Fast, Interpretable, and Agnostic - PISR Voltage Control on a Low-Voltage Grid

Fast, Interpretable, and Agnostic - PISR Voltage Control on a Low-Voltage Grid Sebastian Eichhorn 1,2, Anurag Mohapatra2, Reinaldo Tonkoski1 1Chair of Electric Power Transmission and Distribution, Technical University of Munich, Munich, Germany 2Center for Combined Smart Energy Systems, Technical University of Munich, Munich, Germany {sebastian.eichhorn, anurag.mohapatra, reinaldo.tonkoski}@tum.de Abstract—This paper proposes an online predictive voltage controller using the Physics-Informed Symbolic Regression (PISR) surrogate as the underlying distribution grid model. Traditional model-based voltage controllers require an accurate grid topology. Data-driven methods have other drawbacksthe sensitivity coefficient approach relies on linearization, and online feedback optimization can be too slow to react to large disturbances. PISR creates a fast, non-linear, and data-driven surrogate model of the grid’s voltage response, replacing a power flow solver within an optimization-based predictive control framework. The controller is evaluated on an online digital twin and a physical low-voltage distribution grid with PHiL control. In simulations, it performs on par with a state-of-the-art benchmark based on robust sensitivity. The controller demonstrates stability against sudden load changes, topology modifications, and severe measurement noise. PHiL experiments confirm its rapid convergence and stability, showing resilience to hardware non-linearities and measurement outliers. Since the controller was deployed on a real LV distribution grid, the PHiL results can be considered to be higher than a Technology Readiness Level 6. Our results demonstrate that classical optimization-based predictive controllers can operate effectively in real distribution grids when the underlying model is replaced with a fast datadriven surrogate, such as our PISR model. Index Terms—Data Driven Control, Model Predictive Control, Power Flow, Real-Time, Symbolic Regression I. INTRODUCTION Active distribution grids require real-time voltage control in the face of increasing uncertainty from distributed energy resources (DERs). Conventional grid control requires accurate, computationally intensive models. An alternative uses measurement-based linearized models to reduce this dependency. This approach, however, is challenged by measurement noise, data collinearity, and its reliance on the grid’s operating point [1]. Physics-Informed Symbolic Regression (PISR) addresses these limitations by combining data-driven learning with physical constraints. PISR is based on SymbolicRegression.jl [2]. Unlike black-box neural networks, it produces interpretable equations with microsecond-level inference, enabling integration into real-time control loops [3]. Prior simulation studies demonstrated PISR’s robustness under sparse training and its ability to generalize across operating conditions [3]. Recent Power Hardware-in-the-Loop (PHiL) experiments further validated PISR on real three-phase measurements, confirming its accuracy, data efficiency, and robustness compared to optimized unbalanced AC power flow models [4]. These findings highlight PISR’s potential for deployment in safety-critical grid environments where topology and parameter data are incomplete or unreliable. However, PISR applications have so far been limited to prediction tasks and have not been integrated into control loops. The contribution of this paper is the development of a model predictive control (MPC) framework that leverages a selflearning, Physics-Informed Symbolic Regression (PISR) surrogate model to achieve real-time, topology-agnostic voltage regulation in active distribution grids. The PISR-based MPC is then implemented on multiple programmable inverters in a real low-voltage distribution grid at a research facility and validated under various loading conditions. The experiments can be considered to be at a level higher than Technology Readiness Level (TRL) 6. Overall, the proposed approach combines interpretability, physical consistency, and computational efficiency, enabling reliable voltage control in distribution grids with high DER penetration. II. STATE OF THE ART Several data-driven methodologies have been developed to overcome the limitations of model-based control in distribution grids with high uncertainty. While promising, they introduce distinct trade-offs between accuracy, interpretability, and realtime performance. One common approach is to estimate voltage sensitivity coefficients from historical measurements using techniques such as recursive least squares (RLS) [5]. The resulting linearized models are then used for control optimization [5]. However, their reliance on linearized models makes them susceptible to