Modeling Curtailment in Germany: How Spatial Resolution Impacts Line Congestion
11 Modeling Curtailment in Germany:How Spatial Resolution Impacts Line Congestion
Martha Frysztacki, Tom BrownInstitute for Automation and Applied Informatics, Karlsruhe Institute of Technology,76344 Eggenstein-Leopoldshafen, Germanye-mail: [email protected]
Abstract —This paper investigates the effects of network con-straints in energy system models at transmission level on renew-able energy generation and curtailment as the network is beingspatially aggregated. We seek to reproduce historically measuredcurtailment in Germany for the years 2013-2018 using an openmodel of the transmission system, PyPSA-Eur. Our simulationsinclude spatial and temporal considerations, including congestionper line as well as curtailment per control zone and quarter.Results indicate that curtailment at high network resolutionis significantly overestimated due to inaccurate allocation ofelectricity demand and renewable capacities to overloaded sites.However, high congestion rates of the transmission networkdecrease as the network is clustered to a smaller number ofnodes, thus reducing curtailment. A measure to capture errorsin the assignment of electricity demand and power plants isdefined and hints towards a preferable spatial resolution. Thus,we are able to balance the effects of accurate node assignment andnetwork congestion revealing that a reduced model can capturecurtailment from recent historical data. This shows that it ispossible to reduce the network to improve computation timesand capture the most important effects of network constraintson variable renewable energy feed-in at the same time. keywords : curtailment, spatial clustering, energy systemmodeling at transmission level, renewable energyI. I
NTRODUCTION
To substantially reduce the risks and impacts of climatechange, the European Council has committed to becomingclimate neutral by 2050 [1]. This objective is at the heartof the European Green Deal [2] and in line with the ParisAgreement, that sets out the goal to pursue efforts to limitglobal warming to 1.5 ◦ C [3].The incentives for renewable energy in Germany are reg-ulated by the Renewable Energy Sources Act. If the feed-inof electricity from an installation to generate electricity fromrenewable energy sources is reduced due to a grid systembottleneck, grid system operators must compensate operatorsaffected by their measure for of the lost revenues [4]. Thecompensation payments for the curtailed energy in 2013 were . million euros and have increased ever since, reaching amaximum of . million euros in 2018 [5], [6]. The reason isthat in the last few years significant amounts of wind have beencurtailed because of congestion in the German transmissionsystem.At the same time, the German government has set a targetthat the share of renewables must be increased from in 2019 to by 2030. By 2050 the capacities of today mustat least quintuple even in optimistic scenarios to meet CO reduction targets [7]. Thus, congestion is likely to continueto be present as shares of wind and solar rise, particularlygiven the delays in building new transmission projects. Varioussolutions have been proposed to mitigate congestion: flexibilityfrom sector-coupling [9], the production of green hydrogen [8],innovative new technologies such as dynamic line rating [10]or fast-acting storage [28] could be introduced to the marketto increase available green energy from existing assets.Allowing new flexibility strategies to be tested on openly-available, validated models should increase transparency andinnovation in managing congestion [11]. Therefore, accuratemodelling of the interactions between renewables and the gridis critical to assess future scenarios for the energy system.This work contributes to the literature by validating thehistorical curtailment in the German network in an openmodel of the European power system, PyPSA-Eur, which isfree to download, modify and republish. Model adaptationsand measures are introduced to explore how best to modelthe curtailment while not overloading scarce computationalresources. In particular we vary the spatial resolution ofthe model to understand at what level the most importantbottlenecks are still captured, balancing this against the overallsize of the model. Results are validated against publishedfeed-in management numbers by the German Federal NetworkAgency [15], [16] in time and space.This paper is arranged as follows: In Section II we presentthe full optimisation problem with respect to all its constraintsto model curtailment in Germany. We provide the data inputsand present the applied clustering methodology based on k-means. In Section III, we present our results of clusteringon curtailment. Based on these findings, model results arediscussed on an annual scale for the years 2013-2018, a spatialscale for the four distinct TSO regions in Germany and on atemporal scale discussing results per quarter.II. M ODEL AND M ETHODS
