Deep Learning Surrogates for Low-Voltage Grid Planning

Deep Learning Surrogates for Low-Voltage Grid Planning Elias Franz Hanser1, Anurag Mohapatra2, Beneharo Reveron Baecker1, Thomas Hamacher1,2 1Chair of Renewable and Sustainable Energy Systems, 2Center for Combined Smart Energy Systems Technical University of Munich, Munich, Germany Abstract—We introduce a deep learning surrogate, built on free, open-source data and tools, to predict transformer demand time series under future decarbonization with sector coupling scenarios for any German low-voltage grid. This work directly addresses the current research landscape of opaque national studies, unverifiable or imprecise modeling decisions, and privileged access to real grid data. First, a state-of-the-art, scalable, groundtruth generation tool was developed, which replicates physical grids and populates them with harmonized time series data. This tool generated a representative dataset of 1,000 low-voltage grids for training a transformer architecture-based surrogate intended to replace expensive energy system optimization models. The surrogate reduces computation time by three orders of magnitude, while maintaining peak load prediction errors below 10 % for the majority of our grids. With this surrogate, bottomup results for all 500,000 low-voltage grids in Germany can be obtained within approximately 5 days of computation time. Index Terms—Energy System Modeling, Grid Planning, Machine Learning, Open Source, Surrogates I. INTRODUCTION Low-voltage (LV) distribution grids are projected to host a large share of distributed energy resources (DERs) required for Germany’s decarbonization targets [1]. The increasing intermittency of renewable energy generation, the growing share of inverter-based resources, and the evolving demand patterns resulting from sector coupling require a highly optimized system operation. Furthermore, the costs of expanding power grids to accommodate rising electricity demands pose a major challenge to the energy transition. The German electricity authority conservatively estimates that the necessary distribution grid reinforcements will cost more than 200 billion euros by 2045 [2]. Consequently, there have been multiple attempts at quantifying the electrical load for LV distribution grids under various degrees of decarbonization scenarios and the subsequent transformer and line upgrades needed to reliably operate them [3, 4]. A key element of the mentioned studies is anticipating the change in the simultaneity factor at the transformer after sector-coupling and electrical storage optimization. The net demand at the transformer cannot be a simple inelastic addition of the multi-sectoral demand transferred to electricity, as the prosumers and grid operators will shift towards flexibility measures like photovoltaic (PV) self-consumption or peak curtailment. Instead, depicting flexibility measures on a national level requires a bottom-up approach, taking into account the heterogeneous LV grid level system constraints. The current state-of-the-art for national-level grid expansion and planning studies in Germany is mainly based on representative grids and standard load profiles. The study in [5] uses a set of representative grids for its national model by clustering and filtering over 4,000 LV grid models provided by a few grid operators. Likewise, a recent government-commissioned study on distribution grid expansion due to market and gridoriented flexibility mechanisms assumes a homogeneous and abstracted grid model for the whole country [6]. This same grid abstraction style was also used in [4]. The report in [3] had an even more drastic abstraction level, which avoided performing a load flow altogether. Even when using the methodology of representative grids, the assumptions behind the underlying clusters can be vastly different. As an example, the study of [5] categorizes LV grids into ten representative clusters, the popular SimBench dataset provides a rural, semiurban, and urban grouping [7], and the study in [6] simply assumes the whole country to be a homogeneous grid. These abstractions are understandable due to practical considerations of model-building effort. However, the simplifications can be superficial and opaque for researchers or distribution system operators (DSOs), as the underlying analysis model is seldom published for inspection, and the obtained clustering rules are not verifiable for the user without access to the proprietary grids that generated them. Most nationallevel studies’ results have to be accepted by default due to the lack of alternatives. They are consequently often used indiscriminately for a variety of analyses, regardless of their suitability. This contradicts the principles of open-source research, as access to the input data is limited to a few privileged institutions. Linear optimization models tailored to the user’s LV grids can overcome the limitations of representative grids and can be built using verifiable open-source frameworks. They have been repeatedly and successfully applied to test different flexibility scenarios and the resulting implications on LV grids [8]. Still, two major challenges arise when setting up and solving distribution grid models with grid numbers on a national scale: •Parameterizing these optimization models is challenging and requires