This document summarizes the application of Quantitative Feedback Theory (QFT) for the design of wind turbine speed controllers. QFT is well-suited for controlling wind turbines because it can explicitly account for process uncertainty caused by changing wind conditions. The document first discusses challenges in controlling nonlinear wind turbine systems using classical control methods. It then provides motivation for using QFT, describing its ability to guarantee stability and performance specifications despite process uncertainty. The core concepts of QFT, including the use of templates and frequency domain boundaries, are explained. Finally, the document outlines the modeling of wind turbines needed as the first step of the QFT design process.
This paper aims to design the pitch angle control based on proportional–integral–derivative (PID) controller combined with fuzzy logic for small-scale wind turbine systems. In this control system, the pitch angle is controlled by the PID controller with their parameter is tuned by the fuzzy logic controller. This control system can compensate for the nonlinear characteristic of the pitch angle and wind speed. A comparison between the fuzzy-PID-controller with the conventional PID controller is carried out. The effectiveness of the method is determined by the simulation results of a small wind turbine using a permanent magnet generator (PMSG).
IRJET - Vector Control of Permenant Magnet Synchronous MotorIRJET Journal
This document discusses vector control techniques for permanent magnet synchronous motors (PMSM). It describes field oriented control, direct torque control, voltage vector control, and passivity based control. It then discusses the components of a PMSM drive system, including the motor, inverter, and PID speed controller. It presents the mathematical model and torque equation for vector control of PMSM. Finally, it discusses simulating the PMSM drive system in MATLAB/Simulink using reverse Park transformations, hysteresis current control, and testing in the constant torque region of operation.
Permanent Magnet Synchronous Generator Wind Turbine Pitch Angle Control by Fu...IRJET Journal
This document discusses using fuzzy logic control and PID control together for pitch angle control of wind turbines. It begins with background on wind turbine components and control methods. Existing pitch control methods like PI, PID, and fuzzy logic are described along with their drawbacks. The document then proposes a combined fuzzy-PID controller and simulates it in MATLAB. Simulation results show the combined controller reduces power output fluctuations and improves tracking of reference speeds compared to other methods. It is concluded that fuzzy-PID control is more robust to nonlinearities and provides better performance than individual controllers.
Direct Torque Control for Doubly Fed Induction Machine-Based Wind Turbines un...IJMTST Journal
This document discusses direct torque control for doubly fed induction machine wind turbines under voltage dips. It proposes a rotor flux amplitude reference generation strategy to control the torque and reduce overcurrents during faults like voltage dips. The strategy uses direct torque control accompanied by overall wind turbine control. While it does not eliminate the need for crowbar protection, it can eliminate activation of crowbar protection during low depth voltage dips. Simulation results show that the reference generation strategy maintains machine connection to the grid and power generation during faults by reducing overcurrents and torque oscillations compared to no reference strategy.
This document discusses several topics related to power system operation and control:
1. It defines a control area as a region where all generators swing together in response to load changes or speed governor settings.
2. It explains that voltage stability refers to a power system reaching a stable post-disturbance voltage equilibrium.
3. It describes different approaches for steady-state security analysis, which test the system against contingencies by calculating changes and checking against constraints.
Hysteresis Current Control of Switched Reluctance Motor in Aircraft ApplicationsIAES-IJPEDS
The document discusses hysteresis current control of a switched reluctance motor (SRM) for aircraft applications. It introduces two hysteresis control modes - hard chopping and soft chopping. Hard chopping switches the phase voltage between -U and +U, producing larger current ripples. Soft chopping switches between 0 and +U, allowing better current control with lower ripple. The document presents Simulink models of SRM using hard chopping control at no load with source voltages of 220V and 350V. At higher voltage, phase currents overlap more but torque ripple increases. Hysteresis control aims to maintain torque within a band for steady motor operation.
Starting of induction motor fed with stand-alone DFIGjournalBEEI
The document presents a simulation of a stand-alone doubly fed induction generator (DFIG) supplying power to induction motors (IMs). Applying constant voltage-to-frequency (V/f) control to the DFIG during motor starting reduces the starting current and mitigates voltage sag caused by direct online starting of large IMs. Simulation results show that with the proposed control, a DFIG can start a 5.4 hp IM while maintaining voltage sag below 21% and start a 10 hp IM, addressing the challenges of high starting current and voltage sag without requiring an oversized generator or special starters.
A Lyapunov Based Approach to Enchance Wind Turbine Stabilityijeei-iaes
This paper introduces a nonlinear control of a wind turbine based on a Double Feed Induction Generator. The Rotor Side converter is controlled by using field oriented control and Backstepping strategy to enhance the dynamic stability response. The Grid Side converter is controlled by a sliding mode. These methods aim to increase dynamic system stability for variable wind speed. Hence, The Doubly Fed Induction Generator (DFIG) is studied in order to illustrate its behavior in case of severe disturbance, and its dynamic response in grid connected mode for variable speed wind operation. The model is presented and simulated under Matlab/ Simulink.
This paper aims to design the pitch angle control based on proportional–integral–derivative (PID) controller combined with fuzzy logic for small-scale wind turbine systems. In this control system, the pitch angle is controlled by the PID controller with their parameter is tuned by the fuzzy logic controller. This control system can compensate for the nonlinear characteristic of the pitch angle and wind speed. A comparison between the fuzzy-PID-controller with the conventional PID controller is carried out. The effectiveness of the method is determined by the simulation results of a small wind turbine using a permanent magnet generator (PMSG).
IRJET - Vector Control of Permenant Magnet Synchronous MotorIRJET Journal
This document discusses vector control techniques for permanent magnet synchronous motors (PMSM). It describes field oriented control, direct torque control, voltage vector control, and passivity based control. It then discusses the components of a PMSM drive system, including the motor, inverter, and PID speed controller. It presents the mathematical model and torque equation for vector control of PMSM. Finally, it discusses simulating the PMSM drive system in MATLAB/Simulink using reverse Park transformations, hysteresis current control, and testing in the constant torque region of operation.
Permanent Magnet Synchronous Generator Wind Turbine Pitch Angle Control by Fu...IRJET Journal
This document discusses using fuzzy logic control and PID control together for pitch angle control of wind turbines. It begins with background on wind turbine components and control methods. Existing pitch control methods like PI, PID, and fuzzy logic are described along with their drawbacks. The document then proposes a combined fuzzy-PID controller and simulates it in MATLAB. Simulation results show the combined controller reduces power output fluctuations and improves tracking of reference speeds compared to other methods. It is concluded that fuzzy-PID control is more robust to nonlinearities and provides better performance than individual controllers.
Direct Torque Control for Doubly Fed Induction Machine-Based Wind Turbines un...IJMTST Journal
This document discusses direct torque control for doubly fed induction machine wind turbines under voltage dips. It proposes a rotor flux amplitude reference generation strategy to control the torque and reduce overcurrents during faults like voltage dips. The strategy uses direct torque control accompanied by overall wind turbine control. While it does not eliminate the need for crowbar protection, it can eliminate activation of crowbar protection during low depth voltage dips. Simulation results show that the reference generation strategy maintains machine connection to the grid and power generation during faults by reducing overcurrents and torque oscillations compared to no reference strategy.
This document discusses several topics related to power system operation and control:
1. It defines a control area as a region where all generators swing together in response to load changes or speed governor settings.
2. It explains that voltage stability refers to a power system reaching a stable post-disturbance voltage equilibrium.
3. It describes different approaches for steady-state security analysis, which test the system against contingencies by calculating changes and checking against constraints.
Hysteresis Current Control of Switched Reluctance Motor in Aircraft ApplicationsIAES-IJPEDS
The document discusses hysteresis current control of a switched reluctance motor (SRM) for aircraft applications. It introduces two hysteresis control modes - hard chopping and soft chopping. Hard chopping switches the phase voltage between -U and +U, producing larger current ripples. Soft chopping switches between 0 and +U, allowing better current control with lower ripple. The document presents Simulink models of SRM using hard chopping control at no load with source voltages of 220V and 350V. At higher voltage, phase currents overlap more but torque ripple increases. Hysteresis control aims to maintain torque within a band for steady motor operation.
Starting of induction motor fed with stand-alone DFIGjournalBEEI
The document presents a simulation of a stand-alone doubly fed induction generator (DFIG) supplying power to induction motors (IMs). Applying constant voltage-to-frequency (V/f) control to the DFIG during motor starting reduces the starting current and mitigates voltage sag caused by direct online starting of large IMs. Simulation results show that with the proposed control, a DFIG can start a 5.4 hp IM while maintaining voltage sag below 21% and start a 10 hp IM, addressing the challenges of high starting current and voltage sag without requiring an oversized generator or special starters.
A Lyapunov Based Approach to Enchance Wind Turbine Stabilityijeei-iaes
This paper introduces a nonlinear control of a wind turbine based on a Double Feed Induction Generator. The Rotor Side converter is controlled by using field oriented control and Backstepping strategy to enhance the dynamic stability response. The Grid Side converter is controlled by a sliding mode. These methods aim to increase dynamic system stability for variable wind speed. Hence, The Doubly Fed Induction Generator (DFIG) is studied in order to illustrate its behavior in case of severe disturbance, and its dynamic response in grid connected mode for variable speed wind operation. The model is presented and simulated under Matlab/ Simulink.
Speed Sensor less DTC of VSI fed Induction Motor with Simple Flux Regulation ...IRJET Journal
This document discusses improving speed and torque estimations for direct torque control of an induction motor at low speeds. It proposes using a constant switching frequency controller instead of a 3-level hysteresis torque comparator to maintain constant switching frequency while improving stator flux regulation at low speeds. An extended Kalman filter-based estimator is used to estimate speed feedback for closed-loop speed control without requiring a speed sensor. Simulation results using MATLAB/Simulink software are presented to validate the approach for low speed operation. The goal is to develop a simple sensorless direct torque control method with improved performance at low and zero speeds.
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.
These energy transits constitute a flow going from the substations where the
power plants are connected to the substations where customers are connected;
it is conveyed through the transmission lines and cables and divided up
proportionally to the admittance, i.e. the impedance reciprocal (which is in
some way a marked preference for the "shortest route"). This energy flow is
materialised by the current conveyed through the facilities. The higher the
energy flow is, the greater the current intensities will be. These intensities may
increase, in particular when a facility has tripped following a fault occurrence.
The flow initially borne by this facility will be transferred to the neighbouring
facilities: this is the load transfer phenomenon.
