Surrogate Framework for Energy System Modeling

Surrogate Framework for Energy System Modeling Anurag Mohapatra, Maximilian Hock, Beneharo Reveron Baecker, Thomas Hamacher Technical University of Munich, Germany {anurag.mohapatra, max.hock, beneharo.reveron-baecker, thomas.hamacher}@tum.de Abstract—Energy system modeling (ESM) through Mixedinteger Linear Programming (MILP) is the dominant tool of choice for national level grid expansion or congestion studies. Such models, while being precise, are computationally intensive and produce many datasets which are eventually aggregated to produce one net demand timeseries. This paper introduces a surrogate modeling framework through LSTM and Transformer architecture, which approximates the behavior of MILP based ESM, significantly reducing the computation demand with a reasonable compromise in accuracy. The framework also uses many data augmentation techniques to capture seasonal, weekly and daily patterns in the datasets. The best performing surrogates are able to predict the annual aggregated demand timeseries and peak demand with under 1% error. Once trained, the surrogates can evaluate each new demand scenario in under 5 seconds. Additionally, we employ transfer learning techniques on a pretrained surrogate to accurately learn the behavior of a new grid with only two weeks data per scenario instead of the whole year. The proposed framework offers a scalable and computationally efficient approach to grid planning, making it suitable for national level grid studies where many distribution grids must be evaluated. The transfer learning aspects further highlight their practicality as pre-trained surrogates on benchmark grids can be re-used for new grids without needing extensive new training data. Index Terms—Machine Learning, Energy System Modeling, Active Distribution Grids, LSTM, Transformers I. INTRODUCTION Electrification of heating and mobility sectors through renewable generation is a necessary condition for the global decarbonisation goals. Studies have shown that a majority of the new renewable generation and sector coupling units such as heat pumps and electric car chargers will be deployed at the active distribution grids (ADG), requiring massive LV grid digitization [1]. Simultaneously, the upstream transmission grid would require asset upgrades and expansions to handle the increased electricity peaks and manage dispatch congestions. Therefore, studies on long term operation and grid expansion planning at national levels, generally done through energy system modeling (ESM) frameworks, are needed. A. Background Conventional ESM approach for the national level focuses on the upstream transmission grid with each downstream distribution grid being substituted with single demand timeseries [2]. However, the operation of a sector-coupled ADG will be affected by prosumer behavior from the new distributed energy resources (DER). A major influence emerges from degrees of coordination and flexibility mechanisms within an ADG, which can be implemented through controllable DER. Fig. 1. Typical upstream TxG and downstream ADG setup with various flexibility and coordination mechanisms implemented within. These measures can be motivated from variety of concerns such as mitigating the intermittency of renewable generation, consumer energy cost optimization, grid ancillary services, and reduction in grid upgrade investments [3]. Consequently, as shown in Fig. 1, the aggregated behavior of household demands towards the transformer cannot be directly estimated by combining inelastic demand and generation timeseries at the ADG nodes. Instead, a detailed model for each underlying ADG is required for accurate consideration of their flexibilities, which enables an assessment of their impact on the upstream transmission grid and, better incorporation in energy system planning. A detailed ESM for an ADG involves two optimization problems: capacity planning, which determines optimal DER installation capacities based on demand, costs, and weather data, and economic dispatch (also known as unit commitment), which minimizes operational costs considering sector coupling, storage flexibility, curtailment, and grid electricity prices. These can be solved jointly or separately, depending on model size and computational resources. After the optimization is finished, combining the net energy timeseries at each node of the ADG would give us the true timeseries for the net demand of the whole ADG with respect to the upstream grid - the actual data of interest for upstream grid expansion and planning. The upstream grid needs this aggregated import/export timeseries for all underlying ADG as a reasonable estimate, as opposed to an exact precision, due to the discrete nature of investment decisions and uncertainties of forecasts. As an example, the choice of upgrading a power transformer at the point of grid coupling is a typical investment decision to be made from such an analysis. However, the transformer manufacturer produces the units in standard sizes. Therefore, the decision to upgrade to the next higher size is the same within a range of increased aggregated net demand for the downstream ADG. The same can be said about other major grid assets considered for expansion planning. Furthermore, the grid planner always begins with a