detailed data to represent the diverse grid and settlement structures. The distribution grid models for the whole country cannot be made public as they are considered critical infrastructure. Similarly, generation and demand datasets are difficult to source from measurements. Solutions in the form of heterogeneous tools exist and are 24th Power Systems Computation Conference PSCC 2026 Limassol, Cyprus — June 8-12, 2026 Cost-optimal expansion and operation of: PV, HP, battery, thermal storage, BEV charging MILP & Power Flow – f(X) Ground Truth • Harmonized datasets • State-of-the-art • Open-source Fast Approximation for • Many LV Grids: Full city/country model • Many Scenarios: % DER adoption, peak pricing, weather, curtailment Non-convex AC power flow Target Data – Y Transformer LV side hourly oneyear time series: Active Power (P) Reactive Power (Q) Fourier feature encoding, VMD preprocessing, Transformer Encoder Surrogate Model – f’(X’) Time series for each building: PV, space & water heat, COP, BEV charging & availability, appliance and lighting demand Input Data – X Grid Topology + Line Specs DER Expansion & Operation Aggregate Time Series Data: Expected PV, space & water heat, COP, BEV charging & availability, appliance demand,temp. Surrogate Input Data – X’ Grid: total resist. R, # feeders Aggregate Building Data: # (non)res. bldngs, # households, # occupants, # cars, RegioStaR7, ∑(non)res. bldng. base/floor area Remodeling of real grid & buildings with real census, street & building geometry data Grid & Demand Generation 1,200 LV grids at representative locations in Germany to be �lled with pre-generated grids Training & Testing Data Demand & production pro�les based on physical building simulations and national statistics Building selection of investigated grid Potential User Desired DER Scenario Training Inference Optional: Provide known data (e.g. grid topology) Fig. 1. Schematic summary of the SurroGrid repository. A ground-truth LV grid energy system modeling tool chain was designed based on open-source and harmonized tools, data, and methods. A computationally fast deep learning surrogate model is trained using the results of 1,200 representative grids. With minimal input requirements, potential users can obtain exact but computationally expensive ground-truth results or fast approximate surrogate results. commonly applied to generate synthetic model input data. Yet, inconsistent underlying assumptions among these tools hinder the integration of the resulting data. For example, the space-heating demand of a representative household derived from one tool may not be directly compatible with the electrical load profile provided by another tool. •Even with significant future advances in computational capabilities, performing linear optimizations under varying scenarios for all of the 500,000 German low-voltage grids [9] or any considerably sized subset will remain computationally intractable. We tried to address the quick scenario analysis question for a single given LV grid in [10] and [11] by proposing accurate and transferable LSTM, transformer, and GNN-based surrogate models supplied with a few Mixed Integer Linear Programming (MILP) runs at different DER penetration as training data. The models predicted the net aggregated demand time series at the transformer, with residential flexibility optimization in a 100 % decarbonized distribution grid. The inference time for scenario analysis was drastically reduced, but the input data burden and the intractability for a large number of grids remained a challenge for a national-level surrogate. In this work, we are proposing a methodology for a national LV grid surrogate, as shown in Fig. 1. The repository, SurroGrid, is available at [12]. Our approach is built to be transparent and verifiable, and can improve in accuracy as the underlying tool chain becomes upgraded with time. Our key contributions in this work can be summarized as follows: •Asurrogate model methodology for entire German LV grid network using only publicly available databases such as open-source weather data or street maps. •A state-of-the-art open-source ground-truth generation suite for any LV grid in Germany with harmonized assumptions on the grid, generation, and demand models. The tool requires minimal contribution from the user to create a replica of their non-digitized grids with coherent time series data. •A computationally cheap surrogate model that can be used directly for any LV distribution grid in Germany with a reasonable accuracy expectation. II. METHODOLOGY We constructed the surrogate for a single LV grid in [10, 11] with multiple MILP cost-optimizations at different levels of DER penetration. These runs needed a high-fidelity input dataset of grid topology, hourly demand, and generation profiles from four real and representative grids in the city of Forchheim, Germany. The obvious challenge in producing a surrogate model at the national level is the lack of a vast and diverse set of real distribution grid models and time series data covering the whole country. Popular benchmarks like [7] might be representative of specific real-world conditions, but only offer a small number of grids to reasonably train and evaluate a surrogate model on the full distribution of possible grid topology, generation, and demand. Additionally, even if there