Search results for: Power System Control

Authors: A. Rong, P. B. Luh, R. Lahdelma

Abstract:

High penetration of intermittent renewable energy sources (RES) such as solar power and wind power into the energy system has caused temporal and spatial imbalance between electric power supply and demand for some countries and regions. This brings about the critical need for coordinating power production and power exchange for different regions. As compared with the power-only systems, the combined heat and power (CHP) systems can provide additional flexibility of utilizing RES by exploiting the interdependence of power and heat production in the CHP plant. In the CHP system, power production can be influenced by adjusting heat production level and electric power can be used to satisfy heat demand by electric boiler or heat pump in conjunction with heat storage, which is much cheaper than electric storage. This paper addresses multi-site CHP systems without considering RES, which lay foundation for handling penetration of RES. The problem under study is the unit commitment (UC) of the transmission-constrained multi-site CHP systems. We solve the problem by combining linear relaxation of ON/OFF states and sequential dynamic programming (DP) techniques, where relaxed states are used to reduce the dimension of the UC problem and DP for improving the solution quality. Numerical results for daily scheduling with realistic models and data show that DP-based algorithm is from a few to a few hundred times faster than CPLEX (standard commercial optimization software) with good solution accuracy (less than 1% relative gap from the optimal solution on the average).

Keywords: Dynamic programming, multi-site combined heat and power system, relaxed states, transmission-constrained generation unit commitment.

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Authors: Bo-Wei Song, Yun-Jung Lee

Abstract:

This paper presents an intention interface and controller for a wire-driven heavy object lifting system that assists the operator with moving a heavy object. The handler is designed to allow a comfortable working posture for the operator. Plus, as a human assistive system, the operator is involved in the control loop, where a fuzzy control system is used to consider the human control characteristics. The effectiveness and performance of the proposed system are proved by experiments.

Keywords: Fuzzy controller, Handler design, Heavy object lifting system, Human-assistive device, Human-in-the-loop system.

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Authors: M. Oloomi-Buygi, M. Reza Salehizadeh

Abstract:

In this paper a new approach for transmission pricing is presented. The main idea is voltage angle allocation, i.e. determining the contribution of each contract on the voltage angle of each bus. DC power flow is used to compute a primary solution for angle decomposition. To consider the impacts of system non-linearity on angle decomposition, the primary solution is corrected in different iterations of decoupled Newton-Raphson power flow. Then, the contribution of each contract on power flow of each transmission line is computed based on angle decomposition. Contract-related flows are used as a measure for “extent of use" of transmission network capacity and consequently transmission pricing. The presented approach is applied to a 4-bus test system and IEEE 30-bus test system.

Keywords: Deregulation, Power electric markets, Transmission pricing methodologies, decoupled Newton-Raphson power flow.

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Authors: Jae-Kyung LEE, Byung-Hak CHO, Kyung-Nam Jang, Sun-Chul Jung, Ki-Yong OH, Joon-Young PARK, Jong-Seog Kim

Abstract:

The cables in a nuclear power plant are designed to be used for about 40 years in safe operation environment. However, the heat and radiation in the nuclear power plant causes the rapid performance deterioration of cables in nuclear vessels and heat exchangers, which requires cable lifetime estimation. The most accurate method of estimating the cable lifetime is to evaluate the cables in a laboratory. However, removing cables while the plant is operating is not allowed because of its safety and cost. In this paper, a robot system to estimate the cable lifetime in nuclear power plants is developed and tested. The developed robot system can calculate a modulus value to estimate the cable lifetime even when the nuclear power plant is in operation.

Keywords: Autonomous robot, Cable Inspection, Indenter, Nuclear Power Plant

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Authors: N. A. Salim, M. M. Othman, I. Musirin, M. S. Serwan

Abstract:

Over the past few decades, power system industry in many developing and developed countries has gone through a restructuring process of the industry where they are moving towards deregulated power industry. This situation will lead to competition among the generation and distribution companies to provide quality and efficient production of electric energy, which will reduce the price of electricity. Therefore it is important to obtain an accurate value of the available transfer capability (ATC) and transmission reliability margin (TRM) in order to ensure the effective power transfer between areas during the occurrence of uncertainties in the system. In this paper, the TRM and ATC is determined by taking into consideration the uncertainties of the system operating condition and system cascading collapse by applying the bootstrap technique. A case study of the IEEE RTS-79 is employed to verify the robustness of the technique proposed in the determination of TRM and ATC.

