How does a power plant increase load?
Power plants do not increase load, the customer's served control the load by turning things on and off or adjusting loads to use more power. A power plant connected to a grid can supply a larger share of the load. Viewed simply, the plant does that by increasing its internal voltage to be slightly above the voltage at the grid connection. The grid voltage remains constant, but the current and power supplied by the power plant under consideration increase.
I know the formula for wattage is V*A=W.
For an AC power plant, that is not true. The phase relationship between the voltage in current must be considered. That means that W = V * A * pf, where pf (power factor) is a number between 0 and 1 that accounts for the phase relationship. A power plant could increase power delivered without increasing current by increasing pf.