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

49 CHAPTER 3: DYNAMIC STABILITY EVALUATION 3.1. Techniques of Stability Evaluation Stability can be evaluated by different methods, such as using Eigenvalues, Damping Torques and Time-Domain Simulations. These methods are techniques that are used to determine if the system is stable or unstable. The following sections describes these techniques in details by taking different operating points Stability Evaluation Using Eigenvalues Technique Consider the following state-space equations: (3.1) (3.2) Note that all the partial derivatives above are evaluated at which small perturbation is being analyzed. Now we need to get the state Equations (3.1)-(3.2) in the frequency domain. This is done by taking the Laplace transform as follows: (3.3) (3.4) Rearranging Equation (3.3): (3.5) Dept. of EE, Qatar Univ. P a g e 34

50 This yields to: (3.6) Substituting Equation (3.6) in (3.4) results in (3.7) Note that both Equations (3.6)-(3.7) have two components, one dependent on the initial conditions and the other one dependent on the input [10]. The poles of x(s) and y(s) are obtained from the roots of the characteristic equation of matrix A, which is: (3.8) where s is the eigenvalue of matrix A. The stability of any system is determined by its eigenvalues as follows: 1. The real eigenvalue corresponds to a non-oscillatory mode. If it is negative, this represents the decaying mode, and it decays fast as long as the magnitude of the eigenvalue is high. However if it is positive, this would represent an aperiodic instability. Note that if there is at least one positive real eigenvalue in the system, this would lead the system to instability mode [10]. 2. The complex eigenvalues appear in conjugate pairs, and each pair corresponds to an oscillatory mode. The real component of the complex pair represents the damping, while the imaginary component represents the frequency of oscillations [10]. For a complex pair of eigenvalue: Dept. of EE, Qatar Univ. P a g e 35

51 (3.9) The damping ratio can be expressed as: (3.10) Where the frequency of oscillations in Hz is: (3.11) Equation (3.10) determines the rate of decay of the amplitude of the oscillation. The stability of power system is related to position of the power system eigenvalues in realimaginary plane. The real component of the eigenvalue presents the damping, where the imaginary component presents the frequency of oscillations. If the real part of the eigenvalue is negative, the response is represented as damped oscillations which tends the system to be stable, whereas if it is positive, the response is represented as increasing amplitude oscillations, thus the system is instable Stability Evaluation using Damping Torque Technique Stability of the power system is considered as a case of equilibrium between opposing forces. The input mechanical torque and the output electrical torque of each machine is in equilibrium state under steady-state conditions with a constant speed. If the system is subjected to any disturbance during the equilibrium state, this would result in acceleration or deceleration of the rotor of the machine. The stability of the motor depends on both components of the torque. If any lack of sufficient damping torque occurs in the system, this would lead the system to oscillatory instability. [10] Dept. of EE, Qatar Univ. P a g e 36

52 derived as: Considering the block diagram of Figure (2.5) introduced in section (2.2), where E q is (3.12) Rearranging the equation yields to: (3.13) The expression of the torque-angle loop is given by: (3.14) By changing s to jthen simplifying, Equation (3.14) becomes: (3.15) Suppose and (3.16) Multiplying Equation (3.15) by yields to: (3.18) In Equation (3.18), the imaginary part plays an important role in the stability of the system. If the imaginary part is greater than zero, positive damping is then implied, and hence the Dept. of EE, Qatar Univ. P a g e 37

53 roots move to the left-half plane which makes the system stable. Whereas if it negative, or less than zero, negative damping results which makes the system unstable [1]. For oscillation frequencies of 1 to 3 Hz, the effect of K 4 can be neglected [1]. By separating Equation (3.18) into real and imaginary parts, neglecting the effect of K 4 and setting = 0 for the case of low frequencies, this results in: (3.20) where K s is the synchronizing torque coefficient due to frequencies case and considering a high grain K A, Equation (3.20) becomes:. By setting = 0 for the low (3.21) The imaginary part of Equation (3.18) is: (3.22) The above equation results in a positive damping for K 5 > 0, but a negative damping for K 5 < 0. Our concern here is when K 5 is in negative, and K A is large enough to lead the system to instability. The constant K 5 becomes positive for considering low value of external system reactance and low generator outputs, whereas it is negative for high system reactance and high generator outputs. In this case, this may offset the inherent machine damping torque. Therefore, a Dept. of EE, Qatar Univ. P a g e 38

54 power system stabilizer (PSS) is introduced to eliminate the effect of the negative damping torque and lead the system to stability [1]. The following figure shows the block diagram of the torque angle loop for a singlemachine infinite bus system. T m E ' q K 2 T e 1 2Hs b s K D K S Figure (3.1): Torque-Angle Loop From Figure (3.1) we have: (3.23) After rearranging we get (3.24) The characteristic equation derived from Equation (3.24) is given by: (3.25) Dept. of EE, Qatar Univ. P a g e 39

55 Which is the general form of: (3.26) From Equations (3.25) and (3.26), the undamped natural frequency is (3.27) Also, the damping ratio is (3.28) Therefore the damping frequency can be calculated as: (3.29) An increase in the synchronizing torque coefficient K S causes the natural frequency to increase and hence the damping ratio to decrease. But as the damping ratio coefficient K D increases, this would cause the damping ratio to increase again, in case that the inertia constant does not decrease [10,11] Stability Evaluation using Time-Domain Simulation Technique In this project, Simulink model, that is shown in Figure 2.10, were used to model and simulate SMIB power system discussed in Section 2.2 using a graphical block diagram, then MATLAB can show rotor speed deviation response, rotor angle deviation response and terminal voltage deviation response. Dept. of EE, Qatar Univ. P a g e 40

56 3.2. Dynamic Stability Evaluation of SMIB Consider the following Single-Machine Infinite Bus (SMIB) system with the parameters shown below. The system has been evaluated for stability using the techniques mentioned in the previous section at the nominal operating point. G V t V 0 Re jx e AVR Exciter Line Infinite Bus 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 Dept. of EE, Qatar Univ. P a g e 41

57 SMIB Power System Stability Evaluation Using Eigenvalues Technique MATLAB were used to compute the eigenvalues of the previous SMIB power system for stability evaluation. Table 3.1 shows the eigenvalues of the previous SMIB power system at nominal operating point. Constants [K 1 -K 6 ] are calculated using the Component Connection Technique which was discussed in Section 2.1. Table (3.1): The Eigenvalues and the Constants [K 1 -K 6 ] of the Nominal Operating Point Operating point 1 P (MW) 136 Q (MVAR) 83.2 K K K K K K j j From the table above, it is clear that all real parts of the eigenvalues are negative, which means that the system is stable. By calculating the damping ratio, the rate of decay of the oscillation s amplitude can be obtained, which determines whether the system is stable or not. If the damping ratio is positive, this means that the system has a decreasing oscillation s amplitude, and hence the system is stable which is the case in nominal operating point. By calculating the damping ratio of this operating point considering ( j9.4219), we get Dept. of EE, Qatar Univ. P a g e 42

58 Note that choosing to calculate the damping ratio will end up with the same result as above Dynamic Stability Evaluation of SMIB Using Torques Technique In order to calculate the synchronizing and damping torque for the nominal operating point for the previous SMIB power system, the following expression is used to obtain field flux linkage, which has been derived in section 3.1.2: (3.30) The value of the complex frequency obtained from the rotor oscillations is equal to of nominal operating point which is j Substituting it in Equation (3.30) and simplifying yields to: (3.31) Moreover, the torque due to E q is equal to: (3.32) Which results in (3.33) Dept. of EE, Qatar Univ. P a g e 43

59 From Figure (3.1) it is clear that (p.u) (3.34) in per unit. Hence Substituting j in Equation (3.33) yields to: (3.35) From the result above we can conclude that: (3.36) (3.37) Dept. of EE, Qatar Univ. P a g e 44

60 The total synchronizing torque is equal to: (3.38) From the above results, it is clear that the value of K D and K S are positive, which means that this system is in stable mode. To ensure that the calculations are correct, the damping ratio of the system is calculated using Equation (3.28) as follows: (3.39) (3.40) The damping ratio here is equal to the one obtained in section Therefore the system is stable. The following table summarize all values of torque coefficients and damping ratio and frequency for operating point 1. Table (3.2): Synchronizing and Damping Torques and Damping Ratios and Frequencies for Nominal Operating Point Operating Point 1 K S (p.u torque / rad) K D (p.u torque / rad) n (rad/s) Dept. of EE, Qatar Univ. P a g e 45

61 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on D (rad/s) Dynamic Stability Evaluation of SMIB Using Time-Domain Simulation Technique Time domain simulation technique that was discussed in Section (3.1.3) have been applied to the studied SMIB power system discussed in Section (3.2) to obtain the rotor speed deviation response, rotor angle deviation response and terminal voltage deviation response at the nominal operating point under 1% change in applied at t=3 sec as shown in Figures (3.2) (3.3) Rotor Speed Deviation Time (sec) Figure (3.2): Rotor Speed Deviation Response Under 1% Change in Point at Nominal Operating Dept. of EE, Qatar Univ. P a g e 46

62 Deviation of Terminal Voltage (p.u) Deviation of Rotor Angle (p.u) Design of Power System Stabilizer Based on From Figure (3.2) it is observed that at this operating point and exciter gain, the power system rotor speed deviation goes to zero (i.e nominal value of rotor speed) which means that it is stable. By also looking at the value of constant K 5, the eigenvalues and the damping torque coefficient K D of the power system at the nominal operating point, it is concluded that since all the real parts of the system eigenvalues are negative and the damping torque coefficient K D is positive this means that the system is stable at this operating point, and since K 5 is positive this indicates that the system will be stable at higher values of exciter gain K A Rotor Angle Deviation Response Time (sec) 4 x 10-4 Terminal Voltage Deviation Response Time (sec) Dept. of EE, Qatar Univ. P a g e 47

