A group of researchers from Cranfield University in the United Kingdom have developed a scheduling model for residential heat pump operation that reportedly minimizes electricity costs while maintaining thermal comfort under time-varying rates and uncertain PV power generation.
“In dynamic rate scenarios, the integration of PV generation strengthens the heat pump’s ability to shift load, as it gives the planner an additional low-cost electricity source off the grid,” said the corresponding author Banu Jektin Ekren told pv magazine. “Under dynamic rates, the optimization can coordinate three things at once: 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 favorable, PV rich, or both, and later reduce dependence on expensive network imports.”
Jektin Ekren also explained that PV-assisted operation, compared to relying solely on electricity from the grid, improves flexibility because the system not only responds to rate signals, but also absorbs local renewable generation. “This is especially useful if the building itself can act as short-term thermal storage due to its thermal inertia,” she continued. “As a result, operating costs are reduced, while comfort can still be maintained thanks to the limited opportunity planning framework.”
In the newspaper “Comfort-conscious Distribution-robust chance-constrained scheduling of PV-assisted heat pumps under dynamic rates: a DOE-ANOVA interaction analysis”, published in Applied thermal technology, Yektin Ekren and her colleagues showed up that dynamic rates consistently reduce costs compared to fixed rates, and that the PV-supported robust scheduling setup ensures that that shift can take place without losing comfort reliability.
“An important point is that the benefit is not simply that PV reduces costs,” she further explained. “The real value comes from the interaction between PV uncertainty, rate timing and comfort-aware control. Because PV output is uncertain, the model does not assume perfect renewable energy availability. Instead, it plans conservatively enough to control comfort risk. So the framework represents a more realistic outcome: PV improves the ability to shift load and reduce costs, but robust planning is needed to ensure thermal comfort is not sacrificed when actual PV production lags behind forecast.”
The researchers combined distributionally robust probability-constrained programming (DR-CCP) with statistical design of experiments (DOE) and analysis of variance (ANOVA) to develop what they described as a control strategy for the day-ahead scheduling of PV-powered heat pumps. Rather than relying on perfect predictions or assuming a single probability distribution for PV prediction errors, the model uses distributively robust optimization. In particular, random constraints are formulated in such a way that comfort reliability is guaranteed 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 distribution misspecification.
“PV variability affects both comfort formulations by introducing uncertainty into the indoor thermal trajectory,” said Jektin Ekren. “If PV production is lower than expected, the system may require additional network input or more conservative heating decisions to avoid exceeding comfort limits. The difference is that indoor temperature (IT)-based constraints and predicted average vote (PMV)-based constraints define ‘acceptable comfort’ in different ways.”
IT-based constraints impose direct temperature limits, which can narrow and stiffen the feasible operating area. With uncertain PV generation, this often forces the model to maintain a stronger temperature safety margin, increasing grid usage and operating costs. In contrast, PMV-based constraints describe comfort in a more resident-oriented way. They enable the controller to recognize that comfort depends not only on air temperature, but on the wider thermal sensation range represented by PMV. That can create a more flexible feasible region, allowing the heat pump to utilize tariff and PV capabilities more effectively without violating comfort requirements.
“This is why PMV-based limitations in research lead to lower operating costs,” the researcher said. “They allow the system to maintain meaningful comfort without forcing the indoor temperature into a relatively rigid band at all times. In other words, PMV gives the optimiser more operational freedom while still respecting a recognized comfort standard. This is especially valuable when PV generation is uncertain, as the planner needs room to adjust for forecast errors. The results show that PMV-based comfort modeling consistently delivered lower costs than IT-based limits, across both building sizes and rate regimes.”
In the study, comfort is depicted in two ways. For indoor temperature, the limits are between 15 C and 23 C when using IT-based restrictions. 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 remain within a tighter “neutral” range, while sleeping hours can tolerate a slightly wider bandwidth without undermining occupant acceptability.
The framework also introduces a comfort constraint violation probability (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 allows the system to explicitly balance comfort risk against cost efficiency, rather than relying on deterministic safety margins that can be too conservative or unreliable under real uncertainty.
Through a series of simulations, the group found that PMV-based control consistently leads to lower operating costs compared to IT-based restrictions. This result suggests that more expressive comfort models can increase the feasible operating range, allowing the heat pump to exploit greater scheduling flexibility without compromising occupant comfort. However, this improved cost performance is in some cases accompanied by a slight reduction in the coefficient of performance (COP), indicating a trade-off between thermodynamic efficiency and flexibility-driven cost optimization.
The research group explained that their findings are not limited to one specific electricity market, but are most directly relevant to markets with three characteristics: electrified heating, time-varying tariffs and the increasing 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 Britain, but the broader message is transferable to other regions where households face variable electricity prices and renewable energy uncertainty.
“That said, the numerical results should not be copied directly from one country to another without adjustment,” he stressed Jektin Ekren. “Rate structures, climate conditions, building characteristics, occupant expectations and PV generation patterns all influence the exact balance between cost savings and comfort. So the framework is general, but the quantified results are context-dependent. Precisely, one of the key conclusions of the paper is that tariff benefits and comfort modeling benefits are not uniform; they depend on the building scale and operational context.”
“The proposed framework is flexible enough to be adapted to different types and sizes of heat pumps, because it is built around scheduling logic, comfort constraints, uncertainty modeling and system performance relationships, rather than around a single proprietary device,” emphasizes Yektin Ekren. “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 need to be tailored to the actual unit and building context.”
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