Abstract
This paper deals with the construction of a mathematical model of a wind turbine, which is one of the sources in the Grid-Off
system.
Keywords: mathematical model, wind turbine, Grid-Off system, electric generator, wind conditions.
1 Introduction
As one of the power sources of the Grid-Off system is a wind turbine. It is advantageous to work with a
mathematical model for the need of experimental research. In Fig. 1 is a schematic connection of a wind turbine
to a container, which is a Grid-Off system. [1-4]
Passivity Based Control for PV Applications by Using a Buck Power Converter
The use of power converters for everyday applications is becoming more and more important. Current technological applications simultaneously demand a high level of precision and performance, so DC-DC converters have a very important role in systems requiring energy level conversion and adaptation. As part of the work of this paper, we are interested in an analysis of modeling and control law synthesis approaches to ensure stability and a certain level of performance in the entire operating domain. The objective of our research work is therefore to propose a control law whose synthesis is based on a formalized (modeling & control) approach with a view to obtaining a control law adapted to the operating point. The principles used are based on the control and observation by the theory of passivity for the synthesis of control law of buck power converter for PV Applications.
Cascade forward neural network based on resilient backpropagation for simulta...Mellah Hacene
Cascade-Forward Neural Network Based on Resilient Backpropagation for Simultaneous Parameters and State Space Estimations of Brushed DC Machines
Advances in Modelling and Analysis B
Adaptive maximum power point tracking using neural networks for a photovoltai...Mellah Hacene
Adaptive Maximum Power Point Tracking Using Neural Networks for a Photovoltaic Systems According Grid
Electrical Engineering & Electromechanics, (5), 57–66, 2021. https://doi.org/10.20998/2074-272X.2021.5.08
Power transformer faults diagnosis using undestructive methods and ann for dg...Mellah Hacene
Power transformer faults diagnosis using undestructive methods (Roger and IEC) and artificial neural network for dissolved gas analysis applied on the functional transformer in the Algerian north-eastern: a comparative study
Bouchaoui Lahcene, Kamel Eddine Hemsas, Hacene Mellah, saad eddine benlahneche
Nowadays, power transformer aging and failures are viewed with great attention in power transmission industry. Dissolved gas analysis (DGA) is classified among the biggest widely used methods used within the context of asset management policy to detect the incipient faults in their earlier stage in power transformers. Up to now, several procedures have been employed for the lecture of DGA results. Among these useful means, we find Key Gases, Rogers Ratios, IEC Ratios, the historical technique less used today Doernenburg Ratios, the two types of Duval Pentagons methods, several versions of the Duval Triangles method and Logarithmic Nomograph. Problem. DGA data extracted from different units in service served to verify the ability and reliability of these methods in assessing the state of health of the power transformer. Aim. An improving the quality of diagnostics of electrical power transformer by artificial neural network tools based on two conventional methods in the case of a functional power transformer at Sétif province in East North of Algeria. Methodology. Design an inelegant tool for power transformer diagnosis using neural networks based on traditional methods IEC and Rogers, which allows to early detection faults, to increase the reliability, of the entire electrical energy system from transport to consumers and improve a continuity and quality of service. Results. The solution of the problem was carried out by using feed-forward back-propagation neural networks implemented in MATLAB-Simulink environment. Four real power transformers working under different environment and climate conditions such as: desert, humid, cold were taken into account. The practical results of the diagnosis of these power transformers by the DGA are presented. Practical value.....
Study of Wind Turbine based Variable Reluctance Generator using Hybrid FEMM-M...Yayah Zakaria
Based on exhaustive review of the state of the art of the electric generators fitted to Wind Energy Conversion System (WECS), this study is focused on an innovative machine that is a Variable Reluctance Generator (VRG). Indeed, its simple and rugged structure (low cost), its high torque at low speed (gearless), its fault-tolerance (lowest maintenance), allow it to be a potential candidate for a small wind power application at variable wind
speed. For better accuracy, a finite element model of a studied doubly salient VRG is developed using open source software FEMM to identify the electromagnetic characteristics such as linkage flux, torque or inductance versus rotor position and stator excitation. The obtained data are then transferred into look-up tables of MATLAB/Simulink to perform various simulations. Performance of the proposed wind power system is analyzed for several parameters and results are discussed.
Passivity Based Control for PV Applications by Using a Buck Power Converter
The use of power converters for everyday applications is becoming more and more important. Current technological applications simultaneously demand a high level of precision and performance, so DC-DC converters have a very important role in systems requiring energy level conversion and adaptation. As part of the work of this paper, we are interested in an analysis of modeling and control law synthesis approaches to ensure stability and a certain level of performance in the entire operating domain. The objective of our research work is therefore to propose a control law whose synthesis is based on a formalized (modeling & control) approach with a view to obtaining a control law adapted to the operating point. The principles used are based on the control and observation by the theory of passivity for the synthesis of control law of buck power converter for PV Applications.
Cascade forward neural network based on resilient backpropagation for simulta...Mellah Hacene
Cascade-Forward Neural Network Based on Resilient Backpropagation for Simultaneous Parameters and State Space Estimations of Brushed DC Machines
Advances in Modelling and Analysis B
Adaptive maximum power point tracking using neural networks for a photovoltai...Mellah Hacene
Adaptive Maximum Power Point Tracking Using Neural Networks for a Photovoltaic Systems According Grid
Electrical Engineering & Electromechanics, (5), 57–66, 2021. https://doi.org/10.20998/2074-272X.2021.5.08
Power transformer faults diagnosis using undestructive methods and ann for dg...Mellah Hacene
Power transformer faults diagnosis using undestructive methods (Roger and IEC) and artificial neural network for dissolved gas analysis applied on the functional transformer in the Algerian north-eastern: a comparative study
Bouchaoui Lahcene, Kamel Eddine Hemsas, Hacene Mellah, saad eddine benlahneche
Nowadays, power transformer aging and failures are viewed with great attention in power transmission industry. Dissolved gas analysis (DGA) is classified among the biggest widely used methods used within the context of asset management policy to detect the incipient faults in their earlier stage in power transformers. Up to now, several procedures have been employed for the lecture of DGA results. Among these useful means, we find Key Gases, Rogers Ratios, IEC Ratios, the historical technique less used today Doernenburg Ratios, the two types of Duval Pentagons methods, several versions of the Duval Triangles method and Logarithmic Nomograph. Problem. DGA data extracted from different units in service served to verify the ability and reliability of these methods in assessing the state of health of the power transformer. Aim. An improving the quality of diagnostics of electrical power transformer by artificial neural network tools based on two conventional methods in the case of a functional power transformer at Sétif province in East North of Algeria. Methodology. Design an inelegant tool for power transformer diagnosis using neural networks based on traditional methods IEC and Rogers, which allows to early detection faults, to increase the reliability, of the entire electrical energy system from transport to consumers and improve a continuity and quality of service. Results. The solution of the problem was carried out by using feed-forward back-propagation neural networks implemented in MATLAB-Simulink environment. Four real power transformers working under different environment and climate conditions such as: desert, humid, cold were taken into account. The practical results of the diagnosis of these power transformers by the DGA are presented. Practical value.....
