ATPS - Contingency Selection S8

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Contingency Selection



Performance Index (

PI)

Measure ± how much a particular outage

might affect the PS

Overload Performance Index :

n

l l

flowl

P P PI 2

max )(§!



If n is a large number

� PI will be a small number if all flows are within

limits� PI will be a large number if one or more lines

are overloaded

How to use this PI Problem



Suppose n = 1

A table of PI values, one for each line can

be calculated

Selection Procedure:� Order the PI table from largest value to

least

� Lines corresponding to the top of the list

are then the candidates for the short list ±pick Nc entries



Problems faced when n=1

� PI does not snap from zero to infinity as the

branch exceeds its limit

� It rises as a quadratic function

� A line just below its limit contributes to PI

almost equal to one that is just over its limit

� PI may be large when many lines are loaded

just below their limit

� Thus PI¶s ability to distinguish / detect bad

cases is limited

± ordering PI values results in a list that is

not at all representative of bad cases at the top



1P1Q Method

Way to perform an outage case selection

Decoupled power flow is used

Solution procedure is interrupted after oneiteration

- one P- calculation &

one Q-V calculation

PI can use large n value



1P1Q Contingency Selection

Procedure





Advantage

a. Sufficient information at the end of

First iteration to give a reasonable PI

a. Voltages can also be included in the

PI



PI with voltage magnitude

- difference between voltage magnitude (solved

at the end of 1P1Q procedure) & base case

voltage

- Value set by utility engineers, indicating limit of

a bus voltage from changing on one outage

case

m

i

in

l l

flowl

E

E PI

P

P 2

max

2

max)()( §§

(

(!

i E (

max E (



To complete security analysis PI list is sorted so that largest PI appears at

the top

Security analysis can then start by executing

full power flows with the case at the top of the list

Then solve the second case and so on

This continues until either a fixed number of cases is solved or until

a predetermined number of cases are solvedwhich do not have any alarms



Concentric Relaxation

Another idea for security analysis

Outage has only a limited geographical

effect even though line is high-voltage

line, heavily loaded



To realize any benefit from limited

geographical effect of an outage

Power system

Affected part Unaffected part



Power System Division

Layer zero:

Buses at the end of the outaged line

Layer 1:

Buses that are one transmission line or

transformer from layer zero

Continue this until all the buses in the entire

network are included



Choose some arbitrary number of layers

All buses included in that layer and

lower-numbered layers are solved aspower flow with the outage in place

Buses in higher-numbered layers arekept as constant voltage & phase angle

(reference bus)



Layering of outage effects



Application

1) Solution of layers included becomes Final

Solution of that case and all overloads &

voltage violations are determined from

this power flow

2) Solution is used to form PI for that outage



Concentric Relaxation

Procedure

Proposed by Zaborsky

Trouble:

Requires more layers for circuits whose

influence is felt further from the outage



Bounding

Brandwajn ± solves atleast one of the

problems using concentric relaxation

method using an adjustable regionaround the outage ± applied only to linear

(DC) power flow

Extended for AC network analysis



Analysis in Bounding Technique

Define Three Subsystems of PS:

N1 = subsystem immediately surrounding theoutaged line

N2 = External subsystem that we shall not solvein detail

N3 = Set of boundry buses that separate N1 &N2



Layers used in bounding analysis



Fact behind Bounding method

We can make certain

assumptions about phase angle

spread across lines in N2, giveninjections in N1 & maximum phase

angle appearing across any two

buses in N3

(Refer appendix 11A ± line outage modeling

using injections)



Let

Transmission line in N2 with flow f opq

There is a max. amount that the flow on pq can shift

)](),[( 00max !( pq pq pq pq pq f f f f smaller f

Lo erLimit f

U pperLimit f

pq

pq

p

p



Translation into max. change in

phase angle difference

)(1

q p

pq

pq x

f UU !

)(1

q p

pq

pq x

f UU ((!(

pq pqq p x f maxmax)( (!(( UU



From [2] theorem states that

I & j are any pair of buses in N3

i largest in N3

j smallest in N3

jiq p UUUU ((((



|i ± j| provides an upper limit to

max. change in angular spread across

any circuit in N2

ji pq pq x f UU (((max



Graphical interpretation of

Bounding process



I fig. cannot go over limit

II fig. could go over limit

«« line

represents thepoint where circuit pq will go into

overload

Any value right of dotted line representsan overload

pq pq x f

max

(



Solid line upper limit on

If solid line is left to the dotted line, then

the circuit cannot go into overload

If solid line is right to the dotted line,

the circuit may be shifted in flow due to

outage so as to violate a limit

pq pq x f (



All circuits in N2 are safe from

overload if the value of is

less than the smallest value of over all pairs pq, where pq

corresponds to the buses at the ends

of circuits in N2

jiUU ((

pq pq x f max(



If this condition fails, we have to expand

N1, calculate a new in N3

and rerun the test over the newly definedN2 region circuits

When an N2 is found which passes the

test, only region N1 need be studied

jiUU ((



PROBLEM

Show how bounding technique works sothat not all of the circuits in the system

need be analyzed. Consider the six-bussystem used previously with outage of transmission line 3-6





From bus To bus R (pu) X (pu) BCAP (pu)1 2 0.10 0.20 0.02

1 4 0.05 0.20 0.02

1 5 0.08 0.30 0.03

2 3 0.05 0.25 0.03

2 4 0.05 0.10 0.01

2 5 0.10 0.30 0.02

2 6 0.07 0.20 0.025

3 5 0.12 0.26 0.025

3 6 0.02 0.10 0.01

4 5 0.20 0.40 0.04

5 6 0.10 0.30 0.03

LINE DAT A



Bus

No.

