Surrogate Modeling of Interconnector Flows: A Machine Learning Alternative to Full-Scale Power System Simulations with Application to Cross-Border Electricity Exchange

Technical Summary: Surrogate Modeling of Interconnector Flows

Problem Statement
Cross-border electricity exchanges are critical for the operation and planning of highly renewable power systems. However, Power System Optimization Models (PSOMs) face inherent trade-offs between temporal resolution, technical detail, and spatial scope. To maintain tractability, many studies reduce spatial granularity to a single country or region, treating cross-border exchanges exogenously by prescribing historical import/export time series or scaling them to match new demand levels.

The paper argues that these simplifications become inconsistent as the power system transitions toward high shares of Variable Renewable Energy Sources (VRES). In such systems, flow patterns are increasingly driven by fluctuating renewable availability rather than predictable demand. Consequently, scaling historical time series can lead to misleading assumptions regarding the magnitude and timing of flows, resulting in inaccurate model outcomes and potential infeasibilities (e.g., Energy Not Supplied, ENS) when these flows are imposed as fixed boundary conditions in reduced models.

Methodology
The authors propose a machine learning (ML) surrogate framework designed to map available nodal time series data (hourly demand and renewable generation profiles) to synthetic, interconnector-level flow time series. These synthetic flows serve as consistent boundary conditions for reduced PSOMs.

1. Data Generation: Training data is generated using the open-source LEGO PSOM, a linear DC Optimal Power Flow (DC-OPF) model. The model represents a pan-European network with one node per country, utilizing ENTSO-E TYNDP 2024 National Trends assumptions for the year 2030.
2. Surrogate Models: Two model families are developed and compared:
   • K-Nearest Neighbors (KNN): A non-parametric baseline. Variants include using full feature sets, selected features (via permutation importance), and hyperparameter optimization.
   • Sequential Neural Network (SQU): A feedforward neural network with dense hidden layers and ReLU activation. Variants include full/selected feature sets, hyperparameter optimization, and a novel feasibility-aware custom loss function.
3. Custom Loss Function: For the SQU models, a custom loss term is introduced to penalize physically impossible flow patterns. Specifically, it discourages predicted net exports that exceed the node's maximum available generation capacity plus inflows minus demand. This aims to prevent the reduced single-node PSOM from encountering artificial infeasibilities (ENS) when the surrogate flows are imposed.
4. Evaluation Strategy:
   • Training: Climate Year (CY) 2009.
   • Testing: In-sample (CY 2009) and out-of-sample (CY 1995 and 2008) to test robustness across different weather realizations.
   • Case Studies: Austria (highly interconnected), Germany (large, diverse system), and Spain (weakly interconnected).
   • Downstream Impact: Predicted flows are imposed as fixed boundary conditions in reduced single-country LEGO models. Results (system cost, dispatch, ENS, trade balances) are compared against the corresponding country components of the full European benchmark.

Key Contributions

• Framework Proposal: A novel ML-based surrogate framework that generates hourly interconnector flow time series from demand and renewable generation inputs, enabling reduced PSOM studies without repeatedly solving a full-scale European model.
• Model Comparison: A comprehensive comparison of KNN and feedforward neural network (SQU) surrogates for multi-output flow prediction, evaluating both full and reduced feature sets.
• Feasibility-Aware Training: The introduction of a custom loss function for neural networks that penalizes physically unrealistic net-export profiles, aiming to reduce surrogate-induced infeasibilities in downstream optimization.
• Empirical Validation: Rigorous testing against common practices (reusing/scaling historical profiles) and full-system benchmarks across multiple climate years and countries with distinct structural characteristics.

Results

• Predictive Accuracy: The SQU models consistently outperform KNN baselines, particularly in out-of-sample climate years. SQU models achieve higher $R^2$ and lower Normalized Mean Absolute Error (NMAE) compared to KNN, demonstrating superior generalization to unseen weather patterns.
• Comparison to Historical Scaling: Reusing historical flow profiles (even when scaled to match annual demand or trade totals) results in poor predictive accuracy (often negative $R^2$) and fails to capture the correct hourly flow structure. This leads to significant deviations in dispatch and system costs.
• Downstream Decision Relevance:
  • System Cost: ML-generated flows (particularly SQU variants) produce system cost outcomes in reduced single-country models that closely match the full European benchmark. In contrast, historical scaling methods introduce substantial cost distortions (e.g., up to +81.6% deviation in Germany for 2008).
  • Dispatch and Feasibility: The SQU models better preserve the timing and sign of exchanges, leading to more accurate dispatch patterns for flexible resources (gas, storage).
  • Custom Loss Impact: In Austria, where the full benchmark has no ENS, the custom loss successfully eliminates surrogate-induced ENS in the reduced model. However, in Germany, where the benchmark already contains small ENS, the custom loss reduces ENS further but shifts the trade/dispatch balance away from the benchmark, indicating a trade-off between statistical fidelity and operational feasibility depending on the system context.
• Computational Efficiency: The approach offers significant runtime reductions (up to $\sim$500$\times$) compared to running the full European model. While KNN with extensive feature selection and tuning can incur high preprocessing overhead (sometimes exceeding the full model runtime for complex cases like Germany), SQU models offer a robust trade-off between result quality and computational speed.

Significance and Claims
The paper claims that ML-based flow surrogates provide a viable and necessary alternative to exogenous, history-based flow assumptions for high-renewable power system studies. The authors assert that:

1. Temporal Structure Matters: Accurate modeling of cross-border exchanges requires capturing the intra-annual timing of flows relative to renewable availability and demand, not just annual totals.
2. Generalization: Neural network surrogates (SQU) generalize more robustly across different climate years than KNN or scaled historical data, making them suitable for prospective scenario studies.
3. Decision Relevance: Using ML-generated flows as boundary conditions in reduced PSOMs yields outcomes (costs, dispatch, trade balances) that are significantly more consistent with full-system simulations than traditional methods.
4. Feasibility Awareness: Custom loss functions can be effective in preventing artificial infeasibilities, though their application requires careful consideration of the underlying system's feasibility characteristics.

The study concludes that this framework enables tractable, decision-relevant reduced studies for high-renewable systems, offering substantial computational savings while maintaining the integrity of cross-border interactions. Future work suggested by the authors includes increasing spatial granularity, applying the method to generation expansion planning, and developing probabilistic surrogates.