Keywords: Available transfer capability, bootstrap technique, cascading collapse, transmission reliability margin.

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Authors: Oludamilare Bode Adewuyi, Yanxia Sun, Isaiah Gbadegesin Adebayo

Abstract:

Voltage stability analysis is crucial to the reliable and economic operation of power systems. The power system of developing nations is more susceptible to failures due to the continuously increasing load demand which is not matched with generation increase and efficient transmission infrastructures. Thus, most power systems are heavily stressed and the planning of extra generation from distributed generation sources needs to be efficiently done so as to ensure the security of the power system. In this paper, the performance of a relatively different approach using line voltage stability margin indicator, which has proven to have better accuracy, has been presented and compared with a conventional line voltage stability index for distributed generators (DGs) siting using the Nigerian 28 bus system. Critical Boundary Index (CBI) for voltage stability margin estimation was deployed to identify suitable locations for DG placement and the performance was compared with DG placement using Novel Line Stability Index (NLSI) approach. From the simulation results, both CBI and NLSI agreed greatly on suitable locations for DG on the test system; while CBI identified bus 18 as the most suitable at system overload, NLSI identified bus 8 to be the most suitable. Considering the effect of the DG placement at the selected buses on the voltage magnitude profile, the result shows that the DG placed on bus 18 identified by CBI improved the performance of the power system better.

Keywords: Voltage stability analysis, voltage collapse, voltage stability index, distributed generation.

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Authors: Rattanathip Rattanachai, Piyachai Petchyen, Kunyanuth Kularbphettong

Abstract:

This paper describes the development of a Weight- Balancing Control System based on the Android Operating System and it provides recommendations on ways of balancing of user’s weight based on daily metabolism process and need so that user can make informed decisions on his or her weight controls. The system also depicts more information on nutrition details. Furthermore, it was designed to suggest to users what kinds of foods they should eat and how to exercise in the right ways. We describe the design methods and functional components of this prototype. To evaluate the system performance, questionnaires for system usability and Black Box Testing were used to measure expert and user satisfaction. The results were satisfactory as followed: Means for experts and users were 3.94 and 4.07 respectively.

Keywords: Weight-Balancing Control, Android Operating System, daily metabolism, Black Box Testing.

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Authors: A.H.M.A.Rahim

Abstract:

The impact of fixed speed squirrel cage type as well as variable speed doubly fed induction generators (DFIG) on dynamic performance of a multimachine power system has been investigated. Detailed models of the various components have been presented and the integration of asynchronous and synchronous generators has been carried out through a rotor angle based transform. Simulation studies carried out considering the conventional dynamic model of squirrel cage asynchronous generators show that integration, as such, could degrade to the AC system performance transiently. This article proposes a frequency or power controller which can effectively control the transients and restore normal operation of fixed speed induction generator quickly. Comparison of simulation results between classical cage and doubly-fed induction generators indicate that the doubly fed induction machine is more adaptable to multimachine AC system. Frequency controller installed in the DFIG system can also improve its transient profile.

Keywords: Doubly-fed generator, Induction generator, Multimachine system modeling, Wind energy systems

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Authors: Mustafa Engin Basoğlu, Bekir Çakır

Abstract:

The most important component affecting the efficiency of photovoltaic power systems are solar panels. In other words, efficiency of these systems are significantly affected due to the being low efficiency of solar panel. Thus, solar panels should be operated under maximum power point conditions through a power converter. In this study, design of boost converter has been carried out with maximum power point tracking (MPPT) algorithm which is incremental conductance (Inc-Cond). By using this algorithm, importance of power converter in MPPT hardware design, impacts of MPPT operation have been shown. It is worth noting that initial operation point is the main criteria for determining the MPPT performance. In addition, it is shown that if value of load resistance is lower than critical value, failure operation is realized. For these analyzes, direct duty control is used for simplifying the control.

Keywords: Boost converter, Incremental Conductance (Inc- Cond), MPPT, Solar panel.

