Slide matlab based transient stability analysis of a power system

A Project on:- MATLAB-bas ed transient stability analysis of a PROJECT power system MENTOR:Dr.C.K.Panigrahi By:- MD SAMAR AHMAD (807056) MUKESH KUMAR (807057) ADITYA SAHAY (807007) JYOTI MAYEE PANI (807042) Contents: 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) ABSTRACT INTRODUCTION LITERATURE RIVIEW & MOTIVATION OF THE PRESENT WORK PROBLEM STATEMENT TRANSIENT STABILITY Transient instability Effect of transient instability ELEMENTARY VIEW OF TRANSIENT STABILITY SWING EQUATION EQUAL AREA CRITERION POINT-BY-POINT SOLUTION OF THE SWING EQUTION multi-machine system , differential equations Methods of solution of swing equations mathematical overview Mathematical derivation for computational algorithm Case study Mat-lab code MATLAB Command Window CASE STUDY OF A THREE-MACHINE NINE-BUS SYSTEM SIMULINK References ABSTRACT Power-system stability is a term applied to alternatingcurrent electric power systems, denoting a condition in which the various synchronous machines of the system remain in synchronism, or "in step," with each other Conversely, instability denotes a condition involving loss of synchronism, or falling "out of step." Occurrence of a fault in a power system causes transients To stabilize the system load flow analysis is done Actually in practice the fault generally occurs in the load side As we controlling load side which will lead to complex problem in order avoid that we are controlling the generator side A MATLAB simulation has been carried out to demonstrate the performance of the three-machine nine-bus system INTRODUCTION  BACK GROUND The classical model of a multi machine may be used to study the stability of a power system for a period of time during which the system dynamic response is dependent largely on the kinetic energy in the rotating masses The classical three-machine nine-bus system is the simplest model used in studies of power system dynamics and requires of minimum amounts of data Hence such studies can be connected in a relatively short time under minimum cost Among various method of load flow calculation Newton Raphson method is chosen for calculation of load flow study If the oscillatory response of a power system during the transient period following disturbance is damped and the system settles in a finite time to a new steady operating condition, we say the system is stable If the system is not stable, it is considered unstable This primitive definition of stability requires that the system oscillations should be damped This condition is sometime called asymptotic stability and means that the system contains inherent forces that tend to reduce oscillation LITERATURE RIVIEW & MOTIVATION OF THE PRESENT WORK   In recent years, energy, environment, right-of-way, and cost problems have delayed the construction of both generation facilities and new transmission lines, while the demand for electric power has continued to grow This situation has necessitated a review of the traditional power system concepts and practices to achieve greater operating flexibility and better utilization of existing power systems Transient stability of a transmission is a major area of research from several decades Transient stability restores the system after fault clearance Any unbalance between the generation and load initiates a transients that causes the rotors of the synchronous machines to “swing” because net accelerating torques are exerted on these rotors If these net torques are sufficiently large to cause some of the rotors to swing far enough so that one or more machines “slip a pole” and synchronism is lost So the calculation of transient stability should be needed A system load flow analysis is required for it The transient stability needs to be enhanced to optimize the load ability of a system, where the system can be loaded closer to its thermal limits PROBLEM STATEMENT  Occurrence of fault may lead to instability in a system or the machine fall out of synchronism Load flow study should be done to analyze the transient stability of the power system If the system can’t sustain till the fault is cleared then the fault in-stabilize the whole system If the oscillation in rotor angle around the final position go on increasing and the change in angular speed during transient condition go on increasing then system never come to its final position The unbalanced condition or transient condition may leads to instability where the machines in the power system fall out of synchronism Calculation of load flow equation by Newton Raphson method, Runge Kutta method, and decoupled method gives the rotor angle and initial condition TRANSIENT STABILITY    Each generator operates at the same synchronous speed and frequency of 50 hertz while a delicate balance between the input mechanical power and output electrical power is maintained Whenever generation is less than the actual consumer load, the system frequency falls On the other hand, whenever the generation is more than the actual load, the system