Qatar University College of Engineering Electrical Engineering Department. A Graduation Project Report

Transcription

1 Qatar University College of Engineering Electrical Engineering Department A Graduation Project Report Design of Power System Stabilizer Based on Microcontroller for Power System Stability Enhancement By SAMER SAID SAID OSAMA BASHIR KAHLOUT Supervisors DR. KHALED ELLITHY & DR. TAREK EL-FOULY June 2011

2 ACKNOWLEDGMENT We would like to take the opportunity to thank our supervisor Dr. Khaled Ellithy for his continuous supervision and commitment. Thank also goes to Dr. Tareq EL-Fouly for his support and supervision all through the project. We would like also to thank Dr. Nader Meskin & Eng. Mohammed Ayyad for their support and help throughout the project. We would like to extend our thanks to the Office of Academic Research, for funding our project through the Student Grants (QUST-CENG-DEE-10/11-38). Samer Said Said Osama Bashir EL-Kahlout Dept. of EE, Qatar Univ. P a g e I

3 ABSTRACT The problem of the poorly damped low-frequency (electro-mechanical) oscillations of power systems has been a matter of concern to power engineers for a long time, because they limit power transfers in transmission lines and induce stress in the mechanical shaft of machines. Due to small disturbances, power systems experience these poorly damped low-frequency oscillations. The dynamic stability of power systems are also affected by these low frequency oscillations. With proper design of Power System Stabilizer (PSS), these oscillations can be well damped and hence the system stability is enhanced. The basic functions of the PSS is to add a stabilizing signal that compensates the oscillations of the voltage error of the excitation system during the dynamic/transient state, and to provide a damping component when it s on phase with rotor speed deviation of machine. This project presents a design of PSS based on microcontroller to enhance the dynamic stability of power systems by improving the damping of the low frequency oscillations. Damping torque and eigenvalues analysis are applied to the PSS design. The results of these techniques have been verified by time-domain dynamic simulations. The designed PSS is applied to a power system. The dynamic simulations results are presented for various system disturbances under different system operating points to show the effectiveness and robustness of the designed PSS. a Peripheral Interface Controller (PIC) microcontroller is used to design a PSS to enhance the damping characteristic of power system to improve its stability. The s-domain PSS has been transformed to digital (z-domain) PSS and then it is implemented on microcontroller chip. Dept. of EE, Qatar Univ. P a g e II

4 TABLE OF CONTENTS Acknowledgment... I Abstract... II Table of Contents... III List of Symbols... VII List of Abbreviations... X List of Figures... XI List of Tables... XIV Chapter 1: Introduction Introduction Background Power System and Problem Statement Classification of Power System Stability Damping of Power System Oscillations Design Constraints Power System Constraints Stability Constraints PSS Tuning Parameters Constraints Digital Control & Microcontrollers MATLAB Interfacing IEEE Standards on Machine Models and Excitation Systems Objectives... 8 Chapter 2: Modeling of Power Systems Using Component Connection Technique for Dynamic Stability Study Dept. of EE, Qatar Univ. P a g e III

5 2.1 Overview Modeling of SMIB Power System Using CCT Synchronous Generator Modeling Exciter Modeling AC Network Overall System Model Block Diagram Representation Rotor Mechanical Equations Representation of Flux Decay Representation of Excitation System MATLAB/Simulink Model of the Power System Variation of Constants [K 1 -K 6 ] According to System Operating Points Chapter 3: Dynamic Stability Evaluation Techniques of Stability Evaluation Stability Evaluation Using Eigenvalues Technique Stability Evaluation Using Damping Torque Technique Stability Evaluation Using Time-Domain Simulation Technique Dynamic Stability Evaluation of SMIB Dynamic Stability Evaluation of SMIB Using Eigenvalues Technique Dynamic Stability Evaluation of SMIB Using Torques Technique Dynamic Stability Evaluation of SMIB Using Time-Domain Simulation Technique Effect of Different Operating Points on System Dynamic Stability Effect of Excitation System Parameters on System Stability Dept. of EE, Qatar Univ. P a g e IV

6 Chapter 4: Power System Stabilizer Design Introduction SMIB Power System Model Including PSS Modeling of PSS SMIB Power System Bock Diagram Model Including PSS State-Space Model of SMIB Power System Including PSS MATLAB/Simulink Model of SMIB Power System Including PSS Dynamic Stability Enhancement using PSS Eigenvalues Technique Damping Torque Technique Time-Domain Simulation Technique Tuning of PSS Parameters Dynamic Stability Enhancement of SMIB Power System Eigenvalues of SMIB Power System with PSS Damping Torque of SMIB Power System with PSS Time-Domain Simulation of SMIB Power System with PSS Assessment of the Robustness of the Designed PSS 74 Chapter 5: Design of Microcontroller Based Digital PSS Digital Control What is a Microcontroller? Architecture & Specifications of PIC18 Family Specifications of Microcontroller PIC18F Microcontroller s Basic Circuit Serial Communication USART Dept. of EE, Qatar Univ. P a g e V

7 5.7 Design Constraints Microcontroller Constraints Serial USART Constraints Digital Domain of the Power System Stabilizer s-domain to z-domain (Digital Domain) Transformation Steps in MATLAB Simulation of Digital PSS using Simulink MATLAB and Microcontroller Interfacing Microcontroller Programming Simulink Model of the SMIB Power System with MCU PSS Simulations of the SMIB Power System with MCU PSS Chapter 6: Conclusion & Future Work Conclusion Future Work References Appendix A... A-1 Appendix B... B-1 Dept. of EE, Qatar Univ. P a g e VI