was access to a sufficient amount of real LV grid data, such as in [5], the workflow would not be open-source and thus not verifiable. In this work, as shown in Fig. 2, we use synthetically generated LV grid models, demand, and generation profiles for the entire training dataset using an open-source tool chain. We ensure that the input datasets into these tools are harmonized to guarantee a congruence in key assumptions across grid topology, demand, and generation time series. The methodology for generating an unbiased dataset and training the surrogate model is explained below. A. Ground-Truth Data Generation Procedure 1) Grids: We use the synthetic LV grid generation tool pylovo, which takes open-source geospatial data, government statistics, and empirical grid planning principles to generate consistent radial grids following a street map [13]. The tool 24th Power Systems Computation Conference PSCC 2026 Limassol, Cyprus — June 8-12, 2026 emobpy districtgenerator pvlib MILP Optimization of Building DER Expansion and Operation Non-Convex AC Power Flow Buildings (OSM, CLC, TABULA, Census) Streets, Equipment (OSM, DIN) Weather (PVGIS TMY) pylovo Household Elect. Pro�les (Smart Meters) Nonres. Elect. + Water Heat Prfls. (synPro) When2Heat TechnoEconomic Data Mobility Statistics + BEV Data Building Type, Use Area, Occupancy Electrical Demand Pro�les Temperature, Solar Radiation Temp., Pres., Hum. Building Occupancy Car Ownership + Usage Solar Radiation Wind Speed, Temp. Roof Geometries TemperatureHeat Pump COPs Space + Water Heat Demand Pro�les PV Peak Capacity Usage Pro�les Technology/Operation Costs + Ef�ciencies BEV Charging Availability + Demand Bldng. Use/Type, Age, Geometry, Occupancy Grid Topology, Line Impedances Net Building Node Power Demand Fig. 2. Ground-truth grid forecasting workflow with input datasets (blue) and used tools and methods (green). uses publicly available building and street data to classify building types and estimate the number of households connected to the street network, forming the basis for grid dimensioning. The database in this work integrates OpenStreetMap (OSM), the German census 2012, and Corine Land Cover (CLC). The Typology Approach for Building Stock Energy Assessment (TABULA) is used to derive additional building characteristics, and German DIN norms are used to size and place the assets in the synthetic grids. Additionally, all buildings are assigned use types, occupations, and geometries which are then carried over to the subsequent generation workflow, as shown in Fig. 2. It is worth mentioning here that, aside from a researcher working with open-source data, our subsequent workflow could use digitized real grid topologies and line data from a DSO, as was the case in the [5] study, if the area of investigation is suitably covered by the set of real grids. Similarly, a DSO without fully digitized grids could use the pylovo tool to generate a full proxy grid with a selection of relevant buildings. Ideally, the distribution of possible grid types, including details such as topology, building geometry, and occupation, is obtained by generating all German LV grids and sampling a reasonably sized subset for surrogate training. At the time of creating our dataset, the pylovo tool was limited to grids in only the state of Bavaria. Consequently, we propose an alternative sampling procedure that takes pre-generated grids in Bavaria and links them to matching German locations, leading to an approximate representation of the German LV grid distribution. These same locations are later used to obtain weather and demand statistics for subsequent time series generation steps. However, the pylovo tool is already planned Fig. 3. (a) Sampled grid locations within Germany for obtaining local weather data and statistics for load profile generation. (b) Pre-generated proxy grid locations within Bavaria for obtaining LV grid topologies and building information. (c) Expected distribution of population densities when sampling German grid location (blue) and distribution of population densities in the pre-generated Bavarian grids (green). to be expanded to more German states, which might render the approximate sampling step superfluous for future works. This sampling procedure is based on two basic assumptions: Assumption 1. The LV grid density, counted as the density of transformers, approximately follows the population density to help us sample the grid locations in Germany. This is motivated by the population density of a region being proportional to the resulting demand density, which in turn translates into a grid number density by assuming equally sized transformers over all regions. The suggested ideal sampling procedure is approximated to first-order sampling from the 1 km×1 km population cells obtained from German census data. More sophisticated approaches could consider different proportionality rates due to differing simultaneity factors across different regional structures. Assumption 2. The important characteristics of an LV grid are mostly determined by its underlying population density, i.e., similar degrees of urbanization produce similar building and grid structures. We link the sampled population cells to our set of Bavarian grids. Ideally, a German cell is then linked to a random Bavarian cell with the same population density, in which a new pylovo grid would be generated. We already had available a pre-generated grid dataset of about 5,000 grids within various postal codes, considering the distribution of urban, suburban, 24th Power Systems Computation Conference PSCC 2026 Limassol, Cyprus — June 8-12, 2026 and rural areas (see Fig. 3 (b)). Therefore, we simply assign grids from this set based on population density. As shown in Fig. 3 (c), this set allows the sampling of around 1,200 population cells displayed in Fig. 3 (a), without over-assigning any pre-generated grid. The selected LV grids are split into 800 grids for training, 200 grids for validation, and 200 grids for testing the surrogate model. 