operating-point drift and inaccuracies when capturing non-linear grid behavior. Another category involves two-stage controllers that combine data-driven state estimation with a control agent. These methods typically use a multilayer perceptron (MLP) to estimate downstream voltages from limited substation data [6], [7]. This MLP can be considered a black-box component. The voltage estimates then serve as input to a control layer: •A Reinforcement Learning (RL) agent can be used, which is often a neural network itself [6]. This approach also requires an online training phase of 48 days before full deployment [6]. •Alternatively, an Online Feedback Optimization (OFO) algorithm can serve as the control layer [7]. This avoids the need for online training, making the controller easier to deploy compared to its RL-based counterpart [7]. Feedback Optimization (FO) can also be used as a standalone methodology. It transforms an optimization algorithm into a feedback controller by using real-time measurements to iteratively adjust setpoints until they converge to an optimal solution [8], [9]. Its practical viability has been demonstrated through successful 24/7 deployment in an operational distribution grid, achieving a TRL7 grade result [9]. However, the iterative nature of FO can be slow to react to sudden disturbances or system changes; the reaction time is analyzed in the time ranges of minutes in [9]. There are also challenges with various hyperparameter tuning and step-size adjustments, which were highlighted in [7]. Collectively, existing data-driven approaches trade model dependency for completely new challenges: sensitivity-based methods are limited by linearization; learning-based controllers can involve black-box components and training overhead; and feedback optimization can be slow to react and tricky to tune. Fundamentally, learning accurate power flow models from measurements remains a significant challenge due to limited observability, non-Gaussian noise, and systematic errors from instrumentation [1]. This reveals a critical gap for a control methodology that is not only data-driven and topology-agnostic but also possesses the following features: 1) Yields an interpretable model. 2) Executes near real-time for online deployment. 3) Captures non-linear real grid dynamics. In the remainder of this paper, we shall prove that the controller proposed in this work is designed to address precisely these shortcomings. III. PREDICTIVE VOLTAGE CONTROL FRAMEWORK This section details the proposed predictive control framework, which integrates a data-driven Physics-Informed Symbolic Regression (PISR) model into an optimization routine. This design enables a topology-agnostic controller that overcomes the latency of conventional iterative methods. A. Optimal Power Flow Formulation The control objective is to solve an Optimal Power Flow (OPF) problem that maintains grid voltages within permissible limits at a minimal cost by adjusting the active (P) and reactive (Q) power setpoints of controllable inverters. Priority is given to reactive power modulation, with active power curtailment reserved as a final measure due to its higher economic cost. The control architecture is illustrated in Fig. 1. The controller is completely independent of the grid R/X ratio and any subsequent P, Q coupling with bus voltage, as the PISR model identifies any power-voltage relationship. The controller can adjust both the Pand Qsetpoints of the controllable prosumers, thereby improving the degree of freedom during actuation. Fig. 1. Control architecture using a predictive PISR model within an optimization loop. The controller minimizes a cost function Jthat penalizes power adjustments and voltage violations: J=wPX i ∆P2 i+X i ∆Q2 i+λmax(0,|V|max −Vlimit)2(1) where ∆Piand ∆Qiare the power adjustments for inverter i, wPis a weighting factor to penalize active power curtailment more heavily which here is 30 for demonstration purposes, λ is a penalty for voltage violations, and |V|max is the predicted maximum nodal voltage magnitude across the grid. Real-time operation: Conventional OPF approaches determine |V|max using iterative power flow solvers, which are too computationally intensive for real-time control loops. This work overcomes that latency barrier by replacing the iterative solver with a predictive PISR-based surrogate model. As demonstrated in [4], PISR models can achieve prediction speeds up to 500 times faster than traditional solvers without requiring network topology information, while maintaining high fidelity. It is critical that this surrogate performs robustly for control applications and avoids prediction outliers that could lead to instability. The next subsection is dedicated to describing this PISR voltage surrogate model. B. PISR-Based Voltage Surrogate