Optimal submodule capacitor sizing based on equilibrium optimizer arm current injections for a modular multilevel converter system

• An optimal capacitor sizing is proposed for the submodule capacitor. Approach is based on optimally determining the minimum optimal capacitor and a subsequent stage is employed to find actual capacitance. • The peak-to-peak energy deviation is optimally minimized through an optimal injection of circulating current components. Through a formulation of an optimization problem, the peak-to-peak energy deviation is considered a cost function to be minimized. • The optimal injection circulating injections are defined in terms of amplitude and phase, which are the optimization variables. These variables are determined through the physically inspired Equilibrium Optimizer (EO). A second stage is used to find the actual capacitance which limits the percentage voltage ripple. • The EO is modified to include constraints that ensure proper modular multilevel converter operation and limitations on arm currents as not to degrade converter operation. • Reduction in capacitor size is evaluated in terms of size and actual number of units that become redundant. In addition, a comprehensive loss analysis is presented in the paper which confirm that optimal injections obtained from EO have no significant impact on converter efficiency. Modular Multilevel Converters (MMCs) have emerged as strong competitors among multilevel converter topologies. Nonetheless, high voltage applications of MMC lead to substantial energy storage requirements, not to mention the large number of submodules, which require large capacitors, adversely affecting converter’s size, weight and cost. In this paper, the reduction of capacitor size, which is the largest element in MMC, is achieved by injecting components into the MMC arm currents with the objective of reducing peak-to-peak energy deviation, thereby decreasing the minimum required capacitance. For this purpose, a constrained optimization problem is formulated based on the physically inspired Equilibrium Optimizer (EO) algorithm. The aforementioned algorithm searches for the optimal amplitude and phase of the required current component injections that yield the lowest peak-to-peak energy deviation, thereby achieving optimal minimal capacitance. The proposed method is further enhanced by augmenting the results of the optimization approach with a local search method to obtain the optimal actual capacitance of a submodule. Simulation results verify the ability of the proposed method in reducing capacitor size by up to 48.9 %, which improves size and weight utilization. Moreover, this reduction in capacitor size is characterized not only by size but also in terms of the actual number of commercial capacitor units needed to construct the SM capacitor. The optimal current injections achieved do not cause any significant degradation in the converter’s efficiency (efficiency reduction of only 0.172 % compared to no injection), as peak and RMS arm currents are well constrained in the optimization process.