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Research on Reactive Power Optimization of Offshore Wind Farms Based on Improved Particle Swarm Optimization
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作者 Zhonghao Qian Hanyi Ma +5 位作者 Jun Rao Jun Hu Lichengzi Yu Caoyi Feng Yunxu Qiu Kemo Ding 《Energy Engineering》 EI 2023年第9期2013-2027,共15页
The lack of reactive power in offshore wind farms will affect the voltage stability and power transmission quality of wind farms.To improve the voltage stability and reactive power economy of wind farms,the improved p... The lack of reactive power in offshore wind farms will affect the voltage stability and power transmission quality of wind farms.To improve the voltage stability and reactive power economy of wind farms,the improved particle swarmoptimization is used to optimize the reactive power planning in wind farms.First,the power flow of offshore wind farms is modeled,analyzed and calculated.To improve the global search ability and local optimization ability of particle swarm optimization,the improved particle swarm optimization adopts the adaptive inertia weight and asynchronous learning factor.Taking the minimum active power loss of the offshore wind farms as the objective function,the installation location of the reactive power compensation device is compared according to the node voltage amplitude and the actual engineering needs.Finally,a reactive power optimizationmodel based on Static Var Compensator is established inMATLAB to consider the optimal compensation capacity,network loss,convergence speed and voltage amplitude enhancement effect of SVC.Comparing the compensation methods in several different locations,the compensation scheme with the best reactive power optimization effect is determined.Meanwhile,the optimization results of the standard particle swarm optimization and the improved particle swarm optimization are compared to verify the superiority of the proposed improved algorithm. 展开更多
关键词 Offshore wind farms improved particle swarm optimization reactive power optimization adaptive weight asynchronous learning factor voltage stability
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Chaos quantum particle swarm optimization for reactive power optimization considering voltage stability 被引量:2
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作者 瞿苏寒 马平 蔡兴国 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2010年第3期351-356,共6页
The reactive power optimization considering voltage stability is an effective method to improve voltage stablity margin and decrease network losses,but it is a complex combinatorial optimization problem involving nonl... The reactive power optimization considering voltage stability is an effective method to improve voltage stablity margin and decrease network losses,but it is a complex combinatorial optimization problem involving nonlinear functions having multiple local minima and nonlinear and discontinuous constraints. To deal with the problem,quantum particle swarm optimization (QPSO) is firstly introduced in this paper,and according to QPSO,chaotic quantum particle swarm optimization (CQPSO) is presented,which makes use of the randomness,regularity and ergodicity of chaotic variables to improve the quantum particle swarm optimization algorithm. When the swarm is trapped in local minima,a smaller searching space chaos optimization is used to guide the swarm jumping out the local minima. So it can avoid the premature phenomenon and to trap in a local minima of QPSO. The feasibility and efficiency of the proposed algorithm are verified by the results of calculation and simulation for IEEE 14-buses and IEEE 30-buses systems. 展开更多
关键词 reactive power optimization voltage stability margin quantum particle swarm optimization chaos optimization
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Distribution Network Reactive Power Optimization Based on Ant Colony Optimization and Differential Evolution Algorithm 被引量:1
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作者 Y.L. Zhao Q. Yu C.G. Zhao 《Journal of Energy and Power Engineering》 2011年第6期548-553,共6页
Due to the inherent complexity, traditional ant colony optimization (ACO) algorithm is inadequate and insufficient to the reactive power optimization for distribution network. Therefore, firstly the ACO algorithm is... Due to the inherent complexity, traditional ant colony optimization (ACO) algorithm is inadequate and insufficient to the reactive power optimization for distribution network. Therefore, firstly the ACO algorithm is improved in two aspects: pheromone mutation and re-initialization strategy. Then the thought of differential evolution (DE) algorithm is proposed to be merged into ACO, and by producing new individuals with random deviation disturbance of DE, pheromone quantity left by ants is disturbed appropriately, to search the optimal path, by which the ability of search having been improved. The proposed algorithm is tested on IEEE30-hus system and actual distribution network, and the reactive power optimization results are calculated to verify the feasibility and effectiveness of the improved algorithm. 展开更多
关键词 Ant colony optimization distribution network differential evolution reactive power optimization.