8 LIST OF SYMBOLS δ f Rotor Angle of Synchronous Generator in rad Frequency Oscillations in Hz System Eigenvalue Real Part of Eigenvalue ω b d n Damping Ratio Rotor Speed Deviation in rad/sec (base speed) Damping Frequency Natural (Undamped) Frequency m Zero db Frequency in rad/s D E fd E' q F osc G O.L (s) G PSS (s) G SMIB (s) H H 1 (z) H 2 (z) I d, I q I e d, I e q I e d-bus, I e q-bus Damping Coefficient Excitation System Voltage in p.u. Voltage Proportional to Field Flux Linkages Frequency of Oscillations Transfer Function of Cascaded Connection between PSS and SMIB Power System Transfer Function of the Power System Stabilizer Transfer Function of SMIB Power System Inertia Constant Phase Compensator Transfer Function in z-domain Washout Transfer Function in z-domain d and q Axes Generator Currents d and q axes Stator Currents in Synchronous Reference Frame (SRF) d and q axes Bus Currents in Synchronous Reference Frame (SRF) Dept. of EE, Qatar Univ. P a g e VII

9 I r d, I r q K A K D K PSS K S K S (AVR) n P Q R a R e S b T T A T e T e (AVR) T m T PSS (z) T W T 1 T 2 T' do V b V d,v q d and q Axes Stator Currents in Rotor Reference Frame (RRF) Exciter Gain Damping Torque Coefficient Power System Stabilizer Gain Synchronizing Torque Coefficient Synchronizing Torque Coefficient of AVR Register SPBRG Value Real Power Output Reactive Power Output Armature Resistance Transmission Line Resistance Rated Complex Power Sampling Period Exciter Time Constant Electrical Power Output in p.u. Electrical Power Output of AVR in p.u. Mechanical Power Input in p.u. Power System Stabilizer Transfer Function in z-domain Washout Time Constant Lead Time Constant Lag Time Constant Open Circuit d-axis Time Constant in sec Rated Voltage d and q Axes Generator Voltages Dept. of EE, Qatar Univ. P a g e VIII

10 V e d, V e q V r d, V r q V inf V ref V s V t V w X d X' d X q X' q X e d and q Axes Stator Voltages in Synchronous Reference Frame (SRF) d and q Axes Stator Voltages in Rotor Reference Frame (RRF) Infinite Bus Voltage Exciter Reference Input Power System Stabilizer Output Voltage Terminal Voltage Power System Stabilizer Washout Voltage d-axis Synchronous Reactance in p.u. d-axis Transient Reactance in p.u. q-axis Synchronous Reactance in p.u. q-axis Transient Reactance in p.u. Transmission Line Reactance Dept. of EE, Qatar Univ. P a g e IX

11 LIST OF ABBREVIATIONS AVR CCM CCT RC6 RC7 SMIB Automatic Voltage Regulator Component Connection Model Component Connection Technique Transmitting Pin Receiving Pin Single-Machine Infinite Bus Dept. of EE, Qatar Univ. P a g e X

12 LIST OF FIGURES Figure (2.1): Block Diagram of Component Connection Model (CCM) Figure (2.2): Single Line Diagram of SMIB System Figure (2.3): Block diagram of Synchronous Generator CCM Figure (2.4): Excitation System Figure (2.5): Block Diagram of Overall System using CCM Figure (2.6): The torque-angle Loop of Synchronous Machine Figure (2.7): Flux-Decay Model Figure (2.8): Excitation System Figure (2.9): Overall Block Diagram of the Linearized Power System Figure (2.10): MATLAB/Simulink Model of the SMIB with Exciter Power System Figure (2.11): Variation of K 1 at Different Operating Points Figure (2.12): Variation of K 2 at Different Operating Points Figure (2.13): Variation of K 3 at Different Operating Points Figure (2.14): Variation of K 4 at Different Operating Points Figure (2.15): Variation of K 5 at Different Operating Points Figure (2.16): Variation of K 6 at Different Operating Points Figure (3.1): Torque-Angle Loop Figure (3.2) Rotor Speed Deviation Response Under 1% Change in at Nominal Operating Point Figure (3.3) Rotor Speed Deviation and Terminal Voltage Deviation Response Under 1% Change in at Nominal Operating Point Figure (3.4) Rotor Speed Deviation Response Under 1% Change in at Nominal Operating Point Dept. of EE, Qatar Univ. P a g e XI

13 Figure (3.5) Rotor Speed Deviation Response Under 1% Change in at Operating Point Figure (3.6) Rotor Speed Deviation Response Under 1% Change in at Operating Point Figure (3.7) Rotor Speed Deviation Response Under 1% Change in at Operating Point Figure (3.8) The Effect of Increasing K A to 400 in Operating Point Figure (4.1) Block Diagram of SMIB Power System Including PSS Figure (4.2) Block Diagram of the Excitation System (AVR) Including PSS Figure (4.3) MATLAB/Simulink Model of the SMIB with PSS Power System Figure (4.4) Rotor Speed Deviation Response with & without PSS at nominal operating point under change in of 1% Figure (4.5) Rotor Speed Deviation Response with & without PSS at nominal operating point under change in V_ref of 1% Figure (4.6) Rotor Angle Deviation Response with & without PSS at nominal operating point under change in T_m of 1% Figure (4.7) Terminal Voltage Deviation Response with & without PSS at nominal operating point under change in of 1% Figure (4.8) PSS Stabilizing Signal at nominal operating point under change in T_m of 1% Figure (4.9) Rotor Speed Deviation Response with & without PSS at Operating Point Figure (4.10) Rotor Speed Deviation Response with & without PSS at Unstable Operating Point Figure (4.11) Rotor Speed Deviation Response with & without PSS at Operating Point 3 with Exciter Gain Equal to Figure (5.1) Typical Digital Control System Figure (5.2) Block Diagram of Microcontroller Based Digital Control System Figure (5.3) Microcontroller Basic Circuit Figure (5.4) Quartz Crystal Circuit Configuration Figure (5.5) Data Transformation in Asynchronous Mode Dept. of EE, Qatar Univ. P a g e XII