Study of Wind Turbine based Variable Reluctance Generator using Hybrid FEMM-M...Yayah Zakaria
Based on exhaustive review of the state of the art of the electric generators fitted to Wind Energy Conversion System (WECS), this study is focused on an innovative machine that is a Variable Reluctance Generator (VRG). Indeed, its simple and rugged structure (low cost), its high torque at low speed (gearless), its fault-tolerance (lowest maintenance), allow it to be a potential candidate for a small wind power application at variable wind
speed. For better accuracy, a finite element model of a studied doubly salient VRG is developed using open source software FEMM to identify the electromagnetic characteristics such as linkage flux, torque or inductance versus rotor position and stator excitation. The obtained data are then transferred into look-up tables of MATLAB/Simulink to perform various simulations. Performance of the proposed wind power system is analyzed for several parameters and results are discussed.
Benchmarking study between capacitive and electronic load technic to track I-...IJECEIAES
To detect defects of solar panel and understand the effect of external parameters such as fluctuations in illumination, temperature, and the effect of a type of dust on a photovoltaic (PV) panel, it is essential to plot the Ipv=f(Vpv) characteristic of the PV panel, and the simplest way to plot this I-V characteristic is to use a variable resistor. This paper presents a study of comparison and combination between two methods: capacitive and electronic loading to track I-V characteristic. The comparison was performed in terms of accuracy, response time and instrumentation cost used in each circuit, under standard temperature and illumination conditions by using polycrystalline solar panel type SX330J and monocrystalline solar panels type ET-M53630. The whole system is based on simple components, less expensive and especially widely used in laboratories. The results will be between the datasheet of the manufacturer with the experimental data, refinements and improvements concerning the number of points and the trace time have been made by combining these two methods.
Design and fabrication of rotor lateral shifting in the axial-flux permanent-...IJECEIAES
The development of axial-flux permanent-magnet (AFPM) machines has become a mature technology. The single-stator double-rotor (SSDR) AFPM structure has advantages on the compactness and the low up to medium power applications so the microscale size and low-cost applications are reachable to be designed. The research main objectives are designing and manufacturing the lateral shifting from the north poles of the first rotor face the north poles of the second rotor (NN) to the north poles of the first rotor face the south poles of the second rotor (NS) categories as well as finding the best performance of the proposed method and implementing in a low cost and micro-scale AFPMG. The novel lateral shifting on the one of the rotors shows performance at 19.2 0 has the highest efficiency at 88.39% during lateral shifting from N–N (0 0 ) to N–S (36 0 ) on rotor 2.
Optimizing of the installed capacity of hybrid renewable energy with a modifi...IJECEIAES
The lack of wind speed capacity and the emission of photons from sunlight are the problem in a hybrid system of photovoltaic (PV) panels and wind turbines. To overcome this shortcoming, the incremental conductance (IC) algorithm is applied that could control the converter work cycle and the switching of the buck boost therefore maximum efficiency of maximum power point tracking (MPPT) is reached. The operation of the PV-wind hybrid system, consisting of a 100 W PV array device and a 400 W wind subsystem, 12 V/100 Ah battery energy storage and LED, the PV-wind system requires a hybrid controller for battery charging and usage and load lamp and it’s conducted in experimental setup. The experimental has shown that an average increase in power generated was 38.8% compared to a single system of PV panels or a single wind turbine sub-system. Therefore, the potential opportunities for increasing power production in the tropics wheather could be carried out and applied with this model.
Modified T-type topology of three-phase multi-level inverter for photovoltaic...IJECEIAES
In this article, a three-phase multilevel neutral-point-clamped inverter with a modified t-type structure of switches is proposed. A pulse width modulation (PWM) scheme of the proposed inverter is also developed. The proposed topology of the multilevel inverter has the advantage of being simple, on the one hand since it does contain only semiconductors in reduced number (corresponding to the number of required voltage levels), and no other components such as switching or flying capacitors, and on the other hand, the control scheme is much simpler and more suitable for variable frequency and voltage control. The performances of this inverter are analyzed through simulations carried out in the MATLAB/Simulink environment on a threephase inverter with 9 levels. In all simulations, the proposed topology is connected with R-load or RL-load without any output filter.
This paper presents the modeling and simulation of wind energy Conversion System using the Permanent Magnet Synchronous Generator (PMSG). The objectives are: to extract the maximum power of the wind speed by controlling the electromagnetic torque of the PMSG, to maintain constant the DC-link voltage despite the wind speed variations and to attain the unity power factor. In order to ensure a regulation with high performance and a good robustness against the internal and the external disturbances, a new control strategy called the Active Disturbance Rejection Control (ADRC) is used. Therefore, the Analysis and simulation of the ADRC and PI controllers are developed with MATLAB/Simulink software. The performance of these controllers is compared in term of references tracking, robustness and grid faults.
Simulation of 3 Phase to 3 Phase Power Conversion Using Matrix Converter with...IJERA Editor
This paper proposes a new approach of design and implementation of 3 phase to 3 phase conversion using
matrix converter. It includes the design, modeling and implementation. The entire matrix converter circuits are
developed by mathematical model so as to reduce computational time and performances of the converter are
evaluated using MATLAB/SIMULINK for RL Load. The mathematical expressions relating the input and
output of the three phase matrix converter are implemented by using simulink block set. The duty cycles of the
matrix converter bidirectional switches are calculated using modified venturini algorithm for maximum (0.866)
and minimum (0.5) voltage transfer ratio.
Convergence analysis of the triangular-based power flow method for AC distribu...IJECEIAES
This paper addresses the convergence analysis of the triangular-based power flow (PF) method in alternating current radial distribution networks. The PF formulation is made via upper-triangular matrices, which enables finding a general iterative PF formula that does not require admittance matrix calculations. The convergence analysis of this iterative formula is carried out by applying the Banach fixed-point theorem (BFPT), which allows demonstrating that under an adequate voltage profile the triangular-based PF always converges. Numerical validations are made, on the well-known 33 and 69 distribution networks test systems. Gauss-seidel, newton-raphson, and backward/forward PF methods are considered for the sake of comparison. All the simulations are carried out in MATLAB software.
