power system stability_unit 4 psoc

8/10/2019 Power System Stability_unit 4 PSOC

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Power System Stability

Unit-IV


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What is Stability

Ability of the system to return to normal or

stable operation after having been subjected

to some disturbance

Rotor Angle Stability-ABILITY OF SYSTEM TO

REMAIN IN SYNCHRONISM EVEN AFTER

DISTURBANCE


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Disturbance

Load Changes

Faults

Structural Changes due to isolation of somefaulted elements


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Non-linear , dynamiccontinuously changing

PS

Stability dependent on initial operating

conditions and nature of disturbance

PS maybe stable for some (large ) disturbances

and maynot be stable for another


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Types of Stability


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Rotor Angle Stability

ability of system to remain in synchronism

even after disturbance

Some generators accelerate while others

decelerate losing synchronism

Small signal rotor angle stability, large signal

rotor angle stability


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Small signal rotor angle stability

Maintain synch under small disturbances

Linearized around initial operating conditions

Stability depends only on operating cond andnot disturbance

Instability- non oscillatory periodic inc in rotor

angle or increceasing amplitude of rotoroscillations due to insufficient damping

10-20 sec time frame


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Large signal rotor angle stability

Large disturbance

Instability- large excursions from generator rotorangles

Dependent of initial operating cond ANDdisturbance parameters like type,magnitude,location etc

3-5 sec time frame

Dynamic Stability- Small Signal+ automaticcontrols (outdated terminology)


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Swing Equation

NORMAL-Relative position of the rotor axis andresultant magnetic field axis is FIXED-POWERANGLE or TORQUE ANGLE

DISTURBANCE-rotor will deccelerate or acc w r tsynch rotating air gap mmf

Equation describing relative motion of rotor-SWING EQUATION

No power changerotor angle remains sameotherwise rotor comes to new operating powerangle relative to synch revolving field


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Swing Equation -Derivation

E- no load generated emf

V-terminal voltage

-power angle

Te-electromagnetic torque developed

sm-Synchronous Speed

Tm-Driving Mechanical Torque

J-combined moment of inertia of gen and prime mover m-angular displacement of rotor wrt stationary ref

frame


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Derivation-Begins

Under Steady State cond


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Modeling of Synchronous Machines-

Cylindrical Rotor

Constant voltage, E` and transient reactance

Xd`


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Real Power at node 1


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Power angle curve(Pe vs )

Maximum Power is referred to as Steady State StabilityLimit (SSSL)

Gen o/p can be inc till SSSL


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Modeling of Synchronous Machines-

Considering Saliency


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Under transient conditions


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Steady State Stability


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Transient StabilityEqual Area Control

Equal Area Criteria to analyse stability

Graphical method based on energy stored in

rotating mass.


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Must be zero for stability


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Application of EAC-Sudden increase in

Power Input


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Unit-IV contd


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Application of EAC-three phase fault

Bolted fault at F- no power transfer to infinite

bus,Pe=0( Power angle curve is horizontal axis)

M/c takes total power input,Pm to accelerateand store KE

Fault at sending end


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Fault cleared

at del1

Critical clearing angle: A2>A1 : loss of stability


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Critical Clearing time which is the time taken by the machine to swing from

its initial position to its critical

clearing angle


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Fault in between


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Step by Step solution of swing

equation

the period of interest is divided into several shortintervals

The change in the angular position of the rotorduring a short interval of time is computed by

making the following assumptions1. The accelerating power Pa computed at the

beginning of an interval is constant from themiddle of the proceeding interval to the middle

of the interval considered.2. d/dtis constant throughout any interval at the

value computed at the middle of the interval.


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Factors affecting transient stability


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Auto reclosures

80-90% faults are temporary

Auto reclosing improves transient stability

when done for temporary faults


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Method of improving thetransient stability limit of a power system

Increase of system voltages, use of AVR

Use of high speed excitation system

Reduction in system transfer reactance

Use of high speed reclosing breakers


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Voltage Stability

voltage stability is concerned with the ability of apower system to maintain acceptable voltages at allbuses in the system under normal conditions and afterbeing subjected to a disturbance

voltage instability when a disturbance results in aprogressive and uncontrollable decline in voltage

Following voltage instability, a power systemundergoes voltage collapse if thepost-disturbance

equilibrium voltages near loads are below acceptablelimits.

Voltage collapse may be total (blackout) or partial


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MATHEMATICAL FORMULATION OF VOLTAGE

STABILITY PROBLEM

slower forms of voltage instability are

normally analysed as steady state problems

using power flow simulation

PV curves and QV curves- give steady-state

loadability limits which are related to voltage

stability

Consider the radial two bus system


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V is a double-valued function

P for a particular pf which determines Q interms of P

For each value of pf, the higher voltagesolution indicates stable voltage case, whilethe lower voltage lies in the unstable voltageoperation zone

the changeover occurs at Vcr(critical) andPmax


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Increase beyond Pmax, V(dec), I (inc), drop(inc)

and V further decreases


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QV curve

Consider once again the simple radial system


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Automatic Voltage Restorer


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Reactive Power and Voltage Control

Generator Excitation System-maintains genvoltage and controls reactive power

AVR- to maintain constant terminal voltage

Voltage mag is sensed using PT on a phase

Voltage rectified and compared with the dcsetpoint

Amplified error signal control exciter field and incexciter terminal voltage

Gen field current is inc and then gen emfincreases


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Amplifier model


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Exciter model

Generator model

Sensor Model


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Modified AVR

With stabilizer to improve response

power system stability_unit 4 psoc

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