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Enhancing Autonomy Capability in Regional Power Grids:A Strategic Planning Approach with Multiple Autonomous Evaluation Indexes
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作者 Jie Ma Tong Zhao +8 位作者 Yuanzhao Hao Wenwen Qin Haozheng Yu Mingxuan Du Yuanhong Liu Liang Zhang Shixia Mu Cuiping Li Junhui Li 《Energy Engineering》 EI 2024年第9期2449-2477,共29页
After the integration of large-scale DistributedGeneration(DG)into the distribution network,the randomness and volatility of its output result in a reduction of spatiotemporal alignment between power generation and de... After the integration of large-scale DistributedGeneration(DG)into the distribution network,the randomness and volatility of its output result in a reduction of spatiotemporal alignment between power generation and demand in the distribution network,exacerbating the phenomenon of wind and solar power wastage.As a novel power system model,the fundamental concept of Regional Autonomous Power Grids(RAPGs)is to achieve localized management and energy autonomy,thereby facilitating the effective consumption of DGs.Therefore,this paper proposes a distributed resource planning strategy that enhances the autonomy capabilities of regional power grids by considering multiple evaluation indexes for autonomy.First,a regional Energy Storage(ES)configuration strategy is proposed.This strategy can select a suitable reference value for the upper limit of ES configuration based on the regional load andDGoutput to maximize the elimination of source load deviations in the region as the upper limit constraint of ES capacity.Then,a control strategy for regional ES is proposed,the charging and discharging reference line of ES is set,and multiple autonomy and economic indexes are used as objective functions to select different proportions of ES to control the distributed resources of the regional power grid and establish evaluation indexes of the internal regional generation and load power ratio,the proportion of power supply matching hours,new energy consumption rate and tie line power imbalance outside the region to evaluate changes in the regional autonomy capabilities.The final simulation results showthat in the real regional grid example,the planning method in the planning year in the region of the overall power supply matching hour ratio and new energy consumption rate increased by 3.9%and 4.8%on average,and the power imbalance of the tie line decreased by 7.8%on average.The proposed planning approach enables the maximization of regional autonomy while effectively smoothing the fluctuation of power exchange between the regional grid and the higher-level grid.This presents a rational and effective planning solution for the regional grid,facilitating the coordinated development between the region and the distribution network. 展开更多
关键词 Regional autonomous power grid distributed generation distributed energy storage regional planning strategy evaluation index
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Optimizing Power Flow in Northern Cameroon’s Interconnected Grid: Challenges and Solutions
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作者 Jean Ndoumbe Ivan Basile Kabeina +1 位作者 Michael Koumbou Piembe Martin Ndjock 《Journal of Power and Energy Engineering》 2024年第9期63-83,共21页
This paper presents an analysis of the power flow within the Northern Interconnected Grid of Cameroon. The Newton-Raphson method has been performed, known for its accuracy, under MATLAB software, to model and solve co... This paper presents an analysis of the power flow within the Northern Interconnected Grid of Cameroon. The Newton-Raphson method has been performed, known for its accuracy, under MATLAB software, to model and solve complex power flow equations. This study simulates a series of outage scenarios to evaluate the responsiveness of the grid. The results obtained underline the crucial importance of reactive power management and highlight the urgent need to consolidate the grid infrastructure of North Cameroon. To increase grid resilience and stability, the paper recommends the strategic integration of renewables and the development of interconnections with other power grids. These measures are presented as viable solutions to meet current and future energy distribution challenges, ensuring a reliable and sustainable power supply for Cameroon. 展开更多
关键词 power flow Northern Interconnected grid NEWTON-RAPHSON MATLAB grid stability
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Practice and Thinking on Current Planning Environmental Impact Assessment of Transmission and Transformation Power Grid in Jiangsu Province 被引量:4
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作者 Wang Sheng Wang Huimin +2 位作者 Zhu Fahua Qiu Lei Liu Gang 《Meteorological and Environmental Research》 CAS 2014年第1期44-48,共5页