In this paper, we focus on the modeling and control of a wind power system based on a double-fed induction generator DFIG. We proposed a technique of active and reactive power control to improve the performance and dynamics of variable speed wind system. The objective of the modeling is to apply the direct and indirect vector control stator flux orientation to control independently, the active and reactive power generated doubly-fed induction generator (DFIG). The simulation results are tested and compared in order to evaluate the performance of the proposed system.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
MODELING AND OPTIMIZATION OF PIEZOELECTRIC ENERGY HARVESTING adeij1
In this paper, the modeling, optimization and simulation results of the piezoelectric energy harvesting using bond graph approach are presented. Firstly, a lightweight equivalent model derived from the bond graph is proposed. It’s a comprehensive model, which is suitable for piezoelectric seismic energy harvester investigation and power optimization. The optimal charge impedance for both the resistive load and complex load are given and analysed. Finally a bond graph approach is proposed to allow optimization of the extracted energy while keeping simplicity and standalone capability. The proposed model does not rely on any inductor and is constructed with a simple switch. The power harvested is more than twice the conventional technique one on a wide band of resistive load. The bond graph model is valid close to the analysed mode centre frequency and delivers results compared to experimental and analytical data. Furthermore, we also show that the harvester can be electrically tuned to match the excitation frequency. This makes it possible to maximize the power output for both linear and non-linear loads.
A hybrid algorithm for voltage stability enhancement of distribution systems IJECEIAES
This paper presents a hybrid algorithm by applying a hybrid firefly and particle swarm optimization algorithm (HFPSO) to determine the optimal sizing of distributed generation (DG) and distribution static compensator (D-STATCOM) device. A multi-objective function is employed to enhance the voltage stability, voltage profile, and minimize the total power loss of the radial distribution system (RDS). Firstly, the voltage stability index (VSI) is applied to locate the optimal location of DG and D-STATCOM respectively. Secondly, to overcome the sup-optimal operation of existing algorithms, the HFPSO algorithm is utilized to determine the optimal size of both DG and D-STATCOM. Verification of the proposed algorithm has achieved on the standard IEEE 33-bus and Iraqi 65-bus radial distribution systems through simulation using MATLAB. Comprehensive simulation results of four different cases show that the proposed HFPSO demonstrates significant improvements over other existing algorithms in supporting voltage stability and loss reduction in distribution networks. Furthermore, comparisons have achieved to demonstrate the superiority of HFPSO algorithms over other techniques due to its ability to determine the global optimum solution by easy way and speed converge feature.
Parametric estimation in photovoltaic modules using the crow search algorithmIJECEIAES
The problem of parametric estimation in photovoltaic (PV) modules considering man- ufacturer information is addressed in this research from the perspective of combinatorial optimization. With the data sheet provided by the PV manufacturer, a non-linear non-convex optimization problem is formulated that contains information regarding maximum power, open-circuit, and short-circuit points. To estimate the three parameters of the PV model (i.e., the ideality diode factor (a) and the parallel and series resistances (R p and R )), the crow search algorithm (CSA) is employed, which is a metaheuristic optimization technique inspired by the behavior of the crows searching food deposits. The CSA allows the exploration and exploitation of the solution space through a simple evolution rule derived from the classical PSO method. Numerical simulations reveal the effectiveness and robustness of the CSA to estimate these parameters with objective function values lower than 1 10 s 28 and processing times less than 2 s. All the numerical simulations were developed in MATLAB 2020a and compared with the sine-cosine and vortex search algorithms recently reported in the literature.
Wind Energy Conversion Based On Matrix ConverterIAES-IJPEDS
In recent years renewable sources such as solar, wave and wind are used for the generation of electricity. Wind is one of the major renewable sources. The amount of energy from a Wind Energy Conversion System (WECS) depends not only on the wind at the site, but also on the control strategy used for the WECS. In assistance to get the appropriate wind energy from the conversion system, wind turbine generator will be run in variable speed mode. The variable speed capability is achieved through the use of an advanced power electronic converter. Fixed speed wind turbines and induction generators are often used in wind farms. But the limitations of such generators are low efficiency and poor power quality which necessitates the variable speed wind turbine generators such as Doubly Fed Induction Generator (DFIG) and Permanent Magnet Synchronous Generator (PMSG). A high-performance configuration can be obtained by using a PMSG and a converter in combination AC-DC-AC connect between stator & rotor points for providing the required variable speed operation.
The hardware implementation of sensorless brushless direct current motor drive incorporating H-infinity control strategy with optimized weights by particle swarm optimization in the speed control is carried out in this work. The methodology involved in the design of brushless direct current (BLDC) motor control with sensorless position detection technique, the design of H-infinity speed controller, steps involved in particle swarm optimization for optimizing coefficients of its weights and the hardware implementation is discussed in detail in this paper. Texas Instruments microcontroller board C2000 Delfino Launchpad LAUNCHXL F28377S and driver BOOSTXL DRV8301 are used for realization of the speed controller. The code is developed using C2000 hardware support package in MATLAB/SIMULINK platform. A comprehensive performance analysis is accomplished during starting of the motor and during the fast application and removal of load. This strategy is found to be robust resulting in faster load disturbance rejection and better reference speed tracking. The experimental results of the proposed strategy are compared with that of conventional proportional-integral (PI) controller. The time domain parameters are also compared. It is found that the proposed strategy exhibits better performance characteristics during transients and sudden disturbances in load.
The optimal solution for unit commitment problem using binary hybrid grey wol...IJECEIAES
The aim of this work is to solve the unit commitment (UC) problem in power systems by calculating minimum production cost for the power generation and finding the best distribution of the generation among the units (units scheduling) using binary grey wolf optimizer based on particle swarm optimization (BGWOPSO) algorithm. The minimum production cost calculating is based on using the quadratic programming method and represents the global solution that must be arriving by the BGWOPSO algorithm then appearing units status (on or off). The suggested method was applied on “39 bus IEEE test systems”, the simulation results show the effectiveness of the suggested method over other algorithms in terms of minimizing of production cost and suggesting excellent scheduling of units.
Dynamic Modeling, Control and Simulation of a Wind and PV Hybrid System for G...IJERA Editor
This paper proposes a dynamic modeling and control strategy for a grid connected hybrid wind and photovoltaic (PV) energy system inter-connected to electrical grid through power electronic interface. A gearless permanent magnet synchronous generator (PMSG) is used to capture the maximum wind energy. The PV and wind systems are connected dc-side of the voltage source inverter through a boost converter individually and maintain a fixed dc output at dc link. A proper control scheme is required to operate power converters to match up the grid connection requirements. This study considered the performance of modeled hybrid system under different case scenarios. All simulation models are developed using MATLAB/Simulink.
