No Neutral Switchgear Control Power

We just installed power to switchgear using existing feeders we thought had a neutral but we don't... Some of the control power transformers and meters have a spot for the neutral to land to and I assume reference it as well. I look through the shop drawings and noticed we are taking control power from the incoming phase conductors at 480V single phase then go through the xfmr to get our 120v. That 120v then routes through the undervoltage relay then I assume to the circuit breaker itself. The control power transformers receive control power off both phase a and phase b then hit a 480/277v – 120V xfmr. Now since we don't have a neutral and the xfmr is rated as if we have a neutral I am a little confused here. Could I provide a 120V power source and bypass the little transformers, also my 120V power will be off of batteries and will never lose voltage even while an outage occurs – how will this affect my existing scheme and undervotlage relays that will never engage?