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Electrical Transients in Power System. January 2009 Mehdi Vakilian. Text Books:. 1-Transients in Power Systems by: Lou van der Slius, 2001 2- Electrical Transients in Power System by: Allan Greenwood, 1991.
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Electrical Transients in Power System January 2009 Mehdi Vakilian
Text Books: • 1-Transients in Power Systems by: Lou van der Slius, 2001 • 2- Electrical Transients in Power System by: Allan Greenwood, 1991
COURSE OUTLINE • Fundamental Notions About Electrical Transients • Basic Concepts and Simple Switching Transients • Damping Effect on Switching Transients • Abnormal Switching Transients • Testing of Circuit Breakers • Transient Analysis of 3Ph Power Systems
Course Outline …..continued • Transient Analysis of 3Ph Power Systems • Traveling Waves and Other Transients on Transmission Line • Modeling Power Equipments for Transients • Numerical Simulation of Elec. Transients • Lightning and its Induced Transients • Insulation Coordination • Protection Against Over Voltages
Evaluation System • Assignments : 10% • Mid Term One (items 1 to 4) : 10% • Mid Term Two (items 5 to 7) : 10% • Final : 60% • Class Project : 10%
Chapter One : Fundemental Notions about Electrical Transients • Time Scale in Power System Studies: planning, Load Flow, Dynamic Stability Switching, external disturbances Frequency Content Differential Equations Solution Distributed and Lumped Parameters Calculatable,Controllable, Preventable Tools for Study
CCT Parameters • In Steady State and Transient • Mathematical Presentation & Physical Interpretation
Simple Circuits Characteristic (thumbprint)RC , RL , LC Circuits
Thumbprints: • RC CCT: Time Constant ; RC • RL CCT : Time Constant ; L/R • LC CCT : Period of Oscillation ;
Principle of Superposition • If stimulus s1 produces R1 & s2 produces R2 applying s1+ s2 simultaneously responds R1+R2 in Linear System Linear System: response proportional to : stimulus
CCT Detail I1: Pre-opening current I2: Superposed current to simulate current cease
S.P. application in Closing switch • V1 : voltage across contacts pre-closing • Therefore: -V1 fictitious stimulus superposed simulating the closing action
Solving RC problem with Lap. Trans. • In terms of I in the CCT: Applying L.P. :
Continuing RC CCT solution • The L.T. solution: • The time solution:
RL CCT excited by Battery V • Solving for I in CCT • The L.T. of Eq.: • The response:
Example: 377 MVA Gen field windingL=0.638H, Exciter noload:1.2 MW(480V) • Energy stored in F.W.:
How must the exciter voltage be changed to reduce the field current to zero in 5 Sec
LC CCT cont. solving for Vc • Surge Imp.
Vc characteristic • Vc Osc. Amp depend on V-Vc(0) • Vc starts at Vc(0) as expected • Response for : 1-Vc(0)=-V 2-Vc(0)=0 3-Vc(0)=+V/2 Voltage and Current Relation
Solution of an RL CCT Stimulatedby an Exp. Drive (Ass. I(0)=0)