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Authors: Wook-Won Kim, Je-Seok Shin, Jin-O Kim

Abstract:

As the penetration of Energy Storage System (ESS) increases in the power system due to higher performance and lower cost than ever, ESS is expanding its role to the ancillary service as well as the storage of extra energy from the intermittent renewable energy resources. For multi-ESS with different capacity and SOC level each other, it is required to make the optimal schedule of SOC level use the multi-ESS effectively. This paper proposes the energy allocation method for the multiple battery ESS with reliability constraint, in order to make the ESS discharge the required energy as long as possible. A simple but effective method is proposed in this paper, to satisfy the power for the spinning reserve requirement while improving the system reliability. Modelling of ESS is also proposed, and reliability is evaluated by using the combined reliability model which includes the proposed ESS model and conventional generation one. In the case study, it can be observed that the required power is distributed to each ESS adequately and accordingly, the SOC is scheduled to improve the reliability indices such as Loss of Load Probability (LOLP) and Loss of Load Expectation (LOLE).

Keywords: Multiple energy storage system, energy allocation method, SOC schedule, reliability constraints.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

Based on the component approach, three kinds of dynamic load models, including a single –motor model, a two-motor model and composite load model have been developed for the stability studies of Khuzestan power system. The study results are presented in this paper. Voltage instability is a dynamic phenomenon and therefore requires dynamic representation of the power system components. Industrial loads contain a large fraction of induction machines. Several models of different complexity are available for the description investigations. This study evaluates the dynamic performances of several dynamic load models in combination with the dynamics of a load changing transformer. Case study is steel industrial substation in Khuzestan power systems.

Keywords: Dynamic load, modeling, Voltage Stability.

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Authors: Theerawut Jinayim, Somchai Arunrungrasmi, Tanes Tanitteerapan, Narong Mungkung

Abstract:

Although White LED lighting systems powered by solar cells have presented for many years, they are not widely used in today application because of their cost and low energy conversion efficiency. The proposed system use the dc power generated by fixed solar cells module to energize White LED light sources that are operated by directly connected White LED with current limitation resistors, resulting in much more power consumption. This paper presents the use of white LED as a general lighting application powered by tracking solar cells module and using pulse to apply the electrical power to the White LED. These systems resulted in high efficiency power conversion, low power consumption, and long light of the white LED.

Keywords: Efficiency, lighting, light-emitting diode, pulse, Solar, white LED.

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Authors: Ferenc Kovács, Gábor Hosszú

Abstract:

The paper presents an advanced control system for tennis ball throwing machines to improve their accuracy according to the ball impact points. A further advantage of the system is the much easier calibration process involving the intelligent solution of the automatic adjustment of the stroking parameters according to the ball elasticity, the self-calibration, the use of the safety margin at very flat strokes and the possibility to placing the machine to any position of the half court. The system applies mathematical methods to determine the exact ball trajectories and special approximating processes to access all points on the aimed half court.

Keywords: Control system, robot programming, robot control, sports equipment, throwing machine.

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Authors: Andrés Gomez-Casseres, Rubén Contreras

Abstract:

In this paper, a bidirectional boost converter operated in Discontinuous Conduction Mode (DCM) is presented as a suitable power conditioning circuit for tuning of kinetic energy harvesters without the need of a battery. A nonlinear control scheme, composed by two linear controllers, is used to control the average value of the input current, enabling the synthesization of complex loads. The converter, along with the control system, is validated through SPICE simulations using the LTspice tool. The converter model and the controller transfer functions are derived. From the simulation results, it was found that the input current distortion increases with the introduced phase shift and that, such distortion, is almost entirely present at the zero-crossing point of the input voltage.

Keywords: Average current control, boost converter, electrical tuning, energy harvesting.

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Authors: Paula Ferreira, Madalena Araújo, M.E.J. O’Kelly

Abstract:

Combining energy efficiency with renewable energy sources constitutes a key strategy for a sustainable future. The wind power sector stands out as a fundamental element for the achievement of the European renewable objectives and Portugal is no exception to the increase of the wind energy for the electricity generation. This work proposes an optimization model for the long range electricity power planning in a system similar to the Portuguese one, where the expected impacts of the increasing installed wind power on the operating performance of thermal power plants are taken into account. The main results indicate that the increasing penetration of wind power in the electricity system will have significant effects on the combined cycle gas power plants operation and on the theoretically expected cost reduction and environmental gains. This research demonstrated the need to address the impact that energy sources with variable output may have, not only on the short-term operational planning, but especially on the medium to long range planning activities, in order to meet the strategic objectives for the energy sector.