A. Optimisation problem
While PyPSA-Eur [17], [18] is capable of co-optimisinginvestment in generation and transmission, this research is acase-study to reproduce historical data. Therefore, the objec-tive function minimises solely the operational costs for a fixed $ (cid:13) a r X i v : . [ phy s i c s . s o c - ph ] S e p TABLE IN
OTATION abbrev. descriptiongeneral abbreviations s technology type (generators/sorage) t time discretisation a year n substation/node (cid:96) transmission line N c set of high resolution nodes in cluster c line attributes x (cid:96) reactance l (cid:96) length F a(cid:96) capacity in year af (cid:96),t energy flownodal attributes gdp n gross domestic product in node n pop n population in node nx n , y n coordinates of node nG an,s capacity in year ao n,s variable costs η storage losses or efficiencies for technology d t demant in time t (whole Germany) d n,t demand per node n and time t ¯ g n,s,t capacity factor for RE, ∈ [0 , g n,s,t dispatch A n,s,t availability of renewables in TWhgraph related attributes K an,(cid:96) incidence matrix in year aC a(cid:96),c cycle matrix in year a ; c represents a cylce Usually the context is clear, so the indices accounting for the nodes n, m connected by line (cid:96) n,m are omitted for simplicity reasons. generation and storage fleet and fixed transmission capacities.The historic capacities of the generation and transmission fleetare given exogenously for each year, labeled by an index a . min g i,s,t , f (cid:96),t (cid:104) (cid:88) n,s,t o i,s g i,s,t (cid:105) . (1)The objective to minimise operational expenditures is con-strained to satisfy the electricity demand d n,t at each node n and in each time t , either by local generators and storageoptions or by the energy flow f (cid:96),t from neighboring nodes: (cid:88) n,s,t g n,s,t − d n,t = (cid:88) (cid:96) K an,(cid:96) f (cid:96),t ∀ n, t , (2)where K a(cid:96),t is the incidence matrix of the network, encoding itstopology for each year a , to reflect connections between nodes.This equation represents Kirchhoff’s Current law, stating thatthe sum of currents flowing into a node must equal the sum ofout-flowing currents minus local consumption. The transmis-sion grid is additionally constrained by Kirchhoff’s voltagelaw, stating that the directed sum of potential differencesaround any closed cycle adds to zero. This can be translatedto direct constraints on the flows [19]: (cid:88) (cid:96) C a(cid:96),c x (cid:96) f (cid:96),t = 0 ∀ c, t . (3)Each cycle c is represented in the matrix C a(cid:96),c as a directedcombination of lines (cid:96) . x (cid:96) denotes the inductive reactance.Further, each flow in the transmission grid is constrained bythe line capacity multiplied by a factor of . , a convention used in the past decades to account for N − security, see[20], [21]: | f (cid:96),t | ≤ . · F a(cid:96) ↔ (cid:26) µ a(cid:96),t ≥ µ a(cid:96),t ≥ ∀ (cid:96), t . (4)The shadow prices µ a(cid:96),t and µ a(cid:96),t [ e /MW] are positive, if theflow f (cid:96),t equals of its capacity, and if this constraintis binding, i.e. a better optimum of the overall annual costsaccording to the objective in (1) could be reached by increasing f (cid:96),t beyond this constraint.The dispatch of conventional generators g n,s,t is constrainedby their given capacities G an,s ≤ g n,s,t ≤ G an,s ∀ n, s, t . (5)In case of renewables, an additional availability factor ¯ g n,s,t ∈ [0 , is added to the same constraint to reflect the spatio-temporal variability of weather conditions: ≤ g n,s,t ≤ ¯ g n,s,t · G an,s ∀ n, s, t . (6)The energy levels e n,s,t of all storage units (we only includehydro storage) have to be consistent, i.e. the current storagelevel equals the previous storage level plus what is charged anddischarged, accounting for standing, charging and dischargingefficiencies. The energy level is assumed to be cyclic, suchthat by the end of the simulated year on December 31 st thestorage is filled by the same amount as it was assumed onJanuary 1 st . B. Data Inputs
