Non pilot speaking.
When the Ground Power Unit is connected, there will be a transfer of power that that causes a deliberate break in the lighting circuit. If this failed, the crew might have boosted the Auxiliary Power Unit to compensate. The APU is a small jet engine mounted at the base of tail fin and supplies electrical power whilst on the ground, unless mains power is available.
Certainly sounds like a problem in connecting, and then transferring the a/c services, to the ground power. The increase in thrust may be a perceived, rather than actual acceleration. Of course, if the a/c did move forward when the noise increased, they may have been nudging closer to the air bridge. Although the GPU will not be connected until the a/c has come to a halt, several things are going on.
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