# CHAPTER 2 DYNAMIC STABILITY MODEL OF THE POWER SYSTEM

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 20 CHAPTER 2 DYNAMIC STABILITY MODEL OF THE POWER SYSTEM 2. GENERAL Dynamic stability of a power system is concerned with the dynamic behavior of the system under small perturbations around an operating condition and more specifically it is a phenomena of slow and poorly damped or sustained or even diverging power oscillations which are essentially due to varying system loads and ill controlled controllers of the system. Computer analysis of this problem requires mathematical models which simulate as accurately as the behavior of physical system but at the same time not very complex to handle. This chapter presents the development of the mathematical model for the dynamic stability analysis of Single Machine Infinite Bus System (SMIB) and Multi- machine power system. 2.2 SIMPLIFIED LINEAR MODEL FOR SMIB SYSTEM In stability analysis, the mathematical model is used for dynamic analysis of power systems Assumptions The following assumptions are made for the development of simplified linear model of SMIB system:

2 2. Damper windings both in the d and q axes are neglected. 2. Armature resistance of the machine is neglected. 3. Excitation system is represented by a single time constant. 4. Balanced conditions are assumed and saturation effects are neglected Classical Machine Model In the classical methods of analysis, the simplified model or classical model of the generator is used (Kundur 994). Here, the machine is modeled by an equivalent voltage source behind impedance connected to an infinite-bus as shown in Figure 2.. Infinite Bus An infinite bus is a source of invariable frequency and voltage (both in magnitude and angle). A major bus of a power system of very large capacity compared to the rating of the machine under consideration is approximately an infinite bus. x e Figure 2. One-line diagram of SMIB The state space classical machine model is shown in Figure 2.2.

3 22 K s Figure 2.2 Classical Machine Model The state equations of the classical model are given in equation (2.): p( ω ) = Tm K S D 2H δ ω p( δ ) = ω ω (2.) 0 State vector T x = ( ω δ ) (2.2) And when the effect of flux linkage is included, three states are used to model the generator: ω, δ and E q '. The state equations are given in equation (2.3) as follows: T K K D p ω= - δ- E - ω τ τ τ τ m 2 ' q j j j j p( δ ) = ω ω 0 - K p E = E + E - δ (2.3) ' ' 4 q ' q ' FD ' Kτ 3 do τdo τdo where τ j = 2H, H is the inertia constant.

4 23 State Vector of the SMIB system including the effect of flux linkage is given by equation (2.4) t x [ E' q] = ω δ (2.4) where the variables are E q ' ω δ - quadrature axis component of voltage behind transient reactance - angular velocity of rotor - rotor angle in radians K to K 6 is the Heffron Philips constants (Padiyar 2002). 2.3 EXCITATION SYSTEM REPRESENTATION The excitation system model considered is the simplified form of STA model shown in Figure 2.3. A high exciter gain, without derivative feedback, is used. By inspection of Figure 2.3, the state space equations can be written as, V V t KA + st A E FD Figure 2.3 Excitation System Representation p E FD = -/T A (K A V t + E FD ) (2.5) with T R is neglected, V ref =constant. And V t = K 5 δ + K 6 E q '

5 24 where E FD - Equivalent stator emf proportional to field voltage K A - Gain of the Exciter T A - Time constant of the exciter T R V t - Terminal Voltage Transuder Time Constant - Terminal voltage of the Synchronous machine V ref - Reference voltage of the Synchronous machine Combining the Equations (2.3) with the exciter equation (2.5), the complete state space description of SMIB system including exciter is given in equation (2.6). T K K D p ω= - δ- E - ω τ τ τ τ m 2 ' q j j j j p δ = ω0 ω - K p E = E + E - δ ' ' 4 q ' q ' FD ' Kτ 3 do τdo τdo pe FD = -/T A (K A K 5 δ + K A K 6 E q ' + E FD ) (2.6) The state vector is thus defined by Equation (2.7): t x [ E' q E FD] = ω δ (2.7) 2.4 SMIB SYSTEM REPRESENTATION WITH CPSS The block diagram of the CPSS is shown in Figure 2.4. The state equations for the same can be written as follows. p V 2 = K PSS p ω (/T w ) V 2 (2.8) p V s = (T /T 2 ) p V 2 + (/T 2 ) V 2 (/T 2 ) V s (2.9)

6 25 where K PSS - CPSS gain T, T 2 - Phase compensator time constants T w - Wash out time constant CPSS V t V s Figure 2.4 CPSS Representation State vector of the synchronous machine model including PSS is given by equation (2.0): T x = [ E q' EFD V2 V s] ω δ (2.0) The block diagram of simplified linear model of a synchronous machine connected to an infinite bus with exciter and PSS is shown in Figure 2.5. V t Conventional Power System Stabilizer Figure 2.5 State Space Model of SMIB system representation with CPSS

7 DYNAMIC STABILITY MODEL OF MULTI MACHINE POWER SYSTEM In stability analysis of a multi-machine system, modelling of all the machines in a more detailed manner is exceedingly complex in view of the large number of synchronous machines to be simulated. Therefore simplifying assumptions and approximations are usually made in modelling the system. In this thesis two axis model is used for all machines in the sample system taken for investigation Assumptions Made In this work the synchronous machine is modeled using the twoaxis model (Anderson and Fouad 2003). In the two-axis model the transient effects are accounted for, while the sub transient effects are neglected. The transient effects are dominated by the rotor circuits, which are the field circuit in d-axis and an equivalent circuit in the q-axis formed by the solid rotor. The amortisseur winding effects are neglected. An additional assumption made in this model is that in stator voltage equations the terms pλ d and pλ q are negligible compared to the speed voltage terms and that ω ω =p.u. The R block diagram representation of the synchronous machine in two-axis model is shown in Figure 2.6.

