Hidden Degradation Costs in Energy-Cost-Only HEMS Optimisation: Study on Battery and PV Sensitivity

Technical Summary: Hidden Degradation Costs in Energy-Cost-Only HEMS Optimisation

Problem Statement
Residential Home Energy Management Systems (HEMS) increasingly utilize Model Predictive Control (MPC) to optimize battery energy storage systems (BESS) and photovoltaic (PV) generation under volatile Time-of-Use (TOU) tariffs, such as the UK's Octopus Agile. Current optimisation strategies typically formulate the objective function to minimize net energy costs subject to physical constraints. However, these formulations rarely embed battery degradation as an economic cost within the objective. Consequently, controllers may adopt aggressive, high-cycle-count strategies to maximize arbitrage opportunities. This paper argues that such "energy-cost-only" optimisation systematically underestimates the true system cost by treating batteries as costless buffers, potentially leading to significant unquantified financial losses when deployed on physical systems.

Methodology
The study establishes a receding-horizon Mixed-Integer Linear Programming (MILP) baseline for a UK residential HEMS, solved using Gurobi 13.0. The system model includes PV generation, BESS, and grid connection, utilizing 15-minute resolution data derived from the REFIT dataset (House 5, Loughborough) and historical PVGIS irradiance data. The study period spans September 2019 to July 2021, aligned with Octopus Agile tariff data.

• Optimisation: The MILP minimizes net energy cost (import cost minus export revenue) over a 24-hour horizon. It enforces power balance, State of Charge (SOC) dynamics (bounded between 20% and 80%), inverter limits, and grid import/export exclusivity constraints.
• Sensitivity Study: A 3-by-3 sensitivity analysis was conducted across three battery capacities (5.0, 14.4, and 28.8 kWh) and three PV array areas (16, 28, and 40 m²).
• Degradation Estimation: Following simulation, degradation costs were estimated post-hoc. The study employed rainflow cycle counting to extract cycles from the SOC profile. A semi-empirical stress model (Naumann model) was used to calculate the fraction of battery life consumed per cycle based on Depth of Discharge (DoD) and average SOC. The total degradation cost was calculated by multiplying the consumed life fraction by the battery capacity and a replacement cost of £500/kWh.

Key Results
The sensitivity study reveals that while integrating PV and BESS reduces net energy costs across all configurations, the "true" system cost is significantly higher when degradation is accounted for:

• Hidden Cost Magnitude: In configurations where high PV generation or export revenue drives energy costs near zero, the degradation cost becomes the dominant expense. In the 14.4 kWh / 28 m² configuration, the energy cost was £13.72, while the hidden degradation cost was £125.36, representing 914% of the energy cost. In the 28.8 kWh / 16 m² scenario, degradation costs reached 1,060% of the energy cost.
• Battery Size Dependency: Contrary to the assumption that larger batteries degrade faster due to higher throughput, the study found that degradation costs remained approximately constant for a given battery size regardless of PV array size. This is because the MPC, lacking a degradation penalty, cycles the battery similarly to maximize immediate energy arbitrage.
• True System Viability: Three configurations (14.4 kWh/40 m², 28.8 kWh/28 m², and 28.8 kWh/40 m²) achieved a negative "True Cost" (net profit), indicating that export revenue was sufficient to offset both energy and degradation expenses. However, in other configurations, the naive energy-cost-only view suggested near grid-neutrality, while the true system cost was substantially higher.

Key Contributions

• Quantification of Hidden Costs: The paper provides empirical evidence quantifying the magnitude of degradation costs ignored by standard energy-cost-only MILP formulations in a UK residential context with real TOU data.
• Sensitivity Analysis: It demonstrates that degradation costs are primarily driven by battery size rather than PV configuration, and that aggressive cycling strategies can inflate total system costs by over 1,000% relative to energy savings.
• Methodological Framework: The study establishes a baseline MILP framework coupled with a post-hoc semi-empirical degradation estimation method to highlight the discrepancy between optimisation objectives and physical reality.

Significance and Claims
The authors claim that the "invisibility" of degradation costs within current MILP objectives directly motivates the transition toward degradation-aware control formulations. The results demonstrate that treating batteries as costless buffers is financially risky; standard HEMS controllers systematically underestimate true system costs.

The paper modestly notes limitations, including the assumption of perfect foresight over the 24-hour horizon (which does not hold in practice due to uncertainty in demand and irradiance) and the computational difficulty of introducing non-linear degradation penalties into linear solvers. The authors suggest that while formal co-optimisation of BESS and PV capacity requires further investigation, alternative approaches such as Reinforcement Learning (RL) may offer a pathway to navigate the complex, non-linear relationship between SOC, DoD, and cost without requiring perfect foresight or convex objectives.