63 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on Figure (3.3): Rotor Speed Deviation and Terminal Voltage Deviation Response Under 1% Change in at Nominal Operating Point From Figure (3.3) it is observed that at this operating point and exciter gain, the power system rotor angle deviation, and terminal voltage deviation goes to another steady state value which corresponds to the change in T m. In order to evaluate the system under 1% change in V ref, time domain simulation technique that was discussed in Section (3.1.3) have been applied to the studied SMIB power system discussed in Section (3.2) to obtain the rotor speed deviation response, rotor angle deviation response and terminal voltage deviation response at the nominal operating point Rotor Speed Deviation Time (sec) Figure (3.4): Rotor Speed Deviation Response Under 1% Change in Point at Nominal Operating Dept. of EE, Qatar Univ. P a g e 48

64 From Figure (3.4) it is observed that at this operating point and exciter gain, the power system rotor speed deviation goes to zero (i.e nominal value of rotor speed) which means that it is stable, from this we can conclude that the system will be stable for both types of perturbations changing in T m or V ref Effect of Different Operating Points on System Dynamic Stability In this section, the dynamic stability evaluation techniques discussed in Section (3.1) have been applied to the SMIB power system (given in Section (3.2)) at three different operating points to evaluate the effect of different operating points of system dynamic stability. The different operating points at which the system is evaluated are given in Table (3.1). Table (3.3): Different Operating Points for Power System Stability Evaluation Operating point 1 Operating point 2 Operating point 3 P (MW) Q (MVAR) As show in above table, at operating point 1 the generator is running at normal operating conditions, but at operating point 2 the generator is absorbing reactive power and at operating point 3 the generator is stressed or heavy loaded. The following table shows the results of testing the operating points using the eigenvalues technique. Table (3.4): Testing Operating Points Using Eigenvalues Technique Operating point 1 Operating point 2 Operating point 3 P (MW) Q (MVAR) K K K Dept. of EE, Qatar Univ. P a g e 49

65 K K K i i i i i i From the above table, it is shown that the real part of the complex pair of the eigenvalues of operating point 2 is positive, which means that the system is unstable. However, the other pairs of eigenvalues are having negative real part for the other two operating points, which in turns assures that the system is stable. This is proved by calculating the damping torque coefficient of all operating points and check whether the damping ratio is negative or positive. As shown in Table 3.5, the damping torque coefficient of operating point 2 is negative which proves that the system is unstable, whereas it is positive for the other operating points, therefore the system at each operating point is stable. After testing the system at different operating points using the eigenvalues technique, the torques technique is then used to evaluate the stability of the system. The following table shows the values of synchronizing and damping coefficients and damping ratios and frequencies for the three operating points. Table (3.5): Synchronizing and Damping Torques and Damping Ratios and Frequencies for Three Operating Points Operating Point 1 Operating Point 2 Operating Point 3 K S (p.u torque / rad) K D (p.u torque / rad) Dept. of EE, Qatar Univ. P a g e 50

66 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on n (rad/s) D (rad/s) The results in the above table were as expected. The values of damping coefficient K D and damping ratio are negative for operating point 2 (the unstable system), whereas for the other operating points (the stable systems) they are positive. It is noticed that the damping ratios for the three operating points are equal to the ones calculated for the eigenvalues technique. The Time-Domain Simulation Technique that is discussed in Section (3.1) were used to evaluate the stability at the different operating points mentioned above under 1% change in. Figures (3.6)-(3.8) shows rotor speed deviation at the operating points mentioned above Rotor Speed Deviation Time (sec) Dept. of EE, Qatar Univ. P a g e 51

67 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on Figure (3.5): Rotor Speed Deviation Response under 1% Change in at Operating Point 1 From Figure (3.5) it is observed that at this operating point and exciter gain, the system is stable. By also looking at the value of constant K 5, the eigenvalues and the damping torque coefficient K D of the power system at this operating point, it is concluded that since all the real parts of the system eigenvalues are negative and the damping torque coefficient K D is positive this means that the system is stable at this operating point, and since K 5 is positive this indicates that the system will be stable at higher values of exciter gain K A. 6 Rotor Speed Deviation Time (sec) Figure (3.6): Rotor Speed Deviation Response under 1% Change in at Operating Point 2 From Figure (3.6) it is observed that at this operating point and exciter gain, the power system is unstable. By also looking at the value of constant K 5, the eigenvalues and the damping torque coefficient K D of the power system at this operating point, it is concluded that since two of the system eigenvalues are positive and the damping torque coefficient K D is negative this Dept. of EE, Qatar Univ. P a g e 52

68 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on means that the system is unstable at this operating point, and since K 5 is negative this indicates that the system will be highly unstable at higher values of exciter gain K A Rotor Speed Deviation Time (sec) Figure (3.7): Rotor Speed Deviation Response under 1% Change in at Operating Point 3 From Figure (3.7) it is observed that at this operating point and exciter gain, the power system is stable. By also looking at the value of constant K 5, the eigenvalues and the damping torque coefficient K D of the power system at this operating point, it is concluded that since all the real parts of the system eigenvalues are negative and the damping torque coefficient K D is positive this means that the system is stable at this operating point, and since K 5 is negative this indicates that the system will be unstable at higher values of exciter gain K A. Dept. of EE, Qatar Univ. P a g e 53

69 3.4. The Effect of Excitation System Parameters on System Stability The state-space equation of the system with the exciter is given as: (3.41) (3.42) Consider operating point 3 introduced in section (3.3) where real power (P) = 168 MW, reactive power (Q) = 64 MVAR and K 5 is negative. By increasing the value of K A the power system tend to go to instability, Table (3.6) shows variation of power system damping torque coefficient K D, Synchronizing torque coefficient K S, natural frequency, damping ratio and damping frequency as the exciter gain K A increase in steps of 100 from the nominal value, and Figure (3.8) shows the variation of rotor speed deviation response as the exciter gain K A increase from the nominal value to 400. Table (3.6): Results of Increasing the Gain K A of the Operating Point 3 K A K S K D n D According to the table above, we can see that the value of K D and became negative as K A increase which lead the system to instability Dept. of EE, Qatar Univ. P a g e 54

70 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on Rotor Speed Deviation Exciter Gain 50 Exciter Gain Time (sec) Figure (3.8): The Effect of Increasing K A to 400 in Operating Point 3 Although that the system depends on the excitation constant K A for the stability case, however, the time constant T A has a negligible effect on the stability of the system [10]. It is concluded from the above discussion that at certain operating points where constant K 5 is negative, the excitation system could lead the power system to instability at high values of exciter gain K A, this is because at high values of exciter gain K A with K 5 being negative a negative damping is introduced to the system which eventually lead the system to instability. This is usually compensated for by the use of supplementary controlling signals from the Power System Stabilizer (PSS) to produce positive damping. The design and implementation of Power System Stabilizer based on microcontroller unit will conducted in part 2 of this project Dept. of EE, Qatar Univ. P a g e 55

71 CHAPTER 4: POWER SYSTEM STABILIZER DESIGN 4.1. Introduction Power System Stabilizer (PSS) is a device which provides additional supplementary control loops to the automatic voltage regulators system (AVR). Power system stabilizers (PSS) are often used as an effective means to add damping to the generator rotor oscillations. Adding supplementary control loops to the generator AVR is one of the most common ways of enhancing both dynamic and transient stability. To provide damping for the generator rotor oscillations, PSS must produce a component of electrical torque in phase with rotor speed deviations. 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. [1, 6,7,10] 4.2. SMIB Power System Model Including PSS Modeling of PSS The purpose of a PSS is to introduce a damping torque component in phase with the speed deviation Δω. PSS input signals can be derived from machine speed or power. Where PSS output is connected to the input of the exciter. A direct feedback of Δω would result in a damping torque component if the exciter transfer function K a and the generator transfer function between E fd and Te were pure gains as shown in Figure (4.1). However, in practice both the generator and the exciter exhibit frequency dependent gain and phase characteristic. Therefore, the G PSS (s) transfer function (given in Equation 4.1), as shown in Figure (4.1) should have appropriate phase compensation circuits to compensate for the phase lag between the exciter input and the electrical torque. In the ideal case, with phase characteristic of PSS being an exact inverse of the exciter (AVR) and generator phase Dept. of EE, Qatar Univ. P a g e 56

72 characteristic to be compensated, the G PSS (s) would result in a pure damping torque at all oscillation frequencies. [1, 6,7,10, 28] If the phase-lead network provides more compensation than the phase lag between Te and Vs, the PSS introduces, in addition to a damping component of torque, a negative synchronizing torque component. Conversely, with under-compensation a positive synchronizing torque component is introduced. Usually, the PSS is required to contribute to the damping of the rotor oscillations over a range of frequencies, rather than a single frequency. [1, 6, 7, 10, 27, 28] The Lead Lag PSS transfer function is given as, (4.1) SMIB Power System Block Diagram Model including PSS The theoretical basis for a PSS may be illustrated with the aid of the block diagram shown in Figure (4.1). Dept. of EE, Qatar Univ. P a g e 57

73 PSS 1 + s s 2 v w s w 1 + s w K PSS K 4 V ref K A 1T s A E fd K 3 K 3T s 2 1 ' do E ' q K T e T m 1 2Hs b s V t AVR K 6 D K 1 K 5 Figure (4.1): Block Diagram of SMIB Power System Including PSS Figure (4.2) shows the block diagram of the static excitation system, including AVR and PSS. For small-signal stability study, stabilizer output limits and exciter output limits are not considered so they are omitted in Figure (4.2). As shown in Figure (4.2) the PSS block diagram representation is composed of three blocks: a gain block, a signal washout block and phase compensation block. Dept. of EE, Qatar Univ. P a g e 58