8 Figure 2.6 Block diagram representation of two axis model for synchronous machine 27

9 Synchronous Machine Representation Using the block diagram reduction technique and with the simplifying assumptions the state equations for the two-axis model in p.u. form pe d ' = {-E d ' - (x q -x q ') I q } / τ qo ' pe q ' = {E FD - E q ' - ( x d - x d ' ) I d } / τ do ' pω = {T m - Dω - T e } / τ j pδ = ω - (2.) where the state variables are E d ' - direct axis component of voltage behind transient reactance E q ' - quadrature axis component of voltage behind transient reactance ω - angular velocity of rotor δ - rotor angle in radians and T e = E d 'I d + E q 'I q (x q ' x d ' ) I d I q τ j = 4πfH x d - direct axis synchronous reactance x q - quadrature axis synchronous reactance x d ' - direct axis transient reactance x q ' - quadrature axis transient reactance τ do ' - direct axis open circuit time constant

10 29 τ qo ' - quadrature axis open circuit time constant T e - electrical torque of synchronous machine T m - mechanical torque of synchronous machine D - damping coefficient of synchronous machine E FD - Equivalent stator emf corresponding to field voltage I q - quadrature axis armature current I d - direct axis armature current H - inertia constant of synchronous machine in sec f - frequency in Hz A multi-machine power system is shown in Figure 2.7 and the network has n machines and r loads. The active source nodal voltages in Figure 2.7 are taken as the terminal voltages V i, i =.2.n instead of the internal EMF`s. The loads are represented by constant impedances and the network has n active sources representing the synchronous machines. Figure 2.7 Multi-machine with constant impedance loads

11 30 This network is reduced to a n-node network shown in Figure 2.8 in which the current and voltage phases of each node are expressed in terms of the respective machine reference frame. Figure 2.8 Reduced n-port network The objective here is to derive relations between v di and v qi, i=,2,.n, and the state variables. This will be obtained in the form of a relation between these voltages, the machine currents i qi and i di, and the angles δ i, i=,2,.n. For convenience we will use a complex notation as follows. For a machine i we define the phasors V and I i i as V = V + jv ; I = I + ji (2.2) i qi di i qi di

12 3 where V = v / 3 : V = v / 3 qi qi di di I = i / 3 : I = i / 3 qi qi di di and where the axis q i is taken as the phasor reference in each case. Then we define the complex vectors V and I by V V + jv q V V jv 2 + V = = V V + jv qn n d q 2 d 2 dn (2.3) I I I + ji q d I I + ji 2 q 2 d 2 = = I I + ji qn dn n (2.4) The voltage Vi and thecurrent I i are referred to the q and d axes of machine i. In the other words the different voltages and currents are expressed in terms of different reference. To obtain general network relationships, it is desirable to express the various branch quantities to the same reference which is given by equation (2.5): The node voltages and currents are expressed as Vˆ and ˆI i i, i =,2,..n, and ˆI = YV ˆ (2.5) where Y is the short circuit admittance of the network.

13 Converting to Common Reference Frame Let us assume that we want to convert the phasor Vi V jv qi di = + to the common reference frame (moving at synchronous speed). Let the same voltage, expressed in new notation, be ˆV = V + jv i Qi Di as shown in Figure 2.9. where, = + and ˆV = V + jv i Qi Di (2.6) Vi V jv qi di D ref V Di V i = V ˆi d i q i V qi V di δ i δ i Q ref V Qi Figure 2.9 Two frames of reference for phasor quantities From the Figure 2.9 V Qi = [Vqi cos δ i Vdi cos δ i ] (2.7) V = [V cos δ V cos δ ] Di di i qi i (2.8) V + V = (V cos δ V cos δ ) + (V sin δ + V cos δ ) Qi Di qi i di i qi i di i (2.9) ˆV i j i = V e δ i (2.20)

14 33 The equation (2.20) can be written in generalized matrix form as below jδ V jv e V jv Q D + q d jδ2 V + jv e 0 V jv Q2 D2 + = q2 d V jv + V qn jv Qn Dn j n + δ e dn (2.2) jδ e 0 0 jδ2 e 0 T = 0 0 jδn e (2.22) The equation (2.20) can be written as ˆV = TV (2.23) Thus T is a transformation that transforms the d and q quantities of all machines to the system frame, which a common frame is moving at synchronous speed. The transformation matrix T contains elements only at the leading diagonal and hence we can show that T is orthogonal, i.e. T - = T *. Now the equation (2.23) can be rewritten as * ˆ V=T V (2.24) Similarly for node current Î = TI (2.25)

15 34 * ˆ I = T I (2.26) we get Substituting equation (2.25) and equation (2.23) in equation (2.5), I = MV (2.27) where M = T - YT (2.28) Linearizing equation (2.27) and making necessary substitutions (Anderson and Fouad 2003), the following equations are obtained. I qi = G ii V qi B ii V di + n [ Y ii cos(θ ij - δ ij0 ) V qj ] j= - n [ j= Y ij sin (θ ij - δ ij0 ) V dj ] + n [ Y ij {sin(θ ij - δ ij0 ) V qj0 + cos(θ ij - δ ij0 )V dj0 ] δ ij j= ; i =,...n (2.29) I di = B ii V qi + G ii V di + n [ Y ij cos (θ ij - δ ij0 ) V dj ] j= + n [ j= Y ij sin (θ ij - δ ij0 ) V qj ] + n [ Y ij {sin (θ ij - δ ij0 )V dj0 - cos(θ ij - δ ij0 )V qj0 ] δ ij j= ; i =,...n (2.30) The state space model for linearized system is obtained by linearizing the differential and algebraic equations at an operating point. While doing this linearization process, additional terms involving terminal voltage components (which are not state variables) remain in the differential

