Near optimal PI Control of Cascaded Buck Converters in a DC Micro Grid

Cascaded and tightly regulated power electronic converters suffer from the destabilizing effects caused by the constant power loads (CPLs). Various strategies to cope with instability have been proposed in the literature. We consider the model of a DC microgrid (DCMG) that comprises two cascaded buck converters, where load side converter acts as CPL. Our control strategy employs droop control in the voltage loop and a proportional-integral (PI) controller in the inner current loop. We formulate the PI controller design as an optimal control problem and use linear quadratic regulator (LQR) principle to solve for the controller gains. In this approach, the optimal closed-loop roots are first obtained from the symmetrical root locus plot of the Hamiltonian system. A near optimal PI controller is then obtained by matching the closed-loop polynomial coefficients with a desired characteristic polynomial. Controller robustness is studied by simulating changes in the load current. Our computer simulation results show that the controller is effective in regulating voltages in the DCMG. The design approach can be extended to larger systems with multiple parallel switching converters.