This is a class project done for the course \'Power System Stability\' at Arizona State University. It is a transient stability analysis done with the help of Matlab.
Steady state stability analysis and enhancement of three machine nine bus pow...eSAT Journals
This document presents an analysis of steady state stability for the IEEE 3-machine 9-bus test power system. It first describes the mathematical modeling of the system using linearization and state space representation. Eigenvalue analysis shows the system is purely oscillatory without damping. A thyristor controlled phase shifter (TCPS) FACTS device-based controller is then modeled to enhance stability. The system is analyzed with and without the controller. Results show the controller provides damping, improving stability as seen in eigenvalue analysis and time domain simulations following a disturbance.
Comparative Study of the Success of PI and PI-Fuzzy Controller for Induction ...inventionjournals
Asynchronous motors have a wide range of applications in the industry.Therefore, speed control of asynchronous motors is of great importance.Speed control of asynchronous motors based on vector control techniques to achieve high performance.The vector control technique, motor flux and moment variables can be controlled independently of each other.Because of the nonlinear and complex model of asynchronous motors, the speed control applications of these motors are not provided with great efficiency by classical control methods.Fuzzy logic controllers (FLC), which were successful in many areas, present great performance in speed control of an asynchronous motor.In this study, a simulation study regarding speed control of a threephase squirrel cage asynchronous motor was carried out with a PI-Fuzzy type FLC and a conventional PI type controller.The data obtained by simulation are evaluated and the performances of the control methods are compared.
The document provides an overview of circuit analysis techniques using phasor analysis. It discusses:
1) Representing sinusoidal signals using phasors and complex numbers according to Euler's identity, allowing circuits with sinusoidal sources to be analyzed in the frequency domain.
2) Performing phasor additions and conversions between rectangular and polar forms to solve for unknown voltages and currents.
3) Analyzing AC circuits using complex impedances and applying Kirchhoff's laws with phasors to solve for node voltages and mesh currents.
4) Computing power in AC circuits and determining maximum power transfer conditions.
This document discusses estimating the efficiency of electric machines using magnetic flux circuits. It presents the development of a generalized 4th order dq model equation of an electrical machine expressed in an arbitrary reference frame. The model equations are transformed to use all flux linkage variables instead of current variables. Results using this flux linkage approach are compared to measured machine quantities and good estimations of efficiency are obtained. Magnetic equivalent circuit modeling is an effective method for simulating electric machine performance and estimating efficiency variations in both transient and steady states.
Efficiency, reliability, high power quality and continuous operation are important aspects in electric vehicle attraction system. Therefore, quick fault detection, isolation and enhanced fault-tolerant control for open-switches faults in inverter driving systems become more and more required in this filed. However, fault detection and localization algorithms have been known to have many performance limitations due to speed variations such as wrong decision making of fault occurrence. Those weaknesses are investigated and solved in this paper using currents magnitudes fault indices, current direct component fault indices and a decision system. A simulation model and experimental setup are utilized to validate the proposed concept. Many simulation and experimental results are carried out to show the effectiveness of the proposed fault detection approach.
Control Synthesis of Electro Hydraulic Drive Based on the Concept of Inverse ...ijtsrd
Electro hydraulic drives are widely used in various branches of technology due to a number of its advantages, which include significant specific power the ratio of power developed by the drive to its mass , high speed and the ability to position the output link with a sufficient degree of accuracy. However, hydraulic drives are non linear objects, which makes it difficult to synthesize drive control, which provides the required dynamic characteristics. This paper presents an approach to solving the problem of constructing a control algorithm based on the concept of inverse problems of dynamics by an electro hydraulic drive, consisting structurally of an electro hydraulic amplifier and an executive hydraulic cylinder. Soe Nay Lynn Aung | Akimenko D. A "Control Synthesis of Electro-Hydraulic Drive Based on the Concept of Inverse Dynamics Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27823.pdf Paper URL: https://www.ijtsrd.com/engineering/other/27823/control-synthesis-of-electro-hydraulic-drive-based-on-the-concept-of-inverse-dynamics-problems/soe-nay-lynn-aung
Steady state stability analysis and enhancement of three machine nine bus pow...eSAT Journals
This document presents an analysis of steady state stability for the IEEE 3-machine 9-bus test power system. It first describes the mathematical modeling of the system using linearization and state space representation. Eigenvalue analysis shows the system is purely oscillatory without damping. A thyristor controlled phase shifter (TCPS) FACTS device-based controller is then modeled to enhance stability. The system is analyzed with and without the controller. Results show the controller provides damping, improving stability as seen in eigenvalue analysis and time domain simulations following a disturbance.
Comparative Study of the Success of PI and PI-Fuzzy Controller for Induction ...inventionjournals
Asynchronous motors have a wide range of applications in the industry.Therefore, speed control of asynchronous motors is of great importance.Speed control of asynchronous motors based on vector control techniques to achieve high performance.The vector control technique, motor flux and moment variables can be controlled independently of each other.Because of the nonlinear and complex model of asynchronous motors, the speed control applications of these motors are not provided with great efficiency by classical control methods.Fuzzy logic controllers (FLC), which were successful in many areas, present great performance in speed control of an asynchronous motor.In this study, a simulation study regarding speed control of a threephase squirrel cage asynchronous motor was carried out with a PI-Fuzzy type FLC and a conventional PI type controller.The data obtained by simulation are evaluated and the performances of the control methods are compared.
The document provides an overview of circuit analysis techniques using phasor analysis. It discusses:
1) Representing sinusoidal signals using phasors and complex numbers according to Euler's identity, allowing circuits with sinusoidal sources to be analyzed in the frequency domain.
2) Performing phasor additions and conversions between rectangular and polar forms to solve for unknown voltages and currents.
3) Analyzing AC circuits using complex impedances and applying Kirchhoff's laws with phasors to solve for node voltages and mesh currents.
4) Computing power in AC circuits and determining maximum power transfer conditions.
This document discusses estimating the efficiency of electric machines using magnetic flux circuits. It presents the development of a generalized 4th order dq model equation of an electrical machine expressed in an arbitrary reference frame. The model equations are transformed to use all flux linkage variables instead of current variables. Results using this flux linkage approach are compared to measured machine quantities and good estimations of efficiency are obtained. Magnetic equivalent circuit modeling is an effective method for simulating electric machine performance and estimating efficiency variations in both transient and steady states.
Efficiency, reliability, high power quality and continuous operation are important aspects in electric vehicle attraction system. Therefore, quick fault detection, isolation and enhanced fault-tolerant control for open-switches faults in inverter driving systems become more and more required in this filed. However, fault detection and localization algorithms have been known to have many performance limitations due to speed variations such as wrong decision making of fault occurrence. Those weaknesses are investigated and solved in this paper using currents magnitudes fault indices, current direct component fault indices and a decision system. A simulation model and experimental setup are utilized to validate the proposed concept. Many simulation and experimental results are carried out to show the effectiveness of the proposed fault detection approach.