14 Figure (5.6) Serial UART (RS-232) Communication Circuit Figure (5.7) SMIB Power System Simulink Model Input & Output Ports Highlighted Figure (5.8) Bode Plot of the Cascaded Open-Loop between PSS & SMIB Power System Figure (5.9) Effect of Sampling Frequency on the Frequency Response of the Digital PSS Figure (5.10) Comparison between the Frequency Response of the Designed Digital (z-domain) PSS and the Response of the s-domain PSS Figure (5.11) MATLAB/Simulink Model of the SMIB Power System Including Simulated Digital (z-domain) PSS Power System Figure (5.12) Rotor Speed Deviation Response Comparison of Digital (Simulated) PSS & s- domain PSS at Nominal Operating Point Under Change in of 1% Figure (5.13) MATLAB (Laptop) & PIC18F4520 Microcontroller Interfacing Circuit Figure (5.14) Microcontroller C-Code Flowchart Figure (5.15) MATLAB/Simulink Model of the SMIB Power System Including Digital (Microcontroller) PSS Power System Figure (5.16) Photos from the Microcontroller Based Digital PSS Hardware Figure (5.17) Rotor Speed Deviation Response Comparison of Digital (Microcontroller) PSS & s-domain PSS at Nominal Operating Point Under Change in of 1% Figure (5.18) PSS Stabilizing Signal at nominal operating point under change in T m of 1% Figure (5.19) Rotor Speed Deviation Response Comparison of Digital (Microcontroller) PSS & s-domain PSS at Unstable Operating Point Under Change in of 1% Figure (5.20) Rotor Speed Deviation Response Comparison of Digital & s-domain PSS at Unstable Operating Point of High Exciter Gain Under Change in of 1% Dept. of EE, Qatar Univ. P a g e XIII

15 LIST OF TABLES Table (3.1) The Eigenvalues and the Constants [K 1 -K 6 ] of the Nominal Operating Point Table (3.2) Synchronizing and Damping Torques and Damping Ratios and Frequencies for Nominal Operating Point Table (3.3) Different Operating Points for Power System Stability Evaluation Table (3.4) Testing Operating Points Using Eigenvalues Technique Table (3.5) Synchronizing and Damping Torques and Damping Ratios and Frequencies for Three Operating Points Table (3.6) Results of Increasing the Gain K A of the Operating Point Table (4.1) System Eigenvalues at Nominal Operating Point Table (4.2) Torque Coefficients, Damping Ratio & Damping Frequency at Nominal Operating Point Including PSS Table (4.3) Different Operating Points for PSS Evaluation Table (4.4) Testing Operating Points Using Eigenvalues Technique Table (4.5) Torque Coefficients, Damping Ratios & Damping Frequencies at Three Operating Points Table (A-1) Comparison Between PIC Microcontrollers Families Features... A-1 Dept. of EE, Qatar Univ. P a g e XIV

16 CHAPTER 1: INTRODUCTION 1.1. Introduction Power systems have developed from the original central generating station concept to a modern interconnected system with improved technologies affecting each part of the system separately. Successful operation of a power system depends largely on providing reliable and uninterrupted service to the loads by the power utility. Ideally, constant voltage and frequency should be supplied to the load at all times. In practical terms this means that both voltage and frequency must be held within close tolerances so that the consumer loads run without interruption. For example, the motor loads on the system may stop by a drop in voltage of l0-15% or a drop of the system frequency of only a few hertz. Thus it can be accurately stated that the power system operator must maintain a very high standard of continuous and reliable electrical service. [1,5-7] Small-signal stability, or the dynamic stability, can be defined as the behavior of the power system when subjected to small disturbances. It is usually concerned as a problem of insufficient or poorly damping of system oscillations. These oscillations are undesirable even at lowfrequencies, because they reduce the power transfer in the transmission line and sometimes introduce stress in the system. Several types of these oscillations could be found in the system, but the two most critical types that of concern are the local mode and the inter-area mode. The local mode is associated with a single unit or station with respect to the whole system, whereas the inter-area mode is associated with many units in an area with respect to other units in another area. The aim of this project is to assess these low-frequency disturbances by having fast and efficient computational tools in online stability assessment. [1-3] An important requirement of reliable service is to keep the synchronous generators running in parallel and with appropriate capacity to meet the load demand. If a generator loses synchronism with the rest of the system, significant voltage and current fluctuations may occur and transmission lines may be automatically tripped by their relays disconnecting important loads from service.[7] Dept. of EE, Qatar Univ. P a g e 1

