Extremum Seeking Optimization for Ripple Minimization in Multi-Module Power Factor Correction Systems

In multi-module boost power factor correction (PFC) systems, current ripple is commonly mitigated by applying fixed 180° interleaving between modules; however, this approach relies on matched inductors and ideal symmetry. In practical implementations, inductor mismatch and duty-cycle variations prevent full cancellation, leading to residual ripple that increases losses and electromagnetic interference. To address this issue, several research works have proposed centralized coordination or high-speed communication among units. However, an explicit converter model is necessary, which makes the system more complicated and expensive. To resolve this problem, this paper presents an extremum seeking optimization method for reducing high-frequency ripple in multi-module PFC systems without requiring explicit converter models. The ripple minimization problem is formulated as a nonlinear, time-varying optimization task, where the relative switching phases of the modules are adaptively tuned. The proposed extremum seeking algorithm perturbs the phase shift, evaluates a ripple-based cost function, and updates the phases iteratively. A harmonic analysis is developed to characterize the dependence of ripple on duty ratio, inductor values, and phase displacement. Simulation results show that the method effectively reduces the RMS ripple current across balanced and mismatched operating conditions. In a three-unit system, applying the proposed technique lowered the current THD to 1.29% compared to 1.44% achieved with a fixed phase-shift approach. These findings demonstrate that extremum seeking optimization provides a mathematically rigorous and practically implementable solution for decentralized ripple minimization in multi-module boost PFC systems.