2) Time Series Data: Each building in a selected grid is populated with various time series, as shown in Fig. 2, for the later MILP operation. These time series are electrical demand, space and domestic hot water heat demand, rooftop PV generation, heat pump coefficient of performance (COP), a set of battery electric vehicle (BEV) charging demands, and corresponding home charging availabilities. We fix the heat pump and building appliance operation to fixed power factors of 0.95 (ind.) and 0.959 (ind.) [14], respectively, to obtain reactive components. Similarly, the PV inverter is operated optimally to counteract the heat pump (HP) and appliance reactive power demand while being constrained to remain above a minimum power factor of 0.95. We employ methods that employ physical models tailored to the exact building geometries and apply popular and standard, opensource toolboxes. These will be described in more detail within the next paragraphs. Electrical Demand: We assign real smart meter electrical profiles as per the following steps, which avoids the computational costs of bottom-up appliance-level generation of household electrical demand profiles or the collinearity from assigning standard load profiles: •Step 1 - For each household in a building, sample a yearly electrical demand from the demand by household size distribution [15]. These probability distributions are scaled to remove the domestic hot water heating demand contribution, which has to be covered separately under the assumption of efficient electrification of the heating sector with heat pumps. •Step 2 - To each household assign the closest profile in yearly total demand from the smart meter profile pool and scale it to the actually sampled electrical demand. •Step 3 - Add up all the household profiles to obtain a single building profile. We take a pool of over 1,600 real smart meter measurements in hourly resolution from a pilot project in Bavaria [16]. The smart meter measurements were taken in 2009, which had a low DER and sector-coupling penetration. Thus, they are deemed suitable to provide pure electrical appliance and lighting demands of households. Furthermore, the aggregated profile set was rescaled at each hour such that the expected load profile after the above sampling procedure follows the national BDEW standard load profile H25 [17]. With these steps, we aim to conserve real household variability among each profile on the local level while also preserving the shape of the national standard load profile upon aggregation. Currently, the smart meter dataset from [16] is not yet openly available, but the same three steps can be applied to any reasonably large smart meter measurement dataset. We believe this requirement does not diminish the opensource character of our work, as numerous comparable measurement datasets are publicly available for different regions. Alternatively, though increasing the computation time, the districtgenerator in-built stochastic electrical profile generator can also be employed. Other Time Series: A generation profile based on the building geometry is produced with pvlib [18] for each building roof section. The heating demand is obtained from the districtgenerator’s [19] 5R1C and occupancy models, which are initialized according to a building’s use type, geometry, and occupancy. Mobility charging demand and availability profiles are generated according to the physical driving and usage models of emobpy [20]. The When2Heat [21] methodology allows the determination of temperature-dependent heat pump COPs. Lastly, for nonresidential buildings connected to the LV level, making up approximately 3 % of our building database, electrical load and water heat profiles are obtained from synGHD [22] and rescaled by building size. We ensure that the input datasets obtained from grid generation, such as building geometry, use-type, and occupancy, are consistently used across all tools. The grid’s locationspecific typical meteorological year weather data from the open-source PVGIS project [23] is used coherently across the tools to generate weather-related time series. Mobility statistics for different household types and regions [24] are used for assigning BEVs, where model specifications are sampled from the 50 most selling BEVs of the past 5 years [25]. 