vast list of possible operation and expansion decisions. A sufficiently accurate estimate which captures sector coupling and flexibility of the underlying grid could help quickly narrow down the decisions upstream to a few feasible candidates. B. Research Gap There is a broad consensus that detailed ESM frameworks for ADG, with over a hundred nodes, as a Mixed-Integer Linear Program (MILP) are a computation burden for standard office computers and in some cases, even infeasible [4]. Model decomposition techniques, decentral optimization paradigms, and parallelization have been proposed to tackle these problems, but they add to the complexity of the implementation. Additionally, the numerous economic dispatch and capacity planning sub-problems within such a large optimization model generate a lot of timeseries data at large computation cost. Most of these data do not contribute meaningfully to any insights since the planner is interested in the aggregated behavior at the point of grid coupling. This brings us to the potential of surrogate models, which could provide the practical trade-off between rapid yet reasonable estimates and detailed precision for quick decisionmaking at higher tiers. Surrogate models provide an inputoutput relationship that mimics the behavior of an underlying physical model with significantly less computational time [5]. The field has been enhanced by advances in Machine Learning (ML) techniques with many desirable model architectures, such as recurrent neural networks, convolution neural networks, and transformers, to name a few. In [6], the authors make suggestions on how such methods could be leveraged for the niche requirements of ESM. C. Contribution In this paper, we present a framework to synthesize surrogate models from standard ESM frameworks, using a variety of neural network architectures and data augmentation techniques to predict the aggregated net demand and peak demand timeseries for an ADG. •Once trained, our surrogates stop relying on MILP solvers and instead use ML approximators to provide reasonably accurate results at a fraction of the previous compute time. Thus, the wait-time for detailed scenario analyses on a built model is drastically reduced. •We provide a variety of options for data augmentation as a pre-processing step to extract more information from a single timeseries and thus improve the results significantly. •We train many surrogates with different NN architectures, look-back horizons, data augmentation combinations and list our ten best-performing surrogates with detailed metrics and training times. •Lastly, we apply Transfer Learning techniques to create a surrogate model for a new grid, with considerably less training data requirement, from an existing surrogate model for a benchmark ADG. II. METHODOLOGY The methodology is visualized in Fig. 2, with each component being described below in their respective subsections. A. Data preparation The data preparation step follows the sequence shown in the top row of Fig. 2. We use the Kerber benchmark low voltage grid, modified with DERs, as our baseline ADG to prepare an ESM surrogate. The DERs modeled in our ADG are photovoltaics (PV), heatpumps (HP), and Electric vehicle (EV) charging stations. Flexibility is achieved through batteries (BESS) and sensible thermal storages to allow higher PV and lower HP capacities. We assumed the paradigm of ”100% electrification”, where heating and mobility demands were completely covered by heat pumps and EV chargers, respectively. The scalar input data consisted of the grid topology and techno-economic parameters such as unit costs of investment and operation, depreciation factors, efficiencies, and capacity limits for the possible DER technologies. The timeseries input data are the electrical, heating, and mobility demand profiles for each household, solar irradiation, and the heatpumps’ coefficient of performance (COP) profiles. The exact details of the ESM formulation can be found in [3]. The code was implemented through the ESM framework, urbs, which uses standard MILP solvers for capacity planning, grid expansion, and optimal dispatch problems [7]. At this point, the ADG households were optimized in a coordinated paradigm, where the grid constraints and household DER investment decisions are optimized together. This yields optimized asset capacities at all nodes as well as a variety of output DER timeseries for each of the 8760 annual hourly steps. Combining the optimized DER operation and the given electrical demand for all nodes, the net demand of the ADG was calculated. This timeseries has both positive and negative entries, as the ADG can be a net importer or exporter for the upstream grid. B. Data Augmentation Data augmentation techniques have been shown to improve the generality, reducing the training epochs and generally improving the performance of neural networks [8]. We employ three augmentation techniques in our surrogates which are highlighted in the second row of Fig. 2. 