MODELLING, ANALYSIS AND SIMULATION OF THE PIEZOELECTRIC MICRO PUMPadeij1
The piezoelectricity is a reversible phenomenon, which corresponds to the direct piezoelectric effect. So that, the battery loads arrive at the pump, an electronic module must be established in the circuit. A flow pump must be used and its effectiveness must be evaluated according to the desired need. The system is conceived around 24 hour old clock which can be programmed to provide fluid in variable quantity on a regular basis. The piezo-hydraulic pump presented in this work is composed mainly of shareholder piezoelectric with two valves and a diaphragm of the room reinforced by a hard disk. This one is used to improve the performance of the micro-pump in forecast of pump realization. Modeling, analysis and simulation are carried out under SYMBOLS software.
SIMULATION OF A MATHEMATICAL MODEL OF A WIND TURBINE Mellah Hacene
Abstract
This paper presents a mathematical model of a wind turbine and its simulation. This is one of the main resources available to
the island system (Grid-Off system).
Keywords: wind turbine, island system, Grid-Off system, renewable energy source.
1 Introduction to wind turbine
A wind turbine is basically a converter, or in other words a device that transforms one type of energy into
another. In this case, it is the transformation of mechanical energy into electrical energy.
The source of mechanical energy is the flow (flow) of air, which acts on the turbine blades. The blades are
located on a shaft which is coupled to a permanent magnet (magnet). The magnets are a rotating part, which is
named the rotor. The stator consists of a coil (coils) of wound copper conductor. Due to the changing magnetic
field (PM - permanent magnets), an electrical voltage is induced at the terminals (terminals) of the coil / coils. In
essence, it is a synchronous generator, since the variable electric field is coupled (synchronized) with the speed
of the changing and magnetic fields. [1-5]
A schematic block diagram of a wind turbine as a synchronous generator is shown in Fig. 1.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Benchmarking study between capacitive and electronic load technic to track I-...IJECEIAES
To detect defects of solar panel and understand the effect of external parameters such as fluctuations in illumination, temperature, and the effect of a type of dust on a photovoltaic (PV) panel, it is essential to plot the Ipv=f(Vpv) characteristic of the PV panel, and the simplest way to plot this I-V characteristic is to use a variable resistor. This paper presents a study of comparison and combination between two methods: capacitive and electronic loading to track I-V characteristic. The comparison was performed in terms of accuracy, response time and instrumentation cost used in each circuit, under standard temperature and illumination conditions by using polycrystalline solar panel type SX330J and monocrystalline solar panels type ET-M53630. The whole system is based on simple components, less expensive and especially widely used in laboratories. The results will be between the datasheet of the manufacturer with the experimental data, refinements and improvements concerning the number of points and the trace time have been made by combining these two methods.
Design and fabrication of rotor lateral shifting in the axial-flux permanent-...IJECEIAES
The development of axial-flux permanent-magnet (AFPM) machines has become a mature technology. The single-stator double-rotor (SSDR) AFPM structure has advantages on the compactness and the low up to medium power applications so the microscale size and low-cost applications are reachable to be designed. The research main objectives are designing and manufacturing the lateral shifting from the north poles of the first rotor face the north poles of the second rotor (NN) to the north poles of the first rotor face the south poles of the second rotor (NS) categories as well as finding the best performance of the proposed method and implementing in a low cost and micro-scale AFPMG. The novel lateral shifting on the one of the rotors shows performance at 19.2 0 has the highest efficiency at 88.39% during lateral shifting from N–N (0 0 ) to N–S (36 0 ) on rotor 2.
Optimizing of the installed capacity of hybrid renewable energy with a modifi...IJECEIAES
The lack of wind speed capacity and the emission of photons from sunlight are the problem in a hybrid system of photovoltaic (PV) panels and wind turbines. To overcome this shortcoming, the incremental conductance (IC) algorithm is applied that could control the converter work cycle and the switching of the buck boost therefore maximum efficiency of maximum power point tracking (MPPT) is reached. The operation of the PV-wind hybrid system, consisting of a 100 W PV array device and a 400 W wind subsystem, 12 V/100 Ah battery energy storage and LED, the PV-wind system requires a hybrid controller for battery charging and usage and load lamp and it’s conducted in experimental setup. The experimental has shown that an average increase in power generated was 38.8% compared to a single system of PV panels or a single wind turbine sub-system. Therefore, the potential opportunities for increasing power production in the tropics wheather could be carried out and applied with this model.
Modified T-type topology of three-phase multi-level inverter for photovoltaic...IJECEIAES
In this article, a three-phase multilevel neutral-point-clamped inverter with a modified t-type structure of switches is proposed. A pulse width modulation (PWM) scheme of the proposed inverter is also developed. The proposed topology of the multilevel inverter has the advantage of being simple, on the one hand since it does contain only semiconductors in reduced number (corresponding to the number of required voltage levels), and no other components such as switching or flying capacitors, and on the other hand, the control scheme is much simpler and more suitable for variable frequency and voltage control. The performances of this inverter are analyzed through simulations carried out in the MATLAB/Simulink environment on a threephase inverter with 9 levels. In all simulations, the proposed topology is connected with R-load or RL-load without any output filter.
This paper presents the modeling and simulation of wind energy Conversion System using the Permanent Magnet Synchronous Generator (PMSG). The objectives are: to extract the maximum power of the wind speed by controlling the electromagnetic torque of the PMSG, to maintain constant the DC-link voltage despite the wind speed variations and to attain the unity power factor. In order to ensure a regulation with high performance and a good robustness against the internal and the external disturbances, a new control strategy called the Active Disturbance Rejection Control (ADRC) is used. Therefore, the Analysis and simulation of the ADRC and PI controllers are developed with MATLAB/Simulink software. The performance of these controllers is compared in term of references tracking, robustness and grid faults.
Simulation of 3 Phase to 3 Phase Power Conversion Using Matrix Converter with...IJERA Editor
This paper proposes a new approach of design and implementation of 3 phase to 3 phase conversion using
matrix converter. It includes the design, modeling and implementation. The entire matrix converter circuits are
developed by mathematical model so as to reduce computational time and performances of the converter are
evaluated using MATLAB/SIMULINK for RL Load. The mathematical expressions relating the input and
output of the three phase matrix converter are implemented by using simulink block set. The duty cycles of the
matrix converter bidirectional switches are calculated using modified venturini algorithm for maximum (0.866)
and minimum (0.5) voltage transfer ratio.
