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8/18/2019 IEEE Asia Pacific Conference and Exhibition of the IEEE-Power Engineering Society on Transmission and Distributi

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Transient Stability Preventive Control

Using Critical Clearing Time Sensitivity

J un ic h i

Takaue

K a z u y a

Takahashi

Tos h iya Oh ta ka Sh in ic h i Iwa m oto

Waseda

University, Tokyo.

apanh

Abst ract: Power systems have become larger and more

complicated because of the increase of the electric power

demand, and the analysis

of

a power system needs heavier

computation. On the other hand, the social dependence on

electric power is increasing,

so

the influence of ou tages in power

systems is becoming more crucial. Therefore on-line preventive

control is more important than ever. In this paper, we propose a

generation rescheduling method for transient stability preventive

control. First we sort all contingencies

in

the decreasing order

of

their severity. This process is done by sorting all contingencies

in the increasing order

of

their critical clearing times (CCTs)

computed using the dynamic extended equal-area criterion.

Second we select several contingencies among them as objects

of consideration, and compute generation rescheduling amounts

using rotor angles

of

some machines at the appropriate time and

the linearity relationship between CCTs and outputs of critical

machines. To investigate the validity

of

the proposed method,

simulations camed out using the 9-machine 20-bus system.

Keywords: power system, transient stability, preventive control,

critical clearing time, FEAC, contingency analysis

1.

Introduct ion

Power systems have

become

larger and more

complicated because of the increase o f he electric power

demand, and the analysis

of

a power system n eeds heavier

computation. On the other hand, the social dependence on

electric power is increasing, so the influence of outages in

power systems is becoming more crucial. Therefore

on-line preventive control is more important than ever “ I .

We must assess transient stability at the current

operating condition using quantitative indices fast and

accurately. However, it is very difficult to realize it

because of the heavy burden of the analysis, so few

examples to utilize on-line transient stability assessment

exist. But many methods for

on-line

transient stability

assessment such as the equal-area criterion

[21

and the

transient energy function I” have been developed so far.

Furthermore, the extended equal-area criterion

[41

that

assesses transient stability using almost the

same

concept

0-7803-7525-4/02/ 17.00 200 2

IEEE.

as the equal-area criterion w as developed recently.

Incidentally, the relationship between Critical

Clearing Times (denoted ‘CCT’ below) and outputs of

critical machines has been found almost linear, and

methods for transient stability assessment and transient

stability preventive control have been developed [‘1[51.

These methods compute the partial derivative

of

CCT

with respect to the output of the most critical generator

(denoted ‘CCT sensitivity’ below) numerically

i.e.

estimate the CCTs at the current operating point and

another one using a method such as the transient energy

function and draw a straight line connecting the two

plotted points at the CCT-output plane, and find the

intersection with the circuit breaker tripping time. And in

[ 6 ] ,

we proposed a method for computing the CCT

sensitivity analytically using the parameters of the

One-Machine Infmite Bus equivalent (‘OMIB’) obtained

with the extended equal-area criterion. The aim of the

method is to compute the CC T sensitivity faster than the

numerical approach.

In

this paper, we propose a generation rescheduling

method considering the first swing stability. First we

screen contingencies using CCTs computed with the

extended equal-area criterion, and estimate output limits

for some specified contingencies using the computed

CCTs and the CCT sensitivities. Second we determine the

rescheduling amount using the estimated limits and the

ratio of he magnitude of the rotor angles, and perform the

screening for the operating condition after the

rescheduling. If no unstable contingencies exist, we

terminate the computation, and otherwise, we repeat the

same

process.

To

investigate the validity of the proposed

method, simulations are carried out

using

the 9-machine

20-bus system

[’I.

2 Outp u t l imi t Estimation using CCT sensitivity

We

explain the method for

the

estimation of the most

critical machine (denoted ‘CG’ hereafter) output limit

using the linear relationship between the C CT and the CG

output. First we compute the CCT corresponding to the

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current operating point using the Dynamic Extended

Equal Area Criterion ('DEE AC '). Second we com pute the

CCT sensitivity analytically using

I ) .

Defining

P

as

mechanical output.

I )

represents the partial derivative

of

the CC T with respect to P,,,,(the sum of the mac hines

belonging

to

the critical machine group). If the critical

machines group used for the DEEAC has machine(s)

different from CG, then we have to recalculate the OMIB

parameters by letting the machines belong to the critical

machine group.

where

Using the computed CCT and CCT sensitivity, we

estimate the CCT-CG output graph and find the

intersection with the straight line CCT=

t,, t c ,

is the

circuit breaker tripping time), and the CG output at the

intersection is the estimated CG output limit. For

nomenclatures of this method is shown in Fig.1. The

fundamentals of

I )

are describe d in detail in [ 6 ] .

threshold l ine

analytical direction

't-JK;singurrent

CT

sensitivityperating point

output

stimated limit

Fig.1 The method for the C G output limit estimation

Require time for the analytical sensitivity

computation is lesser than I13 of the numerical approach

due to the unnecessary of the load flow computation and

the CCT computation of the other operating point.

