Building Seasonal Highways for Residential Energy Hubs: Sizing, planning and operating thermal energy storage

arXiv:2610.01489 · eess.SY, cs.SY, math.OC · Submitted 2026-10-01 · Read on arXiv

Listen

Transcript

Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "Building Seasonal Highways for Residential Energy Hubs".

Dev: Building seasonal highways for residential energy hubs addresses the challenge of managing energy storage differences in time-constants and efficiencies across electricity, heat,

Rosa: First, who's behind it and why it matters.

Title and authors: Rosa: Building Seasonal Highways for Residential Energy Hubs: Sizing, planning and operating thermal energy storage presents a framework designed to steer the short-term daily control toward long-term seasonal optimality by using dynamic terminal sets and value functions within a seasonally aware nonlinear economic model predictive controller.

Dev: The core idea is that because optimization horizons shrink in daily operations, the value of those short-term decisions drops due to lower round-trip efficiencies, so they need this method to avoid early depletion.

Taro: So, if the system is only looking at twenty-four hours ahead but the real constraint is a whole season, this framework acts like a GPS that keeps pointing toward the seasonal destination instead of just following the nearest immediate road.

Rosa: Right, and they also show how to optimally size thermal storage and avoid needing yearly simulations by linking those seasonal and daily optimizations through these dynamic components.

Dev: They specifically link those two layers through the terminal set and value function concepts so you don't have to run massive yearly simulations just for the day-to-day control loop.

Taro: That’s smart because running yearly simulations is computationally intensive, and linking it dynamically should make the operational part much more practical for real-time use.

Rosa: They then detail how they learn these dynamic terminal sets by solving their planning model for various rolling horizons, defining the terminal set as the ninety-five percent confidence interval of the resulting thermal energy storage capacity estimate.

Dev: And they learn the value function by repeating seasonal optimizations with different initial conditions and noise realizations to see which operational paths attract more value within those bounds.

Taro: That learning process sounds complex, but if it successfully captures the dynamics of how storage responds to temperature and price changes, it should provide a very robust steering mechanism.

Rosa: The operational layer itself uses an economic MPC with a twenty-four-hour horizon that incorporates physics-based models for battery ageing and nonlinear coefficient-of-performance for the heat pump.

Dev: They tested the SAGeMPC controller, and it performed quite well, achieving the second best mean grid cost of any eMPC at -€two hundred nine while keeping battery degradation control better than linear versions.

Taro: That means they managed to incorporate those complex physical realities—the aging and the heat pump efficiency—and still get a solid economic result without sacrificing longevity.

Rosa: In short, the paper introduces a way to use data-driven terminal sets and value functions to steer operational MPC towards seasonal goals, which leads to better performance across cost, degradation, and comfort metrics.

The paper's summary: Dev: One of the main improvements they propose is moving away from standard hierarchical architectures by favoring an economic MPC over a tracking MPC when dealing with high volatility in the daily energy usage.

Rosa: That’s interesting because tracking controllers usually focus on following a specific trajectory, whereas this framework seems better suited for systems where things are constantly changing, like residential energy hubs.

Taro: If the system is volatile, a tracker might chase noise and get stuck; favoring an economic approach suggests they are prioritizing cost-effectiveness over perfect adherence to some arbitrary path.

Dev: They also improve the operational layer by incorporating detailed non-linear models for BESS physics-based battery ageing and nonlinear coefficient-of-performance for the Heat Pump directly into the MPC.

Rosa: That’s crucial because standard controllers often use simpler approximations, but these physical models allow the controller to make decisions that are more realistic about how long a battery will last or how much heat it can actually produce.

Taro: When you factor in those detailed physical constraints, like cell ageing current effects, the operational layer has a much clearer picture of what is physically possible versus what is just mathematically convenient.

Dev: They aim to design the SAGeMPC controller specifically to optimize for minimizing mean grid cost while simultaneously controlling battery degradation and maintaining thermal comfort without excessive penalty costs.

Rosa: So, the key improvement there isn't just about one thing; it’s about designing a single controller that has multiple objectives working together rather than separate controllers for each objective.

Taro: That integrated optimization is what makes it powerful; you get coordination between cost and comfort, which is something tracking MPC often struggles with when those two things conflict.

Dev: They also show how to steer the system toward seasonal optimality by using the learned terminal set and value function as a real-time decision guide for the daily control layer.

Rosa: So it’s not just a static plan; it's a continuous process where long-term goals influence what happens in the next few hours, which sounds like a significant operational advancement.