3) MILP Optimization: The pre-power flow net building demand is obtained from a MILP cost-minimization of the 1,200 pylovo grids, now populated with corresponding generation and demand time series. Reactive Power Building at Bus i Active Power PVr pPV i,r,t cf PV i,r,t qPV i,r,t κPV i,r pbat,ch i,t i,t delec,q i,t delec i,t dBEV i,c,t ddhw i,t dsh i,t ϵbat,e i,t κbat,p iκbat,e i Battery pbat,dch γTS,ch i,t κTS,p iκTS,e i i,t γTS,dch Thermal Storage γTS,e i,t Heat Domestic HW Space Heating pHP i,t γHP i,t pHP,aux i,t γHP,aux i,t qHP i,t copHP i,t κHP i Heat pump Aux. heat κHP,aux i pWB i,c,t ... ... ... μWB i,c,t i,c,t μBS,dch i,c,t μBS,e i,c κBS,e i,c,t μBS,ch Mobility BEV Storage c Wall box c κWB i,c avaWB i,c,t 0 1 Grid pimp qimp i,t i,t pfeed-in i,t qfeed-in i,t Fig. 4. MILP building reference energy system, including decarbonization options for the heating and mobility sector, as well as decentralized generation and storage of electricity with PV modules and battery. Figure adapted from [26]. Energy System: The building reference energy system for the MILP problem is illustrated in Fig. 4. It enables 24th Power Systems Computation Conference PSCC 2026 Limassol, Cyprus — June 8-12, 2026 the electrification of the distribution system by integrating heat pumps and auxiliary heating rods for peak heating demand in winter. While PV modules and batteries represent decentralized generation and storage sized endogenously by the optimization, charging points in the mobility sector are exogenously allocated to buildings. The BEVs are charged flexibly and cost-optimal within their charging availability duration. The MILP is set up to minimize the installation cost of PV, battery, HP, and thermal storage. This can also be interlinked with an underlying grid cost-optimization problem, which is necessary for curtailment scenarios resulting from grid congestion. Available Scenarios: This setup is based on [8] which originally includes various coverable scenarios: •various degrees of grid side coordination: separated optimization of buildings and grid, curtailment of PV or HP, single planning identity optimizing the combined grid and building cost, •residential flexibility: smart charging of BEV, maximizing PV self consumption, smart storage utilization, •dynamic electricity pricing: variable tariffs, grid fees, or capacity pricing. For the proof of concept, the surrogate training data generation in this work is restricted to a 100 % decarbonization scenario. The term ”decarbonization” in this paper refers to the process of electrifying the mobility and heating-related demands and meeting this total electrical demand with only photovoltaic generation and grid import or export. Moreover, the DER expansion and operation of each building is individually costoptimized. The resulting net electrical demand is met by the passive grid operator, who might need to reinforce the grid. The selected scenario is corresponding to the Coor−F lex+ scenario in [8]. It is similar to the current German LV grid digitization landscape, with a push for home energy management systems to maximize self-consumption of rooftop PV with minimal grid-side interference. Likewise, the installed DER at each household is more likely to be an individual decision by the homeowner without considering potential holistic grid effects. It must be highlighted that the subsequent surrogate could just as well be trained on the full spectrum of coordination, flexibility, and dynamic pricing options known from the literature. 4) Power Flow: The resulting net building load profiles from the MILP stage can be fed into an AC power flow. This gives us the net active and reactive power demand time series at the transformer LV side, as well as violations of current and voltage limits, without any asset reinforcements. From Fig. 5 (a), we can infer the necessity of conducting a power flow to achieve more exact results, especially in grids with fewer buildings, which show relative peak load deviations of about ±10 % after the power flow. This can be attributed to grids with higher losses, as rural grids often have fewer and more dispersed buildings, resulting in longer lines and thus higher voltage deviations. The distribution of maximum voltage deviations across all grids, shown in Fig. 5 (b), is mainly contained in the 0 25 50 75 100 125 150 175 Number of Grid Buildings 10 5 0 5 10 15 Rel. Peak Load Change [%] a) 0.7 0.8 0.9 1.0 1.1 1.2 Voltage Magnitude (p.u.) 1 10 100 LV Grid Count b) > 1.1p.u.: 4.3%< 0.9p.u.: 2.5% Max. Upper Voltage Deviation Max. Lower Voltage Deviation Fig. 5. (a) Relative change in peak transformer load against grid building number after conducting an AC power flow with respect to the peak obtained from simple building load profile addition before the power flow. Positive deviations arise for demand-induced peak loads, and negative deviations arise for feed-in-induced peak loads. (b) Histogram of grid-wide maximum upper and lower voltage deviations recorded over a year. permissible region of ±10% [27]. In fact, only 5.2 % of generated grids ever show a voltage violation. In Fig. 3 (c), we see that the grid set is skewed towards densely populated grids, mirroring the urbanization trends in Germany. The study in [5] clarified that most of the urban grid upgrade costs arise from congestion-related overloads of the transformer and line capacity rather than voltage limits violations. Our voltage trends reinforce this hypothesis within the sampled grid set. We take this as an indirect validation of the representativeness of our ground-truth generation suite. B. Surrogate Model Training 1) Model Architectures: We use a multi-layer perceptron (MLP) as a baseline model, which only acts on a single time step for predicting hourly active and reactive power at the LV side of the transformer. However, the main architecture considered, as illustrated in Fig. 6, relies on the rich interactions between many time steps introduced by the transformer encoder architecture [28]. Both the MLP baseline and the transformer encoder models are developed within PyTorch. 