Conditions for Setting the DTC
WARNING: This page is about a different car, the 2007 GMC Sierra and 2007 Chevrolet Silverado. However, it is still accessible from the selected car via links, so may be relevant.
DTC P2670 sets when the TCM detects a low voltage condition, less than 6.0 volts, in 3 solenoids in the HSD2 circuit.