a contigency ranking method for voltage stability in real time operation of power systems

8/16/2019 A Contigency Ranking Method for Voltage Stability in Real Time Operation of Power Systems

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Paper accepted for presentation at 2003 IE EE B ologna PowerT ech Con ference, June 23-.26, Bologna, Italy

A Contingency Ranking Method for Voltage

Stability in Real Time Operation of Power

Systems

M6rio A . Albuquerque and Carlos A . Castro,

Senior Member, IEEE

Abstract- A contingency ranking procedure regarding

voltage

stability

to

be used in a real time operation environment is

proposed in

t h i s

paper.

The

procedure can be added to the

existing ranking pmcednres for

MW

overloads and voltage

violations) with mild modificat ionsand s m a l l extra computational

effort.

A

performance index PI) is computed for each

contingency. The PI is defined in terns of a b rancb-based voltage

stability proximity index. Several simulations show that the most

critical contingencies can be identified correctly.

Index

Terms- Contingency ranking, Performance index,

Voltage stability,

Secnr i ty

anal ysis, Power systems operation.

I.

INTRODUCTION

he operation and control of power systems in real time

in the Control Center. First of all, the current operating

condition of the system (commonly referred to as

base case

is

obtained through state estimation from real time m easurements

and data base information. Once the base case is known, the

security analysis function is carried out. It is well known that

security analysis is a very demanding task

as

far as

computational effort is concerned.

In case violations are detected for the base case, corrective

control actions should be enforced

so

as to eliminate them.

Afterwards, the impact of the ocurrence of contingencies

should be evaluated. This process, usually called

contingency

analysis, aims to detecting post-contingency operational lim its

violations. The usual limits taken into account are

MW

overloads in transmission lines and transformers and bus over

or

under voltages. In case post-contingency violations are

detected, preventive and/or corrective control strategies are

devised to guarantee acceptable post-contingency operating

conditions

[l] .

A conventional practice is

to

perform the analysis of a

contingency list containing all simple and the most probable

multiple contingencies. This analysis corresponds to solving a

load flow for each contingency, for obtaining the post-

contingency operating state. The total number of contingency

cases to be analyzed is very large for real, interconnected

T

equire that a number of supervision functions be executed

M . A . Albuquerque

is with

Furnas Centrais

EICtricas,

Brazil. He

is

currently

an

operation engineer

(email:

[email protected]).

C.

A. Casu0 is

with tate

University

of

Campinas, Brazil.

He s currently an

associate

professor

email:[email protected]).

0-7803-7967-5/03/ 17.00 02 00 3 IEEE

power systems. Therefore, this procedure is infeasible in a real

time operation environment.

Some utilities c an y ou t contingency analysis of a reduced list

of critical contingencies, which are defined based on the every

day experience in the system's operation. Some developed

methodologies for automatically defining this list. However,

these methodologies are complex,

lack

a clear physical

meaning and demand consideralile computational effort. The

idea is to define a general, simple, and efficient procedure to

defining those critical contingencies,

so

that they are never

missed even after unpredicted load variations or topology

changes, for example.

A very efficient and well-accepted way to improve the

computational efficiency of the contingency analysis function

consists of adding a

contingency ranking and selection

process

that preceeds the contingency evaluation itself [2]. Each

contingency of the list is first analyzed through a simpler

method. For example, performing on e full iteration of the fast

decoupled load flow is a very well-accepted method

[3].

Then,

contingencies are ranked according to a

performance index

(PI), which is a scalar that reflects the severity degree of a

contingency and it is computed from approximate operating

states. Th e top m ost critical contingencies

are

then analyzed in

detail, by following the conventional approach.

Th e main objectives of this paper are twofold:

(a)

include voltage stability considerations in the contingency

ranking process. This inclusion has already been reported

in the literature, as for example in [41. However, most

methodologies demand more than one load flow per

contingency, which is too time consuming for on-line

applications. In this paper a method is proposed

so

as to

fit as much as possible into the traditional contingency

selection process. The idea is to assure that considering

voltage stability aspects in the contingency selection

process would not result in a prohibitive increase in

computational effort.