Bus

type

V

(pu)

Pgen

(pu MW)

Pload

(pu MW)

Qload

(pu MVAR)

1 Swing 1.05

2 Gen 1.05 0.50 0.0 0.0

3 Gen 1.07 0.60 0.0 0.0

4 Load 0.0 0.7 0.7

5 Load 0.0 0.7 0.7

6 Load 0.0 0.7 0.7

BUS DAT A



X matrix for six-bus system



Base case DC power flow



MW limits on transmission lines

Line MW limit

1-2 30

1-4 50

1-5 40

2-3 202-4 40

2-5 20

2-6 30

3-5 203-6 60

4-5 20

5-6 20



Line MW limit

(pu)

1-2 0.30 0.253 0.047 0.20 0.0094

1-4 0.50 0.416 0.084 0.20 0.0168

1-5 0.40 0.331 0.069 0.30 0.02072-3 0.20 0.018 0.182 0.25 0.0455

2-4 0.40 0.325 0.075 0.10 0.0075

2-5 0.20 0.162 0.038 0.30 0.0114

2-6 0.30 0.248 0.052 0.20 0.01043-5 0.20 0.169 0.031 0.26 0.00806

3-6 0.60 0.449 - - -

4-5 0.20 0.041 0.159 0.40 0.0636

5-6 0.20 0.003 0.197 0.30 0.0591

pq pq x f max(max pq f ( pq x

)( pu

f pqQ

100 MVA base



Analysis

Analyze system as if N1 & N3 regions

consist of only line 3-6

If bounding criteria is met, no other

analysis need be done as it

establish that no overloads exist

anywhere in the system



If bounding criteria fails, expand the

bounded region ie, it includes buses

2,3,5 & 6

ie, boundary of region N3 consists of buses 2 & 5

Check bounding criteria, if it satisfies,

stop the analysis



)2(

)(,

nmmmnnk

k iminnmi

X X X x

x X X

!H

nm

i

nmi P

UH

(!,

- sensitivity factor

Pnm - original power flow over line nm (k) before it was dropped

± phase angle

xk - reactance of line k

X - element of X matrix of the system



nnk

k innmi

X x

x X

!,H

mmk

k im

nmi x

x X

!,H

for m = ref. bus

for n = ref. bus



12865.0

)2(

)(

36663336

36363336,3 !

!

X X X x

x X X H

11953.0)2(

)(

36663336

36666336,6 !

! X X X x

x X X H

111437.063 !(( UU

Smallest value of 0075.042 !((!(( UUUU q p

Criteria fails, Consider new region





Calculate

Bounding criteria is satisfied

If d factors are used, all line flows are to

be found out

003564.052!((

UU



Line outage distribution factor

lineK=1

(1-2)

K=2

(1-4)

K=3

(1-5)

K=4

(2-3)

K=5

(2-4)

K=6

(2-5)

K=7

(2-6)

K=8

(3-5)

K=9

(3-6)

K=10

(4-5)

K=11

(5-6)

l=1

(1-2)0.64 0.54 -0.11 -0.5 -0.21 -0.12 -0.14 0.01 0.01 0.13

l=2

(1-4)0.59 0.46 -0.03 0.61 -0.06 -0.04 -0.04 0 -0.33 0.04

l=3

(1-5)0.41 0.36 0.15 -0.11 0.27 0.16 0.18 -0.02 0.32 -0.17

l=4(2-3)

-0.1 -0.03 0.18 0.12 0.23 0.47 -0.4 -0.53 0.17 0.13

l=5

(2-4)-0.59 0.76 -0.17 0.16 0.3 0.17 0.19 -0.02 -0.67 -0.19

l=6

(2-5)-0.19 -0.06 0.33 0.22 0.23 0.24 0.27 -0.03 0.31 -0.26

l=7

(2-6)-0.12 -0.04 0.21 0.51 0.15 0.27 -0.20 0.58 0.20 0.44

l=8

(3-5)-0.12 -0.04 0.2 -0.38 0.14 0.27 -0.17 0.47 0.19 0.42

l=9

(3-6)0.01 0 -0.03 -0.62 -0.02 -0.03 0.64 0.6 -0.02 0.56

l=10

(4-5)0.01 -0.24 0.29 0.13 -0.39 0.24 0.14 0.15 -0.02 -0.15

l=11

(5-6)

0.11 0.03 -0.18 0.12 -0.13 -0.23 0.36 -0.4 0.42 -0.18



Line MW limit

(pu)

1-2 0.30 0.253 0.257

1-4 0.50 0.416 0.416

1-5 0.40 0.331 0.3222-3 0.20 0.018 -0.220

2-4 0.40 0.325 0.316

2-5 0.20 0.162 0.148

2-6 0.30 0.2480.508

3-5 0.20 0.169 0.380

3-6 0.60 0.449 -

4-5 0.20 0.041 0.032

5-6 0.20 0.003 0.191

Power flow using d factors

)(

63

pu

f out

pq

)( pu

f pqQ



Overloads exist on lines 2-3, 2-6, 3-5

These lines are within bounded region

N1 + N3



Reference

1. Allen J.Wood and Bruce F.Woolenberg, ³Power

generation, operation and control´, John Wiley

& sons Inc.

2. Brandwajn, ³Efficient Bounding method for

Linear Contingency Analysis,´ IEEE

Transactions on Power Systems, Vol. 3, No. 1,February 1988, pp.38-43.

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ATPS - Contingency Selection S8

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