Model The PISR model is trained to learn the direct, non-linear mapping from the complex power injections at prosumer buses to the complex nodal voltages throughout the grid [3]. Each time step is treated as an independent static state, analogous to a single load flow calculation. The PISR setup with its hyperparameters is defined in Algorithm 1. The interpretability of the PISR model has been described in detail in [3]. Therefore, our subsequent data-driven controller based on a PISR voltage surrogate model can also be deemed interpretable. MultitargetSRRegressor( binary operators = {+,−,×,÷,line_current} npopulations = usedprocessors * 3 maxsize = 30 niterations = 1020) Algorithm 1: PISR configuration using the custom operators introduced in [3] To ensure the model is safe for control, the slack bus voltage is deliberately excluded as a model input. This prevents the model from conditioning on an uncontrollable input, forcing it to implicitly learn the slack bus’s influence from observable power injections and ensuring better generalization. Model robustness is further enhanced by using the single worstcase prediction error as the primary evaluation metric during training. A low-level predictor that evaluates the final symbolic equations for single input vectors reduces the average inference time to 6µs, a significant acceleration compared to the 10 ms required by a conventional AC solver for a single power flow solution. C. Self-Learning and Online Operation The controller can be deployed as a fully autonomous, topology-agnostic agent that interacts with either a digital twin of the grid or the actual microgrid using a REST API. Its operation consists of three phases: 1) Data Acquisition: The controller collects its own training data by injecting random perturbations into the reactive power setpoints of controllable units. Once a sufficient number of samples (e.g., fifty) of complex power injections and nodal voltages is acquired, a corresponding test set is also generated. 2) Model Training: With the collected datasets, the incremental training sequence is initiated to generate the PISR voltage surrogate model. 3) Online Control Loop: The controller continuously polls the grid’s current active and reactive powers and uses the PISR model to predict voltage magnitudes. If a violation is detected, a low-latency optimizer is invoked to compute the minimal setpoint adjustments (∆P, ∆Q) needed to resolve it, using the cost function in (1). This optimizer leverages the high-speed PISR model to meet real-time latency requirements before sending the adjustments back to the grid. After training the PISR surrogate, the voltage controller operates in an open-loop configuration, without any feedback from voltage measurements. It produces virtual voltages based solely on the injection powers. To ensure adaptivity, the controller monitors the per-bus prediction error. A persistent error exceeding a predefined threshold signals a significant system change, such as a topological modification, and automatically triggers a retraining sequence. Continuous grid deployment would benefit from upstream voltages or a few node voltages to enable reaction to drifting network situations or changed topologies without retraining. IV. VALIDATION SCENARIO SETUP The controller is evaluated in a multi-stage process involving simulation, a real-time digital twin, and a PowerHardware-in-the-Loop (PHiL) testbed within a real LV distribution grid. A. Simulation Environment and Benchmark The validation environment is based on the low-voltage distribution grid at the Combined Smart Energy Systems (CoSES) laboratory at the Technical University of Munich [10]. A Fig. 2. Validation grid setup digital twin of this grid is modeled in Pandapower [11], featuring a reconfigurable topology and a Thevenin equivalent for the external medium-voltage grid (30 MVA short-circuit power). Time-series data for training and testing are generated by executing AC power flows with one-second resolution. The power injections at five prosumer nodes are modeled using an AR(1) stochastic process to create two distinct dataset types: •High-Variability: Spatially decorrelated power profiles to provide rich excitation for model identification. •Correlated: A common base profile (ρ≈0.85) to simulate the highly collinear power injections typical of co-located PV systems. This dataset tests the PISR generalizability against collinear data, which can bias some data-driven training routines. The performance of the PISR-based controller is benchmarked against a state-of-the-art robust sensitivity-based control method inspired by [12], [5]. The benchmark uses the same training data to estimate its voltage sensitivity and confidence coefficients, ensuring a fair comparison. It also employs an identical OPF formulation and cost function as the PISR controller. B. Controller-in-the-Loop and PHiL Validation The controller is validated through two distinct online setups, progressing from pure software simulation to hardware interaction. This two-step process allows for a rigorous evaluation, first testing the controller’s core logic in an ideal environment and then assessing its robustness against realworld imperfections. The three stages of the controller —data acquisition, model training, and online control loop —are triggered by individual scripts to facilitate the reproducibility of results. The automated retraining is deactivated. 