A novel optimum tip speed ratio control of low speed wind turbine generator b...journalBEEI
Variable speed control of wind turbine generator systems have been developed to get maximum output power at every wind speed variation, also called Maximum Power Points Tracking (MPPT). Generally, MPPT control system consists of MPPT algorithm to track the controller reference and generator speed controller. In this paper, MPPT control system is proposed for low speed wind turbine generator systems (WTGs) with MPPT algorithms based on optimum tip speed ratio (TSR) and generator speed controller based on field oriented control using type-2 fuzzy system (T2FS). The WTGs are designed using horizontal axis wind turbines to drive permanent magnet synchronous generators (PMSG). The simulation show that the MPPT system based optimum TSR has been able to control the generator output power around the maximum point at all wind speeds.
Vector control of AC induction motors provides superior dynamic performance compared to scalar control by decoupling torque and flux control. Vector control represents the stator currents as direct and quadrature components (Ids and Iqs) that independently control flux and torque. This allows precise and independent control of torque and flux to eliminate oscillations for applications requiring high performance like robotics. Vector control implementations determine the orientation of Ids and Iqs either directly by measuring airgap flux or indirectly by measuring slip speed to achieve independent control of the current components.
Advanced Optimal PSO, Fuzzy and PI Controller with PMSM and WTGS at 5Hz Side ...IAES-IJPEDS
To use different control systems, like classical PI controller, Expert System
Fuzzy Logic Controller and optimization PSO controller. It used to control
for PMSM which worked in the integration system to Wind Energy. Wind
energy content of wind turbine, PMSM, rectifier, DC bus, inverter, filter,
load and grid. In the first step, to run the PMSM with different speeds to get
a different frequency to select the frequency on the side of a generation with
the rated speed. Second step, solve the mathematical equation to use different
values of wind speed with selected (15,20 m/s and less than with more than
15&20m/s). Third step, calculation the power generation with wind speed
(15 m/5 & 20 m/s). Fourth step, using these component system rectifier, DC
bus, inverter, filter, load & grid with WTGS & PMSM. Final step, uses
different control systems, like classical PI controller, Expert System Fuzzy
Logic controller and optimization PSO controller with PMSM to analyze all
results after using the simulation model of proposed variable speed based on
WECS. The wind turbine is coupled with PMSM. A closed loop control
system with a PI control, fuzzy, PSO in the speed loop with current
controllers. The simulation circuits for PMSM, inverter, speed and current
controllers include all realistic components of the drive system. These results
also confirmed that the transient torque and current never exceed the
maximum permissible value.
Performance Evaluation of Two-Level Photovoltaic Voltage Source Inverter Cons...IJERA Editor
The switching control schemesincluding sinusoidal pulsewidth modulation (SPWM) and space vector modulation (SVM) are very important for the efficiency and accuracyof the voltage source inverter (VSI). Therefore, this paper presents a performance evaluation of a two-level VSI for the photovoltaic (PV) system based on adopted switching controllers namely, SPWM and SVM switching methods. The evaluation procedure and accuracy are demonstrated and investigated using simulations conducted for a 1.5 kW inverter in a MATLAB/Simulink environment. Two types of loads are utilized to assess the performance of the VSI which are resistive (R) load and resistive and inductive (RL) load. Total harmonic distortion (THD) is used for the comparison of the SPWM and the SVM. Results show that the SVM performs better compared with the SPWM in terms of THD rate. The THDs for SVM based system are found to be 0.02% and 0.08% for the R and RL, respectively; whereas the THDsfor SPWM controller are found to be 0.43% and 0.51% for the R and RL, respectively. Furthermore, mean square error (MSE) is also consideredas a statistical indicator. The MSE indicates that the SVM switching controller technique have superior outcomes compared with the SPWM switching controller technique and thus increases the efficiency of the whole system
1. The document presents an intelligent speed control system for an induction motor drive based on fuzzy logic. It replaces the conventional PI controller in the outer speed loop of an indirect vector control system.
2. The fuzzy logic controller uses speed error and change in speed error as inputs and outputs a change in command current. It is composed of fuzzification, fuzzy rules, inference engine, and defuzzification.
3. Simulation results using MATLAB/Simulink show that the proposed fuzzy logic controller provides better performance than a conventional PI controller for different operating conditions like load changes and reference speed changes.
Comparative Analysis of Power System Stabilizer using Artificial Intelligence...ijsrd.com
This document compares the performance of conventional, fuzzy logic-based, and neural network-based power system stabilizers (PSS) for a single machine infinite bus system. It first describes the system model and components. It then explains the design of the conventional PSS and its limitations. Next, it details the design of fuzzy logic-based and neural network-based PSS using speed deviation and acceleration as inputs. Simulation results show that the neural network PSS provides the best damping of oscillations following a disturbance, settling faster than the fuzzy logic or conventional PSS. The document concludes the neural network PSS has the best dynamic performance for stabilizing the power system.
The aim of this paper is to prove that fuzzy logic algorithm is a suitable control technique for fast processes such as electrical machines. This theory has been experimented on different kinds of electrical machines such as stepping motors, dc motors and induction machines (with 6 phases) and the experimental results show that the proposed fuzzy logic algorithm is the most suitable control technique for electrical machines since this algorithm is not time consuming and it is also robust between plant parameters variations.
The document discusses speed control methods for DC motors. It explains that the speed of a DC motor is directly proportional to the back EMF and inversely proportional to flux. For shunt motors, speed can be controlled through flux control by adding resistance in the field winding, or through armature control by adding resistance in series with the armature. For series motors, speed is controlled through flux control using field or armature diverters or tapped field control, or through armature resistance control. Ward-Leonard control provides sensitive speed control for applications like elevators.
Dynamic Modeling of Pump Drive System utilizing Simulink/MATLAB ProgramIRJET Journal
This document summarizes a research paper that models and simulates a pump drive system using MATLAB/Simulink software. The system includes a variable frequency drive connected to an induction motor that drives a centrifugal pump. The summary develops a dynamic model of the system and simulates its performance under open-loop and closed-loop control configurations. Simulation results demonstrate how variable frequency control allows the pump speed to vary based on environmental temperature, improving energy efficiency over a fixed speed system.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
Comparative Performance Study for Closed Loop Operation of an Adjustable Spee...IJPEDS-IAES
In this paper an extensive comparative study is carried out between PI
and PID controlled closed loop model of an adjustable speed Permanent
Magnet Synchronous Motor (PMSM) drive. The incorporation of Sinusoidal
Pulse Width Modulation (SPWM) strategy establishes near sinusoidal
armature phase currents and comparatively less torque ripples without
sacrificing torque/weight ratio. In this closed loop model of PMSM drive, the
information about reference speed is provided to a speed controller, to ensure
that actual drive speed tracks the reference speed with ideally zero steady
state speed error. The entire model of PMSM closed loop drive is divided
into two loops, inner loop current and outer loop speed. By taking the
different combinations of two classical controllers (PI & PID) related with
two loop control structure, different approximations are carried out. Hence a
typical comparative study is introduced to familiar with the different
performance indices of the system corresponding to time domain and
frequency domain specifications. Therefore overall performance of closed
loop PMSM drive is tested and effectiveness of controllers will be
determined for different combinations.
The document discusses power system stabilizers (PSS) and provides context for the thesis. It summarizes that the thesis will investigate modifying the input signal of a specific type of PSS and apply it to a power system to damp low frequency oscillations, without providing an exhaustive literature review. Details of the PSS structure, tuning methods, and considered input signals are given in later chapters.
Damping of Inter-Area Low Frequency Oscillation Using an Adaptive Wide-Area D...Power System Operation
This paper presents an adaptive wide-area damping controller (WADC) based on
generalized predictive control (GPC) and model identification for damping the inter-area low
frequency oscillations in large-scale inter-connected power system. A recursive least-squares algorithm
(RLSA) with a varying forgetting factor is applied to identify online the reduced-order linearlized
model which contains dominant inter-area low frequency oscillations. Based on this linearlized model,
the generalized predictive control scheme considering control output constraints is employed to obtain
the optimal control signal in each sampling interval. Case studies are undertaken on a two-area fourmachine
power system and the New England 10-machine 39-bus power system, respectively.
Simulation results show that the proposed adaptive WADC not only can damp the inter-area
oscillations effectively under a wide range of operation conditions and different disturbances, but also
has better robustness against to the time delay existing in the remote signals. The comparison studies
with the conventional lead-lag WADC are also provided.
IRJET- Performance Analysis of Speed Control of Induction Motor using Pi,...IRJET Journal
This document analyzes and compares the performance of PI, sliding mode, and fuzzy logic controllers for speed control of an induction motor. It first provides background on vector control of induction motors and derives the mathematical models of the motor. It then describes the design and implementation of the three controllers - PI, sliding mode, and fuzzy logic. Simulation results show that the sliding mode controller provides the best dynamic performance and robustness to load disturbances, followed by the fuzzy logic controller, while the PI controller has less satisfactory steady state response and performance under disturbances. The document concludes by comparing the performance of the three controllers.
Direct Torque Control: Stator Flux Regulation Improvement at Low SpeedTELKOMNIKA JOURNAL
A simple method to improve stator flux regulation of a direct torque control (DTC) of induction
motor drive is presented. By using this method, the simple control structure of DTC is retained and no
modification to the voltage vectors look-up table is required. To implement this technique, the index to the
look-up table is modified so that the reverse voltage vectors are selected (instead of zero-voltage vectors)
whenever the stator flux regulation fails. To study the viability and the effectiveness of this simple method
in improving the flux regulation at low speed, experiments are conducted to a ¼ hp induction motor with
DTC technique. The control algorithm is implemented using a DS1104 controller board with Xilinx FPGA.
The paper proposes Direct Torque Control (DTC) of a five-phase induction motor drive with reduced torque ripple. The method presented here is the DTC Backstepping based on the classic DTC working with a constant switching frequency of the inverter. Another remarkable aspect is the complexity of the method proposed, both in the control unit of the inverter and in the number of correctors necessary for the control of the torque. The selection table and hysteresis have been eliminated. This method significantly improves the torque and flux oscillations and improves the dynamics of the drive by making it less sensitive to load torque disturbances. The proposed method is developed and designed using Matlab/SIMULINK to show the eectiveness and performances of the DTC-Backstepping.
This document provides specifications for the Sara Maatje VI, a multipurpose workboat and survey vessel. It details the vessel's tank capacities, accommodation spaces, navigation and communication equipment, classification information, dimensions, machinery and propulsion systems. The vessel has accommodation for 6 crew, a survey room, and various tank capacities including 35,000 liters each of fresh water and fuel. It also lists its navigation equipment which includes multiple radars, echosounders, GPS systems and more.
