COUPLED FIXED POINTS OF SKEW INCREASINGOPERATORS AND APPLICATIONS

In this paper, the skew-increasing operators and their coupled fixed points are defined. It is proved that the existence of coupled fixed points and fixed point theorem for skew-increasing operators, and the iterative formula are given.

Double coupled fixed point for multi-valued mixed increasing operators in ordered Banach spaces

In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered Banach spaces are also given. These results extend and generalize some results of Huang and Fang.

FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS

In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.

MINIMAL AND MAXIMAL FIXED POINT THEOREMS AND ITERATIVE TECHNIQUE FOR NONLINEAR OPERATORS IN PRODUCT SPACES

In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikantham[21 and the results obtained by Lan in [4], and [6].

Common coupled fixed point theorem for two pairs compatible and sub-sequentially continuous mapping

This study establishes a common coupled fixed point for two pairs of compatible and sequentially continuous mappings in the intuitionistic fuzzy metric space that satisfy theφ-contractive conditions.Many basic definitions and theorems have been used from some recent scientific papers about the binary operator,t-norm,t-conorm,intuitionistic fuzzy metric space,and compatible mapping for reaching to the paper’s purpose.

GNN Representation Learning and Multi-Objective Variable Neighborhood Search Algorithm for Wind Farm Layout Optimization

With the increasing demand for electrical services,wind farm layout optimization has been one of the biggest challenges that we have to deal with.Despite the promising performance of the heuristic algorithm on the route network design problem,the expressive capability and search performance of the algorithm on multi-objective problems remain unexplored.In this paper,the wind farm layout optimization problem is defined.Then,a multi-objective algorithm based on Graph Neural Network(GNN)and Variable Neighborhood Search(VNS)algorithm is proposed.GNN provides the basis representations for the following search algorithm so that the expressiveness and search accuracy of the algorithm can be improved.The multi-objective VNS algorithm is put forward by combining it with the multi-objective optimization algorithm to solve the problem with multiple objectives.The proposed algorithm is applied to the 18-node simulation example to evaluate the feasibility and practicality of the developed optimization strategy.The experiment on the simulation example shows that the proposed algorithm yields a reduction of 6.1% in Point of Common Coupling(PCC)over the current state-of-the-art algorithm,which means that the proposed algorithm designs a layout that improves the quality of the power supply by 6.1%at the same cost.The ablation experiments show that the proposed algorithm improves the power quality by more than 8.6% and 7.8% compared to both the original VNS algorithm and the multi-objective VNS algorithm.

Digitalized Accurate Modeling of SPCB with Multi-spiral Surface Based on CPC Algorithm

The main methods of the existing multi-spiral surface geometry modeling include spatial analytic geometry algorithms, graphical method, interpolation and approximation algorithms. However, there are some shortcomings in these modeling methods, such as large amount of calculation, complex process, visible errors, and so on. The above methods have, to some extent, restricted the design and manufacture of the premium and high-precision products with spiral surface considerably. This paper introduces the concepts of the spatially parallel coupling with multi-spiral surface and spatially parallel coupling body. The typical geometry and topological features of each spiral surface forming the multi-spiral surface body are determined, by using the extraction principle of datum point cluster, the algorithm of coupling point cluster by removing singular point, and the ＂spatially parallel coupling＂ principle based on the non-uniform B-spline for each spiral surface. The orientation and quantitative relationships of datum point cluster and coupling point cluster in Euclidean space are determined accurately and in digital description and expression, coupling coalescence of the surfaces with multi-coupling point clusters under the Pro/E environment. The digitally accurate modeling of spatially parallel coupling body with multi-spiral surface is realized. The smooth and fairing processing is done to the three-blade end-milling cutter＇s end section area by applying the principle of spatially parallel coupling with multi-spiral surface, and the alternative entity model is processed in the four axis machining center after the end mill is disposed. And the algorithm is verified and then applied effectively to the transition area among the multi-spiral surface. The proposed model and algorithms may be used in design and manufacture of the multi-spiral surface body products, as well as in solving essentially the problems of considerable modeling errors in computer graphics and engineering in multi-spiral surface＇s connection available with approximate methods or graphical methods.

Control of Distributed Generation Using Non-Sinusoidal Pulse Width Modulation

The islanded mode is one of the connection modes of the grid distributed generation resources.In this study,a distributed generation resource is connected to linear and nonlinear loads via a three-phase inverter where a control method needing no current sensors or compensator elements is applied to the distribute generation system in the islanded mode.This control method has two main loops in each phase.The first loop controls the voltage control loops that adjust the three-phase point of common coupling,the amplitude of the non-sinusoidal reference waveform and the near-state pulse width modulation(NSPWM)method.The next loop compensates the harmonic compensator loop that calculates the voltage harmonics of the point of common coupling in each phase,and injects them to compensate the non-sinusoidal reference waveforms of each phase.The simulation results in MATLAB/SIMULINK show that this method can generate balanced threephase sinusoidal voltage with an acceptable total harmonic distortion(THD)at the joint connection point.

