Integrated Techno-Economic Power System Planning of Transmission and Distribution Grids

The energy transition towards renewable and more distributed power production triggers the need for grid and storage expansion on all voltage levels. Today’s power system planning focuses on certain voltage levels or spatial resolutions. In this work we present an open source software tool eGo which is able to optimize grid and storage expansion throughout all voltage levels in a developed top-down approach. Operation and investment costs are minimized by applying a multi-period linear optimal power flow considering the grid infrastructure of the extra-high and high-voltage (380 to 110 kV) level. Hence, the common differentiation of transmission and distribution grid is partly dissolved, integrating the high-voltage level into the optimization problem. Consecutively, optimized curtailment and storage units are allocated in the medium voltage grid in order to lower medium and low voltage grid expansion needs, that are consequently determined. Here, heuristic optimization methods using the non-linear power flow were developed. Applying the tool on future scenarios we derived cost-efficient grid and storage expansion for all voltage levels in Germany. Due to the integrated approach, storage expansion and curtailment can significantly lower grid expansion costs in medium and low voltage grids and at the same time serve the optimal functioning of the overall system. Nevertheless, the cost-reducing effect for the whole of Germany was marginal. Instead, the consideration of realistic, spatially differentiated time series led to substantial overall savings.


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Historically, in Germany electric energy was supplied by large conventional power plants in the 21 transmission grid to consumers mainly connected to the distribution grid. Distribution grids were 22 therefore dimensioned to ensure power supply in extreme load cases. In this context, the clear division 23 of transmission and distribution operation and planning is reasonable. 24 In the year 2000, the German Renewable Energy Act was introduced in order to reduce greenhouse 25 gas emissions, leading to a strong expansion of renewable energy (RE) systems, which is expected 26 to be continued in the future. By 2050 at least 80 % of Germany's electricity demand is supposed to 27 be supplied by RE production [1]. Due to their relatively small nominal power these power plants 28 are mainly connected to the distribution grid (e.g. [2,3]). This substantial transition of energy supply In addition to feed-in management further innovative options supplementing conventional grid  Furthermore, a number of these novel options as well as the transformation of the generation 148 landscape and the planned electrification of the heat and mobility sectors will impact dependencies and 149 simultaneities on the demand and generation side, making simplified worst-case assumptions based 150 on sweeping standardized factors less precise and thus leading to an over-or underdimensioning of 151 the grid [35]. Numerous studies have therefore analysed and reviewed new innovative grid planning 152 methods and design cases [35,36,[38][39][40], though these are not widely applied by DSOs.

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The software tool eGo aims at optimizing the electrical grid and storage devices throughout all 155 voltage levels. This is achieved by a top-down approach: First, the integrated EHV and HV grid 156 is optimized with the tool eTraGo (Section 3.2). Subsequently, a selection of MV (and subordinate 5 of 29 The two resulting input data models are at an hourly and geographically high resolution. The 175 methods and assumptions of the allocation of electricity consumption and power generation capacities 176 in a high spatial resolution for both data sets are described in a previous article [41]. The developed 177 EHV/HV grid topology model for Germany is based on OSM data and is created with the heuristic 178 abstraction tool osmTGmod [52]. By revising the tool the 110 kV grid was integrated into the grid   exclusive interfaces to the HV level. One of these MV grids is topologically presented in Figure 2(b). The Status Quo grid topology model for the EHV and HV level (a). In (b) one of the 3,376 underlying MV grid topologies and its connection to the HV level is displayed. Its location corresponds to the zoom box in (a). The connected generation (except for MV generators in (b)) and demand as well as transformers are not displayed for better visualization. A visualized bus which seems to connect two voltage levels is actually modelled as two buses connected by a transformer (see also [14])

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Addressing the high complexity of the data model we used certain reduction methods which 219 abstract the temporal and spatial resolution.

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The spatial resolution was reduced by adapting a reduction method described in [9]. Therefore the 221 original number of buses was decreased by applying a k-means clustering algorithm using Python's 222 scikit learn package (cf. [64]). The weighted squared euclidean distances of each k centroid to its 223 1 eGo 100 scenario: includes seven technologies for Germany (biomass, run_of_river, solar, wind_onshore, wind_offshore, geothermal, reservoir) and additionally gas for neighbouring countries.  The weight of each original bus is relative to its today's (referring to the status quo scenario) 230 load and conventional generation capacity. In this work we chose a k of 300. Thus the 11,305 buses 231 (consisting of 7,108 joints and 4,197 buses being connected to load, generation and/or transformer(s)) 232 are reduced to this value. The topological difference before and after clustering can be observed  r, x l,380 = r, x l · 380 v_nom l 2 , ∀ l ∈ L (1) All lines between two clusters are represented as one. The nominal capacities and the admittances 241 of the original lines were summed up accordingly.

