A false data injection attack (FDIA) can alter the measured values, used for power system state estimation, communicated to the control center. One approach to this problem is securing measurements. Due to the expense involved, it is not possible to secure all the measurements. FDIA can be avoided by securing only a set of measurements called a basic measurement set (BMS). There can be multiple BMS in the system and all BMS are not equally effective during the failure of securement of measurements. An algorithm to obtain the optimal BMS is proposed. It may not be possible to secure all measurements in a BMS; for selecting a few measurements to be secured, a novel vulnerability index is proposed. The attacker's freedom is quantified and is used to select measurements to be secured.