The planning environmental impact assessment (EIA) of transmission and transformation power grid at levels of 500 and 220 kV had been finished completely in the 13 municipalities of Jiangsu Province by the end of 20... The planning environmental impact assessment (EIA) of transmission and transformation power grid at levels of 500 and 220 kV had been finished completely in the 13 municipalities of Jiangsu Province by the end of 2012, which played important roles in guiding and planning the following transmission and transformation projects in environmental protection. In this paper, through the detail analysis on the objective and significance of the planning EIA of transmission and transformation power grid, legal basis and planning EIA practices, some suggestions and thinking about the planning EIA of transmission and transformation power grid were put forward. 展开更多
关键词 Jiangsu Province power grid planning environmental impact assessment Current status China
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Analysis and management strategies for the low voltage problems of rural power grid based on the distribution network flow calculation method 被引量:2
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作者 陈曦 何俊宏 HE Yu-cheng 《Journal of Chongqing University》 CAS 2015年第4期134-140,共7页
For a long time, because of the lack of investment capital and enough attentions, the overall constructions of rural power grid were far behind than the urban power grid in Chongqing Jiangbei Power Company. The low vo... For a long time, because of the lack of investment capital and enough attentions, the overall constructions of rural power grid were far behind than the urban power grid in Chongqing Jiangbei Power Company. The low voltage problems were highlighted in the rural power grid due to the characteristics of rural power grid. Using the distribution network flow calculation method, we evaluated the low voltage problems of the rural power grid which belongs to Chongqing Jiangbei Power Company. In addition, we collected the data of distribution transformers in electricity consumption peak period. Some practical management strategies were proposed by the analysis and evaluation of potential and appeared low voltage problems. 展开更多
关键词 RURAL power grid flow CALCULATION method low VOLTAGE PROBLEM management strategy
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Research and application of a power-flow-calculation method in multiterminal VSC-HVDC power grid 被引量:8
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作者 Linlin Wu Xiaowei Fan +4 位作者 Man Xu Zhendong Li Xiao Wang Xiaofei Zhang Haiwang Jin 《Global Energy Interconnection》 2019年第1期37-44,共8页
For demonstrating a multiterminal voltage-source converter(VSC)-based high-voltage DC(HVDC)(VSCHVDC) project, this study puts forward a technical route for calculating the power flow in a 500-kV VSC-HVDC power grid in... For demonstrating a multiterminal voltage-source converter(VSC)-based high-voltage DC(HVDC)(VSCHVDC) project, this study puts forward a technical route for calculating the power flow in a 500-kV VSC-HVDC power grid in comparison with that of an AC power grid. The Jacobian matrix used in the power-flow calculation was deduced through methods such as Newton–Laphson iteration and Taylor series expansion. Further, the operation effect of powerflow calculation on a true bipolar VSC-HVDC power grid was analyzed briefly. The elements of the Jacobian matrix corresponding to VSC were studied under the mode of droop control and the control strategy of VSC-HVDC power grid was analyzed in detail. The power-flow calculation model for VSC-HVDC power grid of the master–slave control mode was simplified using the PQ decomposition method of the power-flow calculation of an AC power grid. Moreover, a four-terminal model of the Zhangbei VSC-HVDC demonstration project was established and tested on MATLAB. The simulation results under two kinds of operating conditions were analyzed and compared to the results of BPA; the deviation between the power-flow results was studied. The results show that the proposed calculation method can provide a feasible support for calculating the power flow in VSC-HVDC grids. 展开更多
关键词 VSC-HVDC grids power-flow CALCULATION JACOBIAN MATRIX Droop control
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Multi-stage power source and grid coordination planning method considering grid uniformity 被引量:1
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作者 Zhiqi Li Xueshan Han +1 位作者 Ming Yang Yiran Ma 《Global Energy Interconnection》 2020年第4期303-312,I0001,共11页
Given the increasing uncertainties in power supply and load,this paper proposes the concept of power source and grid coordination uniformity planning.In this approach,the standard deviation of the transmission line lo... Given the increasing uncertainties in power supply and load,this paper proposes the concept of power source and grid coordination uniformity planning.In this approach,the standard deviation of the transmission line load rate is considered as the uniformity evaluation index for power source and grid planning.A multi-stage and multi-objective optimization model of the power source and grid expansion planning is established to minimize the comprehensive cost of the entire planning cycle.In this study,the improved particle swarm optimization algorithm and genetic algorithm are combined to solve the model,thus improving the efficiency and accuracy of the solution.The analysis of a simple IEEE Garver’s 6-node system shows that the model and solution method are effective and feasible.Moreover,they are suitable for the coordinated planning of the power source and grid under a diversified nature of power supply and load. 展开更多
