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

Dario Slaifstein, Mohammad Khosravi, Gautham Ram Chandra Mouli, Laura Ramirez-Elizondo, Pavol Bauer

arXiv:2610.01489v1eess.SYcs.SYmath.OC

TL;DR

Residential energy hubs must coordinate thermal and electrical storage despite TESS's large size and lower round-trip efficiency. The paper links seasonal planning to daily nonlinear eMPC with dynamic terminal sets and value functions, and reports balanced benchmark performance alongside a battery-degradation trade-off from seasonal steering.

  • Problem

    Sizing and coordinating TESS with electrical storage is challenging because TESS is large and has lower round-trip efficiency, while the amount of thermal storage needed for seasonal variation remains a key question.

    Source: §1 · p. 4

  • Method

    The framework sizes thermal storage and its planning horizon, then links seasonal planning to daily nonlinear eMPC through dynamic terminal sets and value functions.

    Source: §1 · p. 6, §2.5 · p. 14, §5 · pp. 24–25

  • Results

    SAGeMPC offers the most balanced performance, including the second best mean grid cost E[Cgrid] = −€209 and lower mean battery degradation than all linear alternatives.

    Source: §5 · p. 25

  • Takeaways & Limitations

    The case study's optimal TESS capacity of approximately 700 kWh and planning horizon of approximately 180 days avoid intractable yearly stochastic optimizations.

    Source: §5 · p. 24

    Seasonal steering increases capacity loss by 0.34 Ah relative to unconstrained nonlinear MPC because transition-season heat-pump operation raises BESS discharge rates.

    Source: §4 · p. 24

Abstract

from arXiv · show

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 -\texteuro 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.

Highlights

The highlights present a data-driven seasonal highway that steers short-term nonlinear eMPC toward seasonal optimality. The seasonally and ageing-aware controller balances grid cost, battery degradation, and thermal comfort, with a trade-off in battery-degradation control and computation time.

Highlights

  • A data-driven dynamic terminal set and value function steer short-sighted nonlinear eMPC toward seasonal optimality.Source: Highlights · p. 2
  • The seasonally and ageing-aware nonlinear eMPC delivers the most balanced benchmark performance, with approximately 7.4 seconds per optimization.The highlights also report better battery-degradation control than linear alternatives and maintained building thermal comfort.Source: Highlights · p. 2
  • Seasonal thermal steering restrains battery-degradation control and slightly increases computational time.Source: Highlights · p. 2

1. Introduction

Residential energy hubs must coordinate thermal and electrical storage despite their differing operational characteristics, while sizing and storage-service questions remain central. The paper motivates an applied framework for sizing and coordinating these assets, including broader planning horizons and nonlinear operation.

1. Introduction

  • TESS is challenging to operate alongside electrical storage because it is large and has lower round-trip efficiency than BESS.Source: §1 · p. 4
  • Key sizing questions include how much thermal storage seasonal variation needs and how active TESS relates to passive building inertia.Source: §1 · p. 4
  • Traditional hierarchical planning passes long-term patterns to daily control, but economic MPC offers greater flexibility under high short-term volatility.Source: §1 · pp. 4–5
  • Prior coordination approaches face dimensionality or nonlinearity limits, while seasonal-learning studies leave the relationship between storage size and planning horizon unresolved.The cited discussion also frames existing practice as either rigid seasonal-reference tracking, simplified linear dynamics, or seasonal-only thermal-storage sizing.Source: §1 · pp. 5–6
  • The paper proposes a framework to size and coordinate electro-thermal storage with different time-flexibilities for residential energy hubs.Source: §1 · p. 6
  • The sizing methodology determines thermal-storage capacity and planning horizon for seasonal, weekly, and monthly storage needs.Source: §1 · p. 6
  • The proposed operational layer includes soft-constraint objectives and nonlinear continuous dynamics while excluding mixed-integer constraints.Source: §1 · p. 6

2. Thermal-sizing & planning framework

The framework sizes thermal storage, learns seasonal terminal sets and value functions, and adds them to daily economic MPC. These data-driven constraints steer short-horizon operation toward long-term patterns, addressing the risk that short horizons deplete and leave long-term storage unused.