Control Synthesis of Electro Hydraulic Drive Based on the Concept of Inverse ...ijtsrd
Electro hydraulic drives are widely used in various branches of technology due to a number of its advantages, which include significant specific power the ratio of power developed by the drive to its mass , high speed and the ability to position the output link with a sufficient degree of accuracy. However, hydraulic drives are non linear objects, which makes it difficult to synthesize drive control, which provides the required dynamic characteristics. This paper presents an approach to solving the problem of constructing a control algorithm based on the concept of inverse problems of dynamics by an electro hydraulic drive, consisting structurally of an electro hydraulic amplifier and an executive hydraulic cylinder. Soe Nay Lynn Aung | Akimenko D. A "Control Synthesis of Electro-Hydraulic Drive Based on the Concept of Inverse Dynamics Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27823.pdf Paper URL: https://www.ijtsrd.com/engineering/other/27823/control-synthesis-of-electro-hydraulic-drive-based-on-the-concept-of-inverse-dynamics-problems/soe-nay-lynn-aung
This document presents a new method for detecting DC voltage faults in switched reluctance motor (SRM) drives. The method uses K-means clustering to analyze torque waveform data and classify faults using support vector machines (SVM). Simulation results show that torque ripple patterns change with different DC voltage levels. The proposed approach clusters the torque data and uses SVM to detect and classify DC voltage faults, which enables intelligent fault identification and diagnosis in SRM drives.
This document summarizes the system identification and control of a two-cart spring system. Various identification techniques were used, including theoretical modeling, non-parametric methods like impulse response and sine sweeps, and parametric ARX modeling with chirp and square wave inputs. An ARX model with 3 poles was selected based on the identification results. An LQR/LQG controller was then designed and tuned, achieving reasonable closed-loop performance for controlling the position of the second cart.
Three-Level DTC Based on Fuzzy Logic and Neural Network of Sensorless DSSM Us...IJPEDS-IAES
This paper presents a direct torque control is applied for salient-pole double star synchronous machine without mechanical speed and stator flux linkage sensors. The estimation is performed using the extended Kalman filter known by it is ability to process noisy discrete measurements. Two control approaches using fuzzy logic DTC, and neural network DTC are proposed and compared. The validity of the proposed controls scheme is verified by simulation tests of a double star synchronous machine. The stator flux, torque, and speed are determined and compared in the above techniques. Simulation results presented in this paper highlight the improvements produced by the proposed control method based on the extended Kalman filter under various operation conditions.
Park’s Vector Approach to detect an inter turn stator fault in a doubly fed i...cscpconf
An electrical machine failure that is not identified in an initial stage may become catastrophic and it may suffer severe damage. Thus, undetected machine faults may cascade in it failure, which in turn may cause production shutdowns. Such shutdowns are costly in terms of lost production time, maintenance costs, and wasted raw materials. Doubly fed induction generators are used mainly for wind energy conversion in MW power plants. This paper presents a detection of an inter turn stator fault in a doubly fed induction machine whose stator and rotor are supplied by two pulse width modulation (PWM) inverters. The method used in this article to detect this fault, is based on Park’s Vector Approach , using a neural network s.
Design of Synchronous Sequential Circuits - State
Table and State Diagram - Design of Mealy and
Moore FSM
• Overlapping & Non-overlapping Sequence
detector
• Hazards - Hazard free realization - Case study on
Vending Machine FSM.
Adoption of Park’s Transformation for Inverter Fed DriveIJPEDS-IAES
Park’s transformation in the context of ac machine is applied to obtain quadrature voltages for the 3-phase balanced voltages. In the case of a inverter fed drive, one can adopt Park’s transformation to directly derive the quadrature voltages in terms simplified functions of switching parameters. This is the main result of the paper which can be applied to model based and predictive control of electrical machines. Simulation results are used to compare the new dq voltage modelling response to conventional direct – quadrature (dq) axes modelling response in direct torque control – space vector modulation scheme. The proposed model is compact, decreases the computation complexity and time. The model is useful especially in model based control implemented in real time, in terms of a simplified set of switching parameters.
In this paper, a new sliding mode controller is proposed as the indirect control method and compared to a simple direct control method in order to control a buck converter in photovoltaic applications. The solar arrays are dependent power sources with nonlinear voltage-current characteristics under different environmental conditions. From this point of view, the DC/DC converter is particularly suitable for the application of the sliding mode control in photovoltaic application, because of its controllable states. Solar tracking allows more energy to be produced because the solar array is able to remain aligned to the sun. This method has the advantage that it will guarantee the maximum output power possible by the array configuration. Problems and possible improvements will also be presented.
This paper presents a nonlinear Integral backstepping control approach based on field oriented control technique, applied to a Double Star Induction Machine ‘DSIM’ feed by two power voltage sources. We present this technique of integral backstepping by using reduced and complete Model of DSIM. The objective is to improve the robustness of machine under internal parameter variation with nonlinear Integral backstepping control. The robustness test results obtained by simulation prove the effectiveness of control with using complete model of DSIM.
This article presents nonlinear control of wind conversion chain connected to the grid based on a permanent magnet synchronous generator. The control objectives are threefold; i) forcing the generator speed to track a varying reference signal in order to extract the maximum power at different wind speed (MPPT); ii) regulating the rectifier output capacitor voltage; iii) reducing the harmonic and reactive currents injected in the grid. This means that the inverter output current must be sinusoidal and in phase with the AC supply voltage (PFC). To this end, a nonlinear state-feedback control is developed, based on the average nonlinear model of the whole controlled system. This control strategy involves backstepping approach, Lyapunov stability and other tools from theory of linear systems. The proposed state-feedback control strategy is tested by numerical simulation which shows that the developed controller reaches its objectives.
Fuzzy-Logic-Controller-Based Fault Isolation in PWM VSI for Vector Controlled...iosrjce
IOSR Journal of Electrical and Electronics Engineering(IOSR-JEEE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of electrical and electronics engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electrical and electronics engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
This document provides an analysis of the content and lesson plans for a course on power electronics devices. It discusses key components like diacs, triacs, and thyristors. For diacs, it describes their circuit symbol and bidirectional switching operation. Triacs are explained as having two thyristors connected back-to-back to allow bidirectional current flow. Thyristors are also examined. The document includes the specific learning objectives and expectations for trainees for four lesson plans covering the operation and practical applications of these components.
This document provides an analysis of the content and lesson plans for a course on power electronics devices. It discusses the characteristics and operation of diacs, triacs, and thyristors. For diacs, it describes their structure, symbol, and bidirectional switching operation. Triacs are explained as having two thyristors connected back-to-back, allowing bidirectional current flow. Thyristors are also examined. The document includes lesson plans that have objectives of teaching students about the characteristics of these components through both lecture and practical lessons in order to understand their usage in power electronics circuits.
