Design for passivity in the Z-domain for LCL grid-connected converters

This paper develops a design methodology aimed to shape passive the admittance of the LCL grid-connected voltage source converters (VSCs). A novel aspect of this work is the assessment of the range of frequencies for control design: due to discrete and PWM operation, the effectiveness of the control action is more and more reduced as frequency increases; in practice, system delays and non-linear effects tend to impair the passivity properties and also its experimental validation. However, as shown in this paper, those effects can be minimized by including the LCL filter as a part of an outer VSC admittance: this assumption is supported by the fact that high frequency disturbances (generated in the point of connection) are absorbed by the LCL capacitor branch, and hence, are not able to create a positive feedback in the VSC (i.e., the active component). By taking advantage of this remark, the inner VSC admittance can be shaped by a reduced order filter in the Z-domain, which mainly depends on the proportional and active damping (controller) gains. The design hypotheses and the control design methodology are verified by PLECS switching-mode simulations.