We model Germany with a maximum of 306 nodes, in-cluding all transmission lines from the ENTSO-E InteractiveTransmission Map [22] extracted by the GridKit extractiontool [23]. The network is adjusted according to annual reportsfrom local transmission system operators [24]-[28]. Linesthat were not build by the time of e.g. 2014, are removedfrom the optimisation for this year. Lines that have beenstrengthened were reduced in capacity for the optimisation.Electricity demand data [29] and generation time series forhydroelectricity (run of river) are included and fixed. Capaci-ties for conventional and renewable generators are taken fromthe new database provided by the German Federal NetworkAgency, the Marktstammdatenregister [30], see Figure 1 fortheir spatial distribution. Fuel costs, variable operation andmaintenance costs per technology are based on historicalmarket prices [31]. Renewables have no marginal costs, butwere given very small ones to set the curtailment order forwind and solar: 0 ct/MWh el for run of river and geothermal,1 ct/MWh el for solar, 2 ct/MWh el for wind onshore and 3ct/MWh el for wind offshore.Electricity-Demand in [29] is given per country in hourlyresolution d t ; therefore, we need to dis-aggregate it in spaceover Germany. We do this by applying a heuristic based on thegross domestic product gdp n and population pop n per node n based on NUTS3 data [32]: d n,t = d t · (0 . · (cid:107) gdp n (cid:107) max + 0 . · (cid:107) pop n (cid:107) max ) . (7) A similar heuristic was evaluated in [33] and matches theelectricity demand fairly well with a small assignment error.The dataset [30] contains the geographic coordinates orequivalent information, i.e. each generator g lies within a so-called voronoi cell . These cells are defined by a center pointand cover the space that is closest in the sense of the euclideanmetric. Therefore, we assign each generator g to its closestcell, that is represented by the node n of the network via argmin n ∈N (cid:113) ( x n − x g ) + ( y n − y g ) . (8)The data is filtered such, that the commissioning year of eachgenerator matches the one of the demand time series. Thisis a simplification in the sense, that the register does notprovide substations where the respective generator is attachedto, only its geographical coordinates x g and y g , such that thisassignment comes with errors.To assess the assignment errors of both electricity demandand the generation fleet, we can quantify the amount ofrenewable energy available at the node which cannot beconsumed locally or exported due to the constraint (4), i.e.the excess which necessarily must be curtailed: (cid:88) n, s ∈ RE, t (cid:104) A n,s,t − d n,t − (cid:88) (cid:96) i,j ∈L : i = n ∨ j = n . · F a(cid:96) i,j (cid:105) + . (9)The bracket [ · ] + denotes the positive part of a value; max(0 , · ) .Equation (9) captures an assignment imbalance in quantitiesof excess TWh: If the result is positive, it indicates that theinstalled potential at a local substation n is higher than localdemand and higher than the transmission capacity. Buildingsuch a powerplant is uneconomical, because it is known inadvance that its power output cannot be used. Therefore, weassume either the assignment of g to n or the heuristic (7) to beinaccurate. Evaluation of (9) can be done a priori, i.e. withoutsolving the optimisation problem (1) with its correspondingconstraints (2)-(6). C. Network clustering
As renewables energy carriers have gained in capacity overthe past decades, more detailed models are required to detecttransmission bottlenecks, thus optimisation models have grownin size, posing a great challenge to the available computa-tional power. Many methods have been suggested to representlarge models in equivalents of smaller size. To lessen thecomputational power on spatial scale, these methods includek-means clustering [34], k-means++, max-p regions [35] orvariants mixing different of these techniques [36]. Takinginto account the transmission system, clustering on electricaldistances between nodes [37]-[39] or spectral partitioning ofthe Laplacian matrix [40] were also developed.We chose a version of k-means clustering based on the ge-ographical location of the original substations in the network,weighted by the average electricity demand and conventionalcapacity at the substations as introduced in [41]. This repre-sents how the topology of the network was historically plannedto connect major generators to major loads. Figure 2 visualisesthe clustering for three different resolutions of the network.
Fig. 1. Original network model for Germany including all HVAC and HVDCtransmission lines and all the powerplants available for the model in 2018.
Fig. 2. Clustered networks displaying the amount of curtailment for theyears 2015 and 2017 for three different resolutions. The raw clustering isdisplayed in black, additional information for curtailment and line congestionis highlighted in blue and orange. The results for 2015 exclude i.e. the“Th¨uringer Strombr¨ucke“ that was commissioned by the end of 2015 andis hence excluded for the simulation. In 2017, the first part of the “Th¨uringerStrombr¨ucke“ is already included.