1. The document discusses symmetrical components, which allow representation of unbalanced three-phase quantities as the sum of three balanced components.
2. It introduces the positive, negative, and zero sequence components and the transformation matrix used to relate the symmetrical components to the original unbalanced quantities.
3. Symmetrical components are useful for simplifying analysis of unbalanced conditions like single line-to-ground faults in power systems. Sequence impedances can be used to model devices and transmission lines.
This document discusses fault current calculation methods. It covers symmetrical and asymmetrical faults, and describes analyzing power systems under both normal and abnormal operating conditions. The infinite bus method and per unit methods for calculating fault current are introduced. Synchronous machine response to asymmetrical faults is examined, including the subtransient, transient, and steady state stages. Fault current envelopes are presented.
This document summarizes a research paper that investigates optimally locating SVC and IPFC FACTS devices on the IEEE 30-bus system to reduce power losses and improve voltage profiles under normal, overload, and contingency conditions using Particle Swarm Optimization. The paper presents mathematical models of the SVC and IPFC and describes how PSO is used to determine the optimal location and ratings of the devices. Simulation results show that with optimally located SVC and IPFC, total power losses are reduced and voltage profiles are improved under various system conditions compared to without the FACTS devices.
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.
- The document details a state space solver approach for analog mixed-signal simulations using SystemC. It models analog circuits as sets of linear differential equations and solves them using the Runge-Kutta method of numerical integration.
- Two examples are provided: a digital voltage regulator simulation and a digital phase locked loop simulation. Both analog circuits are modeled in state space and simulated alongside a digital design to verify mixed-signal behavior.
- The state space approach allows modeling analog circuits without transistor-level details, improving simulation speed over traditional mixed-mode simulations while still capturing system-level behavior.
Concurrent Detection and Classification of Faults in Matrix Converter using T...IAES-IJPEDS
This paper presents a fault diagnostic algorithm for detecting and locating open-circuit and short-circiut faults in switching components of matrix converters (MCs) which can be effectively used to drive a permanent magnet synchronous motor for research in critical applications. The proposed method is based on monitoring the voltages and currents of the switches. These measurements are used to evaluate the forward trans-conductance of each transistor for different values of switch voltages. These trans-conductance values are then compared to the nominal values. Under healthy conditions, the values obtained for the fault signal is less than the tolerable value. Under the open/short-circuit conditions, the fault signal exceeds the threshold, hence enables the matrix converter drive to detect and exactly identify the location of the faulty IGBT. The main advantages of this diagnostic method include fast detection and locating of the faulty IGBT, easiness of implementation and independency of the modulation strategy of the converter.
This document provides instructions for an experiment involving Kirchhoff's Current and Voltage Laws. The objectives are to learn and apply Kirchhoff's Current Law and Kirchhoff's Voltage Law, obtain further practice with electrical measurements, and compare results with calculations and simulations. The experiment uses a circuit with four resistors to apply the two Kirchhoff's Laws and calculate voltages and currents at various points. Students are instructed to use the laws to derive equations relating node voltages, solve them through calculation and simulation, measure resistor values, and compare results.
Interturn short circuit analysis in an induction machine by femDarío Díaz
This document summarizes research on analyzing inter-turn short-circuits in induction machine stator windings using finite element modeling and field tests. It discusses using inverse sequence impedance and electromagnetic torque analysis to detect short-circuits. Simulations were performed with varying numbers of shorted turns. Results show the inverse sequence impedance decreases and torque is reduced with more shorted turns. Spectral analysis of current signatures also detects short-circuits. Experimental tests on a laboratory bench validate the simulation findings by examining current spectra and Lissajou curves, which become elliptical rather than circular with shorted turns.
This document presents a new method for detecting DC voltage faults in switched reluctance motor (SRM) drives. The method uses K-means clustering to analyze torque waveform data and classify faults using support vector machines (SVM). Simulation results show that torque ripple patterns change with different DC voltage levels. The proposed approach clusters the torque data and uses SVM to detect and classify DC voltage faults, which enables intelligent fault identification and diagnosis in SRM drives.
This document summarizes the system identification and control of a two-cart spring system. Various identification techniques were used, including theoretical modeling, non-parametric methods like impulse response and sine sweeps, and parametric ARX modeling with chirp and square wave inputs. An ARX model with 3 poles was selected based on the identification results. An LQR/LQG controller was then designed and tuned, achieving reasonable closed-loop performance for controlling the position of the second cart.
Three-Level DTC Based on Fuzzy Logic and Neural Network of Sensorless DSSM Us...IJPEDS-IAES
This paper presents a direct torque control is applied for salient-pole double star synchronous machine without mechanical speed and stator flux linkage sensors. The estimation is performed using the extended Kalman filter known by it is ability to process noisy discrete measurements. Two control approaches using fuzzy logic DTC, and neural network DTC are proposed and compared. The validity of the proposed controls scheme is verified by simulation tests of a double star synchronous machine. The stator flux, torque, and speed are determined and compared in the above techniques. Simulation results presented in this paper highlight the improvements produced by the proposed control method based on the extended Kalman filter under various operation conditions.
Park’s Vector Approach to detect an inter turn stator fault in a doubly fed i...cscpconf
An electrical machine failure that is not identified in an initial stage may become catastrophic and it may suffer severe damage. Thus, undetected machine faults may cascade in it failure, which in turn may cause production shutdowns. Such shutdowns are costly in terms of lost production time, maintenance costs, and wasted raw materials. Doubly fed induction generators are used mainly for wind energy conversion in MW power plants. This paper presents a detection of an inter turn stator fault in a doubly fed induction machine whose stator and rotor are supplied by two pulse width modulation (PWM) inverters. The method used in this article to detect this fault, is based on Park’s Vector Approach , using a neural network s.
Design of Synchronous Sequential Circuits - State
Table and State Diagram - Design of Mealy and
Moore FSM
• Overlapping & Non-overlapping Sequence
detector
• Hazards - Hazard free realization - Case study on
Vending Machine FSM.
Adoption of Park’s Transformation for Inverter Fed DriveIJPEDS-IAES
Park’s transformation in the context of ac machine is applied to obtain quadrature voltages for the 3-phase balanced voltages. In the case of a inverter fed drive, one can adopt Park’s transformation to directly derive the quadrature voltages in terms simplified functions of switching parameters. This is the main result of the paper which can be applied to model based and predictive control of electrical machines. Simulation results are used to compare the new dq voltage modelling response to conventional direct – quadrature (dq) axes modelling response in direct torque control – space vector modulation scheme. The proposed model is compact, decreases the computation complexity and time. The model is useful especially in model based control implemented in real time, in terms of a simplified set of switching parameters.