Este documento presenta un gráfico semanal del S&P 500 del 11 de mayo de 2012, que muestra varias medias móviles simples representadas por líneas de diferentes colores y grosores. El documento analiza posibles escenarios futuros para el S&P 500 basados en si mantiene o pierde ciertos niveles de soporte clave, y explica brevemente cómo se construyen los gráficos y cómo se pueden usar las medias móviles para orientar el análisis técnico del mercado.
Speed Sensor less DTC of VSI fed Induction Motor with Simple Flux Regulation ...IRJET Journal
This document discusses improving speed and torque estimations for direct torque control of an induction motor at low speeds. It proposes using a constant switching frequency controller instead of a 3-level hysteresis torque comparator to maintain constant switching frequency while improving stator flux regulation at low speeds. An extended Kalman filter-based estimator is used to estimate speed feedback for closed-loop speed control without requiring a speed sensor. Simulation results using MATLAB/Simulink software are presented to validate the approach for low speed operation. The goal is to develop a simple sensorless direct torque control method with improved performance at low and zero speeds.
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.
These energy transits constitute a flow going from the substations where the
power plants are connected to the substations where customers are connected;
it is conveyed through the transmission lines and cables and divided up
proportionally to the admittance, i.e. the impedance reciprocal (which is in
some way a marked preference for the "shortest route"). This energy flow is
materialised by the current conveyed through the facilities. The higher the
energy flow is, the greater the current intensities will be. These intensities may
increase, in particular when a facility has tripped following a fault occurrence.
The flow initially borne by this facility will be transferred to the neighbouring
facilities: this is the load transfer phenomenon.
A novel optimum tip speed ratio control of low speed wind turbine generator b...journalBEEI
Variable speed control of wind turbine generator systems have been developed to get maximum output power at every wind speed variation, also called Maximum Power Points Tracking (MPPT). Generally, MPPT control system consists of MPPT algorithm to track the controller reference and generator speed controller. In this paper, MPPT control system is proposed for low speed wind turbine generator systems (WTGs) with MPPT algorithms based on optimum tip speed ratio (TSR) and generator speed controller based on field oriented control using type-2 fuzzy system (T2FS). The WTGs are designed using horizontal axis wind turbines to drive permanent magnet synchronous generators (PMSG). The simulation show that the MPPT system based optimum TSR has been able to control the generator output power around the maximum point at all wind speeds.
Vector control of AC induction motors provides superior dynamic performance compared to scalar control by decoupling torque and flux control. Vector control represents the stator currents as direct and quadrature components (Ids and Iqs) that independently control flux and torque. This allows precise and independent control of torque and flux to eliminate oscillations for applications requiring high performance like robotics. Vector control implementations determine the orientation of Ids and Iqs either directly by measuring airgap flux or indirectly by measuring slip speed to achieve independent control of the current components.
Advanced Optimal PSO, Fuzzy and PI Controller with PMSM and WTGS at 5Hz Side ...IAES-IJPEDS
To use different control systems, like classical PI controller, Expert System
Fuzzy Logic Controller and optimization PSO controller. It used to control
for PMSM which worked in the integration system to Wind Energy. Wind
energy content of wind turbine, PMSM, rectifier, DC bus, inverter, filter,
load and grid. In the first step, to run the PMSM with different speeds to get
a different frequency to select the frequency on the side of a generation with
the rated speed. Second step, solve the mathematical equation to use different
values of wind speed with selected (15,20 m/s and less than with more than
15&20m/s). Third step, calculation the power generation with wind speed
(15 m/5 & 20 m/s). Fourth step, using these component system rectifier, DC
bus, inverter, filter, load & grid with WTGS & PMSM. Final step, uses
different control systems, like classical PI controller, Expert System Fuzzy
Logic controller and optimization PSO controller with PMSM to analyze all
results after using the simulation model of proposed variable speed based on
WECS. The wind turbine is coupled with PMSM. A closed loop control
system with a PI control, fuzzy, PSO in the speed loop with current
controllers. The simulation circuits for PMSM, inverter, speed and current
controllers include all realistic components of the drive system. These results
also confirmed that the transient torque and current never exceed the
maximum permissible value.
Performance Evaluation of Two-Level Photovoltaic Voltage Source Inverter Cons...IJERA Editor
The switching control schemesincluding sinusoidal pulsewidth modulation (SPWM) and space vector modulation (SVM) are very important for the efficiency and accuracyof the voltage source inverter (VSI). Therefore, this paper presents a performance evaluation of a two-level VSI for the photovoltaic (PV) system based on adopted switching controllers namely, SPWM and SVM switching methods. The evaluation procedure and accuracy are demonstrated and investigated using simulations conducted for a 1.5 kW inverter in a MATLAB/Simulink environment. Two types of loads are utilized to assess the performance of the VSI which are resistive (R) load and resistive and inductive (RL) load. Total harmonic distortion (THD) is used for the comparison of the SPWM and the SVM. Results show that the SVM performs better compared with the SPWM in terms of THD rate. The THDs for SVM based system are found to be 0.02% and 0.08% for the R and RL, respectively; whereas the THDsfor SPWM controller are found to be 0.43% and 0.51% for the R and RL, respectively. Furthermore, mean square error (MSE) is also consideredas a statistical indicator. The MSE indicates that the SVM switching controller technique have superior outcomes compared with the SPWM switching controller technique and thus increases the efficiency of the whole system
1. The document presents an intelligent speed control system for an induction motor drive based on fuzzy logic. It replaces the conventional PI controller in the outer speed loop of an indirect vector control system.
2. The fuzzy logic controller uses speed error and change in speed error as inputs and outputs a change in command current. It is composed of fuzzification, fuzzy rules, inference engine, and defuzzification.
3. Simulation results using MATLAB/Simulink show that the proposed fuzzy logic controller provides better performance than a conventional PI controller for different operating conditions like load changes and reference speed changes.
Comparative Analysis of Power System Stabilizer using Artificial Intelligence...ijsrd.com
This document compares the performance of conventional, fuzzy logic-based, and neural network-based power system stabilizers (PSS) for a single machine infinite bus system. It first describes the system model and components. It then explains the design of the conventional PSS and its limitations. Next, it details the design of fuzzy logic-based and neural network-based PSS using speed deviation and acceleration as inputs. Simulation results show that the neural network PSS provides the best damping of oscillations following a disturbance, settling faster than the fuzzy logic or conventional PSS. The document concludes the neural network PSS has the best dynamic performance for stabilizing the power system.
The aim of this paper is to prove that fuzzy logic algorithm is a suitable control technique for fast processes such as electrical machines. This theory has been experimented on different kinds of electrical machines such as stepping motors, dc motors and induction machines (with 6 phases) and the experimental results show that the proposed fuzzy logic algorithm is the most suitable control technique for electrical machines since this algorithm is not time consuming and it is also robust between plant parameters variations.
The document discusses speed control methods for DC motors. It explains that the speed of a DC motor is directly proportional to the back EMF and inversely proportional to flux. For shunt motors, speed can be controlled through flux control by adding resistance in the field winding, or through armature control by adding resistance in series with the armature. For series motors, speed is controlled through flux control using field or armature diverters or tapped field control, or through armature resistance control. Ward-Leonard control provides sensitive speed control for applications like elevators.
Dynamic Modeling of Pump Drive System utilizing Simulink/MATLAB ProgramIRJET Journal
This document summarizes a research paper that models and simulates a pump drive system using MATLAB/Simulink software. The system includes a variable frequency drive connected to an induction motor that drives a centrifugal pump. The summary develops a dynamic model of the system and simulates its performance under open-loop and closed-loop control configurations. Simulation results demonstrate how variable frequency control allows the pump speed to vary based on environmental temperature, improving energy efficiency over a fixed speed system.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
Comparative Performance Study for Closed Loop Operation of an Adjustable Spee...IJPEDS-IAES
In this paper an extensive comparative study is carried out between PI
and PID controlled closed loop model of an adjustable speed Permanent
Magnet Synchronous Motor (PMSM) drive. The incorporation of Sinusoidal
Pulse Width Modulation (SPWM) strategy establishes near sinusoidal
armature phase currents and comparatively less torque ripples without
sacrificing torque/weight ratio. In this closed loop model of PMSM drive, the
information about reference speed is provided to a speed controller, to ensure
that actual drive speed tracks the reference speed with ideally zero steady
state speed error. The entire model of PMSM closed loop drive is divided
into two loops, inner loop current and outer loop speed. By taking the
different combinations of two classical controllers (PI & PID) related with
two loop control structure, different approximations are carried out. Hence a
typical comparative study is introduced to familiar with the different
performance indices of the system corresponding to time domain and
frequency domain specifications. Therefore overall performance of closed
loop PMSM drive is tested and effectiveness of controllers will be
determined for different combinations.
The document discusses power system stabilizers (PSS) and provides context for the thesis. It summarizes that the thesis will investigate modifying the input signal of a specific type of PSS and apply it to a power system to damp low frequency oscillations, without providing an exhaustive literature review. Details of the PSS structure, tuning methods, and considered input signals are given in later chapters.
Damping of Inter-Area Low Frequency Oscillation Using an Adaptive Wide-Area D...Power System Operation
This paper presents an adaptive wide-area damping controller (WADC) based on
generalized predictive control (GPC) and model identification for damping the inter-area low
frequency oscillations in large-scale inter-connected power system. A recursive least-squares algorithm
(RLSA) with a varying forgetting factor is applied to identify online the reduced-order linearlized
model which contains dominant inter-area low frequency oscillations. Based on this linearlized model,
the generalized predictive control scheme considering control output constraints is employed to obtain
the optimal control signal in each sampling interval. Case studies are undertaken on a two-area fourmachine
power system and the New England 10-machine 39-bus power system, respectively.
Simulation results show that the proposed adaptive WADC not only can damp the inter-area
oscillations effectively under a wide range of operation conditions and different disturbances, but also
has better robustness against to the time delay existing in the remote signals. The comparison studies
with the conventional lead-lag WADC are also provided.
IRJET- Performance Analysis of Speed Control of Induction Motor using Pi,...IRJET Journal
This document analyzes and compares the performance of PI, sliding mode, and fuzzy logic controllers for speed control of an induction motor. It first provides background on vector control of induction motors and derives the mathematical models of the motor. It then describes the design and implementation of the three controllers - PI, sliding mode, and fuzzy logic. Simulation results show that the sliding mode controller provides the best dynamic performance and robustness to load disturbances, followed by the fuzzy logic controller, while the PI controller has less satisfactory steady state response and performance under disturbances. The document concludes by comparing the performance of the three controllers.
