Modular multilevel converter passivity-based PI control suited for balanced and unbalanced grid conditions

MMC Passivity-based PI Controller: A novel nonlinear global tracking controller was proposed by extending the regulation case. It consists in a linear PI that regulates two constructed signals with respect to which the incremental model of the MMC becomes passive. Estimation of x
_k
: A closed-loop estimator was proposed to estimate the MMC variables in steady state needed as input for the non-linear controller. Such estimator consists on a virtual MMC energy model and both of the differential current reference equations that yielded from mathematical optimization using Lagrange multipliers.