Search results for: Distributed generation Capacitor placement

Authors: Supayotin Na Songkla, Winai Jaikla

Abstract:

This article presents a resistorless current-mode firstorder allpass filter based on second generation current controlled current conveyors (CCCIIs). The features of the circuit are that: the pole frequency can be electronically controlled via the input bias current: the circuit description is very simple, consisting of 2 CCCIIs and single grounded capacitor, without any external resistors and component matching requirements. Consequently, the proposed circuit is very appropriate to further develop into an integrated circuit. Low input and high output impedances of the proposed configuration enable the circuit to be cascaded in current-mode without additional current buffers. The PSpice simulation results are depicted. The given results agree well with the theoretical anticipation. The application example as a current-mode quadrature oscillator is included.

Keywords: First-order all pass filter, current-mode, CCCII.

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Authors: R. Chedid, R. Ghajar

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Lebanon electricity crisis continues to escalate. Rationing hours still apply across the country but with different rates. The capital Beirut is subjected to 3 hours cut while other cities, town and villages may endure 9 to 14 hours of power shortage. To mitigate this situation, private diesel generators distributed illegally all over the country are being used to bridge the gap in power supply. Almost each building in large cities has its own generator and individual villages may have more than one generator supplying their loads. These generators together with their private networks form incomplete and ill-designed and managed microgrids (MG) but can be further developed to become renewable energy-based MG operating in island- or grid-connected modes. This paper will analyze the potential of introducing MG to help resolve the energy crisis in Lebanon. It will investigate the usefulness of developing MG under the prevailing situation of existing private power supply service providers and in light of the developed national energy policy that supports renewable energy development. A case study on a distribution feeder in a rural area will be analyzed using HOMER software to demonstrate the usefulness of introducing photovoltaic (PV) arrays along the existing diesel generators for all the stakeholders; namely, the developers, the customers, the utility and the community at large. Policy recommendations regarding MG development in Lebanon will be presented on the basis of the accumulated experience in private generation and the privatization and public-private partnership laws.

Keywords: Decentralized systems, microgrids, distributed generation, renewable energy.

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Authors: H. Ifassiouen, H. Medromi, N. E. Radhy

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In this paper, we present the recently implemented approach allowing dynamics systems to plan its actions, taking into account the environment perception changes, and to control their execution when uncertainty and incomplete knowledge are the major characteristics of the situated environment [1],[2],[3],[4]. The control distributed architecture has three modules and the approach is related to hierarchical planning: the plan produced by the planner is further refined at the control layer that in turn supervises its execution by a functional level. We propose a new intelligent distributed architecture constituted by: Multi-Agent subsystem of the sensor, of the interpretation and representation of environment [9], of the dynamic localization and of the action. We tested this distributed architecture with dynamic system in the known environment. The autonomous for Rotor Mini Rotorcraft task is described by the primitive actions. The distributed controlbased on multi-agent system is in charge of achieving each task in the best possible way taking into account the context and sensory feedback.

Keywords: Autonomous four rotors helicopter, Control system, Hierarchical planning, Intelligent Distributed Architecture.

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Authors: O. P. Rishi, Rekha Govil, Madhavi Sinha

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Online learning with Intelligent Tutoring System (ITS) is becoming very popular where the system models the student-s learning behavior and presents to the student the learning material (content, questions-answers, assignments) accordingly. In today-s distributed computing environment, the tutoring system can take advantage of networking to utilize the model for a student for students from other similar groups. In the present paper we present a methodology where using Case Based Reasoning (CBR), ITS provides student modeling for online learning in a distributed environment with the help of agents. The paper describes the approach, the architecture, and the agent characteristics for such system. This concept can be deployed to develop ITS where the tutor can author and the students can learn locally whereas the ITS can model the students- learning globally in a distributed environment. The advantage of such an approach is that both the learning material (domain knowledge) and student model can be globally distributed thus enhancing the efficiency of ITS with reducing the bandwidth requirement and complexity of the system.

Keywords: CBR, ITS, student modeling, distributed system, intelligent agent.

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Authors: H. T. Barney, G. C. Low

Abstract:

The design of distributed systems involves the partitioning of the system into components or partitions and the allocation of these components to physical nodes. Techniques have been proposed for both the partitioning and allocation process. However these techniques suffer from a number of limitations. For instance object replication has the potential to greatly improve the performance of an object orientated distributed system but can be difficult to use effectively and there are few techniques that support the developer in harnessing object replication. This paper presents a methodological technique that helps developers decide how objects should be allocated in order to improve performance in a distributed system that supports replication. The performance of the proposed technique is demonstrated and tested on an example system.