306 301 296 291 286 281 276 271 266 261 256 251 246 241 236 231 226 221 216 211 206 201 196 191 186 181 176 171 166 161 156 151 146 141 136 131 126 121 116 111 106 96 91 86 81 76 71 66 61 56 51 46 41 36 31 26 21 16 11 60200040006000800010000 C u r t a il m e n t [ G W h ] onwind offwind solar ror306 301 296 291 286 281 276 271 266 261 256 251 246 241 236 231 226 221 216 211 206 201 196 191 186 181 176 171 166 161 156 151 146 141 136 131 126 121 116 111 106 96 91 86 81 76 71 66 61 56 51 46 41 36 31 26 21 16 11 6 E x c e ss e n e r g y [ G W h ] Fig. 3. Model curtailment in GWh (top), excess energy according to equation (9) in GWh (middle) and renewable availability in TWh (bottom) for theweather year 2017 respective network size interpolating between nodes (the full network) and nodes. After aggregating univalent nodes to their polyvalent neigh-bors, the k-means algorithm minimises the weighted sum ofthe euclidean metric min x c ,y c k (cid:88) c =1 (cid:88) n ∈ N c w n (cid:112) ( x c − x n ) + ( y c − y n ) , (10)where the weight w n equals the sum of installed capacityand electricity demand at node n . This weight decreases theprobability to aggregate nodes with high installed capacity orhigh electricity demand into one cluster N c , such that the linesconnecting nodes with high capacity and electricity demandremain isolated in the network to reflect possible transmissionbottlenecks.The node representing the cluster N c is located at theaverage position. All installed capacities are aggregated bytechnology type and demand profiles are added to the network.The time-dependent availability time series is aggregated witha weighting by technology type, such that the capacity factorof locations with high installed renewables is dominant in theaverage.Lines connecting distinct clusters are represented with asingle representative line with the summed capacity of allinter-cluster high-resolution lines F (cid:96) . The length of the repre-sentative line is determined using the haversine function thatcalculates the great-circle distance between two representativenodes and multiplied by a factor of . to account for routing.We progressively cluster our high resolution German modelwith nodes and - lines (2013/2018) down to a node network and compare results.III. R ESULTS
The original full-resolution network model with assignedpower plants is shown in Figure 1 and can be compared tothree clustered down networks for the years 2015 and 2017in Figure 2, that also shows additional spatial information ofcurtailment. Annual curtailment results for different networkresolutions for the year 2017 are displayed in Figure 3. InIII-A, we discuss a preferable network resolution for most studies and take the result as a basis for further investigation,but inter-cluster variations are discussed as well.Historical model results on curtailment in Germany are val-idated in three separate validation steps. First, on a cumulativescale where we present the total annual curtailment results inFigure 4. Second, on a spatial scale, where results per distinctcontrol zone of the German transmission system operators arepresented in Table II. Finally, the temporal scale is consideredand curtailment is validated per quarter, see Table III.Finally, Figure 5 presents memory consumption and theduration to solve the optimisation problem (1)-(6) as a functionof the network size.We have tested all results for stability by perturbing theassignment of generators g according to (8) with a probabilityof to a node that is within the radius of km of theclosest node n . km account for of the longest east-westextension of Germany. The results are stable with deviationsof below . A. The impact of spatial resolution on modeling results