16 35 equations. To express the voltage components in terms of state variables, the machine currents are also linearized and expressed in terms of state variables and voltage components. Finally the current components are eliminated using the interconnecting network algebraic equations. From the initial conditions, E d ' i0, E q ' i0, I qi0, I di0, E FDi0 and δ i0 are determined. Linearizing equation (2.) we get p E d ' i = {- E d ' i - (x qi - x q ' i ) I qi } / τ qo ' i ; i =,...n p E q ' i = { E FDi - E q ' i + ( x di - x d ' i ) I di } / τ do ' i ; i =,...n p ω i = { T mi (I di0 E d ' i + I qi0 E q ' i + E d ' i0 I di +E q ' i0 I qi )- D i ω i } / τ j ; i =,...n (replacing V by E'): p δ i = ω i ; i =, n (2.3) Substituting equations (2.29) and (2.30) in equation (2.3). p E d i = {[(x qi - x q ' i ) B ii ] E d ' i τ qo ' i + (x qi - x q ' i ) n [ Y ik {sin (θ ik - δ ik0 ) E d ' k -(x qi - x q ' i ) G ii E q ' i k= - (x qi - x q ' i ) n [ Y ik cos (θ ik - δ ik0 ) ] E q ' k k= - (x qi - x q ' i ) n [ Y ik cos(θ ik -δ ik0 )] E d ' k0 +Y ik sin ((θ ik - δ ik0 ) E d ' k0 ] δ ik } k= i =,2.n (2.32)

17 36 p E q ' i = τ ' do i {[(x di x d ' i ) B ii ] E q ' i + (x di x d i ) n [ Y ik {sin (θ ik - δ ik0 )] E d ' k + (x di x d ' i ) G ii E d ' i k= + (x di x d ' i ) n [ Y ik sin (θ ik - δ ik0 ) ] E q ' k k= - (x di x d ' i ) n [ Y ik cos(θ ik -δ ik0 ) E q ' k0 -Y ik sin((θ ik -δ ik0 )E d ' k0 ] δ ik + E FDi )} k= i =,2.n (2.33) p ω i = τ ji {[ T mi - D i ω i -[I di0 + G ii E d ' i0 - B ii E q ' i0 ] E d ' i - [ I qi0 + B ii E d ' i0 + G ii E q ' i0 ] E q 'i - n [ k= Y ik cos (θ ik - δ ik0 ) E d ' i0 - Y ik sin (θ ik - δ ik0 ) E q ' i0 ] E d ' k - n [ k= Y ik sin (θ ik - δ ik0 ) E d ' i0 + Y ik cos (θ ik - δ ik0 ) E q ' i0 ] E q ' k - n [ k= Y ik cos (θ ik - δ ik0 ) (-E q ' k0 E d ' i0 +E d ' k0 E q ' i0 ) + Y ik sin ((θ ik - δ ik0 ) (-E d ' k0 E d ' i0 +E q ' k0 E q ' i0 ) δ ik } i =,2.n (2.34) p δ i = ω - ω i (2.35) i = 2,3.n taking machine as reference.

18 37 The above set of equations (2.32 to 2.35) gives the state space model of n-machine system. 2.6 EXCITER REPRESENTATION The state space equation of the exciter can be derived from the block diagram of the exciter shown in the Figure 2.3. From the Figure 2.3, we get K A EFD = + STA V t (2.36) For n, number of exciters, the state equations is as follows: -K p E = - V + V - E ; ( ) Ai fdi Refi i fdi TAi TAi i=, n (2.37) Now the state vector of the n machine state model including exciter equation is as follows. X T i = [ E d ' i E q ' i ω i δ i E FD i ] ; i=, n (2.38) 2.7 CONVENTIONAL POWER SYSTEM STABILIZER REPRESENTATION The Conventional Power System Stabilizer (PSS) adds damping to the generator rotor oscillations by controlling its excitation using auxiliary stabilizing signals. To provide damping, the stabilizer must produce a component of electrical torque in phase with the rotor speed deviations.

19 38 The important blocks in a power system stabilizer are: Washout circuit. Phase compensator. Stabilizer gain. The state space equation for the power system stabilizer (PSS) can be obtained from the block diagram shown in Figure 2.0. Figure 2.0 Conventional Power System Stabilizer Structure (CPSS) From the wash out block, we get st V = (K ω) w 2 PSS + stw (2.39) p V 2i = K PSSi p ωi (/T wi ) V 2i ; i =,...n (2.40) From the phase compensator block we get + st V V + st 2 = s 2 (2.4) From equation (2.4) we get p V si = (T i /T 2i ) p V 2i +(/T 2i ) V 2i (/T 2i ) V si ; i =,...n (2.42)

20 39 The state vector of the complete system after the inclusion of power system stabilizer is as follows: x T i = [ E' di E' qi ω i δ i E FDi V 2i Vs i ] ; i=, n (2.43) 2.8 FUZZY LOGIC BASED POWER SYSTEM STABILIZER (FPSS) FPSS. Figure 2. shows the schematic block diagram of the system with d dt ω ω FPSS V s + V t - + V ref Power System Generator and Exciter ω Figure 2. Structure of the Power system with FPSS Speed Deviation of the synchronous machine ( ω) and its deviation ( ω ) are chosen as inputs to the FPSS. Simulation of the sample SMIB system without PSS is carried out for several operating conditions and different disturbances and the inputs are normalized using their estimated peak values. Seven labels are taken for both the inputs and output. The labels are LP (large positive), MP (medium positive), SP (small positive), VS (very small), SN (small negative), MN (medium negative) and LN (Large negative). Linear triangular membership function is used in the design of FPSS. In our design of FPSS, the fuzzy sets with triangular membership function for ω are shown in Figure 2.2. The membership function for similar to the above Figure 2.2. ω and Vs are

21 40 LN MN SN VS SP MP LP Figure 2.2 Triangular membership function of ω Khan 2000). Table 2. shows the rules of fuzzy logic based PSS (Lakshmi and Table 2. Rule Table of fuzzy logic PSS ω LP MP SP VS SN MN LN LP LP LP LP LP MP SP VS ω MP LP LP MP MP SP VS SN SP LP MP SP SP VS SN MN VS MP MP SP VS SN MN N SN MP SP VS SN SN MN LN MN SP VS SN MN MN LN LN LN VS SN MN LN LN LN LN

22 4 2.9 CONCLUSION Mathematical model of SMIB system for dynamic stability analysis is presented in this chapter. Various state variables with PSS, system matrix including static exciter and CPSS are included in this chapter. Block diagram of simplified linear model of SMIB including exciter and CPSS is also neatly presented in this chapter. Non linear mathematical model representing the dynamics of the multi machine power system combining the synchronous machine model, excitation system (IEEE Type ST A), with conventional power system stabilizers are described in this chapter. The fuzzy logic based PSS model is also described.