关键词 power source and grid coordination grid uniformity grid expansion planning Evaluation index of uniformity
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The axisymmetric long-wave interfacial stability of core-annular flow of power-law fluid with surfactant 被引量:1
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作者 Xue-Wei Sun Jie Peng Ke-Qin Zhu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第1期24-33,共10页
The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. ... The long wave stability of core-annular flow of power-law fluids with an axial pressure gradient is investigated at low Reynolds number. The interface between the two fluids is populated with an insoluble surfactant. The analytic solution for the growth rate of perturbation is obtained with long wave approximation. We are mainly concerned with the effects of shear-thinning/thickening property and interfacial surfactant on the flow stability. The results show that the influence of shear-thinning/thickening property accounts to the change of the capillary number. For a clean interface, the shear-thinning property enhances the capillary instability when the interface is close to the pipe wall. The converse is true when the interface is close to the pipe centerline. For shear-thickening fluids, the situation is reversed. When the interface is close to the pipe centerline, the capillary instability can be restrained due to the influence of surfactant. A parameter set can be found under which the flow is linearly stable. 展开更多
关键词 Core-annular flow. power-law fluid. Interfacial surfactant Long-wave stability
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Voltage Stability Constrained Optimal Power Flow Using NSGA-II
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作者 Sandeep Panuganti Preetha Roselyn John +1 位作者 Durairaj Devraj Subhransu Sekhar Dash 《Computational Water, Energy, and Environmental Engineering》 2013年第1期1-8,共8页
Voltage stability has become an important issue in planning and operation of many power systems. This work includes multi-objective evolutionary algorithm techniques such as Genetic Algorithm (GA) and Non-dominated So... Voltage stability has become an important issue in planning and operation of many power systems. This work includes multi-objective evolutionary algorithm techniques such as Genetic Algorithm (GA) and Non-dominated Sorting Genetic Algorithm II (NSGA II) approach for solving Voltage Stability Constrained-Optimal Power Flow (VSC-OPF). Base case generator power output, voltage magnitude of generator buses are taken as the control variables and maximum L-index of load buses is used to specify the voltage stability level of the system. Multi-Objective OPF, formulated as a multi-objective mixed integer nonlinear optimization problem, minimizes fuel cost and minimizes emission of gases, as well as improvement of voltage profile in the system. NSGA-II based OPF-case 1-Two objective-Min Fuel cost and Voltage stability index;case 2-Three objective-Min Fuel cost, Min Emission cost and Voltage stability index. The above method is tested on standard IEEE 30-bus test system and simulation results are done for base case and the two severe contingency cases and also on loaded conditions. 展开更多
关键词 VOLTAGE stability Optimal power flow Multi Objective EVOLUTIONARY ALGORITHMS
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Research on Safety and Stability of Regional Power Grids to the Year 2020
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作者 Zhou Qinyong Zhao Liang +1 位作者 Guo Qiang Jin Wen 《Electricity》 2005年第3期26-31,共6页
The safety and stability study on Northeast, North, East, Northwest and Central China power grids had been carried out, which provided technical supports to planning design of regional power grids. By analyzing safety... The safety and stability study on Northeast, North, East, Northwest and Central China power grids had been carried out, which provided technical supports to planning design of regional power grids. By analyzing safety and stability under severe faults in regional power grids, revealed weaknesses on power grid configurations and measures for preventing from loss of stability were presented. In comparison of various schemes of power system safety and stability among parts of power grids, more than two recommended schemes can be chosen as reference in planning design for regional power grids. Considering the safety and stability control measures necessary for each power grids, it is believed the trunk networks of all power grids can fulfill the third criteria of Guideline for Power System Safety and Stability, while the weakness and predominated hydropower may deteriorate safety and stability of power grids. The power grid shall be regulated in line with the variation of boundary conditions. 展开更多
关键词 regional power grid safe and stable power grid planning power system
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Planning Study on National Power Grid Interconnection Centered on Three Gorges Hydropower Station
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作者 Zhou Xiaoqian(President, China Power Crid Construction Corporation) 《Electricity》 1999年第2期2-3,共2页