In this paper, a new sliding mode controller is proposed as the indirect control method and compared to a simple direct control method in order to control a buck converter in photovoltaic applications. The solar arrays are dependent power sources with nonlinear voltage-current characteristics under different environmental conditions. From this point of view, the DC/DC converter is particularly suitable for the application of the sliding mode control in photovoltaic application, because of its controllable states. Solar tracking allows more energy to be produced because the solar array is able to remain aligned to the sun. This method has the advantage that it will guarantee the maximum output power possible by the array configuration. Problems and possible improvements will also be presented.
This paper presents a nonlinear Integral backstepping control approach based on field oriented control technique, applied to a Double Star Induction Machine ‘DSIM’ feed by two power voltage sources. We present this technique of integral backstepping by using reduced and complete Model of DSIM. The objective is to improve the robustness of machine under internal parameter variation with nonlinear Integral backstepping control. The robustness test results obtained by simulation prove the effectiveness of control with using complete model of DSIM.
This article presents nonlinear control of wind conversion chain connected to the grid based on a permanent magnet synchronous generator. The control objectives are threefold; i) forcing the generator speed to track a varying reference signal in order to extract the maximum power at different wind speed (MPPT); ii) regulating the rectifier output capacitor voltage; iii) reducing the harmonic and reactive currents injected in the grid. This means that the inverter output current must be sinusoidal and in phase with the AC supply voltage (PFC). To this end, a nonlinear state-feedback control is developed, based on the average nonlinear model of the whole controlled system. This control strategy involves backstepping approach, Lyapunov stability and other tools from theory of linear systems. The proposed state-feedback control strategy is tested by numerical simulation which shows that the developed controller reaches its objectives.
Fuzzy-Logic-Controller-Based Fault Isolation in PWM VSI for Vector Controlled...iosrjce
IOSR Journal of Electrical and Electronics Engineering(IOSR-JEEE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of electrical and electronics engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electrical and electronics engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
This document provides an analysis of the content and lesson plans for a course on power electronics devices. It discusses key components like diacs, triacs, and thyristors. For diacs, it describes their circuit symbol and bidirectional switching operation. Triacs are explained as having two thyristors connected back-to-back to allow bidirectional current flow. Thyristors are also examined. The document includes the specific learning objectives and expectations for trainees for four lesson plans covering the operation and practical applications of these components.
This document provides an analysis of the content and lesson plans for a course on power electronics devices. It discusses the characteristics and operation of diacs, triacs, and thyristors. For diacs, it describes their structure, symbol, and bidirectional switching operation. Triacs are explained as having two thyristors connected back-to-back, allowing bidirectional current flow. Thyristors are also examined. The document includes lesson plans that have objectives of teaching students about the characteristics of these components through both lecture and practical lessons in order to understand their usage in power electronics circuits.
1. The document discusses symmetrical components, which allow representation of unbalanced three-phase quantities as the sum of three balanced components.
2. It introduces the positive, negative, and zero sequence components and the transformation matrix used to relate the symmetrical components to the original unbalanced quantities.
3. Symmetrical components are useful for simplifying analysis of unbalanced conditions like single line-to-ground faults in power systems. Sequence impedances can be used to model devices and transmission lines.
This document discusses fault current calculation methods. It covers symmetrical and asymmetrical faults, and describes analyzing power systems under both normal and abnormal operating conditions. The infinite bus method and per unit methods for calculating fault current are introduced. Synchronous machine response to asymmetrical faults is examined, including the subtransient, transient, and steady state stages. Fault current envelopes are presented.
This document summarizes a research paper that investigates optimally locating SVC and IPFC FACTS devices on the IEEE 30-bus system to reduce power losses and improve voltage profiles under normal, overload, and contingency conditions using Particle Swarm Optimization. The paper presents mathematical models of the SVC and IPFC and describes how PSO is used to determine the optimal location and ratings of the devices. Simulation results show that with optimally located SVC and IPFC, total power losses are reduced and voltage profiles are improved under various system conditions compared to without the FACTS devices.
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.
- The document details a state space solver approach for analog mixed-signal simulations using SystemC. It models analog circuits as sets of linear differential equations and solves them using the Runge-Kutta method of numerical integration.
- Two examples are provided: a digital voltage regulator simulation and a digital phase locked loop simulation. Both analog circuits are modeled in state space and simulated alongside a digital design to verify mixed-signal behavior.
- The state space approach allows modeling analog circuits without transistor-level details, improving simulation speed over traditional mixed-mode simulations while still capturing system-level behavior.
Concurrent Detection and Classification of Faults in Matrix Converter using T...IAES-IJPEDS
This paper presents a fault diagnostic algorithm for detecting and locating open-circuit and short-circiut faults in switching components of matrix converters (MCs) which can be effectively used to drive a permanent magnet synchronous motor for research in critical applications. The proposed method is based on monitoring the voltages and currents of the switches. These measurements are used to evaluate the forward trans-conductance of each transistor for different values of switch voltages. These trans-conductance values are then compared to the nominal values. Under healthy conditions, the values obtained for the fault signal is less than the tolerable value. Under the open/short-circuit conditions, the fault signal exceeds the threshold, hence enables the matrix converter drive to detect and exactly identify the location of the faulty IGBT. The main advantages of this diagnostic method include fast detection and locating of the faulty IGBT, easiness of implementation and independency of the modulation strategy of the converter.
This document provides instructions for an experiment involving Kirchhoff's Current and Voltage Laws. The objectives are to learn and apply Kirchhoff's Current Law and Kirchhoff's Voltage Law, obtain further practice with electrical measurements, and compare results with calculations and simulations. The experiment uses a circuit with four resistors to apply the two Kirchhoff's Laws and calculate voltages and currents at various points. Students are instructed to use the laws to derive equations relating node voltages, solve them through calculation and simulation, measure resistor values, and compare results.
Interturn short circuit analysis in an induction machine by femDarío Díaz
This document summarizes research on analyzing inter-turn short-circuits in induction machine stator windings using finite element modeling and field tests. It discusses using inverse sequence impedance and electromagnetic torque analysis to detect short-circuits. Simulations were performed with varying numbers of shorted turns. Results show the inverse sequence impedance decreases and torque is reduced with more shorted turns. Spectral analysis of current signatures also detects short-circuits. Experimental tests on a laboratory bench validate the simulation findings by examining current spectra and Lissajou curves, which become elliptical rather than circular with shorted turns.