17 Subsequent adjustments of generation due to random changes in load are taking place at all times which makes steady state operation of power system not actually true state. Furthermore, major changes do take place at times, e.g., a fault on the network, failure in a piece of equipment, sudden application of a major load, or loss of a line or generating unit. We may look at any of these as a change from one equilibrium state to another. So successful operation requires only that the new state be a stable state. For example, if a generator is lost, the remaining connected generators must be capable of meeting the load demand; or if a line is lost, the power it was carrying must be obtainable from another source, but this view is wrong in one important aspect: it neglects the dynamics of the transition from one equilibrium state to another. Synchronism frequently may be lost in that transition period, or growing oscillations may occur over a transmission line, eventually leading to its tripping. [7-8] Extensive emphasis on the economic design of generators, especially those of large ratings was placed in the middle of the 20 th century. This leads to the development of machines with very large values for steady-state synchronous reactance, and that resulted in poor load-voltage characteristics, especially when connected through long transmission lines. On load, significant drop in the overall synchronizing torque caused by reduction of field flux which is due to the armature reaction. Therefore, the transient stability related problems for synchronous operation became the major concern. The problem was resolved by using high gain, fast acting excitation control systems that provide sufficient synchronizing torque by virtually eliminating the effect of armature reaction on reduction in synchronizing torque. However, voltage regulator action was found to introduce negative damping torque at high power output and weak external network conditions represented by long overhead transmission lines, a very common operating situation in power systems around the world. Negative damping gave rise to an oscillatory instability problem. The contradicting performance of the excitation control loop was resolved by adjusting the voltage regulator reference input through an additional stabilizing signal, which was meant to produce positive damping torque. The control circuitry producing this signal was termed a power system stabilizer (PSS) [10-12]. Dept. of EE, Qatar Univ. P a g e 2

18 Power system operating conditions are subjected to changes due to many reasons. One of these reasons is the load changes in the system. These operating conditions affect the stability of the synchronous machine. Therefore, in order to provide an estimate of the stability of the system which is based on operating conditions of the system that is obtained by either computer simulations or measurements, a small-signal stability analysis should be conducted [13,16]. Small-signal stability (also called dynamic stability) analysis studies the behavior of power systems under small perturbations. Its main objective is to evaluate the low-frequency oscillations (LFO) resulting from poorly damped rotor oscillations. The most important types of these oscillations are the local-mode, which occurs between one machine and the rest of the system, and the interarea-mode oscillations that occurs between interconnected machines. Stability assessment of these low frequency oscillations is a vital concern and essential for secure power system operation and control. Local-mode oscillations are the concern of this project. [1,10,13] Traditionally, small-signal stability analyses are carried out in frequency domain using modal analysis method. This method implies estimation of the characteristic modes of a linearized model of the system. It requires first load flow analysis, linearization of the power system around the operating point, developing a state-space model of the power system, then computing the eigenvalues, eigenvectors, and participation factors. Although eigenvalue analysis is powerful, however, it is not suitable for online application in power system operation, as it requires significantly large computational efforts. Alternative method based on electromagnetic torque deviation has been developed. Torque deviation can be decomposed into synchronizing and damping torques. The synchronizing and damping torques are usually expressed in terms of the torque coefficients Ks and Kd. These coefficients can be calculated repeatedly and this makes it suitable for online stability assessment. [13,15-16] Dept. of EE, Qatar Univ. P a g e 3

19 1.2. Background Power System and Problem statement Power system stability may be generally defined as the characteristic of a power system that enables it to remain in a state of operating equilibrium under normal operating conditions and to regain an acceptable state of equilibrium after being subjected to a disturbance. The stability of the power system is concerned with the behavior of the synchronous machines after they have been disturbed. If the disturbance does not involve any net change in power, the machines should return to their original state. If an unbalance between the supply and demand is created by a change in load, in generation, or in network conditions, a new operating state is necessary. In any case all interconnected synchronous machines should remain in synchronism if the system is stable; i.e., they should all remain operating in parallel and at the same speed. [7-8, 10] In the evaluation of stability, the concern is the behavior of the power system when subjected to disturbance. The disturbance may be small or large. Small disturbances in the form of load changes take place continually, and the system adjusts itself to the changing conditions. The system must be able to operate satisfactory under these conditions and successfully supply the maximum amount of load. It must also be capable of surviving numerous disturbance of a severe nature, such as short-circuit of a transmission line, loss of large generator or load, or loss of a tie between two subsystems. Much of the equipments are involved & affected during the system response to a disturbance. For example, a short-circuit on a critical element followed by its isolation by protective relays will cause variations in power transfers, machine rotor speeds, and bus voltages; the voltage variations will actuate both generator and transmission system voltage regulators; the speed variations will actuate prime mover governors; the change in tie line loadings may actuate generation controls; the changes in voltage and frequency will affect loads on the system in varying degrees depending on their individual characteristics. [10-11] Interconnected AC generators produce torques that depend on the relative angular displacement of their rotors. These torques act to keep the generators in synchronism. Thus, if the Dept. of EE, Qatar Univ. P a g e 4