74 Power System Stabilizer Phase Compensation Washout Gain 1 + s s 2 v w s w 1 + s w K PSS V t K A 1T s A E fd V ref Figure (4.2): Block Diagram of the Excitation System (AVR) Including PSS The stabilizer gain (K PSS ) function is to determine the amount of damping introduced by the PSS. [1, 6, 7, 10, 18, 21, 28] The basic function of the washout block is to serve as a high-pass filter, also it allows the PSS to respond only to changes in speed and it prevent the steady changes in speed to modify the terminal voltage. From the viewpoint of the washout function, the value of T w is not critical and may be in the range of 1 to 20 seconds. The main consideration is that it is long enough to pass stabilizing signals at the frequencies of interest unchanged. The function of the phase compensation block is to provides the appropriate phase-lead characteristic to compensate for the phase lag between the exciter input and the generator electrical (air-gap) torque. In Figure (4.2) a single first-order phase compensation block were used to represent the phase compensation circuit. However, in practice two or more first-order blocks may be used to achieve the desired phase compensation. In some cases, second-order blocks with complex roots have been used. Normally, the frequency range is 0.1 to 2 Hz, and the Dept. of EE, Qatar Univ. P a g e 59

75 phase-lead network should provide compensation over this entire frequency range. The phase characteristic to be compensated changes with system conditions; therefore, a compromise is made and a characteristic acceptable for different conditions is selected. Generally some undercompensation is desirable so that the PSS, in addition to significantly increasing the damping torque, results in slight increase of the synchronizing torque. [1, 6, 7, 10, 21, 28] State-Space Model of SMIB Power System Including PSS In this section the SMIB with PSS power system state-space model will be derived using the aid of static exciter with AVR and PSS block diagram which is shown in Figure (4.2). Using exciter block in Figure (4.2), (4.2) and (4.3) Substituting Equation (4.3) in Equation (4.2), (4.4) Using Gain and Washout Blocks in Figure (4.2), and taking the output signal of the washout block to be Dept. of EE, Qatar Univ. P a g e 60

76 (4.5) and according to Figure (4.1), (4.6) and (4.7) Taking in Equation (4.6) and substituting Equation (4.7) in Equation (4.6) (4.8) Substituting Equation (4.8) in Equation (4.5) (4.9) Using phase compensation block in Figure (4.2), (4.10) Substituting Equation (4.9) in Equation (4.10) Dept. of EE, Qatar Univ. P a g e 61

77 (4.11) The overall state-space model of the power system (SMIB including PSS) [1] is (4.12) (4.13) MATLAB/Simulink Model of SMIB Power System including PSS MATLAB/Simulink was used to simulate the overall block diagram (SMIB with PSS) that was shown in Figure (4.1). This MATLAB/Simulink model will be used to evaluate the dynamic stability of the SMIB power system with PSS. Figure (4.3) shows MATLAB/Simulink model of the SMIB with exciter power system. The PSS input signal was taken from exciter input voltage as, and the PSS output signal was introduced to Dept. of EE, Qatar Univ. P a g e 62

78 0 Clock V ref Delta- Vs To Workspace (Time) k4 K4 To Workspace (Delta Te) Delta_Te delta-te Voltage Regulator-Exciter Delta- Eq' KA K3 K2 TA.s+1 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) T1.s+1 Tw.s T2.s+1 Tw.s+1 Stage1 Phase Comp Washout Delta- Omega Delta - Tm Rotating Mass 1 Wb (2.*H)s Base Freq Delta- Td Damping Torque Coffiecent-KD KD Constant-k1 K1 Constant-k5 K5 Kpss PSS-Gain Delta_Omega To Workspace (Delta Omega) Delta Omega 1 s Delta_delta To Workspace (Delta delta) delta-delta Delta- delta t Figure (4.3): MATLAB/Simulink Model of the SMIB with PSS Power System Dept. of EE, Qatar Univ. P a g e 63

79 4.3. Dynamic Stability Enhancement using PSS In this section, stability enhancement of the SMIB power system is achieved by including PSS in the system. The stability enhancement is evaluated by using the techniques that were discussed in Chapter 3, namely the eigenvalues and damping torque. The results of using the two techniques are verified using time-domain simulations. The following sections evaluates the stability of the system at different operating points using these techniques Eigenvalues Technique The eigenvalues technique is used to evaluate the dynamic stability of the system. The eigenvalues of matrix A of the state-space equation given in Equation (4.12) is used in evaluating the stability Damping Torque Technique In this section, the damping torque expression is derived for the system with PSS. From the block diagram of Figure (4.1), due to PSS can be expressed as: (4.14) where (4.15) Moreover, it is known that (4.16) Dept. of EE, Qatar Univ. P a g e 64

80 Substituting (4.14)-(4.15) into (4.16) yields to: (4.17) Converting s to j yields to: (4.18) Hence the synchronizing and damping torques after simplifying will be: (4.19) (4.20) The above expressions (4.19)-(4.20) are calculated for obtaining the synchronizing and damping torques under the effect of the PSS only. In order to obtain the overall torques from the system, these expressions should be added to the ones derived in Section of the overall system without the effect of PSS, as follows: (4.21) Dept. of EE, Qatar Univ. P a g e 65

81 (4.22) where Time Domain Simulation Technique In this project, Simulink model shown in Figure (4.3), is used to simulate the time domain response of SMIB with PSS power system that was discussed in Section (4.2) Tuning of PSS Parameters There are many ways to tune the PSS parameters such as root-locus, frequency-response, and state-space design methods. In this project, the technique discussed in [1,27] is used to tune the PSS parameters. Typical values of the PSS parameters are: is in the range of 0.1 to 50 is the lead time constant, 0.2 to 1.5 sec is the lag time constant, 0.02 to 0.15 sec. is the washout time constant and it is equal to 10 sec. The desired stabilizer gain ( is obtained by first finding the gain at which the system becomes unstable. This may be obtained be actual test or by root locus study. Then washout time constant ( ) is set at 10 sec. The purpose of this constant is to ensure that there is no steady- Dept. of EE, Qatar Univ. P a g e 66

82 state error of voltage reference due to speed deviation. is then set at 1/3 of *, where * is the gain at which the system becomes unstable. Lead & lag time constants (T 1 and T 2 ) are set to values that is within the range. In this project the PSS parameters [1] were chosen to be: = = 0.75 sec = sec = 10 sec 4.5. Dynamic Stability Enhancement of SMIB Power System Consider the Single-Machine Infinite Bus (SMIB) system having the parameters given in section 3.2. The dynamic stability of this system is enhanced using PSS Eigenvalues of SMIB Power System with PSS The following table shows the eigenvalues of the given system with PSS at nominal operating point. Table 4.1: System Eigenvalues at Nominal Operating Point Nominal Operating Point P (136 MW) Q (83.2 MVAR) j j Dept. of EE, Qatar Univ. P a g e 67

83 It is seen from the above table that all real parts of the eigenvalues are negative, which proofs that the system is stable. Moreover, the damping of this operating point considering the eigenvalue ( j ) is: The damping ratio is positive and greater than the value without PSS ( indicates that the designed PSS has enhanced the stability of the system. ), which Damping Torque of SMIB Power System with PSS In order to calculate the synchronizing and damping torques of the given SMIB power system at the nominal operating point, Equation (4.18) is used. Substituting in this equation the value of eigenvalue as the complex frequency yields to: (4.23) It is known that In per unit. Hence Dept. of EE, Qatar Univ. P a g e 68

84 Substituting in Equation (4.23) yields to Therefore, The next step is to repeat the calculations made in section for calculating without PSS at the new obtained eigenvalue. Using Equation (3.15): (4.24) Dept. of EE, Qatar Univ. P a g e 69

85 where (4.25) Substituting (4.25) in (4.24), yields to (4.26) The torques are Therefore the total synchronizing and damping torques with the PSS are equal to: From the obtained results, it is clear that the effect of PSS has raised the value of K D and K S, which has improved the stability of the system. By calculating also at the damping ratio and damping frequency using Equations (3.27)-(3.29): Dept. of EE, Qatar Univ. P a g e 70

86 It is noticed that the both damping ratio and damping frequency have increased, which also improved the system stability. The following table summarize all values of torque coefficients, damping ratio and damping frequency at nominal operating point including PSS in the system. Table (4.2): Torque Coefficients, Damping Ratio & Damping Frequency at Nominal Operating Point Including PSS Nominal Operating Point K S (p.u torque / rad) K D (p.u torque / rad) n (rad/s) D (rad/s) Dept. of EE, Qatar Univ. P a g e 71

87 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on Time Domain Simulation of SMIB Power System with PSS Time domain simulations have been obtained with PSS at the nominal operating point under 1% change in as shown in Figure (4.4) Rotor Speed Deviation With PSS Without PSS Time (sec) Figure (4.4): Rotor Speed Deviation Response with & without PSS at nominal operating point under change in of 1% From Figure (4.4) it is observed that the PSS has introduced a positive damping to the power system, and this is obvious by looking at the settling time of the rotor speed response with PSS it is much shorter than it without PSS. Dept. of EE, Qatar Univ. P a g e 72

88 Deviation of Terminal Voltage (p.u) Deviation of PSS Stabilizing Signal Voltage (p.u) Deviation of Rotor Speed (Rad/s) Deviation of Rotor Angle (p.u) Design of Power System Stabilizer Based on Rotor Speed Deviation With PSS Without PSS Rotor Angle Deviation Response With PSS Without PSS Time (sec) Time (sec) Figure (4.5): Rotor Speed Deviation Response with & without PSS at nominal operating point under change in of 1% Figure (4.6): Rotor Angle Deviation Response with & without PSS at nominal operating point under change in of 1% x 10-3 Terminal Voltage Deviation Response With PSS Without PSS 1.5 x 10-3 PSS Stabilizing Signal Voltage Deviation Response 1 PSS Stabilizing Sginal Time (sec) Time (sec) 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 of 1% As observed in Figures (4.5)-(4.8), it is observed that the presence of the PSS has also introduced damping to the rotor speed deviation response under different disturbance source which is changing of the reference voltage ( = 1% ), moreover, it is observed that the rotor Dept. of EE, Qatar Univ. P a g e 73

