This paper proposes a cost-effective compensator to suppress harmonics and compensate the power factor of all-electric shipboard power systems (SPSs). This compensator, which is based on a fixed capacitor-thyristor controlled reactor (FC-TCR), behaves as a low-pass filter and therefore can reject both low and high-order harmonics. Moreover, the FC-TCR compensator is featured by the low switching losses; hence, it can effectively be implemented for low and medium voltage applications. The design of the filter is detailed via equivalent lossy circuits, which exhibit the mechanism of the harmonic mitigation. Furthermore, theoretical analyses and mathematical developments are suggested to enhance the filtering performance. Besides, details of the Fixed-Point iteration technique which is applied to extract the firing angle of the TCR are conducted. A practical SPS is selected to ensure and demonstrate the performance of proposed methodology via thorough simulations under MATLAB/Simulink environment. The obtained results verify the theoretical analyses and confirm the effectiveness of proposed solution.