20 angular difference between generators increases, an electrical torque is produced that tries to reduce the angular displacement. The angular displacements should settle to values that maintain the required power flows through the transmission network and supply the system load. If the disturbance is large on the transmission system, the nonlinear nature of the synchronizing torque may not be able to return the generator angles to a steady state. Some or all generators then loose synchronism and the system exhibits transient instability. On the other hand, if the disturbance is small, the synchronizing torques keep the generators nominally in synchronism, but the generators relative angles oscillate. In a correctly designed and operated system, these oscillations decay. In an overstressed system, small disturbances may result in oscillations that increase in amplitude exponentially and lead the power system to instability. Moreover, The transient following a system perturbation is oscillatory in nature; but if the system is stable, these oscillations will be damped toward a new non-oscillatory operating condition. These oscillations, however, are reflected as fluctuations in the power flow over the transmission lines. If a certain line connecting two groups of machines undergoes excessive power fluctuations, it may be tripped out by its protective equipment thereby disconnecting the two groups of machines. [1,7] Classification of Power System Stability Classification of power system stability can take many forms, but they all fallout into two main stability types. Transient stability which is the ability to maintain synchronism when the system is subjected to a large disturbance. In the resulting system response, the changes in the dynamic variables are large and the nonlinear behavior of the system is important. [10] Small Signal Stability (dynamic stability) which is the ability of the system to maintain stability under small disturbance. Such disturbances occur continuously in the normal operation of a power system due to small variations in load and generation. The disturbances are considered sufficiently small to permit the use of linearized system model in the analysis of the small signal stability. [1,10] Dept. of EE, Qatar Univ. P a g e 5

21 Damping of Power System Oscillations Early investigations considered attention in the literature of the excitation system and its ability in enhancing stability of the power system. Researchers have found that the negative damping of large interconnected coupled system introduced by voltage regulators with high gain was the main reason to experience oscillations. A solution to improve the damping in the system was achieved by introducing a stabilizing signal into the excitation system. This signal should be taken from power system stabilizer [7,8] Design Constrains Power System Constraints The Power System should meet some constraints in which it does not exceed the limits of the generation. These constraints are summarized as follows: The system should have the ability to supply the total generation (demand and losses). Each bus in the system should not exceed its voltage magnitude beyond ±5% of the nominal bus voltage. Each generator should not exceed the real and reactive power capability constraints. All the transmission lines and the transformers should not be overloaded Stability Constraints The system stability depends on the electric torque of a synchronous machine, which in turns depends on the synchronizing and damping torque. If the synchronizing torque increased above or decreased beyond a certain limit, this will lead the system to instability through an nonperiodic drift in the rotor angle. Whereas, if this happened in the damping torque, it will lead the system to oscillatory instability. Dept. of EE, Qatar Univ. P a g e 6

22 PSS Tuning Parameters Constraints The Power System Stabilizer tuning parameters should meet some constraints to make an effective and useful stabilizing signal. These constraints are: The effect of the damping torque should cancel the effect of the negative one introduced by the Auto-Voltage Regulator (AVR) of the excitation system. This is done by increasing the damping torque to a high level. The PSS should include an appropriate phase compensation circuits, in which the phase lag between the electrical torque and the exciter input is compensated. The PSS gain should not exceed the stabilizing signal limits Digital Control & Microcontrollers MATLAB Interfacing The purpose of developing the digital control theory is to be able to understand, design and build control systems where a computer is used as the controller in the system. In addition to the normal control task, a computer can perform supervisory functions, such as reading data from a keyboard, displaying data on a screen, turning a light or a buzzer on or off and so on. Interest in digital control has grown rapidly in the last several decades since the introduction of microcontrollers. A microcontroller is a single-chip computer, including most of a computer s features, but in limited sizes. Today, there are hundreds of different types of microcontrollers, ranging from 8-pin devices to 40-pin, or even 64-pin or higher pin devices. [30 32] Microcontrollers had its beginnings in the development of technology of integrated circuits. This development has stored hundreds of thousands of transistors into one chip. The first computers were made by adding external peripherals such as memory, input/output lines, timers and others to it. Further increasing of package density resulted in creating an integrated circuit which contained both processor and peripherals. That is how the first chip containing a microcomputer, later known as a microcontroller, was developed. Microcontrollers are used nowadays in automatically controlled products and devices, such as automobile engine control Dept. of EE, Qatar Univ. P a g e 7

23 systems, remote controls, office machines, power systems. Furthermore, the relatively fast computational speed and the simplicity of implementing instructions into control systems makes the microcontroller the optimum solution for implementing the PSS on it. [17] Manufacturing companies are designing different types of microcontrollers, which are all available in the market, such as Amtel AVR, Hyperstone, MIPS, PowerPC, Intel 8051, PIC, Texas Instruments Microcontrollers, Parallax Propeller, etc. Each type has its own specifications and they all differ in the capability of functioning. [17,29, 31] Microchip Technology has developed the Peripheral Interface Controller (PIC) and integrated it with a central processing unit, serial communication functionality, and some peripherals such as memory, timer and input/output functions on an integrated circuit. Similar to other microcontrollers, PICs are usually programmed in order to perform a certain function or computation, so it is usually integrated in control system with other peripherals to control a plant. PIC microcontrollers are more popular to industrial developers and hobbyists alike due to there lower cost, wide availability, serial programming capability, and can be loaded with large user base. Moreover, the serial communication capability of PIC microcontrollers with the MATLAB software along with the Simulink, which is a graphical design tools in MATLAB, contributes in developing many programs which are used in simulating and controlling electrical & mechanical systems. The microcontroller used in this project is the PIC microcontroller which controls the SMIB power system. [17,29, 31,33] 1.5. IEEE Standards on Machine Models and Excitation Systems In this project, the model of synchronous generators and excitation systems is used in the dynamic stability analysis according to the IEEE standards [36-39] Objectives The objectives of this project are summed into the following outlines: Dept. of EE, Qatar Univ. P a g e 8

