Benjamin Schäfer

Julius Trebbien, Leonardo Rydin Gorjão, Aaron Praktiknjo et al.

Electricity prices in liberalized markets are determined by the supply and demand for electric power, which are in turn driven by various external influences that vary strongly in time. In perfect competition, the merit order principle describes that dispatchable power plants enter the market in the order of their marginal costs to meet the residual load, i.e. the difference of load and renewable generation. Many market models implement this principle to predict electricity prices but typically require certain assumptions and simplifications. In this article, we present an explainable machine learning model for the prices on the German day-ahead market, which substantially outperforms a benchmark model based on the merit order principle. Our model is designed for the ex-post analysis of prices and thus builds on various external features. Using Shapley Additive exPlanation (SHAP) values, we can disentangle the role of the different features and quantify their importance from empiric data. Load, wind and solar generation are most important, as expected, but wind power appears to affect prices stronger than solar power does. Fuel prices also rank highly and show nontrivial dependencies, including strong interactions with other features revealed by a SHAP interaction analysis. Large generation ramps are correlated with high prices, again with strong feature interactions, due to the limited flexibility of nuclear and lignite plants. Our results further contribute to model development by providing quantitative insights directly from data.

Matthias Hertel, Maximilian Beichter, Benedikt Heidrich et al.

In the smart grid of the future, accurate load forecasts on the level of individual clients can help to balance supply and demand locally and to prevent grid outages. While the number of monitored clients will increase with the ongoing smart meter rollout, the amount of data per client will always be limited. We evaluate whether a Transformer load forecasting model benefits from a transfer learning strategy, where a global univariate model is trained on the load time series from multiple clients. In experiments with two datasets containing load time series from several hundred clients, we find that the global training strategy is superior to the multivariate and local training strategies used in related work. On average, the global training strategy results in 21.8% and 12.8% lower forecasting errors than the two other strategies, measured across forecasting horizons from one day to one month into the future. A comparison to linear models, multi-layer perceptrons and LSTMs shows that Transformers are effective for load forecasting when they are trained with the global training strategy.

Sebastian Pütz, Benjamin Schäfer, Dirk Witthaut et al.

The energy transition introduces more volatile energy sources into the power grids. In this context, power transfer between different synchronous areas through High Voltage Direct Current (HVDC) links becomes increasingly important. Such links can balance volatile generation by enabling long-distance transport or by leveraging their fast control behavior. Here, we investigate the interaction of power imbalances - represented through the power grid frequency - and power flows on HVDC links between synchronous areas in Europe. We use explainable machine learning to identify key dependencies and disentangle the interaction of critical features. Our results show that market-based HVDC flows introduce deterministic frequency deviations, which however can be mitigated through strict ramping limits. Moreover, varying HVDC operation modes strongly affect the interaction with the grid. In particular, we show that load-frequency control via HVDC links can both have control-like or disturbance-like impacts on frequency stability.

Julius Trebbien, Sebastian Pütz, Benjamin Schäfer et al.

Accurate forecasts of electricity prices are crucial for the management of electric power systems and the development of smart applications. European electricity prices have risen substantially and became highly volatile after the Russian invasion of Ukraine, challenging established forecasting methods. Here, we present a Long Short-Term Memory (LSTM) model for the German-Luxembourg day-ahead electricity prices addressing these challenges. The recurrent structure of the LSTM allows the model to adapt to trends, while the joint prediction of both mean and standard deviation enables a probabilistic prediction. Using a physics-inspired approach - superstatistics - to derive an explanation for the statistics of prices, we show that the LSTM model faithfully reproduces both prices and their volatility.

Thorbjørn Lund Onsaker, Heidi S. Nygård, Damià Gomila et al.