Convergence analysis of the triangular-based power flow method for AC distribu...IJECEIAES
This paper addresses the convergence analysis of the triangular-based power flow (PF) method in alternating current radial distribution networks. The PF formulation is made via upper-triangular matrices, which enables finding a general iterative PF formula that does not require admittance matrix calculations. The convergence analysis of this iterative formula is carried out by applying the Banach fixed-point theorem (BFPT), which allows demonstrating that under an adequate voltage profile the triangular-based PF always converges. Numerical validations are made, on the well-known 33 and 69 distribution networks test systems. Gauss-seidel, newton-raphson, and backward/forward PF methods are considered for the sake of comparison. All the simulations are carried out in MATLAB software.
In this paper, we focus on the modeling and control of a wind power system based on a double-fed induction generator DFIG. We proposed a technique of active and reactive power control to improve the performance and dynamics of variable speed wind system. The objective of the modeling is to apply the direct and indirect vector control stator flux orientation to control independently, the active and reactive power generated doubly-fed induction generator (DFIG). The simulation results are tested and compared in order to evaluate the performance of the proposed system.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
MODELING AND OPTIMIZATION OF PIEZOELECTRIC ENERGY HARVESTING adeij1
In this paper, the modeling, optimization and simulation results of the piezoelectric energy harvesting using bond graph approach are presented. Firstly, a lightweight equivalent model derived from the bond graph is proposed. It’s a comprehensive model, which is suitable for piezoelectric seismic energy harvester investigation and power optimization. The optimal charge impedance for both the resistive load and complex load are given and analysed. Finally a bond graph approach is proposed to allow optimization of the extracted energy while keeping simplicity and standalone capability. The proposed model does not rely on any inductor and is constructed with a simple switch. The power harvested is more than twice the conventional technique one on a wide band of resistive load. The bond graph model is valid close to the analysed mode centre frequency and delivers results compared to experimental and analytical data. Furthermore, we also show that the harvester can be electrically tuned to match the excitation frequency. This makes it possible to maximize the power output for both linear and non-linear loads.
A hybrid algorithm for voltage stability enhancement of distribution systems IJECEIAES
This paper presents a hybrid algorithm by applying a hybrid firefly and particle swarm optimization algorithm (HFPSO) to determine the optimal sizing of distributed generation (DG) and distribution static compensator (D-STATCOM) device. A multi-objective function is employed to enhance the voltage stability, voltage profile, and minimize the total power loss of the radial distribution system (RDS). Firstly, the voltage stability index (VSI) is applied to locate the optimal location of DG and D-STATCOM respectively. Secondly, to overcome the sup-optimal operation of existing algorithms, the HFPSO algorithm is utilized to determine the optimal size of both DG and D-STATCOM. Verification of the proposed algorithm has achieved on the standard IEEE 33-bus and Iraqi 65-bus radial distribution systems through simulation using MATLAB. Comprehensive simulation results of four different cases show that the proposed HFPSO demonstrates significant improvements over other existing algorithms in supporting voltage stability and loss reduction in distribution networks. Furthermore, comparisons have achieved to demonstrate the superiority of HFPSO algorithms over other techniques due to its ability to determine the global optimum solution by easy way and speed converge feature.
Parametric estimation in photovoltaic modules using the crow search algorithmIJECEIAES
The problem of parametric estimation in photovoltaic (PV) modules considering man- ufacturer information is addressed in this research from the perspective of combinatorial optimization. With the data sheet provided by the PV manufacturer, a non-linear non-convex optimization problem is formulated that contains information regarding maximum power, open-circuit, and short-circuit points. To estimate the three parameters of the PV model (i.e., the ideality diode factor (a) and the parallel and series resistances (R p and R )), the crow search algorithm (CSA) is employed, which is a metaheuristic optimization technique inspired by the behavior of the crows searching food deposits. The CSA allows the exploration and exploitation of the solution space through a simple evolution rule derived from the classical PSO method. Numerical simulations reveal the effectiveness and robustness of the CSA to estimate these parameters with objective function values lower than 1 10 s 28 and processing times less than 2 s. All the numerical simulations were developed in MATLAB 2020a and compared with the sine-cosine and vortex search algorithms recently reported in the literature.
Wind Energy Conversion Based On Matrix ConverterIAES-IJPEDS
In recent years renewable sources such as solar, wave and wind are used for the generation of electricity. Wind is one of the major renewable sources. The amount of energy from a Wind Energy Conversion System (WECS) depends not only on the wind at the site, but also on the control strategy used for the WECS. In assistance to get the appropriate wind energy from the conversion system, wind turbine generator will be run in variable speed mode. The variable speed capability is achieved through the use of an advanced power electronic converter. Fixed speed wind turbines and induction generators are often used in wind farms. But the limitations of such generators are low efficiency and poor power quality which necessitates the variable speed wind turbine generators such as Doubly Fed Induction Generator (DFIG) and Permanent Magnet Synchronous Generator (PMSG). A high-performance configuration can be obtained by using a PMSG and a converter in combination AC-DC-AC connect between stator & rotor points for providing the required variable speed operation.
The hardware implementation of sensorless brushless direct current motor drive incorporating H-infinity control strategy with optimized weights by particle swarm optimization in the speed control is carried out in this work. The methodology involved in the design of brushless direct current (BLDC) motor control with sensorless position detection technique, the design of H-infinity speed controller, steps involved in particle swarm optimization for optimizing coefficients of its weights and the hardware implementation is discussed in detail in this paper. Texas Instruments microcontroller board C2000 Delfino Launchpad LAUNCHXL F28377S and driver BOOSTXL DRV8301 are used for realization of the speed controller. The code is developed using C2000 hardware support package in MATLAB/SIMULINK platform. A comprehensive performance analysis is accomplished during starting of the motor and during the fast application and removal of load. This strategy is found to be robust resulting in faster load disturbance rejection and better reference speed tracking. The experimental results of the proposed strategy are compared with that of conventional proportional-integral (PI) controller. The time domain parameters are also compared. It is found that the proposed strategy exhibits better performance characteristics during transients and sudden disturbances in load.
The optimal solution for unit commitment problem using binary hybrid grey wol...IJECEIAES
The aim of this work is to solve the unit commitment (UC) problem in power systems by calculating minimum production cost for the power generation and finding the best distribution of the generation among the units (units scheduling) using binary grey wolf optimizer based on particle swarm optimization (BGWOPSO) algorithm. The minimum production cost calculating is based on using the quadratic programming method and represents the global solution that must be arriving by the BGWOPSO algorithm then appearing units status (on or off). The suggested method was applied on “39 bus IEEE test systems”, the simulation results show the effectiveness of the suggested method over other algorithms in terms of minimizing of production cost and suggesting excellent scheduling of units.