(b) propose a PI able to detect the most critical contingencies

as far as voltage stability. Particularly, the id ea is to detect

those contingencies that result in the smallest loading

margin capacities. In this paper the PI will be defined in

terms of branch-based voltage stability proximity indices.


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11.

CONTINGENCY

RANKING

FOR VOLTAGE STABILITl

The post-contingency operational violations usually taken into

account in contingency analysis are MW overload s in

transmission lines and transformers and bus over and under

voltages. However, voltage stability had become a very

important aspect of power systems analysis. The changes in

operating conditions due to load increasing and lack of

corresponding expansion in generation and transmission led

power systems to operate closer to their vo ltage stability limits.

Voltage instabilities and collapse occurs mainly in highly

loaded systems. It is usually associated to inadequate reactive

power support.

Fig. 1 shows a typical PV curve, which is recognized as an

important tool for helping voltage stability analysis. Consider

that a power system operates with a load demand and a voltage

magnitude of respectively P o and v o . n this case, the

maximum load for stable operation is

P

and the loading

margin

is p . A

small load increase beyond

P’

leads the

system to experience voltage stability problems and even to

voltage collapse.

PO P’

P

Fig. I

PV

curve

and

voltage

stability

limit.

This scenario justifies the need of adding voltage stability

aspects into the Contingency analysis function. Particularly,

detecting the critical contingencies

as

far as their impact on the

system’s loading margin is

of

paramount importance. The

maximum loading point and consequently

the

loading margin

can he precisely computed by continuation methods

[ 5 ]

However, they demand intensive computational effort. The

challenge here is to develop a ranking criterion

(a

PI) that

reflects appropriately the post-contingency situation. It must be

simple, efficient from the computational standpoint, and

present a clear physical meaning. On the other hand, the

voltage stability problem is very complex and results from a

strongly nonlinear behavior of the system.

So

there is a clear

trade-off between precision and efficiency to be overcom e.

111.VOLTAGE

STABILITY

INDICES

Consider a load fed by a generator through a transmission line

as shown in Fig. 2.

Rg.2.

Examplepawer system

The real power delivered to the load at the receiving end bus

R

of the transmission line is

v,’ cos q ZR

P

=-

z, 1+

z,

z , y 2 z, Z , ) C O S 8 - q z ,

I )

It can be shown that the point

of

maximum power transfer

occurs for

Z,

/ z ,

=

1. Substituting

this

value in ( I ) , one

gets

The branch-based voltage stability proximity indicator

proposed in

[ 6 ]

s given by

PR

L,,

=-

p-

3)

A

similar index can be obtained for reactive power. In

this

paper, a new apparent power-based index is proposed.

The

idea is to consider both real and reactive power flows

simultaneously. The apparent power flow is given by


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and the m aximum power transfer is

IV. PROPOSED METHOD

FOR

CONTINGENCY RANKING

The method proposed in this paper consists of ranking

contingencies according to

a

performance index that reflects

the post-contingency loading margin. Contingencies with large

PI present a small post-contingency loading margin, and are

considered severe from the vo ltage stability standpoint. A very

important constraint that has been imposed is that the

computation of PI for volta,se stability should require

approximately the sam e computational effort as the equivalent

computation for branch overloads and voltage magnitude

violations. The idea

is

to perform

all

three rankings using the

same framework.

5 )

6) The performance index for a certain contingency k is

computed as follows.

Th e new voltage stability index is

1.

2.

Perform one load flow iteration.

In case one or more generation units have reached their

he indices given by (3) and (6) approach unity as the system

load appr oaches the maximum loading point. Fig. 3 show s an

example power system used to evaluate the behavior of the

voltage stability indicator.

Bus

1 0 s 6

BUS 5

Rg.3. Six bus test system

BUS 2

Rg.3. Six bus test system

S

Fig. 4 shows that the voltage stability index LsRfor branch

6 increases as the load of bus 3 increases, approaching unity ai

the maximum loading point,

q .....

O

35 45 55 65 75 85 95 105

Real power at bus 3

Rg.4.

Behaviorof

the

voltage stability proximity indicator

-

respective reactive power generation limits, perform

another load flow iteration. In this case, generation buses

with violated generation lintits are treated as load buses,

as it is usually done in conventional load flow

calculations.

