WWJMRD 2016; 2(6): 41-45 www.wwjmrd.com Impact Factor MJIF: 4.25 e-issn: 2454-6615 Oyediran Oyebode Olumide Department of Computer Engineering, Osun State Polytechnic Iree, Osun State, Nigeria Ogunwuyi Ogunmakinde Jimoh Department of Elect/Elect, Osun State Polytechnic Iree, Osun State, Nigeria Lawal Akeem Olaide Department of Elect/Elect, Osun State Polytechnic Iree, Osun State, Nigeria Enhancement of transient stability analysis of multimachine power system Oyediran Oyebode Olumide, Ogunwuyi Ogunmakinde Jimoh, Lawal Akeem Olaide Abstract Transient stability is the ability of a power system to maintain synchronism when subjected to a severe disturbance such as fault, loss or addition of a large load, and loss of generation. Unlike small-signal stability, in transient stability a large-signal disturbance is considered. Therefor nonlinear differential equations of the system should be employed to represent the system. The methodology used is the modification of Newton Raphson for performing the load flow analysis of the bus system. Stable operations of a power system depends on the ability of system generators to meet active and reactive power demand of the loads. As a result, it is important to accurately represent the load to capture the dependence of it real and reactive power on the system variables, e.g bus voltage. Therefore, load modelling plays an important role in transient stability analysis. In this work, a software tool is developed to implement the simulation algorithm in MATLAB 8.1. The software is capable of representing several load and generator models and can handle the PSS/E native file format. Evaluation of result was done based on the Delta angle of generators, Speed deviation of generators, Field circuit flux of generators, Bus voltages and Internal delta angles with respect to time. Keywords: Bus Voltage, Fault, Field Flux, Generator, Stability, Transient Correspondence: Oyediran Oyebode Olumide Department of Computer Engineering, Osun State Polytechnic Iree, Osun State, Nigeria Introduction 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. 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 instabilise 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(vaidya et al, 2012). 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. In stability assessment the critical clearing time (CCT) is a very important parameter in order maintain the stability of power system. The CCT is maximum time duration that a fault may occur in power system without loss of stability. Fault clearing time is set randomly. If the fault clearing time (FCT) is more than CCT then the relative rotor angles will go out of step and the system will lose stability(grainer, 1999). Review of Related Works 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. ~ 41 ~
Multimachine equations can be written Similar to the onemachine system connected to the infinite bus. In order to reduce the complexity of the transient stability analysis, similar simplifying assumptions are made as follows. -Each synchronous machine is represented by a constant voltage source behind the direct axis transient reactance(prabha, 1994). This representation Neglects the effect of saliency and assumes Constant flux linkages. The governor s action are neglected and the input powers are assumed to remain constant during the entire period of simulation. -Using the prefault bus voltages, all loads are converted to equivalent admittances to ground and are assumed to remain constant. -Damping or asynchronous powers are Ignored. The mechanical rotor angle of each machine coincides with the angle of the voltage behind the machine reactance. - Machines belonging to the same station swing together and are said to be coherent. A group of coherent machines is represented by one equivalent machine Transient stability analysis is very complex, therefore to reduce its complexity, certain assumptions are made: i. The power given as input is assumed to be constant for the entire simulation period. ii. iii. The action of the governor is neglected. In order to neglect the effect of saliency and assume constant flux linkage, synchronous machine is represented as a constant voltage source. iv. All loads should be converted to an equivalent admittance to ground which is assumed constant, using the bus voltages before fault. v. Mechanical rotor angle of all machines coincides vi. vii. with voltage angle behind machine reactance. Asynchronous powers are neglected. Machines which belong to same station are coherent and a group of such coherent machines is showing a single equivalent machine ( ) (Sara, 2012) (1) Where Ibus is the vector of the injected bus currents Vbus is the vector of bus voltage measured from the reference node. Prefault bus matrix During Fault Bus Matrix Once the fault is cleared by removing the line, simultaneously opening the circuit breaker at the either ends of the line between buses, prefault ybus has to be modified again. Post fault bus matrix Once the fault is cleared by removing the line, simultaneously opening the circuit breaker at either end of the line between buses, pre fault has to be modified again. During fault power angle equation (9) (4) (7) (8) (5) [ ] (10) Post Fault Power Angle Equations ) (11) (6) Where: M is the number of generators is the terminal voltage of the ith generator are the generator real and active powers. All unknown values are determine from the initial power flow solution The generator