Keywords: Allocation, Distributed Systems, Replication.

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Authors: T. Sattarpour, D. Nazarpour

Abstract:

This paper investigates the effect of simultaneous placement of DGs and smart meters (SMs), on voltage profile improvement in active distribution networks (ADNs). A substantial center of attention has recently been on responsive loads initiated in power system problem studies such as distributed generations (DGs). Existence of responsive loads in active distribution networks (ADNs) would have undeniable effect on sizing and siting of DGs. For this reason, an optimal framework is proposed for sizing and siting of DGs and SMs in ADNs. SMs are taken into consideration for the sake of successful implementing of demand response programs (DRPs) such as direct load control (DLC) with end-side consumers. Looking for voltage profile improvement, the optimization procedure is solved by genetic algorithm (GA) and tested on IEEE 33-bus distribution test system. Different scenarios with variations in the number of DG units, individual or simultaneous placing of DGs and SMs, and adaptive power factor (APF) mode for DGs to support reactive power have been established. The obtained results confirm the significant effect of DRPs and APF mode in determining the optimal size and site of DGs to be connected in ADN resulting to the improvement of voltage profile as well.

Keywords: Active distribution network (ADN), distributed generations (DGs), smart meters (SMs), demand response programs (DRPs), adaptive power factor (APF).

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Authors: J. P. P. Andrade, V. A. F. Campos

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This work presents an application of Linear Matrix Inequalities (LMI) for the robust control of an F-16 aircraft through an algorithm ensuring the damping factor to the closed loop system. The results show that the zero and gain settings are sufficient to ensure robust performance and stability with respect to various operating points. The technique used is the pole placement, which aims to put the system in closed loop poles in a specific region of the complex plane. Test results using a dynamic model of the F-16 aircraft are presented and discussed.

Keywords: F-16 Aircraft, linear matrix inequalities, pole placement, robust control.

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Authors: Praloy Kumar Biswas, Prof. Dipanwita Roy Chowdhury

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Grobner basis calculation forms a key part of computational commutative algebra and many other areas. One important ramification of the theory of Grobner basis provides a means to solve a system of non-linear equations. This is why it has become very important in the areas where the solution of non-linear equations is needed, for instance in algebraic cryptanalysis and coding theory. This paper explores on a parallel-distributed implementation for Grobner basis calculation over GF(2). For doing so Buchberger algorithm is used. OpenMP and MPI-C language constructs have been used to implement the scheme. Some relevant results have been furnished to compare the performances between the standalone and hybrid (parallel-distributed) implementation.

Keywords: Grobner basis, Buchberger Algorithm, Distributed- Parallel Computation, OpenMP, MPI.

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Authors: Shaibu Baanni Azumah, Ignatius Tindjina, Stella Obanyi, Tara N. Wood

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This study examined the effect of Urea Deep Placement (UDP) technology on the output of irrigated rice farmers in the northern region of Ghana. Multi-stage sampling technique was used to select 142 rice farmers from the Golinga and Bontanga irrigation schemes, around Tamale. A treatment effect model was estimated at two stages; firstly, to determine the factors that influenced farmers’ decision to adopt the UDP technology and secondly, to determine the effect of the adoption of the UDP technology on the output of rice farmers. The significant variables that influenced rice farmers’ adoption of the UPD technology were sex of the farmer, land ownership, off-farm activity, extension service, farmer group participation and training. The results also revealed that farm size and the adoption of UDP technology significantly influenced the output of rice farmers in the northern region of Ghana. In addition to the potential of the technology to improve yields, it also presents an employment opportunity for women and youth, who are engaged in the deep placement of Urea Super Granules (USG), as well as in the transplantation of rice. It is recommended that the government of Ghana work closely with the IFDC to embed the UDP technology in the national agricultural programmes and policies. The study also recommends an effective collaboration between the government, through the Ministry of Food and Agriculture (MoFA) and the International Fertilizer Development Center (IFDC) to train agricultural extension agents on UDP technology in the rice producing areas of the country.

Keywords: Northern Ghana, output, irrigation rice farmers, treatment effect model, urea deep placement.