### 1 Unified Power Flow Controller (UPFC)

Power flow control with UPFC Rusejla Sadikovic Internal report 1 Unified Power Flow Controller (UPFC) The UPFC can provide simultaneous control of all basic power system parameters ( transmission voltage,

### Comparative Study of Synchronous Machine, Model 1.0 and Model 1.1 in Transient Stability Studies with and without PSS

Comparative Study of Synchronous Machine, Model 1.0 and Model 1.1 in Transient Stability Studies with and without PSS Abhijit N Morab, Abhishek P Jinde, Jayakrishna Narra, Omkar Kokane Guide: Kiran R Patil

### Dynamics of the synchronous machine

ELEC0047 - Power system dynamics, control and stability Dynamics of the synchronous machine Thierry Van Cutsem t.vancutsem@ulg.ac.be www.montefiore.ulg.ac.be/~vct October 2018 1 / 38 Time constants and

### Analysis of Bifurcations in a Power System Model with Excitation Limits

Analysis of Bifurcations in a Power System Model with Excitation Limits Rajesh G. Kavasseri and K. R. Padiyar Department of Electrical Engineering Indian Institute of Science, Bangalore, India Abstract

### ECE 422/522 Power System Operations & Planning/Power Systems Analysis II : 7 - Transient Stability

ECE 4/5 Power System Operations & Planning/Power Systems Analysis II : 7 - Transient Stability Spring 014 Instructor: Kai Sun 1 Transient Stability The ability of the power system to maintain synchronism

### From now, we ignore the superbar - with variables in per unit. ψ ψ. l ad ad ad ψ. ψ ψ ψ

From now, we ignore the superbar - with variables in per unit. ψ 0 L0 i0 ψ L + L L L i d l ad ad ad d ψ F Lad LF MR if = ψ D Lad MR LD id ψ q Ll + Laq L aq i q ψ Q Laq LQ iq 41 Equivalent Circuits for

### CHAPTER 3 MATHEMATICAL MODELING OF HYDEL AND STEAM POWER SYSTEMS CONSIDERING GT DYNAMICS

28 CHAPTER 3 MATHEMATICAL MODELING OF HYDEL AND STEAM POWER SYSTEMS CONSIDERING GT DYNAMICS 3.1 INTRODUCTION This chapter focuses on the mathematical state space modeling of all configurations involved

### SCHOOL OF ELECTRICAL, MECHANICAL AND MECHATRONIC SYSTEMS. Transient Stability LECTURE NOTES SPRING SEMESTER, 2008

SCHOOL OF ELECTRICAL, MECHANICAL AND MECHATRONIC SYSTEMS LECTURE NOTES Transient Stability SPRING SEMESTER, 008 October 7, 008 Transient Stability Transient stability refers to the ability of a synchronous

### CHAPTER 3 SYSTEM MODELLING

32 CHAPTER 3 SYSTEM MODELLING 3.1 INTRODUCTION Models for power system components have to be selected according to the purpose of the system study, and hence, one must be aware of what models in terms

### The synchronous machine (detailed model)

ELEC0029 - Electric Power System Analysis The synchronous machine (detailed model) Thierry Van Cutsem t.vancutsem@ulg.ac.be www.montefiore.ulg.ac.be/~vct February 2018 1 / 6 Objectives The synchronous

### The Effects of Machine Components on Bifurcation and Chaos as Applied to Multimachine System

1 The Effects of Machine Components on Bifurcation and Chaos as Applied to Multimachine System M. M. Alomari and B. S. Rodanski University of Technology, Sydney (UTS) P.O. Box 123, Broadway NSW 2007, Australia

### EE 742 Chapter 3: Power System in the Steady State. Y. Baghzouz

EE 742 Chapter 3: Power System in the Steady State Y. Baghzouz Transmission Line Model Distributed Parameter Model: Terminal Voltage/Current Relations: Characteristic impedance: Propagation constant: π

### A Power System Dynamic Simulation Program Using MATLAB/ Simulink

A Power System Dynamic Simulation Program Using MATLAB/ Simulink Linash P. Kunjumuhammed Post doctoral fellow, Department of Electrical and Electronic Engineering, Imperial College London, United Kingdom

### ECE 585 Power System Stability

Homework 1, Due on January 29 ECE 585 Power System Stability Consider the power system below. The network frequency is 60 Hz. At the pre-fault steady state (a) the power generated by the machine is 400

### Lesson 17: Synchronous Machines

Lesson 17: Synchronous Machines ET 332b Ac Motors, Generators and Power Systems Lesson 17_et332b.pptx 1 Learning Objectives After this presentation you will be able to: Explain how synchronous machines

### DESIGN OF POWER SYSTEM STABILIZER USING FUZZY BASED SLIDING MODE CONTROL TECHNIQUE

DESIGN OF POWER SYSTEM STABILIZER USING FUZZY BASED SLIDING MODE CONTROL TECHNIQUE LATHA.R Department of Instrumentation and Control Systems Engineering, PSG College of Technology, Coimbatore, 641004,

### Equivalent Circuits with Multiple Damper Windings (e.g. Round rotor Machines)

Equivalent Circuits with Multiple Damper Windings (e.g. Round rotor Machines) d axis: L fd L F - M R fd F L 1d L D - M R 1d D R fd R F e fd e F R 1d R D Subscript Notations: ( ) fd ~ field winding quantities

### Behaviour of synchronous machine during a short-circuit (a simple example of electromagnetic transients)

ELEC0047 - Power system dynamics, control and stability (a simple example of electromagnetic transients) Thierry Van Cutsem t.vancutsem@ulg.ac.be www.montefiore.ulg.ac.be/~vct October 2018 1 / 25 Objectives