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The generators and storage units at the buses are aggregated with respect to the carrier type.

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Considering weather-dependent resources (i.e. wind and solar) which differ from one weather cell to 244 another, the power plants normalized maximal possible power outputs are weighted by their capacities 245 within one carrier type. In case of storage units the aggregation differentiate additionally according to 246 the power-to-energy (P-E) ratio.

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The temporal resolution can be reduced by various clustering methods. Coming to inter-temporal 248 restrictions which the dispatch of storage units imply, many of those methods are limited in their 249 performance. In this work, we chose a simple solution which periodically leaves out snapshots (cf. [9]).

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Particularly we considered only every fifth hour. This reduces the run-time of eTraGo substantially and 251 also implies significant run-time savings for the following processes in eDisGo (see Section 3.3.3).

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The reduced data set was subject to a linear optimal power flow method (LOPF) [65]. As 253 optimization variables are grid (F ) and storage investments (H n,s ) as well as the dispatch variables 254 of generators (g n,r,t ) and storage units (h n,s,t ) (see Equation 2). The indices , n, r, s, t label branches, marginal costs (EUR/MWh) for generators (o n,r ) and storage units (o n,s ). Due to the applied temporal 257 complexity reduction each snapshot is weighted as w t = 5. The specific capital costs (EUR/MW) for 258 each branch (power line, link or transformer) and each storage unit s are defined by c and c n,s . 259 min F ,H n,s g n,r,t ,h n,s,t ∑ c · F + ∑ n,r,t (w t · o n,r · g n,r,t ) The assumptions on the investment costs can be observed in Table 1 were considered potentially providing short-term and long-term flexibility to a future electricity system.

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Battery storage units could be built at every node and operate on an hourly scale being able to store and 273 provide energy for six hours at full capacity [43]. In contrast the hydrogen storage units have a much 274 higher P-E ratio of 1/168 and could only be built at certain buses where the potential of natural salt 275 caverns is given [43]. Moreover, all lines, DC links and transformers were assumed to be extendable.

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The grid expansion was limited such that each line can be extended by a maximum of four times its according to the osmTGmod data model the average number of parallel power line systems is 1,9 The optimized dispatch of this second LOPF is used for all generators and storage units as p set 294 which has to be met within the PF problem. All aggregated generator are modelled as PV generator 295 since a resolution of k=300 leads to sufficient aggregate sizes. Consequently, the reactive power 296 dispatch will be a variable to be determined by the PF. The reactive power will be produced locally 297 where it is demanded. The reactive behavior of the grid components and the aggregated loads is 298 considered. The aggregated loads are assumed to have a power factor cos φ of 0.95 (inductive) [14,68].

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The bus with the largest annual dispatch in the LOPF is defined as the slack bus for the PF [14,69].  The central reference points for the interface are HV-MV substations. In open_eGo, they are 306 identified throughout the above described data processing [41,42]. HV-MV substations represent the 307 highest resolution for the top-level optimization (generators and loads are aggregated at this level). At 308 the same time they serve as slack buses for the subordinate MV grids.

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As described above, a clustering method is applied to the integrated EHV and HV grid in order to 310 reduce its spatial complexity. For this reason, the first step of the interface consists of distributing the 311 optimization results back to the original HV-MV substations, a process which is called disaggregation.

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During disaggregation, the optimization results obtained for the clustered optimization problem 313 are distributed uniformly using specific weights, depending on which type of component the results

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where computed for. More specifically, for each generator representing a cluster, its active and reactive The distribution of state of charge, denoted by soc, and power output, denoted by h, is governed 329 by Equations. 5 and 6, which are similar to Equation 4, except that they have to take into account the 330 current snapshot t, as the values they are distributing are time dependent.
Again, the values are distributed as weighted averages, except that the weights are determined With regard to fluctuating generators (wind and solar), the dispatch comprises the uncurtailed 347 potential only. In addition to the potential, an absolute amount of curtailment is calculated per energy 348 carrier and weather cell. This approach allows certain degrees of freedom when allocating the absolute 349 amount of curtailed energy to the individual generators in eDisGo (cf. Section 3.3.3).

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In eTraGo, the installation of storage units is an essential parameter of the investment optimization.