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Authors: P. Suryakumari, P. Kantarao

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Optimal Power Flow (OPF) problem in electrical power system is considered as a static, non-linear, multi-objective or a single objective optimization problem. This paper presents an algorithm for solving the voltage stability objective reactive power dispatch problem in a power system .The proposed approach employs cat swarm optimization algorithm for optimal settings of RPD control variables. Generator terminal voltages, reactive power generation of the capacitor banks and tap changing transformer setting are taken as the optimization variables. CSO algorithm is tested on standard IEEE 30 bus system and the results are compared with other methods to prove the effectiveness of the new algorithm. As a result, the proposed method is the best for solving optimal reactive power dispatch problem.

Keywords: RPD problem, voltage stability enhancement, CSO algorithm.

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Authors: Yitao Lei, Xingxiang Zhai, Burra Venkata Durga Kumar

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As the quantity and complexity of computing in large-scale software systems increase, distributed system computing becomes increasingly important. The distributed system realizes high-performance computing by collaboration between different computing resources. If there are no efficient resource scheduling resources, the abuse of distributed computing may cause resource waste and high costs. However, resource scheduling is usually an NP-hard problem, so we cannot find a general solution. However, some optimization algorithms exist like genetic algorithm, ant colony optimization, etc. The large scale of distributed systems makes this traditional optimization algorithm challenging to work with. Heuristic and machine learning algorithms are usually applied in this situation to ease the computing load. As a result, we do a review of traditional resource scheduling optimization algorithms and try to introduce a deep reinforcement learning method that utilizes the perceptual ability of neural networks and the decision-making ability of reinforcement learning. Using the machine learning method, we try to find important factors that influence the performance of distributed system computing and help the distributed system do an efficient computing resource scheduling. This paper surveys the application of deep reinforcement learning on distributed system computing resource scheduling. The research proposes a deep reinforcement learning method that uses a recurrent neural network to optimize the resource scheduling. The paper concludes the challenges and improvement directions for Deep Reinforcement Learning-based resource scheduling algorithms.

Keywords: Resource scheduling, deep reinforcement learning, distributed system, artificial intelligence.

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Authors: S. A. Faizi, S. Yoshitomi

Abstract:

The optimal design procedure of buckling restrained braces (BRBs) in reinforced concrete (RC) building structures can provide the distribution of horizontal stiffness of BRBs at each story, which minimizes story drift response of the structure under the constraint of specified total stiffness of BRBs. In this paper, a simple rule is proposed to convert continuous horizontal stiffness of BRBs into sectional sizes of BRB which are available from standardized section list assuming realistic structural design stage.

Keywords: Buckling restrained brace, building engineering, optimal damper placement, structural engineering.

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Authors: Maria Eliophotou Menon

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School leadership is commonly considered to have a significant influence on school effectiveness and improvement. Effective school leaders are expected to successfully introduce and support change and innovation at the school unit. Despite an abundance of studies on educational leadership, very few studies have provided evidence on the link between leadership models, and specific educational and school outcomes. This is true of a popular contemporary approach to leadership, namely, distributed leadership. The paper provides an overview of research findings on the effect of distributed leadership on educational outcomes. The theoretical basis for this approach to leadership is presented, with reference to methodological and research limitations. The paper discusses research findings and draws their implications for educational research on school leadership.

Keywords: Distributed leadership, educational outcomes, leadership research.

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Authors: Sharjeel Aslam, Vassil Vassilev, Karim Ouazzane

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Ontologies and various semantic repositories became a convenient approach for implementing model-driven architectures of distributed systems on the Web. SPARQL is the standard query language for querying such. However, although SPARQL is well-established standard for querying semantic repositories in RDF and OWL format and there are commonly used APIs which supports it, like Jena for Java, its parallel option is not incorporated in them. This article presents a complete framework consisting of an object algebra for parallel RDF and an index-based implementation of the parallel query engine capable of dealing with the distributed RDF ontologies which share common vocabulary. It has been implemented in Java, and for validation of the algorithms has been applied to the problem of organizing virtual exhibitions on the Web.

Keywords: Distributed ontologies, parallel querying, semantic indexing, shared vocabulary, SPARQL.