### Power system modelling under the phasor approximation

ELEC0047 - Power system dynamics, control and stability Thierry Van Cutsem t.vancutsem@ulg.ac.be www.montefiore.ulg.ac.be/~vct October 2018 1 / 16 Electromagnetic transient vs. phasor-mode simulations

### JRE SCHOOL OF Engineering

JRE SCHOOL OF Engineering Class Test-1 Examinations September 2014 Subject Name Electromechanical Energy Conversion-II Subject Code EEE -501 Roll No. of Student Max Marks 30 Marks Max Duration 1 hour Date

### CHAPTER 3 ANALYSIS OF THREE PHASE AND SINGLE PHASE SELF-EXCITED INDUCTION GENERATORS

26 CHAPTER 3 ANALYSIS OF THREE PHASE AND SINGLE PHASE SELF-EXCITED INDUCTION GENERATORS 3.1. INTRODUCTION Recently increase in energy demand and limited energy sources in the world caused the researchers

### Symmetrical Components Fall 2007

0.1 Variables STEADYSTATE ANALYSIS OF SALIENT-POLESYNCHRONOUS GENERATORS This paper is intended to provide a procedure for calculating the internal voltage of a salientpole synchronous generator given

### Power System Stability and Control. Dr. B. Kalyan Kumar, Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India

Power System Stability and Control Dr. B. Kalyan Kumar, Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India Contents Chapter 1 Introduction to Power System Stability

### Mathematical Model of a Synchronous Machine under Complicated Fault Conditions

Mathematical Model of a Synchronous Machine under Complicated Fault Conditions Prof. Hani Obeid PhD EE, P.Eng.,SMIEEE, Applied Sciences University, P.O.Box 950674, Amman 11195- Jordan. Abstract This paper

### CURENT Course Power System Coherency and Model Reduction

CURENT Course Power System Coherency and Model Reduction Prof. Joe H. Chow Rensselaer Polytechnic Institute ECSE Department November 1, 2017 Slow Coherency A large power system usually consists of tightly

### Design of PSS and SVC Controller Using PSO Algorithm to Enhancing Power System Stability

IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE) e-issn: 2278-1676,p-ISSN: 2320-3331, Volume 10, Issue 2 Ver. II (Mar Apr. 2015), PP 01-09 www.iosrjournals.org Design of PSS and SVC Controller

### Introduction to Synchronous. Machines. Kevin Gaughan

Introduction to Synchronous Machines Kevin Gaughan The Synchronous Machine An AC machine (generator or motor) with a stator winding (usually 3 phase) generating a rotating magnetic field and a rotor carrying

### Unified Power Flow Controller (UPFC) Based Damping Controllers for Damping Low Frequency Oscillations in a Power System

Unified Power Flow Controller (UPFC) Based Damping Controllers for Damping Low Frequency Oscillations in a Power System (Ms) N Tambey, Non-member Prof M L Kothari, Member This paper presents a systematic

### THE UNIVERSITY OF NEW SOUTH WALES. School of Electrical Engineering & Telecommunications FINALEXAMINATION. Session

Name: Student ID: Signature: THE UNIVERSITY OF NEW SOUTH WALES School of Electrical Engineering & Telecommunications FINALEXAMINATION Session 00 ELEC46 Power System Analysis TIME ALLOWED: 3 hours TOTAL

### In these notes, we will address (2) and then return to (1) in the next class.

Linearized Analysis of the Synchronous Machine for PSS Chapter 6 does two basic things:. Shows how to linearize the 7-state model (model #2, IEEE #2., called full model without G-cct. ) of a synchronous

### The synchronous machine (SM) in the power system (2) (Where does the electricity come from)?

1 The synchronous machine (SM) in the power system (2) (Where does the electricity come from)? 2 Lecture overview Synchronous machines with more than 2 magnetic poles The relation between the number of

### Lecture 9: Space-Vector Models

1 / 30 Lecture 9: Space-Vector Models ELEC-E8405 Electric Drives (5 ECTS) Marko Hinkkanen Autumn 2017 2 / 30 Learning Outcomes After this lecture and exercises you will be able to: Include the number of

### Module 3 : Sequence Components and Fault Analysis

Module 3 : Sequence Components and Fault Analysis Lecture 12 : Sequence Modeling of Power Apparatus Objectives In this lecture we will discuss Per unit calculation and its advantages. Modeling aspects

### CHAPTER 6 STEADY-STATE ANALYSIS OF SINGLE-PHASE SELF-EXCITED INDUCTION GENERATORS

79 CHAPTER 6 STEADY-STATE ANALYSIS OF SINGLE-PHASE SELF-EXCITED INDUCTION GENERATORS 6.. INTRODUCTION The steady-state analysis of six-phase and three-phase self-excited induction generators has been presented

### POWER SYSTEM STABILITY

LESSON SUMMARY-1:- POWER SYSTEM STABILITY 1. Introduction 2. Classification of Power System Stability 3. Dynamic Equation of Synchronous Machine Power system stability involves the study of the dynamics

### Power System Stability GENERATOR CONTROL AND PROTECTION

Power System Stability Outline Basis for Steady-State Stability Transient Stability Effect of Excitation System on Stability Small Signal Stability Power System Stabilizers Speed Based Integral of Accelerating

### Mitigating Subsynchronous resonance torques using dynamic braking resistor S. Helmy and Amged S. El-Wakeel M. Abdel Rahman and M. A. L.

