11 - transient stability
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Copyright 2003 Operation Technology, Inc.
Transient Stability
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 2
Time Frame of Power System Dynamic Phenomena
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 3
Introduction
• TS is also called Rotor Stability, Dynamic Stability
• Electromechanical Phenomenon• All synchronous machines must remain in
synchronism with one another• TS is no longer only the utility’s concern• Co-generation plants face TS problems
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 4
Analogy
• Which vehicles will pushed hardest?• How much energy gained by each vehicle?• Which direction will they move?• Height of the hill must they climb to go over?
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 5
Introduction (cont’d)
• System protection requires consideration of:Critical Fault Clearing Time (CFCT)Critical Separation Time (CST)Fast load transferringLoad Shedding…
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 6
Causes of Instability
• Short-circuits• Loss of utility connections• Loss of a portion of in-plant generation• Starting of a large motor• Switching operations (lines or capacitors)• Impact loading on motors• Sudden large change in load and generation
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 7
Consequences of Instability
• Synchronous machine slip poles –generator tripping
• Power swing• Misoperation of protective devices• Interruption of critical loads• Low-voltage conditions – motor drop-offs• Damage to equipment• Area wide blackout• …
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 8
Synchronous Machines
• Torque Equation (generator case)
T = mechanical torqueP = number of polesφair = air-gap fluxFr = rotor field MMFδ = rotor angle
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 9
Swing Equation
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 10
Synchronous Machines (cont’d)• Swing Equation
M = inertia constantD = damping constantPmech = input mechanical powerPelec = output electrical power
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 11
Rotor Angle Responses
• Case 1: Steady-state stable• Case 2: Transient stable • Case 3: Small-signal unstable • Case 4: First swing unstable
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 12
Power and Rotor Angle (Classical 2-Machine Example)
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 13
Power and Rotor Angle (cont’d)
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 14
Power and Rotor Angle (Parallel Lines)
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 15
Both Lines In Service
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 16
One Line Out of Service
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 17
Equal Area Criterion
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 18
Equal Area Criterion
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 19
Equal Area - Stable
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 20
Equal Area – Unstable
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 21
Equal Area - Unstable
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 22
Power System Stability Limit• Steady-State Stability Limit
After small disturbance, the synchronous generator reaches a steady state operating condition identical or close to the pre-disturbance
Limit: δ < 90°
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 23
Power System Stability Limit (con’d)• Transient and Dynamic Stability Limit
After a severe disturbance, the synchronous generator reaches a steady-state operating condition without a prolonged loss of synchronism
Limit: δ < 180° during swing
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 24
Generator Modeling
• MachineEquivalent Model / Transient Model / Subtransient Model
• Exciter and Automatic Voltage Regulator (AVR)
• Prime Mover and Speed Governor• Power System Stabilizer (PSS)
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 25
Generator Modeling (con’d)• Typical synchronous machine data
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 26
Factors Influencing TS• Post-Disturbance Reactance seen from generator. Reactance ↓ Pmax ↓
• Duration of the fault clearing time. Fault time ↑ Rotor Acceleration ↑ Kinetic Energy ↑Dissipation Time during deceleration ↑
• Generator Inertia.Inertia ↑ Rate of change of Angle ↓ Kinetic Energy ↓
• Generator Internal VoltageInternal Voltage ↓ Pmax ↓
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 27
Factors Influencing TS• Generator Loading Prior To DisturbanceLoading ↑ Closer to Pmax. Unstable during acceleration
• Generator Internal Reactance Reactance ↓ Peak Power ↑ Initial Rotor Angle ↓Dissipation Time during deceleration ↑
• Generator Output During FaultFunction of Fault Location and Type of Fault
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 28
Solution to Stability Problems• Improve system design
Increase synchronizing power
• Design and selection of rotating equipmentUse of induction machinesIncrease moment of inertiaReduce transient reactanceImprove voltage regulator and exciter characteristics
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 29
Solution to Stability Problems• Reduction of Transmission System
Reactance• High Speed Fault Clearing• Dynamic Braking• Regulate Shunt Compensation• Steam Turbine Fast Valving• Generator Tripping• Adjustable Speed Synchronous Machines
Copyright 2003 Operation Technology, Inc. – Workshop Notes: Transient Stability Slide 30
Solution to Stability Problems• HVDC Link Control• Current Injection from VSI devices• Application of Power System Stabilizer
(PSS)• Add system protections
Fast fault clearanceLoad SheddingSystem separation
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