89 angle of deviation response has also damped to a higher value faster than the response of the power system without PSS and the same applies for the terminal voltage but it damped out to a lower value. It is also observed that the PSS stabilizing signal goes to zero at the steady state, this is because it only passes stabilizing signals only in the case of the disturbance Assessment of the Robustness of the Designed PSS In this section, the robustness of the designed PSS is evaluated on the SMIB power system, given in section (3.2), to test the effect of the designed PSS on the system at different operating points using dynamic stability evaluation techniques. These operating points are given in Table (4.3). Table (4.3): Different Operating Points for PSS Evaluation Operating point 1 Operating point 2 Operating point 3 P (MW) Q (MVAR) As show in above table, at operating point 1 the generator is running at normal operating conditions, but at operating point 2 the generator is absorbing reactive power and at operating point 3 the generator is stressed or heavy loaded. The following table shows the results of testing the operating points using the eigenvalues technique. Table (4.4): Testing Operating Points Using Eigenvalues Technique Operating point 1 P (144 MW) Q (96 MVAR) Operating point 2 P (112 MW) Q (-32 MVAR) Operating point 3 P (168 MW) Q (64 MVAR) i i i i i Dept. of EE, Qatar Univ. P a g e 74

90 i i From the above table, it is clear that all the eigenvalues, which are derived from the A matrix of the state-space model, have negative real parts among the three operating points, and the damping ratios are positive for the three cases. These results confirms that the system at each operating point is stable. After testing the system at different operating points using the eigenvalues technique, the damping torque technique is then used to evaluate the stability of the system. Table (4.5) shows the values of synchronizing and damping coefficients, damping ratios and damping frequencies at the given three operating points. Table (4.5): Torque Coefficients, Damping Ratios & Damping Frequencies at Three Operating Points Operating point 1 P (144 MW) Q (96 MVAR) Operating point 2 P (112 MW) Q (-32 MVAR) Operating point 3 P (168 MW) Q (64 MVAR) K S (p.u torque / rad) K D (p.u torque / rad) n (rad/s) D (rad/s) The results in the above table were as expected. The values of damping coefficient K D and damping ratio are positive at all operating points, even at the unstable operating point which is Dept. of EE, Qatar Univ. P a g e 75

91 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on operating point 2. It is noticed that the damping ratios for the three operating points are equal to the ones calculated for the eigenvalues technique. Time domain simulation technique was also applied to test the robustness of the PSS by observing the rotor speed deviation response of the SMIB with PSS power system at the three different operating points. Figure (4.9) shows the rotor speed deviation response with & without PSS at operating point Rotor Speed Deviation Without PSS With PSS Time (sec) Figure (4.9): Rotor Speed Deviation Response with & without PSS at Operating Point 1 From Figure (4.9) it is observed that the PSS has introduced a positive damping to the power system, and this is obvious by looking at the settling time of the rotor speed deviation response of the SMIB power system with PSS it is much shorter than it without PSS. Dept. of EE, Qatar Univ. P a g e 76

92 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on As shown in Figure (4.10) time domain simulation technique was also applied at operating point 2 (discussed in section 3.3) at which the power system is unstable, to see the effect of PSS in stabilizing the power system With PSS Without PSS Rotor Speed Deviation Time (sec) Figure (4.10): Rotor Speed Deviation Response with & without PSS at Unstable Operating Point From Figure (4.10), it is observed that the PSS has introduced a positive damping to the power system and it stabilized the system and this is obvious by looking at the rotor speed deviation response with PSS. Time domain simulation technique was applied on operating point 3, at which the system is unstable at higher values of exciter gain, so to test the robustness of the PSS, rotor speed deviation response of the SMIB with PSS power system were observed at 400 exciter gain as shown in Figure (4.11). Dept. of EE, Qatar Univ. P a g e 77

93 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on Rotor Speed Deviation With PSS Without PSS Time (sec) Figure (4.11): Rotor Speed Deviation Response with & without PSS at Operating Point 3 with Exciter Gain Equal to 400 From Figure (4.11), it is observed that the PSS has introduced a positive damping to the power system and it stabilized the system even at higher values of exciter gain and this is obvious by looking at the rotor speed deviation response with PSS. After testing the robustness of the PSS, it is concluded that it plays an important role in improving the system s stability. Not only it increasing the damping coefficient and damping ratio of the unstable system, but also it enhances the behavior of the system at different operating points, which ensures that the system by any means would not lead to instability. The third technique, or the time-domain simulation s technique, illustrated the simulations of the PSS at Dept. of EE, Qatar Univ. P a g e 78

94 different operating points, and showed that it enhanced and increased the damping of the system which led it to stability. Dept. of EE, Qatar Univ. P a g e 79

95 CHAPTER 5: DESIGN OF MICROCONTROLLER BASED DIGITAL PSS 5.1. Digital Control Nowadays, digital computers and microcontrollers are mostly used in control engineering applications. Figure (5.1) illustrates an example of a typical computer controlled system. The error signal in this system is analog, and an analog-to-digital (A/D) converter is used to convert the signal and make it digital so that the computer can read it. The process of (A/D) conversion is by sampling the input signal periodically and covert these samples into a digital code so that the computer can process it. Then, the digital code is being run by a software for executing the given actions in the code. [9, 30-32] Input + _ A/D Digital Controller (Computer) D/A Plant Output sensor Figure (5.1): Typical Digital Control System Converting the digital signal that comes from the computer into an analog signal is normally done by using a digital-to-analog (D/A) converter. The operation of this converter is usually approximated by zero-order hold transfer function. The A/D and D/A converter circuits are built-in in many types of microcontrollers, so that the microcontrollers can be connected directly to any analog signal or to the plant. In Figure (5.1), the reference set point, sensor output and the plant (SMIB power system in this project) input and output are all analog signals. In Figure (5.2) shows the block diagram of microcontroller based digital control system. It is shown that microcontroller part includes builtin A/D and D/A converters. [9, 30-32] Dept. of EE, Qatar Univ. P a g e 80

96 Microcontroller Input + _ A/D Digital Controller D/A Plant Output sensor Figure (5.2): Block Diagram of Microcontroller Based Digital Control System 5.2. What is a Microcontroller? The microcontroller is considered as a self-contained computer system, which is designed to have, in general, a microprocessor, memory and I/O connections in one small chip. This is considered as an advantage where it doesn t need other specialized external components for its applications, because all necessary circuits are already built-in it. The microcontroller, when invented, was used to control machinery, which is different than the microprocessor that was used as a replacement for the CPU in a mainframe. Some of the earliest major applications of microcontrollers were the Epson dot matrix printer FX-80, which was built around the 8048 microcontroller where it brought low-cost printers to the marketplace, and the IBM personal computer s keyboard, which contained a universal peripheral interface (UPI) that appeared in 1977 as a microcontroller. This microcontroller was used to read keystrokes from the computer s keyboard. [17, 29, 31, 34] Assembly language is the traditional language that was used to program the microcontrollers. Today, the microcontrollers are programmed using high-level languages such as BASIC, PASCAL or C language, which present numerous advantages that are summarized as follows: Easier to develop programs using a high-level language. Dept. of EE, Qatar Univ. P a g e 81

97 Maintenance of programs is easier Testing programs is much easier. More user-friendly and less prone for making errors. Documenting programs is much easier. Although of the several advantages of the high-level languages, however it has some disadvantages. The memory usually has larger code length than the code length of the assembly, and the programs developed using the high-level languages usually run slower than those developed using assembly. In this project, the microcontroller type PIC is used as a digital controller, and it is programmed using high-level C language, and a comparison between PIC microcontroller families is found in Appendix A. [17, 29, 31, 34] 5.3. Architecture & Specifications of PIC18 Family The PIC microcontroller is drawn as a single block in the PIC-based system, because, as discussed earlier, it contains the memory and I/O pins for most its applications. However, additional memory or I/O capabilities can be connected to the microcontroller, but usually the ones provided on the PIC is sufficiently enough for most applications. The PIC18 microcontroller has different versions or packages that depends upon its manufacturing and the number of pins. Some of these packages are PDIP (Plastic Dual Inline Package), SOIC (Small Outline Integrated Circuit), PLCC (Plastic Leadless Chip Carrier), and SSOP (Small Shrink Outline Package). The number of pins ranges from 18 to 128 pins, which varies among the different packages. I/O pins in PDIP packages are limited to ports A and B in 18-pin versions, port A, B, and C in 28-pin versions, and port A,B,C,D, and E in 40-pin versions. In all types of microcontrollers, the power supply connections are VDD for connection to a nominal +5.0 V power supply, and VSS for connection to ground. The maximum allowable supple voltage can reach to +7.5 V. Generally, the amount of power supply current ranges from 60 A to 12 ma. In addition, the clocking frequency affects the amount of power supply current, which means that a 31-KHz clock results in 60 A current, while a 40-MHz clock or higher ends Dept. of EE, Qatar Univ. P a g e 82

98 up with 12 ma current. The maximum total allowable chip current is 200 ma, and the maximum pin current is 25 ma per pin as long as 200 ma is not exceeded for the entire chip. [17,28,34] 5.4. Specifications of Microcontroller PIC18F4520 Instruction set of 75 instructions Operating frequency DC 40 MHz Four Crystal modes, up to 40 MHz o Two External RC modes, up to 4 MHz o Two External Clock modes, up to 40 MHz o 8 user selectable frequencies, from 31 khz to 8 MHz Fail-Safe Clock Monitor o Allows for safe shutdown if peripheral clock stops Power supply voltage V o Timer1 oscillation: 1.8uA (2.0 V, 32 KHz), down to 5.8 ua (Idle mode), down to 0.1 ua (Sleep mode) Programmable high/low-voltage detect Programmable Brown-out Reset o With software enable option 36 input/output pins 256 bytes EEPROM memory o With 1,000,000 erase/write cycle data EEPROM memory typical 1536 bytes RAM memory A/D converter: o 13-channels, 10-bit resolution Enhanced USART module o Supports RS-485, RS-232 and LIN 1.2 o RS-232 operation using internal oscillator block o Auto-Baud Detect Master Synchronous Serial Port (MSSP) o Supports SPI and I 2 C mode Dept. of EE, Qatar Univ. P a g e 83