Dynamic Modeling, Control and Simulation of a Wind and PV Hybrid System for G...IJERA Editor
This paper proposes a dynamic modeling and control strategy for a grid connected hybrid wind and photovoltaic (PV) energy system inter-connected to electrical grid through power electronic interface. A gearless permanent magnet synchronous generator (PMSG) is used to capture the maximum wind energy. The PV and wind systems are connected dc-side of the voltage source inverter through a boost converter individually and maintain a fixed dc output at dc link. A proper control scheme is required to operate power converters to match up the grid connection requirements. This study considered the performance of modeled hybrid system under different case scenarios. All simulation models are developed using MATLAB/Simulink.
MODELLING, ANALYSIS AND SIMULATION OF THE PIEZOELECTRIC MICRO PUMPadeij1
The piezoelectricity is a reversible phenomenon, which corresponds to the direct piezoelectric effect. So that, the battery loads arrive at the pump, an electronic module must be established in the circuit. A flow pump must be used and its effectiveness must be evaluated according to the desired need. The system is conceived around 24 hour old clock which can be programmed to provide fluid in variable quantity on a regular basis. The piezo-hydraulic pump presented in this work is composed mainly of shareholder piezoelectric with two valves and a diaphragm of the room reinforced by a hard disk. This one is used to improve the performance of the micro-pump in forecast of pump realization. Modeling, analysis and simulation are carried out under SYMBOLS software.
SIMULATION OF A MATHEMATICAL MODEL OF A WIND TURBINE Mellah Hacene
Abstract
This paper presents a mathematical model of a wind turbine and its simulation. This is one of the main resources available to
the island system (Grid-Off system).
Keywords: wind turbine, island system, Grid-Off system, renewable energy source.
1 Introduction to wind turbine
A wind turbine is basically a converter, or in other words a device that transforms one type of energy into
another. In this case, it is the transformation of mechanical energy into electrical energy.
The source of mechanical energy is the flow (flow) of air, which acts on the turbine blades. The blades are
located on a shaft which is coupled to a permanent magnet (magnet). The magnets are a rotating part, which is
named the rotor. The stator consists of a coil (coils) of wound copper conductor. Due to the changing magnetic
field (PM - permanent magnets), an electrical voltage is induced at the terminals (terminals) of the coil / coils. In
essence, it is a synchronous generator, since the variable electric field is coupled (synchronized) with the speed
of the changing and magnetic fields. [1-5]
A schematic block diagram of a wind turbine as a synchronous generator is shown in Fig. 1.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Modeling of Wind Energy on Isolated AreaIJPEDS-IAES
In this paper, a model of the wind turbine (WT) with permanent magnet generator (PMSG) and its associated controllers is presented. The increase of wind power penetration in power systems has meant that conventional power plants are gradually being replaced by wind farms. In fact, today wind farms are required to actively participate in power system operation in the same way as conventional power plants. In fact, power system operators have revised the grid connection requirements for wind turbines and wind farms and now demand that these installations be able to carry out more or less the same control tasks as conventional power plants. For dynamic power system simulations, the PMSG wind turbine model includes an aerodynamic rotor model, a lumped mass representation of the drive train system and generator model. In this paper we propose a model with an implementation in MATLAB / Simulink, each of the system components off-grid small wind turbines.
Study of Wind Turbine based Variable Reluctance Generator using Hybrid FEMM-M...IJECEIAES
Based on exhaustive review of the state of the art of the electric generators fitted to Wind Energy Conversion System (WECS), this study is focused on an innovative machine that is a Variable Reluctance Generator (VRG). Indeed, its simple and rugged structure (low cost), its high torque at low speed (gearless), its fault-tolerance (lowest maintenance), allow it to be a potential candidate for a small wind power application at variable wind speed. For better accuracy, a finite element model of a studied doubly salient VRG is developed using open source software FEMM to identify the electromagnetic characteristics such as linkage flux, torque or inductance versus rotor position and stator excitation. The obtained data are then transferred into look-up tables of MATLAB/Simulink to perform various simulations. Performance of the proposed wind power system is analyzed for several parameters and results are discussed.
Wind energy has many advantages, it does not pollute and it is an inexhaustible source. However, the cost of this energy is still too high to compete with traditional fossil sources. The yield of a wind turbine depends on three parameters: the power of the wind, the turbine power curve and the ability of the generator to respond to fluctuations in the wind. This article presented the MPPT of a wind turbine system equipped with an asynchronous generator has dual power under MatlabSimulink program, in the first time we simulated all the conversion chain with complete model of DFIG and vector control in second stepthen applied the extracted maximum power MPPT strategists, this command is effective and has several advantages it offered to kept the maximum power delivered to network despite all the parameter is change.
Wind Turbine Generator Tied To Grid Using Inverter Techniques and Its DesignsIJSRD
This paper proposes a method of using small sizes WTG of 300W low capacity turbine in small grid channel with inverter techniques. Power can be fed directly to grid by improving durability and eliminating battery usage, using WTG inverter technique. The proposed wind tied with grid by PMG includes boost converter and three phase inverter. For tracking wind speed with variations of wind power MPPT method is used. Interleaving technique is adopted for different frequency variables to improve power capacity. Final result proves WTG helps in improving wind power application as shown in simulation result.
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Modeling and Control of a Doubly-Fed Induction Generator for Wind Turbine-Gen...IJPEDS-IAES
This paper presents a vector control direct (FOC) of double fed induction generator intended to control the generated stator powers. This device is intended to be implemented in a variable-speed wind-energy conversion system connected to the grid. In order to control the active and reactive power exchanged between the machine stator and the grid, the rotor is fed by a bi-directional converter. The DFIG is controlled by standard relay controllers. Details of the control strategy and system simulation were performed using Simulink and the results are presented in this here to show the effectiveness of the proposed control strategy.
In this paper, we focus on the modeling and control of a wind power system based on a Permanent Magnet Synchronous Generator (PMSG). We proposed a technique of control strategies to have the maximum power from wind turbine (WT). This study deals with the problem of Maximum Power Point Tracking (MPPT) based on Takagi Sugeno fuzzy model. The stability analysis is achieved. The gains of the designed controller are calculated by solving Linear Matrix Inequality (LMI). Finally, simulation results are provided to demonstrate the validity and the effectiveness of the proposed method.
This paper focuses on the modeling and control of a wind energy conversion chain using a permanent magnet synchronous machine. This system behaves a turbine, a generator, DC/DC and DC/AC power converters. These are connected on both sides to the DC bus, where the inverter is followed by a filter which is connected to the grid. In this paper, we have been used two types of controllers. For the stator side converter, we consider the Takagi-Sugeno approach where the parameters of controller have been computed by the theory of linear matrix inequalities. The stability synthesis has been checked using the Lyapunov theory. According to the grid side converter, the proportional integral controller is exploited to keep a constant voltage on the DC bus and control both types of powers. The simulation results demonstrate the robustness of the approach used.