24 Conduct a literature survey on the power system dynamic models for dynamic stability analysis; Conduct a literature survey on the component connection technique (CCT) for power system modeling; Conduct a literature survey on different techniques for power system stabilizer (PSS) design; Conduct a literature survey on microcontrollers (MCU); Derive the state-space equations of a SMIB power system; Develop the SMIB model on Simulink; Evaluate dynamic stability using eigenvalue analysis; Evaluate dynamic stability using synchronizing and damping torques concept; Implement time-domain simulations using the system developed on Simulink; Study the effect of the system operating point conditions and the excitation system parameters on the system dynamic stability; Design a power system stabilizer to enhance system dynamic stability; Perform the time-domain simulations with and without the designed PSS; Transformation of the PSS transfer function in s-domain to z-domain; Implementation of the digital PSS on microcontroller; Perform the time-domain simulations with the designed PSS based on microcontroller. Dept. of EE, Qatar Univ. P a g e 9

25 CHAPTER 2: MODELLING OF POWER SYSTEMS USING COMPONENT CONNECTION TECHNIQUE FOR DYNAMIC STABILITY STUDY 2.1. Overview The component connection technique (CCT) is a method for the evaluation of the system state matrix which is then used to determine system stability. There are few methods for the formulation of the state matrix, but the main drawback of these methods is that they require extensive matrix inversions. As a result of these inversions, the system parameters are no longer explicitly available in the overall system state matrix. Moreover, it may require formidable work to form overall system state matrix for some large scale systems using the other methods. [24,25] CCT details the formulation of the overall system state matrices from the state matrices of the different subsystems forming the overall system. Modeling the system using Component Connection Technique is called component connection model (CCM). The CCM of a linear dynamical system consists of a set of two vector matrix equations separately describing component dynamics and component interconnections. [24,25] The main advantage of CCT is illustrated in the formulation of the overall system state matrices from the state matrices of the component subsystems. Moreover, another important advantage of CCT is the flexibility in subsystem modeling. The subsystems may be modeled to any degree of detail as long as subsystem inputs and outputs remain the same, without necessitating any change in the interconnection matrix. This is particularly useful for the evaluation of different order models for a given system which requires the state matrix to be determined for each of the alternative models. [24] Consider an interconnected power system that is a composed of interconnected components and let the component have input vector output vector and state vector Denote the linear state model for the component by Dept. of EE, Qatar Univ. P a g e 10

26 (2.1) where are constant matrices of appropriate dimension. The composite component state model is constructed by stacking the n component equations together. Symbolically, the composite component state model can be expressed as (2.2) where x x x and Dept. of EE, Qatar Univ. P a g e 11

27 Here, n is the number of components and in general is not equal to the number of states. Component and system interconnections take the form y (2.3) where is the system input vector, is the system output vector and are the connection matrices. Figure (2.1) shows the block diagram of the component connection model. L 22 a1 1 b1 a2 2 b2 u a b L 12 L 21 y an n bn L 11 Figure (2.1): Block Diagram of Component Connection Model (CCM) Under the assumption that the composite component state vector composite system state vector, the composite system state model has the form coincides with the (2.4) Dept. of EE, Qatar Univ. P a g e 12

28 According to literature [25], (2.4.1) (2.4.2) (2.4.3) (2.4.4) and 2.2. Modeling of SMIB Power System Using CCT In this section, the single machine connected to an infinite bus through transmission line is considered in this study. Figure (2.2) shows the single line diagram of the SMIB system. Turbine-governor dynamics is neglected. Dept. of EE, Qatar Univ. P a g e 13

29 G V t V 0 Re jx e AVR Exciter Line Infinite Bus Figure (2.2): Single Line Diagram of SMIB System. The parameters of the studied SMIB power system are taken from literature [7] as below. Common System Parameters Voltage Regulator Exciter Parameters Rated (Base) operating frequency ( ) = 314 rad/s Exciter gain constant ( ) = 50 Rated complex power ( ) = 160 MVA Voltage Regulator time constant ( )= 0.05 s Rated voltage ( ) = 15 KV Transmission Line Parameters Synchronous Generator Parameters Transmission line resistance ( ) = 0.02 p.u Synchronous d-axis Reactance ( ) = 1.7 p.u Transmission line reactance ( ) = 0.4 p.u Synchronous q-axis Reactance ( ) = 1.64 p.u Transient d-axis Reactance ( ) = p.u Field open circuit Time Constant ( ) = 5.9 s Generator moment of inertia (H) = 2.37 Mechanical Input torque ( ) = 1.64 p.u Machine Damping coefficient (D) = 0 Nominal Operating Point Real Power (P) = 136 MW Reactive Power (Q) = 83.2 MVAR Terminal Voltage (V t ) = 17.3 KV 16.6 o Infinite Bus Voltage (V inf ) = 15 KV 0 o Rotor Angle of Generator (δ) = o Synchronous Generator Modeling For synchronous generator modeling third-order model of synchronous generator was used. To develop the component connection model (CCM) of the synchronous generator the model was divided into components as shown in Figure (2.3). Dept. of EE, Qatar Univ. P a g e 14