关键词 planning Study on National power grid Interconnection Centered on Three Gorges Hydropower Station grid
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Influence of Control Modes of Grid-Connected Solar Photovoltaic Generation on Grid Power Flow
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作者 Zakaria Al-Omari 《Engineering(科研)》 2014年第13期914-922,共9页
Integration of Solar Photovoltaic (PV) generation into an existing distribution system has many impacts on the system, with the power flow being one of the major issues. This impact is not generic for any network, but... Integration of Solar Photovoltaic (PV) generation into an existing distribution system has many impacts on the system, with the power flow being one of the major issues. This impact is not generic for any network, but it may manifest itself either positively or negatively, depending on the grid configuration, interface control modes, operation mode, and load profile. Grid-connected PV systems have three control options of the local voltage controller of the interface DC-AC converter. These control modes are Power Factor control, voltage control, and Droop Voltage control. This paper aims at evaluating and comparing the impacts of those control modes on the grid power flow. A set of evaluation criteria and indices is defined and mathematically formulated. Based on the requirements of the used program (Power Factory Dig Silent V14.1.3), a computation plan (algorithm) has been proposed. The algorithm has been applied to a typical weak network and a wide range of simulations has been carried out. Simulation results have been thoroughly discussed and important findings have been concluded. 展开更多
关键词 grid-CONNECTED PV Control MODES power flow power FACTORY DIG SILENT Software
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Connecting Wind Turbine Generator to Distribution Power Grid--A Preload Flow Calculation Stage
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作者 Agbetuyi Ayoade Felix Awosope Cladius Ojo Aremu Awelewa Ayokunle Ajibola Adoghe Uwakhonye Anthony Odigwe Ani Ishioma Samuel Adekunle Isaac 《Journal of Energy and Power Engineering》 2014年第10期1811-1815,共5页
A distribution grid is generally characterized by a high R/X (resistance/reactance) ratio and it is radial in nature. By design, a distribution grid system is not an active network, and it is normally designed in su... A distribution grid is generally characterized by a high R/X (resistance/reactance) ratio and it is radial in nature. By design, a distribution grid system is not an active network, and it is normally designed in such a way that power flows from transmission system via distribution system to consumers. But in a situation when wind turbines are connected to the distribution grid, the power source will change from one source to two sources, in this case, network is said to be active. This may probably have an impact on the distribution grid to whenever the wind turbine is connected. The best way to know the impact of wind turbine on the distribution grid in question is by carrying out load flow analysis on that system with and without the connection of wind turbines. Two major fundamental calculations: the steady-state voltage variation at the PCC (point of common coupling) and the calculation of short-circuit power of the grid system at the POC (point of connection) are necessary before carrying out the load flow study on the distribution grid. This paper, therefore, considers these pre-load flow calculations that are necessary before carrying out load flow study on the test distribution grid. These calculations are carded out on a test distribution system. 展开更多
关键词 Distribution grid power quality wind turbine generator load flow.
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Research on Grid Planning of Dual Power Distribution Network Based on Parallel Ant Colony Optimization Algorithm
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作者 Shuaixiang Wang 《Journal of Electronic Research and Application》 2023年第1期32-41,共10页
A distribution network plays an extremely important role in the safe and efficient operation of a power grid.As the core part of a power grid’s operation,a distribution network will have a significant impact on the s... A distribution network plays an extremely important role in the safe and efficient operation of a power grid.As the core part of a power grid’s operation,a distribution network will have a significant impact on the safety and reliability of residential electricity consumption.it is necessary to actively plan and modify the distribution network’s structure in the power grid,improve the quality of the distribution network,and optimize the planning of the distribution network,so that the network can be fully utilized to meet the needs of electricity consumption.In this paper,a distribution network grid planning algorithm based on the reliability of electricity consumption was completed using ant colony algorithm.For the distribution network structure planning of dual power sources,the parallel ant colony algorithm was used to prove that the premise of parallelism is the interactive process of ant colonies,and the dual power distribution network structure model is established based on the principle of the lowest cost.The artificial ants in the algorithm were compared with real ants in nature,and the basic steps and working principle of the ant colony optimization algorithm was studied with the help of the travelling salesman problem(TSP).Then,the limitations of the ant colony algorithm were analyzed,and an improvement strategy was proposed by using python for digital simulation.The results demonstrated the reliability of model-building and algorithm improvement. 展开更多