Proceedings of the 14 th International Middle East Power Systems Conference (MEPCON 1), Cairo University, Egypt, December 19-21, 21, Paper ID 192. Mitigating Subsynchronous resonance torques using dynamic

### A Computer Application for Power System Control Studies

A Computer Application for Power System Control Studies Dinis C. A. Bucho Student nº55262 of Instituto Superior Técnico Technical University of Lisbon Lisbon, Portugal Abstract - This thesis presents studies

### DESIGNING POWER SYSTEM STABILIZER WITH PID CONTROLLER

International Journal on Technical and Physical Problems of Engineering (IJTPE) Published by International Organization on TPE (IOTPE) ISSN 2077-3528 IJTPE Journal www.iotpe.com ijtpe@iotpe.com June 2010

### Transient Stability Analysis with PowerWorld Simulator

Transient Stability Analysis with PowerWorld Simulator T1: Transient Stability Overview, Models and Relationships 2001 South First Street Champaign, Illinois 61820 +1 (217) 384.6330 support@powerworld.com

### (Refer Slide Time: 00:55) Friends, today we shall continue to study about the modelling of synchronous machine. (Refer Slide Time: 01:09)

(Refer Slide Time: 00:55) Power System Dynamics Prof. M. L. Kothari Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 09 Modelling of Synchronous Machine (Contd ) Friends,

### Simulations and Control of Direct Driven Permanent Magnet Synchronous Generator

Simulations and Control of Direct Driven Permanent Magnet Synchronous Generator Project Work Dmitry Svechkarenko Royal Institute of Technology Department of Electrical Engineering Electrical Machines and

### Robust Tuning of Power System Stabilizers Using Coefficient Diagram Method

International Journal of Electrical Engineering. ISSN 0974-2158 Volume 7, Number 2 (2014), pp. 257-270 International Research Publication House http://www.irphouse.com Robust Tuning of Power System Stabilizers

### Understanding the Inductances

Understanding the Inductances We have identified six different inductances (or reactances) for characterizing machine dynamics. These are: d, q (synchronous), ' d, ' q (transient), '' d,'' q (subtransient)

### STUDY OF SMALL SIGNAL STABILITY WITH STATIC SYNCHRONOUS SERIESCOMPENSATOR FOR AN SMIB SYSTEM

STUDY OF SMLL SIGNL STBILITY WITH STTIC SYNCHRONOUS SERIESCOMPENSTOR FOR N SMIB SYSTEM K.Geetha, Dr.T.R.Jyothsna 2 M.Tech Student, Electrical Engineering, ndhra University, India 2 Professor,Electrical

### FUZZY SLIDING MODE CONTROLLER FOR POWER SYSTEM SMIB

FUZZY SLIDING MODE CONTROLLER FOR POWER SYSTEM SMIB KHADDOUJ BEN MEZIANE, FAIZA DIB, 2 ISMAIL BOUMHIDI PhD Student, LESSI Laboratory, Department of Physics, Faculty of Sciences Dhar El Mahraz,Sidi Mohamed

### ECE 421/521 Electric Energy Systems Power Systems Analysis I 3 Generators, Transformers and the Per-Unit System. Instructor: Kai Sun Fall 2013

ECE 41/51 Electric Energy Systems Power Systems Analysis I 3 Generators, Transformers and the Per-Unit System Instructor: Kai Sun Fall 013 1 Outline Synchronous Generators Power Transformers The Per-Unit

### Chapter 4. Synchronous Generators. Basic Topology

Basic Topology Chapter 4 ynchronous Generators In stator, a three-phase winding similar to the one described in chapter 4. ince the main voltage is induced in this winding, it is also called armature winding.

### The Mathematical Model of Power System with Thyristor Controlled Series Capacitor in Long Transmission Line

American Journal of Applied Sciences 9 (5): 654-658, 01 ISSN 1546-939 01 Science Publications The Mathematical Model of Power System with Thyristor Controlled Series Capacitor in Long Transmission Line

### International Journal of Advance Engineering and Research Development SIMULATION OF FIELD ORIENTED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTOR

Scientific Journal of Impact Factor(SJIF): 3.134 e-issn(o): 2348-4470 p-issn(p): 2348-6406 International Journal of Advance Engineering and Research Development Volume 2,Issue 4, April -2015 SIMULATION

### QFT Framework for Robust Tuning of Power System Stabilizers

45-E-PSS-75 QFT Framework for Robust Tuning of Power System Stabilizers Seyyed Mohammad Mahdi Alavi, Roozbeh Izadi-Zamanabadi Department of Control Engineering, Aalborg University, Denmark Correspondence

### 3 d Calculate the product of the motor constant and the pole flux KΦ in this operating point. 2 e Calculate the torque.

Exam Electrical Machines and Drives (ET4117) 11 November 011 from 14.00 to 17.00. This exam consists of 5 problems on 4 pages. Page 5 can be used to answer problem 4 question b. The number before a question

### CHAPTER 2 CAPACITANCE REQUIREMENTS OF SIX-PHASE SELF-EXCITED INDUCTION GENERATORS

9 CHAPTER 2 CAPACITANCE REQUIREMENTS OF SIX-PHASE SELF-EXCITED INDUCTION GENERATORS 2.. INTRODUCTION Rapidly depleting rate of conventional energy sources, has led the scientists to explore the possibility

### Self-Tuning Control for Synchronous Machine Stabilization

http://dx.doi.org/.5755/j.eee.2.4.2773 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 392-25, VOL. 2, NO. 4, 25 Self-Tuning Control for Synchronous Machine Stabilization Jozef Ritonja Faculty of Electrical Engineering

### LabVIEW Based Simulation of Static VAR Compensator for Transient Stability Enhancement in Electric Power Systems

International Journal of Electrical Engineering. ISSN 0974-2158 Volume 4, Number 1 (2011), pp.143-160 International Research Publication House http://www.irphouse.com LabVIEW Based Simulation of Static

### ECE 325 Electric Energy System Components 7- Synchronous Machines. Instructor: Kai Sun Fall 2015

ECE 325 Electric Energy System Components 7- Synchronous Machines Instructor: Kai Sun Fall 2015 1 Content (Materials are from Chapters 16-17) Synchronous Generators Synchronous Motors 2 Synchronous Generators

### Examples of Applications of Potential Functions in Problem Solving (Web Appendix to the Paper)

Examples of Applications of otential Functions in roblem Solving (Web Appendix to the aper) Ali Mehrizi-Sani and Reza Iravani May 5, 2010 1 Introduction otential functions may be exploited to formulate

