Circulating Current Suppressing Strategy for MMC-HVDC Based on Nonideal Proportional Resonant Controllers Under Unbalanced Grid Conditions

Capacitor Voltage Estimation Scheme With Reduced Number of Sensors for Modular Multilevel Converters

“…To estimate the voltage value in one prediction step ahead, the previous voltage at −1 ( ̂( −1 ) ) has to be included in the algorithm process as well as the error calculated in (13) multiplied by the adaptive gain ( ( ) ) which has been calculated in (12). In the first initial step ̂( 0 ) =̂( − 1) = 0, therefore, achieving this goal for the estimation of the upper capacitor voltages at is achieved as follows:…”

“…However, some rearrangements have to be considered. For example, in (12), (15) and (16) = + 1, + 2 … .2 instead of = 1,2 … . It worth noting that the sorting algorithm used in Fig.…”

“…It worth noting that the sorting algorithm used in Fig. 4 is similar to that presented in [12], and it should be also noted that, the voltage-balancing (i.e. the sorting algorithm) used in this paper has nothing to do with the proposed estimation method.…”

“…The voltage-balancing method used for the upper arm is shown in Fig. 5, where more detail about the technique can be found in [12].…”

“…These advantages have made the MMC a promising candidate for various applications such as battery storage systems, variable speed drives, flexible AC transmission systems (FACTS) [2,9], and high-voltage direct current systems (HVDC) [3,[10][11][12][13].…”