Control-Oriented Scenario Tree Construction through Reinforcement Learning

Multistage stochastic model predictive control (MPC) handles uncertainty by optimizing over a scenario tree, a finite branching approximation of future outcomes constructed from sampled forecasts. To build such a tree, conventional methods focus on matching the underlying probability distribution---e.g., via Wasserstein-based scenario reduction---but improved distributional accuracy does not necessarily yield better control performance. We propose a control-oriented approach that learns scenario tree construction directly from its impact on downstream decisions. Fixing the tree topology, we formulate tree construction as a sequential assignment of sampled scenarios to leaves. This assignment is parameterized by an attention-based policy over the scenario set and trained using reinforcement learning, with closed-loop control profit as the objective. Training is stabilized by an asymmetric critic that leverages realized future trajectories. We evaluate the method on a risk-averse battery arbitrage problem. Across a range of forecast set sizes, the learned construction consistently achieves the highest profit, outperforming classical forward and backward reduction methods and certainty-equivalent (single-trajectory forecast) control. The learned policy also exhibits greater robustness on challenging instances, consistently demonstrating better tail-risk characteristics. Analysis of the resulting trees indicates that our method constructs compact, selectively branching structures that capture high-impact events while keeping most trajectories nearly deterministic. These findings highlight that the value of a scenario tree depends critically on the decisions it supports, and provide an effective framework to train scenario tree constructors merely based on the closed-loop control optimization signal.

S3TS: Stochastic Scenario-Structured Tree Search for Advanced Planning Under Uncertainty

Effective scheduling in the energy sector is essential to ensure the reliable operation of electrical grids and their connected assets by, for instance, optimizing the dispatch of generation units and storage systems. An effective planning strategy must (a) accommodate advanced and potentially non-linear system models -- exploiting the increasing data availability of modern grids, and (b) explicitly handle uncertainties arising, for instance, from the integration of renewable energy sources. While existing approaches can address either non-linearity (e.g., Monte Carlo Tree Search) or uncertainty (e.g., stochastic mathematical optimization), there is a lack of planning techniques capable of addressing both challenges simultaneously. To bridge this gap, we propose a Stochastic Scenario-Structured Tree Search (S3TS) algorithm that explicitly represents uncertainty through scenario trees while enabling the integration of advanced non-linear models. We evaluate S3TS on a simulated demand response signal publication problem, largely mimicking the imbalance settlement mechanism in Belgium. The results demonstrate near-optimal performance in linear, analytically tractable settings, with costs within 14% of the mathematically optimal solution conditioned to the scenario trees. In highly non-linear scenarios, S3TS significantly outperforms baseline methods, achieving cost reductions of up to 51% and 5.4% compared to a myopic algorithm and deterministic MCTS, respectively.

Neural Network-Assisted Model Predictive Control for Implicit Balancing

In Europe, balance responsible parties can deliberately take out-of-balance positions to support transmission system operators (TSOs) in maintaining grid stability and earn profit, a practice called implicit balancing. Model predictive control (MPC) is widely adopted as an effective approach for implicit balancing. The balancing market model accuracy in MPC is critical to decision quality. Previous studies modeled this market using either (i) a convex market clearing approximation, ignoring proactive manual actions by TSOs and the market sub-quarter-hour dynamics, or (ii) machine learning methods, which cannot be directly integrated into MPC. To address these shortcomings, we propose a data-driven balancing market model integrated into MPC using an input convex neural network to ensure convexity while capturing uncertainties. To keep the core network computationally efficient, we incorporate attention-based input gating mechanisms to remove irrelevant data. Evaluating on Belgian data shows that the proposed model both improves MPC decisions and reduces computational time.