Direct Torque Control: Stator Flux Regulation Improvement at Low SpeedTELKOMNIKA JOURNAL
A simple method to improve stator flux regulation of a direct torque control (DTC) of induction
motor drive is presented. By using this method, the simple control structure of DTC is retained and no
modification to the voltage vectors look-up table is required. To implement this technique, the index to the
look-up table is modified so that the reverse voltage vectors are selected (instead of zero-voltage vectors)
whenever the stator flux regulation fails. To study the viability and the effectiveness of this simple method
in improving the flux regulation at low speed, experiments are conducted to a ¼ hp induction motor with
DTC technique. The control algorithm is implemented using a DS1104 controller board with Xilinx FPGA.
The paper proposes Direct Torque Control (DTC) of a five-phase induction motor drive with reduced torque ripple. The method presented here is the DTC Backstepping based on the classic DTC working with a constant switching frequency of the inverter. Another remarkable aspect is the complexity of the method proposed, both in the control unit of the inverter and in the number of correctors necessary for the control of the torque. The selection table and hysteresis have been eliminated. This method significantly improves the torque and flux oscillations and improves the dynamics of the drive by making it less sensitive to load torque disturbances. The proposed method is developed and designed using Matlab/SIMULINK to show the eectiveness and performances of the DTC-Backstepping.
This document provides specifications for the Sara Maatje VI, a multipurpose workboat and survey vessel. It details the vessel's tank capacities, accommodation spaces, navigation and communication equipment, classification information, dimensions, machinery and propulsion systems. The vessel has accommodation for 6 crew, a survey room, and various tank capacities including 35,000 liters each of fresh water and fuel. It also lists its navigation equipment which includes multiple radars, echosounders, GPS systems and more.
Este documento presenta un gráfico semanal del S&P 500 del 11 de mayo de 2012, que muestra varias medias móviles simples representadas por líneas de diferentes colores y grosores. El documento analiza posibles escenarios futuros para el S&P 500 basados en si mantiene o pierde ciertos niveles de soporte clave, y explica brevemente cómo se construyen los gráficos y cómo se pueden usar las medias móviles para orientar el análisis técnico del mercado.
This document provides specifications for a multi-purpose work boat called the Suffolk Spirit, including its dimensions, capacities, performance, and machinery. It has an overall length of 26 meters, a beam of 10.4 meters, and a maximum draft of 3.35 meters. Propulsion is provided by two Doosan 800Hp main engines, with a service speed of 10 knots. It has capabilities including towing, pushing, dredger support, mooring, and survey work.
Grafico diario del dax perfomance index para el 07 05-2012Experiencia Trading
Este documento presenta un análisis técnico del índice Dax Performance usando medias móviles simples de Fibonacci. Muestra que mientras el índice se mantenga por encima de 6,400 puntos existe una tendencia alcista con objetivos de 7,285 a 7,500 puntos, pero si pierde los 6,400 puntos el objetivo sería de 6,000 a 5,200 puntos. Explica que las medias móviles se usan para identificar niveles de soporte y resistencia y tendencias del mercado, pero que el futuro no puede pre
Este documento presenta un gráfico diario del S&P 500 del 7 de mayo de 2012 con varias líneas que representan medias simples de 1 a 610 períodos. Analiza posibles escenarios futuros para el S&P 500 dependiendo de si mantiene o pierde ciertos niveles de soporte clave entre 1,280 y 1,360. También incluye explicaciones sobre cómo las medias simples pueden orientar el comportamiento del mercado y consideraciones sobre el análisis técnico.
El documento analiza el gráfico semanal del Euro-dólar del 11 de mayo de 2012. Indica que el Euro-dólar es bajista a menos que recupere el nivel de 1,39 y se mantenga allí. Si supera 1,33 podría subir a 1,36, y si supera 1,37 podría subir a 1,40. Mientras se mantenga por debajo de las líneas roja y azul, que representan las medias de 233 y 34 períodos respectivamente, los mercados son bajistas en esos períodos de tiempo
Desafios para o uso de TICs aplicadas à educaçãoUFPE
O documento discute os desafios do uso das tecnologias da informação e comunicação aplicadas à educação e saúde. Aborda os desafios da complexidade do trabalho docente, da avaliação em educação a distância, da gestão de conteúdo em ambientes de ensino e da percepção social em interfaces web e ambientes síncronos. Também discute fenômenos cognitivos como a natureza da prática docente, modalidades de aprendizagem colaborativa e a distância transacional na educação a distância.
Cortana Analytics Workshop: Cortana Analytics for MarketingMSAdvAnalytics
Tao Wu. Microsoft has helped many customers like Mendeley realize the full potential of marketing using cloud-based machine learning. In this session, we will present how Cortana Analytics brings key capabilities to next-generation marketing. Examples include: (1) Accurate lead scoring that helps substantially improve effectiveness of marketing and sales; (2) Early identification of core users that allows brands to engage with users better; and (3) Real-time marketing that enables personalized and contextualized marketing decisions. With Cortana Analytics, you can quickly deploy marketing solutions, gain user insights, and engage with customers with improved accuracy and efficiency, all backed by Azure's scale and elasticity. Go to https://channel9.msdn.com/ to find the recording of this session.
A New Control Method for the Multi-Area LFC System Based on Port-Hamiltonian ...IRJET Journal
This document presents a new control method for load frequency control (LFC) in a multi-area power system based on Port-Hamiltonian and cascade systems. The proposed method uses PID control laws that decouple total tie-line power flow and provide robust disturbance rejection. Simulation results in Matlab/Simulink validate that the proposed method performs better than existing PID methods by achieving faster response speeds and smaller overshoots for changes in tie-line power and frequency deviations in both two-area and four-area test systems with and without reheated turbines.
This document discusses the design of closed-loop control for region 2 operation of a wind turbine using a continuously variable transmission (CVT). It motivates using a CVT to reduce the cost of wind energy and improve capture. It outlines presenting the modeling of the rotor-drivetrain-generator system and developing closed-loop CVT control. The performance of the full modeled system is analyzed through simulations using 10 minutes of recorded wind data.
Induction motor harmonic reduction using space vector modulation algorithmjournalBEEI
The vector control was proposed as an alternative to the scalar control for AC machines control. Vector control provide high operation performance in steady state and transient operation. However, the variable switching frequency of vector control causes high flux and torque ripples which lead to an acoustical noise and degrade the performance of the control scheme. The insertion of the space vector modulation was a very useful solution to reduce the high ripples level inspite of its complexity. Numerical simulation results obtained in MATLAB/Simulink show the good dynamic performance of the proposed vector control technique and the effectiveness of the proposed sensorless strategy in the presence of the sudden load torque basing on the integral backstepping approach capabilities on instant perturbation rejection.
Keywords
Speed Control Techniques for Induction Motor - A Reviewijsrd.com
In this paper, various types of speed control methods for the single phase induction motor are described. Speed can be controlled to control the frequency or slip can be controlled to control the torque. Then flux and torque are also function of frequency and voltage. Various methods are used to control the flux and voltage. This paper is focused on sliding mode control technique for induction motor.
Wind turbines form complex nonlinear mechanical systems exposed to uncontrolled wind
profiles. This makes turbine controller design a challenging task. As such, control of wind energy
conversion systems (WECS) is difficult due to the lack of systematic methods to identify requisite
robust and sufficiently stable conditions, to guarantee performance. The problem becomes more
complex when plant parameters become uncertain. This paper considers the wind energy curtailment
for which it provides a combinatorial planning model to maximize wind power utilization. The major
objective of this study is to develop an effective method for optimizing size of wind. A novel multiobjective
adaptation of the fuzzy based Harmony Search algorithm is proposed and tested for
efficiently solving the problem of optimally deploying wind turbines in wind farms. In this paper,
Harmony Search Algorithm (HSA) using fuzzy controller to achieve better optimization results and to
increase performance. A general formulation of this algorithm is presented together with an analytical
and mathematical modeling to solve the stability and performance of the system.
COMPARATIVE STUDY OF CLOSED LOOP CONTROL DFIG BY USING FUZZY LOGIC AND PI CON...IRJET Journal
This document summarizes a research paper that compares the use of fuzzy logic and PI controllers for controlling a doubly-fed induction generator (DFIG) used in wind turbines. The goal is to independently control the stator active and reactive power as well as optimal speed tracking for maximum energy capture. A vector control strategy is developed for the rotor side converter using fuzzy logic and PI controllers. Simulation results in MATLAB/SIMULINK are presented and analyzed to determine which control method provides better control of the DFIG under different conditions. The paper aims to contribute to improved control strategies for wind energy generation systems.
This document compares two control strategies - SVM based voltage oriented control and hysteresis current control - for interfacing a permanent magnet synchronous generator (PMSG) to the grid. Simulation results show that under constant and variable wind speeds:
1) The SVM control strategy regulates the grid voltage, current and DC link voltage more precisely with faster settling time compared to hysteresis control.
2) Both controllers effectively transfer maximum power from the PMSG to the grid while maintaining unity power factor.
3) Under variable wind speeds, the SVM control provides smoother transition of the generator speed, grid current, and active/reactive power compared to hysteresis control.
Grid Connected Wind Turbine Generator with Real and Reactive Power ControlIRJET Journal
This document proposes a grid-connected wind turbine system with a permanent magnet synchronous generator (PMSG) for variable speed operation. A diode bridge rectifier converts the AC voltage from the PMSG to DC, which is fed to a boost converter for voltage regulation. The output of the boost converter feeds a three-phase inverter to inject real and reactive power into the grid using PI controllers with grid current and voltage feedback. Maximum power point tracking (MPPT) is achieved by varying the turbine pitch angle using a voltage-controlled technique to extract maximum power for varying wind speeds. Simulation results in MATLAB/Simulink demonstrate the performance of the system.
Improvise 3-Level DTC of Induction Machine using Constant Switching Frequency...IJPEDS-IAES
This paper presents the advantage of using optimal PI parameter tuning strategy of constant switching method in the three phase Direct torque control (DTC) scheme. The DTC system is known to offer fast decoupled control of torque and flux via a simple control structure. Nevertheless, DTC system has two major drawbacks, which are the variable inverter switching frequency and high torque output ripple. The major factorthat contributes to these problems the usage of hysteresis based comparators to control the output torque. The implementation of PI based constant switching method in DTC able to solve these problems while retaining the simple control structure of conventional DTC. The combination usage of 3-level CHMI in this system can further minimize the output torque ripple by providing greater number of vectors. This paper presents detail explanation and calculationof optimal PI parameter tuning strategyconsecutively to enhance the performance of 3-level DTC system. In order to validate the feasibility, the proposed method compared with convention DTC system via simulation and experiment results.