99 The datasheet of the used microcontroller is presented in Appendix B 5.5. Microcontroller s Basic Circuit As shown in Figure (5.3), in order to enable the microcontroller to operate properly it is necessary to provide: Power Supply Reset Signal Clock Signal Figure (5.3): Microcontroller Basic Circuit [29] Dept. of EE, Qatar Univ. P a g e 84

100 POWER SUPPLY The power supply circuit is composed of AC or DC (6-12V) power supply input along with full bridge rectified to convert AC to DC and then LM7805 is used to provides high-quality voltage stability and quite enough current (up to 1A) to enable the microcontroller and peripheral electronics to operate normally. [17, 29, 34] RESET SIGNAL In order that the microcontroller can operate properly, a logic one (VCC) must be applied on the reset pin. The push button connecting the reset pin MCLR to GND is not necessary. However, it is almost always provided because it enables the microcontroller to return safely to normal operating conditions if something goes wrong. By pushing this button, 0V is brought to the pin, the microcontroller is reset and the program execution starts from the beginning. A10K resistor is used to allow 0V to be applied to the MCLR pin, via the push button, without shorting the 5VDCrail to earth. [17, 29, 34] CLOCK SIGNAL Even though the microcontroller has a built-in oscillator, it cannot operate without external components which stabilize its operation and determine its frequency (operating speed of the microcontroller). Depending on elements in use as well as their frequencies, the oscillator can be run in four different modes: LP Low Power Crystal XT Crystal / Resonator HS High Speed Crystal / Resonator RC Resistor / Capacitor QUARTZ CRYSTAL In this project, the quartz crystal was used for frequency stabilization. the advantage of using quartz crystal is that it ensures the built-in oscillator to operate at a precise frequency which Dept. of EE, Qatar Univ. P a g e 85

101 is not affected by changes in temperature and power supply voltage. This frequency is usually labeled on the crystal casing. Apart from the crystal, capacitors C1 and C2 must also be connected as shown in Figure (5.4). Their capacitance is not of great importance. Therefore, the values provided in the table shown in Figure (5.4) below should be considered as a recommendation, not as a strict rule. [17, 29, 34] Figure (5.4): Quartz Crystal Circuit Configuration [29] 5.6. Serial Communication USART The Universal Synchronous/Asynchronous Receiver/Transmitter (USART), or it is also known as Serial Communications Interface (SCI), transmits and receives synchronous or asynchronous serial data using interrupts during normal operation. It contains all clock generators, shift registers and data buffers necessary to perform an input/output serial data transfer independently of the device program execution. Synchronous data are sent with a clock pulse for synchronization, where asynchronous data are sent without clock pulse. Moreover, there are three modes of sending serial data, which are Simplex, Half-Duplex and Full-Duplex. Basically, Simplex mode is transmitting data in one direction, Half-Duplex mode is transmitting or receiving information but in only one direction at a time, and Full-Duplex mode transmits and receives information simultaneously. [17, 29, 34] Dept. of EE, Qatar Univ. P a g e 86

102 Most data today are asynchronous data. It usually has a size of 10 bits, which starts with a start bit and ends with at least one stop bit, where data in between these bits are usually eight bits, with the least significant bit sent first. Bit rate, or often called baud rate, should be determined so that data are received successfully. For instance, if data are transmitted at bps (bits per second), then 1920 characters or bytes are transmitted per second because each character is 10 bit times. Therefore the bit rate is 1/19200 or s per bit, and the data rate is 1920 Bps (Bytes per second). [17, 29, 34] Synchronous data are not very common today. Unlike the asynchronous data, the synchronous data does not contain any start or stop pulse, where instead it is using 10 bit times for a byte and only 8 bit times are used per byte. As a result, it takes less time to transmit information than the asynchronous data. Synchronous data are normally transmitted in packets containing fixed number of bytes, which includes bytes that indicates the start and end of the packet. [17, 29, 34] As discussed earlier, the asynchronous mode does not use the clock signal, because it transmits and receives data using a standard non-return-to-zero (NRZ) format. The following Figure (5.5) illustrates the transformation of data in the asynchronous mode. Figure (5.5): Data Transformation in Asynchronous Mode [34] As it is shown in the figure, each data is transferred in the following mechanism: Data line has a logic one (1) during the idle state; Transmission of a data starts with a logic zero (0); Dept. of EE, Qatar Univ. P a g e 87

103 Data is transmitted through an 8-bit wide; Data is received at centre of each bit time; Transmission of a data end with a logic one (1). The bit rate of the serial data is calculated using a programmable baud rate generator in the USART. This generator is programmed by loading a value n in a register called SPBRG, which divides the system clock by the number loaded into the register. Three equations are used for calculating the baud rate of synchronous and asynchronous data as follows: Asynchronous baud rate at low speed: (5.1) Asynchronous baud rate at high speed: (5.2) Synchronous baud rate: (5.3) where F osc is the clock frequency. Usually, the default baud rate of serial interface operating asynchronously on PC with 8 data bits is at 9600 bps. As shown in Figure (5.6), the USART uses on some of the PIC18 family microcontrollers two pins for transmitting and receiving data, which are RC6 (transmitter TX) and RC7 (receiver RX), where other pins are used for transmitting and receiving in other family members. Logic levels in the standard RS-232C are defined as logic zero at 3 V to 25 V and logic one at -3 V and -25 V. [17, 29, 34] Dept. of EE, Qatar Univ. P a g e 88

104 Figure (5.6): Serial UART (RS-232) Communication Circuit [29] 5.7. Design Constraints Microcontroller Constraints The microcontroller normal operation temperature capacity should be high, so a PIC18F4520 have been selected that have normal operation temperature capacity of 85 o Serial USART Constraints Microcontroller voltage level is 5 V which is different from the computer voltage level so MAX232 chip was used to shift the voltage level of the microcontroller to a level of voltage that the computer understands Dept. of EE, Qatar Univ. P a g e 89

105 5.8. Digital Domain of the Power System Stabilizer The input signal to the microcontroller is the sampled signal of the deviation in rotor speed which comes from the MATLAB. The MATLAB/Simulink model is shown in Figure (4.3). Since the PSS transfer function is in the frequency domain so it needs to be converted to digital domain. Bilinear Transformation (Tustin Transformation) will be used to transfer the PSS transfer function from the s domain to z domain. Before doing the transformation, the region of stability should be determined first using the Laplace transform of a discrete-time (digital domain) system, which is: (5.4) where T is the sampling period. It is known that the region of stability on the s-plane is in the left half of it, therefore the region of stability on the z-domain is evaluated using the definition by letting s in Equation (5.4) equals to : (5.5) (5.6) When mapping each point in the s-plane into the z-plane, three different cases are faced. The first case is when is positive or in the right half of the s-plane. From Equation (5.6), the magnitudes of the mapped points are. Therefore, the points in the right half of the s- plane are mapped outside the unit circle of the z-plane. By looking at the second case where the points are mapped on the j-axis, the points have zero values of which yield to points on the z-plane with magnitudes equal to 1, the unit circle. Dept. of EE, Qatar Univ. P a g e 90

106 Therefore the points that exists on the j-axis of the s-plane are mapped into points on the unit circle of the z-plane. The third case is where the points are on the left half of the s-plane. This case yields to negative values of, which are inturns mapped into the inside of the unit circle of the z-plane. We conclude from these cases that a digital control system is: Stable if all poles of the closedloop transfer function are inside the unit circle of the z-plane, Unstable if at least one pole is outside the unit circle, and Marginally stable if at least one pole are on the unit circle and all other poles are inside the unit circle. [9, 30-32] After determining the region of stability in the z-domain, the transformation from s-domain to z-domain is obtained as follows: Using Equation (5.4): (5.7) Writing Equation (5.7) in terms of z yields to: (5.8) The PSS loop includes two transfer functions multiplied by a gain which is K PSS, as it is shown in Figure (4.2). Transforming the Phase Compensator transfer function to the z-domain gives: Dept. of EE, Qatar Univ. P a g e 91

107 (5.9) where a = T 1 and b = T 2. Simplifying the equation: (5.10) where,,, and. Multiplying by gives: (5.11) Now transforming the washout transfer function and letting T w = c: Dept. of EE, Qatar Univ. P a g e 92

108 (5.12) where,, and. Multiplying Equation (5.11) by (5.12) then by the gain K PSS to get the open-loop transfer function: Multiplying both sides by gives: (5.13) And after substituting Equation (5.13) by : (5.14) From Equation (5.14): (5.15) It should be noted that when multiplying y[n] or x[n] by z -m it becomes y[n-m] or x[n-m]. Therefore after solving for y[n], Equation (5.15) becomes: Dept. of EE, Qatar Univ. P a g e 93

109 (5.16) Equation (5.16) is the digital PSS difference Equation (Function), which can be converted to C language code and then used in a for loop to perform the function of the digital PSS. The selection of the sampling time is the key for matching the s-domain PSS to the z- domain PSS frequency response. According to the literature [35], Astrom and Wittenmart (1984) have developed a guideline for selecting the sampling interval. According to them the value of T in seconds should be in the range of 0.15/ to 0.5/, where is the zero db frequency (rad/s) of the magnitude frequency response curve for the cascaded analog compensator. [9, 30 32, 35] Bode plot should be drawn in order to determine the zero db frequency of the cascaded connection between the PSS and the SMIB power system. The following steps shows how MATLAB can be used as a tool to get the open-loop of the system using the Simulink. The output and the input of the SMIB power system have been identified, using output port y and input port u as shown in Figure (5.7) (highlighted in blue), and then it should be saved as Simulink file (in this project it was saved as under the name Open_Loop ) Dept. of EE, Qatar Univ. P a g e 94