2) Training Data Selection and Preprocessing: The surrogate input datasets are shown in Table I. The electricity, PV, space heat, and water heat profiles can be generated normally with the ground-truth tool chain, due to their low generation/assignment times as seen in Fig. 7. As the MILP model does not install 100 % of the possibly available yearly PV energy capacity, we refrain from providing this as the input 24th Power Systems Computation Conference PSCC 2026 Limassol, Cyprus — June 8-12, 2026 MLP MLP MLP MLP … Drop … Drop Transformer Encoder shared shared MLP MLP Embed Encode Inputs P,Q Readout Time [h] Core Core Pad Pad Fig. 6. Surrogate model architecture. The target time series is split into smaller, potentially padded, individually inferred core slices. A shared MLP embeds a multivariate input time step into a higher dimension. The transformer encoder architecture allows rich interaction encoding within a slice. Finally, a per-time-step, shared readout MLP reduces the output to a joint prediction of active and reactive power. TABLE I SURROGATE MODEL TRAINING AND INFERENCE INPUT DATASETS. Rationale Input Features Unit Grid Agg. Temp. Res. Cheap Ground Truth Electr. Demand MWel Sum Hourly Exp. PV Production MWel Sum Hourly Water Heat Demand MWth Sum Hourly Space Heat Demand MWth Sum Hourly Heat Pump COP - Weighted Avg. Hourly Mobility Proxies Temperature ◦C Grid Wide Hourly # Cars - Sum Const. RegioStaR7 Region - Grid Wide Const. Power Flow Proxies Grid Resistance ΩTransf. LV Side Const. # Feeders - Sum Const. # Buildings (Non-)Res. - Sum Const. Disagg. Bldng. Base/Use Area m2Sum Const. # Households, # Occup. - Sum Const. time series. Instead, from the training grid set, we see that the MILP only builds PV capacities to harness around 68 % of the maximally available yearly energy potential. Therefore, for an unseen grid, we install PV capacities on the most productive roof sections with pvlib until reaching the predetermined aggregated annual energy production threshold. The BEV profile generation time is significantly longer and is therefore skipped. These missing time series are instead replaced by representative proxies as listed in Table I. Similarly, aggregating time series over all buildings introduces information losses, which we try to counteract by adding additional building information as input. Any constant scalar inputs were expanded to a full year-long constant time series. Information on the position within the annual time series is provided by sine and cosine features covering the power spectral density modes of the input and output time series, where the number of added modes is left as a hyperparameter. Additionally, only within the transformer architecture, all pure time series data is decomposed with a variational mode decomposition (VMD) [29], where the number of modes is again left as a hyperparameter. The final multivariate time series across all grids is then standardized. The target Pand Qtime series were jointly rescaled by standardization of the resulting apparent power Stime series. 3) Loss Functions: The base loss function for predicting active and reactive power is chosen as the following normalized mean absolute error (NMAE): NAE(y, ˆy, t) = |ˆy(t)−y(t)| ⟨|y|⟩ , NMAE(y, ˆy) = 1 T1−T0 T1 X t=T0 NMAE(y, ˆy, t), NMAE =NMAE(P, ˆ P) + NMAE(Q, ˆ Q), (1) where y(t)denotes the ground-truth target time series and ˆy(t) the prediction for a given LV grid. The normalization factor ⟨|y|⟩ is always determined with respect to a given grid’s whole time series. This leads to an equal contribution of grids to the loss function even though their demands might lie on different scales. The prediction for a given grid is conducted in multiple disjoint steps with a time series core window length T1−T0. This reduces computational cost (as transformer self-attention scales with O(n2)), while preserving accuracy if providing enough core window context length. As peak loads are of special importance for a grid operator, a further loss function focusing on peak reconstruction is introduced: z(t) = y(t)− ⟨y⟩ σ(y), P eak(y, ˆy, t) = max(1, z(t)) ·NAE(y, ˆy, t) +z(t)·NAE(y, ˆy, t)2,(2) P eak =1 T1−T0 T1 X t=T0 P eak(P, ˆ P , t) + P eak(Q, ˆ Q, t). This has a base linear component forcing errors to zero. At ground-truth values further away from the time series mean, an increasingly high squared penalty term is assigned. Additionally, the slope of the linear loss is increasing above a z-score of one. Thus, for peak loads that show a large deviation from the time series mean, a higher reconstruction importance is assigned. 