In this paper, a novel risk-based, two-objective (technical and economical) optimal reactive POWER dispatch method in a wind-integrated POWER system is proposed which is more consistent with operational criteria.  The technical objective includes the minimization of the new voltage instability risk index. The economical objective includes cost minimization of reactive POWER generation and active POWER loss. The proposed voltage instability risk employs a hybrid possibilistic (Delphi-Fuzzy)-probabilistic approach that takes into consideration the operator’s experience, the wind speed and demand forecast uncertainties when quantifying the risk index. The decision variables are the reactive POWER resources of the system. To solve the problem, the modified multi-objective particle swarm optimization algorithm with sine and cosine acceleration coefficients is utilized. The method is implemented on the modified IEEE 30-bus system. The proposed method is compared with those in the previously published literature, and the results confirm that the proposed risk index is better at estimating the voltage instability risk of the system, especially in cases with severe impact and low probability. In addition, according to the simulation results compared to typical security-based planning, the proposed risk-based planning may increase the security and economy of the system due to better utilization of system resources.

A reconfigurable COMPACT small size multiband meander line POWER divider with low insertion loss using two varactor diodes is presented in this paper. Design methods along with analysis equations are provided. The reconfigurable responses are realized by tuning the controlling voltages of the two varactor diodes thereby resulting COMPACT size and less loss. One diode is used to tune the return loss of the input port and the other diode is utilized to tune the return loss of the two output ports and the isolation between the two ports. The tuning frequency range is from 0.8 GHz to 1.2 GHz. By tuning the bias voltages of the diodes, POWER divider can operate in 0.8 GHz to 1.2 GHz frequency bands.  A reconfigurable POWER divider is designed, fabricated and measured to validate the proposed methods. The POWER divider has the merits of COMPACTness, low insertion loss, good isolation between two output ports, good return loss, and only two varactor diodes.

In this paper an ultra-wideband POWER divider has been designed, simulated and fabricated. In this structure, the quarterwave transformer in the conventional Wilkinson POWER divider, is replaced by an exponentially tapered microstrip line. Since the tapered line provides a consistent impedance transformation across all frequencies, very low amplitude ripple of 0. 5dB peak-to-peak in the transmission coefficient and superior input return loss better than 15dB are achieved over an ultra-wide bandwidth. By optimizing the physical locations of the two additional standard resistors added along the tapered line, the output return loss and isolation are improved. The simulation results achieved by full wave analysis based on Finite Element Method (FEM) and the measured results confirm the good performance of the proposed circuit. The return loss of the output ports is better than 15dB and the isolation between the output ports is better than 20dB across the band 6-16GHz. Finally a comparison between ultra-wideband POWER dividers is provided. It is clear that the proposed divider in terms of the aforementioned important features, has a good performance related to the other ultra-wideband POWER dividers.

In this paper, we introduce a proper generalization of that of Hop, an modules, called -Hop, an modules. A right R-module M is said to be -hopfian, if any surjective endomorphism of M has a -small kernel. Some basic characterizations of -modules are proved. We prove that a ring R is semisimple cosingular if and only if every R-module is -hopfian. Further, we prove that the -property is preserved under Morita equiva-lences. Some other properties of -hopfian modules are also obtained with examples.

In this paper, we introduce and study the concept of generalized monoform modules ($G-M$ modules, for short) which is a proper generalization of that of monoform modules. We present some of their examples, properties and characterizations. It is shown that over a commutative ring $R$, the properties monoform, small monoform, $G-M$, compressible, uniform and weakly co-Hopfian are all equivalent. Moreover, we demonstrate that a ring $R$ is an injective semisimple ring iff any $R$-module is $G-M$. Further, we prove a similar theorem to Hilbert's basis theorem for monoform, small monoform and $G-M$ modules.