110 0 Clock V ref u 1 t To Workspace (Time ) Voltage Regulator -Exciter Delta - Eq' KA K3 K2 TA.s+1 Delta - Efd (K3.*TDP )s+1 Delta - Te Constant -k2 Delta - Vt delta -Vt Delta _Vt To Workspace (Delta Vt ) Constant -k6 K6 To Workspace (Delta Te ) Delta _Te delta -Te Delta - Ts k4 K4 Delta - Tm Delta - Td Rotating Mass 1 (2.*H)s Damping Torque Coffiecent -KD KD Constant -k1 K1 Constant -k5 K5 Delta - Omega Wb Base Freq Delta _Omega To Workspace (Delta Omega ) Delta Omega y 1 1 s Delta _delta To Workspace (Delta delta ) delta -delta Delta - delta Design of Power System Stabilizer Based on Figure (5.7): SMIB Power System Simulink Model Input & Output Ports Highlighted Dept. of EE, Qatar Univ. P a g e 95

111 The SMIB power system open loop transfer function has been computed at nominal operating point using the following MATLAB code. [A,B,C,D]=linmod('Open_Loop'); % Obtains state-space linear models from Simulink model [num_o,den_o]=ss2tf(a,b,c,d); % to get the transfer function from the statespace model. The open-loop transfer function of the SMIB power system is computed as (5.17) While the PSS open loop transfer function can be computed as (5.18) (5.19) So the overall open-loop transfer function of the cascaded connection between the PSS and the SMIB power system (5.20) (5.21) Dept. of EE, Qatar Univ. P a g e 96

112 Phase (deg) Magnitude (db) Design of Power System Stabilizer Based on The plotting of the cascaded open-loop connection between PSS and SMIB power system is done using the following MATLAB code. >> num_ov = [( *10^-14) ( *10^-12) ( ) ( ) ( *10^-11) 0]; >> den_ov = [(0.75) ( ) ( ) ( ) ( ) ( ) (7979.1)]; >> sys = tf(num_ov,den_ov); % to create a system model out of the transfer function numerator and denominator >> bodeplot(sys) % to plot the bode plot of the system The bode plot of the cascaded open-loop connection between PSS and SMIB power system is shown in Figure (5.8) Bode Diagram System: sys Frequency (rad/sec): 8.73 Magnitude (db): Frequency (rad/sec) Figure (5.8): Bode plot of the Cascaded Open-Loop between PSS & SMIB Power System Dept. of EE, Qatar Univ. P a g e 97

113 angle (rad) magnitude Design of Power System Stabilizer Based on According the bode plot in Figure (5.8), it is observed the zero db frequency is approximately equal to 8.73 rad/s, so the limits of the sampling interval are and, so the sampling frequency should between Hz and Hz. As mentioned earlier that the sampling frequency or the sampling time is the key for matching the s-domain PSS to the z-domain PSS frequency response, since the range of sampling frequency has been determined it is important to see the effect of sampling frequency on the frequency response of the system and to choose the best sampling frequency based on closest frequency response of digital PSS to the s-domain PSS frequency response. Figure (5.9) shows the effect of sampling frequency on the frequency response of the digital PSS, it is observed that as the sampling frequency increases in the range of the sampling frequency mentioned above, the frequency response of the digital filter gets closer to the s- domain filter z-domain at 25 Hz 4 z-domain at 35 Hz z-domain at 45 Hz 2 z-domain at 55 Hz s-domain frequency (Hz) z-domain at 25 Hz z-domain at 35 Hz z-domain at 45 Hz z-domain at 55 Hz s-domain frequency (Hz) Figure (5.9): Effect of Sampling Frequency on the Frequency Response of the Digital PSS Dept. of EE, Qatar Univ. P a g e 98

114 In our project the sampling frequency f s have been selected as 55 Hz, and this is because at this sampling frequency, the digital PSS has the closest frequency response the s-domain PSS. In order to convert the digital PSS transfer function into C-code which can be implemented in microcontroller to perform the digital PSS transfer function, the selected sampling time, which is T= = = sec, should be substituted in the difference equation (Equation 5.16) as shown in Equation 5.22 (5.22) This difference function can be transformed into the following C code, y = *x *xn *xn *yn *yn2; xn2 = xn1; xn1 = x; yn2 = yn1; yn1 = y; Where x is x[n], xn1 is x[n-1], and xn2 is x[n-2] and same applies for y variable. This code can be implemented on microcontroller using C language programming s-domain to z-domain (Digital Domain) Transformation Steps in MATLAB In order to transfer the PSS transfer function from s-domain to z-domain in MATLAB, the following steps should be followed. 1- The PSS transfer function of Equation (4.1) should be rewritten as (5.23) Two variables are defined as num and den as shown below, Dept. of EE, Qatar Univ. P a g e 99

115 Num = Kpss.*[(T1.*Tw) (Tw) 0]; Den = [(T2.*Tw) (T2+Tw) 1]; 2- Specifying the sampling frequency as for the bilinear transformation. 3- The nominator numd and denominator dend coefficients of the digital PSS transfer function (z-domain) can be formed using: [numd,dend] = bilinear(num,den,55); % to convert the s-domain transfer function to z-domain transfer function with sampling frequency of 55 Hz The digital domain of the PSS transfer function is now specified by the numd and dend obtained from step 3. Before going a further step in the implementation, the stability of the digital transfer function needs to be checked. This is done using a MATLAB simple command or function isstable( ). this function take the structure of the digital filter, numerator and denominator and it checks the poles of the digital transfer function if they are inside the unit circle or not. It returns the value 1 if the filter is stable or 0 if the filter is not stable. The last step is to check the frequency response of the s-domain transfer function and z- domain digital transfer function. Using freqs( ) function in MATLAB to get the frequency response of the s-domain transfer function and freqz( ) to get the frequency response of the z- domain transfer function. In order to check correctness of the designed Digital PSS (shown in the previous section) we will apply the steps mentioned above to the designed s-domain PSS mentioned in the previous chapter. Using the PSS parameters which is mentioned in Section 4.4: (5.24) Dept. of EE, Qatar Univ. P a g e 100

116 Applying Equation (5.24) it in MATLAB m-file to transfer it to z-domain as shown below: %PSS Parameters Kpss = 1.111; Tw = 10; T1 = 0.75; T2 = 0.075; Num = Kpss.*[(T1.*Tw) (Tw) 0]; Den = [(T2.*Tw) (T2+Tw) 1]; [numd,dend] = bilinear(num,den,55) numd dend The output on the MATLAB work space is >> numd numd = >> dend dend = The above result confirms the digital PSS transfer function parameters calculation mentioned in the previous section. Now to check the stability of the designed PSS, the following MATLAB code is applied. Dept. of EE, Qatar Univ. P a g e 101

117 Hd = dfilt.df2(numd,dend); % returns a discrete-time filter with a STRUCTURE of type Direct-form II isstable(hd) % ISSTABLE(Hd) returns 1 if filter Hd is stable, and 0 otherwise The output on the MATLAB work space is >> isstable(hd) % to check if the system is stable or not. ans = 1 So this confirms the stability of the designed digital PSS. In order to plot the frequency response of the designed digital PSS and compare it to the designed s-domain PSS, the following MATLAB code is applied. s = tf(num,den); % to create an s-domain transfer func. Model (obj) to the designed PSS x = 1:1:180; y = freqs(num,den,x); % to plot the s-domain frequency response of the s-domain PSS. [h,w] = freqz(numd,dend,55); % to plot the z-domain frequency response of the s-domain PSS. subplot(2,1,1) plot(w*(180/pi),abs(h),x,abs(y),':r') xlabel('frequency (Hz)'); ylabel('magnitude'); grid; legend('z-domain','s-domain','location','northeast'); subplot(2,1,2) plot(w*(180/pi),angle(h),x,angle(y),':r') xlabel('frequency (Hz)'); ylabel('angle (rad)'); grid; legend('z-domain','s-domain','northwest'); Figure (5.10) shows the frequency response of the designed digital PSS compared to the s- domain PSS. Dept. of EE, Qatar Univ. P a g e 102

118 angle (rad) magnitude Design of Power System Stabilizer Based on z-domain s-domain frequency (Hz) 1 z-domain s-domain frequency (Hz) Figure (5.10): Comparison between the Frequency Response of the Designed Digital (z-domain) PSS and the Response of the s-domain PSS As shown in Figure (5.10), the designed Digital PSS frequency response is almost identical to the frequency response of the s-domain designed PSS, which proves the effectiveness of the designed digital PSS Simulation of Digital PSS using Simulink In order to simulate the designed digital PSS, a digital filter block in Simulink is used to implement the z-domain transfer function with the numerator numd and denominator dend obtained from the bilinear transformation, as shown in Figure (5.11). Dept. of EE, Qatar Univ. P a g e 103

119 0 Clock V ref To Workspace (Time ) k4 K4 To Workspace (Delta Te ) Delta _Te delta -Te Voltage Regulator -Exciter Delta - Eq' KA K3 K2 TA.s+1 Delta - Efd (K3.*TDP )s+1 Delta - Te Constant -k2 Delta - Vt Delta - Ts delta -Vt K6 Constant -k6 Delta _Vt To Workspace (Delta Vt ) Delta - Vs Digital Filter DFILT : Hd Zero -Order Hold Delta - Omega Delta - Tm Rotating Mass 1 Wb (2.*H)s Base Freq Delta - Td Damping Torque Coffiecent -KD KD Constant -k1 K1 Constant -k5 K5 Delta _Omega To Workspace (Delta Omega ) Delta Omega 1 s Delta _delta To Workspace (Delta delta ) delta -delta Delta - delta t Figure (5.11): MATLAB/Simulink Model of the SMIB Power System Including Simulated Digital (z-domain) PSS Power System Dept. of EE, Qatar Univ. P a g e 104

120 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on The output response of the system model with the digital filter gives the same response obtained from the s-domain transfer function with a slight mismatch due to bilinear transformation as shown in Figure (5.12) Rotor Speed Deviation z-domain Simulated PSS s-domain PSS Time (sec) Figure (5.12): Rotor Speed Deviation Response Comparison of Digital (Simulated) PSS & s- domain PSS at Nominal Operating Point Under Change in of 1% It is observed in Figure (5.12) that there is a high level of agreement between the digital (simulated) PSS and s-domain PSS SMIB power system rotor speed deviation responses. Dept. of EE, Qatar Univ. P a g e 105