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Research of Rural Power Network Reactive Power Optimization Based on Improved ACOA
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作者 YU Qian ZHAO Yulin WANG Xintao 《Journal of Northeast Agricultural University(English Edition)》 CAS 2010年第3期48-52,共5页
In view of the serious reactive power loss in the rural network, improved ant colony optimization algorithm (ACOA) was used to optimize the reactive power compensation for the rural distribution system. In this stud... In view of the serious reactive power loss in the rural network, improved ant colony optimization algorithm (ACOA) was used to optimize the reactive power compensation for the rural distribution system. In this study, the traditional ACOA was improved in two aspects: one was the local search strategy, and the other was pheromone mutation and re-initialization strategies. The reactive power optimization for a county's distribution network showed that the improved ACOA was practicable. 展开更多
关键词 rural power network reactive power optimization ant colony optimization algorithm local search strategy pheromone mutation and re-initialization strategy
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An Improved Catastrophic Genetic Algorithm and Its Application in Reactive Power Optimization 被引量:4
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作者 Ouyang Sen 《Energy and Power Engineering》 2010年第4期306-312,共7页
This paper presents an Improved Catastrophic Genetic Algorithm (ICGA) for optimal reactive power optimization. Firstly, a new catastrophic operator to enhance the genetic algorithms’ convergence stability is proposed... This paper presents an Improved Catastrophic Genetic Algorithm (ICGA) for optimal reactive power optimization. Firstly, a new catastrophic operator to enhance the genetic algorithms’ convergence stability is proposed. Then, a new probability algorithm of crossover depending on the number of generations, and a new probability algorithm of mutation depending on the fitness value are designed to solving the main conflict of the convergent speed with the global astringency. In these ways, the ICGA can prevent premature convergence and instability of genetic-catastrophic algorithms (GCA). Finally, the ICGA is applied for power system reactive power optimization and evaluated on the IEEE 14-bus power system, and the application results show that the proposed method is suitable for reactive power optimization in power system. 展开更多
关键词 GENETIC ALGORITHMS reactive power optimization CATASTROPHE power System
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Power System Reactive Power Optimization Based on Fuzzy Formulation and Interior Point Filter Algorithm 被引量:1
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作者 Zheng Fan Wei Wang +3 位作者 Tian-jiao Pu Guang-yi Liu Zhi Cai Ning Yang 《Energy and Power Engineering》 2013年第4期693-697,共5页
Considering the soft constraint characteristics of voltage constraints, the Interior-Point Filter Algorithm is applied to solve the formulation of fuzzy model for the power system reactive power optimization with a la... Considering the soft constraint characteristics of voltage constraints, the Interior-Point Filter Algorithm is applied to solve the formulation of fuzzy model for the power system reactive power optimization with a large number of equality and inequality constraints. Based on the primal-dual interior-point algorithm, the algorithm maintains an updating “filter” at each iteration in order to decide whether to admit correction of iteration point which can avoid effectively oscillation due to the conflict between the decrease of objective function and the satisfaction of constraints and ensure the global convergence. Moreover, the “filter” improves computational efficiency because it filters the unnecessary iteration points. The calculation results of a practical power system indicate that the algorithm can effectively deal with the large number of inequality constraints of the fuzzy model of reactive power optimization and satisfy the requirement of online calculation which realizes to decrease the network loss and maintain specified margins of voltage. 展开更多
关键词 power System reactive power optimization FUZZY Filter INTERIOR-POINT Algorithm Online Calculation
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A Genetic Algorithm for Reactive Power Optimizationof Power System
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作者 蔡兴国 刘林强 +1 位作者 柳焯 郭冬梅 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 1998年第2期63-66,共4页
Tis paper presents a genetic algorithm for reactive power optimization of power system in a more effective and rapid manner, and verifies the results with an IEEE 30-bus test system.