Keywords: Wind power, electricity planning model, cost, emissions.

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Authors: Aye Aye Mon

Abstract:

The application of a simple microcontroller to deal with a three variable input and a single output fuzzy logic controller, with Proportional – Integral – Derivative (PID) response control built-in has been tested for an automatic voltage regulator. The fuzzifiers are based on fixed range of the variables of output voltage. The control output is used to control the wiper motor of the auto transformer to adjust the voltage, using fuzzy logic principles, so that the voltage is stabilized. In this report, the author will demonstrate how fuzzy logic might provide elegant and efficient solutions in the design of multivariable control based on experimental results rather than on mathematical models.

Keywords: Fuzzy logic system, PID Controller, control systems, controlled A V R

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Authors: A.K.Balirsingh, S.C.Swain, S. Panda

Abstract:

Recently, Genetic Algorithms (GA) and Differential Evolution (DE) algorithm technique have attracted considerable attention among various modern heuristic optimization techniques. Since the two approaches are supposed to find a solution to a given objective function but employ different strategies and computational effort, it is appropriate to compare their performance. This paper presents the application and performance comparison of DE and GA optimization techniques, for flexible ac transmission system (FACTS)-based controller design. The design objective is to enhance the power system stability. The design problem of the FACTS-based controller is formulated as an optimization problem and both the PSO and GA optimization techniques are employed to search for optimal controller parameters. The performance of both optimization techniques has been compared. Further, the optimized controllers are tested on a weekly connected power system subjected to different disturbances, and their performance is compared with the conventional power system stabilizer (CPSS). The eigenvalue analysis and non-linear simulation results are presented and compared to show the effectiveness of both the techniques in designing a FACTS-based controller, to enhance power system stability.

Keywords: Differential Evolution, Flexible AC TransmissionSystems (FACTS), Genetic Algorithm, Low Frequency Oscillations, Single-machine Infinite Bus Power System.

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Authors: Hongkun Zhang, Hermann Winner, Wenjun Li

Abstract:

This paper describes the development, modeling, and testing of skyhook and MiniMax control strategies of semi-active suspension. The control performances are investigated using Matlab/Simulink [1], with a two-degree-of-freedom quarter car semiactive suspension system model. The comparison and evaluation of control result are made using software-in-the-loop simulation (SILS) method. This paper also outlines the development of a hardware-inthe- loop simulation (HILS) system. The simulation results show that skyhook strategy can significantly reduce the resonant peak of body and provide improvement in vehicle ride comfort. Otherwise, MiniMax strategy can be employed to effectively improve drive safety of vehicle by influencing wheel load. The two strategies can be switched to control semi-active suspension system to fulfill different requirement of vehicle in different stages.

Keywords: Hardware-in-the-loop simulation, Semi-active suspension, Skyhook control, MiniMax control.

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Authors: N. A. Salim, M. M. Othman, I. Musirin, M. S. Serwan

Abstract:

Uncertainty of system operating conditions is one of the causative reasons which may render to the instability of a transmission system. For that reason, accurate assessment of transmission reliability margin (TRM) is essential to ensure effective power transfer between areas during the occurrence of system uncertainties. The power transfer is also called as the available transfer capability (ATC) which is the information required by the utilities and marketers to instigate selling and buying the electric energy. This paper proposes a computationally effective approach to estimate TRM and ATC by considering the uncertainties of system cascading collapse and transmission line outages. In accordance to the results that have been obtained, the proposed method is essential for the transmission providers which could help the power marketers and planning sectors in the operation and reserving transmission services based on the ATC calculated.

Keywords: Available transfer capability, System cascading collapse, Transmission line outages, Transmission reliability margin.

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Authors: Kittaya Somsai, Thanatchai Kulworawanichpong, Nitus Voraphonpiput

Abstract:

This paper presents the DC voltage control design of D-STATCOM when the D-STATCOM is used for load voltage regulation. Although, the DC voltage can be controlled by active current of the D-STATCOM, reactive current still affects the DC voltage. To eliminate this effect, the control strategy with elimination effect of the reactive current is proposed and the results of the control with and without the elimination the effect of the reactive current are compared. For obtaining the proportional and integral gains of the PI controllers, the symmetrical optimum and genetic algorithms methods are applied. The stability margin of these methods are obtained and discussed in detail. In addition, the performance of the DC voltage control based on symmetrical optimum and genetic algorithms methods are compared. Effectiveness of the controllers designed was verified through computer simulation performed by using Power System Tool Block (PSB) in SIMULINK/MATLAB. The simulation results demonstrated that the DC voltage control proposed is effective in regulating DC voltage when the DSTATCOM is used for load voltage regulation.

