Neural Network-Assisted Model Predictive Control for Implicit Balancing

Seyed Soroush Karimi Madahi; Kenneth Bruninx; Bert Claessens; Chris Develder

eess.SYApr 2, 2026

Neural Network-Assisted Model Predictive Control for Implicit Balancing

Authors: Seyed Soroush Karimi Madahi, Kenneth Bruninx, Bert Claessens, Chris Develder

Organizations: IDLab, Ghent University – imec, Ghent, Belgium · Faculty of Technology, Policy & Management, Delft University of Technology, Delft, The Netherlands · Beebop.ai, Belgium

Abstract

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.

Figures & tables

Fig. 1 : The proposed implicit balancing framework.

Fig. 2 : The attention layer architecture used in the proposed market model.

Horizon	SI Forecast	Method	Profit (€/ MW/ QH)
Horizon	SI Forecast	Method	All	$\|\text{SI}\|\geq$ 20 MW	$\|\text{SI}\|<$ 20 MW
1 QH	PF	Optimal	9.59	11.23	8.06
		Clearing Approx.	8.01	9.89	6.27
		Proposed	8.4 $\pm$ 0.08 *	10.43 $\pm$ 0.15	6.49 $\pm$ 0.14
	Noise	Clearing Approx.	5.58	10.51	1.02
	Noise	Proposed	7.68 $\pm$ 0.19	10.56 $\pm$ 0.15	4.99 $\pm$ 0.45

TABLE I : Imbalance profit for 1 MW/ 2 MWh battery on December 2023.

Fig. 4 : Price prediction error and the probability of idle action for 1 MW/ 2 MWh battery.

Battery	SI Forecast	Method	Profit (€/ MW/ QH)
Battery	SI Forecast	Method	All	$\|\text{SI}\|\geq$ 20 MW	$\|\text{SI}\|<$ 20 MW
10 MW/ 20 MWh	PF	Clearing Approx.	6.41	11.04	2.59
	PF	Proposed	6.93 $\pm$ 0.22 *	11.73 $\pm$ 0.37	2.98 $\pm$ 0.27
	Noise	Clearing Approx.	3.54	10.51	$-$ 2.36
	Noise	Proposed	6.83 $\pm$ 0.18	11.72 $\pm$ 0.36	2.79 $\pm$ 0.22
50 MW/ 100 MWh	PF	Clearing Approx.	2.76	6.19	0.49

TABLE II : Imbalance profit for large batteries with 4 QH look-ahead horizon on December 2023.

Fig. 5 : Price prediction error and the probability of idle action for 50 MW/ 100 MWh battery.

Panel of Figure 8 — Fig. 6 : The QH profit spread of the 50 MW battery for quarter hours with small SI (a) PF (b) noise.

Model Predictive Control

Model Predictive Control optimizes future actions with a system model, repeatedly applying the first action as new information arrives.

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Bilinear Mamba-Koopman Neural MPC for Varying Dynamics

Matan Pagi, Zohar Sorek

Psistar AI

Optimal Control Dynamical Systems Koopman Operator Learning Nonlinear MPC Robust Control Model Predictive Control+2

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Koopman-based neural MPC models generate time-varying dynamics from historical data, but preserve convexity by enforcing that the system operator is independent of the current control input. This conditional independence constraint limits adaptation to changing dynamics within a single MPC horizon, particularly under time-varying conditions and under stale-plan execution. We propose Bilinear Mamba-Koopman Neural MPC, a minimal extension that introduces control-dependent coupling in the latent dynamics, allowing the effective operator to adapt to the current input. The resulting model is a strict generalization of the standard linear, conditional-independence formulation, adds less than 1% parameters through a low-rank structure, and admits exact model Jacobians that enable efficient Sequential Convex Programming (SCP) with monotone-descent and KKT convergence results under standard trust-region assumptions. Across CartPole and RSCP benchmarks in time-invariant and time-varying regimes, the proposed model matches or improves forecasting accuracy on every cell when training noise is averaged out, with strict gains where control-state coupling is structurally present. Its main closed-loop gains appear in the RSCP TV task, where iterative SCP improves adaptation within the horizon and substantially stabilizes training; in CartPole TV, the gains are modest but consistent. In delayed re-planning experiments on the time-varying variants, the bilinear model degrades more gracefully under stale-plan execution, maintaining a consistent advantage on CartPole TV and a substantially larger robustness margin on RSCP TV. These results show that control-dependent latent dynamics provide a simple and effective mechanism for robust MPC under varying conditions.

Abstract

Model Predictive Control

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