In Figure 3 we display the impact of clustering on cur-tailment results in Germany in 2017. The total amount ofcurtailment experiences four distinct stages, where in eachstage the cumulative annual value is approximately steady,deviating from the mean by only .Those four stages can be distinguished by applying theexcess energy measure discussed in (9): (i) First, at high modelresolution, results are highly overestimated by more than on average. Both curtailment and excess energy results arerelatively stable with minor deviations of up to . This isbecause both the assignment of electricity demand and powerplants according to (7) and (8) in some cases is not precise,hence a mismatch emerges between low demand and highgeneration with lacking transmission capacities to transport theexcess. (ii) Second, at intermediate model resolution between250 and 150 nodes, curtailment results match the historicalones by on average , i.e. deviating from historical num-bers by . At this stage, the effect of clustering overcomes (143.%) (30.4%) (63.3%) (79.1%) (130.%) (152.%) Model Curtailment [GWh] onwindoffwindsolarror2013 2014 2015 2016 2017 2018020004000
159 795 3572 3300 4818 4626Historical Curtailment [GWh] wind (aggregated)
Fig. 4. Model results on historical curtailment in 2013-2018 due to congestionof transmission lines in the transmission system (top). The number in percentdepicts the agreement with historical data (bottom) where curtailment wascaused by congestion in the transmission system [5]. Results are extracted ata network resolution of 246 nodes. the errors made by assigning electricity demand and generatorsto nodes, but at the same time, clustering preserves majortransmission bottlenecks. Excess energy is still available dueto the uncertainty of weather conditions, but is low at − of available renewable energy. (iii) The third stage rangesfrom an intermediate to low resolution network ( to nodes) where both curtailment and excess results have largefluctuations. This high variance is because the probability tocluster important transmission lines becomes higher as fewerclusters are available for aggregation: Similar resolutions ofplus or minus 10 nodes result in different minima of the k-means objective (10), and the choice of N c to preserve majorbottlenecks is crucial. (iv) In the final stage, the clusteringtechnique overcomes the transmission constraints (2)-(4) andhence curtailment is highly underrated by ± : Withouttransmission constraints, all renewable energy is consumedbecause of its low marginal cost. B. Cumulative results
Model results to simulate historical curtailment are shownin Figure 4, presenting a breakdown per carrier. It also displaysthe installed capacity of renewables.Although the marginal costs of renewables were artificiallyassigned for the optimisation in (1) to fix the curtailment order,the energy-mix deviates from the historical mix only by . on average. We differentiate between solar, wind (onshore andoffshore) and hydroelectricity.The chosen resolution to model historical curtailment takesinto account the analysis of the previous Section III-A tobalance the mismatch of assigning input data to nodes versusclustering the transmission grid and overcoming importanttransmission bottlenecks. We choose a resolution of nodesas the excess according to (9) is in the range of − ofthe annual available renewable energy. Minor fluctuations aretolerated as they might not be compensated due to uncertainweather conditions. However, if excess energy accounts for TABLE IIC
URTAILMENT PER C ONTROL Z ONE
Year TSO zone Historical share [%] Model share [%] Error2017 50Hertz 17.7 20.1 +1 . TenneT 81.6 80.0 − . Transnet 0.1 0 − . amprion 0.7 0 − . +9 . TenneT 87 78.4 − . Transnet 0.3 0 − . amprion 0.7 0 − . Historical and model share in percent of curtailment per control zone inGermany in the years 2017 and 2018. The right column displays the modelerror compared to the historical data of [15]. All results are extracted fromnetworks at a resolution of 246 nodes. more than of the annual available energy, it would be ahighly uneconomical location of the power plant, because itis known in advance that a large amount of the years energycan not be used.A trend is seen that before 2017, the model tends tounderestimate the total curtailment, with only 80% of thehistorical curtailment captured in 2016. However as windgeneration grows, the model overestimates the congestionand therefore the curtailment, reaching 50% more than thehistorical numbers in 2018.
C. Curtailment per TSO area