### Chapter 9: Transient Stability

Chapter 9: Transient Stability 9.1 Introduction The first electric power system was a dc system built by Edison in 1882. The subsequent power systems that were constructed in the late 19 th century were

### Synchronous Machines

Synchronous Machines Synchronous generators or alternators are used to convert mechanical power derived from steam, gas, or hydraulic-turbine to ac electric power Synchronous generators are the primary

### The Mathematical Model of Power System with Static Var Compensator in Long Transmission Line

American Journal of Applied Sciences 9 (6): 846-850, 01 ISSN 1546-939 01 Science Publications The Mathematical Model of Power System with Static Var Compensator in Long Transmission Line Prechanon Kumkratug

### Fuzzy Applications in a Multi-Machine Power System Stabilizer

Journal of Electrical Engineering & Technology Vol. 5, No. 3, pp. 503~510, 2010 503 D.K.Sambariya and Rajeev Gupta* Abstract - This paper proposes the use of fuzzy applications to a 4-machine and 10-bus

### LESSON 20 ALTERNATOR OPERATION OF SYNCHRONOUS MACHINES

ET 332b Ac Motors, Generators and Power Systems LESSON 20 ALTERNATOR OPERATION OF SYNCHRONOUS MACHINES 1 LEARNING OBJECTIVES After this presentation you will be able to: Interpret alternator phasor diagrams

### EE2351 POWER SYSTEM OPERATION AND CONTROL UNIT I THE POWER SYSTEM AN OVERVIEW AND MODELLING PART A

EE2351 POWER SYSTEM OPERATION AND CONTROL UNIT I THE POWER SYSTEM AN OVERVIEW AND MODELLING PART A 1. What are the advantages of an inter connected system? The advantages of an inter-connected system are

### B.E. / B.Tech. Degree Examination, April / May 2010 Sixth Semester. Electrical and Electronics Engineering. EE 1352 Power System Analysis

B.E. / B.Tech. Degree Examination, April / May 2010 Sixth Semester Electrical and Electronics Engineering EE 1352 Power System Analysis (Regulation 2008) Time: Three hours Answer all questions Part A (10

### An Introduction to Electrical Machines. P. Di Barba, University of Pavia, Italy

An Introduction to Electrical Machines P. Di Barba, University of Pavia, Italy Academic year 0-0 Contents Transformer. An overview of the device. Principle of operation of a single-phase transformer 3.

### Step Motor Modeling. Step Motor Modeling K. Craig 1

Step Motor Modeling Step Motor Modeling K. Craig 1 Stepper Motor Models Under steady operation at low speeds, we usually do not need to differentiate between VR motors and PM motors (a hybrid motor is

### Dynamic Modeling of Surface Mounted Permanent Synchronous Motor for Servo motor application

797 Dynamic Modeling of Surface Mounted Permanent Synchronous Motor for Servo motor application Ritu Tak 1, Sudhir Y Kumar 2, B.S.Rajpurohit 3 1,2 Electrical Engineering, Mody University of Science & Technology,

### COMPARISON OF DAMPING PERFORMANCE OF CONVENTIONAL AND NEURO FUZZY BASED POWER SYSTEM STABILIZERS APPLIED IN MULTI MACHINE POWER SYSTEMS

Journal of ELECTRICAL ENGINEERING, VOL. 64, NO. 6, 2013, 366 370 COMPARISON OF DAMPING PERFORMANCE OF CONVENTIONAL AND NEURO FUZZY BASED POWER SYSTEM STABILIZERS APPLIED IN MULTI MACHINE POWER SYSTEMS

### A STUDY OF THE EIGENVALUE ANALYSIS CAPABILITIES OF POWER SYSTEM DYNAMICS SIMULATION SOFTWARE

A STUDY OF THE EIGENVALUE ANALYSIS CAPABILITIES OF POWER SYSTEM DYNAMICS SIMULATION SOFTWARE J.G. Slootweg 1, J. Persson 2, A.M. van Voorden 1, G.C. Paap 1, W.L. Kling 1 1 Electrical Power Systems Laboratory,

### Final Exam, Second Semester: 2015/2016 Electrical Engineering Department

Philadelphia University Faculty of Engineering Student Name Student No: Serial No Final Exam, Second Semester: 2015/2016 Electrical Engineering Department Course Title: Power II Date: 21 st June 2016 Course

### Spontaneous Speed Reversals in Stepper Motors

Spontaneous Speed Reversals in Stepper Motors Marc Bodson University of Utah Electrical & Computer Engineering 50 S Central Campus Dr Rm 3280 Salt Lake City, UT 84112, U.S.A. Jeffrey S. Sato & Stephen

### Frequency and Damping Characteristics of Generators in Power Systems

Frequency and Damping Characteristics of Generators in Power Systems Xiaolan Zou Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the

### 7. Transient stability

1 7. Transient stability In AC power system, each generator is to keep phase relationship according to the relevant power flow, i.e. for a certain reactance X, the both terminal voltages V1and V2, and

### Synchronous Machines

Synchronous machine 1. Construction Generator Exciter View of a twopole round rotor generator and exciter. A Stator with laminated iron core C Slots with phase winding B A B Rotor with dc winding B N S

### Parameter Sensitivity Analysis of an Industrial Synchronous Generator

Parameter Sensitivity Analysis of an Industrial Synchronous Generator Attila Fodor, Attila Magyar, Katalin M. Hangos Abstract A previously developed simple dynamic model of an industrial size synchronous

### 6. Oscillatory Stability and RE Design

6. Oscillatory Stability and RE Design In chapter 4 and 5, it was clarified that voltage stability and transient synchronous stability are deeply influenced by power system model (power system load model

### LOC-PSS Design for Improved Power System Stabilizer

Journal of pplied Dynamic Systems and Control, Vol., No., 8: 7 5 7 LOCPSS Design for Improved Power System Stabilizer Masoud Radmehr *, Mehdi Mohammadjafari, Mahmoud Reza GhadiSahebi bstract power system