This paper presents a study analysis of a complete wind energy conversion system, the system based on a doubly fed induction generator (DFIG); a vector control with stator flux orientation of the DFIG is also used to control independently the active and reactive powers. A comparative study have been performed between the conventional PI controller and fuzzy logic control to investigate its dynamic and static performances. This research work involves the study of a phase in advance, to provide effective assistance, to all those who have to make decisions regarding the planning and implementation of wind energy projects. The main objective is to model the wind chain and the use of two types of strategies for the control of this generator to ensure a good regulation we started with the modeling of the wind chain then the modeling of the DFIG and then the use of the two strategies for the regulation of the latter .The complete system is modeled and simulated in the MATLAB/ Simulink. The performance and robustness are analyzed and compared by Matlab / Simulink .Simulation results prove the excellent performance of fuzzy control unit as improving power quality and stability of wind turbine.
Direct and indirect vector control of a doubly fed induction generator based ...IJECEIAES
In the recent years, the development and the exploitation of renewable energy knew a great evolution. Among these energy resources, the wind power represents an important potential for that the wind system has been the subject of several researches. The purpose of this study is to improve the power extracted from wind energy, taking into consideration the variation of wind speed which causes a problem in energy production. For this purpose, we have controlled the powers whether it is active or reactive delivered by the generator. This paper, presents essentially the modeling and control of doubly- fed induction generator (DFIG), which is connected to a variable speed wind turbine. Firstly, the model of the wind power system with the maximum power point tracking (MPPT) strategy is shown. Then, the modeling of doubly- fed induction generator (DFIG) and its power control is presented. Finnaly, to ensure the attitude of these controls the simulations is presented in the Matlab/Simulink environment.
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Environmental factors such as air pollution and increase in global warming by using polluting fuels are the most important reasons of using renewable and clean energy that runs in global community. Wind energy is one of the most suitable and widely used kind of renewable energy which had been in consideration so well. This paper introduces an electric power generation
system of wind based on Y-source and improved Y-source inverter to deliver optimal electrical power to the network. This new converter is from impedance source converters family. This presented converter has more degrees of freedom to adjust voltage gain and modulation. Also, by limiting the range of simultaneous control (shooting through) while it maintains the
highest power of maximizer, it can operate in higher modulation range. This causes the reduce of stress in switching and thus it will improve the quality of output. Recommended system had been simulated in MATLAB/Simulink and shown results indicate accurate functionality.
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Slide 2: Introduction to Extrachromosomal Inheritance
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Bio
Dr. Michel Dumontier is the Distinguished Professor of Data Science at Maastricht University, founder and executive director of the Institute of Data Science, and co-founder of the FAIR (Findable, Accessible, Interoperable and Reusable) data principles. His research explores socio-technological approaches for responsible discovery science, which includes collaborative multi-modal knowledge graphs, privacy-preserving distributed data mining, and AI methods for drug discovery and personalized medicine. His work is supported through the Dutch National Research Agenda, the Netherlands Organisation for Scientific Research, Horizon Europe, the European Open Science Cloud, the US National Institutes of Health, and a Marie-Curie Innovative Training Network. He is the editor-in-chief for the journal Data Science and is internationally recognized for his contributions in bioinformatics, biomedical informatics, and semantic technologies including ontologies and linked data.
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MATHEMATICAL MODEL OF WIND TURBINE IN GRID-OFF SYSTEM
1. Milan Jus / University Review, Vol. 14, 2020, No. 1, p. 10-13
1
MATHEMATICAL MODEL OF WIND TURBINE IN GRID-OFF SYSTEM
Milan JUS
Ing. Milan Jus, PhD., Faculty o Special Technology, Alexander Dubček University of Trenčín, Pri Parku 19, 911 06
Trenčín, Slovakia
Corresponding author E-mail address: milan.jus@tnuni.sk
Abstract
This paper deals with the construction of a mathematical model of a wind turbine, which is one of the sources in the Grid-Off
system.
Keywords: mathematical model, wind turbine, Grid-Off system, electric generator, wind conditions.
1 Introduction
As one of the power sources of the Grid-Off system is a wind turbine. It is advantageous to work with a
mathematical model for the need of experimental research. In Fig. 1 is a schematic connection of a wind turbine
to a container, which is a Grid-Off system. [1-4]
Fig. 1 Wind turbine connection - Grid-Off system
The process of producing electricity is, which in this case applies is as follows. The wind is carrying kinetic
energy. Basically, the flow of air mass. The wind causes the propeller blades to rotate, so the kinetic energy is
converted to mechanical energy. Subsequently, this mechanical energy is transformed into electrical energy by
means of a suitable generator.
The mass flow energy passing through the area S determines the power of the intact air flow
𝑃 =
1
2
𝜌𝑆𝑣3
(1)
where is air density ([] = kg/m3
), S is area ([S] = m2
) and v is velocity of flowing air ([v] = m/s).
The mechanical energy that can be obtained by converting the kinetic energy of the air flow corresponds to
the difference in power of the air flow upstream and downstream of the turbine, as shown in Fig. 2. The
mathematical expression is as follows:
𝑃 =
1
2
𝜌𝑆1 𝑣1
3
−
1
2
𝜌𝑆2 𝑣2
3
(2)
Fig. 2 Air flow through turbine
Based on the continuity equation is valid
Container
S1
S
S2
v2
v1
v
2. Milan Jus / University Review, Vol. 14, 2020, No. 1, p. 10-13
2
𝜌𝑆1 𝑣1 = 𝜌𝑆2 𝑣2 = 𝜌𝑆3 𝑣3 (3)
We can then equation (2) using equation (3) shaped in the form
𝑃 =
1
2
𝜌𝑆1 𝑣1(𝑣1
2
− 𝑣2
2) (4)
The mechanical power of the wind turbine rotor can be expressed by relation (4) considering the momentum
conservation law and its mathematical expression is
𝑃 =
1
4
𝜌𝑆𝑣1
3
(1 −
𝑣2
2
𝑣1
2 +
𝑣2
𝑣1
−
𝑣2
3
𝑣1
3) =
1
2
(1 −
𝑣2
2
𝑣1
2 +
𝑣2
𝑣1
−
𝑣2
3
𝑣1
3)
⏟
𝐶 𝑝
1
2
𝜌𝑆𝑣1
3
⏟
𝑃 𝑤
(5)
where Cp is dimensionless ratio of the extractable power P to the kinetic power Pw available in the undistributed
stream. [4-5]
Maximum mechanical performance can only be achieved under certain conditions when the ratio v2/v1 is 1/3.