To investigate the spatial distribution of curtailment acrossGermany, results per control area are presented in Table II forthe years 2017 and 2018 in percent of annual curtailment. Forconsistency, the model resolution is chosen such as in SectionIII-B. Results indicate, that curtailment numbers in our modeldeviate by up to from historical values, and by . onaverage.A validation of how these result change with the numberof nodes representing the model show the same four stagesas discussed in Section III-A: In stage (i), where curtailmentresults are highly overestimated and electricity demand andgenerators were assigned to incorrect nodes, curtailment in2017 is split
92 : 8 between TenneT and 50Hertz,
87 : 12 in 2018. These numbers deviate in both years by ± as thenetwork resolution changes. The balancing of stage (ii) resultsin a stable
80 : 20 split between TenneT and 50Hertz in 2017,and
78 : 22 in 2018 with deviations of up to in bothyears as the network resolution changes. Stage (iii) remainsrelatively random, which is true for stage (iv) as well, butin the latter, total annual curtailment is so low, such that theproportionality has no meaning. D. Curtailment per Quarter
Finally, we consider curtailment per quarter in the years2015-2018. Results are displayed in Table III in percent ofannual curtailment. The model resolution is chosen the sameas in Section III-B for reasons of consistency. Results indicatethat the distribution of curtailment at an hourly resolution
TABLE IIIC
URTAILMENT PER Q UARTER
Year Quarter Historical share [%] Model share [%] Error2015 I 24.0 33.4 +9.4II 15.6 10.6 -5.0III 17.3 14.2 -3.1IV 43.1 41.8 -1.32016 I 40.7 48.2 +7.5II 14.3 6.3 -8.0III 14.7 8.3 -6.4IV 30.3 37.2 +7.22017 I 25.6 23.3 -2.3II 24.7 19.7 -4.0III 7.9 8.7 +0.8IV 41.8 48.3 +6.52018 I 36.5 39.6 +3.1II 17.5 13.0 -4.5III 13.4 11.1 -2.3IV 32.6 36.3 +3.7Historical and model shares per quarter in percent of curtailment for theyears 2015-2018. The right column displays the model error compared tothe historical data of [16]. All results are extracted from networks at aresolution of 246 nodes. number of clusters R A M [ M B ] Memory consumption number of clusters s o l v i n g t i m e [ m i nu t e s ] Solving time
Fig. 5. Memory consumption and solving time per cluster resolution,exemplary numbers for the year 2017. model reflect the historical distribution with an error of inaverage . .Again, these results are validated on how they change withthe cluster size. Here, a positive trend can be observed asthe clustering happens mainly in space and not in time, suchthat results are stable for stages (i)-(iii). The average shareis reflects the number in Table III, while it starts fluctuatingtowards stage (iv), where we know that the overall curtailmenttends to , such that the proportionality has no meaning. E. Memory consumption and Solving times
Solving the full optimisation problem with a full resolutionnetwork of nodes and more than
HVAC or HVDClines requires approximately GB Random-Access-Memory(RAM) and runs for almost an hour, while a clustered networkof only nodes is twice as fast and needs about lessRAM, while providing more accurate results. IV. C
RITICAL APPRAISAL
This case-study covers Germany only, neglecting the factthat power can also be exchanged with bordering countries,such as France, Denmark, Poland, the Czech Republic, Austriaor Switzerland, reducing the overall curtailment of renewablesin Germany. Previous studies have pointed out, that interna-tional cooperation benefits renewable electricity markets [42].Further, to avoid the difficulty of keeping track of differentvoltage levels as the network is reduced, all lines are mappedto their electrical equivalents at 380 kV, the most prevalentvoltage in the German transmission system. The electrical pa-rameters and capacities of the lines use standard assumptionsfor kV circuits whereas in reality they vary from line toline. In addition, we use constant summer thermal ratings foran outside temperature of 20 Celsius throughout the year anddo not adapt them for lower temperatures or wind conditions.The use of winter ratings as well as dynamic line rating [10]on some congested lines today may account for the lowerhistorical curtailment compared to our model.Finally, the capacity factors for wind and solar from weatherdata overestimate historical production, so we linearly reducedthem by a factor of 0.9 for wind and 0.8 for solar for eachpoint in time and space.V. D