关键词 power system GENETIC algorithm(GA) reactive power optimization
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Data-driven Reactive Power Optimization of Distribution Networks via Graph Attention Networks
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作者 Wenlong Liao Dechang Yang +3 位作者 Qi Liu Yixiong Jia Chenxi Wang Zhe Yang 《Journal of Modern Power Systems and Clean Energy》 SCIE EI CSCD 2024年第3期874-885,共12页
Reactive power optimization of distribution networks is traditionally addressed by physical model based methods,which often lead to locally optimal solutions and require heavy online inference time consumption.To impr... Reactive power optimization of distribution networks is traditionally addressed by physical model based methods,which often lead to locally optimal solutions and require heavy online inference time consumption.To improve the quality of the solution and reduce the inference time burden,this paper proposes a new graph attention networks based method to directly map the complex nonlinear relationship between graphs(topology and power loads)and reactive power scheduling schemes of distribution networks,from a data-driven perspective.The graph attention network is tailored specifically to this problem and incorporates several innovative features such as a self-loop in the adjacency matrix,a customized loss function,and the use of max-pooling layers.Additionally,a rulebased strategy is proposed to adjust infeasible solutions that violate constraints.Simulation results on multiple distribution networks demonstrate that the proposed method outperforms other machine learning based methods in terms of the solution quality and robustness to varying load conditions.Moreover,its online inference time is significantly faster than traditional physical model based methods,particularly for large-scale distribution networks. 展开更多
关键词 reactive power optimization graph neural network distribution network machine learning DATA-DRIVEN
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The design and simulation of TCR(thyristor control reactor) reactive power compensation system based on Arene
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作者 王淑芳 张丽 +1 位作者 姜建国 王汝琳 《Journal of Coal Science & Engineering(China)》 2004年第2期101-104,共4页
Inevitably, the question of reactive power compensation was aroused by applied of power electronics. Based on the study of the instantaneous reactive power theory, the designs of TCR(thyristor control reactor) thyrist... Inevitably, the question of reactive power compensation was aroused by applied of power electronics. Based on the study of the instantaneous reactive power theory, the designs of TCR(thyristor control reactor) thyristor control reactor reac- tive power compensation system and TCR single closed loop strategy was pro- posed. In addition, as digital simulation software, Arene was applied to simulate the Jining coal mine No.2 system. The simulation results validate that the design is effective to improve power factor and stabilization of the system. 展开更多
关键词 TCR reactive power compensation instantaneous reactive power
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Optimal Reactive Power Compensation of Distribution Network to Prevent Reactive Power Reverse
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作者 XING Jie CAO Ruilin +1 位作者 QUAN Zhaolong YUAN Zhiqiang 《Journal of Donghua University(English Edition)》 CAS 2021年第3期199-205,共7页
The capacitive reactive power reversal in the urban distribution grid is increasingly prominent at the period of light load in the last years.In severe cases,it will endanger the security and stability of power grid.T... The capacitive reactive power reversal in the urban distribution grid is increasingly prominent at the period of light load in the last years.In severe cases,it will endanger the security and stability of power grid.This paper presents an optimal reactive power compensation method of distribution network to prevent reactive power reverse.Firstly,an integrated reactive power planning(RPP)model with power factor constraints is established.Capacitors and reactors are considered to be installed in the distribution system at the same time.The objective function is the cost minimization of compensation and real power loss with transformers and lines during the planning period.Nodal power factor limits and reactor capacity constraints are new constraints.Then,power factor sensitivity with respect to reactive power is derived.An improved genetic algorithm by power factor sensitivity is used to solve the model.The optimal locations and sizes of reactors and capacitors can avoid reactive power reversal and power factor exceeding the limit.Finally,the effectiveness of the model and algorithm is proven by a typical high-voltage distribution network. 展开更多
关键词 reactive compensation planning high voltage distribution network power actor improved genetic algorithm
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Dynamic reactive power planning method for CSP-PV hybrid power generation system
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作者 ZHANG Hong DONG Hai-ying +2 位作者 CHEN Zhao HUANG Rong DING Kun 《Journal of Measurement Science and Instrumentation》 CAS CSCD 2020年第3期258-266,共9页