Flux Based Sensorless Speed Sensing and Real and Reactive Power Flow Control ...ijeei-iaes
This document discusses flux-based sensorless speed sensing and real and reactive power flow control with look-up table based maximum power point tracking (MPPT) technique for a grid-connected doubly fed induction generator (DFIG). It aims to design controllers for the DFIG converters and MPPT for the turbine to maintain rotor speed and generator torque equilibrium while meeting desired real and reactive power references during wind and grid disturbances. The rotor side converter helps achieve optimal real and reactive power from the generator by varying the rotor current to keep the rotor rotating at an optimal speed set by the MPPT. Rotor speed is estimated using a stator and rotor flux estimation algorithm. The performance of the DFIG is compared under variations in just wind speed
This document discusses implementing pitch control of a wind turbine using Simulink. It presents a mathematical model of a variable speed wind turbine system with a PI controller and actuator model to simulate adjusting the blade pitch angle. The simulation results show the controller accurately regulates rotor speed by varying the pitch angle to maintain a constant output power. It also provides background on modeling wind turbines, the components involved, dynamic modeling, and discusses maximizing power capture through varying the tip speed ratio and pitch angle.
This document presents a study on using an artificial neural network technique for flux position estimation and sector selection in direct torque control of an induction motor. Direct torque control aims to provide quick torque response without complex transformations but suffers from high torque ripples. The proposed method uses a neural network for flux position estimation and sector selection to determine the optimal voltage vector, with the goal of reducing torque and flux ripples. The neural network structure is simple to facilitate short training and processing times. Simulation results show the neural network based controller provides high performance speed control of the induction motor.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
This document presents a new control method for improving the performance of low power wind-driven wound rotor induction generators. The proposed method combines input voltage control and slip power control to achieve better efficiency and power factor over a wide range of speeds. Simulation and experimental results show that the combined control method improves both efficiency and power factor compared to conventional slip power control alone. The combined control allows the generator to operate closer to its maximum torque point for higher efficiency at each operating speed.
The purpose of this work is to present the advantages of the power control (active and reactive) of a wind energy system in order to improve the quality of the energy produced to the grid by presenting two control strategies applied to the conversion system of wind energy equipped with an asynchronous generator with dual power supply. Both techniques are studied and developed and consist of a field control (FOC) and a sliding mode control. They find their strongest justifications for the problem of using a nonlinear control law that is robust to the uncertainties of the model. The goal is to apply these two commands to independently control the active and reactive powers generated by the decoupled asynchronous machine by flow orientation. Thus, a study of these commands will be detailed and validated in the Matlab / Simulink environment with the simultaneous use of the "Pitch Control" and "Maximum Power Point Tracking (MPPT)" techniques. The results of numerical simulations obtained show the increasing interest of the two controls in the electrical systems. They also attest that the quality of the active and reactive powers and voltages of the wind system is considerably improved.
ADAPTIVE BANDWIDTH APPROACH ON DTC CONTROLLED INDUCTION MOTORijcisjournal
Induction motors are most commonly used motor type in industrial applications because of its well-known advantages like robust structure, cheaper prices etc. Today, field oriented control (FOC) and direct torque control (DTC) methods, also called vector control, are most famous control methods in high-performance applications. The main structural and behavioural differences between the both methods can be summarized as: the FOC has parameter dependence while the DTC has high torque ripples. In this study, a new adaptive bandwidth approach was presented to reduce torque ripples in DTC controlled induction motor drives. With the proposed method, instead of fixed bandwidth, adaptive bandwidth approach was investigated in hysteresis controllers on the DTC method. Both the conventional DTC(C-DTC) method and adaptive bandwidth DTC (AB-DTC) for induction motor were simulated in MATLAB/SIMULINK and the results were presented and discussed to verify the proposed control. The comparisons shown that, torque ripples were reduced remarkably with the proposed AB-DTC method.
ADAPTIVE BANDWIDTH APPROACH ON DTC CONTROLLED INDUCTION MOTORijics
Induction motors are most commonly used motor type in industrial applications because of its well-known
advantages like robust structure, cheaper prices etc. Today, field oriented control (FOC) and direct torque
control (DTC) methods, also called vector control, are most famous control methods in high-performance
applications. The main structural and behavioural differences between the both methods can be
summarized as: the FOC has parameter dependence while the DTC has high torque ripples. In this study, a
new adaptive bandwidth approach was presented to reduce torque ripples in DTC controlled induction
motor drives. With the proposed method, instead of fixed bandwidth, adaptive bandwidth approach was
investigated in hysteresis controllers on the DTC method. Both the conventional DTC(C-DTC) method and
adaptive bandwidth DTC (AB-DTC) for induction motor were simulated in MATLAB/SIMULINK and the
results were presented and discussed to verify the proposed control. The comparisons shown that, torque
ripples were reduced remarkably with the proposed AB-DTC method.
IRJET- Comparative Study of Load Frequency Control using PID and Fuzzy- PID C...IRJET Journal
This document compares the use of PID and fuzzy-PID controllers for load frequency control in a two-area power system. It describes the system model, including thermal and hydro units. The control objectives are to maintain frequency and regulate tie-line power exchange errors. Simulation results show that the fuzzy-PID controller provides better dynamic response than the PID controller, with lower undershoot, shorter settling time, and improved transients in frequency response and tie-line power exchange for both areas when subject to a 1% load disturbance.
Induction motors are work-horse of the industry and major element in energy conversion. The replacement of the existing non-adjustable speed drives with the modern variable frequency drives would save considerable amount of electricity. A proper control scheme for variable frequency drives can enhance the efficiency and performance of the drive. This paper attempt to provide a rigorous review of various control schemes for the induction motor control and provides critical analysis and guidelines for the future research work. A detailed study of sensor based control schemes and sensor-less control schemes has been investigated. The operation, advantages, and limitations of the various control schemes are highlighted and different types of optimization techniques have been suggested to overcome the limitations of control techniques.
Review of the DTC Controller and Estimation of Stator Resistance in IM DrivesIAES-IJPEDS
In recent years an advanced control method called direct torque control
(DTC) has gained importance due to its capability to produce fast torque
control of induction motor. Although in these systems such variables as
torque, flux modulus and flux sector are required, resulting DTC structure is
particularly simplistic. Conventional DTC does not require any mechanical
sensor or current regulator and coordinate transformation is not present, thus
reducing the complexity. Fast and good dynamic performances and
robustness has made DTC popular and is now used widely in all industrial
applications. Despite these advantages it has some disadvantages such as
high torque ripple and slow transient response to step changes during start
up. Torque ripple in DTC is because of hysteresis controller for stator flux
linkage and torque. The ripples can be reduced if the errors of the torque and
the flux linkage and the angular region of the flux linkage are subdivided into
several smaller subsections. Since the errors are divided into smaller sections
different voltage vector is selected for small difference in error, thus a more
accurate voltage vector is selected and hence the torque and flux linkage
errors are reduced. The stator resistance changes due to change in
temperature during the operation of machine. At high speeds, the stator
resistance drop is small and can be neglected. At low speeds, this drop
becomes dominant. Any change in stator resistance gives wrong estimation
of stator flux and consequently of the torque and flux. Therefore, it is
necessary to estimate the stator resistance correctly. This paper aims to
review some of the control techniques of DTC drives and stator resistance
estimation methods.
Design and Control of the Pitch of Wind Turbine through PIDIRJET Journal
This document describes the design and control of the pitch angle of a wind turbine using a PID controller. It begins with an introduction to wind energy and the need for pitch control to reduce loads on turbine blades. It then presents the mathematical models of the pitch actuator and drive train components. Next, it discusses implementation of a conventional PID controller in the Simulink model and compares the performance with and without control. The results show the PID controller provides better control of the pitch angle with lower delay and rise time though with some oscillations. Future work could explore adaptive fuzzy PID control or individual pitch control to further improve performance.
Similar to Application of Quantitative Feedback Theory for Wind Turbine Controller Design (20)
Design and Control of the Pitch of Wind Turbine through PID
Application of Quantitative Feedback Theory for Wind Turbine Controller Design
1. Application of Quantitative Feedback Theory for Wind Turbine Controller Design
Goran Benčić*, Mate Jelavić**, Nedjeljko Perić***
* KONČAR – Power Plant and Electric Traction Engineering, Zagreb, Croatia
(goran.bencic@koncar-ket.hr)
** KONČAR – Electrical Engineering Institute, Zagreb, Croatia
(mjelavic@koncar-institut.hr)
*** Faculty of Electrical Engineering and Computing, Zagreb, Croatia
(nedjeljko.peric@fer.hr)
Abstract: To enable wind turbines to produce power under great variety of wind conditions a
sophisticated control system is needed. Wind turbine system is highly nonlinear and its dynamics changes
rapidly with the change of wind speed. Many classical control methods fail to properly address this
uncertainty of wind turbine dynamics. For that reason Quantitative Feedback Theory is presented and its
application to synthesis of rotor speed controller.
1. INTRODUCTION
Modern wind turbines have to operate in wide range of
operating conditions determined primarily by wind speed. To
make it possible for wind turbine to produce power in such a
variety of operating conditions a sophisticated control system
is needed that will account for changes in operating
conditions and accompanying changes in wind turbine
dynamics [1]. The power of air that moves at speed vw over
the area swept by turbine rotor of radius R is given by (1):
ܲௐ ൌ
1
2
ߩܴଶ
ߨݒ௪
ଷ (1)
where ρair is density of air. From expression (1) it is clear that
wind energy increases rapidly with increase in wind speed.
This results in two very different operation regions of wind
turbine, each of them placing specific demands upon control
system. During weak winds power contained in the wind is
lower than the rated power output of wind turbine generator.
Therefore, the main task of the control system in this region
is to maximize wind turbine power output by maximizing
wind energy capture. It can be shown [2] that for each value
of wind speed energy conversion efficiency is maximal for
only one particular value of rotor speed. Since modern wind
turbines are connected to grid using AC-DC-AC frequency
converters, generator frequency is decoupled from grid
frequency which enables variable speed operation. Therefore
it becomes possible to vary the rotor speed and to maintain
optimal energy conversion during varying wind speeds. On
the other hand, during strong winds power of the wind is
greater than the rated power output of wind turbine generator.
