Analysing drivers and interdependencies in European electricity markets using XAI

Abstract: Electricity markets are inherently complex systems characterised by strong nonlinearities, high-dimensional interactions, and increasing interdependence across regions. While deep neural networks (DNNs) have demonstrated strong predictive capabilities for electricity prices, their lack of interpretability limits their usefulness for understanding the underlying drivers of price formation. This paper addresses this gap by combining DNN models with explainable artificial intelligence (XAI) techniques to analyse the determinants of electricity prices across 39 European bidding zones. We employ SHAP (SHapley Additive exPlanations) to quantify feature contributions and apply and extend SSHAP, an aggregation framework to improve interpretability in high-dimensional settings. The analysis identifies that renewable energy sources, particularly solar, play a disproportionately important role in price formation despite their lower share in total power generation. Gas prices remain a dominant and consistent driver across electricity markets, while interconnections significantly shape price dynamics, highlighting the strong interdependence of European electricity systems. In addition, a synthetic EU-wide electricity market is constructed to explore the counterfactual scenario of a fully integrated market with a single price.

• The paper demonstrates that integrating SHAP and SSHAP reveals solar's disproportionate impact, reducing EU prices by up to €60/MWh despite constituting only 10% of generation.
• The paper highlights that cross-border interdependencies account for 61% of domestic price determination, emphasizing the dominance of interconnected markets over national features.
• The paper confirms gas prices as persistent key drivers and validates SSHAP as an effective method to overcome high-dimensional interpretability challenges in European market modeling.

Analysing Electricity Price Drivers and Interdependencies in Europe via XAI

Introduction and Technical Motivation

The European electricity market exhibits high-dimensional nonlinear dynamics, driven by a complex mix of generation portfolios, volatile fuel costs, and cross-border interactions. Deep neural networks (DNN) yield state-of-the-art predictive accuracy for electricity price estimation but lack transparency regarding causal feature contributions. This paper provides a methodologically rigorous bridge between high-performing DNNs and interpretability by leveraging SHAP (SHapley Additive exPlanations) and a high-dimensional aggregation framework dubbed SSHAP, quantifying the importance of both domestic and cross-zonal drivers in European price formation across 39 bidding zones.

Methodology: DNNs, Feature Partitioning, and XAI

Model Architecture and Data

Models are multi-layer perceptrons with two hidden layers optimized via Adam, using load, generation mix (7 main categories), neighboring bidding zone variables (where interconnected), and gas price as regressors. Data cover 2023–2025 and leverage the ENTSO-E Transparency Platform. Importantly, lagged variables are excluded, focusing the analysis on contemporaneous explanatory power rather than forecasting per se—an explicit design choice to facilitate interpretability of price formation mechanisms instead of pure predictive performance.

Explainability Framework

The SHAP methodology, grounded in coalitional game theory, is deployed to obtain local and global feature attributions on de-normalized outputs ($€/MWh$), with conditional expectations estimated via Monte Carlo sampling. To address feature collinearity and high dimensionality, the SSHAP framework is used: features are grouped into "super-features" (e.g., entire generation categories or entire neighboring zones), and their netted contributions are computed before global aggregation—preserving important additivity and efficiency properties of the Shapley value [lundberg_unified_2017, chen_algorithms_2023, pesenti_explaining_2025]. This allows meaningful ranking and decomposition of explanatory effects, particularly in dense interconnected networks.

Principal Results and Claims

Super-Feature Decomposition: Solar’s Disproportionate Impact

Through SSHAP analysis, the paper demonstrates that solar generation, despite comprising only 10% of aggregate production, is the super-feature with the largest impact on price formation EU-wide. This is manifested by solar exhibiting the highest mean absolute SSHAP values, with the capacity to reduce the EU-wide price by up to €60/MWh when high output occurs, vastly exceeding its proportional generation share. In contrast, nuclear (24% of output, stable base load) exerts a secondary impact due to low variability and intraday price responsiveness.

Cross-Border Interdependence: Neighbors as Primary Price Determinants

A central finding is that interconnection features (aggregated neighbor SSHAP values) are responsible, on average, for 61% of domestic price determination. Only 13 of 39 zones have their own domestic variables as the dominant SSHAP determinant. For instance, 6 out of Germany's 11 neighbors have German variables as their principal explanatory super-feature. This aligns with the significant transfer capacities and system sizes, reinforcing the thesis that European price formation is a function of coupled zonal dynamics rather than isolated national phenomena.