Interturn short circuit analysis in an induction machine by fem
Eee598 P3
1. TRANSIENT STABILITY ANALYSIS OF A SAMPLE
FOUR MACHINE SYSTEM USING MATLAB
A PROJECT REPORT
Submitted by
Members of Group 5
Fei Gao
Supriya Chathadi
Changxu Chen
Habibou Maiga
Submitted to
Dr. Vijay Vittal
In partial fulfillment for completion of the course
EEE598: POWER SYSTEM STABILITY
at
ARIZONA STATE UNIVERSITY, TEMPE
2. EEE598-Group 5
Table of Contents
1. Introduction ............................................................................................................................. 3
2. Machine Modelling................................................................................................................... 3
2.1. Two-Axis Model ...................................................................................................................3
2.1.1. Initial Conditions ..................................................................................................... 3
2.2. E’’ Model ..............................................................................................................................4
2.2.1. Initial Conditions ..................................................................................................... 5
2.3. Classical Model .....................................................................................................................5
2.3.1. Initial Conditions ..................................................................................................... 6
3. Network Parameters ................................................................................................................ 6
4. Simulation using MATLAB ...................................................................................................... 7
5. Results ..................................................................................................................................... 7
5.1. Without Damping..................................................................................................................7
5.2. With Damping.......................................................................................................................9
6. Conclusion ............................................................................................................................. 10
7. References ............................................................................................................................. 10
APPENDIX: MATLAB CODES .................................................................................................... i
Arizona State University 2
3. EEE598-Group 5
1. Introduction
The sample four-machine two-area system [1] was analyzed in project 1, and the critical
clearing time was determined, for a three-phase fault at bus 5. The same system is now taken
into account for transient stability analysis using Matlab.
Many simplified models such as E’’, two-axis and classical models are used for the purpose
of study. In this specific case, the machines are modelled as shown below.
Machine 1 – Two-axis model
Machines 2 and 3 – E’’ model
Machine 4 – Classical model
The machine parameters are taken from the dynamic file of project 1. And the missing
parameters are assumed from example 12.6 of reference [1].
2. Machine Modelling
Different machines are modelled differently as specified in the previous section. The
differential equations and the initial conditions which define every model are explained
below.
2.1. Two-Axis Model
The two-axis model is a simplified way to model a synchronous machine, in which only the
transient effects are taken into account and the sub-transient effects are neglected. The
machine is represented by an equivalent circuit which has transient emf and reactance.
2.1.1. Initial Conditions
Before doing the initial condition calculations, all the generator parameters are converted into
S G
a common system base, i.e., X sys X gen base , H sys H gen base .
Gbase Sbase
The initial conditions of the two-axis model are calculated from the equations shown below.
Currents, voltages along with their angles from the q-axis are calculated.
,
Arizona State University 3
4. EEE598-Group 5
Ir Ia cos , Ix Ia sin
xq I r rI x
tan 1
Va rI r xq I x
I q I a cos
I d I a sin
Vq Vt cos( )
Vd Vt sin( )
The field current is calculated, from which all the flux linkages are obtained.
E Vq rIQ xd I d EFD
3E
iF
LAD
d Ld id LADiF
q Lqiq
D LADid LADiF
Q LAQiq
D D / 3
Q Q / 3
The two-axis model is represented by the following equations.
d ' d Ld 'id
q ' q Lq 'iq
eq ' d '
ed ' q '
wR 1
Ed ' ed ' / 3
Eq ' eq ' / 3
2.2. E’’ Model
Both transient and sub-transient effects are accounted for in this case. The machine is
modeled by neglecting the transformer voltage terms compared to the speed voltage terms in
the stator voltage equations. The E” model is relatively a detailed model among the various
simplified models, where a machine is represented by the sub-transient emf and reactance.
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Where:
2.2.1. Initial Conditions
The initial condition calculations are quite similar to the procedure followed for two-axis
model. Currents, voltages and flux linkages are obtained from the same equations, as
mentioned earlier and E” model is represented by the following.
d '' d Ld ''id
q '' q Lq ''iq
eq '' d ''
ed '' q ''
Ed '' ed '' / 3
Eq '' eq '' / 3
2.3. Classical Model
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Classical model is the simplest way of modeling a machine, which assumes that the
mechanical power input remains constant during the period of transient and the damping
power is neglected. Thus, the machine is modeled as constant voltage behind transient
reactance, with network parameters in steady state.
2.3.1. Initial Conditions
For classical model, the initial value for power angle is obtained from internal voltage
Pgen jQgen
E Vt , angle( E ) , the direction of E is set as q axis. The values for the Vt,
Vt
Pgen and Qgen are obtained from the power flow data. The angle between current and q axis
is angle(V t ) , and then
I q I a cos ,
I d I a sin ,
3. Network Parameters
Step 1: Calculate Zeq for all the generators, based on the model used.
r xd 1
Z eq T '
r
T
xq
cos sin
T
sin cos
The sub-transient reactances are used in the above equation if it is an E” model.
Step 2: As the values of Eq and Ed are known, the current equations can be written as
follows.
1
r xd 1
Yeq T '
r
T
xq
1
IQ r xd Eq ' VQ
I T x ' ' Yeq
D q r Ed VD
Step 3: From the values of passive network parameters, the equations can be further modified
as shown.
I Q G B VQ
I B G V
D D
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IQ GVQ BVD
I D BVQ GVD
Step 4: Thus the voltages can be calculated from the below equation.
VQ 1 I eq
V Y augument 0
D
4. Simulation using MATLAB
Step 1: Read the data from the dynamic data file and the power-flow data file.
Step 2: Generate Y-bus for pre-fault, faulted and post-fault conditions.
Step 3: Model the generators using the appropriate differential equations and initial values,
corresponding to the model used.
Step 4: Integrate the differential equations to calculate the values of angle δ and angular
speeds, and use Euler’s method to find their values at various time steps.
Step 5: Plot the relative rotor angles, which would give a measure of the stability of the
system.
Step 6: By trial and error method, find out the critical clearing time for a 3-phase fault at bus
5 of the system.
The Mat lab codes are shown in Appendix
5. Results
From the simulation, it is seen that the clearing time for a 3-phase fault is dependent on the
damping co-efficient used. When there is no damping (as specified in [1]), the critical
clearing time for a 3-phase fault at bus 5 is approximately 9 cycles. If damping is included
(say, D=2 p.u. from Appendix D of reference [2]), the critical clearing time appears to be
10.6 cycles. The relative power angle plots for stable, critically stable and unstable cases;
with and without damping are shown below.