Determining Potential Passive Islanding Detection Indicators for Single-point Single Inverter,Single-point Multi-inverter and Multi-point Multi-inverter Scenarios

Distributed Generation(DG)sources,predominantly renewable energy-based,such as solar photovoltaic and wind energy sources,have significantly penetrated into power system networks.This high penetration of DG sources may lead to the formation of unintentional islands,which is hazardous to both the equipment and personnel,if sustained.In this paper,46 passive parameters are considered to find out which candidate(s)are promising for detecting sustained unintentional islands and avoid false DG trips.These 46 parameters are derived from point of common coupling(PCC)voltage,DG output current,frequency,power factor angle,active and reactive powers.All these parameters are tested on standard IEEE 13 and 34 bus distribution networks,integrated with inverter-interfaced DGs at different locations for different penetration levels in the MATLAB/SIMULINK environment.The parameters are tested for different islanding events(comprising of various local loads,such as conventional parallel RLC resonant load,R,RC,and RL loads)and for different non-islanding events.The parameters are then ranked accordingly by a suitable averaging approach based performance ranking technique.From this analysis,the best candidates are obtained for detecting inverter DG islands at single-point(or single PCC)locations and multi-point(or multiple PCCs)locations.Multiple best passive candidates are obtained for different island scenarios from which a set of promising islanding detection indicators are proposed.

Integrated Optimal Siting and Sizing for VSCHVDC-link-based Offshore Wind Farms and Shunt Capacitors

It is economic and secure to determine the optimal siting and sizing of the offshore wind farms(OWFs)integrated into the AC system through voltage-source converter high-voltage direct current(VSC-HVDC)links.In this paper,an integrated planning model for the VSC-HVDC-link-based OWFs and the capacitors is proposed,where a decomposition technique is presented to solve the proposed mixed-integer nonlinear programming(MINLP)problem and obtain the optimal solution.This model can optimize the siting and sizing of the OWFs to improve the voltage profile and reduce the adverse influence of the reactive power of the OWFs.With the proposed planning model,the total investment costs,operation costs and maintenance costs of the OWFs,VSC-HVDC links,and the capacitors can be minimized.Simulations on the modified IEEE 118-bus system show that the proposed integrated planning model can provide more economic scheme than the independent planning scheme,in which the capacitors are planned after the OWFs.Besides,a series of sensitivity analysis on certain equipment costs are studied to obtain the regular pattern for sizing VSC stations.

Study of Improved Load Sharing Methodologies for Distributed Generation Units Connected in a Microgrid

In this paper,an improved load sharing strategy is proposed for distributed generation units(DGs)connected in a microgrid.Conventional frequency and voltage droop control result in unacceptable active and reactive power sharing.The proposed method formulates a suitable algorithm for load sharing in the islanded microgrid.The feeder power loss and the line impedance voltage drops are minimized so as to regulate the voltage at the point of common coupling(PCC)at its nominal value.The desired DG output voltages are calculated and a linear relationship is obtained between the shared active and reactive powers and the DG output voltages.A master DG controller sets the frequency which is followed by other DG units.The reference powers for the DG units are adjusted so as to maintain the rated PCC voltage.The proposed strategy is verified taking into account the DG ratings,unequal line impedance drops,feeder losses,change in system impedance and effect of DG local loads and formulates an improved power sharing strategy that also facilitates PCC voltage regulation under variable loading conditions.Simulation and experimental results are presented to verify the effectiveness of the proposed method.

Series transformer based diode-bridge-type solid state fault current limiter

We propose a novel series transformer based diode-bridge-type solid state fault current limiter （SSFCL）. To control the fault current, a series RLC branch is connected to the secondary side of an isolation series transformer. Based on this RLC branch, two current limiting modes are created. In the first mode, R and C are bypassed via a paralleled power electronic switch （insulated-gate bipolar transistor, IGBT） and L remains connected to the secondary side of the transformer as a DC reactor. In the second mode, the series reactor impedance is not enough to limit the fault current. In this case, the fault current can be con- trolled by selecting a proper on-off duration of the parallel IGBT, across the series damping resistor （R） and capacitor, which inserts high impedance into the line to limit the fault current. Then, by controlling the magnitude of the DC reactor current, the fault current is reduced and the voltage of the point of common coupling （PCC） is kept at an acceptable level. In addition, in the new SSFCL, the series RC branch, connected in parallel with the IGBT, serves as a snubber circuit for decreasing the transient recovery voltage （TRV） of the IGBT during on-off states. Therefore, the power quality indices can be improved. The measure- ment results of a built prototype are presented to support the simulation and theoretical studies. The proposed SSFCL can limit the fault current without any delay and successfully smooth the fault current waveform.

Enhanced AC Fault Ride-through Control for MMC-integrated System Based on Active PCC Voltage Drop

When a renewable energy station(RES)connects to the rectifier station(RS)of a modular multilevel converterbased high-voltage direct current(MMC-HVDC)system,the voltage at the point of common coupling(PCC)is determined by RS control methods.For example,RS control may become saturated under fault,and causes the RS to change from an equivalent voltage source to an equivalent current source,making fault analysis more complicated.In addition,the grid code of the fault ride-through(FRT)requires the RES to output current according to its terminal voltage.This changes the fault point voltage and leads to RES voltage regulation and current redistribution,resulting in fault response interactions.To address these issues,this study describes how an MMC-integrated system has five operation modes and three common characteristics under the duration of the fault.The study also reveals several instances of RS performance degradation such as AC voltage loop saturation,and shows that RS power reversal can be significantly improved.An enhanced AC FRT control method is proposed to achieve controllable PCC voltage and continuous power transmission by actively reducing the PCC voltage amplitude.The robustness of the method is theoretically proven under parameter variation and operation mode switching.Finally,the feasibility of the proposed method is verified through MATLAB/Simulink results.