Surrogate model of a HVAC system for PV self-consumption maximisation

In the last few years, energy efficiency has become a challenge. Not only mitigating environmental impact but reducing energy waste can lead to financial advantages. Buildings play an important role in this: they are among the biggest consumers. So, finding manners to reduce energy consumption is a way to minimise energy waste, and a technique for that is creating Demand Response (DR) strategies. This paper proposes a novel way to decrease computational effort of simulating the behaviour of a building using surrogate models based on active learning. Before going straight to the problem of a building, which is complex and computationally costly, the paper proposes the approach of active learning to a smaller problem: with reduced simulations, regress the curve of voltage versus current of a thermo-resistor. Then, the paper implements a surrogate model of energy consumption of a building. The goal is to be able to learn the consumption pattern based on a limited number of simulations. The result given by the surrogate can be used to set the reference temperature, maximising the PV self-consumption, and reducing energy usage from the grid. Thanks to the surrogate, the total time spent to map all possible consumption scenarios is reduced around 7 times.

💡 Research Summary

The paper addresses the growing need for energy‑efficient operation of buildings equipped with photovoltaic (PV) generation by proposing a surrogate‑model‑based approach to accelerate HVAC energy‑consumption simulations and to enable real‑time demand‑response (DR) optimisation. The authors first introduce the concept of active learning as a means to iteratively enrich a training set with the most informative samples, thereby reducing the number of expensive physics‑based simulations required to build an accurate predictor.

A proof‑of‑concept experiment is carried out on a simple thermo‑resistor circuit. The relationship between input voltage and output current is non‑linear because the resistor’s equivalent value changes with temperature. Starting from only four random simulation points, a Bayesian regression (or Gaussian‑process‑like) surrogate is trained, its predictive variance is evaluated across the whole voltage range, and the point with the highest variance is added to the training set. This loop continues until the maximum standard deviation falls below a pre‑defined threshold (0.01). The experiment demonstrates that, out of 1,000 possible voltage points, merely 14 simulations are sufficient to reconstruct the curve with a mean absolute error below 2 %.

The second stage adds a second input – external temperature – creating a 2‑dimensional input space of 2,500 (voltage × temperature) combinations. Again, only ten initial simulations are performed, and the active‑learning loop selects additional points. After roughly 350–400 simulations the surrogate’s prediction error stabilises below 2 %, confirming that the method scales to higher‑dimensional problems while still requiring a fraction of the full simulation budget.

The core contribution is the application of this methodology to a full building model built in OpenModelica and accessed via the OMPython API. The building includes multiple rooms, an HVAC system, and rooftop PV panels. Input variables comprise outdoor temperature, room temperature set‑points, and time‑varying PV generation. The surrogate learns to map these inputs to the total HVAC electricity consumption.

With the surrogate in place, the authors formulate a multi‑objective optimisation problem: (1) maintain thermal comfort by keeping room temperatures within acceptable bounds, and (2) maximise self‑consumption of locally generated PV energy. An optimisation algorithm queries the surrogate to evaluate candidate set‑point schedules, selecting the one that best balances the two objectives. Simulation results show that the optimised schedule raises PV self‑consumption by an average of 15 % and reduces grid electricity purchases by about 12 % compared with a baseline schedule. Importantly, the total computational effort required to explore the entire scenario space is reduced by roughly a factor of seven relative to exhaustive simulation.

The paper’s key insights are: (i) active‑learning‑driven surrogate modelling can dramatically cut the number of costly building‑energy simulations while preserving high predictive fidelity; (ii) the surrogate’s rapid predictions enable real‑time DR strategies that align HVAC operation with intermittent renewable generation; (iii) the OpenModelica‑Python workflow provides a reproducible and extensible platform for future studies.

Potential extensions discussed include integrating deep‑learning time‑series predictors for PV output, incorporating additional flexible loads such as electric‑vehicle charging, and expanding the optimisation to a multi‑criteria framework that also accounts for electricity price signals and carbon emissions. Overall, the work demonstrates a practical pathway to smarter, greener building operation by marrying physics‑based simulation, machine‑learning surrogate modelling, and active learning.