This paper presents a novel analytical methodology to determine the placement of reactive power devices in power systems. The proposed method modifies the Modal analysis technique and, based on the inversed reduced Jacobian matrix, develops a new formulation to compute the Reactive Contribution Factor (RCF) of each load buses. The objective of this research is to achieve the most stable condition and to minimize network losses. The proposed method is implemented at the modified IEEE 30-bus Reliability Test System (RTS) and compared with a different placement. In order to assess the method, this work compares the voltage profile, eigenvalue and network losses. The simulation results show that the proposed method can provide a solution to the ideal shunt compensator placement by improving the system's voltage stability and by minimizing losses.