5.1. Without Damping
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Relative Power Angles
80
Gen1
Gen2
60
Gen3
Gen4
40
20
Delta, degrees
0
-20
-40
-60
-80
0 0.5 1 1.5 2 2.5 3 3.5 4
Time, seconds
Fig. 1: Stable System (4 cycles)
Relative Power Angles
150
Gen1
Gen2
Gen3
100 Gen4
50
Delta, degrees
0
-50
-100
0 0.5 1 1.5 2 2.5 3 3.5 4
Time, seconds
Fig. 2: Marginally Stable System (9 cycles)
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Relative Power Angles
200
Gen1
Gen2
Gen3
150
Gen4
100
Delta, degrees
50
0
-50
-100
0 0.5 1 1.5 2 2.5 3 3.5 4
Time, seconds
Fig. 3: Unstable System (9.1 cycles)
5.2. With Damping
Relative Power Angles
120
Gen1
100 Gen2
Gen3
80 Gen4
60
40
Delta, degrees
20
0
-20
-40
-60
-80
0 0.5 1 1.5 2 2.5 3 3.5 4
Time, seconds
Fig. 4: Stable System (8 cycles)
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Relative Power Angles
150
Gen1
Gen2
Gen3
100 Gen4
50
Delta, degrees
0
-50
-100
0 0.5 1 1.5 2 2.5 3 3.5 4
Time, seconds
Fig. 5: Marginally Stable System (10.6 cycles)
Relative Power Angles
400
Gen1
350 Gen2
Gen3
300 Gen4
250
200
Delta, degrees
150
100
50
0
-50
-100
0 0.5 1 1.5 2 2.5 3 3.5 4
Time, seconds
Fig. 6: Unstable System (10.7 cycles)
6. Conclusion
To conclude, it is seen that a three phase fault applied at bus 5 of the sample four-machine,
two area system has a critical clearing time of about 9 cycles without damping and 10.6
cycles, when damping is included. This is also dependant on the type of model used for
modeling each machine.
7. References
[1] P. Kundur, “Power System Stability and Control”, McGraw-Hill, Inc., Publications, 1994
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[2] P.M. Anderson and A.A. Fouad, “Power System Control and Stability”, A John Wiley
and Sons, Inc., Publications, 2003.
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APPENDIX: MATLAB CODES
MAIN.M
%********* Transient simulation Controls and options*****************
%********************************************************************
%System base
Sbn=100;
w=1;
%initial angluar speed and frequency
omega = [1,1,1,1];
f=60;
%faulted bus
bfault=5;
%simualation duration in seconds
tsend=5;
% Time when fault is applied in seconds
tfault=0.1;
%Duration of the fault in cycles
tclear=9;
%Time when fault is cleared in Cyles
tfclear = tfault + tclear/60;
%simulation steps
dtime = 0.001;
%************************Initial condition calculations*****************
%***********************************************************************
% Machine dynamic data
[r,xd,xdtr,xdstr,xq,xqstr,xqtr,xl,H,D,td0tr,td0str,tq0tr,tq0str,x,Ldstr,Ldt
r,Ld,Lqstr,Lqtr,Lq,ld,lq,LAD,LF,LD,LAQ,LG,LQ,lF,lD,lG,lQ,K1,K2,K3,K4,Kd,Kq,
xxd,xxq,tj] = inputdyn(Sbn);
% Y matrice and power flow input data
[nbus,ngen,Y,B,G,v,vang,Pg,Qg] = inputpf(Sbn);
% Initial conditon values of Machines
[Vt,It,Ia,E,PF,Ir,Ix,deltabeta,gamma,delta,Id,Iq,Vq,Vd,Efd,iq,id,vq,vd,iF,L
amd,LamF,LamD,LamAD,Lamq,LamG,LamQ,LamAQ,Tm,Eq,Ed,Edtr,Eqtr,Edstr,Eqstr] =
inicond(w,ngen,v,vang,Pg,Qg,xqtr,xdtr,Lqstr,Ldstr,xq,xd,r,LAD,Ld,LAQ,Lq,LF)
;
%Ieq calculations and injected current vector. initial injected currents.
Ii=zeros(2*nbus,1);
[Ii] =
ieqcalc(Ii,ngen,delta,xqtr,xdtr,xqstr,xdstr,Ed,E,Edtr,Eqtr,Edstr,Eqstr);
%Y augmented matrix
[Yeq,Y1,Y2] = yaugmented(nbus,ngen,B,G,bfault,x);
%********************Fault Simulation*************************************
%*************************************************************************
Vexy=eye(12)/(Y1)*(Ii);
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for k=1:nbus
Ve(k)=Vexy(2*k-1)+1i*Vexy(2*k);
end
%*********** start itegrations******************************
%pointer recording data
cur = 1;
for t = 0:dtime:tsend
for k = 4; % gen4, Classical model
Te(k) =abs(E(k))*Iq(k);
Ve(k) = abs(E(k));
end
for k=2 % gen2 and 3, E" model
dLamD = (-LamD(k) + Eqtr(k) + (xdtr - xl)*Id(k))/td0str;
dEqtr = (-Eqtr(k) + Efd(k) -Kd*Eqtr(k) + Kd*LamD(k) +
xxd*Id(k))/td0tr;
LamD(k) = LamD(k) + dLamD*dtime;
Eqtr(k) = Eqtr(k) + dEqtr*dtime;
Eqstr(k) = K1*Eqtr(k) + K2*LamD(k);
dLamQ = (-LamQ(k) - Edtr(k) + (xqtr - xl)*Iq(k))/tq0str;
dEdtr = (-Edtr(k) - Kq*Edtr(k) - Kq*LamQ(k) - xxq*Iq(k))/tq0tr;
LamQ(k) = LamQ(k) + dLamQ*dtime;
Edtr(k) = Edtr(k) + dEdtr*dtime;
Edstr(k) = K3*Edtr(k) - K4*LamQ(k);
Te(k) = (Eqstr(k)*Iq(k) + Edstr(k)*Id(k));
t;
dEdtr;
end
for k=3
dLamD = (-LamD(k) + Eqtr(k) + (xdtr - xl)*Id(k))/td0str;
