Incomplete Air Mixing Reduces the Efficiency of Commercial Buildings Behaving as Virtual Batteries

Commercial building Heating, Ventilation, and Air Conditioning (HVAC) systems can provide flexibility to the electricity grid. Some researchers have found it convenient to model HVAC systems as virtual batteries. These models also better align with models used by grid planners and operators. However, experiments have shown that HVAC load shifting can be inefficient, and virtual battery models do not capture this inefficiency well. While the models typically use the average room temperature as the system's ``state of charge," they do not capture other factors that affect HVAC power/energy such as airflow and mixing. Here, we develop a new analytical building model to explore how incomplete mixing of supply air into a conditioned space leads to inefficiency in a virtual battery capturing the dynamics of HVAC fan power load shifting. The model qualitatively matches experimental results better than previous models, and shows that, as mixing becomes worse, the virtual battery becomes less efficient. Unfortunately, air mixing is unmeasured/unmeasurable. However, we show that, by closing the loop around measurements of fan power, we can improve the virtual battery's performance without the need for air mixing measurements. For example, in one case, we show a roundtrip efficiency improvement from 0.75 to 0.99.