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

ortner@eeg.tuwien.ac.at

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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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