1) Controller-in-the-Loop (CIL) Validation: The initial online validation uses a Controller-in-the-Loop (CIL) configuration, as depicted in Fig. 3. CIL is a simulation technique where the physical system is replaced by a software model. This method enables the safe, repeatable, and rapid testing of the control algorithm’s logic and performance before connecting it to physical hardware. The CIL configuration operates as a closed loop entirely in software, where every 100 ms the PISR or the benchmark sensitivity controller calculates optimal power adjustments and sends them via a REST API to an online digital twin. This digital twin, a high-fidelity grid model running in Pandapower [11], simulates the grid’s response to the controller’s commands by calculating the new network state every 50 ms. The simulated measurements are then sent back to the controller, completing the loop. This setup is used to test the controller’s online performance and its response to simulated events, such as sudden load changes or network reconfigurations, by changing the state of breaker Q1. Fig. 3. Controller-in-the-Loop (CIL) validation setup, showing the pure software interaction between the controller and the Pandapower digital twin. 2) Power-Hardware-in-the-Loop (PHiL) Validation: The controller’s practical viability is then confirmed in a PowerHardware-in-the-Loop (PHiL) testbed, shown in Fig. 4. In PHiL, critical components of the software simulation are replaced with actual physical hardware. In this case, the LV grid consists of physical cables connected to the public grid via a station transformer; the prosumers are represented by EGSTON power amplifiers, which influence the actual voltage in the low-voltage grid. This step is essential for evaluating the controller’s robustness against real-world edge cases. In the PHiL setup, the 10 Hz controller sends power setpoints through a 20 Hz interface service to an NI Veristand gateway. The gateway commands the physical power amplifiers using a 100 Hz OPC-UA refresh rate. The amplifiers then use a fast 5 kHz internal loop for the real-time power injection. Physical voltage measurements are returned through the gateway to the controller, closing the control loop. >TRL6 Result: A PHiL validation is accepted as a TRL6 level result within the community [13], [14] and does not require access to a real LV grid. A public utility grid deployment would qualify as TRL7. Since our PHiL validation includes a real LV grid, we consider it suitable to claim it as higher than TRL6, but not quite a TRL7-grade result. Our controller deployment on the real LV grid provides a much higher level of confidence than the simulation tests by introducing several real-world complexities. A key challenge is the presence of hardware non-linearities, where inherent errors between the requested setpoint and the delivered power act as an unmodeled disturbance. The signal path through gateways and communication protocols also introduces unpredictable latencies not present in the CIL setup. Furthermore, the controller must remain stable despite receiving imperfect training data from physical sensors, which are subject to noise, calibration errors, and severe outliers. Finally, controller’s robustness to model mismatch is tested as the PISR model for is trained on only 50 samples from the hardware. This showcases that the controller can operate effectively despite the inherent mismatch between its sparse model and the complex physical reality. Fig. 4. Power-Hardware-in-the-Loop (PHiL) validation setup, where the software controller interacts with the physical distribution grid and power amplifiers. V. EVALUATION This section evaluates the performance of the PISR-based control framework, beginning with the surrogate model’s precision and offline performance. The controller’s stability is then tested in a real-time simulation under severe disturbances and validated on a Power-Hardware-in-the-Loop (PHiL) testbed. A. Impact of Training Data on Model Precision The precision of the PISR surrogate model is highly dependent on the quality of the training data. To investigate this, the model was trained on two distinct datasets: one with