New Generalized Ekeland’s Variational Principle, Critical Point Theorems and Common Fuzzy Fixed Point Theorems Induced by Lin-Du’s Abstract Maximal Element Principle

In this paper, by applying the abstract maximal element principle of Lin and Du, we present some new existence theorems related with critical point theorem, maximal element theorem, generalized Ekeland’s variational principle and common (fuzzy) fixed point theorem for essential distances.

Dynamic Effect of Input-Voltage Feedforward in Three-Phase Grid-Forming Inverters

Grid-connected and grid-forming inverters play essential roles in the utilization of renewable energy. One problem of such a converter system is the voltage deviations in the DC-link between the source and the inverter that can disrupt the inverter output voltage. A common method to prevent these voltage deviations is to apply an input-voltage feedforward control. However, the feedforward control has detrimental effects on the inverter dynamics. It is shown that the effect of the feedforward in the input-to-output dynamics is not ideal due to the delay in the digital control system. The delay affects the input-to-output dynamics at high frequencies, and only a minor improvement can be achieved by low-pass filtering the feedforward control signal. Furthermore, the feedforward control can remarkably affect the inverter input admittance, and therefore, impedance-based stability problems may arise at the DC interface. This paper proposes a method based on linearization and extra element theorem to model the effect of the feedforward control in the inverter dynamics. Experimental measurements are shown to demonstrate the effectiveness of the proposed model.

A note on the FIP property for extensions of commutative rings

A ring extension R ? S is said to be FIP if it has only finitely many intermediate rings between R and S. The main purpose of this paper is to characterize the FIP property for a ring extension, where R is not (necessarily) an integral domain and S may not be an integral domain. Precisely, we establish a generalization of the classical Primitive Element Theorem for an arbitrary ring extension. Also, various sufficient and necessary conditions are given for a ring extension to have or not to have FIP, where S = R[?] with ? a nilpotent element of S.