This paper examines the control strategy adopted for six-phase machines that have been designed as double three-phase machines without a displacement between the magnetic axes of the two sets of three-phase windings (6PH-ZS). The approach is based on vector control principles, enabling the independent control of direct- and quadrature-current components in both three-phase windings. The advantages of such an approach stem from the flexibility of the current distribution between windings, which aims to achieve the required flux and torque. The proposed control strategy is considered for both motor and generator operating regimes. However, an additional quasi-transformer regime is also addressed. While the classic operation regime requires the machine to produce either driving or generating/braking torque, the quasi-transformer regime enables the control of electric power flow between two three-phase windings. A theoretical analysis of the machine model and control algorithm for the flow of electric power through machines is presented for the three aforementioned operating regimes. Verification of the proposed control algorithm is performed through extensive experimental verification.