ISCUSSION AND C ONCLUSIONS
We have shown that historic curtailment in Germany canbe reproduced in the open model PyPSA-Eur using the latestdatabase for the locations of existing renewable generators.Results agree well in time (curtailment per quarter) and space(curtailment per TSO region), provided a balancing resolutionis used that is low enough to overcome assignment-errors andhigh enough to account for important transmission routes. Wesuggest to cluster the 306 node network to well below 280nodes, but not below 150 nodes. In this range, curtailmentin the model provides the best match with historical data. Aresolution below 100 nodes for Germany using a weightedk-means clustering scheme is not advisable.A
CKNOWLEDGMENTS
We thank Fabian Neumann, Elisabeth Zeyen and FrederickUnnewehr for helpful discussions, suggestions and comments.R
EFERENCES[1] European Comission: , Publications Office ofthe European Union, 2020, https://ec . europa . eu/clima/policies/strategies/2050 en/[2] European Comission: What is the European Green Deal? , PublicationsOffice of the European Union, 12/2019, https://doi . org/10 . Paris Agreement , UN Treaty Collection, II(27), 2016[4] Bundesministerium der Justiz und f¨ur Verbraucherschutz:
Gesetz f¨ur denAusbau erneuerbarer Energien , 754-27, 2014[5] Bundesnetzagentur f¨ur Elektrizit¨at, Gas, Telekommunikation, Post undEisenbahnen:
EEG in Zahlen 2018 , chapter 9.2[6] Bundesnetzagentur f¨ur Elektrizit¨at, Gas, Telekommunikation, Post undEisenbahnen:
Monitoringbericht 2019 , 01/2020[7] Sterchele, P., Brandes, J., Heilig, J., Wrede, D., Kost, C., Schlegl,T., Bett, A. & Henning, H.:
Wege zu einem klimaneutralen En-ergiesystem. Die deutsche Energiewende im Kontext gesellschaftlicherVerhaltensweisen , Fraunhofer ISE, 2020, http://ise . fraunhofer . de/de/veroeffentlichungen/ [8] Die Nationale Wasserstoffstrategie . bmbf . de[9] Brown, T., Schlachtberger, D., Kies, A., Schramm, S. & Greiner, M.: Synergies of sector coupling and transmission reinforcement in a cost-optimised, highly renewable European energy system , Energy, 160: 720-739, 10/2018, https://doi . org/10 . . energy . . . Impact From Dynamic LineRating on Wind Power Integration , IEEE Transactions on Smart Grid,6(1): 343-350, 08/2014, https://doi . org/10 . . . Opening the black box of energy modelling: Strategiesand lessons learned , Energy Strategy Reviews, 19: 63-71, 01/2018, https://doi . org/10 . . esr . . . Quartalsbericht 2015 zu Netz- und Systemsicherheitsmaß-nahmen; Viertes Quartal 2015 sowie Gesamtjahresbetrachtung 2015 ,chapter 3[13] Bundesnetzagentur f¨ur Elektrizit¨at, Gas, Telekommunikation, Post undEisenbahnen:
Quartalsbericht zu Netz- und Systemsicherheitsmaßnah-men; Viertes Quartal und Gesamtjahr 2016 , chapter 3[14] Bundesnetzagentur f¨ur Elektrizit¨at, Gas, Telekommunikation, Post undEisenbahnen:
Quartalsbericht zu Netz- und Systemsicherheitsmaßnah-men; Gesamtjahr und Viertes Quartal 2017 , chapter 3[15] Bundesnetzagentur f¨ur Elektrizit¨at, Gas, Telekommunikation, Post undEisenbahnen:
Quartalsbericht zu Netz- und Systemsicherheitsmaßnah-men; Gesamtjahr und Viertes Quartal 2018 , chapter 3[16] Bundesnetzagentur f¨ur Elektrizit¨at, Gas, Telekommunikation, Post undEisenbahnen:
Quartalsbericht zu Netz- und Systemsicherheitsmaßnah-men; Erstes Quartal 2019 , chapter 2[17] Brown, T., H¨orsch, J. & Schlachtberger, D.:
PyPSA: Python for PowerSystem Analysis , Journal of Open Research Software, 01/2018, vol 6(1),https://doi . org/10 . . PyPSA-Eur: An open optimisation model of the European transmission system
