Geometric Optimization for Predictive Control of Low-Capacitance CHB-SVGs via Boundary-Chain Search

Large capacitor-voltage ripple in low-capacitance cascaded H-bridge static var generators (CHB-SVGs) couples current tracking and cluster-voltage balancing. Computing the optimal switching-level solution under the resulting current-band and phase-output constraints requires fast identification of the active constraint faces. This paper proposes a geometric direct model predictive control method for this task. The voltage-balancing objective is rewritten as a weighted distance, converting the constrained optimization into an ellipsoid–polytope first-contact problem. A fast boundary-chain construction and search method is then developed to locate the optimal contact. Auxiliary projections select the relevant constraint faces and guide the construction of boundary chains containing this contact. Weighted-normal criteria direct the search along these chains to identify the active set, from which the optimal switching-level solution is computed. This approach replaces exhaustive active-set enumeration with a directed geometric search while preserving the continuous optimum. Its three-variable phase-level formulation keeps the candidate workload independent of the module count. Simulation and experimental results verify coordinated current tracking and cluster-voltage balancing with the proposed method.