Therefore, the wind energy conversion has to be constrained
in this region to assure generator operation without
overloading. Very efficient method for constraining wind
energy conversion is pitching the rotor blades around their
longitudinal axis which deteriorates their aerodynamic
efficiency and therefore only a part of wind energy is used for
driving the generator.
The main task of wind turbine control system is to obtain
continuous power production under operating conditions
determined by various wind speeds. As turbine power is
directly proportional to its speed, power control can be done
by controlling turbine speed. The principle scheme of wind
turbine speed control system is shown in Fig. 1.
Fig. 1. Principle scheme of wind turbine control system [3]
As it can be seen in this figure turbine speed can be
influenced and thus controlled by two means – by generator
electromagnetic torque ܯ which opposes rotor driving
torque ܯ and by pitch angle ߚ which alters the wind energy
conversion. For this reason turbine speed control system
consists of two control loops: torque control loop and pitch
control loop. Those control loops operate simultaneously but
depending on operation region one of them is dominant. In
the below rated operation region the torque control loop is
used to control turbine speed to values that will result in
maximal wind power capture. This control loop is not in the
scope of this paper. Details on its specifics can be found in
e.g. [3]. In the above rated region this control loop just holds
generator torque at its rated value. The pitch control loop is
used for setting the adequate pitch angle that will keep
turbine speed at its reference value under all operating
conditions determined by various winds. Below rated wind
speed this loop sets pitch angle to value that assures maximal
wind power capture which is usually around 0°. In this paper
2. we assume that all blades have the same pitch angle what is
known as collective pitch. Controller in this loop, although
used to control turbine speed, is commonly termed pitch
controller. Blade positioning is mostly done using electrical
servo drives that rotate blades by means of gearboxes and
slewing rings. Position control of servo drives is usually
achieved using frequency converters. This control loop
design is rather simple and is not in the scope of the paper.
2. PROBLEMS OF CLASSICAL CONTROL SYSTEMS
The main problem for most of classical control methods is
handling of nonlinear dynamical systems. Even simple
models of wind turbines are highly nonlinear due to nature of
aerodynamic conversion that takes place on all rotor blades.
These models usually don’t take into consideration
aeroelasticity of the blades, wake effects, yaw errors, stall
effect, tower shadow, wind shear effects etc. and still present
a tough challenge for most of classical methods. The core of
the problem mostly lies in inability of methods to explicitly
account for uncertainty of process dynamical behavior that
arises from changes in working conditions (higher wind
speed, lower wind speed). Furthermore, when a controller is
parametrized, there are usually no guarantees of stability and
quality of disturbance rejection when operating point
changes. For that reason it is necessary to perform extensive
time simulations to a posteriori determine if initial
specifications for stability and disturbance rejections are
satisfied in all cases. QFT on the other hand rises up to this
challenge as it can a priori process uncertainty, quantify it
and used it in combination with closed loop specifications. It
can also a priori guarantee fulfillment of closed loop
specification.
3. MOTIVATION FOR UTILIZATION OF QFT
In the beginning of 1960s Horowitz introduced a new
frequency domain based control method called Quantitative
Feedback Theory (abbr. QFT) which presented a
generalization of Bode's frequency domain work [4]. During
Horowitz' involvement in the development of control system
for Israeli battle aircrafts, QFT method was completed and
received a form in which it is used today [4]. Successful
utilization of QFT in aircraft control has proved the power of
the method and enabled its application in helicopter control
systems. When one takes into consideration that much of
wind turbine aerodynamical modelling stems directly from
helicopter aerodynamical modelling, it is only logical to
conclude that QFT should handle in a satisfying manner
control of rotor speed above rated wind speed. The main
characteristic of QFT is the ability to explicitly take into
account uncertainty of process that is to be controlled, and
use this knowledge to develop a controller able to meet
certain specifications (i.e. for efficient disturbance rejection,
noise reduction, etc.). Due to high transparency of the method
it is possible to surveil almost every aspect of the problem in
hand and thus make needed trade-offs between quality of
disturbance rejection, amount of stability margins, controller
complexity and bandwidth utilization. This feature is
especially appealing as it enables engineers to synthesize
efficient low-bandwidth linear controllers of low order.
Utilization of low-bandwidth controllers decreases system’s
sensitivity to noise and unmodelled dynamics. QFT is a
completely rounded control method as it is applicable to
various control systems: linear, nonlinear, time (non)varying,
continuous and discrete, (non)minimum phased, Multiple
Input Single Output (abbr. MISO), Multiple Input Multiple
Output (abbr. MIMO), with output and state signals
feedback, time-delayed (variant of QFT Smith predictor was
developed for this purpose) [5]. It is even applicable to
certain class of uncertain distributed systems whose behavior
is described with partial differential equations (i.e. control of
large scale manipulators) [5].
4. MISO QFT
The basis of all QFT methods (all variants of MIMO QFT,
discrete QFT, QFT for non-minimum phased systems) is
comprised in 2-degree of freedom structure called MISO
QFT [5] shown in Fig. 2.
Fig. 2. MISO QFT control structure
The elements in Fig. 2 are described below:
࣪ – a set of transfer functions where ܲሺ݆߱ሻ א ࣪ describing
the area of process parametric uncertainty.
ܩ – QFT controller intended to make this feedback system
robust, reject disturbances and reduce sensitivity to noise.
ܨ – prefilter that enables quality tracking of reference signal
ܴ.
Signals in Fig. 2 are: measurement noise ܰ, disturbance
ܦଵ on process ܲ input, disturbance ܦଶ on process ܲ output,
reference signal ܴ.
The process of obtaining an adequate QFT controller ܩሺݏሻ
and prefilter ܨሺݏሻ can be described through following steps:
1) Determine the set of transfer functions ࣪ ൌ ሼܲሺ݆߱ሻሽ that
describe the whole range of process dynamical behavior.
2) Choose a nominal process ܲሺ݆߱ሻ from the given set ࣪
(any one will do).
3) Choose discrete frequency set ߗ ൌ ሼ߱ଵ, ߱ଶ, … , ߱ெሽ from
frequency range relevant for control. Further controller
synthesis is performed on this discrete set .
4) Generate templates (sets that describe area of phase vs
amplitude variations) for every frequency from . In
other words, if phase and amplitude values are calculated
for every ܲ א ࣪ for certain frequency ߱ א Ω, then this
set of values is called the template Πሺ݆߱ሻ.
3. 5) Determine a set of specification for closed loop system
behavior (i.e. allowable upper and lower boundary for
tracking of ܴ, upper boundary for disturbance rejection,
stability, control effort, etc.) and translate them to
frequency domain.
6) Using Nichols chart, given specifications and templates,
find frequency boundaries ࣜ on Nichols chart. For every
specification there is a set of boundaries ࣜ generated on
Nichols chart. This set is calculated only for frequencies
from . For example, ࣜሺ݆߱ሻ would present a boundary
for i-th specification evaluated on ߱. Crucial detail of
this algorithm is that all of these boundaries are calculated
in dependence of before mentioned nominal process
ܲሺ݆߱ሻ.
7) Draw the nominal open loop ܮሺ݆߱ሻ ൌ ܲሺ݆߱ሻ ܩሺ݆߱ሻ on
the same Nichols chart and commence with classical loop
shaping procedures in order to satisfy calculated
boundaries.
8) Draw the whole set of closed loop transfer functions on
Bode diagram and find suitable prefilter ܨ to satisfy servo
specifications (if such exist) for tracking of reference ܴ
signal.
9) Perform frequency and time validation of control design.
Iterate if necessary.
Step 6) is crucial for QFT method and will be explained in a
graphical manner which could offer the reader a better
insight. For example, a stability margin specification is given
as (2):
ቤ
ܮሺ݆߱ሻ
1 ܮሺ݆߱ሻ
ቤ ܯ
(2)
This relation is represented as exterior of a red closed curve
around the critical point (-180°, 0 dB) on Nichols chart on
Fig. 3.
Fig. 3. Closed curve around critical point and the template
Πሺ݆߱ሻ
÷ሺ݆߱ሻ represents the process template and ܲሺ݆߱ሻ
represents the nominal process. The template needs to remain
outside the region enclosed by the red curve. Firstly the
template needs to be moved maximally close to the red curve
(none of the points belonging to the template are allowed to
enter the enclosed region) and the position of the nominal
process need to be marked for every position of the template.
Such movement of the template in magnitude-phase plane
(Nichols chart) is possible if controller is connected as it
enables adjustment of phase and magnitude i.e. translation
Connect these markings of the nominal process (green line in
Fig.4.). This green line actually represents the stability
boundary ୱሺjω୧ሻ on frequency ߱. If during step 7) the
value of open loop transfer function ܮሺ݆߱ሻ remains outside
the ୱሺjω୧ሻ, then there is a guarantee that none of all possible
closed loop systems values on ߱ will be within forbidden
enclosed area. Similar graphical logic applies to other types
of specifications. QFT software tools handle boundary
generations by extracting template boundary (thus reducing
the computation burden due to many insignificant interior
points) and then solving systems of quadratic inequalities.
The controller synthesis is finally performed on a set of
resultant boundaries that represent the intersection of all
boundaries.
Fig. 4. Template moved around the curve forming a stability
boundary ࣜ௦ሺ݆߱ሻ
5. WIND TURBINE MODELLING
The first step in control system design is to obtain a suitable
process model to describe dynamical behavior of wind
turbine. Combination of blade element and momentum theory
yields quite satisfactory description of wind turbine
aerodynamic effects which are at center of scope in
modelling. It is primarily utilized in simulation tools but
lacks simplicity in order to be suitably used in the process of
controller design due to iterative nature of the method. For
this reason a different, more analytical, approach is used that
develops a simplified mathematical model usual in the
literature dealing with controller design. It will be described
briefly, while the details on it can be found in [6] and [7].
Wind power ܲ௪, given by expression (1), can never be
completely transformed into wind turbine power ܲ௪௧ and
afterwards into electrical power ܲ. The amount of wind
power that is converted into turbine power ܲ௪௧ can be
described by expression (3):
ܲ௪௧ ൌ ܲ௪ܥ (3)
where ܥ represents a performance coefficient.
The theoretical maximum for ܥ is determined by the Betz'
law [2] and equals 16/27ൎ0.59. The interesting part about
4. assumptions made in deriving Betz’ law is that no particular
turbine design was considered and no additional losses were
included (wake losses, friction losses, etc.) which means that
16/27 is an absolute limit for power extraction process.