highvariability, decorrelated inputs to provide rich system excitation, and another with highly correlated inputs to simulate the collinear power injections typical of co-located PV systems. Figure 5 illustrates the training progress by tracking the Mean Absolute Error (MAE) on an independent test set for models trained with each dataset. The results show that while the model trained on correlated data has a lower initial error, the model trained on the high-variability dataset converges to a significantly and consistently lower final MAE. This superior performance is critical for control stability, as a lower error indicates a more accurate surrogate model that is less prone to the kind of prediction outliers that can destabilize a controller. Consequently, to ensure the highest level of robustness, the high-variability dataset training is used for the following offline optimization evaluation. 0 200 400 600 800 1000 0.002 0.004 0.006 Mean MAE (p.u.) Correlated mean MAE High-variability mean MAE Fig. 5. PISR training progress comparing the Mean Absolute Error (MAE) on a test set for models trained with correlated (blue) versus high-variability (orange) data. The high-variability dataset results in a lower final error. B. Offline Performance: Control Efficacy and Computational Speed The controller’s efficacy and speed were first validated by applying the optimization function offline to a test dataset. As illustrated in Fig. 6, the uncontrolled grid voltage frequently exceeds the 1.05 p.u. limit, whereas the PISR-based controller successfully regulates the maximum voltage to this limit with only minor deviations. The predicted voltage based on the optimization is shown in green. The orange trend is the actual voltage, which includes the prediction error. Crucially, the PISR surrogate model enables a significant computational speedup. With a model inference time of approximately 6 µs, the optimization consistently converged to a stable solution in just 10 ms. This represents a performance increase of about 2000 times compared to an equivalent optimization using a conventional AC power flow solver, confirming the framework’s suitability for time-critical online applications. Based on these results, we can confidently claim that our proposed controller is real-time capable for an online deployment 0 20 40 60 80 100 1.03 1.04 1.05 1.06 1.07 Voltage Limit Maximum Uncontrolled Test Dataset Voltage Maximum Controlled Test Dataset Voltage Maximum Controlled Voltage predicted by PISR Fig. 6. Offline optimization results applied to the test dataset, showing the uncontrolled voltage (blue) violating the limit (dashed red) and the successfully regulated voltage from both the simulation (orange) and the PISR model’s prediction (green). C. Online Resilience to Disturbances and Topology Changes Prior to the online evaluation, the PISR model was automatically generated using an API polling script that collects training data directly from the CIL digital twin. The script actively perturbs the system with random power injections to gather the necessary fifty training samples for model identification. The controller’s subsequent online resilience was then evaluated against a state-of-the-art robust sensitivity-based benchmark inspired by [12], [5] under a sequence of severe operational challenges. As shown in Fig. 7, both controllers reacted promptly to a large active and reactive power disturbance at t= 1s. They adjust the controlled inverters reactive power and introduce minimal active power curtailment to maintain the 1.05 p.u. voltage limit. At t= 5s, the grid topology was changed by closing breaker Q1, a condition on which the PISR and the sensitivity model were not trained. Despite this, both controllers remained stable and effective when the disturbance was repeated at t= 6s. As the network is now a ring instead of a radial network, the open-loop PISR control introduces a larger offset and an overreaction of the controller, in opposition to the measurement-based sensitivity control. Finally, after restoring the topology and introducing measurement noise at t= 10s, both controllers successfully regulated the voltage during a third disturbance at t= 12s. Both controllers settle their response within one optimization cycle. The results demonstrate that the PISR-based controller is as effective as the SOTA benchmark, validating its capability for robust online control. D. Power-Hardware-in-the-Loop Validation (>TRL6) The PISR model for the PHiL validation is also trained directly on the physical hardware. The same automated API polling script is used to collect 50 training samples by actively perturbing the power setpoints of the laboratory’s amplifiers with up to 3kW and 3kvar disturbance. This process allows the model to learn the real-world system