1) Changing the installed DER capacities: For a given weather pattern, grid topology, and consumer demand, the net demand of an ADG, as calculated in Sec.II-A, is strongly correlated to the installed DER capacities in the grid. Therefore, to generate the training dataset, we create new scenarios for the same grid with different installed capacities for PV, BESS, and HP as shown in Tab. II. This yields a total of 27 scenarios for the same ADG, leading to 27 x 8760 = 236520 Fig. 2. Schematic overview of the surrogate creation process. TABLE I TRAINING DATASET CREATED WITH 8760 (1 YEAR)INPUT-OUTPUT PAIRS. Type with units Spatial resolution Temporal resolution Inputs Electrical demand, kWel Sum over all households Hourly Domestic hot water demand, kWth Space heating demand, kWth Mobility demand, kWel Solar irradiation capacity factor Weighted mean over all households Heat pump COP Charging station availability Battery capacity, kWel Sum over all households As installed Rooftop PV, kWp Heat Pump, kWel Charging stations, kWel Output Net demand of the grid, kWel Aggregated for grid Hourly input-output pairs in the final training dataset. Each of these 27 scenarios represents a feasible DER capacity for the grid, with one among them representing the optimal investment decision for coordinated houses. This augmentation is efficient as the solution space of the problem can be substantially reduced by fixing the capacity variables and, therefore, solving a dispatch optimization problem. This is a valid approach as the surrogate is designed to understand the relations between different DER asset capacity penetrations and the net import rather than the optimal capacity of a system. Moreover, it allows the neural network to be trained on the necessary amount of data. TABLE II SCENARIO PADDING WITH DIFFERENT INSTALLED CAPACITIES. DER Variations on optimal installed capacity at every node PV 60%, 80%, 100% Total 27 (33) scenarios from permutations of capacities BESS 80%, 100%, 120% HP 80%, 100%, 120% The last scenario is used as testing data, which is 3.70 % of all data for a dataset with 27 scenarios. The validation and training data is taken from the other 26 scenarios, and the first 80 % are used for training and the last 20 % for validation. This proportion is selected as it is common in ML training, though the ideal ratio depends on the exact problem. 2) Trend/Mode decomposition: The training process can be further improved by providing information on repeated patterns, constant residuals on the data, or simply resampling the timeseries. We employ these techniques since the renewable generation and consumer annual demand timeseries have strong seasonal, weekly, and diurnal correlations. The input data tuple, for each of the 8760 rows is then padded with more elements from the resampled timeseries. We tested the following trend or mode decomposition techniques in this paper. Seasonal Trend Decomposition (STL) uses the locally estimated scatterplot smoothing (LOESS) to split a timeseries into the following components for a given length of a season - a repeating seasonal pattern in the data, a trend component for the long-term progression or direction in the data and a residual component for the noise or variability not explained by seasonality or trends [9]. Multiple Seasonal Trend Decomposition (MSTL) is an extension of STL that allows multiple seasonal trends of different lengths. This enables it to capture patterns of daily, weekly, monthly, and quarterly trends. Variable Mode Decomposition (VMD) is an extension of the empirical mode decomposition (EMD) technique to recursively decompose a signal into its intrinsic mode functions. It can be compared in principle to wavelet and Fourier transform. The strict mathematical definition of a mode can be found in known literature such as in [10]. The EMD algorithm recursively subtracts a found mode from the timeseries until no more modes can be extracted, leaving behind a residual component. However, since the EMD algorithm automatically determines the number of intrinsic modes, this could lead to mode-mixing where multiple trends get pooled into one mode, leading to poor augmentation. VMD improves this by specifying the number of extracted modes from a timeseries and decomposing concurrently, leaving no residuals behind. VMD can also be described as a method that initially identifies a set of modes defined by a center frequency and a narrow frequency band around each of them, which together represent the original timeseries. [11]. Among the various decomposition methods, MSTL and VMD stand out as the most suitable for data augmentation for our application. These two approaches offer distinct levels of user control. MSTL provides flexibility by allowing the user to define the seasonal length, which enhances control over the decomposition process. However, this also requires a deeper understanding of the underlying seasonal patterns. In contrast, VMD automates the identification of modes, streamlining the process but limiting the user to a predefined number of modes. This constraint could lead to poorly defined modes, potentially hindering the ability of the neural network to capture the true underlying patterns in the data 3) Auxiliary inputs: Incorporating auxiliary data, such as timestamps, is another effective form of data augmentation that can assist neural networks in identifying recurring patterns. This is particularly useful in contexts like power grid demand and renewable generation timeseries, where factors such as the day of the week, time of day, or seasonality can heavily influence power consumption. We pad our input tuple row