-2
0
2
4
6
8
10
12
5
x 10
Reduction of the initial grid according to critical branches.
16
T t results
Test
lt (cont’ed)
(
t’ d)
 If the most connected nodes are selected as medoids (post-processing),
(post processing) the representative
nodes of each zone correspond to the most significant nodes in the network.
6
Medoids map
x 10
Medoids selected by connectivity
Connectivity map
2.8
2.6
2.6
2.4
24
2.4
2.2
2.2
2
2
18
1.8
1.8
1.6
1.6
1.4
1.4
1.2
1.2
1
1
-4
-2
0
2
4
6
8
10
-4
-2
0
2
4
6
8
10
12
5
x 10
Reduction of the initial grid according to critical branches.
17
E i l t reduced
Equivalent
d
d network
t
k
 Obtain reactances and capacities of zonal (reduced) network.
 The equivalent network is unique for all the snapshots.
 The inter-zonal network is represented by equivalent corridors
 Both critical and non
non-critical
critical branches.
branches
 But special lines must be represented explicitly
 Idea: inter-zonal flows of the zonal network “must” match inter-zonal flows in the nodal network.
Reduction of the initial grid according to critical branches.
18
R
Reactances
t
off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 The reactances of the inter-zonal corridors are calculated so that the differences in inter-zonal flows
between the existing nodal network and the equivalent zonal network are minimized.
 Reactances that minimize the Euclidean norm of the difference between inter
inter-zonal
zonal power
flows.
 A single reactance is obtained for all snapshots.
Shi, D., and Tylavsky, D.J. “An improved bus aggregation technique for generating network equivalents”
IEEE Power and Energy Society General Meeting, July 2012 10.1109/PESGM.2012.6344668
Reduction of the initial grid according to critical branches.
19
R
Reactances
t
off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 The reactances of the inter-zonal corridors are calculated so that the differences in inter-zonal flows
between the existing nodal network and the equivalent zonal network are minimized.
 Reactances that minimize the Euclidean norm of the difference between inter
inter-zonal
zonal power
flows.
 A single reactance is obtained for all snapshots.
Equivalent
reactances
Shi, D., and Tylavsky, D.J. “An improved bus aggregation technique for generating network equivalents”
IEEE Power and Energy Society General Meeting, July 2012 10.1109/PESGM.2012.6344668
Reduction of the initial grid according to critical branches.
20
R
Reactances
t
off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 Example: 9 nodes – 3 zones
R
Reactances
t
off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 Example: 9 nodes – 3 zones
Zone A
Zone B
Zone C
R
Reactances
t
off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 Example: 9 nodes – 3 zones
Z
Zone
A
Zone A
X=0.0172
Zone B
Zone B
X=0.0760
X=0.0767
X=0.04
Zone C
Flow A-B
Fl
A B = -41
41
Flow A-C = 16
Flow B-C = -25
These two lines may have
different characteristics
Zone C
Flow A
Fl
A-B
B = -41
41
Flow A-C = 16
Flow B-C = -25
Reduction of the initial grid according to critical branches.
23
C
Capacity
it off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 Lack of references: usually aggregation of capacity
 The capacities of the inter-zonal corridors are calculated so that they allow the maximum interinter
zonal flows that could happen in the nodal network
 Idea
Nodal
network
Maximum power
transfer among
zones
Zonal
network
 Warning: overestimate/underestimate capacities among zones
Flows
Equivalent
capacities
Reduction of the initial grid according to critical branches.
24
C
Capacity
it off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 The capacities of the inter-zonal corridors are calculated so that they allow the maximum interzonal flows that could happen in the nodal network.
1.
Maximum power transfer among zones in the nodal network
 Maximum power that may be exchanged among zones
 Use several operation situations: snapshots
 Look for maximum inter-zonal flows
 Diversity of situations
Zone C
Zone A
Z
Zone
B
Reduction of the initial grid according to critical branches.
25
C
Capacity
it off equivalent
i l t corridors
id
Zone C
Zone A
Gen
Zone C
Zone A
Zone B
Dem
Gen
Zone B
Dem
Reduction of the initial grid according to critical branches.
26
C
Capacity
it off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 The capacities of the inter-zonal corridors are calculated so that they allow the maximum interzonal flows that could happen in the nodal network
1.