### Synchronous Machines

Synchronous Machines Synchronous Machines n 1 Φ f n 1 Φ f I f I f I f damper (run-up) winding Stator: similar to induction (asynchronous) machine ( 3 phase windings that forms a rotational circular magnetic

### Reduced Size Rule Set Based Fuzzy Logic Dual Input Power System Stabilizer

772 NATIONAL POWER SYSTEMS CONFERENCE, NPSC 2002 Reduced Size Rule Set Based Fuzzy Logic Dual Input Power System Stabilizer Avdhesh Sharma and MLKothari Abstract-- The paper deals with design of fuzzy

### Dynamic Stability Enhancement of Power System Using Fuzzy Logic Based Power System Stabilizer

Dynamic Stability Enhancement of Power System Using Fuzzy Logic Based Power System Stabilizer Kamalesh Chandra Rout Department of Electrical Engineering National Institute of Technology,Rourkela Rourkela-769008,

### Chapter 3 AUTOMATIC VOLTAGE CONTROL

Chapter 3 AUTOMATIC VOLTAGE CONTROL . INTRODUCTION TO EXCITATION SYSTEM The basic function of an excitation system is to provide direct current to the field winding of the synchronous generator. The excitation

### Design and Application of Fuzzy PSS for Power Systems Subject to Random Abrupt Variations of the Load

Design and Application of Fuzzy PSS for Power Systems Subject to Random Abrupt Variations of the Load N. S. D. Arrifano, V. A. Oliveira and R. A. Ramos Abstract In this paper, a design method and application

### Dynamic analysis of Single Machine Infinite Bus system using Single input and Dual input PSS

Dynamic analysis of Single Machine Infinite Bus system using Single input and Dual input PSS P. PAVAN KUMAR M.Tech Student, EEE Department, Gitam University, Visakhapatnam, Andhra Pradesh, India-533045,

### ECE 422/522 Power System Operations & Planning/ Power Systems Analysis II 2 Synchronous Machine Modeling

ECE 422/522 Power System Operations & Planning/ Power Systems Analysis II 2 Synchronous achine odeling Spring 214 Instructor: Kai Sun 1 Outline Synchronous achine odeling Per Unit Representation Simplified

### Dynamics of the synchronous machine

ELEC0047 - Power system ynamics, control an stability Dynamics of the synchronous machine Thierry Van Cutsem t.vancutsem@ulg.ac.be www.montefiore.ulg.ac.be/~vct These slies follow those presente in course

### EE2351 POWER SYSTEM ANALYSIS UNIT I: INTRODUCTION

EE2351 POWER SYSTEM ANALYSIS UNIT I: INTRODUCTION PART: A 1. Define per unit value of an electrical quantity. Write equation for base impedance with respect to 3-phase system. 2. What is bus admittance

### DAMPING OF SUBSYNCHRONOUS MODES OF OSCILLATIONS

Journal of Engineering Science and Technology Vol. 1, No. 1 (26) 76-88 School of Engineering, Taylor s College DAMPING OF SUBSYNCHRONOUS MODES OF OSCILLATIONS JAGADEESH PASUPULETI School of Engineering,

### You know for EE 303 that electrical speed for a generator equals the mechanical speed times the number of poles, per eq. (1).

Stability 1 1. Introduction We now begin Chapter 14.1 in your text. Our previous work in this course has focused on analysis of currents during faulted conditions in order to design protective systems

### CHAPTER 5 STEADY-STATE ANALYSIS OF THREE-PHASE SELF-EXCITED INDUCTION GENERATORS

6 CHAPTER 5 STEADY-STATE ANALYSIS OF THREE-PHASE SELF-EXCITED INDUCTION GENERATORS 5.. INTRODUCTION The steady-state analysis of six-phase SEIG has been discussed in the previous chapters. In this chapter,

### EE 451 Power System Stability

EE 451 Power System Stability Power system operates in synchronous mode Power system is subjected to a wide range of disturbances (small and large) - Loads and generation changes - Network changes - Faults

### EE 6501 POWER SYSTEMS UNIT I INTRODUCTION

EE 6501 POWER SYSTEMS UNIT I INTRODUCTION PART A (2 MARKS) 1. What is single line diagram? A Single line diagram is diagrammatic representation of power system in which the components are represented by

### Three Phase Circuits

Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/ OUTLINE Previously on ELCN102 Three Phase Circuits Balanced

### University of Jordan Faculty of Engineering & Technology Electric Power Engineering Department

University of Jordan Faculty of Engineering & Technology Electric Power Engineering Department EE471: Electrical Machines-II Tutorial # 2: 3-ph Induction Motor/Generator Question #1 A 100 hp, 60-Hz, three-phase

### SPEED-GRADIENT-BASED CONTROL OF POWER NETWORK: CASE STUDY

CYBERNETICS AND PHYSICS, VOL. 5, NO. 3, 2016, 85 90 SPEED-GRADIENT-BASED CONTROL OF POWER NETWORK: CASE STUDY Igor Furtat Control of Complex Systems ITMO University Russia cainenash@mail.ru Nikita Tergoev

### (a) Torsional spring-mass system. (b) Spring element.

m v s T s v a (a) T a (b) T a FIGURE 2.1 (a) Torsional spring-mass system. (b) Spring element. by ky Wall friction, b Mass M k y M y r(t) Force r(t) (a) (b) FIGURE 2.2 (a) Spring-mass-damper system. (b)

### Nonlinear Control Design of Series FACTS Devices for Damping Power System Oscillation

American Journal of Applied Sciences 8 (): 4-8, 0 ISSN 546-939 00 Science Publications Nonlinear Control Design of Series FACTS Devices for Damping Power System Oscillation Prechanon Kumkratug Department

### EVALUATION OF THE IMPACT OF POWER SECTOR REFORM ON THE NIGERIA POWER SYSTEM TRANSIENT STABILITY

EVALUATION OF THE IMPACT OF POWER SECTOR REFORM ON THE NIGERIA POWER SYSTEM TRANSIENT STABILITY F. I. Izuegbunam * Department of Electrical & Electronic Engineering, Federal University of Technology, Imo