dynamics, including inherent hardware non-linearities, before control is initiated. The controller’s practical viability is deployed on the PHiL testbed, controlling a physical distribution grid within a research facility that is connected to the public grid. Fig. 8 shows the controller being toggled on and off; when enabled, it instantly brings the voltages from a state of violation down to the prescribed limit by adjusting both active and reactive power setpoints. The detailed transient response upon activation is shown in Fig. 9. The plots reveal a rapid and stable reaction, with the control action initiating at approximately t= 1.92s and the system’s voltage settling below the limit in under 100 ms. This PHiL validation highlights a key advantage of the predictive approach: its inherent resilience to the heavy voltage measurement outliers observed in the lab setup. These outliers don’t destabilize the control action, demonstrating a robustness that would be challenging for direct feedback methods without introducing additional filtering delays. At this stage, we can confidently claim that our controller is able to capture nonlinear real grid dynamics. 0 2 4 6 8 10 12 14 16 1.025 1.050 1.075 1.100 Max voltage [p.u.] Voltage Limit Uncontrolled Ro bust Sensitiv ity PISR 0 2 4 6 8 10 12 14 16 −40 −20 0 Total dP in W Uncontrolled total dP Ro bust Sensitiv ity total dP PISR total dP 0 2 4 6 8 10 12 14 16 Time [s] −50 0 50 100 Total dQ in VAr Uncontrolled total dQ Ro bust Sensitiv ity total dQ PISR total dQ Fig. 7. CIL validation of controllers reacting to a repeated power disturbance under escalating challenges. The top panel shows the maximum grid voltage, while the middle and bottom panels show the total active and reactive power adjustments, respectively. Key events include an unmodeled topology change (at t = 5s) and the introduction of measurement noise (at t = 10s). 1.04 1.06 1.08 Voltage in p.u. SF1.S_EU_Ma g_A SF2.S_EU_Ma g_A SF4.S_EU_Ma g_A SF6.S_EU_Ma g_A Voltage Limit 1.05 p.u. −8 −6 −4 −2 Active Power in W SF1_Egston.P _A SF2_Egston.P _A SF4_Egston.P _A SF6_Egston.P _A SF3_PV.S_EP 0.0 10.0 20.0 30.0 40.0 50.0 Time [s] −2 0 2 4 6 Reactive Power in VAr SF1_Egston.Q _A SF2_Egston.Q _A SF4_Egston.Q _A SF6_Egston.Q _A SF3_PV.S_EQ Fig. 8. PHiL Validation of the PISR controller being repeatedly enabled (at green dashed lines) and disabled (at blue dashed lines). When active, the controller successfully regulates grid voltages (top panel) by modulating active (middle) and reactive (bottom) power, proving its effectiveness and stability in a hardware environment with significant measurement noise. VI. CONCLUSION This work successfully demonstrates the integration of a Physics-Informed Symbolic Regression (PISR) model into an online, open-loop optimization framework for real-time voltage control in active distribution grids. Our approach overcomes the limitation of not only the traditional, computationally intensive power flow models but also the limitations of both and simpler, linear data-driven methods by developing an interpretable, real-time capable and non-linear grid dynamics surrogate for the grid’s voltage response. 1.04 1.05 1.06 1.07 Voltage n p.u. SF1.S_EU_Ma g_A SF2.S_EU_Ma g_A SF4.S_EU_Ma g_A SF6.S_EU_Ma g_A −8 −6 −4 Act ve Power n kW SF1_Egston.P _A SF2_Egston.P _A SF4_Egston.P _A SF6_Egston.P _A SF3_PV.S_EP 1.8 1.85 1.9 1.95 2.0 2.05 2.1 T me [s] −2 0 2 React ve Power n kVAr SF1_Egston.Q _A SF2_Egston.Q _A SF4_Egston.Q _A SF6_Egston.Q _A SF3_PV.S_EQ Fig. 9. Detailed transient response upon controller activation in the PHiL validation. The plots show the system voltage (top) stabilizing below the limit in under 100 ms following the rapid adjustment of active (middle) and reactive (bottom) power. We use a non-linear data-driven model based on PISR that accurately captures grid behavior without requiring topological information. This model served as the core of an optimization strategy designed to minimize control actions while strictly enforcing voltage constraints. The entire framework is designed as an online controller, capable of self-supervised learning and adaptation to changing grid conditions, such as unmodeled topology changes. The controller’s performance and stability are rigorously evaluated through simulation, proving its effectiveness against large disturbances and topological changes, performing on par with a state-of-the-art sensitivity-based benchmark. Crucially, the controller’s practical viability is confirmed through PowerHardware-in-the-Loop (PHiL) validation in a real low-voltage grid. This step introduced real-world complexities, including hardware non-linearities and severe measurement outliers, which are argued as a higher than TRL6 grade result. The PHiL tests highlighted a significant advantage of this modelbased