How exactly does the grid handle small deviations in power consumption?
For tiny variations of load, the grid voltage changes slightly, which causes the power consumption of all of the other loads to change accordingly.

For example, if your 1 GW load suddenly becomes 0.999999 GW (-1 ppm), it only takes a voltage rise of +0.5 ppm to bring the consumption back up to 1 GW. This is enough of a rise to  cause the power that was being consumed by the switched-off load to be distributed across all of the other loads.