The paper's improvements: Dev: To wrap up, the paper on "Building Seasonal Highways for Residential Energy Hubs: Sizing, planning and operating thermal energy storage" shows that combining dynamic terminal sets and value functions within a seasonally aware nonlinear economic model predictive controller is effective at steering short-term control toward seasonal goals.

Rosa: And the key results they highlight are the SAGeMPC achieving the second best mean grid cost of -€two hundred nine which beats linear alternatives in terms of battery degradation control and thermal comfort.

Taro: From my side, I think this work is important because it shows that you can effectively coordinate different energy carriers—electricity, heat, mobility—into a single optimized system without needing impossibly long planning horizons for every single component.

Dev: The authors also address the sizing aspect by showing how to determine the optimal TESS capacity is around seven hundred kWh under specific financial parameters, leading to a planning horizon of about one hundred eighty days.

Rosa: It’s clear that this framework provides a concrete solution for managing residential energy hubs by linking long-term planning and short-term operations in a way that feels practical for current deployment.

Taro: I think the implication is that we can start thinking about these interconnected systems as holistic entities rather than just separate pieces, which opens up new avenues for how we design smart energy infrastructure across different domains.

Conclusion: Rosa: So, to wrap up, this paper on "Building Seasonal Highways for Residential Energy Hubs: Sizing, planning and operating thermal energy storage" demonstrates how using dynamic terminal sets and value functions in a seasonally aware nonlinear economic model predictive controller can steer short-term daily control toward long-term seasonal optimality.

Dev: Exactly, it shows that by incorporating physics-based models for battery ageing and heat pump performance directly into the operational layer, they can achieve better performance across cost, degradation, and comfort metrics than linear counterparts.

Taro: The implications here are pretty big because it tackles the coordination challenge between different time scales—the daily operations versus the seasonal demands—in a way that actually works in a real setting.

Rosa: I think what really stands out is how they link the seasonal and daily optimizations through those dynamic components, like the terminal set and value function, which avoids needing massive yearly simulations just for day-to-day control.

Dev: From an engineering standpoint, I'm really interested in how they handle that loop rate; if the dynamic sets are learned offline as confidence intervals of TTESS estimates, we need to be sure that the real-time application doesn't introduce latency issues during those state transitions.

Taro: If the world misbehaves and demand shifts unexpectedly, I wonder how robust this approach is when those initial conditions for learning the value function are significantly off from reality; does it still steer well?

Rosa: The authors suggest that they can extend this framework to include EV charging and bidirectional flexibility, which opens up a whole new area for energy management.

Dev: That would definitely put more pressure on the optimization horizon, so we'd need to check how the control loop rate holds up when integrating those slower, long-duration assets like EVs into the fast twenty-four-hour MPC.

Taro: It’s exciting because it suggests that energy hubs can become much more resilient and self-optimizing over a yearly cycle, which is something we need to consider when thinking about decentralized energy networks.

Rosa: That’s the core of it; the ability for these systems to proactively manage their own lifespan while balancing immediate cost and comfort is really what makes this research significant.

Dev: It's a solid piece of work showing how complex nonlinear dynamics can be handled economically, provided you have a way to effectively learn those value functions from varied initial conditions.

Taro: So, the idea that the operational MPC is steered by learned long-term knowledge rather than just immediate forecasts is what makes this paper so compelling for autonomy researchers.

Rosa: It’s certainly a lot to think about; we need to see how this translates when we move these concepts from a residential setting to larger, more complex industrial hubs.

Dev: Well, I think the next step would be seeing some real-world field data on how quickly that learning process converges under highly volatile conditions.

Taro: That convergence study is where the real test is, showing how fast this seasonal highway can actually adapt when things get chaotic.

Dar´ıo Slaifstein, Mohammad Khosravi, Gautham Ram Chandra Mouli, Laura Ramirez-Elizondo, Pavol Bauer

Delft University of Technology

eess.SY, cs.SY, math.OC

Submitted: 2026-10-01

Updated: 2026-10-01

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

Importance score: 81/100

The gist: Building seasonal highways for residential energy hubs addresses the challenge of managing energy storage differences in time-constants and efficiencies across electricity, heat, and mobility

Key concepts

Dynamic Terminal Sets (S_p^t): This concept learns a set of future storage capacity bounds based on 95% confidence intervals derived from various planning horizons. It acts as a guide for short-term daily control, ensuring that immediate decisions do not lead to early depletion by respecting the long-term seasonal constraints.
Value Function (V_p^t(·)): The value function identifies which operational states or 'lanes' within the terminal set offer the highest future value. It helps guide the daily control layer by indicating which paths are most beneficial for achieving the overall long-term seasonal objective.
Seasonal-Aware Nonlinear MPC (eMPC): This is a controller that optimizes immediate daily actions while being informed by long-term seasonal requirements. It incorporates non-linear models for battery aging and heat pump efficiency, balancing short-term economic costs with the need to maintain seasonal energy balance.
Mean Grid Cost (E[C]): This is the primary metric minimized by the framework, representing the expected total monetary cost over time. It includes costs from electricity purchases, battery capacity fade due to use, and penalties for thermal discomfort.

