Unmet heating hours

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Yes, there are scenarios where that could be the case. For example a central air reheat system where the reheat coils are not sized large enough. The solar gains act like reheat, until they don't because of the shade. If the heating load is small compared to the reheating load, the reheat coils might be sized too small to meet the heating setpoint. The window shades may decrease window U-value some, and I guess that is why you say you have less heating load, but that can be a small change in a small heating load compared to the power needed to reheat cold air from a terminal unit during times of very low zone heat gain. The solar gains are more significant than the heat lost out the window at night.

We would need a great deal more information on the type of HVAC system and building. As always, look at the time series data and figure out when the unmet hours are occuring.