关键词 Parallel ant colony optimization algorithm Dual power sources Distribution network grid planning
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Development and Prospect of China Power Grids 被引量:1
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作者 赵遵廉 《Electricity》 2004年第1期6-11,共6页
In this paper the growing process of China power grid from formation of local power grids to nationwide interconnection is reviewed. The scale and structure of power grid construction in the near future, especially th... In this paper the growing process of China power grid from formation of local power grids to nationwide interconnection is reviewed. The scale and structure of power grid construction in the near future, especially the planning on sending power from west to east, North-South supplementation and nationwide interconnection are introduced. In addition, the technologies to be extended in future grid development are briefed, such as HVDC, FACTS and compact transmission line, etc. 展开更多
关键词 power grid planning in terconnection transmission technology
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A multi-objective gravitational search algorithm based approach of power system stability enhancement with UPFC 被引量:6
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作者 Ajami Ali Armaghan Mehdi 《Journal of Central South University》 SCIE EI CAS 2013年第6期1536-1544,共9页
On the basis of the theoretical analysis of a single-machine infinite-bus (SMIB), using the modified linearized Phil- lips-Heffron model installed with unified power flow controller (UPFC), the potential of the UP... On the basis of the theoretical analysis of a single-machine infinite-bus (SMIB), using the modified linearized Phil- lips-Heffron model installed with unified power flow controller (UPFC), the potential of the UPFC supplementary controller to enhance the dynamic stability of a power system is evaluated by measuring the electromechanical controllability through singular value decomposition (SVD) analysis. This controller is tuned to simultaneously shift the undamped electromeehanical modes to a prescribed zone in the s-plane. The problem of robust UPFC based damping controller is formulated as an optimization problem according to the eigenvalue-based multi-objective function comprising the damping factor, and the damping ratio of the undamped electromechanical modes to be solved using gravitational search algorithm (GSA) that has a strong ability to find the most optimistic results. The different loading conditions are simulated on a SMIB system and the rotor speed deviation, internal voltage deviation, DC voltage deviation and electrical power deviation responses are studied with the effect of this flexible AC transmission systems (FACTS) controller. The results reveal that the tuned GSA based UPFC controller using the proposed multi-objective function has an excellent capability in damping power system with low frequency oscillations and greatly enhances the dynamic stability of the power systems. 展开更多
关键词 unified power flow controller gravitational search algorithm power system stability
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Practice and Thinking of Plan Environmental Impact Assessment of Power Transmission and Transformation Grid in Nanjing 被引量:1
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作者 Fei QI 《Meteorological and Environmental Research》 CAS 2020年第3期86-88,92,共4页
At present,the plan environmental impact assessment of power transmission and transformation grid is relatively mature. How to further improve the quality of plan environmental impact assessment of power grid during t... At present,the plan environmental impact assessment of power transmission and transformation grid is relatively mature. How to further improve the quality of plan environmental impact assessment of power grid during the "14^(th) Five-Year Plan" period is very important. In this paper,the plan environmental impact assessment of power grid in the Development Plan for Power Grid in Nanjing during the "13^(th) Five-Year Plan" Period is studied to further discuss the ideas,evaluation system and content framework of plan environmental impact assessment of power grid. 展开更多
关键词 power grid Plan environmental impact assessment PRACTICE THINKING
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The Continuation Power Flow Considering Both Generator Excitation Current Limits and Armature Current Limits 被引量:4
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作者 ZHAO Jinquan QIAN Tianneng 《中国电机工程学报》 EI CSCD 北大核心 2012年第22期I0016-I0016,10,共1页
