A group of researchers from Cranfield University in the United Kingdom has developed a scheduling model for residential heat pump operation that reportedly minimizes electricity costs while maintaining thermal comfort under time-varying tariffs and uncertain PV power generation.
“In scenarios with dynamic tariffs, the integration of PV generation strengthens the heat pump’s load-shifting potential because it gives the scheduler an additional low-cost electricity source beyond the grid,” corresponding author Banu Yektin Ekren told pv magazine. “Under dynamic tariffs, the optimization can coordinate three things at the same time: when electricity is cheap, when PV is available, and how much thermal flexibility the building can provide. In practice, this means the heat pump can preheat or maintain comfort during periods that are either price-favourable, PV-rich, or both, and reduce reliance on expensive grid imports later.”
Yektin Ekren also explained that, compared with relying only on grid electricity, PV-assisted operation improves flexibility because the system is not only reacting to tariff signals but also absorbing local renewable generation. “This is especially useful when the building itself can act as short-term thermal storage through its thermal inertia,” she went on to say. “As a result, operating costs fall, while comfort can still be preserved through the chance-constrained scheduling framework.”
In the paper “Comfort-aware Distributionally robust chance-constrained scheduling of PV-assisted heat pumps under dynamic tariffs: A DOE–ANOVA interaction analysis,” published in Applied Thermal Engineering, Yektin Ekren and her colleagues showed that dynamic tariffs consistently reduce cost relative to fixed tariffs, and the PV-assisted robust scheduling setup is what allows that shifting to happen without losing comfort reliability.
“A key point is that the benefit is not simply that PV lowers cost,” she further explained. “The real value comes from the interaction between PV uncertainty, tariff timing, and comfort-aware control. Because PV output is uncertain, the model does not assume perfect renewable availability. Instead, it schedules conservatively enough to keep comfort risk under control. So the framework captures a more realistic outcome: PV improves the opportunity to shift load and reduce costs, but robust scheduling is needed to make sure that thermal comfort is not sacrificed when actual PV production falls short of the forecast.”
The researchers combined distributionally robust chance-constrained programming (DR-CCP) with a statistical design of experiments (DOE) and analysis of variance (ANOVA) to develop what they described as a control strategy for day-ahead scheduling of PV-driven heat pumps. Instead of relying on perfect forecasts or assuming a single probability distribution for PV forecast errors, the model uses distributionally robust optimization. In particular, chance constraints are formulated in a way that guarantees comfort reliability even when the true distribution of PV errors is unknown but bounded by observed statistical properties. This is achieved using a moment-based ambiguity set constructed from historical PV data, ensuring that the optimization remains valid under distributional misspecification.
“PV variability affects both comfort formulations by introducing uncertainty into the indoor thermal trajectory,” said Yektin Ekren. “When PV production is lower than expected, the system may need extra grid import or more conservative heating decisions to avoid violating comfort limits. The difference is that indoor-temperature (IT)-based constraints and predicted mean vote (PMV)-based constraints define ‘acceptable comfort' in different ways.”
IT-based constraints impose direct temperature bounds, which can make the feasible operating region narrower and more rigid. Under uncertain PV generation, that often forces the model to maintain a stronger temperature safety margin, increasing grid use and operating cost. PMV-based constraints, by contrast, describe comfort in a more occupant-centred way. They allow the controller to recognize that comfort does not depend on air temperature alone, but on the broader thermal sensation envelope represented by PMV. That can create a more flexible feasible region, allowing the heat pump to exploit tariff and PV opportunities more effectively without violating comfort requirements.
“This is why PMV-based constraints lead to lower operating costs in the study,” said the researcher. “They let the system preserve meaningful comfort without forcing indoor temperature to remain inside a comparatively rigid band at all times. In other words, PMV gives the optimiser more operational freedom while still respecting a recognised comfort standard. That is particularly valuable when PV generation is uncertain, because the scheduler needs room to adapt to forecast errors. The results show that PMV-based comfort modelling consistently produced lower cost than IT-based bounds across both building sizes and tariff regimes.”
In the study, comfort is represented in two ways. For indoor temperature, the bounds are 15 C to 23 C when IT-based constraints are used. For PMV, the comfort range is stricter during the day, from -0.5 to 0.5, and more relaxed at night, from -1 to 1. This reflects a practical interpretation of minimum acceptable comfort: daytime comfort should stay within a tighter “neutral” range, while sleeping hours can tolerate a somewhat wider band without undermining occupant acceptability.
The framework also introduces a probability of comfort constraint violation (PoCCV), which acts as a tunable reliability parameter. Lower PoCCV values correspond to stricter comfort guarantees, while higher values allow more flexibility in operation. This probabilistic structure enables the system to explicitly balance comfort risk against cost efficiency, rather than relying on deterministic safety margins that may be overly conservative or unreliable under real-world uncertainty.
Through a series of simulations, the group found that PMV-based control consistently leads to lower operating costs compared to IT-based constraints. This result suggests that more expressive comfort models can expand the feasible operating region, allowing the heat pump to exploit greater flexibility in scheduling without compromising occupant comfort. However, this improved cost performance comes with a slight reduction in the coefficient of performance (COP) in some cases, indicating a trade-off between thermodynamic efficiency and flexibility-driven cost optimisation.
The research group explained that their findings are not limited to one specific electricity market, but they are most directly relevant to markets that have three characteristics: electrified heating, time-varying tariffs, and growing deployment of behind-the-meter renewables such as rooftop PV. The case study uses dynamic electricity prices and a residential heat-pump context that are highly relevant to Europe and the UK, but the broader message is transferable to other regions where households face variable electricity prices and renewable uncertainty.
“That said, the numerical results should not be copied directly from one country to another without adaptation,” stressed Yektin Ekren. “Tariff structures, climate conditions, building characteristics, occupant expectations, and PV generation patterns all affect the exact balance between cost savings and comfort. So the framework is general, but the quantified outcomes are context-dependent. In fact, one of the main conclusions of the paper is precisely that tariff benefits and comfort-modelling benefits are not uniform; they depend on building scale and operating context.”
“The proposed framework is flexible enough to be adapted to different kinds and sizes of heat pumps, because it is built around scheduling logic, comfort constraints, uncertainty modelling, and system performance relationships rather than around a single proprietary device,” Yektin Ekren emphasized. “However, practical implementation would require calibration for the specific heat pump technology and installation. Different heat pumps have different COP characteristics, modulation ranges, thermal response, and control capabilities. So the optimization structure is general, but the input data and performance parameters must be tailored to the actual unit and building context.”
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