121 5.11. MATLAB and Microcontroller Interfacing The interfacing between the MATLAB and the microcontroller is done using serial communication. It is performed using serial COM port1 in the computer and TX (RC6) and RX (RC7) pins in the microcontroller. Because of the difference in the voltage level between the microcontroller and the computer, MAX232 is used to match the voltage level between the microcontroller (0 5V) and the computer (-10 10V). The overall system is represented in Figure (5.13). Figure (5.13): MATLAB (Laptop) & PIC18F4520 Microcontroller Interfacing Circuit [29] Dept. of EE, Qatar Univ. P a g e 106

122 Microcontroller Programming There are many programming languages that could be used to program the microcontroller such as C, basic and assembly. In this project C language has been used to program the microcontroller, and it has been chosen because of the advantage of these languages which is the simplicity of program writing. In this project the microcontroller C code had two main functions, first function is microcontroller interfacing with MATLAB/Simulink and the other function it acts as digital PSS that will give the same response as time domain PSS which was simulated in Chapter 4. Figure (5.14) shows the microcontroller code flow chart, while the C code of the microcontroller is shown below the figure. Dept. of EE, Qatar Univ. P a g e 107

123 Start Variable Declaration float m; float xn1=0.0; float xn2=0.0; float yn1=0.0; float yn2=0.0; float y; int i; int j; float rec; char txt[25]; char txt2[25]; char *res; UART1_Write_Text(res); //Send the Data from UART Module 1 to Laptop (Simulink) Beginning of Main Function Void Main () ADCON1 = 0x07; // Configure AN pins as digital CCP1CON = 0x00; // Disable Comparator 1 CCP2CON = 0x00; // Disable Comparator 2 res = strcat(txt2, "\r"); //add \r terminator to (txt2) array and save it in (res) variable FloatToStr(y,txt2); //convert (y) to string (txt2) array for(i=0;i<25;i++) for(i=0;i<25;i++) Digital PSS Difference Function Code y= *m *xn *xn *yn *yn2; xn2=xn1; xn1=m; yn2=yn1; yn1=y; txt[i]="\0"; //clear txt array (fill with null character) txt2[i]="\0"; //clear txt2 array (fill with null character) txt[i]="\0"; //clear txt array (fill with null character) txt2[i]="\0"; //clear txt2 array (fill with null character) m=atof(txt); //convert txt from string to float No i = 25 i = 25 No UART1_Read_Text(txt, "\r", 255); //Read the Data from UART Module 1 and save it into txt string array Yes Yes Yes UART1_Init(19200); // Initialize UART module at bps Delay_ms(500); // Wait for UART module to stabilize i= 0; While (1) if (UART1_Data_Ready()==1) //if the microcontroller received data No Figure (5.14): Microcontroller C-Code Flowchart Dept. of EE, Qatar Univ. P a g e 108

124 // Declaration of variables float m; float xn1 = 0.0; float xn2 = 0.0; float yn1 = 0.0; float yn2 = 0.0; float y; int i; int j; float rec; char txt[25]; char txt2[25]; char *res; void main() { ADCON1 = 0x07; // Configure AN pins as digital CCP1CON = 0x00; // Disable comparator module 1 CCP2CON = 0x00; // Disable comparator module 2 for(i=0;i<25;i++) { txt[i]="\0"; txt2[i]="\0"; } UART1_Init(19200); Delay_ms(500); i=0; // Clear string arrays (txt) & (txt2) // Initialize UART module at bps // Wait for UART module to stabilize while (1) { if (UART1_Data_Ready()==1) // If data is present on the receive buffer { UART1_Read_Text(txt, "\r", 255); // read data until terminator \r if found //======================================= // Beginning Digital PSS Code //======================================= m = atof(txt); // Convert and save txt string array of received data to float variable m y = *m *xn *xn *yn *yn2; xn2 = xn1; xn1 = m; yn2 = yn1; yn1 = y; FloatToStr(y,txt2); // Convert y float PSS output data to string array txt2 //======================================= // End of Calculations //======================================= Dept. of EE, Qatar Univ. P a g e 109

125 res = strcat(txt2, "\r"); // Add terminator \r at the end of the PSS string output data and save it in variable res UART1_Write_Text(res); // send res to the MATLAB in a form of string array } for(i=0;i<25;i++) // Clear string arrays (txt) & (txt2) { txt[i]="\0"; txt2[i]="\0"; } } } In this project, MikroC Pro have been used for coding the microcontroller using C language, the advantage of this compiler it provides a library of commands or functions that is easy to use, and it facilitates the coding of microcontroller interaction with other system peripherals (i.e UART module, Analogue to digital converter, LCD, etc ). First of all we started our code by configuring some PIC18F4520 microcontroller special function registers (SFRS), ADCON1 = 0x07 was used to configure AN pins to digital since serial communication is based on digital communication, also the comparator modules have been disabled using CCP1CON = 0x00 and CCP2CON = 0x00 commands. As shown in the above code to interface with MATLAB/Simulink one UART (UART1) module has been used, and UART1_Init(19200) command was used to initializes hardware UART1 module with the desired baud rate which is bps. Then UART1_Data_Ready() was used to test if data in receive buffer is ready for reading. After that UART1_Read_Text(txt, "\r", 255) was used to read characters received via UART until the \r terminator is detected. The read sequence is stored in the string array (txt), where 255 parameter is to allow the microprocessor keeps searching for \r terminator continuously. UART1_Write_Text(res) was used to sends string (res) via UART to MATLAB/Simulink, where (res) is the string array that contains the result of Digital PSS difference function ended by \r terminator. Dept. of EE, Qatar Univ. P a g e 110

126 Digital PSS difference function has been applied in the microcontroller C code using normal multiplication and addition mathematical operations, besides some of the C commands has been used such as atof(txt) to convert the received data from string type to float type, moreover FloatToStr(y,txt2) has been used to convert the float output of the digital PSS difference function (y) to (txt2) string array, which will be sent back to the MATLAB/Simulink Simulink Model of the SMIB Power System with MCU PSS To communicate between MATLAB and the microcontroller via the serial port it is necessary to create a serial port object (which is named scom ) in MATLAB and specify the port properties as in the microcontroller, Baud Rate, Data Bit, Parity Bit, stop bit and Hand- Shaking. Then the serial port is opened using fopen(serial object) function. Consequently, the communication channel is opened and ready to send and receive data. fprintf ( ) and fscanf( ) functions are used to send and receive data respectively. Since the microcontroller sends data as strings, so the function srt2num( ) is used to convert the received string to number. Finally, the serial port is closed using fclose(serial object) function. The serial communications used in the interfacing has the flowing characteristics: Data bit: 8-bit Baud rate: bps Parity: none Stop Bit: 1 Handshaking: none In this project, a MATLAB function (shown in the code block below) has been written that is used as MATLAB function block in the Simulink model that will act as digital PSS in the simulated SMIB power system. The main role of this MATLAB function is: 1- Defining a serial port object; 2- Opening the serial port; 3- Converting data to string format; Dept. of EE, Qatar Univ. P a g e 111

127 4- Sending the data to the digital PSS (microcontroller); 5- Receiving the data from the digital PSS (microcontroller); 6- Converting the data from string type to numbers. function y = ssr(u) scom=serial('com1','baudrate',19200,'databits',8,'timeout',30,'terminator',13); %define a serial communication object fopen(scom); % Open the serial port s = num2str(u, '%1.10f'); fprintf(scom,'%s\r',s); % Send u to the MCU r = fscanf(scom); % receive from the MCU and store it in s fclose(scom); % close the serial port y = str2num(r); % Convert string s to number y end As shown in Figure (5.15), the time domain PSS have been replaced with Zero Order Hold and MATLAB Function Simulink block, and these two blocks will act as digital PSS to the SMIB power system. Zero Order Hold Simulink block is used to sample the frequency simulated signal of the Simulink with 1/f s sampling time, which is equal to seconds. Moreover, the above MATLAB function has been used to interface with the digital PSS. Dept. of EE, Qatar Univ. P a g e 112

128 0 Clock V ref To Workspace (Time ) k4 K4 To Workspace (Delta Te ) Delta _Te delta -Te Voltage Regulator -Exciter Delta - Eq' KA K3 K2 TA.s+1 Delta - Efd (K3.*TDP )s+1 Delta - Te Constant -k2 Delta - Vt Delta - Ts delta -Vt K6 Constant -k6 Delta _Vt To Workspace (Delta Vt ) Delta - Vs Digital PSS MATLAB Function Zero -Order Hold Delta - Omega Delta - Tm Rotating Mass 1 Wb (2.*H)s Base Freq Delta - Td Damping Torque Coffiecent -KD KD Constant -k1 K1 Constant -k5 K5 Delta _Omega To Workspace (Delta Omega ) Delta Omega 1 s Delta _delta To Workspace (Delta delta ) delta -delta Delta - delta t Figure (5.15): MATLAB/Simulink Model of the SMIB Power System including Digital (Microcontroller) PSS Power System Dept. of EE, Qatar Univ. P a g e 113

129 5.12. Simulations of the SMIB Power System with MCU PSS As a final stage, a microcontroller based digital PSS has been implemented and it is had successfully interfaced with MATLAB/Simulink, moreover it has also stabilized the simulated SMIB power system at different operating points. Figure (5.16) shows photos of the hardware of the designed microcontroller based digital PSS interfaced with MATLAB/Simulink workstation. Figure (5.16): Photos from the Microcontroller Based Digital PSS Hardware Dept. of EE, Qatar Univ. P a g e 114