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Authors: Carlos Alberto Riveros, Edwin Fabián García, Javier Enrique Rivero

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The measured data obtained from sensors in continuous monitoring of civil structures are mainly used for modal identification and damage detection. Therefore, when modal identification analysis is carried out the quality in the identification of the modes will highly influence the damage detection results. It is also widely recognized that the usefulness of the measured data used for modal identification and damage detection is significantly influenced by the number and locations of sensors. The objective of this study is the numerical implementation of two widely known optimum sensor placement methods in beam-like structures.

Keywords: Optimum sensor placement, structural damage detection, modal identification, beam-like structures.

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Authors: Florin Pop

Abstract:

Simulation is a very powerful method used for highperformance and high-quality design in distributed system, and now maybe the only one, considering the heterogeneity, complexity and cost of distributed systems. In Grid environments, foe example, it is hard and even impossible to perform scheduler performance evaluation in a repeatable and controllable manner as resources and users are distributed across multiple organizations with their own policies. In addition, Grid test-beds are limited and creating an adequately-sized test-bed is expensive and time consuming. Scalability, reliability and fault-tolerance become important requirements for distributed systems in order to support distributed computation. A distributed system with such characteristics is called dependable. Large environments, like Cloud, offer unique advantages, such as low cost, dependability and satisfy QoS for all users. Resource management in large environments address performant scheduling algorithm guided by QoS constrains. This paper presents the performance evaluation of scheduling heuristics guided by different optimization criteria. The algorithms for distributed scheduling are analyzed in order to satisfy users constrains considering in the same time independent capabilities of resources. This analysis acts like a profiling step for algorithm calibration. The performance evaluation is based on simulation. The simulator is MONARC, a powerful tool for large scale distributed systems simulation. The novelty of this paper consists in synthetic analysis results that offer guidelines for scheduler service configuration and sustain the empirical-based decision. The results could be used in decisions regarding optimizations to existing Grid DAG Scheduling and for selecting the proper algorithm for DAG scheduling in various actual situations.

Keywords: Scheduling, Simulation, Performance Evaluation, QoS, Distributed Systems, MONARC

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Authors: Mohamed H. S. Mohamed, Yang Xiao-zong, Liu Hong-wei, Wu Zhi-bo

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The reliability of distributed systems and computer networks have been modeled by a probabilistic network or a graph G. Computing the residual connectedness reliability (RCR), denoted by R(G), under the node fault model is very useful, but is an NP-hard problem. Since it may need exponential time of the network size to compute the exact value of R(G), it is important to calculate its tight approximate value, especially its lower bound, at a moderate calculation time. In this paper, we propose an efficient algorithm for reliability lower bound of distributed systems with unreliable nodes. We also applied our algorithm to several typical classes of networks to evaluate the lower bounds and show the effectiveness of our algorithm.

Keywords: Distributed systems, probabilistic network, residual connectedness reliability, lower bound.

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Authors: Xizhi Li

Abstract:

Both software applications and their development environment are becoming more and more distributed. This trend impacts not only the way software computes, but also how it looks. This article proposes a Human Computer Interface (HCI) template from three representative applications we have developed. These applications include a Multi-Agent System based software, a 3D Internet computer game with distributed game world logic, and a programming language environment used in constructing distributed neural network and its visualizations. HCI concepts that are common to these applications are described in abstract terms in the template. These include off-line presentation of global entities, entities inside a hierarchical namespace, communication and languages, reconfiguration of entity references in a graph, impersonation and access right, etc. We believe the metaphor that underlies an HCI concept as well as the relationships between a bunch of HCI concepts are crucial to the design of software systems and vice versa.

Keywords: HCI, MAS, computer game, programming language

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Authors: Nazleeni Samiha Haron, Anang Hudaya Muhamad Amin, Mohd Hilmi Hasan, Izzatdin Abdul Aziz, Wirdhayu Mohd Wahid

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In any distributed systems, process scheduling plays a vital role in determining the efficiency of the system. Process scheduling algorithms are used to ensure that the components of the system would be able to maximize its utilization and able to complete all the processes assigned in a specified period of time. This paper focuses on the development of comparative simulator for distributed process scheduling algorithms. The objectives of the works that have been carried out include the development of the comparative simulator, as well as to implement a comparative study between three distributed process scheduling algorithms; senderinitiated, receiver-initiated and hybrid sender-receiver-initiated algorithms. The comparative study was done based on the Average Waiting Time (AWT) and Average Turnaround Time (ATT) of the processes involved. The simulation results show that the performance of the algorithms depends on the number of nodes in the system.