4) Hyperparameter Optimization: The architecture implementation, dropouts, weight decays, optimizer, learning rate, and learning schedule are determined by a hyperparameter optimization. We use the Ray Tune multivariate tree-structured Parzen estimator with a random warm-up sampling of search space dimension d+ 1 initial samples and a grace period of five epochs. An asynchronous successive halving approach is employed for higher epoch numbers, with up to 45 epochs and successive continuation of training for the best third of models. Computational resources of one day of wall clock time on a NVIDIA A100 Tensor Core GPU are provided to each model, resulting in about 120 trained surrogates per approach. After hyperparameter optimization, the best model is retrained on the combined training and validation set of 1,000 grids, where we reduce the number of epochs inversely with the increase in training data. 24th Power Systems Computation Conference PSCC 2026 Limassol, Cyprus — June 8-12, 2026 5) Differences to Prior Studies: Two salient points have to be highlighted about this surrogate. The specialized surrogates in our prior work [10, 11] used multiple scenarios at various levels of DER penetrations in a single grid to predict active power demand. The current generalized surrogate is trained on one scenario over hundreds of grids, intending to be able to forecast active and reactive power for any distribution grid in Germany. Thus, with decreased focus, reduced information on any single grid, and increased output requirements, we expect a degradation compared to previously observed error metrics for time series reconstruction, peak demand, and aggregate demand of around 2 %. Secondly, readers may note that we are not clustering our grids, as compared to the other national studies such as [5] or [7]. The variations across different types of grids at a national level are instead intended to be captured by the deep learning architecture through a rich set of training grids, approximately following the real grid type distribution remodeled by our ground-truth tool chain. III. RESULTS AND DISCUSSION A. Computational Resources The required computation time distributions of various data generation steps are shown in Fig. 7. The ground-truth calculation tool chain is dominated by the mobility generation and MILP and necessitates, on average 36 h of computation time per grid on a single CPU core. The surrogate model tool chain is dominated by the heat generation and requires, on average, only about 6 min per grid. This is a difference of three orders of magnitude. Moreover, the maximum process RAM RSS never exceeded a peak of around 18.5 GB which was reached during the inference preprocessing. In total, the whole Ground-Truth Generation Process Surrogate Prediction Fig. 7. Computation times of the data generation steps (measured as total CPU core hours on an Intel®Xeon®Platinum 8380) as well as of the total pre-/postprocessing CPU core hours and active GPU inference time of the surrogate model (NVIDIA A100 Tensor Core GPU, where the inference makes up only (0.10 ±0.03) % of total surrogate computation time). ground-truth data generation for 1,200 grids takes about 4.5 days when employing 25 parallel compute nodes with 16 CPU cores respectively. Subsequent scenarios would be reduced in time as only a new MILP and power flow would need to be run over the grid already populated with time series data. Applying the same computational resources for the surrogate model workflow, we can obtain load forecasts for all 500,000 LV grids [9] in Germany within about 5.2 days. B. Numerical Results The normalized expected transformer load and the normalized surrogate prediction error over a year at daily aggregation are shown in Fig. 8. The average transformer load generally peaks in winter due to high heat demands, whereas in summer, mobility and appliance demand are reduced by PV production. At hourly aggregation, there would be additional daily net feed-in peaks during summer. While the prediction error remains relatively constant over the year, there is a marked increase in prediction variance during summer. This can be attributed to the PV component, which must be additionally modeled in summer compared to the rest of the year. The Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Normalized Transformer Load Apparent Power |S| Expected Time Series 68% Percentile Band 96% Percentile Band Prediction MAE Median Time Series 68% Percentile Band 96% Percentile Band Fig. 8. Normalized transformer load (|S|(t)/⟨|S|⟩)and normalized prediction MAE distributions for testing grids at daily aggregation over one year. The expected/median time series and percentile bands are obtained from each individual day’s normalized load/error distribution over all grids. median error metrics of the evaluated surrogate models for active power P, reactive power Q, and derived apparent power Stime series with hourly and daily aggregation levels are shown in Table II. The metrics are obtained for the testing grids and displayed with differences to the 5th and the 95th percentile. For reactive power, we only show the import metrics as the grids are acting purely inductive with negligible reactive power export. It can be observed that the metrics generally improve at higher temporal aggregation levels, as prediction uncertainties (e.g., in mobility charging demand modeling) cancel out over larger time scales. The reactive power metrics are better captured compared to the active or apparent power counterparts. This can be attributed to the simplified reactive power relationship in the reference energy diagram of Fig. 4, which is dependent only on electrical appliance load, heat pump operation, and PV