Model Predictive Control-Guided Reinforcement Learning for Implicit Balancing

In Europe, profit-seeking balance responsible parties can deviate in real time from their day-ahead nominations to assist transmission system operators in maintaining the supply-demand balance. Model predictive control (MPC) strategies to exploit these implicit balancing strategies capture arbitrage opportunities, but fail to accurately capture the price-formation process in the European imbalance markets and face high computational costs. Model-free reinforcement learning (RL) methods are fast to execute, but require data-intensive training and usually rely on real-time and historical data for decision-making. This paper proposes an MPC-guided RL method that combines the complementary strengths of both MPC and RL. The proposed method can effectively incorporate forecasts into the decision-making process (as in MPC), while maintaining the fast inference capability of RL. The performance of the proposed method is evaluated on the implicit balancing battery control problem using Belgian balancing data from 2023. First, we analyze the performance of the standalone state-of-the-art RL and MPC methods from various angles, to highlight their individual strengths and limitations. Next, we show an arbitrage profit benefit of the proposed MPC-guided RL method of 16.15% and 54.36%, compared to standalone RL and MPC.

Predicting and Publishing Accurate Imbalance Prices Using Monte Carlo Tree Search

The growing reliance on renewable energy sources, particularly solar and wind, has introduced challenges due to their uncontrollable production. This complicates maintaining the electrical grid balance, prompting some transmission system operators in Western Europe to implement imbalance tariffs that penalize unsustainable power deviations. These tariffs create an implicit demand response framework to mitigate grid instability. Yet, several challenges limit active participation. In Belgium, for example, imbalance prices are only calculated at the end of each 15-minute settlement period, creating high risk due to price uncertainty. This risk is further amplified by the inherent volatility of imbalance prices, discouraging participation. Although transmission system operators provide minute-based price predictions, the system imbalance volatility makes accurate price predictions challenging to obtain and requires sophisticated techniques. Moreover, publishing price estimates can prompt participants to adjust their schedules, potentially affecting the system balance and the final price, adding further complexity. To address these challenges, we propose a Monte Carlo Tree Search method that publishes accurate imbalance prices while accounting for potential response actions. Our approach models the system dynamics using a neural network forecaster and a cluster of virtual batteries controlled by reinforcement learning agents. Compared to Belgium's current publication method, our technique improves price accuracy by 20.4% under ideal conditions and by 12.8% in more realistic scenarios. This research addresses an unexplored, yet crucial problem, positioning this paper as a pioneering work in analyzing the potential of more advanced imbalance price publishing techniques.

Control Policy Correction Framework for Reinforcement Learning-based Energy Arbitrage Strategies

A continuous rise in the penetration of renewable energy sources, along with the use of the single imbalance pricing, provides a new opportunity for balance responsible parties to reduce their cost through energy arbitrage in the imbalance settlement mechanism. Model-free reinforcement learning (RL) methods are an appropriate choice for solving the energy arbitrage problem due to their outstanding performance in solving complex stochastic sequential problems. However, RL is rarely deployed in real-world applications since its learned policy does not necessarily guarantee safety during the execution phase. In this paper, we propose a new RL-based control framework for batteries to obtain a safe energy arbitrage strategy in the imbalance settlement mechanism. In our proposed control framework, the agent initially aims to optimize the arbitrage revenue. Subsequently, in the post-processing step, we correct (constrain) the learned policy following a knowledge distillation process based on properties that follow human intuition. Our post-processing step is a generic method and is not restricted to the energy arbitrage domain. We use the Belgian imbalance price of 2023 to evaluate the performance of our proposed framework. Furthermore, we deploy our proposed control framework on a real battery to show its capability in the real world.

Probabilistic forecasting of power system imbalance using neural network-based ensembles

Keeping the balance between electricity generation and consumption is becoming increasingly challenging and costly, mainly due to the rising share of renewables, electric vehicles and heat pumps and electrification of industrial processes. Accurate imbalance forecasts, along with reliable uncertainty estimations, enable transmission system operators (TSOs) to dispatch appropriate reserve volumes, reducing balancing costs. Further, market parties can use these probabilistic forecasts to design strategies that exploit asset flexibility to help balance the grid, generating revenue with known risks. Despite its importance, literature regarding system imbalance (SI) forecasting is limited. Further, existing methods do not focus on situations with high imbalance magnitude, which are crucial to forecast accurately for both TSOs and market parties. Hence, we propose an ensemble of C-VSNs, which are our adaptation of variable selection networks (VSNs). Each minute, our model predicts the imbalance of the current and upcoming two quarter-hours, along with uncertainty estimations on these forecasts. We evaluate our approach by forecasting the imbalance of Belgium, where high imbalance magnitude is defined as $|$SI$| > 500\,$MW (occurs 1.3% of the time in Belgium). For high imbalance magnitude situations, our model outperforms the state-of-the-art by 23.4% (in terms of continuous ranked probability score (CRPS), which evaluates probabilistic forecasts), while also attaining a 6.5% improvement in overall CRPS. Similar improvements are achieved in terms of root-mean-squared error. Additionally, we developed a fine-tuning methodology to effectively include new inputs with limited history in our model. This work was performed in collaboration with Elia (the Belgian TSO) to further improve their imbalance forecasts, demonstrating the relevance of our work.

