DC-Link Capacitance Design for Cascaded H-Bridge STATCOM with Sum of Squares Formulation

This article has proposed a generic capacitor sizing method for delta-connected cascaded H-bridge (CHB) used for static synchronous compensator (STATCOM), which can be operated in capacitive, inductive, and harmonic modes. The sizing method takes power quality, peak, and peak-to-peak capacitor voltage limitations into consideration. By transforming the sines and cosines into tangent, the limitations are formulated as nonnegative univariate polynomials. Because the polynomials coefficients are related with the capacitance value, a feasible capacitance value guarantees their nonnegativity. Since nonnegativity and sum of squares (SOS) are equivalent, the SOS program is combined with an iterative algorithm to find the minimal capacitance. Moreover, a guide for selecting the average capacitor voltage is given. The proposed capacitance sizing method does not need approximation, therefore it is accurate. Compared with the existing capacitance sizing methods for the capacitive/inductive mode, another feature of the method raised in this article is that it is able to determine the capacitance value even if STATCOM is operated in harmonic mode. The proposed method is also feasible when grid faults, such as unbalanced/harmonic voltages, appear. Comprehensive simulations and experiments are conducted, showing the effectiveness and accuracy of the proposed capacitance sizing method.