Keywords: D-STATCOM, DC voltage control, Symmetrical optimum, Genetic algorithms

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Authors: P. Ruttanee, K-N. Areerak, K-L. Areerak

Abstract:

Dynamic models of power converters are normally time-varying because of their switching actions. Several approaches are applied to analyze the power converters to achieve the timeinvariant models suitable for system analysis and design via the classical control theory. The paper presents how to derive dynamic models of the power system consisting of a three-phase controlled rectifier feeding an uncontrolled buck converter by using the combination between the well known techniques called the DQ and the generalized state-space averaging methods. The intensive timedomain simulations of the exact topology model are used to support the accuracies of the reported model. The results show that the proposed model can provide good accuracies in both transient and steady-state responses.

Keywords: DQ method, Generalized state-space averaging method, Three-phase controlled rectifier, Uncontrolled buck converter, Averaging model, Modeling, Simulation.

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Authors: Kleanthis Prekas, Maria Rangoussi, Savvas Vassiliadis, George Prekas

Abstract:

Intelligent tutoring systems constitute an evolution of computer-aided educational software. We present here the modules of an intelligent tutoring system for Automatic Control, developed in our department. Through the software application developed,students can perform complete automatic control laboratory experiments, either over the departmental local area network or over the Internet. Monitoring of access to the system (local as well as international), along with student performance statistics, has yielded strongly encouraging results (as of fall 2004), despite the advanced technical content of the presented paradigm, thus showing the potential of the system developed for education and for training.

Keywords: Automatic control, tutoring system, Internet access, laboratory experiments.

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Authors: S. Leghmizi, S. Liu, F. Naeim

Abstract:

This paper presents a fuzzy control system for a three degree of freedom (3-DOF) stabilized platform with explicit decoupling scheme. The system under consideration is a system with strong interactions between three channels. By using the concept of decentralized control, a control structure is developed that is composed of three control loops, each of which is associated with a single-variable fuzzy controller and a decoupling unit. Takagi-Sugeno (TS) fuzzy control algorithm is used to implement the fuzzy controller. The decoupling units design is based on the adaptive theory reasoning. Simulation tests were established using Simulink of Matlab. The obtained results have demonstrated the feasibility and effectiveness of the proposed approach. Simulation results are represented in this paper.

Keywords: 3-DOF platform of a ship carried antenna, the concept of decentralized control, Takagi-Sugeno (TS) fuzzy control algorithm, Simulink.

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Authors: Dong-Woo Lim, Chang-Jae Chun, Hyung-Myung Kim

Abstract:

We consider a two-way relay network where two sources exchange information. A relay helps the two sources exchange information using the decode-and-XOR-forward protocol. We investigate the power minimization problem with minimum rate constraints. The system needs two time slots and in each time slot the required rate pair should be achievable. The power consumption is minimized in each time slot and we obtained the closed form solution. The simulation results confirm that the proposed power allocation scheme consumes lower total power than the conventional schemes.

Keywords: Decode-and-XOR-forward, power minimization, two-way relay

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Authors: Sung-Hun Lee, Yun-Seong Lee, Jin-O Kim

Abstract:

Reliability Centered Maintenance(RCM) is one of most widely used methods in the modern power system to schedule a maintenance cycle and determine the priority of inspection. In order to apply the RCM method to the Smart Grid, a precedence study for the new structure of rearranged system should be performed due to introduction of additional installation such as renewable and sustainable energy resources, energy storage devices and advanced metering infrastructure. This paper proposes a new method to evaluate the priority of maintenance and inspection of the power system facilities in the Smart Grid using the Risk Priority Number. In order to calculate that risk index, it is required that the reliability block diagram should be analyzed for the Smart Grid system. Finally, the feasible technical method is discussed to estimate the risk potential as part of the RCM procedure.