frequency rise The generators are also interconnected with each other and with the loads they supply via high voltage transmission line An important feature of the electric power system is that electricity has to be generated when it is needed because it cannot be efficiently stored Hence using a sophisticated load forecasting procedure generators are scheduled for every hour in day to match the load In addition, generators are also placed in active standby to provide electricity in times of emergency This is referred as spinning reserved TRANSIENT STABILITY(cont.) • The power system is routinely subjected to a variety of disturbances Even the act of switching on an appliance in the house can be regarded as a disturbance • However, given the size of the system and the scale of the perturbation caused by the switching of an appliance in comparison to the size and capability of the interconnected system, the effects are not measurable Large disturbance occur on the system These include severe lightning strikes, loss of transmission line carrying bulk power due to overloading • The ability of power system to survive the transition following a large disturbance and reach an acceptable operating condition is called transient stability TRANSIENT STABILITY(cont.) The physical phenomenon following a large disturbance can be described as follows:• Any disturbance in the system will cause the imbalance between the mechanical power input to the generator and electrical power output of the generator to be affected As a result, some of the generators will tend to speed up and some will tend to slow down • If, for a particular generator, this tendency is too great, it will no longer remain in synchronism with the rest of the system and will be automatically disconnected from the system This phenomenon is referred to as a generator going out of step Transient instability Transient instability refers to the condition where there is a disturbance on the system that causes a disruption in the synchronism or balance of the system The disturbance can be a number of types of varying degrees of severity: • The opening of a transmission line increasing the XL of the system • The occurrence of a fault decreasing voltage on the system (The voltage at the fault goes to zero, decreasing all system voltages in the area.) • The loss of a generator disturbing the energy balance and requiring an increase in the angular separation as other generators adjust to make up the lost energy • The loss of a large block of load in an exporting area Method of solution of swing equations(mathematical overview ) : Assumptions:The only assumption is that accelerating power is assumed as constant throughout the time interval ∆t and has the value computed for the beginning of the interval M (d2 δ /dt2) = Pa  Integrating both sides: dδ /dt= ω = ωo +(Pat/M); ……………(1) δ = δo+ tωo +(Pat2/2M); ………… (2)  Dividing the time interval t in n intervals  From equations (1) &(2) ωn = ωn-1 +(Pa(n-1) ∆t /M); ………… (3) δn = δn-1+ ∆tωn-1+(Pa(n-1)(∆t )2/2M); …… (4) The increments of speed and angle during the nth interval are: ∆ ωn = ωn - ωn-1=(Pa(n-1) ∆t /M); ……………(5) ∆ δn = δn -δn-1 =∆tωn-1+(Pa(n-1)(∆t )2/2M);….(6)  ematical derivation for computational algo  The equations 3,4,5&6 are suitable for point-by-point calculation the preceding interval can be calculated as ωn-1 = ωn-2 +(Pa(n-2) ∆t /M); …….(7) δn-1 = δn-2+ ∆t ωn-2 +(Pa(n-2)(∆t )2/2M); …… (8) Subtract eq.7 from 4: (δn - δn-1 )= (δn-1 -δn-2 )+ ∆t(ωn-1 -ωn-2 ) +(Pa(n-1)(∆t )2/2M)-(Pa(n-2)(∆t )2/2M) ; …………….(9) but ; δn - δn-1 = ∆δn ; or, δn-1 - δn-2 = ∆δn-1 ; or, ωn -1 - ωn-2 = ∆ωn-1 ; From equation (5) ∆ ωn-1 = (Pa(n-2) ∆t /M); ………….(10) using eq (9) &(10) ∆ δn = ∆δn-1 + ∆t Pa(n-2) ∆t /M +(Pa(n-1) - Pa(n-2)) (∆t )2/2M; Or, ∆ δn = ∆δn-1 +(Pa(n-1) + Pa(n-2)) (∆t )2/2M ; …… (final eq for point by point soln.) Case study based on point by point sol  Case:- a synchronous machine performing oscillation of small amplitude with respect to an infinite bus ,its power output may be assumed to be directly proportional to its angular displacement from the infinite bus considering a 50 cycle machine for which H = 2.7 Mj-per Mva And which is operating in the steady state with input and output of 1.00 pu and angular displacement of 45o (elec.) with respect to an infinite bus upon occurrence of a fault ,we assume that the input remains constant and that output is given by Pu=δ/90o even though the amplitude of oscillation may be great The initial conditions are :δ = (pi/4) ; dδ/dt = 0; The period of oscillation is given by :T = (2*pi)/sqrt.(2/(pi*M)); or, = pi*sqrt.(2*pi*M); The inertial constant is :M = H /(pi*f) =2.7/(pi*50) = 017188(unit power sec.2 per elec.rad) or ,M = H/(180*f) =0.30micro (unit power sec.2 per elec.deg.) ‘Mat-lab code of Point by solution of swing equation Code :- clc ,clear all, close all; Problem='Point by solution of swing equation by Method ' Assumptions=':the synchronous machine performing oscillation of small amplitude with respect to an infinite bus ,its power output may be assumed to be directly proportional to its angular displacement from infinite bus under steady state input and output of 1pu input remain constant and output is given by =del/90(degree) ' data ='required' are=':-1 step size for numerical computation range of time of operation inertial constant(H) in mega frequency of operation initial displacement delta' s=1; while s[...]