2. Thermal-sizing & planning framework

  • The framework extends seasonal MPC with storage sizing, stochastic planning, soft constraints, and nonlinear daily control using battery ageing and heat-pump performance models.The learned terminal set and value function are added to daily eMPC as a seasonal highway for real-time power-flow decisions.Source: §2 · p. 9

2.1. Dynamic behavior & Operational constraints

  • The hub’s decision variables are asset power flows and states, while electrical and thermal balances link demands, generation, and storage through the heat pump.Exogenous inputs include prices, irradiance, load, ambient temperature, and occupancy.Source: §2.1 · pp. 9–10

2.2. Uncertainty characterization

  • Seasonal prices, ambient temperature, and irradiance use year-long hourly histograms, while load, EV availability, and occupancy use daily 15-minute histograms.Historical inputs include Netherlands day-ahead prices from 2020–2024, KNMI temperature and irradiance from 2005–2023, and confidence bounds shown at 50%, 75%, and 95%.Source: §2.2 · p. 11, Figure 4 · p. 11

2.3. Long-term storage sizing

  • Larger TESS capacities reduce grid cost, but linearly increasing investment creates a trade-off that determines the selected size.Yearly sizing optimizations compare candidate capacities under a mean exogenous scenario.Source: §2.3 · p. 12

2.4. Thermal Planning layer

  • The shorter planning horizon Hp < Hy reduces computational load; stochastic planning learns a dynamic terminal set from the 95% confidence interval of TESS temperatures and a value function.The sizing and horizon choices are used to avoid time-consuming yearly planning optimizations.Source: §2.4 · p. 13

2.5. Operational layer

  • Daily operation uses a 24-hour economic MPC with detailed nonlinear models for all carriers and storage, including physics-based battery ageing and nonlinear heat-pump coefficient of performance.Source: §2.5 · p. 14

3. Case Study & Results

The case study sizes thermal storage and links seasonal planning to daily control with dynamic terminal sets and value functions. It compares linear and nonlinear controllers on grid cost, battery degradation, thermal comfort, and computation.

3.1. Sizing Thermal Storage

  • Larger TESS sizes filter higher-frequency disturbances; ambient temperature and energy-price disturbances show common peaks at 8, 12, 24, and 36 hours.The TESS charges early in the year, discharges during winter, and recharges through spring and summer toward fall.Source: §3.1 · pp. 15–16, Figure 6 · p. 16
  • At an interest rate ir = 6% and unit cost cTESS = 200€/kWh, the optimal TESS capacity is approximately 700 kWh, with a corresponding slowest natural time constant τk = 60.83 days.Larger TESS sizes monotonically decrease grid cost, while investment increases linearly with size, creating a tradeoff.Source: §3.1 · pp. 15–16

3.2. Learning terminal set & value function

  • The dynamic terminal set bounds TESS temperatures using the 95% confidence interval of seasonal trajectories, while the value function ranks states within that operating envelope.The value function favors discharging in the first two horizons and maintaining a high TESS temperature during spring and summer.Source: §3.2 · p. 17

3.3. Short-term Operation

  • E[Cgrid] = −€209 and E[Qloss] = 3.29Ah for SAGeMPC, which has the second-lowest mean grid cost among MPCs and the second-best mean battery degradation.It also has acceptable thermal comfort and a mean computational time of 7.4s.Source: Figure 8 · p. 20, §3.3 · pp. 20, 22
  • Nonlinear controllers consistently achieve lower grid cost than linear controllers, while linear controllers provide better thermal comfort; the yearly optimum performs best on its optimized metrics but excludes battery degradation.The comparison evaluates the electro-thermal interaction of BESS, TESS, and the heat pump, leaving EV mobility out of the main benchmark.Source: §3 · pp. 14–15, §3.3 · p. 20
  • Seasonal terminal sets prevent myopic controllers from rapidly depleting TESS, while the value function alone does not reliably steer daily operation toward seasonal optimality.Using seasonal steering trades off battery-degradation control; the learned seasonal policies mainly minimize grid cost and are unaware of battery ageing.Source: §3.3 · p. 21

4. Discussion

The discussion weighs seasonal steering against daily flexibility and battery degradation, and identifies where the framework’s offline planning and terminal components may be constrained. It also relates the cost gap between daily and yearly optimization to their horizon mismatch.