在传统连续潮流算法中,发电机无功限制采用定上、下限值来处理,随着有功负荷增加,无功限值通常不变,得到的电压稳定裕度偏大。根据同步发电机的无功出力特性,提出同时计及发电机励磁电流约束和电枢电流约束的连续潮流模型和方法。当相... 在传统连续潮流算法中,发电机无功限制采用定上、下限值来处理,随着有功负荷增加,无功限值通常不变,得到的电压稳定裕度偏大。根据同步发电机的无功出力特性,提出同时计及发电机励磁电流约束和电枢电流约束的连续潮流模型和方法。当相应参数越限时,将发电机节点转换为励磁恒定模型或者电枢电流恒定模型进行计算。所提PV、PEq、PIa节点类型双向转换逻辑可在潮流迭代内进行发电机限制模式的转换,模拟实际系统无功能力的变化。分岔点类型识别模块可以识别崩溃点类型及关键约束。通过新英格兰39节点算例的仿真,证明所提算法是有效的。 展开更多
关键词 发电机励磁 连续潮流 电枢电流 电流限制 功率限制 负荷裕度 稳定评估 CPF
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Neuro-Fuzzy Based Interline Power Flow Controller for Real Time Power Flow Control in Multiline Power System 被引量:3
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作者 A. Saraswathi S. Sutha 《Circuits and Systems》 2016年第9期2807-2820,共14页
This article investigates the power quality enhancement in power system using one of the most famous series converter based FACTS controller like IPFC (Interline Power Flow Controller) in Power Injection Model (PIM). ... This article investigates the power quality enhancement in power system using one of the most famous series converter based FACTS controller like IPFC (Interline Power Flow Controller) in Power Injection Model (PIM). The parameters of PIM are derived with help of the Newton-Raphson power flow algorithm. In general, a sample test power system without FACTs devices has generated more reactive power, decreased real power, more harmonics, small power factor and poor dynamic performance under line and load variations. In order to improve the real power, compensating the reactive power, proficient power factor and excellent load voltage regulation in the sample test power system, an IPFC is designed. The D-Q technique is utilized here to derive the reference current of the converter and its D.C link capacitor voltage is regulated. Also, the reference voltage of the inverter is arrived by park transformation technique and its load voltage is controlled. Here, a sample 230 KV test power system is taken for study. Further as the conventional PI controllers are designed at one nominal operating point they are not competent to respond satisfactorily in dynamic operating conditions. This can be circumvented by a Fuzzy and Neural network based IPFC and its detailed Simulink model is developed using MATLAB and the overall performance analysis is carried out under different operating state of affairs. 展开更多
关键词 FACTS Controller Fuzzy Logic Controller Interline power flow Controller Reactive power Compensation (RPC) Voltage stability
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Three-defense Line Coordination Strategy of the Guizhou Power Grid with the New Security Situation
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作者 Wencheng Zheng Tao Yu 《Energy and Power Engineering》 2013年第3期36-41,共6页
In order to meet the requirements of Decree of the State Council of the People's Republic of China (No.599), this paper presents a three-defense line coordination strategy based on the Decree of the State Council ... In order to meet the requirements of Decree of the State Council of the People's Republic of China (No.599), this paper presents a three-defense line coordination strategy based on the Decree of the State Council (No.599). Taking the Guizhou power grid of 220 kV&500 kV as an example, the security and stability problem of the Guizhou power grid is analyzed. The strategy using three-defense line coordination for lowering the level of electricity safety accidents is researched. The analysis results show that the proposed coordination strategy is feasible, which can lower the level of electricity safety accidents under the same fault in same operation mode. Through studying the three-defense line of the Guizhou power grid, this paper presents a basic idea of the three-defense line coordination strategy based on the Decree of the State Council (No.599). The three-defense line coordination strategy provides reference for other provinces power grid. 展开更多
关键词 Security and stability Three-defense LINE the GUIZHOU power grid Decree of the State COUNCIL (No.599)
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A Critical Eigenvalues Tracing Method for the Small Signal Stability Analysis of Power Systems
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作者 Shao-Hong Tsai Yuan-Kang Wu Ching-Yin Lee 《Energy and Power Engineering》 2013年第4期677-682,共6页
The continuation power flow method combined with the Jacobi-Davidson method is presented to trace the critical eigenvalues for power system small signal stability analysis. The continuation power flow based on a predi... The continuation power flow method combined with the Jacobi-Davidson method is presented to trace the critical eigenvalues for power system small signal stability analysis. The continuation power flow based on a predictor- corrector technique is applied to evaluate a continuum of steady state power flow solutions as system parameters change;meanwhile, the critical eigenvalues are found by the Jacobi-Davidson method, and thereby the trajectories of the critical eigenvalues, Hopf bifurcation and saddle node bifurcation points can also be found by the proposed method. The numerical simulations are studied in the IEEE 30-bus test system. 展开更多
关键词 Critical EIGENVALUE Trajectory CONTINUATION power flow HOPF BIFURCATION SADDLE Node BIFURCATION Small Signal stability JACOBI-DAVIDSON Method
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