Johnson's Theorem

Let X, Y and Z be normed spaces over the field F. A mapping ᶲ : X ˣ Y → Z is said to be bilinear if 1. for each y ϵ Y, the mapping x → ᶲ (x;y) is linear, 2. for each x ϵ X, the mapping y → ᶲ (x;y) is linear as well

Double Deadbeat plus Repetitive Control Scheme for Microgrid System

Parallel connection of converters is a convenient choice when system capacity is to be increased. Parallel-connected voltage source converters, especially neutral point clamped converters, are one of the best choices for its range. However, with the parallel connectivity, the converter possesses a circulating current in its legs, which consequently threatens the safe operation of the system. To alleviate this circulating current problem, in this paper, a double deadbeat (DD) plus repetitive control (RC) scheme is proposed. The RC scheme is employed to mitigate the circulating currents and the DD loop control scheme is employed to achieve a high operating bandwidth for voltage and current characteristics. Furthermore, the DD loop is associated with an adaptive controlling technique, which adjusts internally by itself and provides better performance for nonlinear loads. The proposed DD method forces the equivalent system elements to be placed outside the closed loop, which does not affect the system stability. Initially, the system has been executed with a conventional proportional + integral scheme and then with the proposed DD + RC scheme. The proposed method is verified by implementing a Simulink model in the OPAL-RT platform. Furthermore, the proposed method is built with a prototype, and its results are explored