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It is important to note that the intended purpose of storage units is not only limited to a temporal 352 balance of energy. They can be furthermore used in a grid-supportive manner. In order to make this 353 grid-supportive characteristic available also to MV grids, eDisGo optimizes the spatial distribution of As mentioned in Section 3.2, the temporal resolution was reduced by only considering every 360 fifth hour. Furthermore, a spatial clustering was applied to the original HV-EHV network. In order 361 to achieve acceptable computation times, another spatial reduction was necessary with regard to the 362 MV grids. Simulating the total number of over 3,000 MV grids was beyond the scope of this study.

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Instead, the objective here was to estimate the total costs of grid expansion, based on a smaller number 364 of representative MV grids. To achieve this, a k-means clustering algorithm as described in 3.2 was 365 applied.

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Clustering is a process of finding natural groups in a set of data [70]. As a basis for this analysis a By defining numeric attributes, each MV grid can be described as a point in a multidimensional space (cf. Figure 3). The k-means algorithm then takes the task to identify clusters of points within this space. Due to the usage of the Euclidean distance an equal weight is assigned to each attribute. Therefore, as a first step the attribute data is normalized as follows where each value x a,i represents an attribute a ∈ {1, ..., N a } of grid i ∈ {1, ..., N i }.

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After the successful convergence of the k-means algorithm a representative grid is chosen for 377 each cluster. This grid is the one with the shortest distance to the cluster center representing all grids 378 within this cluster. In order to calculate expansion costs for all grids the results for one representative 379 is multiplied by its weight which is determined by the amount of grids in the particular cluster. In Relative deviation of grid expansion costs of different k cluster approximations compared to the calculation of all MV grids using the simple worst-case method. weighting of the 600 representative grids as well as the corresponding members of each cluster can be 389 observed in Figure 6.   side and modelled as a PV node with a set voltage of 1 p.u..

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The set allowed equipment loading and voltage deviations used in this study to identify grid 438 expansion needs are listed in Table 3 and 4, respectively. Different limits are applied for the HLF 439 and the RPF, among other due to the prevailing planning principle of (n-1) security for consumers  k n,r,t = a · (V n,t − V threshold ) where k n,r,t is the curtailed power of generator r at node n and time step t, V n,t is the bus voltage, 465 V threshold is the voltage above which solar and wind generators are curtailed and a is the slope factor of 466 the linear relation.

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The method is adapted in such a way that the curtailment of a DG is not only a function of the 468 bus voltage but also of the weather-dependent availability, whereby DG with higher bus voltages and 469 availability are potentially curtailed stronger. Furthermore, an offset is added in order to guarantee the 470 fulfillment of curtailment requirements. The derived linear relation is shown in Figure 8 and stated in 471 Equation 9. 472 k n,r,t g n,r,t · G n,r = a · (V n,t − V threshold,n,t ) + o f f set Here,ḡ n,r,t and G n,r are the weather-dependent normalized availability and the nominal power well becomes dependent on these two variables and is calculated according to where V n station ,t is the voltage at the station's secondary side, and ∆V n allowed is the allowed voltage 480 deviation in the RPF (cf. Table 4). s.t. ∑ n,r k n,r,t = K t ∀n, r ∈ (solar, wind) (12) k n,r,t ≤ḡ n,r,t · G n,r ∀n, r ∈ (solar, wind), t where H g is the storage capacity to be distributed in the respective MV grid.

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Since storage capacity is limited and might not be sufficient for peak shaving in each feeder, 512 all MV feeders in the MV grid are first ranked by grid expansion costs that arise from necessary 513 grid expansion needs without storage, applying the grid expansion measures described above. The 514 following four steps are then conducted for each feeder, starting with the feeder the highest costs can 515 be attributed to.

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First, a PF is conducted to determine if any overloading or voltage issues occur in the respective 517 MV feeder. If that is the case, storage nominal power is determined in a second step by finding the 518 storage size that minimizes the maximum load in the feeder using Equation 16. Here, l f t is the applicable load factor in the respective time step depending on whether it is a HLF 520 or a RPF (see Table 3). P f ,t is the active power in the feeder at the HV/MV substation calculated from 521 the electrical load d n,t , the generator dispatch g n,r,t and grid losses l f ,t in the feeder (see Equation 17).

