Radeon 7550 with 300w power Supply

Solution
Yes you can install and it should work with no problem.
The HD 7750 is a very power efficient card and does not require any power connector.
Jul 5, 2013
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400W (or greater) power supply recommended

500W power supply (or greater) recommended for AMD CrossFire™ technology

NOTE: Minimum recommended system power supply wattage is based on the specific graphics card and the typical power requirements of other system components. Your system may require more or less power.

Certified power supplies are recommended. Refer to http://ati.amd.com/certifiedPSU for a list of Certified products