Grid tied inverter voltage is slightly higher than that of grid but once the tie is closed voltage will be equal then how the current will be injected from the inverter
The inverter voltage has to be slightly higher than that of the grid to make the current flow to the grid.
It's like water flowing between two tanks. If both tanks are at the same level there is no flow. You need a difference in heights to make the water flow. You need a difference in voltage to make current flow.
Grid-tied inverter first checks the grid voltage (and frequency and phase, in order to completely synchronize with it) before producing any output.
Then it outputs a voltage about the same as, or very slightly higher than, the grid voltage in order to start feeding the current back into the grid.
At the same time, it continuously monitors the amount and the direction of the current flow, and it keeps increasing it up to a set limit, making sure it always flows out to the grid and never above the set limit (or never above the power-producing capability of a solar array at the moment, for example).
If anything happens on the grid (like a short-circuit, sudden, significant voltage drop, anything greatly exceeding the set limits), the inverter disconnects to protect itself and starts with step 1 again after a short time.
At the point of connection to the grid, the output voltage of the inverter is the same as the grid voltage. However, at the point of common coupling between the your section of the grid and the section that supplies the nearest load, the grid voltage is slightly lower. That slight difference allows the inverter to supply energy to the grid. That also means that your inverter supplies the nearest neighbor that is receiving energy from the grid.