dEqtr = (-Eqtr(k) + Efd(k) -Kd*Eqtr(k) + Kd*LamD(k) +
xxd*Id(k))/td0tr;
LamD(k) = LamD(k) + dLamD*dtime;
Eqtr(k) = Eqtr(k) + dEqtr*dtime;
Eqstr(k) = K1*Eqtr(k) + K2*LamD(k);
dLamQ = (-LamQ(k) - Edtr(k) + (xqtr - xl)*Iq(k))/tq0str;
dEdtr = (-Edtr(k) - Kq*Edtr(k) - Kq*LamQ(k) - xxq*Iq(k))/tq0tr;
LamQ(k) = LamQ(k) + dLamQ*dtime;
Edtr(k) = Edtr(k) + dEdtr*dtime;
Edstr(k) = K3*Edtr(k) - K4*LamQ(k);
Te(k) = (Eqstr(k)*Iq(k) + Edstr(k)*Id(k));
end
for k = 1;% gen1, two axis model
dEdtr(k) = (-Edtr(k) - (xq-xqtr)*Iq(k))/tq0tr;
dEqtr(k) = (Efd(k) - Eqtr(k) + (xd-xdtr)*Id(k))/td0tr;
Edtr(k) = Edtr(k) + dEdtr(k)*dtime;
Eqtr(k) = Eqtr(k) + dEqtr(k)*dtime;
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Ixi(k) = gx(k)*Edstr(k)+bx(k)*Eqstr(k);
Iyi(k) = by(k)*Edstr(k)+gy(k)*Eqstr(k);
Ii(2*k-1) = Ixi(k);
Ii(2*k) = Iyi(k);
end
end
for k=1:ngen
Iq(k) = cos(delta(k))*IDQ(2*k-1) + sin(delta(k))*IDQ(2*k);
Id(k) = -sin(delta(k))*IDQ(2*k-1) + cos(delta(k))*IDQ(2*k);
end
% record resultomegas
resultomega(1,cur) = t;
resultomega(2:5,cur) = omega;
resultdelta(1,cur) = t;
resultdelta(2:5,cur) = delta*180/pi; % conversion to degree
cur = cur + 1;
end
%******************* plot the curves**************************
%*************************************************************
close all
figure('name', 'relative power angles');
for k = 1:4
subplot(2,2,k);
plot(resultomega(1,:),resultdelta(k+1,:)-resultdelta(4,:),'LineWidth',1.5);
title(strcat('gen #',int2str(k)));
xlabel('time (second)');
ylabel('delta (degree)');
grid
end
figure('name', 'relative power angles');
plot(resultomega(1,:),resultdelta(1+1,:)-
resultdelta(4,:),':',resultomega(1,:),resultdelta(2+1,:)-
resultdelta(4,:),'--',resultomega(1,:),resultdelta(3+1,:)-
resultdelta(4,:),resultomega(1,:),resultdelta(4+1,:)-resultdelta(4,:),'-
.');
legend('Gen1','Gen2','Gen3','Gen4')
grid
INPUTDYN.M
function
[r,xd,xdtr,xdstr,xq,xqstr,xqtr,xl,H,D,td0tr,td0str,tq0tr,tq0str,x,Ldstr,Ldt
r,Ld,Lqstr,Lqtr,Lq,ld,lq,LAD,LF,LD,LAQ,LG,LQ,lF,lD,lG,lQ,K1,K2,K3,K4,Kd,Kq,
xxd,xxq,tj] = inputdyn(Sbn)
Sbold= 900;
% Machine dynamic data from kundur book example 12.6
r=0;
xd=1.8;
xdtr=0.3;
xdstr=0.25;
xq=1.7;
xqtr=0.55;
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xqstr=0.25;
xl=0.2;
H=6.5;
D=0;
td0tr=8;
td0str=0.03;
tq0tr = 0.4;
tq0str = 0.05;
% conversion to new base
r=r*Sbn/Sbold;
xd=xd*Sbn/Sbold;
xdtr=xdtr*Sbn/Sbold;
xdstr=xdstr*Sbn/Sbold;
xq=xq*Sbn/Sbold;
xqtr=xqtr*Sbn/Sbold;
xqstr=xqstr*Sbn/Sbold;
xl=xl*(Sbn/Sbold);
H=H/(Sbn/Sbold);
D=D/(Sbn/Sbold);
% vector that stores all the reactances
x=[xdtr;xdstr;xdstr;xdtr];%Two-axis,E",E",Classical
% Machine inductances calculations in per unit
Ldstr = xdstr;
Ldtr = xdtr;
Ld = xd;
Lqstr = xqstr;
Lqtr = xqtr;
Lq = xq;
ld = xl;
lq = ld;
LAD = Ld - ld;
LF = LAD^2/(Ld - Ldtr);
LD = LAD^2/LF + (Ldtr - ld)^2/(Ldtr - Ldstr);
LAQ = Lq - lq;
LG = LAQ^2/(Lq - Lqtr);
LQ = LAQ^2/LG + (Lqtr - lq)^2/(Lqtr - Lqstr);
lF = LF - LAD;
lD = LD - LAD;
lG = LG - LAQ;
lQ = LQ - LAQ;
%Constantes described in AA found book on page 137
K1 = (xdstr - xl)/(xdtr - xl);
K2 = 1 - K1;
K3 = (xqstr - xl)/(xqtr - xl);
K4 = 1 - K3;
Kd = (xd - xdtr)*(xdtr - xdstr)/(xdtr - xl)^2;
Kq = (xq - xqtr)*(xqtr - xqstr)/(xqtr - xl)^2;
xxd = (xd - xdtr)*(xdstr - xl)/(xdtr - xl);
xxq = (xq - xqtr)*(xqstr - xl)/(xqtr - xl);
tj = 2*H;
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end
INPUTPF.M
function [nbus,ngen,Y,B,G,v,vang,Pg,Qg] = inputpf(Sbn)
% *********************Power data**********************
% data are taken from the 4mflow file
% number of bus and generators
nbus=6;
ngen=4;
v=[1.03,1.01,1.03,1.01,0.9773,0.9898];
vang=[-44.25,-55.09,0,-9.85,-64.04,-18.08];
Pga=[790,790,719.19,740,0,0];
Qga=[77.59,363.59,71.85,212.38,0,0];
Pload=[0,0,0,0,1241,1699];
Qload=[0,0,0,0,100,100];
Pg=Pga/Sbn;
Qg=Qga/Sbn;
Pl=Pload/Sbn;
Ql=Qload/Sbn;
vang=vang*pi/180; % convert angles from degrees to radians
% shunt impedances
yc=[0,0,0,0,1i*2.235,1i*2.58];
% line impedances
z12=2.5E-3+1i*2.5E-2;
z25=1E-3+1i*1E-2;
z34=2.5E-3+1i*2.5E-2;
z46=1E-3+1i*1E-2;
z56=2.2E-3+1i*2.2E-2;
%***** original Y matrix*************
for k = 1:nbus
Yl(k) = (Pl(k) - 1i*Ql(k))/v(k)^2 - yc(k);
end
Y=zeros(nbus,nbus);
% off diagonal elements
Y(1,2)=-1/z12;
Y(2,1)=Y(1,2);
Y(2,5)=-1/z25;
Y(5,2)=Y(2,5);
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Y(5,6)=-1/z56;
Y(6,5)=Y(5,6);
Y(6,4)=-1/z46;