Aiming at the faults of some weak nodes in the concentrated solar power-photovoltaic(CSP-PV)hybrid power generation system,it is impossible to restore the transient voltage only relying on the reactive power regulatio... Aiming at the faults of some weak nodes in the concentrated solar power-photovoltaic(CSP-PV)hybrid power generation system,it is impossible to restore the transient voltage only relying on the reactive power regulation capability of the system itself.We propose a dynamic reactive power planning method suitable for CSP-PV hybrid power generation system.The method determines the installation node of the dynamic reactive power compensation device and its compensation capacity based on the reactive power adjustment capability of the system itself.The critical fault node is determined by the transient voltage stability recovery index,and the weak node of the system is initially determined.Based on this,the sensitivity index is used to determine the installation node of the dynamic reactive power compensation device.Dynamic reactive power planning optimization model is established with the lowest investment cost of dynamic reactive power compensation device and the improvement of system transient voltage stability.Furthermore,the component of the reactive power compensation node is optimized by particle swarm optimization based on differential evolution(DE-PSO).The simulation results of the example system show that compared with the dynamic position compensation device installation location optimization method,the proposed method can improve the transient voltage stability of the system under the same reactive power compensation cost. 展开更多
关键词 transient voltage recovery index sensitivity index dynamic reactive power planning optimization particle swarm optimization based on differential evolution(DE-PSO)
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An Adaptive Many-objective Robust Optimization Model of Dynamic Reactive Power Sources for Voltage Stability Enhancement
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作者 Yuan Chi Anqi Tao +2 位作者 Xiaolong Xu Qianggang Wang Niancheng Zhou 《Journal of Modern Power Systems and Clean Energy》 SCIE EI CSCD 2023年第6期1756-1769,共14页
The deployment of dynamic reactive power sourcecan effectively improve the voltage performance after a disturbance for a power system with increasing wind power penetration level and ubiquitous induction loads.To impr... The deployment of dynamic reactive power sourcecan effectively improve the voltage performance after a disturbance for a power system with increasing wind power penetration level and ubiquitous induction loads.To improve the voltage stability of the power system,this paper proposes an adaptive many-objective robust optimization model to deal with thedeployment issue of dynamic reactive power sources.Firstly,two metrics are adopted to assess the voltage stability of the system at two different stages,and one metric is proposed to assess the tie-line reactive power flow.Then,a robustness index isdeveloped to assess the sensitivity of a solution when subjectedto operational uncertainties,using the estimation of acceptablesensitivity region(ASR)and D-vine Copula.Five objectives areoptimized simultaneously:①total equipment investment;②adaptive short-term voltage stability evaluation;③tie-line power flow evaluation;④prioritized steady-state voltage stabilityevaluation;and⑤robustness evaluation.Finally,an anglebased adaptive many-objective evolutionary algorithm(MaOEA)is developed with two improvements designed for the application in a practical engineering problem:①adaptive mutationrate;and②elimination procedure without a requirement for athreshold value.The proposed model is verified on a modifiedNordic 74-bus system and a real-world power system.Numerical results demonstrate the effectiveness and efficiency of theproposed model. 展开更多
关键词 Voltage stability reactive power planning robust many-objective optimization TIE-LINE correlated uncertainty
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Allocation and sizing of reactive power compensators considering PV power and load demand uncertainty using beetle-antenna grey wolf optimization
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作者 Rasha Elazab M.Ser-Alkhatm +1 位作者 Maged A.Abu Adma K.M.Abdel-Latif 《Clean Energy》 EI CSCD 2023年第2期350-362,共13页
Distributed photovoltaic(PV)systems play an important role in supplying many recent microgrids.The absence of reactive power support for these small-scale PV plants increases total microgrid losses and voltage-instabi... Distributed photovoltaic(PV)systems play an important role in supplying many recent microgrids.The absence of reactive power support for these small-scale PV plants increases total microgrid losses and voltage-instability threats.Reactive power compensations(RPCs)should be integrated to enhance both microgrid losses and voltage profiles.RPC planning is a non-linear,complicated problem.In this paper,a combined RPC allocation and sizing algorithm is proposed.The RPC-integrating buses are selected using a new adaptive approach of loss sensitivity analysis.In the sizing process,the uncertainties in PV power and load demand are modelled using proper probability density functions.Three simulation techniques for handling uncertainties are compared to define the accurate and fast accurate method as follows:Monte Carlo simulation(MCS),scenario tree construction and reduction method,and point estimation method(PEM).The load flow equations are solved using the forward-backward sweep method.RPCs are optimally sized using the beetle-antenna-based strategy with grey wolf optimization(BGWO)to overcome the local minima problem that appeared in the other pre-proposed methods.Results have been compared using particle swarm optimization and conventional GWO.The proposed model is verified using the IEEE 33 radial bus system.The expected power loss has been reduced by 22% and 31% using compensation of 26% and 44%,respectively.The results obtained prove that the BGWO optimal power flow and PEM to handle the uncertainty can significantly reduce the computation time with sufficient accuracy.Under the study conditions,PEM reduces the computation time to 4 minutes compared with 4 hours for MCS,with only a 3% error compared with MCS as an uncertainty benchmark method. 展开更多