30 T m I b E fd r q E ' q r E V qd q V r q I r qd I e qd e V qd Figure (2.3): Block diagram of Synchronous Generator CCM 1- Component 1: Voltage proportional to field flux linkage (2.5) 2- Component 2: Prime mover equations (2.6) 3- Component 3: Stator currents in Rotor Reference Frame (RRF) (2.7) Dept. of EE, Qatar Univ. P a g e 15

31 4- Component 4: Voltage back of q-axis synchronous reactance (2.7) 5- Component 5: Stator voltage in RRF (2.8) 6- Component 6: Stator currents in Synchronous Reference Frame (SRF) (2.9) Armature resistance space final model may be written as. The linearized synchronous generator state (2.10) Dept. of EE, Qatar Univ. P a g e 16

32 Where the input-output vectors are defined as (2.11) The final machine matrices was computed using the component connection technique discussed in Section (2.1), for the SMIB power system given in Figure (2.2) at nominal operating point., (2.12) The matrices number of inputs outputs variables. are dependent on the type of generator model used, and the Dept. of EE, Qatar Univ. P a g e 17

33 Exciter modeling Static exciter was used for AVR-exciter model. The Static exciter model is shown in Figure (2.4). V t K A 1T s A E fd V ref Figure (2.4): Excitation System Static Exciter Component (2.13) The linearized exciter state space final model may be written as (2.14) Where the input-output vectors are defined as (2.15) The final exciter matrices was computed using the component connection technique discussed in Section (2.1), for the SMIB power system given in Figure (2.2) at nominal operating point. Dept. of EE, Qatar Univ. P a g e 18

34 (2.16) AC Network AC Network Component (2.17) The linearized AC network state space subsystem model may be written as (2.18) Where the input-output vectors are defined as (2.19) and the final AC network matrices was computed using the component connection technique discussed in Section (2.1), for the SMIB system given in Figure (2.2) at nominal operating point. Dept. of EE, Qatar Univ. P a g e 19

35 (2.20) Relation Component (2.21) The linearized relation state space subsystem model may be written as (2.22) Where the input-output vectors are defined as (2.23) and the final relation matrices was computed using the component connection technique discussed in Section (2.1), for the SMIB system given in Figure (2.2) at nominal operating point. (2.24) Dept. of EE, Qatar Univ. P a g e 20

36 2.3. Overall System Model To develop the overall system component connection model the component connection technique discussed in section (2.4.1) was used to interconnect the subsystems together. The overall system is composed of synchronous generator subsystem, AC network & relation subsystem and static exciter subsystem. Figure (2.5) shows the overall system component connection model (CCM). Machine V t e V qd Static Exciter (AVR) E fd e I qd AC Network V ref E fd E ' q b T m Figure (2.5): Block Diagram of Overall System using CCM Final matrices of subsystems was used as a components to develop the overall system. The linearized overall system state space model may be written as (2.25) Where the input-output vectors are defined as Dept. of EE, Qatar Univ. P a g e 21

37 (2.26) The overall state-space model of the system (SMIB final matrices) is, [1, 13, 24, 25] (2.27) (2.28) the overall system matrices was computed using the component connection technique discussed in Section (2.1), for the SMIB system given in Figure (2.2) at nominal operating point. Dept. of EE, Qatar Univ. P a g e 22

38 (2.29) It is observed that the B matrix and D matrix, 4x1 matrix instead of 4x2 and this is because turbine-governor dynamics was neglected. In a power system described by Equations (2.27)-(2.28), the dynamic stability of the system can be studied through the eigenvalues of the matrix A F. The eigenvalues are related to different modes in the system. while the real part is a measure of the amount of damping, the imaginary part is related to the natural frequency of oscillation of the corresponding modes. All real eigenvalues and the real part of complex eigenvalues must be negative for system stability. Constants [K 1 -K 6 ] can be calculated from the overall matrices of the power system, as follows K 1 = C F (4,3)= K 2 = C F (4,1)= K 3 = -1/(T do *A F (1,1))= K 4 = -T do *A F (1,3)= K 5 = C F (3,3)= K 6 = C F (3,1)= where Dept. of EE, Qatar Univ. P a g e 23

39 K 1 = = the change in electrical torque for a change in rotor angle with considering constant flux linkages in the d-axis. K 2 = = the change in the electrical torque for a change in the flux linkages in the d-axis with considering a constant rotor angle. K 3 = = the impedance factor in which the external impedance is a pure reactance K 4 = = the demagnetizing effect of a change in rotor angle K 5 = = the change in the terminal voltage with respect to the change in the rotor angle with considering a constant flux linkages in the d-axis K 6 = = the change in the terminal voltage with respect to the change in flux linkages in the d-axis for a constant value of the rotor angle 2.4. Block Diagram Representation Rotor Mechanical Equations The following equations represents the torque angle loop of the synchronous machine: where K 1 and K 2 are derived from section (2.3), and (2.30) Dept. of EE, Qatar Univ. P a g e 24

40 (2.31) (2.32) The following block diagram represents the torque-angle loop of the synchronous machine. [11] T m E ' q K 2 T e 1 2Hs b s K D K S Figure (2.6): The Torque-Angle Loop of Synchronous Machine Representation of Flux Decay From Equation (2.32), the field winding s equation can be expressed as: where K 3 and K 4 are derived from section (2.3). The following block diagram represent the flux decay model. (2.33) Dept. of EE, Qatar Univ. P a g e 25