further, by providing a numbered index for the hour of the year (0 to 8759), hour of the day (1 to 24), day of the week (1 to 7) and week of the year (1 to 52). C. Creating the Surrogates We use two Deep Neural Network (DNN) architectures, namely Long Short Term Memory (LSTM) and Transformers, to build our surrogates. Both of these methods were chosen due to their well-accepted properties of being able to predict timeseries relationships. LSTM neurons include memory of a previous input and logic gates that decide whether to store or ignore the current input and whether to propagate it to the output. This allows them to carry information from the previous timestep into the current calculation, which improves timeseries pattern recognition. The concept was initially published by Hochreiter and Schmidhuber in 1997 but proved its effectiveness only when the computation state-of-the-art had caught up [12]. The Transformer neurons can take in the whole timeseries simultaneously, while the LSTM neurons handle the timeseries sequentially. This enables Transformer architectures to find patterns from earlier timesteps in contrast to the focus on more recent timesteps of LSTM [13]. The surrogates were implemented in Python using the Keras 3 framework [14]. This allows the code to be implementation agnostic, concise and use existing standard approaches e.g., layer definition code or training loop code. The Keras-Tuner was used for hypertuning. The surrogates were trained on a campus shared server stack that uses containerization to enable stable and reproducible software environments. Each server node has a CPU with varying number of cores and multiple identical GPUs of type NVIDIA P100 with 16 GB, V100 with 40 GB, or A100 with 80 GB. Only one GPU was used for the hypertuning, training and inference. III. RESULTS A. Best performing surrogates A variety of surrogates are created due to the various mode decomposition methods, look-back windows, and architectures. The ten best-performing models are listed in Tab. III. The surrogates perform accurately on the testing data with the top performer achieving below 1 % deviation in aggregated demand and peak demand and 5.455 % in peak feed-in. Between the top ten surrogates different ones perform best in different metrics as can be seen in Table III. It is also notable that the top performing surrogates are a mix of LSTM and transformers which implies that the grid model can be captured by both architectures to a similar degree. The combination of timestamps and VMD with 5 modes appears in the top three models, with 7 modes appearing in the next three models. This indicates that these augmentations boost the performance of the surrogate and that the exact number of modes is flexible. This behavior can also be seen in Fig.3, where the MSE drops further for both training and validation datasets with the augmentations. 25 50 75 100 125 150 1750 200 epoch 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.075 0.275 loss TrainDeltaLoss_LSTM24_TS-VMD5 TrainDeltaLoss_LSTM24_NoAugment Fig. 3. Training loss with and without data augmentation Most of the top surrogates use a 24 h timeseries window with only two using 36 h, which implies that 24 h is the minimum window necessary to capture the grid model. This result is aligned with the empirical assumptions of a unit commitment model for a grid with only household storages as energy buffer units. Since we are analyzing only small residential storages in the distribution grid, it is fair to assume that they will be operated for short-term daily flexibility and not for long-term seasonal storage cycles. Therefore, a 24 h timeseries window in Tab. III, captures the daily flexibility cycle quite adequately. Fig. 4 shows the predicted annual aggregated demand timeseries from the best surrogate model shown in Tab. III. It can be seen that the surrogate is able to capture broad seasonal trends in aggregated demand data. The figure also shows the performance of the surrogate for a winter week in January and a summer week in June. It can be seen that the peak demand is predicted quite accurately for both the net importer in winter and net exporter in summer scenarios. B. Computation time comparison with ESM The hyperparameter tuning and training time for the ten best surrogates are listed in Tab. III. On average it takes 3:45 TABLE III 10 BEST-PERFORMING SURROGATE MODEL COMBINATIONS,SORTED BY PERFORMANCE ERRORS Label MSE MAE [kW] Net Demand [%] Peak Demand [%] Peak Feed-in [%] Hypertuning Time [h] Training Time [h] Evaluation Time [s] TrainDeltaLoss Transformer24 TS-VMD5 0.048 19.441 0.882 0.826 5.455 03:15:09 01:05:36 4.509 TrainDeltaLoss LSTM24 TS-VMD5 0.049 19.238 7.985 1.404 1.461 03:07:20 00:59:42 4.047 TrainDeltaLoss LSTM36 TS-VMD5 0.059 20.954 5.752 2.278 1.138 09:50:29 01:04:12 4.311 TrainDeltaLoss LSTM24 TS-VMD7 0.047 18.991 8.819 5.536 1.947 06:01:53 01:04:28 3.919 TrainDeltaLoss Transformer24 TS-VMD7 0.052 22.050 5.632 5.445 6.539 03:28:51 01:02:50 4.561 TrainDeltaLoss Transformer24 VMD7 0.052 21.903 0.194 8.151 8.406 03:07:32 00:16:13 3.470 TrainDeltaLoss Transformer24 NoAugment 0.062 23.004 3.765 1.994 10.636 01:12:08 00:16:55 3.572 TrainDeltaLoss Transformer24 VMD3 0.049 20.246 3.507 12.485 8.785 03:15:57 01:05:42 4.413 TrainDeltaLoss Transformer24 TS-MSTL 0.056 23.427 6.527 