A novel Voltage Modulated Direct Power Control (VM-DPC) is firstly designed for a Back-to-Back (BTB) converter in the Doubly Fed Induction Generator (DFIG) system. The proposed VM-DPC is built in the stator stationary reference frame ($\alpha\beta$). The proposed method uses a simple feed-forward and feedback structure without a phase-locked loop and the Park transformation. Therefore, it can be easily implemented in the BTB converter. Another essential advantage of the proposed VM-DPC is that it can transform the closed-loop DFIG system into a linear-time-invariant one, which can be analyzed and designed through multiple linear control techniques. The proposed method guarantees exponential stability in the stiff grid as well as in weak-grid integration, which is proved based on eigenvalue analysis. Simulation results demonstrate that the proposed VM-DPC has a faster transient response than conventional Vector Oriented Control (VOC). Also, it maintains a satisfactory steady-state performance at the same level as the VOC. The robustness of proposed VM-DPC against distorted voltage conditions and parameter mismatch is also tested. Finally, the proposed VM-DPC control strategy is validated in an experimental hardware prototype of a 7.5 kW DFIG system operating in real-time.