... is advanced software which is increasingly being used as a basic building block in many areas of research As such, it holds a great potential in the area of power system example to demonstrate the features and scope of Simulink based model for transient stability analysis The stability of power systems continues to be major concern in system operation Modern electrical power systems have grown to a. .. Pa (d δ) =A2 (negative area); EQUAL AREA CRITERION (cont.) A 1= Area of acceleration A2 = Area of deceleration If the area of acceleration is larger than the area of deceleration, i.e., A 1 > A2 The generator load angle will then cross the point δm, beyond which the electrical power will be less than the mechanical power forcing the accelerating power to be positive The generator will therefore start... process is the computational of the angular positions, and perhaps also of the angular speeds at the end of the time interval from a knowledge of the positions and speeds at the beginning of the interval and the accelerating power assumed constant for interval The second process is the computational of the accelerating power of each machine from the angular position of all machines of the system The second... to a large generating units and extra high voltage tie-lines, etc The transient stability is a function of both operating conditions and disturbances Thus the analysis of transient stability is complicated Simulink is an interactive environment for modeling, analyzing and simulating a wide variety of dynamic systems The key features of Simulink are: Interactive simulations with live display; A comprehensive... solution of this equation gives δ as a function of t A graph of the solution is known as a swing curve Inspection of the swing curves of all the machines of a system will show whether the machines will remain in synchronism after a disturbance In a multi machines system , the output and hence the accelerating power of each machine depend upon the angular positions –and also upon the angular speeds -of all... attain the steady state If the two areas are equal, i.e., A 1 = A 2 , then the accelerating area is equal to decelerating area and this is defines the boundary of the stability limit POINT-BY-POINT SOLUTION OF THE SWING EQUTION M (d2 δ /dt2) =P a Where , δ= displacement angle of rotor w.r.t to a reference axis rotating at speed M = Inertia constant of machine normal P a = accelerating power t = time... be constant or to vary according to assumed laws throughout a short interval of time ∆t , so that as a result of the assumptions made the equations can be solved for the changes in the other 2variables during the same time interval Then, from the values of the other variables at the end of the interval, new value can be calculated for the variables which were assumed constant These new value are then... York, 1964) RAMNARAYAN PATEL, T S BHATTI and D P KOTHARI Centre for Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi, India MATLAB/ Simulink -based transient stability analysis of a multi-machine power system ”September 1,2003 Edward Wilson Kimbark , -Power System Stability volume1( IEEE Press; Wiley Inter-science , New York,1948) bing.com; google.co.in library.nu Thank you ... start accelerating before is slows down completely and will eventually become unstable If, on the other hand, A1 < A2 , i.e., the decelerating area is larger than the accelerating area, the machine will decelerated completely before accelerating again The rotor inertia will force the subsequent acceleration and deceleration areas to be smaller than the first ones and the machine will eventually attain... output2='output data of second data input' time2=transpose(t) electrical_opower2=transpose(ele) accelrating _power2 =transpose(acc) change_angular_velocity_deg_sec2=transpose(Dwn) angular_velocity_deg_sec2=transpose(wn) change_in _power_ angle_degree2=transpose(Dd) power_ angle_degree2=transpose(d) end end plot(time1 ,power_ angle_degree1,time2 ,power_ angle_degree2) xlabel('time(sec.)') ylabel('displacement angle del(electrical ... Pa (d δ) =A2 (negative area); EQUAL AREA CRITERION (cont.) A 1= Area of acceleration A2 = Area of deceleration If the area of acceleration is larger than the area of deceleration, i.e., A > A2 ... achieve greater operating flexibility and better utilization of existing power systems Transient stability of a transmission is a major area of research from several decades Transient stability. .. overview Mathematical derivation for computational algorithm Case study Mat-lab code MATLAB Command Window CASE STUDY OF A THREE-MACHINE NINE-BUS SYSTEM SIMULINK References ABSTRACT Power- system stability