amature resistances are usually neglected and voltage behind the transient resistance are then obtained. (Sara, 2012) (2) Next, all load are converted to equivalent admittance using the relation To include voltages behind transient reactances, m buses are added to the n bus power system network. In power system one generator is taken as reference generator and other two are studied for stability ourpose. Fault occur at point p in thhe system, and two loads are connected to the system at and (3) ~ 42 ~ Swing Equation During Fault ) ) Swing Equation Post Fault ) (14) [ { )}] ) (12) (13) [ { )}] (15) (16) ) (Yan, 2012) (17) Methodology The procedure used for the implementation is as follows Step 1: Each synchronous machine is represented by a constant voltage behind xd (neglect salience and flux change) Step 2: Input power remain constant
Step 3: Using prefault bus voltages, all load in equivalent admittances to ground Step 4: Damping and asynchronous effects are ignored Step 5: δmech = δ( machine belongs to the same station swing together and are said to be coherent, coherent machine can equivalent to one machine. solution to multimachine syste Step 6: Solve initial power flow and determine initial bus voltage magnitude and phase angle. Step 7: Swing solution of multi-machine system - + )= (18) Fig 1: Diagram for multimachine stability are the element of the faulted reduced bus admittance matrix Step 8: Solve the State variable model of swing equation using Matlab = (19) = ( ) (20) =, = (21) Step 9: Calculating load equivalent admittance (22) Generate the Nodal equation of the system [ ]= [ ] [ ] (23) Step 11: Classical transient stability study is based on the application of three phase fault { } - + ) (24) Results and Discussion Fig 2: 12 Bus System Models Table1: Power Flow Solution by Newton-Raphson ~ 43 ~
Delta angle of generators vs. time Bus voltages vs. time Fig 6: Bus voltages with time for a three phase Internal delta angles vs. time Fig 3: angle of generators with time for a three phase machine Speed deviation of generators vs. time Fig 7: Internal delta angles with time for a three phase Fig 4: speed deviation of generators with time for a three phase machine Field circuit flux of generators vs. time Fig 5: Field circuit flux of generators with time for a 3phase ~ 44 ~ Fig.3and 4 are showing the variation of the angle δ and the angular velocity of the rotor, while Fig.4 and 5 show the variations of the field flux and Bus Voltage of the generator in time for the system. we find that the angle δ of the rotor continues to increase following an increasing pace; it does not pass through a maximum and increases indefinitely At the default, the electrical power drops to zero, the rotor accelerates and the generation is getting greater than the pow-er (Fig.6). We can also note from (Fig.7) that the power storing the kinetic energy of rotation continues to oscillate rapidly and indefinite way, this can be easily explained by the fact that the mechanical torque is higher than the electrical torque. Then a large amount of energy has been accumulated by the generator what put the rotor in over speed after elimi-nation of the fault. Conclusion In order to improve the power system, it requires an evaluation of system's ability to withstand the disturbances simultaneously maintaining the service quality. For transient stability analysis of power system, various techniques have already been proposed such as extended equal area criteria, the time domain solution and a few direct stability methods such as transient energy function. In most of these methods, a transformation is done from
multi-machine system to an equivalent machine as well as an infinite bus system. An analysis of transient stability for the power system using an individual machine is done with the help of an accurate algorithm is done in this paper. This paper describes the fault conditions in the infinite bus bar with the multi-machine system Reference 1. A.P.Vaidya and Rohit V.Patil (2012), Comparison of Different Types of Transient Stability Assessments During Congestion, IEEE-International Conference On Advances In Engineering, Science And Management (ICAESM -2012) March 30, 31, 2012. 2. C. APPRAEZ (2012), Etude Comparative De Méthodes De Simulation De La Stabi-lité Transitoire, école de technologie supérieure, Uni-versité du Québec, Avril 2012. 3. Grainer, Willam D. Stevenson JR: Power System Analysis, McGraw-Hill International Editions, 1999. USA 4. Hadi Saadat(1999): Power System Analysis, McGraw- Hill International Editions, 1999. John J. 5. H. Alkhatib (2008), Etude De La Stabilité Aux Petites Perturbations Dans Les Grandes Réseaux Electriques : Optimisation De La Régulation Par Une Mé-thode Métaheuristique, Thèse de Doctorat, Université PAUL CEZANNE D AIX- MARSEILLE (AIX- MARSEILLE III), Décembre 2008. 6. Ho Van Hien(2003): Transmission and Distribution of Power System, National University of HoChiMinh City Press, 2003. Holand 7. Power System Analysis Tata McGraw-Hill, 2003 Power system stability by Mrinal K Pal IEEE/CIGRE Joint Task Force on Stability Terms and Definitions, Definition and Classification of Power System Stability, IEEE Trans On Power Systems, Vol. 19, No. 2, May 2004. 8. Sara Eftekharneja(2012), Impact of Increased Penetration of Photovoltaic Generation on Power Systems, IEEE Trans on Power System, 2012. 9. Stability, McGraw-Hill International Editions,1994.. I. J. Nagrath and D. P. Kothari Modern. UK ~ 45 ~