A new bi-directional circuit breaker is presented for medium-voltage dc (MVDC) systems. The Y-source impedance network topology is used to implement the breaker. The current transfer function is derived to show the frequency response and the breaker operation with the high frequencies. Mathematical analysis is achieved with different conditions of coupling among the breaker inductors. The minimum level of the magnetic coupling is determined, which is represented by the null condition. The effect of the turns-ratio on this condition is investigated as well. The breaker is designed with two types of fault conductance slope rates. The Y-source breaker is simulated, and the results verify the breaker operation during the fault condition and the load change. The results also demonstrate the effect of the coupling level on the minimum values of the source current when the fault occurs. Based on the expected fault type in the MVDC systems, the proposed breaker is developed to interrupt the overcurrent due to any of these fault types. A protection scheme is proposed for a 12-bus, two-level micro-grid, where the Y-source breakers are used in the bi-directional zones. The results verify the ability of the breaker to conduct and interrupt the current in both directions of the power flow.