2.748 12.911 03:09:05 01:02:42 4.516 TrainDeltaLoss LSTM36 NoAugment 0.060 21.154 6.225 9.521 3.893 01:10:20 00:15:47 2.865 Legend - Train: Training Data as loss target; DeltaLoss: Distance-weighted sum of MSE and MAE as loss function; TransformerXX/LSTMXX: Architecture type with a look-back window of size XX; TS/VMDX/MSTL: Data augmentation method, X indicates number of modes for VMD; NoAugment: No auxiliary inputs and modes 0 2000 4000 6000 8000 2 0 2 F u ll Ye a r 0 2500 5000 7500 Du r a tion Curve 0 50 100 150 2 0 2 Win te r Tr u e Pr e d 3800 3850 3900 3950 Sum m e r H ou r s N or m a lise d Aggr e g a te d De m a n d Fig. 4. Demand performances for best model. hours for hyperparameter tuning and 0:49 hours for training the surrogates. In comparison, it takes between 2.5 to 3 hours to run each scenario through the ESM framework urbs. We used a standard computation server with Intel Xeon Gold 6140 18C 2.3GHz processor, with 36 cores and 512GB RAM. Although 27 scenarios were needed to build the surrogates, once trained they are able to evaluate a new input dataset (as shown in Tab. II-A) in under 5 seconds. Most ESM analysis ends up being scenario runs on different demand levels and renewable energy penetration. Our surrogates can cut down the time spent on such analysis to near negligible inference times, after accounting the the time required for training data generation. We have to remark that the ESM framework and surrogates are using different hardware, and therefore, these durations are not directly comparable. However, since we used standard hardware for both methodologies, the results are quite representative of what other practitioners might experience. Additionally, it has to be mentioned that the reduced computation time can also be attributed to the parallel execution of the surrogate as compared to the serial execution in MILP. C. Transfer Learning We applied a finetuning-based transfer learning to test our pre-trained surrogates using input data from a completely different ADG. The rationale being that the surrogate would require significantly less new data from the new ADG to give comparably accurate information. A real distribution grid from the Forchheim region in Germany was taken as the new ADG. We follow the same steps as mentioned in II-A and then create the 27 different scenarios - 26 for training, validation and 1 for testing. However, now we only take 2 representative weeks of data - one winter week and one summer week. To generate these, we use the “tsam” package [15] that optimizes clusters based on the RMSE to represent the original timeseries data with a chosen number of type periods ntand hours per period nh (For our application nt= 2, nh= 168). Thus the new training dataset is approximately 3.8% the size of the original dataset. In Fig. 5, we show the performance of the surrogate with and without applying Transfer Learning on a completely new grid dataset. The MSE decreases from 0.581 to 0.015 after applying Transfer learning on the new dataset. In Tab. IV, we show the performance metrics of the best-performing LSTM and Transformer model, along with a model that has no data augmentation steps. It can be seen that the relative metrics are similar to Tab. III results. These results are not entirely surprising as there are many similarities in distribution grids despite their distinctive characteristics. These shared attributes occur due to geographic continuity, prevalent patterns in consumer behavior, urban development, and climatic zones. Consequently, when an upstream grid interfaces with numerous underlying ADGs, TABLE IV TRANSFER LEARNING ON 26 SCENARIOS WITH EACH SCENARIO CONSISTING OF 2 WEEKS OF DATA. Label MSE MAE (kW) Agg. Demand (%) Peak Demand (%) Peak Feed-In (%) TrainDeltaLoss LSTM24 TS-VMD5 0.042 6.270 0.397 2.819 12.874 TrainDeltaLoss Transformer24 NoAugment 0.038 5.498 2.385 13.818 1.779 TrainDeltaLoss Transformer24 TS-VMD5 0.050 6.169 2.808 8.439 1.131 0 50 100 150 200 250 300 3 2 1 0 1 2True TrainDeltaLoss-Transformer24-TS-VMD5 TrainDeltaLoss-Transformer24-TS-VMD5-Transfer Hours Normalised Aggregated Demand Fig. 5. Performance of best surrogate on Forchheim dataset with and without transfer learning it might be unnecessary to individually model each lower ADG to derive a unique surrogate from scratch for each of them. Such domain-specific intuition cannot be applied to ESM frameworks. However, surrogate modeling allows us to leverage these pattern overlaps using Transfer Learning techniques. Studies show that there are approximately 500,000 LV grids in Germany with over 1.1 million kms in grid length [16]. Any modelling paradigm that relaxes the need to model these grids individually and still provide reasonable estimates for upstream grid expansion planning could have significant consequences. IV. CONCLUSION This work presents a surrogate modeling framework for ADG, offering an efficient alternative to traditional MILPbased methods. Using deep learning architectures and data augmentation, the surrogates accurately predict aggregated and peak demand while significantly reducing computational costs. Transfer learning further enhances the framework’s applicability, allowing surrogate models to adapt to new grid scenarios with minimal additional data. 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