Terminology

Steering — 9× in this paper · explained in 2 episodes
Benchmark — 8× in this paper · explained in 2 episodes
Core — 5× in this paper · explained in 2 episodes
Model Predictive Control — 4× in this paper
Energy Efficiency — 2× in this paper · explained in 3 episodes
Objective Function — 2× in this paper · explained in 2 episodes
ARK — 1× in this paper · explained in 1 episode
Abstraction — 1× in this paper · explained in 1 episode
Curse of Dimensionality — 1× in this paper · explained in 6 episodes
Explainability — 1× in this paper · explained in 3 episodes
Model Predictive Control (MPC) — 1× in this paper · explained in 5 episodes
PID Controller — 1× in this paper · explained in 2 episodes
Physical Constraints — 1× in this paper · explained in 7 episodes
Reinforcement Learning — 1× in this paper · explained in 4 episodes
Robustness — 1× in this paper · explained in 5 episodes
Sparsity — 1× in this paper · explained in 4 episodes
Unified Framework — 1× in this paper · explained in 5 episodes

Summary

Building seasonal highways for residential energy hubs addresses the challenge of managing energy storage differences in time-constants and efficiencies across electricity, heat, and mobility carriers by proposing a data-driven framework to steer short-term daily control towards long-term seasonal optimality. The core finding is that a seasonally-aware nonlinear economic model predictive controller (eMPC) achieves the most balanced performance, offering the second best mean grid cost of all MPCs at -€209 while maintaining better battery degradation control than linear counterparts and achieving the best thermal comfort among nonlinear benchmarks.

The Proposed Methodology

The framework links seasonal and daily optimizations through dynamic terminal sets and value functions. This approach is designed to avoid early depletion during operation by steering the short-term daily control towards long-term optimality, addressing the issue where optimization horizons shrink, reducing supplied value due to lower round-trip efficiencies. The methodology also presents how to optimally size thermal storage and avoids yearly simulations by linking seasonal and daily optimizations through these dynamic components.

Thermal Sizing & Planning Framework

The primary goal is to minimize the mean monetary stage cost, i.e. E[C], over the exogenous random process W ∈ DW. This involves choosing an optimal size x∗a and power dispatch pa,t by minimizing a cost function C which comprises the net grid cost (Cgrid), battery capacity fade cost (Closs), and a thermal comfort penalty (pT). The general stochastic sizing problem is formulated to find the optimal TESS capacity QTESS and minimum planning horizon Hp needed beyond seasonal storage, including weekly and monthly sizes.

Learning Terminal Set & Value Function

To learn the dynamic terminal set S p t, the planning model (Eq. 6) is solved for scenarios as many rolling horizons Hp as necessary, and the terminal set is defined as the 95% confidence interval of the resulting TTESS,i,t. To learn the planning value function V p t(·), each seasonal optimization of horizon Hp is repeated with different initial conditions T0 and Ns realizations for each. The concept is that the terminal set S p t bounds the trajectories of TTESS,t as time passes, guiding the shortsighted daily operational layer, while the value function V p t(·) indicates which lanes attract more value within those bounds.

Short-term Operation and Performance

The operational layer is an economic MPC with an optimization horizon Hd = 24hs, incorporating detailed non-linear models for BESS physics-based battery ageing and nonlinear coefficient-of-performance for the Heat Pump. The most balanced controller tested is the SAGeMPC, which achieves the second best mean grid cost of any eMPC (E[Cgrid] = −€209), better capacity fade Qloss than all linear versions, the best nonlinear thermal comfort pT and a mean computational time on par with the linear eMPCs. The framework successfully steers the system towards seasonal optimality by combining the dynamic terminal set S p t and value function V p t(·).

Key Results Summary

The optimal TESS capacity Q∗ TESS is determined by balancing fixed costs and operational costs, leading to an optimal capacity of approximately 700 kWh for the case study under specific financial parameters. The resulting planning horizon Hp ≈ 180 days is derived from the slowest natural time-constant of the TESS response to ambient temperature and price disturbances. The combination of S p t and V p t(·) effectively steers the nonlinear eMPC towards seasonal optimality, demonstrating that neither component alone is sufficient. The SAGeMPC represents the most balanced performance among tested controllers.

