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Security AnalysisSecurity Analysis

To execute very quickly 3basic ways

Study PS with approximate but very fast

algorithms

Select only important cases for detailed analysis

Use computer system made up of multipleprocessors

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Approximate ModelApproximate Model

Various names: D factor methods

Linear sensitivity methods

DC power flow methods

Linear sensitivity method Only branch MW flows are calculated (within 5% accuracy)

No knowledge of MVAR flows & voltage magnitudes

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Contingency SelectionContingency Selection

This technique is also called Contingency Screening

Eliminate all or most of the nonviolation cases

Only run complete power flows on critical cases

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Computer systemComputer system

Many processors

Running separate cases

In parallel

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Linear Sensitivity FactorsLinear Sensitivity Factors

One of the easiest ways to provide quick calculation

of possible overloads

Show approximate change in line flows for changesin generation on the network configuration

Derived from DC load flow

Basically TWO typesGeneration shift factors

Line outage distribution factors

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Generation shift factorsGeneration shift factors(Linear estimates)(Linear estimates)

Defined as

i

lli

P

fa

(

(!

!l Line index

where

!i Bus index

!( lf Change in MW power flow on linel

when a change ingeneration occurs at bus i

!(i

P Change in generation at bus i

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Assumption:

Change in generation is exactlycompensated by an opposite change in

generation at the reference bus

All other generators remain fixed

Then the factor represents the

sensitivity of the flow on the line l to achange in generation at bus i

iP(

ia

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Case 1:Case 1:

Outage of a large generating unitOutage of a large generating unit

Assumed that all the generation lost would be made up by the

reference generation

If generator was generating MW, and it was lost

New power flow on each line could be calculated using a

precalculated set of a factors as follows

forl= 1..L

r

iP

iPr

iP

ilill Paff S

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Outage flow on each line can be compared to its limit

Those exceeding their limit is flagged for alarming. i.e.loss of generator on bus i would result in an overload online l

Using Superposition, the effects of simultaneous changeson several generating buses can be calculated (since aare Linear estimates)

!

lf Flow on line lafter the generator on bus ifails

!

lf Flow before the failure

lf

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Case 2 : Loss of generator on bus iwere

compensated by governor action throughoutthe interconnected system

Assumption :

Remaining generators pick up in proportion to theirmaximum MW rating

Thus, the proportion of generation pick up fromunit j (j i) would be

!

k

k

j

jiP

P

max

max

K

k i

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Flow on line l, under the assumption that all the

generators in the interconnection participate inmaking up the loss

Assumes that no unit will actually hit its maximum

More detailed generation pick up algorithm that took

account of generation limits would be required, if

this is apt to be the case

!maxk

P Maximum MW rating for generator k

!jiK Proportionality factor for pick up on generating

unit jwhen unit ifails

{

((ij

ijiljilill PaPaff ][ KS

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Line outage distribution factorsLine outage distribution factors

Apply to the testing for overloads whentransmission circuits are lost

S

k

lkl

f

fd

(!

, where

!kld ,

!( lf

!S

kf

Line outage distribution factor when monitoring line

lafter an outage on line k

Change in MW flow on line l

Original flow on line kbefore it was outaged

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If power on line l & line k is known, the flow on line l with line k out

can be determined using d factors

By precalculating line outage distribution factors, a very fast

procedure can be set up to test all lines in the network for overload

for the outage of a particular line

This procedure can be repeated for the outage of each line in turn,

with overloads reported to the operations personnel in the form of

alarm messages

SS

kklll fdff ,!

!kl ff , Preoutage flows on lines l& k, respectively

!

lf Flow on line lwith line kout

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Contingency analysis usingContingency analysis usingsensitivity factorssensitivity factors

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Line flows must be checked against - as well as

Assumptions:

1. Generator output for each of the generators in the system is

available

Line flow for each transmission line in the network is also available

(satisfied with telemetry system or with state estimation technique)

max

lfmax

lf

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2. Sensitivity factors have been calculated & stored & they are

correct

(Valid as long as transmission network has not undergone any

significant switching operations that would change its structure -

have provision for updating the factors when the network is

switched)

3. All generation pick up will be made on the reference bus

(If this is not the case, substitute the corresponding equation in

generator outage loop)

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ReferenceReference

AllenAllen JJ..WoodWood andand BruceBruce FF..Woolenberg,Woolenberg,

PowerPower generation,generation, operationoperation andand control,control,JohnJohn WileyWiley && sonssons IncInc..