In the context of a rise in the use of static power converters, the beneficial features of Multilevel Modular Converters (MMCs) have led to their popularization. However, as the number of voltage levels and the number of phases increases, these converters have an increasing number of degrees of freedom to handle. Thus, MMCs represent a challenge for control because the number of control variables is higher than the constraints to be satisfied, making them overactuated systems and opening the way to optimization. Having first appeared in the 1980s in aeronautics to take advantage of the multiplicity of aerodynamic and redundant surfaces that an aircraft presents in order to control its trajectory (flaps, ailerons, control surfaces...), the control allocation methods have proven their worth and were progressively applied in different technologic fields. At the same time, control allocation has been the topic of research works leading to the integration of optimization algorithms in these control methods.The thesis concerns the development and implementation of real-time control allocation methods, with a focus on online optimization, for an MMC-based power conversion system.The first part of the thesis focuses on the control-oriented modelling of the MMC converter for the application of allocation methods. This step involves the development of different control models with different levels of detail and complexity. A strong result of this first part is a control model whose complexity is no longer impacted by the number of phases of the considered electrical system.The second part of the work concerns the development of a new allocation method for MMCs that takes advantage of the beneficial features of state-of-the-art methods. This approach leads to the programming of a new allocation algorithm with dynamic and static characteristics that can be easily adjusted and adapted. Its integration with existing methods is readily and seamlessly achieved.The third part of the work combines the two previous steps. First in simulation, the control allocation method of the converter is programmed and then tested and validated. For control, different architectures are designed and compared in order to evaluate their ability to achieve the performance required for the proper operation of the system. An analysis of the different control algorithms is then carried out. The main result of this part is the design of a new allocation algorithm allowing one to control the voltages across the capacitors as well as all the currents in each branch of the converter, achieving this result independently of the number of phases.The fourth step is about the experimental validation of the developed methods. To do so, the MMC converter available at the LAPLACE laboratory is used as well as a set of rapid prototyping tools (OPAL-RT) allowing to test and develop the algorithms in a safe and efficient way using a Hardware-In-the-Loop (HIL) technique.The fifth part of the work concerns the extension of the control algorithms outside the nominal operating zone of the converter. An approach is considered highlighting the capabilities of the allocation methods to reconfigure the operation of the MMC when a fault appears in one of the sub-modules. The results obtained in simulations show an improvement of the resilience of the converter, i.e., a continuity of operation in the presence of faults that justifies a future continuation of the work in that direction.The proposed contributions then conclude with perspectives for future exploration and investigation on the topic of allocation methods in electrical engineering.