Keywords: Expert System, FMECA, Fuzzy Theory, Reliability Centered Maintenance, Risk Priority Number

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Authors: Apidet Booranawong, Wiklom Teerapabkajorndet

Abstract:

An enhanced ad-hoc on-demand distance vector routing (E-AODV) protocol for control system applications in wireless sensor and actuator networks (WSANs) is proposed. Our routing algorithm is designed by considering both wireless network communication and the control system aspects. Control system error and network delay are the main selection criteria in our routing protocol. The control and communication performance is evaluated on multi-hop IEEE 802.15.4 networks for building-temperature control systems. The Gilbert-Elliott error model is employed to simulate packet loss in wireless networks. The simulation results demonstrate that the E-AODV routing approach can significantly improve the communication performance better than an original AODV routing under various packet loss rates. However, the control performance result by our approach is not much improved compared with the AODV routing solution.

Keywords: WSANs, building temperature control, AODV routing protocol, control system error, settling time, delay, delivery ratio.

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Authors: Markus Mazzola, Gunther Schaaf

Abstract:

A vehicle driving with an Adaptive Cruise Control System (ACC) is usually controlled decentrally, based on the information of radar systems and in some publications based on C2X-Communication (CACC) to guarantee stable platoons. In this paper we present a Model Predictive Control (MPC) design of a centralized, server-based ACC-System, whereby the vehicular platoon is modeled and controlled as a whole. It is then proven that the proposed MPC design guarantees asymptotic stability and hence string stability of the platoon. The Networked MPC design is chosen to be able to integrate system constraints optimally as well as to reduce the effects of communication delay and packet loss. The performance of the proposed controller is then simulated and analyzed in an LTE communication scenario using the LTE/EPC Network Simulator LENA, which is based on the ns-3 network simulator.

Keywords: Adaptive Cruise Control, Centralized Server, Networked Model Predictive Control, String Stability.

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Authors: Ahmet Turer

Abstract:

Middle-gate is located in Hasankeyf, Batman dating back to 1800 BC and is one of the important historical structures in Turkey. The ancient structure has suffered major structural cracks due to aging as well as lateral pressure of a cracked rock which is predicted to be about 100 tons. The existing support system was found to be inadequate to support the load especially after a recent rock fall in the close vicinity. Concerns were increased since the existing support system that is integral with a damaged and cracked gate wall needed to be replaced by a new support system. The replacement process must be carefully monitored by crackmeters and control mechanisms should be integrated to prevent cracks to expand while the same crack width needs to be maintained after the operation. The control system and actions taken during the intervention are explained in this paper.

Keywords: structural control, crack width, replacement, support

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Authors: M. Tarafdar Haque, A.M. Kashtiban

Abstract:

The electric power industry is currently undergoing an unprecedented reform. One of the most exciting and potentially profitable recent developments is increasing usage of artificial intelligence techniques. The intention of this paper is to give an overview of using neural network (NN) techniques in power systems. According to the growth rate of NNs application in some power system subjects, this paper introduce a brief overview in fault diagnosis, security assessment, load forecasting, economic dispatch and harmonic analyzing. Advantages and disadvantages of using NNs in above mentioned subjects and the main challenges in these fields have been explained, too.

Keywords: Neural network, power system, security assessment, fault diagnosis, load forecasting, economic dispatch, harmonic analyzing.

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Authors: A. R. Tavakolpour-Saleh, H. Jokar

Abstract:

Liquid level control of conical tank system is known to be a great challenge in many industries such as food processing, hydrometallurgical industries and wastewater treatment plant due to its highly nonlinear characteristics. In this research, an adaptive fuzzy PID control scheme is applied to the problem of liquid level control in a nonlinear tank process. A conical tank process is first modeled and primarily simulated. A PID controller is then applied to the plant model as a suitable benchmark for comparison and the dynamic responses of the control system to different step inputs were investigated. It is found that the conventional PID controller is not able to fulfill the controller design criteria such as desired time constant due to highly nonlinear characteristics of the plant model. Consequently, a nonlinear control strategy based on gain-scheduling adaptive control incorporating a fuzzy logic observer is proposed to accurately control the nonlinear tank system. The simulation results clearly demonstrated the superiority of the proposed adaptive fuzzy control method over the conventional PID controller.

Keywords: Adaptive control, fuzzy logic, conical tank, PID controller.

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