The geomagnetic field changes acutely during geomagnetic storms. According to Faraday's law of the electromagnetic induction, the change of the geomagnetic field produces a geomagnetically induced current in the power grid, which directly damages the power equipment and threatens the safe operation of the power grid. The more dramatically geomagnetic field changes, the bigger geomagnetically induced current in the power grid becomes, and thus, the greater harm to the power grid. In this paper, based on the H and D components of the recent geomagnetic storm data measured by several mid-to-low latitude geomagnetic observatories, the variation law of the amplitude of north-south and east-west geomagnetic component change rate (dX/dt and dY/dt) pulses with geomagnetic latitude is analyzed when the geomagnetic field changes very severely. Finally, the possibilities of the power grid in different directions being affected by GIC with the change of latitude are discussed. The analysis results will contribute to the evaluation, the measurement and the control of GIC in the current and future power grids in China.