Discussion and Future Work

The framework improves upon standard hierarchical architectures by being flexible under high volatility DW, favoring economic MPC over tracking MPC. Future work includes extending the framework to include EV charging and bidirectional (V2G) flexibility, investigating on-line updating of seasonal components during operation to relax dependency on offline planning, and characterizing how the storage-size ratio governs the convergence of Hp towards Hy. The trade-off between degradation control and seasonal coordination is evident: enforcing long-term thermal steering leads to a modest increase in capacity loss (3.29Ah) relative to unconstrained non-linear MPC (2.95Ah). The cost difference between the yearly optimal control and the eMPC is attributed to the mismatch between horizons Hd and Hy.

The Gist

The data-driven seasonal highway steers short-term daily control towards long-term optimality by combining a dynamic terminal set S p t and value function V p t(·) within a seasonally-aware nonlinear economic model predictive controller, resulting in the most balanced performance among tested controllers.

**Table 1: Objective function components summary µ ± σ.

Improvements for AI systems

Here are specific improvements for AI systems based on the presented research, along with what those improved systems can achieve:

Incorporate a Seasonal Highway framework into existing Model Predictive Control (MPC) architectures for energy management systems (EMS).
Develop a data-driven methodology to dynamically determine the optimal sizing of thermal energy storage (TESS capacity, QTESS) and the necessary planning horizon (Hp) required to capture seasonal patterns.
Implement a dual terminal set strategy within operational MPC:

A. A dynamic terminal set (Spt), learned offline from long-term stochastic planning simulations, which constrains the TESS state trajectories based on forecasted exogenous processes (temperature, price).

B. A dynamic value function (Vpt), also learned offline, which provides economic guidance within the constraints of Spt.

Integrate physics-based nonlinear models directly into operational MPC controllers to account for:

A. Physics-based battery degradation (e.g., cell ageing current, State of Charge effects).

B. Nonlinear Heat Pump Coefficient of Performance (COP) variations based on inlet/outlet temperatures and ambient conditions.

Design a Seasonally and Ageing Aware Nonlinear MPC (SAGeMPC) controller that simultaneously optimizes for:

A. Minimizing mean grid cost (Cgrid).

B. Controlling battery degradation (Qloss).

C. Maintaining building thermal comfort without excessive penalty costs.

Enable the AI system to perform real-time trade-off analysis between long-term seasonal coordination and short-term operational needs by using the learned terminal set (Spt) and value function (Vpt) as a decision guide in real time, effectively steering the short-sighted daily control towards seasonal optimality.

This improved AI system can achieve:

Optimize residential energy hub operation to minimize mean grid costs by proactively scheduling energy flow across multiple carriers (electricity, heat, mobility).
Significantly extend the operational lifetime of battery energy storage systems (BESS) by actively managing degradation through physics-aware modeling, achieving a 26-34% reduction in capacity loss compared to linear benchmarks.
Guarantee optimal thermal comfort within specified bounds during daily operation by dynamically adjusting TESS charging/discharging based on seasonal temperature forecasts and price signals.
Provide robust, long-term planning capabilities by reducing the computational burden of yearly stochastic optimizations through a data-driven sizing policy (QTESS) and an optimized planning horizon (Hp).
Achieve highly balanced performance across cost, degradation, and comfort metrics, representing the best available solution among tested MPC frameworks.

Abstract

The operation of residential energy hubs with multiple energy carriers (electricity, heat, mobility) poses a significant challenge due to the energy storage differences in time-constants, round-trip efficiencies and self-discharge rates. Usually, thermal storage exhibits flexibility in yearly planning optimizations or long-term scenarios. However, as optimization horizons shrink (1-48hs) so does their supplied value due to the lower round-trip efficiencies. To avoid this early depletion during operation this paper proposes a data-driven highway to steer the short-term daily control towards long-term optimality. The proposed methodology also presents how to optimally size the thermal storage and avoid yearly simulations and how all of this is related to nonlinearities in the daily operation. The presented framework links seasonal and daily optimizations through dynamic terminal sets and value functions. The seasonally-aware nonlinear economic model predictive controller achieves the most balanced performance, with the second best mean grid cost of all MPCs at - 209. It also achieves better battery degradation control than its linear counterparts (between 26-34%) and the best thermal comfort of the nonlinear benchmarks. Nevertheless, the data-driven seasonal highway restrains the ability to control battery degradation and slightly increases computational time.