4. Discussion

  • High short-term volatility and scarce long-term scenario data motivate flexible daily economic MPC and careful choice of terminal components.Source: §4 · p. 23
  • The terminal value function guides TESS only within its terminal set and provides no useful information outside it.It was learned on planning scenarios with Hp > Hd, where TESS temperature lies within the set.Source: §4 · p. 23
  • The seasonal value function is only a linear regressor, and the discussion calls for exploring other regressor classes, including deep learning and MILP.Source: §4 · p. 23
  • The framework’s explainability helps interpret storage operating on different timescales, and its dynamic models can be linear or nonlinear.Source: §4 · p. 23
  • Because seasonal components are precomputed from historical scenarios, severe climate anomalies or structural price events could shift viable operating boundaries.A low-frequency sliding-window re-synthesis is proposed to update bounds and value functions while retaining short-horizon online control.Source: §4 · p. 23
  • The reported result is a 26-34% reduction in BESS capacity loss compared to linear MPC formulations.Source: §4 · p. 24
  • 3.29Ah versus 2.95Ah: long-term thermal steering raises capacity loss relative to unconstrained nonlinear MPC as transition-season heat-pump use drives higher BESS peak discharge.The authors describe the 0.34Ah penalty as a trade-off for avoiding seasonal depletion and maintaining long-term thermal self-sufficiency.Source: §4 · p. 24
  • The cost gap between yearly and daily optimization is attributed to their horizon mismatch; convergence with larger seasonal storage ratios is left out of scope.The authors note that the financial parameters are already optimistic, making even larger TESS sizes unrealistic.Source: §4 · p. 24

5. Conclusions & Future works

The paper presents a framework for sizing thermal storage and linking seasonal planning to daily economic control. Its nonlinear, ageing- and seasonally-aware controller balances cost, degradation, comfort, and computation, while future work targets additional flexibility and online updating.

5. Conclusions & Future works

  • Frequency response combined with financial information determines optimal TESS capacity and minimum planning horizon, avoiding yearly stochastic optimization at the planning stage.In the case study, Q*TESS was approximately 700kWh and Hp approximately 180 days, based on the slowest TESS response time-constant.Source: §5 · p. 24
  • The dynamic terminal set and value function link seasonal planning to daily eMPC, and neither component alone reliably steers the daily policy toward seasonal optimality.Source: §5 · p. 25
  • E[Cgrid] = −€209 (second best among eMPCs), E[Qloss] = 3.29Ah (below all linear alternatives), acceptable comfort, and ∆=7.4s make SAGeMPC the most balanced tested controller.Source: §5 · p. 25
  • Future work will add EV charging and V2G flexibility, examine online seasonal updates, and study how storage-size ratios affect planning-horizon convergence.Source: §5 · p. 25

Appendix A. Device Models

The appendix outlines device models used in the paper, covering electrical balance, building dynamics, heat pumps, thermal storage, and battery performance and degradation.

Appendix A. Device Models

  • The appendix identifies models for the electrical power balance and building dynamics.Source: Appendix A · pp. 25–26
  • The heat pump uses a nonlinear coefficient of performance in the eMPC model and a fixed COP of 3 in planning; TESS dynamics are modeled linearly.Source: Appendix A · p. 26
  • A complete model for battery performance and degradation is also presented.Source: Appendix A · pp. 26–27

Appendix B. Thermal Planning simulations

The appendix reports intermediate results from thermal planning simulations, including scenario trajectories for the building and TESS and value functions associated with planning horizons.

Appendix B. Thermal Planning simulations

  • The appendix presents intermediate results from the thermal planning simulations.Source: Appendix B · p. 27
  • TESS temperature trajectories across scenarios define the operating envelope in response to ambient-temperature scenarios.Source: Appendix B · p. 27
  • The resulting terminal value functions are presented for each planning horizon Hp.Source: Appendix B · p. 27
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