Modelling, forecasting and overall understanding of the dynamics of the power grid and its frequency are essential for the safe operation of existing and future power grids. Much previous research was focused on large continental areas, while small systems, such as islands are less well-studied. These natural island systems are ideal testing environments for microgrid proposals and artificially islanded grid operation. In the present paper, we utilize measurements of the power grid frequency obtained in European islands: the Faroe Islands, Ireland, the Balearic Islands and Iceland and investigate how their frequency can be predicted, compared to the Nordic power system, acting as a reference. The Balearic islands are found to be particularly deterministic and easy to predict in contrast to hard-to-predict Iceland. Furthermore, we show that typically 2-4 weeks of data are needed to improve prediction performance beyond simple benchmarks.

Matthias Hertel, Sebastian Pütz, Ralf Mikut et al.

Time-series forecasts are essential for planning and decision-making in many domains. Explainability is key to building user trust and meeting transparency requirements. Shapley Additive Explanations (SHAP) is a popular explainable AI framework, but it lacks efficient implementations for time series and often assumes feature independence when sampling counterfactuals. We introduce SHAPformer, an accurate, fast and sampling-free explainable time-series forecasting model based on the Transformer architecture. It leverages attention manipulation to make predictions based on feature subsets. SHAPformer generates explanations in under one second, several orders of magnitude faster than the SHAP Permutation Explainer. On synthetic data with ground truth explanations, SHAPformer provides explanations that are true to the data. Applied to real-world electrical load data, it achieves competitive predictive performance and delivers meaningful local and global insights, such as identifying the past load as the key predictor and revealing a distinct model behavior during the Christmas period.

Wenlong Liao, Benjamin Schäfer, Dalin Qin et al.

To reduce the heavy computational burden of reactive power optimization of distribution networks, machine learning models are receiving increasing attention. However, most machine learning models (e.g., neural networks) are usually considered as black boxes, making it challenging for power system operators to identify and comprehend potential biases or errors in the decision-making process of machine learning models. To address this issue, an explainable machine-learning framework is proposed to optimize the reactive power in distribution networks. Firstly, a Shapley additive explanation framework is presented to measure the contribution of each input feature to the solution of reactive power optimizations generated from machine learning models. Secondly, a model-agnostic approximation method is developed to estimate Shapley values, so as to avoid the heavy computational burden associated with direct calculations of Shapley values. The simulation results show that the proposed explainable framework can accurately explain the solution of the machine learning model-based reactive power optimization by using visual analytics, from both global and instance perspectives. Moreover, the proposed explainable framework is model-agnostic, and thus applicable to various models (e.g., neural networks).

Hankun He, Takuya Boehringer, Benjamin Schäfer et al.

By employing superstatistical methods and machine learning, we analyze time series data of water quality indicators for the River Thames, with a specific focus on the dynamics of dissolved oxygen. After detrending, the probability density functions of dissolved oxygen fluctuations exhibit heavy tails that are effectively modeled using $q$-Gaussian distributions. Our findings indicate that the multiplicative Empirical Mode Decomposition method stands out as the most effective detrending technique, yielding the highest log-likelihood in nearly all fittings. We also observe that the optimally fitted width parameter of the $q$-Gaussian shows a negative correlation with the distance to the sea, highlighting the influence of geographical factors on water quality dynamics. In the context of same-time prediction of dissolved oxygen, regression analysis incorporating various water quality indicators and temporal features identify the Light Gradient Boosting Machine as the best model. SHapley Additive exPlanations reveal that temperature, pH, and time of year play crucial roles in the predictions. Furthermore, we use the Transformer to forecast dissolved oxygen concentrations. For long-term forecasting, the Informer model consistently delivers superior performance, achieving the lowest MAE and SMAPE with the 192 historical time steps that we used. This performance is attributed to the Informer's ProbSparse self-attention mechanism, which allows it to capture long-range dependencies in time-series data more effectively than other machine learning models. It effectively recognizes the half-life cycle of dissolved oxygen, with particular attention to key intervals. Our findings provide valuable insights for policymakers involved in ecological health assessments, aiding in accurate predictions of river water quality and the maintenance of healthy aquatic ecosystems.