关键词 distributed PV plants reactive power compensator sizing PV uncertainty beetle-antenna grey wolf optimization
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Two-stage ADMM-based distributed optimal reactive power control method for wind farms considering wake effects 被引量:3
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作者 Zhenming Li Zhao Xu +2 位作者 Yawen Xie Donglian Qi Jianliang Zhang 《Global Energy Interconnection》 EI CAS CSCD 2021年第3期251-260,共10页
Since the connection of small-scale wind farms to distribution networks,power grid voltage stability has been reduced with increasing wind penetration in recent years,owing to the variable reactive power consumption o... Since the connection of small-scale wind farms to distribution networks,power grid voltage stability has been reduced with increasing wind penetration in recent years,owing to the variable reactive power consumption of wind generators.In this study,a two-stage reactive power optimization method based on the alternating direction method of multipliers(ADMM)algorithm is proposed for achieving optimal reactive power dispatch in wind farm-integrated distribution systems.Unlike existing optimal reactive power control methods,the proposed method enables distributed reactive power flow optimization with a two-stage optimization structure.Furthermore,under the partition concept,the consensus protocol is not needed to solve the optimization problems.In this method,the influence of the wake effect of each wind turbine is also considered in the control design.Simulation results for a mid-voltage distribution system based on MATLAB verified the effectiveness of the proposed method. 展开更多
关键词 Two-stage optimization reactive power optimization Grid-connected wind farms Alternating direction method of multipliers(ADMM)
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Analysis on the Application of Reactive Power Compensation Technology in Electrical Automation 被引量:1
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作者 Rumin LIU Lingzhi YANG Haiming LIU 《International Journal of Technology Management》 2015年第2期118-121,共4页
This paper introduces in detail the reactive power compensation technology and its characteristics, to reduce the loss of reactive power compensation technology 1N power distribution system and the electrical automati... This paper introduces in detail the reactive power compensation technology and its characteristics, to reduce the loss of reactive power compensation technology 1N power distribution system and the electrical automation, improve the utilization rate, and realize the control of the voltage amplitude in the system network, voltage stability of power distribution system, has carried on the system analysis to reduce failure of the harmonic current to the power supply system and other functions. And the paper in-depth study on the application of reactive power compensation technology in electrical automation from the reactive compensation technology, substation and distribution line reactive power compensation, power users of reactive power compensation and other aspects. 展开更多
关键词 reactive power compensation electrical automation reactive power harmonic elimination
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Design to conditioning circuits of dynamic compensation of reactive power in the intelligence voltage controller
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作者 Yong-qin WEI,Yin-jing GUO (College of Infor.&Elec.Eng,Shan dong university of science of technology,Qingdao266510,china) 《Journal of Measurement Science and Instrumentation》 CAS 2010年第S1期111-113,共3页
The paper introduces one design idea that making use of SCM to control Real-timely the dynamic compensation of reactive power.Firstly,design one Circuit to Sample the voltage and current,and by these datas we can easi... The paper introduces one design idea that making use of SCM to control Real-timely the dynamic compensation of reactive power.Firstly,design one Circuit to Sample the voltage and current,and by these datas we can easily calculate the power factor,and Voltage controller in the microcontroller to determine whether input the compensation capacitance according to the size of power factor,the paper also analyzes the principle of capacitance compensation and calculation method. Dynamic compensation for the entire process is quick and accurate. 展开更多
关键词 reactive power compensation Real-timely control DYNAMIC power factor
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Microcontroller Control of Reactive Power Compensation for Growing Industrial Loads
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作者 Edwin N. Mbinkar Derek Ajesam Asoh Sulayman Kujabi 《Energy and Power Engineering》 CAS 2022年第9期460-476,共17页
