Transmission grid representations in power system modelsThe trade-off between model accuracy and computational time
Andre Ortner*, Tomas Kruijer*Technical University of Vienna, Gusshausstraße 25-29, A-1040 Vienna
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Motivation
In electric power systems the thermal capacity of power lines in transmis-
sion and distribution grids represent a limit on the maximum amount of
electricity that can be transferred between different buses. In contrast to
other network industries (e.g. gas, water) the injection at a certain bus in
an electric power system has a considerable influence on most of the line
flows in the whole grid. To take this into account complex descriptions
of line flows need to be integrated in power system models. In the case
of large-scale power systems this leads to computationally intractable
models (see Fig. 1). Consequently, there is a need for grid simplification
methods and the key issues are to identify an appropriate approach and
to find the optimal trade-off between model accuracy and computational
effort.
Model Accuracy
Error in Average/
Maximum inter-zonal
power flows
Computational effort
Number of power lines,
price zones, power
plant aggregation
Fig. 1: Trade-off decision to be made for large-scale power system models containing
grid representations
Applications power system models with grid re-
presentations
• Three different applications of power system models with transmission
grid constraints can be differentiated (see Tab. 1)
• According to application the grid model needs to incorporate specific
characteristics of its elements
• Question of choosing the appropriate method is directly linked to the
purpose of the power system model
• In this study the focus is laid on the identification of appropriate me-
thods for economic power system models (market models)
• These models consist of price zones in which it is assumed that no
transmission grid limits power flows (copper plate assumption)
• Transport models vs. Flow-based market coupling
Transient analyses Static analyses Economic analyses
Dynamic stability,
fault analysis
Power flow analysis,
grid planning
Optimal power flow,
market coupling
[10],[11] [12],[6] [4],[1]
Tab. 1: Main applications of transmission grid representations in power system models
Simplification methods applied in electricity mar-
ket models
• High grid resolution representations (Markets with nodal pricing, e.g.
PJM, ISO-NE, ISO-NY)
• Separation according to congested lines (Markets with zonal pricing,
e.g. Italy, Sweden)
• Net Transfer Capacities NTCs (commercial trade restrictions between
countries, e.g. EPEX Spot, [7])
• Reduction methodologies based on a certain base case (e.g. [2], [3],
Approach 1 in this analysis)
• Selection of dedicated lines of interest (e.g. [1], [6], Approach 2 in this
analysis)
nodes
INTRA-zonal
flows
INTER-zonal
flows
Zone i Zone jzP
lP
lP
zl PP
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Methodology
Simplification Approaches
• Both approaches aim to model accurate inter-zonal power flows
• Approach 1 is calibrated to a certain base case and has a reduced
artificial PTDF matrix as result
• Approach 2 is not based on any base case and assumes some simplifi-
cations on part of the power plant dispatch
Identify zones within each country
(Search algorithm based on
electrical distance)
Approach 1
Build reduced PTDF matrix
(Match inter-zonal flows
in a predefined base case)
Assign thermal capacities for inter-
zonal power lines
Calculate error metrics for a set of
injection scenarios
Determine model run-time applying
reduced PTDF matrix
Identify groups of power plants
with same marginal costs
(on technology level)
Approach 2
Replace nodal injection variable of
each group by a scaling parameter
Remove thermal capacities of intra-
zonal power lines
Calculate error metrics based on
two model runs
(original vs. reduced system)
Compare model-run times of the
two models
Fig. 2: Process steps of the two model simplification approaches applied within this
analysis
Calculation of the PTDF matrices
The l(ines)-by-n(nodes) Power Transfer Distribution Matrix Φln is being
calculated via the standard method of multiplying the branch supscep-
tance matrix Bbranch and the inverse of the bus supsceptance matrix
Bbus of the linearized system.
Pinj = Bbus · θ (1)
Pflow = Bbranch · θ (2)
Φln = Bbranch ·B−1bus (3)
Bbranch and Bbus are derived via the node-branch incidence matrix C
(l-by-n) and the line reactances x
Bbranch = diag(1/x) · C
Bbus = CT ·Bbranch
Definition of error metric
Errors are defined as average relative deviations of inter-zonal power flows
in the reduced models vs. the sum of inter-zonal line flows of the original
system:
∆flow = Average(s, z)
[1∑Capl
·(P flow,z −
∑Γ · P flow,l
)](4)
Case study
The described approaches have been tested on part of the ENTSO-E
(European Network of Transmission System Operators for Electricity)
transmission grid including the countries Germany, Netherlands, Aus-
tria, Czech Republic and Slovakia. In total the grid is comprised of 1451
nodes, 5741 lines and 1475 power plants that are connected.
Fig. 3: Overview of the study grid used to test the simplification methods
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Results
Fig. 4: Relative error in intra-zonal power flows in the whole study grid as share of
zonal transfer capacity subject to the percentage of nodes in the simplified grid.
• The countries differ in their error sensitivity related to the cluster den-
sity
• Three different error thresholds have been selected (Reduction 1-3) and
the maximum cluster intensity on country level until those thresholds
were used to run a corresponding power system model
• The results of the trade-off between model-run time of the power sys-
tem model and the three reduction scenarios can be seen in Fig. 5.
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100
Model run-t
ime in %
of fu
ll-g
rid
model
Error in % of maximum error
Fig. 5: Model run-time as a function of error in zonal power flows.
Conclusions
• Approach 1 leads to average maximum errors in the range of 0.8 to 2.2
times the zonal transfer capacity
• Depending on the topology of the grid in a certain country, different
cluster densities lead to the same average errors
• At low simplification levels the model-run time can be considerable
reduced without strongly increasing average errors
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