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

The use of residential photovoltaics has increased dramatically in recent years. With battery systems becoming more affordable, the optimal operation of a photovoltaic-battery system can bring significant savings to households. Optimal control requires correct forecasts of underlying parameters, such as photovoltaic power generation, to schedule the battery. While forecasting models have become increasingly accurate due to algorithmic advances and data availability, accuracy is typically measured in generic metrics which might not align with the downstream application. This study proposes a decision-focused learning framework that integrates optimization and prediction by training a Long Short-Term Memory photovoltaic energy forecaster on the downstream optimal scheduling of a battery system. The proposed methodology is compared against a standard two-phase approach. Across a 14-month evaluation period, the decision-focused method reduced average electricity costs across twenty buildings by 3.6% when normalized against performance bounds defined by a perfect forecast and a baseline of no optimization. Critically, this financial improvement was achieved despite the model exhibiting a root mean squared error of 19.9%, significantly higher than the decoupled model's 8.2%. Warm-starting the decision-focused model further improves results, lowering average cost by approximately 8%, while also mitigating the negative impact on statistical accuracy (root mean squared error of 13.7%). The findings are statistically significant at the 0.001 level across the twenty households and for each household individually. These results demonstrate that aligning forecast models with optimization goals is key for achieving cost advantages in PV-battery systems. Future research should replicate these findings on other datasets, alternate forecasting models and alternate optimization algorithms.

This paper compares rule-based and learning-based pricing mechanisms for peer-to-peer (P2P) electricity trading in residential photovoltaic communities. The rule-based benchmarks comprise bill-sharing as an ex post allocation mechanism, the mid-market rate, and supply-demand-ratio pricing. The reinforcement-learning (RL) formulation is implemented through a Deep Q-Network and evaluated under multiplier-based and learnable SDR-shaped pricing, with a fixed-parameter SDR variant as a non-learning control. Performance is assessed through community savings together with complementary financial and operational indicators. In the base PV-only configuration, the rule-based benchmarks outperform the best RL policy. With battery energy storage, evaluated for the RL policies only, community savings under the best RL policy increase from EUR 734.23 to EUR 978.52. Across the learning-based modes and in both configurations, SDR-shaped pricing outperforms the multiplier-based parameterization considered. The results indicate that rule-based pricing remains highly competitive wherever the two families are compared directly, and that storage substantially improves the learning-based outcomes under this accounting, while the distribution of benefits remains heterogeneous across households.

This paper extends Mixed-Integer Differentiable Predictive Control (MI-DPC) to multi-modal discrete decisions and nonconvex polynomial dynamics arising in Underground Pumped Hydro Energy Storage Systems (UPHES). A neural policy mapping problem parameters to continuous setpoints and integer mode selections via a Gumbel-Softmax layer is trained in a self-supervised manner by differentiating the expectation of the finite horizon control objective through the nonlinear dynamics model. Three methodological contributions enable this extension: a parallel differentiable simulator that preserves gradient magnitude, a Transformer encoder that captures long-range temporal dependencies, and a Gumbel-Softmax temperature annealing schedule that regularizes the combinatorial search. We demonstrate the framework on day-ahead scheduling of a UPHES, a large-scale mixed-integer optimal control problem with nonlinear unit performance curves and volume-head coupling. MI-DPC achieves only 1.6% suboptimality relative to a piecewise mixed-integer quadratic programming baseline, while providing five orders of magnitude speedup in online scheduling time.