Keywords: Distributed Systems, Load Sharing, Process Scheduling, AWT and ATT

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Authors: N. Nouali, H. Drias, A. Doucet

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During more than a decade, many proposals and standards have been designed to deal with the mobility issues; however, there are still some serious limitations in basing solutions on them. In this paper we discuss the possibility of handling mobility at the application layer. We do this while revisiting the conventional implementation of the Two Phase Commit (2PC) protocol which is a fundamental asset of transactional technology for ensuring the consistent commitment of distributed transactions. The solution is based on an execution framework providing an efficient extension that is aware of the mobility and preserves the 2PC principle.

Keywords: Application layer, distributed mobile protocols, mobility management, mobile transaction processing.

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Authors: Yong Jun Choi, Juman Byun, Simon Berkovich

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One of the ubiquitous routines in medical practice is searching through voluminous piles of clinical documents. In this paper we introduce a distributed system to search and exchange clinical documents. Clinical documents are distributed peer-to-peer. Relevant information is found in multiple iterations of cross-searches between the clinical text and its domain encyclopedia.

Keywords: Clinical documents, cross-search, document exchange, information retrieval, peer-to-peer.

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Authors: Nyah C. Temaneh, F. A. Phiri, E. Ruhunga

Abstract:

Most of the well known methods for generating Gaussian variables require at least one standard uniform distributed value, for each Gaussian variable generated. The length of the random number generator therefore, limits the number of independent Gaussian distributed variables that can be generated meanwhile the statistical solution of complex systems requires a large number of random numbers for their statistical analysis. We propose an alternative simple method of generating almost infinite number of Gaussian distributed variables using a limited number of standard uniform distributed random numbers.

Keywords: Gaussian variable, statistical analysis, simulation ofCommunication Network, Random numbers.

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Authors: Hiroaki Sumi, Kiichiro Hayashi

Abstract:

Now, the use of renewable energy power generation has been advanced. In this paper, we compared the usable amount of resource for photovoltaic power generation which was estimated using the NEDO formula and the expansion support policy of photovoltaic power generation which was researched using Internet in the municipality level in Hokkaido and Aichi Prefecture, Japan. This paper will contribute to grasp the current situation especially about the policy. As a result, there were municipalities which seemed to be no consideration of fitting the amount of resources. We think it would need to consider the suitability between the resources and policies.

Keywords: Photovoltaic power generation, expansion support policy, amount of resources, Japan.

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Authors: Sanjeeb Kumar Kar

Abstract:

The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach.

Keywords: Optimal control, linear systems, distributed parametersystems, Legendre polynomials.

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Authors: Li Xu, Shouming Zhong

Abstract:

The reachable set bounding estimation for distributed delay systems with disturbances is a new problem. In this paper,we consider this problem subject to not only time varying delay and polytopic uncertainties but also distributed delay systems which is not studied fully untill now. we can obtain improved non-ellipsoidal reachable set estimation for neural networks with time-varying delay by the maximal Lyapunov-Krasovskii fuctional which is constructed as the pointwise maximum of a family of Lyapunov-Krasovskii fuctionals corresponds to vertexes of uncertain polytope.On the other hand,matrix inequalities containing only one scalar and Matlabs LMI Toolbox is utilized to give a non-ellipsoidal description of the reachable set.finally,numerical examples are given to illustrate the existing results.

Keywords: Reachable set, Distributed delay, Lyapunov-Krasovskii function, Polytopic uncertainties.

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Authors: P. Valsalal, S. Thangalakshmi

Abstract:

There is a widespread changeover in the electrical power industry universally from old-style monopolistic outline towards a horizontally distributed competitive structure to come across the demand of rising consumption. When the transmission lines of derestricted system are incapable to oblige the entire service needs, the lines are overloaded or congested. The governor between customer and power producer is nominated as Independent System Operator (ISO) to lessen the congestion without obstructing transmission line restrictions. Among the existing approaches for congestion management, the frequently used approaches are reorganizing the generation and load curbing. There is a boundary for reorganizing the generators, and further loads may not be supplemented with the prevailing resources unless more private power producers are added in the system by considerably raising the cost. Hence, congestion is relaxed by appropriate Flexible AC Transmission Systems (FACTS) devices which boost the existing transfer capacity of transmission lines. The FACTs device, namely, Unified Power Flow Controller (UPFC) is preferred, and the correct placement of UPFC is more vital and should be positioned in the highly congested line. Hence, the weak line is identified by using power flow performance index with the new objective function with proposed hybrid Fish – Bee algorithm. Further, the location of UPFC at appropriate line reduces the branch loading and minimizes the voltage deviation. The power transfer capacity of lines is determined with and without UPFC in the identified congested line of IEEE 30 bus structure and the simulated results are compared with prevailing algorithms. It is observed that the transfer capacity of existing line is increased with the presented algorithm and thus alleviating the congestion.