130 Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on As shown in Figure (5.17) the time domain simulation of the SMIB power system including the digital (z-domain) PSS has been compared to the time domain simulations of the SMIB power including s-domain PSS at nominal operating point. Moreover, the robustness of the designed digital PSS has been evaluated by comparing the SMIB power system time domain response with digital PSS and with s-domain PSS, at different operating points (mentioned in Section 4.6) as shown in Figures (5.18) (5.19) Rotor Speed Deviation Digital PSS s-domain PSS Time (sec) Figure (5.17): Rotor Speed Deviation Response Comparison of Digital (Microcontroller) PSS & s-domain PSS at Nominal Operating Point Under Change in of 1% It is observed in Figure (5.17) that there is a high level of agreement between the digital (Microcontroller) PSS and s-domain PSS SMIB power system rotor speed deviation responses, it is also observed that the s-domain PSS response has more damping and that is normal, because it Dept. of EE, Qatar Univ. P a g e 115

131 Deviation of PSS Stabilizing Signal Voltage (p.u) Design of Power System Stabilizer Based on is continuous time so more samples from the frequency deviation signal are processed, and thus more stabilizing signals samples are introduced to the power system. 1.5 x 10-3 PSS Stabilizing Signal Voltage Deviation Response Digital PSS s-domain PSS Time (sec) Figure (5.18): PSS Stabilizing Signal at nominal operating point under change in T m of 1% It s observed from Figure (5.18) that both the stabilizing signal of the s-domain PSS and the z-domain PSS have a high level of agreement and this ensures the effectiveness of the implemented microcontroller digital PSS. Dept. of EE, Qatar Univ. P a g e 116

132 Deviation of Rotor Speed (Rad/s) Deviation of Rotor Speed (Rad/s) Design of Power System Stabilizer Based on Rotor Speed Deviation Digital PSS s-domain PSS Rotor Speed Deviation Digital PSS s-domain PSS Time (sec) Time (sec) 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% It is observed in Figure (5.19) that the Digital (Microcontroller) PSS has also stabilized the system at the unstable operating point. It is also observed from the figure that SMIB power system response of Digital PSS and s-domain PSS were almost identical, which proves the effectiveness of the designed Digital PSS. As shown in Figure (5.20), the SMIB power system including the Digital (Microcontroller) PSS is stable at higher exciter gain unstable operating point. From Figures (5.17)-(5.20), it is concluded that the designed Digital (Microcontroller) PSS is robust at different operating points. Moreover, there is a high level of agreement between the Digital (Microcontroller) PSS compared to s-domain PSS SMIB Power System rotor speed deviation responses, and this proves the effectiveness of the designed Digital (Microcontroller) PSS. Dept. of EE, Qatar Univ. P a g e 117

133 CHAPTER 6: CONCLUSIONS AND FUTURE WORK 6.1. Conclusions The developed state space model and Simulink model of the SMIB power system have been used to evaluate the stability of the system. A robust PSS has been designed to improve the system stability under different operating points. Eigenvalues analysis, damping torque and time-domain simulations have been used to evaluate stability of the power system at different operating points The s-domain PSS have been transformed to z-domain using bilinear (Tustin) transformation The digital (z-domain) PSS have been simulated using Simulink. MATLAB/Simulink have been interfaced with microcontroller using serial UART interfacing. Digital PSS have been implemented on microcontroller The SMIB power system stability with the designed microcontroller PSS have been evaluated using time domain simulation technique The robustness PSS based microcontroller have also been evaluated at different operating points Future Work Design of Fuzzy logic PSS based microcontroller. Implement the designed PSS based microcontroller to multi-machine power systems. Dept. of EE, Qatar Univ. P a g e 118

134 References [1] P.W.Peter and M.A.Pai, Power System Dynamics and Stability, Prentice-Hall Press [2] Y.L. Abdel-Magid, M.A. Abido, and A.H. Mantawy, "Robust Tuning of Power System Stabilizers in Multimachine Power Systems", IEEE Transactions on Power Systems, Vol. 15, No. 2, May [3] M. Klein, G. J. Rogers, and P. Kundur, A Fundamental Study of Inter-area Oscillations in Power Systems, 91 WM PWRS. [4] D. C. Lee, R. E. Beaulieu and J. R. Service, A Power Stabilizer Using Speed and Electrical Power Inputs Design and Field Experience, IEEE Transactions on power apparatus and systems, Vol. PAS-100, No.9, September [5] R. V. Larsen and D. A. Swann, Applying Power System Stabilizers, In Three Parts, IEEE Transactions on power apparatus and systems, Vol. PAS-100, No.6, June [6] K. R. Padiyar, Power System Dynamics Stability and Control, John Wiley & Sons Press [7] P. M. Anderson, and A. A. Fouad, Power System Control and Stability, IEEE Press [8] C. L. Chen and Y.Y. Hsu, Coordinated Synthesis of Multi-machine Power System Stabilizer Using an Efficient Decentralized Modal Control Algorithm, IEEE Transactions on Power Systems, Vol.2, No.3, August [9] K. Ogata, Modern Control Engineering, Prentice-Hall [10] P. Kundur, Power System Stability and Control, McGraw-Hill Press [11] F. P. Demello and C. Concordia, Concepts of Synchronous Machine Stability as Effected by Excitation Control, IEEE Transactions on power apparatus and systems,vol.pas-88, No.4,April Dept. of EE, Qatar Univ. P a g e 119

135 [12] V.Arcidiacono, E.Ferrari, R.Marconato, J.Dos Ghali, D.Grandez Evaluation and Improvement of Electromechanical Oscillation Damping by Means of Eigenvalue- Eigenvector - Analysis & practical results in the central peru power system, IEEE Transactions on power apparatus and systems, Vol PAS-100,No.1, Jan [13] E.A. Feilat, Performance Comparison of Adaptive Estimation Techniques for Power System Small-Signal Stability Assessment, Proceedings of ICCCP 2009, Sultan Qaboos University, Feb [14] H. A. Moussa, Y. Yu, Optimal Power System Stabilization Through Excitation and/or Governor Control, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-91, pp , [15] R. J. Fleming and J. Sun, An Optimal Multivariable Stabilizer For a Multi-Machine Plant, IEEE Transactions on Energy Conversion, Vol.5, No.1,March [16] A. Ghosh, G. Ledwich, O. P. Malik and G. S. Hope, Power System Stabilizer Based on Adaptive Control Techniques, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-103, No.8, August [17] M. Verle, PIC Microcontrollers, mikroelektronika [18] S. Cheng, Y. S. Chow, O. P. Malik and G. S. Hope, An Adaptive Synchronous Machine Stabilizer, IEEE Transactions on Power Apparatus and Systems, Vol. PWRS-1, No.3, August [19] V. Vittal, N. Bhatia, A. A. Fouad, Analysis of Inter-area Mode Phenomenon in Power Systems Following Large Disturbances., IEEE Transactions on Power Systems, Vol.6, No.4, November [20] A. R. Messina, J. M. Ramirez, J. M. Canedo, An Investigation on The Use of Power System Stabilizers for Damping Inter-area Oscillations in Longitudinal Power Systems., IEEE Transactions on Power Systems, Vol.13, No.2, May Dept. of EE, Qatar Univ. P a g e 120

136 [21] C.M.Ong, Dynamic Simulation of Electric Machinery Using MATLAB /SIMULINK, Prentice-Hall Press [22] D.S. Watkins, "Fundamentals of Matrix Computations", John Wiley and Sons, [23] S.M. Bamasak, "FACTS-Based Stabilizers for power system stability enhancement", Msc Thesis, King Fahd University of Petroleum & Minerals, May [24] Qureshy, Farooq Ahmad, "Steady State Stability Analysis of AC-DC Power Systems" (1985). Open Dissertations and Theses. Paper [25] Wasynczuk, O., & Decarlo, R. A. (1981). The Component Connection Model and Structure Preserving Model Order Reduction. Automatica, Vol. 17, No.4, [26] Y.L. Abdel-Magid, M.A. Abido, S. Al-Baiyat, and A.H. Mantawy, "Simultaneous Stabilization of Multimachine Power Systems via Genetic Algorithms", IEEE Transaction on Power Systems, Volume 14, No. 4, November [27] J. H. Chow, G. E. Boukarim, and A. Murdoch, Power System Stabilizers as Undergraduate Control Design Projects, IEEE Transactions on Power Systems, Special Issue on Power Engineering Education, vol. 19, pp , [28] L. Vanfretti, Modeling and simulation of the synchronous machine and its operation in power systems, Electrical Engineering Degree - Licenciatura Thesis, Universidad de San Carlos de Guatemala, May [29] M.Verle, PIC Microcontrollers - Programming in C, mikroelektronika, [30] N.S. Nise, Control Systems Engineering, John Wiley & Sons, [31] D. Ibrahim, Microcontroller Based Applied Digital Control, John Wiley & Sons, [32] C. L. Phillips & H. T. Nagle, Digital Control System Analysis and Design, Prentice-Hall Press, Dept. of EE, Qatar Univ. P a g e 121

137 [33] S.H. Lee, Y.F. Li and V. Kapila, "Development of a Matlab-Based Graphical User Interface Environment for PIC Microcontroller Projects", Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition, Session 2220, [34] B. Brey, Applying PIC18 Microcontrollers: Architecture, Programming, and Interfacing using C and Assembly, Prentice-Hall Press, [35] K. J. Astrom & B. Wittenmark, Computer Controller Systems, Longman Higher Education, [36] IEEE Std 1110, "IEEE Guide for Synchronous Generator Modeling Practices and Application in Power System Stability Analysis", [37] IEEE Standard Definitions for Excitation Systems for Syn-chronous Machines, IEEE Standard 421.1, [38] "Approved IEEE Draft Standard Definitions for Excitation Systems for Synchronous Machines (Revision of IEEE ), IEEE Approved Std P421.1/D7, Nov 2006, vol. no [39] "IEEE Recommended Practice for Excitation System Models for Power System Stability Studies, IEEE Std (Revision of IEEE Std ), vol. no. pp.0_1-85, 2006 Dept. of EE, Qatar Univ. P a g e 122

138 Appendix A: PIC Microcontrollers Comparison The following table shows a comparison between PIC microcontrollers Families features. Table (A-1): Comparison Between PIC Microcontrollers Families Features [17] Dept. of EE, Qatar Univ. P a g e A- 1