Nonlinear Control Design and Stability Analysis of Single Phase Half Bridge Interleaved Buck Shunt Active Power Filter

 Abstract

This paper deals with nonlinear control of a single phase half-bridge interleaved buck shunt active power filter(HBIB-SAPF) with a nonlinear load. The control objective for the system is twofold: performing power factor correction by compensating for harmonics and reactive current consumed bythe nonlinear load from one hand and tightly regulating the HBIB converter DC capacitor voltage. Both objectives are accomplished using a two-loop nonlinear controller. The inner loop acts on the switching devices so that the active filter current tracks its reference with the aim of ensuring a unity power factor. This loop is tackled using backstepping technique and Lyapunov approach. The outer loop is responsible for regulating the DC capacitor voltage to its desired value, using a PI controller with a pre-filter. The stability analysis of the closed-loop system is formally performed by using the averaging theory. The validity of the designed nonlinear controller is checked by simulations in Matlab/Simpower System showing its robustness and accuracy under various conditions.

Index Terms—Nonlinear control design, Interleaved buck converter, Shunt active power filter, Lyapunov stability analysis, Averaging theory.

Block Diagram:

                                  Fig. 1. Schematic circuit diagram of a single-phase HBIB-SAPF.

Expected Simulation Results:

                               Fig. 2. (a) Load current iL in time domain, (b) FFT spectrum.

                                               Fig. 3. Simulation results under nonlinear load.

Fig. 4. Simulation results under voltage step changes.

Fig. 5. Simulation results under supply grid voltage changes.

Conclusion:

This work dealt with the problem of controlling a single phase shunt active power filter based on half-bridge interleaved buck converter. As a first step, an equivalent average model was proposed in which the filter system dynamics was described by the 4th order nonlinear state-space representation. Then, on the basis of such a model, a nonlinear cascade controller was designed using various tools from control theory like, system averaging theory and Lyapunov design. The results obtained in numerical simulation as well as in theoretical analysis demonstrate that the developed nonlinear controller performs well in terms of tracking and robustness against uncertainty. Finally, it was formally proven that the overall system is globally asymptotically stable and that the control requirements are met, including i) compensation of harmonics and reactive power absorbed by the nonlinear loads; ii) a tight voltage regulation at the half-bridge interleaved buck converter output capacitor.

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