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Analogously to P f ,t , Q f ,t is the reactive power in the feeder calculated from the reactive power of loads 523 and generators, d n,t and g n,r,t , respectively, and the reactive power losses l f ,t (see Equation 18).
The storage size that minimizes Equation 16

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The results are presented for the scenarios NEP 2035 and eGo 100 with respect to the methods and 558 assumptions described in the previous section. The co-optimization of grid, storage and dispatch on the HV and EHV levels reveals that it is 561 most cost effective to substantially invest into the grid infrastructure. Hence, a total (n-0) capacity of 562 57.1 GVA should be additionally built. Due to the consideration of (n-1) security the value represents a 563 total capacity of 89.4 GVA. This additional capacity implies an increase of 5.5 % compared to the status 564 quo grid (considering the reduced network with k=300 nodes). In terms of overnight costs the grid 565 expansion in the entire model region adds up to 7.3 bn EUR. Table 7 provides an overview of how 566 these costs are regionally allocated.

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The more specific spatial allocation of grid expansion measures in the EHV/HV can be observed 568 in Figure 10. Mainly northern and cross-border line capacities are expanded. The substantial overall 569 investment into cross-border line capacities accounts for 21 % of the overall grid investment (cf. Table   570 7). In contrast, storage investment is merely needed. Only a negligible capacity of 11.4 MW is built 571 near the border to Austria (see Figure 10). The share of RE in energy production is 56.9 % for the to use this energy to substitute conventional energy production it is more cost effective to use the 576 flexibility of available conventional power plants, which are expected to still be existent in this scenario 577 (cf. Figure 1). Moreover, the mentioned strong interconnections to the neighboring countries provide 578 additional cost effective energy balancing resulting in a net import of 10 % compared to the German 579 load.

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As described in Section 3.2 after two LOPF a PF was performed that converged in every snapshot.

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Hence, the results include and consider reactive power loads and grid losses. As the 300 buses were all 582 modelled as PV nodes reactive power was supplied locally. Grid losses for the German system were 583 reasonably low at 0.6 % compared to the demand. For the MV/LV level additional losses between 584 1.1 % in case of the RPF and 1.4 % during HLF were calculated.

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The grid expansion costs for the MV and LV level for the four approaches Flex, Reference,

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Worst-Case-600, and Worst-Case-3591 described in Section 3.3.3 can be observed in Table 6  In this scenario the optimized power plant dispatch leads to an overall RE share of 99.9 % (0.1% 599 are produced by the gas fired power plants in the countries surrounding Germany, cf. Figure 1).

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Furthermore the co-optimization depicts a grid expansion of 73.2 GVA in the EHV and HV levels.

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Considering the (n-1) security this value rises to a total expansion of 114 GVA and a monetary overnight 602 investment of 8.6 bn EUR (cf. Table 7). This implies 28 % more grid expansion than needed in the NEP 603 2035 scenario.

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In contrast to the NEP 2035 scenario the system requires a significant amount of storage units. An corresponds to an investment of 11 bn EUR (cf. Table 7). In Figure 11 the spatial allocation of these grid  Table 6). This implies that the usage of  weather-dependent power output is reduced accordingly. Since the maximum RPF is highly significant

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In this work, complexity reduction plays an important role. The spatial complexity is reduced 743 not only on the MV level but also on the EHV/HV level by the usage of k-means algorithms. This 744 method only finds local optima and is thereby sensitive to the initial random guess of cluster centroids. 745 We minimized this effect by choosing many iterations with different initial settings and small inertia 746 tolerances in order to get more robust results. Furthermore, the computing of Euclidean distances 747 makes the MV clustering sensitive to outliers, i.e. MV grids with extraordinary attributes. To avoid 748 this, a utilization of a k-medoid algorithm can be reasonable [80]. However, [71] showed that the feasible for the overall system. Only for 0.9 % of all MV grids in Germany this prerequisite was given.

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Accordingly, the overall investment cost saving was only marginal. In this context, the optimal usage 782 of curtailment did also not reduce the overall MV grid expansion costs significantly although in some 783 grids the cost savings are reaching 30 %. Reasons for this effect have been discussed and need to be 784 further analysed.

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Comparing the results to grid expansion costs derived by a state of the art worst-case approach, 786 substantial savings depending on the scenario of about 50 % were calculated. It can be concluded that 787 the usage of realistic, spatially differentiated time series instead of using general simultaneity factors 788 leads to significant saving potential for distribution grid planning. Nevertheless, this outcome is 789 biased by a linear downscaling of the potential weather-dependent generation time series, minimizing 790 potential and relevant worst cases. As a future research it will be a task to find a more sophisticated 791 correction method which would reflect the weather behavior more accurately. Further research will 792 also be directed toward including the expected electrification of the heat and mobility sectors in the 793 future scenarios that might significantly increase the load in the distribution grids. This could further 794 increase the relevance of an integrated grid planning in order to leverage flexibility potential these 795 new loads could provide and keep resulting grid expansion needs at a minimum.