For a system using a single Radeon HD 6770 graphics card AMD specifies a minimum of a 450 Watt or greater system power supply. The power supply should also have a maximum combined +12 Volt continuous current rating of 25 Amps or greater and have at least one 6-pin PCI Express supplementary power connector.
Total Power Supply Wattage is NOT the crucial factor in power supply selection!!! Sufficient Total Combined Continuous Power/Current Available on the +12V Rail(s) rated at 45°C - 50°C ambient temperature, is the most critical factor.
Overclocking of the CPU and/or GPU(s) will require an additional increase to the maximum combined +12 Volt continuous current ratings, recommended above, to meet the increase in power required for the overclock. The additional amount required will depend on the magnitude of the overclock being attempted.
You may find power supplies on the market that supply more than enough Wattage to run the system. However, some of them lack Sufficient Amperage capacity on the critical +12 Volt rail, which is necessary to properly power the critical components in the system (i.e. CPU and GPUs). This is the reason why graphics card manufacturers may overstate the power supply wattage, usually by at least 50 Watts, in an attempt to take into account some of those power supplies that have the weaker +12 Volt rail(s).
The Corsair VS Series VS450 (SKU# 75-001835 / CP-9020049), with its maximum combined +12 Volt continuous current rating of 34 Amps and with one (6+2)-pin PCI Express supplementary power connector, is more than sufficient to power your system configuration with a single Radeon HD 6770 graphics card.