Improvement of Control Law Derivation and Region Selection for ${D}{-}\Sigma$ Digital Control

Abstract

A division–summation $({D}{-}\mathbf{\Sigma})$ digital control for three-phase inverters to achieve active and reactive power injection has been presented. It can overcome the limitation of abc to dq frame transformation. However, the ${D}{-}\mathbf{\Sigma}$ control requires four sets of control laws to cover four quadrant operations, namely, grid connection (power factor (PF) 1 $\sim\pm$ 0.866), rectification with PF correction, PF leading (0 $\sim$ 0.866), and PF lagging (0 $\sim$ −0.866). Moreover, the switching sequences for the four modes are also different from each other, increasing complexity of firmware programming. In this paper, improvement of the control law derivation and region selection for the ${D}{-}\mathbf{\Sigma}$ digital control is presented. By selecting the zero-crossing points of phase voltages as region transitions, the control laws and the related parameter tables for the four modes can be unified to a general form. The switching sequences of the four modes are also unified to the switching pattern of the grid-connection mode. Additionally, a ${D}{-}\mathbf{\Sigma}$ transformation matrix is identified to simplify the derivation procedure of the division $(D)$ and summation $({\Sigma})$ , which can obtain the control law directly. Measured results from a 10-kVA 3 $\phi$ bidirectional inverter have been presented to confirm the improvement.