Modern wind turbines reach at best performance coefficient
of 0.5. The value of ܥ varies in dependence on wind speed
ݒ௪, rotor speed ߱ and blade pitch angle ߚ. Wind speed and
rotor tip speed are usually bound together introducing
parameter ߣ that is called tip speed ratio [2] given by
expression:
ߣ ൌ
ܴ߱
ݒ௪
(4)
Typical dependence of performance coefficient upon tip
speed ratio with pitch angle used as a parameter is shown in
Fig. 5.
Fig. 5. Performance coefficient as a function of tip speed
ratio [1]
Aerodynamic torque that drives wind turbine rotor is given
by (5):
ܯ ൌ
ܲ
߱
ൌ
1
2
ߩܴଶ
ߨݒ௪
ଷ
ܥሺߣ, ߚሻ
߱
(5)
Using relation defined by (4) a rearrangement of expression
(5) is obtained as follows (6):
ܯ ൌ
1
2
ߩܴଷ
ߨݒ௪
ଶ
ܥሺߣ, ߚሻ
ߣ
(6)
A quotient of performance coefficient ܥ and tip speed ratio
ߣ forms a new dimensionless parameter known as torque
coefficient ܥொ [2]:
ܥொሺߣ, ߚሻ ൌ
ܥሺߣ, ߚሻ
ߣ
(7)
Now the rotor speed ߱ can easily be found using principle
equation of motion given by :
ܬ௧
݀߱
݀ݐ
ൌ ܯ െ ܯ െ ܯ௦௦
(8)
where ܯ is generator electromagnetic torque, ܬ௧ is total
moment of inertia of generator rotor and wind turbine, while
ܯ௦௦ is loss torque caused by friction losses (usually
neglectable).
Wind turbine considered in this paper is In this paper we
consider wind turbine with generator that is directly coupled
with turbine rotor. This turbine setting known as direct drive
system uses synchronous multipole generator that rotates at
small speed of turbine rotor. Since rotor and generator speeds
are the same no distinction between them is made throughout
the paper. Because there is no gearbox between rotor and
generator their moments of inertia can just be summed
together in order to calculate total moment of inertia Jt. The
coupling of rotor to the generator in direct drive solutions is
very stiff and it can be considered as rigid thus removing any
torsional oscillations what simplifies the control system
design.
Before going further an important issue has to be addressed.
Namely, expressions (5), (6) and (7) in this form would be
valid only for structure with rigid tower and blades. In real
situation the absolute wind speed ݒ௪ in mentioned
expressions has to be replaced by wind speed that is "seen"
by rotor blades. This wind speed seen by the rotor is the
resultant of three factors: absolute wind speed ݒ௪, speed of
the tower movement perpendicular to wind speed (i.e. tower
nodding speed) ݔሶ௧ and speed of blade movement
perpendicular to wind speed (i.e. speed of blade flapwise
movement). Influence of tower nodding on wind turbine
control is much more pronounced than influence of blade
flapwise movement. Therefore we focus only on tower
nodding considering rotor blades as rigid. This results in a
following expression describing the wind “seen” by rotor
blades:
ݒ௪
כ
ൌ ݒ௪ െ ݔ௧ሶ (9)
Tower nodding originates from the fact that wind turbine
tower is very lightly damped structure due to its great height
(more than 100 meters in modern wind turbines) and need for
moderate mass. To model the wind turbine tower precisely
we would have to use model with distributed parameters and
to describe it in terms of mass and stiffness distribution. Such
a model wouldn't be very suitable for controller design so it
has to be substituted by model with concentrated parameters.
This can be done using modal analysis that is very common
tool in wind turbine analysis [1], [3]. It describes a complex
oscillatory structure as a composition of several simple
oscillatory systems each of them being described by means of
mass, stiffness and damping. By this representation complex
tower oscillations are seen as a sum of many simple
oscillations characterized by their modal frequencies which
are one of the most important structural properties of wind
turbine. It has been shown in practice [5] that fairly good
modeling of wind turbine tower nodding can be achieved
using two modal frequencies (two modes). Since we are here
primarily interested in building model suitable for controller
design we use only the first modal frequency. The
justification for this lies in the fact that for the turbine in
scope second modal frequency is more than 6 times greater
than the first modal frequency and therefore falls out of the
controller frequency bandwidth.
By using only one modal frequency tower dynamics can be
described as:
ݔܯሷ௧ ݔܦ௧ ݔܥ௧ ൌ ܨሺݐሻሶ (10)
5. where ,ܯ ,ܦ and ܥ are modal mass damping and stiffness
respectively and ܨሺݐሻ is the generalized force that is
originated by wind and that causes wind turbine tower
oscillations. Tower modal properties in expression (10) are
related to first tower modal frequency ߱௧ as follows [6]:
ܦ ൌ 2ߞ௧߱௧ܯ
ܥ ൌ ሺ߱௧ሻଶ
ܯ
(11)
where ߞ௧ is structural damping. For steel structure structural
damping is mostly set to 0.005 [6]. Modal mass M can be
calculated as [2]:
ܯ ൌ න ݉ሺ݄ሻΦሺ݄ሻଶ
݄݀
(12)
where ݄௧ is the height of the tower, ݉ሺ݄ሻ is the mass
distribution along the tower height and Φሺ݄ሻ is the tower's
first mode shape. Note that actual distribution of mass along
the tower has to be modified in order to include mass of the
rotor and the nacelle which is assumed to be concentrated at
the tower top.
Driving force ܨ is mostly the rotor thrust force ܨ௧ caused by
the wind. It can be shown [6] that thrust force, similar to
aerodynamic torque, depends on wind speed, rotor speed and
pitch angle. So similarly to (6) it can be expressed as [6]:
ܨ௧ ൌ
1
2
ߩܴଶ
ߨݒ௪
ଶ
ܥ௧ሺߣ, ߚሻ
(13)
where ܥ௧ is the, so called, thrust coefficient.
Expressions (6), (8), (10) and (13) form the simplified
nonlinear model of wind turbine that is used in the following
sections for controller design. Model is summarized below
taking into account the fact that wind speed seen by the rotor
is a sum of wind speed and tower nodding speed:
ܬ௧
݀߱
݀ݐ
ൌ ܯ െ ܯ െ ܯ௦௦
ܯ ൌ
1
2
ߩܴଷ
ߨሺݒ௪ െ ݔ௧ሶ ሻଶ
ܥொሺߣ, ߚሻ
ܨ௧ ൌ
1
2
ߩܴଶ
ߨሺݒ௪ െ ݔ௧ሶ ሻଶ
ܥ௧ሺߣ, ߚሻ
ݔܯሷ௧ ݔܦ௧ ݔܥ௧ ൌ ܨሺݐሻሶ
(14)
Torque and thrust coefficients ܥ and ܥ௧ are usually provided
by wind turbine blade manufacturers or can be calculated
using professional simulation tools.
On Fig. 6. a block diagram depicts the simulation model of
the wind turbine used to obtain results that follow. The
central part of it is the aerodynamical model shown on Fig.
7. that implements equations (6) and (13) defining ܯ and ܨ௧.
ܥொ and ܥ௧ are represented by 2D look-up tables with pitch
angle ߚ and tip speed ratio ߣ as their input signals. Torque
ܯ and thrust force ܨ௧ represent resulting output signals. The
control system of the pitch drive will not be addressed in this
paper and can be approximated, for small reference pitch
changes, in a satisfactory manner by 2nd
order aperiodical
system. In reality, pitch drive would use cascaded position
and speed control loops that would have to overcome
aerodynamic torque developed around the longitudinal blade
axes, stiction and friction induced torques inside the blade
bearings.
Fig. 6. Block diagram of the wind turbine simulation model
Fig. 7 Block diagram of aerodynamical model
In order to use QFT method for speed controller synthesis a
linear model is required. From system of equations given by
(14), second and third equation need to be linearized as
shown below:
Δܯ ൌ
߲ܯ
߲ݒ௪
ฬ
ை..
ሺΔݒ௪ െ Δݔ௧ሶ ሻ
߲ܯ
߲ߚ
ฬ
ை..
Δߚ
߲ܯ
߲߱
ฬ
ை..
Δ߱ (15)
Δܨ௧ ൌ
߲ܨ௧
߲ݒ௪
ฬ
ை..
ሺΔݒ௪ െ Δݔ௧ሶ ሻ
߲ܨ௧
߲ߚ
ฬ
ை..
Δߚ
߲ܨ௧
߲߱
ฬ
ை..
Δ߱ (16)
Term O.P. used in equations above is an abbreviation for
operating point. An automated procedure was used in order to
obtain partial derivatives in (15) and (16). Perturbation was
introduced to stationary values of input signals and it was
observed on output points in which extent these perturbations
were amplified. Discrete wind range ࣰ௪ was used to define
operating points above rated wind speed (approximately 12
m/s):
ࣰ௪ ൌ ሼ12,13,14, … ,24,25ሽ ሾ݉/ݏሿ (17)
In this regime of operation it can be considered that constant
nominal generator torque ܯ is used, so no Δ݃ܯ is
introduced into the system. Therefore this dynamics will be
neglected. By combining linearized equations (15) and (16)
with (8) and (10) an expression can be obtained that brings
together into a classical relation pitch angle ߚ (plant input)
and wind speed ݒ௪ (disturbance input) with rotor speed ߱
(plant output):
߱ሺݏሻ ൌ ܩሺݏሻߚሺݏሻ ܩௗሺݏሻݒ௪ሺݏሻ (18)
For every wind speed ݒ௪, א ࣰ௪ accompanying pair of
transfer functions ܩሺݏሻ א ࣡ and ܩௗ,ሺݏሻ א ࣡ௗ is obtained.
6. Families ࣡ and ࣡ௗ of transfer functions are shown on Fig. 8.
and Fig. 9.
Fig. 8. Bode plot of transfer function family ࣡
Fig. 9. Bode plot of transfer function family ࣡ௗ
Observe a phase shift on lower (relevant) frequency range by
180° on Fig. 8. that relates rotor speed change to pitch angle
change. This means that a small rise in pitch angle produces
negative change, due to phase shift, in rotor speed i.e.
slowing down of the rotor. Physically this causes a decrease
in angle of attack and consequently lowering of tangential
forces on blade sections is caused. This in turn cumulatively
decreases the value of driving torque ܯ when contributions
of all blades and all blade sections are summed.
