Ageing-aware Energy Management for Residential Multi-Carrier Energy Systems

1. Problem Statement

The decarbonization of the energy sector requires the integration of multiple energy carriers (electricity, heat, and mobility) within residential buildings. While Energy Management Systems (EMS) are essential for optimizing these Multi-Carrier Energy Systems (MCES), current approaches face significant limitations:

• Inaccurate Battery Modeling: Most EMS rely on empirical ageing models (e.g., Coulomb counting with fitted degradation curves). These models are chemistry-specific, prone to overfitting, lack extrapolation capabilities, and fail to capture complex dynamic profiles (like Electric Vehicle usage).
• Over-simplification: Existing models often linearize battery dynamics or ignore the distinction between different battery chemistries (e.g., NMC vs. LFP) and ageing states (new vs. aged).
• Short-sighted Optimization: Traditional controllers prioritize immediate grid cost reduction (energy arbitrage) without accounting for the long-term degradation costs of storage assets, leading to accelerated battery failure.
• Lack of Thermal Coupling: Many studies treat thermal and electrical systems separately or use simplified linear models for thermal storage, missing synergies in a multi-carrier context.

2. Methodology

The authors propose an Ageing-aware Nonlinear Economic Model Predictive Controller (eMPC) that integrates Physics-Based Reduced-Order Models (PBROM) directly into the EMS optimization loop.

A. System Architecture

The system manages a residential MCES comprising:

• Electrical: Solar PV (SPV), Battery Energy Storage System (BESS), Electric Vehicle (EV), and Grid connection.
• Thermal: Heat Pump (HP), Solar Thermal (ST), and Thermal Energy Storage System (TESS).
• Control Structure: A two-layer architecture:
  1. Day-Ahead (DA) Planner: Generates a 24-hour schedule based on forecasts.
  2. MPC Layer: Executes real-time control (15-min intervals) to correct for forecast errors and disturbances.

B. Core Modeling Innovations

1. Physics-Based Degradation (PBROM):
   • Instead of empirical fits, the controller uses a PBROM (based on Jin et al.) that explicitly models degradation mechanisms: Solid Electrolyte Interphase (SEI) layer growth and Active Material (AM) loss.
   • The model distinguishes between capacity fade (loss of $Q$) and power fade (increase in internal resistance $R_0$).
   • It accounts for specific cathode chemistries (NMC and LFP) by adjusting physical parameters (e.g., electrolyte properties, activation energies) rather than re-fitting equations.
2. Multi-Carrier Terminal Sets:
   • To handle the different dynamics of storage, the authors designed distinct terminal constraints:
     • BESS: Flexible daily periodicity (SoC at start of day = SoC at end of day) to allow arbitrage without forcing a fixed state.
     • EV: Soft-tracking penalty to ensure the required State of Charge (SoC) at departure time.
     • TESS: No terminal constraint, allowing it to operate on its natural thermal time constant.
3. Objective Function:
   The controller minimizes a weighted sum of:
   • Grid Cost ($C_{grid}$): Electricity purchase/sale costs.
   • Degradation Cost ($C_{loss}$): Calculated based on the physics-based capacity fade current ($i_{loss}$).
   • Penalties: For unmet EV departure SoC and TESS overcharging.

C. Simulation Framework

• High-Fidelity Simulator: The control policy is tested against a high-fidelity simulator using LiiBRA.jl (for PBROM performance) and PyBaMM datasets.
• Closed-Loop: The simulator provides "plant measurements" (actual SoC, voltage, degradation) back to the planner, correcting for model-plant mismatch.

3. Key Contributions

1. Integration of PBROM into Residential EMS: This is one of the first works to successfully integrate complex, non-convex physics-based battery ageing models into a residential multi-carrier MPC framework, moving beyond standalone battery applications.
2. Chemistry-Aware Dispatch: The algorithm can distinguish between NMC and LFP chemistries within the same optimization framework, dynamically adjusting dispatch strategies based on the specific degradation physics of the installed battery.
3. Aging-State Adaptability: The controller effectively manages both fresh and aged batteries (e.g., 90% State of Health). It adapts to the shift in dominant degradation mechanisms (from calendar ageing in new cells to cyclic ageing in older cells).
4. Novel Terminal Conditions: The introduction of flexible terminal sets for BESS, EV, and TESS allows the non-convex optimization problem to converge to feasible, locally optimal solutions while respecting the unique operational constraints of each asset.

4. Results

The study was validated through three case studies using real-world data (TU Delft Green Village) over summer and winter periods.

Case Study I: Degradation Model Comparison

• Comparison: Proposed CPBDeg (Physics-based) vs. CEmpDeg (Empirical) vs. BNoDeg (No degradation).
• Findings:
  • CPBDeg achieved a 10% reduction in grid cost and a 20% reduction in capacity fade compared to benchmarks in summer.
  • It demonstrated the lowest degradation per equivalent full cycle ($\partial Q_{loss} / \partial FEC$), proving it optimizes the trade-off between cycling and longevity better than empirical models.
  • Computational time remained low (1–5 seconds), proving feasibility for real-time application.

Case Study II: Cathode Chemistry (NMC vs. LFP)

• Findings:
  • The controller successfully adapted to LFP chemistry, resulting in 10% lower grid costs and 20% lower degradation compared to NMC in summer.
  • LFP cells allowed for deeper discharges and more frequent V2G (Vehicle-to-Grid) usage due to their lower sensitivity to SEI growth, which the PBROM correctly identified.
  • This highlights that the EMS can exploit the inherent physical advantages of specific chemistries without manual re-tuning.

Case Study III: Aged vs. Fresh Batteries

• Findings:
  • When managing an aged battery (90% SoH), the CPBDeg controller improved performance by 6% in grid cost and reduced degradation by 30–45% compared to a linear benchmark (BNoDeg).
  • The linear benchmark failed to adapt, treating the aged battery as new, leading to excessive cycling and higher costs.
  • The PBROM correctly identified that as batteries age, cyclic degradation (AM loss) becomes dominant over calendar degradation, allowing the controller to optimize accordingly.

5. Significance and Implications

• Total Cost of Ownership (TCO): By shifting from "bill minimization" to "lifecycle optimization," the proposed system extends battery lifespan, significantly improving the Net Present Value (NPV) of residential energy systems.
• Technology Agnosticism: The framework allows users to switch battery chemistries (e.g., from NMC to LFP) or use aged batteries without redesigning the control algorithm, as the physics-based model adapts automatically.
• Scalability: The computational efficiency (solved in seconds) suggests this approach is viable for real-time residential controllers and can be scaled to commercial or industrial microgrids.
• Future Direction: The paper establishes a benchmark for "Ageing-aware" control, suggesting that future residential EMS must move beyond empirical look-up tables to physics-based state estimation to fully realize the potential of electrified, multi-carrier homes.