Fossil Gas and Merit Order Persistence

Gas price is confirmed as persistently dominant among all non-generation features, comprising 11.5% of total SSHAP impact at the EU level and emerging as the single most important feature in 17 out of 39 bidding zone models. This is in line with external findings that fossil gases act as price setters a majority of the time [zakeri_role_2023, gasparella_merit_2023].

Germany’s Centrality

Germany’s wind and solar generation in particular are persistently ranked among the top contributors to EU-wide price dynamics, both in absolute SHAP and SSHAP analyses. These features exhibit substantial negative tails, evidencing their capacity to “pull” prices downward under high generation.

Outlier Markets and Counterexamples

The SSHAP analysis also highlights specific structural exceptions:

• Spain, due to limited interconnector capacity (29% of mean load), is more isolated, with domestic features contributing >50% to price formation.
• Poland, with 72% fossil generation but solar as the most important SSHAP driver for price, reflects the asymmetry between mean production and price-setting variability.
• Scandinavian hydro-dominated zones exhibit low means and standard deviation but retain cross-border sensitivity according to SSHAP decomposition.

Discussion: Theoretical and Practical Implications

Toward Market Integration and Design Insights

By constructing a synthetic, fully integrated EU market model, the analysis exposes the scale of pan-European price co-determination and the potential impact of further interconnection on price stability, volatility, and decentralization of price-setting mechanisms.

This XAI-based quantification goes beyond prior white-box econometric models and machine learning studies which, despite recognizing gas and renewables as drivers, could not attribute magnitude or accurately net-out feature interactions due to dimensionality or linearity constraints [maciejowska_forecasting_2022, trebbien_understanding_2023, tschora_electricity_2022].

SSHAP as a Solution to High-Dimensional XAI

The SSHAP method represents a novel aggregation solution to a well-known problem in SHAP/XAI research: high-dimensionality leading to overestimated or noisy importance allocations due to cancellation effects among collinear inputs [pesenti_explaining_2025]. By enabling super-feature netting, SSHAP recovers meaningful rankings, which is vital for infrastructure planning, regulation, and policy evaluations focused on collective impacts (e.g., effects of interconnection or sector-level generation shifts).

Limitations and Extensions

Current models do not explicitly embed transmission constraints or congestion effects, which remain essential for a physically accurate market simulation. Furthermore, features are contemporaneous; causal inference in path-dependent market shocks or lagged inter-zonal spillovers is not addressed. Price spike or tail event analysis is noted as a future direction, given that SSHAP contributions for renewables are asymmetric—capable of strongly depressing, but not elevating, price extremes.

Conclusion

This study advances the field of electricity market analysis by providing a tractable, XAI-based decomposition of price driving factors across a pan-European context where high-dimensional data and cross-border dependencies preclude classical interpretability. The paper’s most consequential technical findings are:

• Solar, despite its minimal share of generation, is a top driver of prices due to its volatility and regional correlation across Europe.
• Gas prices remain the global price-setter for Europe, especially under merit order dispatch.
• Inter-zonal (neighbor) features account for the majority of price formation in most markets, highlighting the futility of national-only interventions.
• SSHAP enables sound super-feature attribution in dense DNNs, remedying SHAP’s high-dimensional limitations.

For AI and market theory, the results support further investigation of interpretable aggregation methods in other high-dimensional, interconnected systems, as well as the need for hybrid models embedding transmission physics for dynamic market design evaluation. Practically, market participants and regulators are provided with actionable, interpretable metrics for policy, infrastructure investment, and risk management.

References:

• "Analysing drivers and interdependencies in European electricity markets using XAI" (2606.19118)
• "Explaining deep neural network models for electricity price forecasting with XAI" [pesenti_explaining_2025]
• "The role of natural gas in setting electricity prices in Europe" [zakeri_role_2023]
• "The Merit Order and Price-Setting Dynamics in European Electricity Markets" [gasparella_merit_2023]
• "A Unified Approach to Interpreting Model Predictions" [lundberg_unified_2017]
• "Algorithms to estimate Shapley value feature attributions" [chen_algorithms_2023]