Maximum power transfer among zones in the nodal network
 Two different methods:
1) Calculated among zones connected by corridors
 For each snapshot
 Repeated for every two pair of zones and in both directions
 One zone is exporting and the other is importing (the other way is also considered)
•
Increase generation in exporting and increase demand in importing
homothetically
Zone C
Zone A
Gen
Zone B
Dem
 Obtain a set of new power injections
Reduction of the initial grid according to critical branches.
27
C
Capacity
it off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 The capacities of the inter-zonal corridors are calculated so that they allow the maximum interzonal flows that could happen in the nodal network
1.
Maximum power transfer among zones in the nodal network
 Two different methods:
1) Calculated among zones connected by corridors
 For each snapshot
 Repeated for every two pair of zones and in both directions
 One zone is exporting and the other is importing (the other way is also considered)
•
Increase generation in exporting and increase demand in importing
homothetically
Zone C
Zone A
Dem
Zone B
Gen
 Obtain a set of new power injections
Reduction of the initial grid according to critical branches.
28
C
Capacity
it off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 The capacities of the inter-zonal corridors are calculated so that they allow the maximum interzonal flows that could happen in the nodal network
1.
Maximum power transfer among zones in the nodal network
 Two different methods:
2) Calculated for the whole system
 Only once for each snapshot
 Now exporting and importing nodes, not zones
•
Increase generation in exporting and increase demand in importing
homothetically
Dem
Zone C
Zone A
Gen
Gen
Zone B
Dem
Gen
 Obtain a set of new power injections
Dem
Reduction of the initial grid according to critical branches.
29
C
Capacity
it off equivalent
i l t corridors
id
Maximum transfer calculated before:
nett sett off power injections
i j ti
Reduction of the initial grid according to critical branches.
30
C
Capacity
it off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 Example: 9 nodes – 3 zones
Z
Zone
A
Zone A
Zone B
X=0.0172
Zone B
X=0.0760
X=0.0767
NTC=500
These ttwo
o lines ma
may ha
have
e
different characteristics
Zone C
Capacity
Among
zones
Whole
system
Aggregate
(usual)
A-B
88
69
100
A-C
167
81
1000
BC
B-C
175
72
500
Zone C
Intra-zonal constraints
affect inter-zonal corridor
capacities
Reduction of the initial grid according to critical branches.
31
C
Capacity
it off equivalent
i l t corridors
id
 Inter-zonal corridors are the equivalents of the set of lines connecting two zones in the nodal network
model.
model
 Example: 9 nodes – 3 zones
Z
Zone
A
Zone A
Zone B
X=0.0172
Zone B
X=0.0760
X=0.0767
NTC=500
These ttwo
o lines ma
may ha
have
e
different characteristics
Zone C
Capacity
Among
zones
Whole
system
Aggregate
(usual)
A-B
88
69
100
A-C
167
81
1000
BC
B-C
175
72
500
Zone C
Explore the option that
intra-zonal constraints do
not affect inter-zonal NTC
Reduction of the initial grid according to critical branches.
32
C
Case
study:
t d d
description
i ti
 2012 French-Spanish HV system
 Neighbor countries modeled as a reduced set of nodes
Number of nodes
2,196
Number of external nodes (no FR-ES)
211
Number of 400kV nodes
548
Number of lines
3,715
Number of 400kV lines
981
Number of 400kV PST
8
Number of 400kV interconnexion lines
45
Number of HVDC lines
0
Reduction of the initial grid according to critical branches.
33
C
Case
study:
t d d
description
i ti
 2012 French-Spanish HV system
 Neighbor countries modeled as a reduced set of nodes
 Two different scenarios are built for 2050
 Values of installed capacities are interpolated for 2030 and 2040: three time horizons
France
Scenario 1
Scenario 2
Spain
Decrease nuclear g
generation
End of nuclear g
generation by
y 2050
Increase wind and solar capacities by
a factor 3 by 2050
Increase wind and solar capacities
Constant load
Increase load by 50% by 2050
Increase hydro generation
No change in hydro
Increase gas and coal generation
No change in thermal
Increase wind and solar capacities by
50% by 2050
Increase wind and solar capacities by
50% by 2050
Increase load by 30% by 2050
Constant load
High increase in SP
demand
compensated with
wind and solar in FR
Increase demand in
FR
 For each scenario and time horizon 10 Monte-Carlo years are generated
Reduction of the initial grid according to critical branches.
34