Eike Cramer, Leonardo Rydin Gorjão, Alexander Mitsos et al.

The design and operation of modern energy systems are heavily influenced by time-dependent and uncertain parameters, e.g., renewable electricity generation, load-demand, and electricity prices. These are typically represented by a set of discrete realizations known as scenarios. A popular scenario generation approach uses deep generative models (DGM) that allow scenario generation without prior assumptions about the data distribution. However, the validation of generated scenarios is difficult, and a comprehensive discussion about appropriate validation methods is currently lacking. To start this discussion, we provide a critical assessment of the currently used validation methods in the energy scenario generation literature. In particular, we assess validation methods based on probability density, auto-correlation, and power spectral density. Furthermore, we propose using the multifractal detrended fluctuation analysis (MFDFA) as an additional validation method for non-trivial features like peaks, bursts, and plateaus. As representative examples, we train generative adversarial networks (GANs), Wasserstein GANs (WGANs), and variational autoencoders (VAEs) on two renewable power generation time series (photovoltaic and wind from Germany in 2013 to 2015) and an intra-day electricity price time series form the European Energy Exchange in 2017 to 2019. We apply the four validation methods to both the historical and the generated data and discuss the interpretation of validation results as well as common mistakes, pitfalls, and limitations of the validation methods. Our assessment shows that no single method sufficiently characterizes a scenario but ideally validation should include multiple methods and be interpreted carefully in the context of scenarios over short time periods.

Johannes Kruse, Benjamin Schäfer, Dirk Witthaut

The transition to a renewable energy system poses challenges for power grid operation and stability. Secondary control is key in restoring the power system to its reference following a disturbance. Underestimating the necessary control capacity may require emergency measures, such as load shedding. Hence, a solid understanding of the emerging risks and the driving factors of control is needed. In this contribution, we establish an explainable machine learning model for the activation of secondary control power in Germany. Training gradient boosted trees, we obtain an accurate description of control activation. Using SHapely Additive exPlanation (SHAP) values, we investigate the dependency between control activation and external features such as the generation mix, forecasting errors, and electricity market data. Thereby, our analysis reveals drivers that lead to high reserve requirements in the German power system. Our transparent approach, utilizing open data and making machine learning models interpretable, opens new scientific discovery avenues.

Johannes Kruse, Benjamin Schäfer, Dirk Witthaut

Deterministic frequency deviations (DFDs) critically affect power grid frequency quality and power system stability. A better understanding of these events is urgently needed as frequency deviations have been growing in the European grid in recent years. DFDs are partially explained by the rapid adjustment of power generation following the intervals of electricity trading, but this intuitive picture fails especially before and around noonday. In this article, we provide a detailed analysis of DFDs and their relation to external features using methods from explainable Artificial Intelligence. We establish a machine learning model that well describes the daily cycle of DFDs and elucidate key interdependencies using SHapley Additive exPlanations (SHAP). Thereby, we identify solar ramps as critical to explain patterns in the Rate of Change of Frequency (RoCoF).

Johannes Kruse, Benjamin Schäfer, Dirk Witthaut

The power grid frequency is the central observable in power system control, as it measures the balance of electrical supply and demand. A reliable frequency forecast can facilitate rapid control actions and may thus greatly improve power system stability. Here, we develop a weighted-nearest-neighbor (WNN) predictor to investigate how predictable the frequency trajectories are. Our forecasts for up to one hour are more precise than averaged daily profiles and could increase the efficiency of frequency control actions. Furthermore, we gain an increased understanding of the specific properties of different synchronous areas by interpreting the optimal prediction parameters (number of nearest neighbors, the prediction horizon, etc.) in terms of the physical system. Finally, prediction errors indicate the occurrence of exceptional external perturbations. Overall, we provide a diagnostics tool and an accurate predictor of the power grid frequency time series, allowing better understanding of the underlying dynamics.