6. DESIGN SPECIFICATIONS
Two types of specifications are defined and later on
accompanying open loop boundaries on Nichols chart are
calculated in order to facilitate controller design process. First
appropriate discrete set of design frequencies needs to be
specified. Regarding this problem there are no strict rules,
instead some useful guidelines exist. Generally it is useful to
choose frequencies that give results with meaningful
differences in calculated boundaries. This can be
computationally bothersome as it requires iterations. As a
rule of thumb frequencies separated by an octave inside
meaningful frequency range should suffice. Special care
should be taken if process dynamics exhibits resonances at
certain frequencies as then few frequencies around the
resonance frequency should be chosen to appropriately
describe abrupt phase and magnitude changes. Below is given
the set Ω of frequencies that were used in calculations:
Ω ൌ ሼ10ିଷ
, 10ିଶ
, 10ିଵ
, 0.5,1,2.5,3.3,3.38,3.47,5,20ሽ (19)
Due to natural frequency of tower first mode at ଼߱ ൌ
3.38 ,ݏ/݀ܽݎ nearby frequencies ߱ ൌ 3.3 ݏ/݀ܽݎ and
߱ଽ ൌ 3.47 ݏ/݀ܽݎ were chosen. All the frequencies above
20 ݏ/݀ܽݎ are represented by ߱ଵଵ ൌ 20 ݏ/݀ܽݎ as their
templates degenerate into virtually same shape that is solely
dominated by variations of process magnitude. This can be
stated as follows:
ܩሺ݆߱ሻ ൎ
ሺఠሻഊ when ߱ ب ߱ (20)
where ߣ represents pole excess, ߱ represents bandwidth
frequency and ܭ א ሾܭ, ܭ௫ሿ represents amplitude
variation. This fact is depicted on Fig. 10. by the template on
20 ݏ/݀ܽݎ that shows very small variations in phase values
and dominant variations in amplitude values.
Fig. 10. Process templates representing variations of
amplitude vs phase
First type of specifications refers to defining of stability
margin factors. Instead of amplitude and phase margin,
another relation was used that wraps them together stating
(see expression (2)):
ቤ
ܥሺ݆߱ሻܩሺ݆߱ሻ
1 ܥሺ݆߱ሻܩሺ݆߱ሻ
ቤ ܯ ݂ݎ ܩ א ࣡
(21)
where ܥሺ݆߱ሻ represents controller transfer function.
Amplitude margin (A.M.) and phase margin (P.M.) are bound
together to ܯ as follows:
.ܣ .ܯ ൌ െ20 log ൬
ܯ
1 ܯ
൰
ܲ. .ܯ ൌ 180° െ acos ൬
1
2ܯ
ଶ
െ 1൰
(22)
7. Fig. 11 shows visually the meaning of relation (21) depicting
A.M. and P.M. as extremes of amplitude and phase distance
to critical point ሺെ180°, 0 ݀ܤሻ.
Fig. 11. Stability margin specifications on Nichols chart for
ܯ ൌ 1.1
Second type of specifications refers to quality of disturbance
compensation i.e. ability to maintain nominal rotation speed
in spite of acting wind gust. Following relation needs to be
satisfied:
߱ሺݏሻ
ݒ௪ሺݏሻ
ൌ ฬ
ܩௗ,ሺݏሻ
1 ܩሺݏሻܥሺݏሻ
ฬ |ܩௗ௦௧ሺݏሻ| (23)
for ܩௗ, א ࣡ௗ and ܩ א ࣡. ܩௗ௦௧ሺݏሻ is defined as:
ܩௗ௦௧ሺݏሻ ൌ
1.8ݏଶ
3.557ݏ
ݏଶ 1.456ݏ 0.526
(24)
Unit step response and frequency amplitude characteristic of
(24) is shown on Fig. 12.
Fig. 12. Specified characteristic of response to unit step
disturbance and accompanying frequency amplitude
characteristic
There is no particular restriction on the initial part of the
response which explains almost constant attenuation
frequency characteristic in high frequency range. Namely,
process response cannot suddenly jump at ݐ ൌ 0 ݏ to certain
value in a step like manner so there would be no point in
defining any particular shape of response in initial period of
time as this requires unnecessarily aggressive and complex
controller design due to dominate high frequency design
requests.
7. CONTROLLER DESIGN
Using defined specifications, discrete frequency set Ω and
templates generated for ߱ א Ω it possible to calculate,
solving systems of quadratic inequalities, necessary stability
and disturbance boundaries and depict their intersection
(resultant boundaries) on Nichols chart.
Fig. 13. Resultant boundaries on Nichols chart
A 12 ݉/ݏ linearized model was chosen as nominal plant
process ܩሺݏሻ so all the boundaries on Nichols chart were
calculated in reference to this model. This in turn means that
adequate loopshaping of open loop characteristic ܮሺݏሻ ൌ
ܥሺݏሻܩሺݏሻ that satisfies given boundaries results in a fact
that all closed/open loop characteristics satisfy accompanying
closed/open loop characteristic. Controller transfer function is
given as:
ܥሺݏሻ ൌ െ1.65
ሺݏ 0.5ሻሺݏ 1.4ሻ
ݏሺݏ 5ሻ
(25)
On Fig. 14. it can be observed that point ߱ସ ൌ 0.5 ݏ/݀ܽݎ is
not completely out of its boundary which was done on
purpose as this would require movement of controller zero
ݖଵ ൌ െ0.5 even closer to zero. This in turn weakens the
integral action of the controller necessary for precision of
stationary part of response as this zero would nearly cancel
its action. Rise in complexity of the controller would be able
to solve this issue but this is where QFT transparency comes
handy as it enables us to make tradeoffs in controller design.
It was also observed that neglecting of initial shape of
response on Fig. 12 made the design easier with no evident
loss in quality of response i.e. more simple controller was
obtained that performs almost equally well. ݖଶ ൌ െ1.4 was
inserted in order to obtain raise in the phase value of open
loop so as to circumvent the round boundaries on their lower
8. right part. “Optimal” QFT controllers would have to
minimize the cost of feedback, meaning that minimum of
bandwidth should be utilized to satisfy given specifications.
In order to gain such a controller points on nominal open
loop characteristic ܮሺ݆߱ሻ should be maximally close to their
boundary.
Fig. 14. Nominal open loop on Nichols chart vs calculated
open loop boundaries
8. DESIGN VALIDATION
It remains to perform a validation of design by checking if for
all family members prescribed specifications are satisfied.
Fig. 15. shows validation of stability on all linear models.
Fig. 15. Validation of stability specifications in frequency
domain (boundary marked with red diamond markers)
Likewise Fig. 16. and Fig. 17. validate satisfactory
behaviour in time and frequency domain of all linear models.
Small ripple superimposed on rotor speed response stems
from the fact that the tower top is oscillating towards/from
the direction of wind meaning that relative wind speed ݒ௪
כ
given by (9) is oscillatory changing. This in turn causes
oscillatory changes in angle of attack of all blade sections
and, cumulatively, introduction of oscillatory component in
turbine drive torque.
Fig. 16. Validation of disturbance specifications in frequency
domain (boundary marked with red diamond markers)
Fig. 17. Validation of disturbance specifications in time
domain (boundary marked with red diamond markers)
So far validation was performed on family of linear models
obtained by linearization of model given by (14) for wind
speed ranging from 12 to 25 m/s. Plot on Fig. 18. confirms
that given specifications have been satisfied even for
nonlinear model. No particular differences are observed
comparing validation performed on family of linear models
and on nonlinear model. It is interesting to observe how the
controller ܥሺݏሻ behaves when faced with a simulation on a
professional wind turbine simulation tool (Bladed, [8]) that
also offers possibility of obtaining family of linear models of
very high order (>40). This model besides the first and
second mode of fore-aft movement, also includes equal
number of side-side tower modes and rotor in-plane and out-
plane modes that were neglected in simplified nonlinear
model given by (14). The response of rotor speed and pitch
9. angle when performing simulations in Bladed is given on Fig.
19. It shows almost equal “main” dynamic of responses
compared to responses of simplified nonlinear process.
Response from Bladed contains though richer contents due to
high order effects originating, among others, from in-plane
and out-plane movement of blade sections in reference to
their stationary position. Controller ܥሺݏሻ would perform
better if it was designed upon boundaries generated in
reference to high order linear models obtained from Bladed.
In this case an introduction of gain scheduling that reduces
gain in high wind speed range would aid the controller and
reduce the blade oscillatory movement thus reducing tear-
and-wear.
Fig. 18. Validation on nonlinear model
Fig. 19. Validation in Bladed
9. CONCLUSION
QFT proved to be an adequate method for synthesis of rotor
speed controller despite existing variations in wind turbine
dynamics. This should not come as a surprise as it was
mentioned earlier that QFT had been very successfully
integrated in helicopter and airplane control systems. Usually
robust controllers are of high order but in this case, due to
transparency of the QFT and its ability to explicitly address
the uncertainty of wind turbine dynamics, an efficient
controller of second order was obtained that uses no other
aids (feedforward action, gain scheduling, etc.) to achieve
specified closed loop behavior. Strong point of this method is
also the ability it gives the user to perceive when the
combination of process uncertainty and performance
demands poses to big of an obstacle for chosen control
structure. In this case it was possible to conclude that
(judging by Bladed simulation results) introduction of gain
reducing element scheduled on pitch angle would aid the
performance of the controller in high wind regime thus
obtaining a hybrid solution that combines adaptive and robust
algorithms.
ACKNOWLEDGMENTS
This work was financially supported by Končar – Electrical
Engineering Institute and the Ministry of Science Education
and Sports of the Republic of Croatia.
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Appendix A. QFT GUI
Although several tools exist that offer the possibility of
interactive QFT controller design (see [9], [10], [11]), an
attempt was made to implement a simple QFT tool within
Matlab® environment. As a result QFT GUI application (see
Fig. 20) was implemented which offers its user the
possibility to define the process in a structure given by (18).
Furthermore, sensor and actuator dynamics can also be
selected. This test version of GUI enables defining of two
types of specification that were used in this article
(disturbance rejection, stability margin). Calculate button
translates given specification on to the Nichols chart (in the
form of open loop boundaries) where controller design
commences. The controller is designed interactively as the
effects of either movement, deletion or addition of zeroes and
poles are seen on Nichols chart. At any point the user can
validate quality of controller design in time and frequency
domain. It is important to stress that the validation is
performed on the user defined set of linear processes. It is up
to user to validate if the controller design is adequate on a
nonlinear process model.
Fig. 20. QFT GUI application