Explainable Reinforcement Learning-based Home Energy Management Systems using Differentiable Decision Trees

With the ongoing energy transition, demand-side flexibility has become an important aspect of the modern power grid for providing grid support and allowing further integration of sustainable energy sources. Besides traditional sources, the residential sector is another major and largely untapped source of flexibility, driven by the increased adoption of solar PV, home batteries, and EVs. However, unlocking this residential flexibility is challenging as it requires a control framework that can effectively manage household energy consumption, and maintain user comfort while being readily scalable across different, diverse houses. We aim to address this challenging problem and introduce a reinforcement learning-based approach using differentiable decision trees. This approach integrates the scalability of data-driven reinforcement learning with the explainability of (differentiable) decision trees. This leads to a controller that can be easily adapted across different houses and provides a simple control policy that can be explained to end-users, further improving user acceptance. As a proof-of-concept, we analyze our method using a home energy management problem, comparing its performance with commercially available rule-based baseline and standard neural network-based RL controllers. Through this preliminary study, we show that the performance of our proposed method is comparable to standard RL-based controllers, outperforming baseline controllers by ~20% in terms of daily cost savings while being straightforward to explain.

Distill2Explain: Differentiable decision trees for explainable reinforcement learning in energy application controllers

Demand-side flexibility is gaining importance as a crucial element in the energy transition process. Accounting for about 25% of final energy consumption globally, the residential sector is an important (potential) source of energy flexibility. However, unlocking this flexibility requires developing a control framework that (1) easily scales across different houses, (2) is easy to maintain, and (3) is simple to understand for end-users. A potential control framework for such a task is data-driven control, specifically model-free reinforcement learning (RL). Such RL-based controllers learn a good control policy by interacting with their environment, learning purely based on data and with minimal human intervention. Yet, they lack explainability, which hampers user acceptance. Moreover, limited hardware capabilities of residential assets forms a hurdle (e.g., using deep neural networks). To overcome both those challenges, we propose a novel method to obtain explainable RL policies by using differentiable decision trees. Using a policy distillation approach, we train these differentiable decision trees to mimic standard RL-based controllers, leading to a decision tree-based control policy that is data-driven and easy to explain. As a proof-of-concept, we examine the performance and explainability of our proposed approach in a battery-based home energy management system to reduce energy costs. For this use case, we show that our proposed approach can outperform baseline rule-based policies by about 20-25%, while providing simple, explainable control policies. We further compare these explainable policies with standard RL policies and examine the performance trade-offs associated with this increased explainability.

Distributional Reinforcement Learning-based Energy Arbitrage Strategies in Imbalance Settlement Mechanism

Growth in the penetration of renewable energy sources makes supply more uncertain and leads to an increase in the system imbalance. This trend, together with the single imbalance pricing, opens an opportunity for balance responsible parties (BRPs) to perform energy arbitrage in the imbalance settlement mechanism. To this end, we propose a battery control framework based on distributional reinforcement learning (DRL). Our proposed control framework takes a risk-sensitive perspective, allowing BRPs to adjust their risk preferences: we aim to optimize a weighted sum of the arbitrage profit and a risk measure while constraining the daily number of cycles for the battery. We assess the performance of our proposed control framework using the Belgian imbalance prices of 2022 and compare two state-of-the-art RL methods, deep Q learning and soft actor-critic. Results reveal that the distributional soft actor-critic method can outperform other methods. Moreover, we note that our fully risk-averse agent appropriately learns to hedge against the risk related to the unknown imbalance price by (dis)charging the battery only when the agent is more certain about the price.