Lagrangian modeling and passivity-based control of three-phase AC/DC voltage-source converters

In this paper, we investigate the dc-bus voltage regulation problem for a three-phase boost-type pulsewidth-modulated (PWM) ac/dc converter using passivity-based control theory of Euler-Lagrange (EL) systems. The three-phase PWM ac/dc converters modeled in the a-b-c reference frame are first shown to be EL systems whose EL parameters are explicitly identified. The energy-dissipative properties of this model are fully retained under the d-q-axis transformation. Based on the transformed d-q EL model, passivity-based controllers are then synthesized using the techniques of energy shaping and damping injection. Two possible passivity-based feedback designs are discussed, leading to a feasible dynamic current-loop controller. Motivated from the usual power electronics control schemes and the study of Lee, the internal dc-bus voltage dynamics are regulated via an outer loop proportional plus integral (PI) controller cascaded to the d-axis current loop. Nonlinear PI control results of Desoer and Lin are applied to theoretically validate the proposed outer loop control scheme. The PWM ac/dc converter controlled by the proposed passivity-based current control scheme with outer loop PI compensation has the features of enhanced robustness under model uncertainties, decoupled current-loop dynamics, guaranteed zero steady-state error, and asymptotic rejection of constant load disturbance. Experimental results on a 1.5-kVA PC-based controlled prototype provide verification of these salient features. The experimental responses of a classical linear PI scheme are also included for comparative study.