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Abstract: We prove several basic properties for difference ascending chains, including a necessary and sufficient condition for an ascending chain to be the characteristic set of its saturation ideal and a necessary and sufficient condition for an ascending chain to be the characteristic set of a reflexive prime ideal. Based on these properties, we propose an algorithm to decompose the zero set of a finite set of difference polynomials into the union of zero sets of certain ascending chains. This decomposition algorithm is implemented and used to solve the perfect ideal membership problem, and to prove certain difference identities automatically. [Copyright &y& Elsevier]

High-voltage dc/dc converters play an important role in HVDC grids. Isolated modular dc/dc converters (IMDCCs) based on modular multilevel converter technology provide a good solution to high-voltage applications. In order to reduce the size of the system, the IMDCC is required to be operated with a high ac-link frequency, but this will lead to increased switching loss and thus degraded efficiency. This paper proposes a soft-switching operation scheme for such an IMDCC. In this scheme, a quasi-square-wave (QSW) modulation method is employed, where the chain-links generate quasi-square terminal voltages with reduced dv/dt. With such chain-link terminal voltages, the arm currents which provide good condition for the soft-switching operation of the QSW-IMDCC can be obtained. Since soft switching can be achieved for the power switches, the proposed scheme will suffer less switching loss, thus improving the efficiency of the converter. Moreover, a capacitor voltage-balancing control strategy is proposed. This strategy does not need any arm current sensors, thus reducing the cost. The proposed soft-switching operation scheme and capacitor voltage-balancing control strategy are verified by the simulation results. [ABSTRACT FROM PUBLISHER]