Many industrial installations in developing countries start-up as small factories, without regard for the need of compensation of reactive power, leading to significant financial losses in the long term. By improving ... Many industrial installations in developing countries start-up as small factories, without regard for the need of compensation of reactive power, leading to significant financial losses in the long term. By improving the power factor, the customer can reduce its power demand and potentially increase efficiency of their equipment. A PIC microcontroller is used to switch capacitor banks to compensate for the reactive power. In order to determine the size of the capacitor bank needed, the microcontroller calculates the phase difference between the voltage and the current. The results obtained based on the lagging power factor for three test loads show an improvement in the power factor from 0.52 to 0.96 under different test load conditions. 展开更多
关键词 power Factor compensation Capacitor Bank PIC Microcontroller reactive power
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Fuzzy Decision Method Applied in Action of Reactive Power Compensation Devices in Wind System
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作者 Xueming Li Li Feng +1 位作者 Yi Tang Yonghua Chen 《Journal of Power and Energy Engineering》 2014年第4期280-287,共8页
Frequent occurrence of large-scale cascading trip-off of wind turbine raises the concern about the decision process of ordered control of reactive power compensation devices. The theory of fuzzy multi-attribute decisi... Frequent occurrence of large-scale cascading trip-off of wind turbine raises the concern about the decision process of ordered control of reactive power compensation devices. The theory of fuzzy multi-attribute decision making is adopted to ascertain the action sequence of reactive power compensation devices. First, a set of evaluation indexes including control sensitivity, regulation margin, response time, response level and cost is set up, and fuzziness of the proposed qualitative indexes is introduced to make them comparable to the proposed quantitative indexes. Then a method to calculate fuzzy weight of each index is put forward for evaluating relative importance of the proposed indexes. Finally, the action sequence of reactive power compensation devices is determined through the theory of fuzzy compromise decision making. The case study shows that the proposed method is effective to obtain the action sequence of reactive power compensation device which correspond to experience. 展开更多
关键词 WIND power SYSTEM reactive power compensation Device ORDERED Control Fuzzy MULTI-ATTRIBUTE DECISION Making Evaluation Index
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Reactive Power in One-phase Circuits with Periodical Voltages - Reactive Power Compensation
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作者 S. Slabosz 《Journal of Energy and Power Engineering》 2010年第9期60-64,共5页
The article states about reactive power compensation methods for circuits with non-sinusoidal voltages. An basic introduction to reactive power theory has been given, together with the optimal capacitance selection th... The article states about reactive power compensation methods for circuits with non-sinusoidal voltages. An basic introduction to reactive power theory has been given, together with the optimal capacitance selection theory. There have been presented selected theories application in order to compensate the reactive power in one-phase circuits. The measurement results before the compensation have been discussed and measurement results after compensation of an actual object supplied from an non-sinusoidal voltage source were presented. The algorithms of optimal capacity selection were given, which connected in parallel to the circuit with inductive character will cause current root-mean-square value minimization. The measurement results after applying the reactive power minimization algorithm have shown improvement in compensation of strongly nonlinear receivers supplied with distorted signals. 展开更多
关键词 Electrical theoretical electric measurements reactive power power compensation
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A New Filter Collaborative State Transition Algorithm for Two-Objective Dynamic Reactive Power Optimization 被引量:3
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作者 Hongli Zhang Cong Wang Wenhui Fan 《Tsinghua Science and Technology》 SCIE EI CAS CSCD 2019年第1期30-43,共14页
Dynamic Reactive Power Optimization(DRPO) is a large-scale, multi-period, and strongly coupled nonlinear mixed-integer programming problem that is difficult to solve directly. First, to handle discrete variables and s... Dynamic Reactive Power Optimization(DRPO) is a large-scale, multi-period, and strongly coupled nonlinear mixed-integer programming problem that is difficult to solve directly. First, to handle discrete variables and switching operation constraints, DRPO is formulated as a nonlinear constrained two-objective optimization problem in this paper. The first objective is to minimize the real power loss and the Total Voltage Deviations(TVDs), and the second objective is to minimize incremental system loss. Then a Filter Collaborative State Transition Algorithm(FCSTA) is presented for solving DRPO problems. Two populations corresponding to two different objectives are employed. Moreover, the filter technique is utilized to deal with constraints. Finally, the effectiveness of the proposed method is demonstrated through the results obtained for a 24-hour test on Ward & Hale 6 bus, IEEE 14 bus, and IEEE 30 bus test power systems. To substantiate the effectiveness of the proposed algorithms, the obtained results are compared with different approaches in the literature. 展开更多
关键词 dynamic reactive power optimization filter collaborative state transition algorithm Ward & Hale 6 bus IEEE 14 bus IEEE 30 bus
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