Compute the voltage stability proximity indices for all

branches according to (6).

3.

4.

Compute the performance index for contingency

k

according to

where and Lc re respectively the base case and post-

contingency indices for branch i L,,,, is the largest index

after contingency k and n r comesponds to the number of

branches. PI takes into account the index variation from pre- to

post-contingency operating conditions. This variation is

multiplied by a weight (&/L: , tm) . The

PI

for a certain

branch will he

small

even if there is a large index variation,

provided that the index for

this

branch is

sinall

if compared to

the largest index.

k

The addition of step 2 was necwary since voltage stability

problems and reactive power support are tightly related.

Therefore, violations of reactive power generation limits

strongly influence the final result;. Performing step 2 results in

a computational time overhead. However, it will not he

performed for all contingencies. Actually, this step is

necessary for the most severe contingencies only. In practice,


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VIII. BIOGRAPHIES

ABLE Iv

CAFTLlrtE RATIOS

FOR

THE 904 BUS SYSIEM

Mririo deALmeida

e

Albuquerquewas born

in N i td i , Bras il , on November

11,1956.

He obtained the BS degree

f rom the

Federal University from Ria de

Janeiro

in 1980.

He is with Fumas Csntais

El6uicas. Brazil,

where he is

responsible

for

supervising the operation of

part

of the southeast

area

of the

brazilian power system. He is pursuing i s MS egree at the State University

of

Campinas (UNICAMP).

Carlos A. Castro S’1990, M1994 , ;M2000) btained his BS and MS

degrees from UNICAM P in

1982

and

1985,

respectively. H e also obtained the

PhD

degree from A rizona State University,

USA,

in

1993. He is

currently an

associateprofessorat~ICAMP.

n the particular case of the

904

bus system, there were no

advantages in using the second PI.

VI.

CONCLUSIONS

The objective of

this

paper was to propose a contingency

ranking procedure for selecting the most critical contingencies

for voltage stability. Additionally, the ranking process should

take

the smallest extra computational effort possible with

respect to the current screeening practices (for

MW

overload

and vo ltage violation analyses). In other words, only one load

flow iteration should be computed for each contingency. This

constitutes an important constraint if compared to other

selection procedures proposed in the literature. Results have

shown that a second iteration is necessary in case of reactive

power generation limit violations at generation buses.

Therefore, the conventional contingency selection procedure

was preserved with mild modifications.

The

proposed

procedure requires in average less than two load flow

iterations per contingency. A very simple, easy to und erstand,

and easy to compute voltage stability proximity index was

used.

This

index was incorporated into a performance index

for ranking the contingencies. Results showed that the

proposed method can correctly identify the critical

contingencies for voltage stability.

VII.

REFERENCES

B. Ston,

0

A l s q .

and

A.]. Monticelli,

“Security analysis and

optimization,”

Proceedings

of

the IEEE, ~01.75,

n.12,pp.1623-1644,

1987.

G.C.

Ejebe

and B.F. Berg, “Automatic Contingency Selection,” IEEE

Trans. on Power Apparofus and System, vol PAS-98, pp.97-109, 1979.

E Albuyeh,

A.

Bose, and

B.

Heath, “Reactive power considerations

in

automatic contingency selection,”

IEEE

Transactions on

Power

Apparolus

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vol.PAS-101, n.1, pp.lO7- ll2, 19 82.

E.

Vaahedi, C. Fuchs, W. Xu, Y. Mansour, H. Hamadaniradeh, and

G.K.

Morison

“Voltage stability contingency screening and

ranking,”

IEEE

Transactions on

Power

System, ~01 .14, .1, pp.256-265. 1999.

V.

Ajjarapu

and C. Christy, ‘The continuation

power

flow: a tml for

steady

s t a l

voltage stability analysis,” IEEE Transactions on Power

Sysfem,vo1.7,n.2,pp.416-423. 1992.

Moghavvemi. M and F. M mar,

“A

Line Outage Study

for

Prediction

of Static Voltage Collapse,”IEEE Power Engineering

Review,

1998.

L.L. Freris and A.M. Sasson, Investigation

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a contigency ranking method for voltage stability in real time operation of power systems

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