41 K 4 E fd K 3 K T s 1 3 ' do E ' q Figure (2.7): Flux-Decay Model Representation of Excitation System The equation of the exciter in the system is: Where K 5 and K 6 are derived from section (2.3). The following block diagram represents the excitation system s block diagram. (2.34) K 5 E ' q K 6 V t K A 1T s A E fd V ref Figure (2.8): Excitation System The overall system block diagram representation consists of combining the block diagrams of rotor swing equations, flux decay and excitation system. A single line representation of single machine infinite bus (SMIB) with voltage regulator-excitation system is shown in Figure (2.2). Dept. of EE, Qatar Univ. P a g e 26

42 The generator is connected to voltage regulator-static excitation system. For small oscillation stability analysis, the fast stator transients can be neglected. Moreover, since d and q damper windings always produce positive damping, they are often neglected for performance analysis of power system stabilizers. Based on the above assumptions, the synchronous generator third-order model along with voltage regulator-static exciter can be combined to form fourth-order model with changes in the load angle Δδ, the rotor speed Δω, the internal voltage of the generator, and the field voltage, as the state variables. The state-space model of the system will be discussed in the following section and the details of modeling procedure and the involvement of the simplifying assumptions were discussed completely in the previous sections. The linear time invariant model for this system is constructed by linearizing the system equations about any given steady-state operating condition. The system inputs are the voltage regulator voltage reference ( ), and synchronous generator input mechanical torque (. Figure (2.9) shows the overall block diagram of the linearized system. K 4 T m V ref K A 1T s A E fd K 3 K 3T s 2 1 ' do E ' q K T e 1 2Hs b s V t K 6 D K 1 K 5 Figure (2.9): Overall Block Diagram of the Linearized Power System Dept. of EE, Qatar Univ. P a g e 27

43 2.5. MATLAB/Simulink Model of the Power System MATLAB/Simulink was used to simulate the overall block diagram (SMIB with voltage regulator-exciter power system) that was shown in Figure (2.9). This MATLAB/Simulink model will be used in later sections to study the dynamic response of the power system. Figure (2.10) shows MATLAB/Simulink model of the SMIB with exciter power system. The power system inputs and was implemented as step input to the system, and the power system output signals,, and were taken to scope and to the MATLAB workstation so they can observed and used in computations. Dept. of EE, Qatar Univ. P a g e 28

44 0 Clock V ref To Workspace (Time) k4 K4 To Workspace (Delta Te) Delta_Te delta-te Voltage Regulator-Exciter KA TA.s+1 K3 Delta- Eq' K2 Delta- Efd (K3.*TDP)s+1 Delta- Te Constant-k2 Delta- Vt K6 Delta- Ts delta-vt Constant-k6 Delta_Vt To Workspace (Delta Vt) Delta_Omega Delta- Omega To Workspace (Delta Omega) Delta - Tm Rotating Mass Delta Omega 1 Wb (2.*H)s Base Freq 1 s Delta- Td Damping Torque Coffiecent-KD KD Constant-k1 K1 Constant-k5 K5 Delta_delta To Workspace (Delta delta) delta-delta Delta- delta t Figure (2.10): MATLAB/Simulink Model of the SMIB with Exciter Power System Dept. of EE, Qatar Univ. P a g e 29

45 Constant K1 Design of Power System Stabilizer Based on 2.6. Variation of Constants K 1 -K 6 According to System Operating Points The stability of the SMIB power system is related to the constants [K 1 -K 6 ]. These constants vary according to the variation of operating points. In order to evaluate the stability of SMIB power system discussed in section (2.2), Figures (2.11) (2.16) shows the variations of these constants according to following operating points. (p.u) (2.35) (p.u) (2.36) where these operating points were calculated using the power flow solution. Power flow solution is the computation of voltage magnitude and phase angle at each bus in a power system under balanced three-phase steady-state conditions. As a by-product of this calculations, real and reactive power flows in equipment such as transmission lines and transformers, as well as equipment losses, is computed. Newton-Raphson method is used to obtain power flow solution. Variation of K1 at different operating points Reactive Power, Q (MVAR) Real Power, P (MW) Figure (2.11): Variation of K 1 at Different Operating Points Dept. of EE, Qatar Univ. P a g e 30

46 Constant K3 Constant K2 Design of Power System Stabilizer Based on Variation of K2 at different operating points Reactive Power, Q (MVAR) Real Power, P (MW) Figure (2.12): Variation of K 2 at Different Operating Points Variation of K3 at different operating points Reactive Power,Q (MVAR) Real Power, P (MW) Figure (2.13): Variation of K 3 at Different Operating Points Dept. of EE, Qatar Univ. P a g e 31

47 Constant K5 Constant K4 Design of Power System Stabilizer Based on Variation of K4 at different operating points Reactive Power, Q (MVAR) Real Power,P (MW) Figure (2.14): Variation of K 4 at Different Operating Points Variation of K5 at different operating points Reactive Power,Q (MVAR) Real Power,P (MW) Figure (2.15): Variation of K 5 at Different Operating Points Dept. of EE, Qatar Univ. P a g e 32

48 Constant K6 Design of Power System Stabilizer Based on Variation of K6 at different operating points Reactive Power,Q (MVAR) Real Power, P (MW) Figure (2.16): Variation of K 6 at Different Operating Points From the figures shown above, it is observed that [K 1 -K 6 ] are always positive except K 5 which sometime might go to negative value and that is an indication for system instability. Figure (2.15) shows that at operating points that stress the generator or at operating points that the generator is absorbing reactive power, constant K 5 is negative. Dept. of EE, Qatar Univ. P a g e 33