In this case, the theoretical value of 59. 26 % is reached. [6]
The ratio of the peripheral speed of the rotor blade tip to the speed of the intact air flow upstream of the
turbine is called turbine speed [7]
𝜆 =
𝜔 𝑟 𝑅 𝑡
𝑣1
(6)
Next, we express the relation for the calculation of the mechanical moment Tm of the turbine rotor
𝑇 𝑚 =
𝑃
𝜔 𝑟
=
𝐶 𝑝
1
2
𝜌𝑆𝑣1
3
𝜔 𝑟
=
1
2
𝜌𝑆
𝐶 𝑝 𝑣1
3
𝜆𝑣1
𝑅 𝑡
=
1
2
𝜌𝑆𝑣1
2
𝑅𝑡
𝐶 𝑝
𝜆⏟
𝐶 𝑞
=
1
2
𝜌𝑆𝑣1
2
𝑅𝑡 𝐶 𝑞 (7)
where Cq is turbine rotor torque coefficient. [8-9]
2 Synchronous generator
The transformation of mechanical energy into electrical energy is carried out by means of a wind turbine,
which is a synchronous generator with permanent magnets. The schematic diagram of the generator is shown in
Fig. 3.
Fig. 3 Transformation of mechanical energy into electrical energy
The wind turbine includes blades that rotate the shaft on which the rotor of the permanent magnet
synchronous generator is mounted. The rotor is formed by a permanent magnet, which causes a time-varying
magnetic field, which results in voltage generation in the stator winding.
A schematic representation of a synchronous generator with a rotor of a permeable magnet and a stator
formed by a winding is shown in Fig. 4.
GeneratorWind
3. Milan Jus / University Review, Vol. 14, 2020, No. 1, p. 10-13
3
Fig. 4 A schematic representation of a synchronous generator
Depending on the torque balance condition, the dynamic system applies
𝑇 𝑚 = 𝑇𝑔 + 𝐽 𝑎
𝑑𝜔 𝑟
𝑑𝑡
(8)
where Tm is the turbine torque produced by the wind on its blades, Tg is the braking torque of the generator with
the load acting against the mechanical torque of the turbine and Jt is the moment of inertia of the aggregate. If we
use the equation (7) and equation (8) we can adapt to the shape
𝑑𝜔 𝑟
𝑑𝑡
=
𝑇 𝑚−𝑇 𝑔
𝐽 𝑎
=
1
2
𝜌𝑆𝑣1
2 𝑅 𝑡 𝐶 𝑞−𝑇 𝑔
𝐽 𝑎
(9)
The permanent magnets in the rotor, by their rotation around the stator, induce the internal voltage of the
generator, for which
𝐸𝑔 = K 𝑝𝑚
𝜔 𝑟 𝑛 𝑝
2
(10)
where Kpm is constant, which expresses the magnetic field strength of the permanent magnets of the generator, 𝑛p
is the number of poles of the generator and 𝜔r is the angular velocity of the rotor. [10-13]
If X is the reactance of the generator coil (X = 𝜔gLs, 𝜔g = 𝑛p 𝜔r/2), and is angle between Ug and Eg, the
equation applies to the terminal voltage Ug
𝑼 𝑔 = 𝑬 𝑔 − j𝑋𝑰 𝑔 = |𝑬 𝑔|e 𝑗𝛿
− 𝑋|𝑰 𝑔|e 𝑗
𝜋
2 = 𝐸𝑔cos(𝛿) + j𝐸𝑔sin(𝛿) − j𝑋𝐼𝑔⏟
0
= 𝐸𝑔cos(𝛿) (11)
where
𝐸𝑔 sin(𝛿) = 𝑋𝐼𝑔 (12)
The active power of the generator can be expressed as
𝑃𝑔 =
3𝐸 𝑔 𝑈 𝑔
𝑋
sin(𝛿) (13)
Equation (13) using equation (11) and (10) can be modified to shape
𝑃𝑔 =
3𝐸 𝑔 𝐸 𝑔
𝑋
cos(𝛿) sin(𝛿)⏟
1
2
sin(2𝛿)
=
3𝐸 𝑔
2
2𝑋
sin(2𝛿) =
3(K 𝑝𝑚
𝜔 𝑟 𝑛 𝑝
2
)
2
2𝑋
sin(2𝛿) =
3
8𝑋
(K 𝑝𝑚 𝜔𝑟 𝑛 𝑝)
2
sin(2𝛿) (14)
If we consider equation (12), then equation (14) can be expressed as
𝑃𝑔 =
3𝐸 𝑔
2
𝑋
cos(𝛿) sin(𝛿) =
3(
𝑋𝐼 𝑔
sin(𝛿)
)
2
𝑋
cos(𝛿) sin(𝛿) =
3𝐼 𝑔
2 𝑋
tan(𝛿)
(15)
Generator moment Tg can be expressed depending on which equation we use, whether (15) or (14)
𝑇𝑔 =
𝑃 𝑔
𝜔 𝑟
=
3𝐼 𝑔
2 𝑋
𝜔 𝑟 tan(𝛿)
=
3𝐼 𝑔
2 𝐿 𝑠 𝑛 𝑝
2 tan(𝛿)
(16)
r
Permanent magnet (rotor)
Coil (stator)
Ls
4. Milan Jus / University Review, Vol. 14, 2020, No. 1, p. 10-13
4
𝑇𝑔 =
𝑃 𝑔
𝜔 𝑟
=
3
8𝑋𝜔 𝑟
(K 𝑝𝑚 𝜔𝑟 𝑛 𝑝)
2
sin(2𝛿) (17)
Based on these mathematical expressions, it is possible to construct a mathematical model by considering the
particular parameters of a real wind turbine in the equations. The input parameter is the wind speed and the
electrical output generated. It is also possible to add a connected load or use a more sophisticated wind model.
Also in the model could be expressed regulation of wind turbine blades, possibly supplemented generator with
speed control (angular speed).
3 Conclusion
In this paper is analyzed generator of electric energy, which is formed by wind turbine. It's about using that
generator in the Grid-Off system. Mathematically, the continuity and continuity between the kinetic energy
conversion that is contained in the wind and converted to the mechanical energy of the turbine are expressed.
Subsequently, this mechanical energy is transformed into electrical energy by means of a synchronous permanent
magnet generator.
Acknowledgements
The paper was treated within the project no. ITMS 26220220083 "Research technological base for designing
applications for renewable energy in practice" EU operational program "Research and Development".
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