optimization in its inherent resilience to noisy conditions that would likely destabilize direct feedback methods. Our work validates that classical optimization methods can meet the stringent demands of real-time control in modern power systems by replacing slow, model-based solvers with a fast and robust data-driven surrogate. In the future, we will focus on online self-adaptation, which will enable long-term deployment in a real grid and accommodate severe topology changes. We will also deploy the controller on a public utility grid as the next step in the product development cycle. REFERENCES [1] R. K. Gupta, P. A. Pegoraro, O. Stanojev, A. Abur, C. Muscas, G. Hug, and M. Paolone, “Learning Power Flow Models and Constraints From Time-Synchronized Measurements: A Review,” Proceedings of the IEEE, vol. 112, no. 12, pp. 1799–1830, Dec. 2024, number: 12. [Online]. Available: https://ieeexplore.ieee.org/document/10934057 [2] M. Cranmer, “Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl,” May 2023, issue: arXiv:2305.01582 arXiv:2305.01582 [astro-ph]. [Online]. Available: http://arxiv.org/abs/ 2305.01582 [3] S. Eichhorn, A. Mohapatra, and C. Goebel, “PISR: Physics-Informed Symbolic Regression for Predicting Power System Voltage,” in Proceedings of the 16th ACM International Conference on Future and Sustainable Energy Systems. Rotterdam Netherlands: ACM, Jun. 2025, pp. 92–107. [Online]. Available: https://dl.acm.org/doi/10.1145/ 3679240.3734622 [4] S. Eichhorn, A. Mohapatra, and E. Okoyomon, “PHIL Validation of Physics-Informed Symbolic Regression for Power System Voltage Prediction,” accepted at ISGT EUROPE 2025. [5] R. Gupta and M. Paolone, “Experimental Validation of Modelless Robust Voltage Control using Measurement-based Estimated Voltage Sensitivity Coefficients,” Apr. 2023, issue: arXiv:2304.13638 arXiv:2304.13638 [eess]. [Online]. Available: http://arxiv.org/abs/2304. 13638 [6] H. ¨ Ozlemis¸, E. Mora, J. Schubert, A. Mohapatra, M. Duckheim, and S. Niessen, “Low-Voltage Grid Control Based On Data-Driven State Estimation and Reinforcement Learning,” in 2024 IEEE Power & Energy Society General Meeting (PESGM), Jul. 2024, pp. 1–5, iSSN: 1944-9933. [Online]. Available: https://ieeexplore.ieee.org/document/ 10689213 [7] J. Schubert, E. Mora, M. Duckheim, and S. Niessen, “Low-Voltage Grid Control Based on Data-Driven State Estimation and Online Feedback Optimization,” in 2024 IEEE PES Innovative Smart Grid Technologies Europe (ISGT EUROPE). Dubrovnik, Croatia: IEEE, Oct. 2024, pp. 1– 5. [Online]. Available: https://ieeexplore.ieee.org/document/10863026/ [8] L. Ortmann, A. Hauswirth, I. Caduff, F. D¨ orfler, and S. Bolognani, “Experimental validation of feedback optimization in power distribution grids,” Electric Power Systems Research, vol. 189, p. 106782, Dec. 2020. [Online]. Available: https://linkinghub.elsevier.com/retrieve/pii/ S037877962030585X [9] L. Ortmann, C. Rubin, A. Scozzafava, J. Lehmann, S. Bolognani, and F. D¨ orfler, “Deployment of an Online Feedback Optimization Controller for Reactive Power Flow Optimization in a Distribution Grid,” Aug. 2023, issue: arXiv:2305.06702 arXiv:2305.06702 [eess]. [Online]. Available: http://arxiv.org/abs/2305.06702 [10] V. S. Peri´ c, T. Hamacher, A. Mohapatra, F. Christiange, D. Zinsmeister, P. Tzscheutschler, U. Wagner, C. Aigner, and R. Witzmann, “CoSES Laboratory for Combined Energy Systems At TU Munich,” in 2020 IEEE Power & Energy Society General Meeting (PESGM), Aug. 2020, pp. 1–5, iSSN: 1944-9933. [Online]. Available: https: //ieeexplore.ieee.org/document/9281442 [11] L. Thurner, A. Scheidler, F. Sch¨ afer, J.-H. Menke, J. Dollichon, F. Meier, S. Meinecke, and M. Braun, “pandapower - an Open Source Python Tool for Convenient Modeling, Analysis and Optimization of Electric Power Systems,” IEEE Transactions on Power Systems, vol. 33, no. 6, pp. 6510–6521, Nov. 2018, arXiv:1709.06743 [cs]. [Online]. Available: http://arxiv.org/abs/1709.06743 [12] R. Gupta, F. Sossan, and M. Paolone, “Model-less robust voltage control in active distribution networks using sensitivity coefficients estimated from measurements,” Electric Power Systems Research, vol. 212, p. 108547, Nov. 2022. [Online]. Available: https://www. sciencedirect.com/science/article/pii/S0378779622006277 [13] J. Wu, R. Marshall, and C. Plet, “Meshed HVDC Transmission Network Technology Readiness Level Review,” DNV GL; PROMOTioN Project, Tech. Rep. D12.a, May 2020. [Online]. Available: https: //www.promotion-offshore.net/fileadmin/PDFs/D12.a Meshed HVDC Transmission Network Technology Readiness Level Review.pdf [14] T. Thiele, A. G¨ ulhan, and H. Olivier, “Instrumentation and Aerothermal Postflight Analysis of the Rocket Technology Flight Experiment ROTEX-T,” Journal of Spacecraft and Rockets, vol. 55, no. 5, pp. 1050– 1073, 2018.