# Integral of "Zone Air Heat Balance Air Energy Storage Rate" does not correspond to "Zone Mean Air Temperature"

Hello everyone,

I am developing a simplified thermal model for one building (RC model), and, for the estimation of thermal capacitances, I wanted to use the Energy Storage Rate to estimate the zone air capacitance more accurately. However, once I extracted the data from the simulation and tried integrating the Air Energy Storage Rate (to get a variable corresponding to the temperature) per following equations:

$Q_{sto}^{air} = C_{air} * {d T_{air}}/{dt}$

$T_{air} \mid_{t} = 1/C_{air} * \int_{0}^{t} { Q_{sto}^{air}*dt } + T_{air} \mid_{t=0}$

I discovered that there's a strange component in the Energy Storage Rate that makes the integral drift away (you can check it on this graph). I have found a way to remove this component (by removing the drift on a daily basis and fitting the signal for a constant capacitance over the whole year), but I would still like to know what is causing this issue (the physical meaning of that component). Does anybody have any clue?

I have tried reducing the simulation time step even to 1 minute, but, unfortunately, that did not resolve the issue.

Thank you.

Kind regards, Milan

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