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Facilities operating in cycles, such as particles accelerators, require pulsed power. Directly drawing this pulsed power from the industrial network is generally not acceptable. A system with a local energy storage system lessens the impact on the network. In this work, a power supply is proposed that allows pulsed operation of a proton synchrotron without disturbing the industrial network with large variations of active power. The context of this study is the search of a completely static replace ment of an existing inertial energy storage device. The application is the proton synchrotron of the CERN. Several solutions to store the energy needed by the proton synchrotron are studied, they include inertial energy storage, capacitive energy storage and magnetic energy storage. On this basis, the solution based on capacitive energy storage with interleaved multilevel converters is retained. The sizing of the storage elements and the filter is carried out. The control strategies are studied and designed. They are composed of a current balancing control for the parallel connected converters and a voltage balance techniques for the DC buses of the series connected converters. Based on the pseudo-continuous modeling and controller sizing techniques, an advanced model for interleaved multilevel converters is established. It allows to have a better definition of the step response of the system. It is possible to use a PID controller instead of a PI controller to obtain of better step response. Numerical simulations are carried out to verify the control strategies of the system. A system with a multilevel converter is simulated with all control strategies and with the losses compensation rules. A low power system is built to study and verify the control algorithms of the power supply.