production. The feed-in metrics are generally worse than the import metrics - as was hypothesized by our prior analysis of Fig. 8. We also introduce a metric shown as ∆tfor the peak feedin and import, which tracks the error in predicting the time step at which the peaks occur. The high uncertainties in active power peak ∆tare due to the lack of knowledge 24th Power Systems Computation Conference PSCC 2026 Limassol, Cyprus — June 8-12, 2026 of the hourly mobility demand profiles, which were omitted to save computation time. The peak apparent power load is generally well captured with prediction errors of below 10 % for most grids. Yet, for a small number of grids, it shows a high uncertainty in the peak apparent power load ∆t. This is caused by grids that have similar levels of peak import in winter and peak feed-in in summer. Small errors in load prediction can then result in a 6-month offset in peak occurrence. This problem would arise for any predictor and is thus not considered problematic. Lastly, even though the per-time-step MLP already captures the time series behavior rather well, it is outperformed in almost all metrics by the interaction between time steps introduced by the transformer model. We also register a vast improvement in almost all loss metrics by focusing on the peak reconstruction with the loss function defined in Eq. (2). IV. CONCLUSION AND OUTLOOK We developed a generalized surrogate to accurately predict transformer net demands for any LV grid in Germany under flexibility measures and a 100 % decarbonization scenario. Training our national LV grid surrogate required us to create a state-of-the-art ground-truth generation tool. A user can apply this tool to the entirety of the German LV grid with minimal input requirements and obtain grid-tailored load forecasts under various scenarios of DER expansion and flexibility measures. The data generation tool chain uses harmonized assumptions to create representative replicas of the underlying grids, loads, and PV generation profiles. The deep learning surrogate was trained on a representative distribution of 1,000 LV grids generated with this workflow. The resulting possibilities available to the user are manifold. Unlike other national studies, our entire workflow is verifiable, open-source, and relies on open-source weather data, street maps, publicly available databases, and other freely available tools and methods. This allows the direct modification of energy system modeling assumptions and datasets without restrictions. Furthermore, researchers and grid planners can obtain future projections from load profiles and an MILP exactly tailored to their grids. Alternatively, they can quickly play out many scenarios across their whole grid region with the slightly reduced accuracy of the surrogate model. Moreover, national-level studies can now be conducted by any researcher, in a purely bottom-up approach without the need for privileged access to real grid data, unverifiable assumptions, or inaccurate abstractions such as in [3, 4, 5, 6]. Concretely, the surrogate model reduces computation time by three orders of magnitude over the ground-truth generation process. Our best surrogate can forecast hourly active and reactive power time series over a full year with an error on transformer peak load of below 10 % for most LV grids. Given the required input data, a Germanywide bottom-up load forecast for all 500,000 national LV grids could now be obtained within 5.2 days of computation time, assuming access to similar computational resources as used in this work. TABLE II MEDIAN ERROR METRICS OF THE SURROGATE MODELS. MLP Transformer Metric Agg. NMAE NMAE Peak P Agg. Feed-In MdAPE [%] All 9.7+34.8 −8.812.1+28.9 −10.611.0+39.1 −10.0 Agg. Import MdAPE [%] All 4.8+7.8 −4.51.8+7.3 −1.61.7+6.6 −1.6 Median NMAE [%] 1 h 18.5+13.2 −3.813.8+14.9 −3.613.6+15.9 −4.0 24 h 10.8+11.5 −3.56.8+12.4 −2.56.2+12.0 −2.4 Peak Feed-In MdAPE [%] 1 h 16.8+24.3 −12.723.4+17.3 −18.914.4+18.9 −12.9 24 h 10.6+30.0 −9.416.2+38.4 −13.312.1+34.5 −11.4 Peak Feed-In Median ∆t [d] 1 h 22.0+48.2 −22.019.0+53.0 −19.016.0+48.3 −16.0 24 h 5.0+39.1 −5.04.0+47.1 −4.05.0+48.2 −5.0 Peak Import MdAPE [%] 1 h 16.3+14.3 −12.410.1+12.4 −8.28.6+13.7 −7.5 24 h 4.9+7.7 −4.53.2+5.3 −2.81.6+3.5 −1.4 Peak Import Median ∆t [d] 1 h 2.4+50.6 −2.42.1+40.8 −2.12.0+41.5 −2.0 24 h 0.0+31.4 −0.00.0+22.2 −0.00.0+26.0 −0.0 Q Agg. Feed-In MdAPE [%] All 3.2+6.5 −2.61.9+4.2 −1.61.6+5.2 −1.4 Median NMAE [%] 1 h 14.5+7.8 −3.47.6+5.1 −1.97.7+6.1 −2.1 24 h 8.2+4.1 −3.03.4+3.5 −1.23.7+5.0 −1.3 Peak Import MdAPE [%] 1 h 3.1+8.3 −2.83.4+12.0 −3.22.9+11.4 −2.6 24 h 3.8+7.1 −3.52.6+6.5 −2.21.6+4.7 −1.5 Peak Import Median ∆t [d] 1 h 1.0+47.7 −1.01.0+54.2 −1.01.0+51.4 −1.0 24 h 0.0+27.1 −0.00.0+17.7 −0.00.0+27.0 −0.0 |S| Agg. Import MdAPE [%] All 3.5+8.2 −3.02.4+5.3 −2.22.0+5.9 −1.9 Median NMAE [%] 1 h 18.0+10.8 −3.613.3+13.9 −3.512.9+14.2 −3.7 24 h 9.0+7.2 −2.95.5+8.4 −1.75.3+9.8 −1.9 Peak Load MdAPE [%] 1 h 15.6+15.0 −11.911.5+14.3 −8.88.7+15.4 −7.8 24 h 5.0+7.4 −4.63.1+5.0 −2.61.5+3.6 −1.3 Peak Load Median ∆t [d] 1 h 10.0+133.9 −10.07.0+159.3 −7.05.0+152.7 −5.0 24 h 0.0+39.3 −0.00.0+26.0 −0.00.0+26.2 −0.0 In future work, we aim to further enhance both the underlying ground-truth data generation pipeline as well as the surrogate itself. 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