Keywords: Available line transfer capability, congestion management, FACTS device, hybrid fish-bee algorithm, ISO, UPFC.

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Authors: Ali Reza Rajabi, Shahab Rashnoei, Mojtaba Hakimzadeh, Amir Habibi

Abstract:

At any point of time, a power system operating condition should be stable, meeting various operational criteria and it should also be secure in the event of any credible contingency. Present day power systems are being operated closer to their stability limits due to economic and environmental constraints. Maintaining a stable and secure operation of a power system is therefore a very important and challenging issue. Voltage instability has been given much attention by power system researchers and planners in recent years, and is being regarded as one of the major sources of power system insecurity. Voltage instability phenomena are the ones in which the receiving end voltage decreases well below its normal value and does not come back even after setting restoring mechanisms such as VAR compensators, or continues to oscillate for lack of damping against the disturbances. Reactive power limit of power system is one of the major causes of voltage instability. This paper investigates the effects of coordinated series capacitors (SC) with static VAR compensators (SVC) on steady-state voltage stability of a power system. Also, the influence of the presence of series capacitor on static VAR compensator controller parameters and ratings required to stabilize load voltages at certain values are highlighted.

Keywords: Static VAR Compensator (SVC), Series Capacitor (SC), voltage stability, reactive power.

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Authors: M. Farshbaf, M. R. Feizi-Derakhshi

Abstract:

Graph partitioning is a NP-hard problem with multiple conflicting objectives. The graph partitioning should minimize the inter-partition relationship while maximizing the intra-partition relationship. Furthermore, the partition load should be evenly distributed over the respective partitions. Therefore this is a multiobjective optimization problem (MOO). One of the approaches to MOO is Pareto optimization which has been used in this paper. The proposed methods of this paper used to improve the performance are injecting best solutions of previous runs into the first generation of next runs and also storing the non-dominated set of previous generations to combine with later generation's non-dominated set. These improvements prevent the GA from getting stuck in the local optima and increase the probability of finding more optimal solutions. Finally, a simulation research is carried out to investigate the effectiveness of the proposed algorithm. The simulation results confirm the effectiveness of the proposed method.

Keywords: Graph partitioning, Genetic algorithm, Multiobjective optimization, Pareto front.

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Authors: S. H. Oudjana, A. Hellal, I. Hadj Mahammed

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Photovoltaic power generation forecasting is an important task in renewable energy power system planning and operating. This paper explores the application of neural networks (NN) to study the design of photovoltaic power generation forecasting systems for one week ahead using weather databases include the global irradiance, and temperature of Ghardaia city (south of Algeria) using a data acquisition system. Simulations were run and the results are discussed showing that neural networks Technique is capable to decrease the photovoltaic power generation forecasting error.

Keywords: Photovoltaic Power Forecasting, Regression, Neural Networks.

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Authors: A. Pereira, S. Haffner, L. V. Gasperin

Abstract:

This paper presents two simplified models to determine nodal voltages in power distribution networks. These models allow estimating the impact of the installation of reactive power compensations equipments like fixed or switched capacitor banks. The procedure used to develop the models is similar to the procedure used to develop linear power flow models of transmission lines, which have been widely used in optimization problems of operation planning and system expansion. The steady state non-linear load flow equations are approximated by linear equations relating the voltage amplitude and currents. The approximations of the linear equations are based on the high relationship between line resistance and line reactance (ratio R/X), which is valid for power distribution networks. The performance and accuracy of the models are evaluated through comparisons with the exact results obtained from the solution of the load flow using two test networks: a hypothetical network with 23 nodes and a real network with 217 nodes.

Keywords: Distribution network models, distribution systems, optimization, power system planning.

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