Energy Strategy Reviews, 22: 207-215, 11/2018, https://doi . org/10 . . esr . . . Linear optimalpower flow using cycle flows , Electric Power Systems Research, 158: 126- 135, 05/2018, https://doi . org/10 . . epsr . . . Gutachten zur Ermittlung des erforderlichen Netzausbausim deutschen ¨Ubertragungsnetz , Technische Universit¨at Graz, 12/2012,https://data . netzausbau . de/2022/NEP/NEMO II . pdf[21] Fuchs, B., Roehder, A., Mittelstaedt, M., Massmann, J., Natemeyer, H.& Schnettler, A.: Studie zu Aspekten der elektrischen Systemstabilit¨atim deutschen ¨Ubertragungsnetz bis 2023 , RWTH Aachen University,06/2015, https://bundesnetzagentur . de/SharedDocs/Downloads/DE/Sachgebiete/Energie/Unternehmen Institutionen/Versorgungssicherheit/System- u Netzsicherheit/Gutachten IFHT RWTH Systemstabilitaet2015 . pdf? blob=publicationFile&v=1[22] ENTSO-E: Transmission System Map . entsoe . eu/data/map/[23] Wiegmans, B.: GridKit extract of ENTSO-E interactive map , 06/2016,https://doi . org/10 . . NetzentwicklungsplanStrom 2013. Zweiter Entwurf der ¨Ubertragungsnetzbetreiber , 50HertzTransmission, Amprion, TenneT TSO & TransnetBW, 07/2013, chap-ter 7, https://netzentwicklungsplan . de/sites/default/files/paragraphs-files/nep 2013 2 entwurf teil 1 kap 1 bis 9 . pdf[25] Feix, O., Obermann, R., Strecker, M. & Regina, K.: Netzentwick-lungsplan Strom 2014. Zweiter Entwurf der ¨Ubertragungsnetzbetreiber ,50Hertz Transmission, Amprion, TenneT TSO & TransnetBW, 11/2014,chapter 5, https://netzentwicklungsplan . de/sites/default/files/nep 20141 entwurf teil1 . pdf[26] Feix, O., Wiede, T., Meinecke, M. & Regina, K.: Netzentwicklungsplan Strom 2025, Version 2015. Zweiter Entwurf der ¨Ubertragungsnetzbetreiber , 50Hertz Transmission,Amprion, TenneT TSO & TransnetBW, 02/2016, chapter 5,https://netzentwicklungsplan . de/sites/default/files/paragraphs-files/NEP 2025 1 Entwurf Teil1 0 . pdf[27] Rippel, K. M., Wiede, T., Meinecke, M. & Regina, K.: Netzentwicklungsplan Strom 2030, Version 2017. ZweiterEntwurf der ¨Ubertragungsnetzbetreiber , 50Hertz Transmission,Amprion, TenneT TSO & TransnetBW, 05/2017, chapter 5,https://netzentwicklungsplan . de/sites/default/files/paragraphs-files/NEP 2030 1 Entwurf Teil1 0 . pdf[28] Rippel, K. M., Wiede, T., Meinecke, M. & Regina, K.: Netzentwicklungsplan Strom 2030, Version 2019. ZweiterEntwurf der ¨Ubertragungsnetzbetreiber , 50Hertz Transmission,Amprion, TenneT TSO & TransnetBW, 04/2019, chapter 6,https://netzentwicklungsplan . de/sites/default/files/paragraphs-files/NEP 2030 V2019 1 Entwurf Teil1 1 . pdf/[29] Open Power System Data: Load, wind and solar, prices in hourlyresolution , 06/2019, https://doi . org/10 . Marktstammdatenregister: Stromerzeugungsein-heiten . marktstammdatenregister . de/MaStR[31] Schr¨oder, A., Kunz, F., Meiss, J., Mendelevitch R. & von Hirschhausen,C.: Current and prospective costs of electricity generation until 2050 ,Deutsches Institut f¨ur Wirtschaftsforschung (DIW), 2013, https://doi . org/10419/80348[32] eurostat: Nomenclature of Territorial Units for Statistics (NUTS)3 , 2013, https://ec . europa . eu/eurostat/web/gisco/geodata/reference-data/administrative-units-statistical-units[33] Q. Zhou & J. W. Bialek: Approximate Model of European InterconnectedSystem as a Benchmark System to Study Effects of Cross-Border Trades ,IEEE Transactions on Power Systems, 20(2): 782-788, 05/2005, https://doi . org/10 . . . Algorithm AS 136: A K-Means ClusteringAlgorithm , Applied Statistics, 28(1): 100-108, 1979, https://doi . org/10 . THE MAX-P-REGIONS PROBLEM ,Journal of Regional Science, 52(3): 397-419, 12/2011, https://doi . org/10 . . . . . x[36] Siala, K. & Mahfouz, M.: Impact of the choice of regions on energysystem models , Energy System Reviews, 25: 75-85, 08/2019, https://doi . org/10 . . esr . . Application of partitioningtechniques for decomposing large-scale electric power networks , Inter-national Journal of Electrical Power & Energy Systems, 16(5): 301-309,10/1994, https://doi . org/10 . Definingpower network zones from measures of electrical distance , IEEE PowerEnergy Society General Meeting, 07/2009, https://doi . org/10 . . . Multi-Attribute Partitioning of Power Networks Based on ElectricalDistance , IEEE Transactions on Power Systems, 28(4): 4979-4987,05/2013, https://doi . org/10 . . . Two partitioningmethods for multi-area studies in large power systems , InternationalTransactions on Electrical Energy Systems, 25(4): 648-660, 01/2014,https://doi . org/10 . . The role of spatial scale in joint optimisations ofgeneration and transmission for European highly renewable scenarios ,14th International Conference on the European Energy Market, 06/2017,https://doi . org/10 . . . Thebenefits of cooperation in a highly renewable European electric-ity network , Energy, 134: 469-481, 09/2017, https://doi . org/10 . . energy . . ..