Y(4,6)=Y(6,4);
Y(4,3)=-1/z34;
Y(3,4)=Y(4,3);
%**********diagonal elements
for m=1:nbus
for n=1:nbus
Y(m,m) = (Y(m,m)-Y(m,n));
end
Y(m,m) = Y(m,m) + Yl(m);
end
for m=1:nbus
for n=1:nbus
G(m,n)=real(Y(m,n));
B(m,n)=imag(Y(m,n));
end
end
end
INICOND.M
function
[Vt,It,Ia,E,PF,Ir,Ix,deltabeta,gamma,delta,Id,Iq,Vq,Vd,Efd,iq,id,vq,vd,iF,L
amd,LamF,LamD,LamAD,Lamq,LamG,LamQ,LamAQ,Tm,Eq,Ed,Edtr,Eqtr,Edstr,Eqstr] =
inicond(w,ngen,v,vang,Pg,Qg,xqtr,xdtr,Lqstr,Ldstr,xq,xd,r,LAD,Ld,LAQ,Lq,LF)
% Initial conditon values of Machines
for j=1:ngen
Vt(j) = v(j)*(cos(vang(j)) + 1i*sin(vang(j)));
It(j) = (Pg(j) - 1i*Qg(j))/conj(Vt(j));
Ia(j)=abs(It(j));
E(j) = Vt(j) + It(j)*1i*xdtr; %internal voltage
PF(j) = atan(Qg(j)/Pg(j));
Ir(j) = Ia(j)*cos(PF(j));
Ix(j) = -Ia(j)*sin(PF(j));
deltabeta(j) = atan((xq*Ir(j) + r*Ix(j))/(v(j) + r*Ir(j) - xq*Ix(j)));
gamma(j) = deltabeta(j) + PF(j);
delta(j) = deltabeta(j) + vang(j);
Id(j)=-Ia(j)*sin(gamma(j)); Iq(j)=Ia(j)*cos(gamma(j));
Vq(j) = v(j)*cos(deltabeta(j)); Vd(j) = -v(j)*sin(deltabeta(j));
Efd(j)= Vq(j) - xd*Id(j);
end
iq = sqrt(3)*Iq;
id = sqrt(3)*Id;
vq = sqrt(3)*Vq;
vd = sqrt(3)*Vd;
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iF = sqrt(3)*Efd/LAD;
%****** FLux linkages*********************
Lamd = (Ld*id + LAD*iF)/sqrt(3);
LamF = (LAD*id + LF*iF)/sqrt(3);
LamD = (LAD*id + LAD*iF)/sqrt(3);
LamAD = (LAD*(id + iF))/sqrt(3);
Lamq = (Lq*iq)/sqrt(3);
LamG = (LAQ*iq)/sqrt(3);
LamQ = (LAQ*iq)/sqrt(3);
LamAQ = (LAQ*iq)/sqrt(3);
Tm=zeros(ngen,1);
Tm = (iq.*Lamd - id.*Lamq)/sqrt(3); % mechanical torque is equal to the
steady state electrical torque
% initial conditions
% CASE : gen2 classical, gen 1 and 3 are E", gen 4 is two axis
% gen 2, classical model
E1 = abs(E(2));
delta(2) = angle(E(2));
gamma(2) = delta(2) - vang(2) + PF(2);
Iq(2) = Ia(2)*cos(gamma(2));
Id(2) = -Ia(2)*sin(gamma(2));
delta(1) = deltabeta(1) + vang(1);
delta(3) = deltabeta(3) + vang(3);
delta(4) = deltabeta(4) + vang(4);
% ***************************************************************
% Ed and Eq initial conditions chap 4 page 132, 138,
for k=1:ngen
if k == 4 % gen 4, classical model % we need t0 check this statement
Eq(k) = E(k);
Ed(k) = 0;
elseif k == 1 % gen 1, two axis model
Edtr(k)= Vd(k) + xqtr*Iq(k);
Eqtr(k)= Vq(k) - xdtr*Id(k);
else % gen 2 and 3, E” model
Edtr(k)= Vd(k) + xqtr*Iq(k);
Eqtr(k)= Vq(k) - xdtr*Id(k);
Edstr(k) = -w*(Lamq(k) - Lqstr*Iq(k));
Eqstr(k) = w*(Lamd(k) - Ldstr*Id(k));
end
end
end
IEQCALC.M
function[Ii] =
ieqcalc(Ii,ngen,delta,xqtr,xdtr,xqstr,xdstr,Ed,E,Edtr,Eqtr,Edstr,Eqstr)
%Ieq calculations and injected current vector
for k=1:ngen
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% used to calculate Ieq
%***** used to also build yeq***
if k == 4 % gen 4, classical model
gx(k) = cos(delta(k))/xqtr; bx(k) = sin(delta(k))/xdtr;
by(k) = sin(delta(k))/xqtr; gy(k) = -cos(delta(k))/xdtr;
Ixi(k) = gx(k)*Ed(k) + bx(k)*abs(E(k));
Iyi(k) = by(k)*Ed(k) + gy(k)*abs(E(k));
Ii(2*k-1) = Ixi(k); Ii(2*k) = Iyi(k); %storing all the currents to
one vector Ii
elseif k == 1 % gen 1, two axis model
gx(k) = cos(delta(k))/xqtr; bx(k) = sin(delta(k))/xdtr;
by(k) = sin(delta(k))/xqtr; gy(k) = -cos(delta(k))/xdtr;
Ixi(k) = gx(k)*Edtr(k)+bx(k)*Eqtr(k);
Iyi(k) = by(k)*Edtr(k)+gy(k)*Eqtr(k);
Ii(2*k-1) = Ixi(k);
Ii(2*k) = Iyi(k);
else % gen 2 and 3, E” model
gx(k) = cos(delta(k))/xqstr; bx(k) = sin(delta(k))/xdstr;
by(k) = sin(delta(k))/xqstr; gy(k) = -cos(delta(k))/xdstr;
Ixi(k) = gx(k)*Edstr(k)+bx(k)*Eqstr(k);
Iyi(k) = by(k)*Edstr(k)+gy(k)*Eqstr(k);
Ii(2*k-1) = Ixi(k);
Ii(2*k) = Iyi(k);
end
end
end
YAUGMENTED.M
function [Yeq,Y1,Y2] = yaugmented(nbus,ngen,B,G,bfault,x)
%Y augmented matrix
Y1=zeros(2*nbus,2*nbus);
Y2=zeros(2*nbus,2*nbus);
for m=1:nbus
for n=1:nbus
if(m==n && n<=ngen)
Y1(2*m-1,2*n)=-B(m,n)+1/x(m);
Y1(2*m,2*n-1)=B(m,n)-1/x(m);
Yeq(2*m-1,2*n)=+1/x(m);
Yeq(2*m,2*n-1)=-1/x(m);
else
Y1(2*m-1,2*n)=-B(m,n);
Y1(2*m,2*n-1)=B(m,n);
end
Y1(2*m-1,2*n-1)=G(m,n);
Y1(2*m,2*n)=G(m,n);
end
%Y augmented matrix during the three phase fault at bus bfault
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for m=1:2*nbus
for n=1:2*nbus
if( m~=n && (m==(2*bfault)|| n==(2*bfault)|| m==(2*bfault-1) ||
n==(2*bfault-1)))
Y2(m,n)=0;
elseif ((m==n && m==(2*bfault))|| (m==n && m==(2*bfault-1)))
Y2(m,n)=99999999999;
else
Y2(m,n)=Y1(m,n);
end
end
end
end
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