In the wide range of applications for power supplies, the ones dedicated to feeding superconducting magnets occupy a niche. This particular kind of magnets has the intrinsic property of having zero resistance, and is only used in high-end facilities for fundamental research or medical application to produce large magnetic fields. This implies that powering superconducting magnets requires a very high current combined with a low voltage only due to the interface between the power supply and the superconducting circuit. The case study developed in this thesis is based on CERN High Luminosity LHC project where an upgrade of the present Large Hadron Collider (LHC) installations needs to be developed. The objective is to increase the overall performances of the collider, targeting to augment the experimental data sets by one order of magnitude compared to the present one. To achieve this goal, a stronger magnetic field is needed to enhance the collision rate of particles by having a thinner particle beam, thus directly impacting the power supply ratings and driving many design choices for the power supply. This thesis is divided into two parts where at first a global system level approach is adopted, the definition of the operational requirements and the constraints related to high-current low-voltage power supplies in the context of CERN environment are detailed. As the new powering scheme of the dedicated Inner-Triplet magnets imposes a 2-quadrant operation of the supply, there is a need to locally integrate an energy storage solution in the supply to recover the magnetic energy when de-energizing the magnet. The integration of such storage element impacts the complete power flow of the power supply, as well as the sizing of the various stages of power conversion. To this extent a study of the best location of the storage within the supply is conducted and gives the basis for the power converters sizing. Additionally, a complete overview of the selected storage technologies is conducted, where supercapacitors and batteries are compared. The overall layout and suitable storage technologies are highlighted regarding the design of this new 2-quadrant high-current low-voltage power supply for superconducting magnets. The second part focuses on the power stage which processes the high current, the DC/DC output stage. By nature, because of the high level of current, the strict precision and the extended lifetime required for the power supply are such that a modular design is mandatory. Considering the case of a 18 kA nominal current output rating, an in-depth study of an optimized novel 2-quadrant high-current low-voltage DC/DC building block is presented. It is achieved through a multi-objective optimization that includes the core elements of the topology as well as the defined optimal modulation pattern. Volume and efficiency are considered as the main criteria during this process, the best compromise between those two is considered as the optimal solution. An elementary building block rated for 250 A, ±10 V is selected, where eight paralleled blocks are composing a sub-converter, and nine of those sub-converters in parallel allow to reach the nominal current requirement. The overall control strategy and experimental performances are demonstrated at a small scale, paving the way to a viable full-scale demonstrator that could effectively be used in a new generation of power supplies for superconducting magnet at CERN.