However, considering the fact that the relationship

between the CCT and the CG output is almost linear hut

not perfectly, the approximation error of the CCT

sensitivity computation itself exists, and the CCT

computation using the DEEAC is not perfectly accurate.

Thus it is possible that the estimated output limit is larger

than the actual one. Therefore, a tuning

is

needed in order

to prevent the harmful effects caused by the error.

For

example, set tC,+ktci k 2

),

i.e. shift the thre shold line in

Fig.1 somewhat upward.

k

defined

as

tuning coefficient

and its value should be determined by the off-line trials.

In

this

paper, we assume l.05.

3. Transient stabil i ty preventive control

In this paper, the stability scenario is that a

three-phase short-circuit occurs at a generator bus at e

subsequently cleared by tripping one line adjacent to the

fault location at W C . G output value corresponding to

CCT=t,, can be estimated by the method described in the

previous chapter. We apply

it

to the transient stability

preventive control that is performed using a generation

rescheduling.

3.1 Contingency screening

Generally, power systems are very large systems, and

it

is

impossible to assess the transient stability for

all

contingencies in detail. Therefore some of the

contingencies have to be targeted as the particular severe

ones (contingency screening). The procedure is as follows

and the flow chart

is

shown in Fig.2. The numbers of

0-

@ in the following description on the procedure

correspond to the one s in Fig.2.

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I

I J

I

I

I

Fig.2 The screening algorithm

Compute the CCTs of all contingencies using the

DEEAC, and sort all the contingencies in increasing

order of the CCTs (contingency ranking). Further,

identify CG corresponding to each contingency using

the result of Critical Machine Ranking Method

(‘CMR’) a+@+@.

2 Check whether contingencies whose CCTs

are

smaller

than

tci

(the group of these contingencies is defmed as

A) are stable or not using the time-domain simulation

program in the order of the contingency ranking. And

go to step

3

if an unstable contingency is found @+@

+a+@+D). If not, go to step 4 @+@+a+@

+@+a).

urthermore,

unless A exist, go

to

step

4

@+@a)).

3 The severest unstable contingency becomes ‘the main

target’, and the corresponding CG is ‘the main CG‘. If

an unstable contingency whose CG is different from the

main CG is found in A, it becomes ‘the sub targetl’ and

the corresponding CG is ‘the sub CGI’, and a stable

contingency in

A

whose CG is different from the m ain

CG and the

sub

CGI becomes ‘sub target2’ and the

corresponding CG is ‘the sub CG2’. If the screening is

not the fEst time and a m achine that was the main CG

or

sub CGI or sub

CG2

more than once up

to

the

previous screening is neither the main CG nor the sub

CG I, the machine becomes also the sub CG2 (This step

is

a-@

s a w hole.). Next, compute the rescheduling

amount.

4 Check whether contingencies whose CCTs

are

larger

than

tct

and smaller than

t,,‘=tc,+O.05s

(the group of

these contingencies is defined as B) are stable or not. If

an unstable contingency is found, it becomes the main

target and the corresponding CG is the main CG. If

contingencies whose

CGs

are different from the main

CG are found in A, they become the sub target2 and

corresponding CGs are the sub CG2. And whether A

exists or not, if the screening is not the first and a

machine that was either the main CG, sub CGI

or

sub

CG2 more than once up to the previous screening is

neither the main CG nor

the

sub CG I, then the machine

becomes also the sub CG2

@+@+@+@).

If

unstable contingencies are not found at all, the

screening and rescheduling are stopped

a+@+@.

3.2 Generation rescheduling

In this section, we propose a generation rescheduling

method for transient stability preventive control. At first,

we d efine the following notations The definitions of

PO

and NE are described later).

mtc:

main ta rge t

sfcl: ub

argetl

stc2: sub target2

M C G : main CG

S C G l :

sub

CGl

group

SCGZ:

sub CG2 group

PO: group

of

machines belonging to PO

NE: roup of machines belonging to NE

The procedure of the generation rescheduling is as

follows.

1

If contingencies belonging to

the

sub targetl exist,

compute the sensitivity of its CCT with respect to the

sub CGI output,

and estimate the

sub CGI output imit

corresponding to CCT=f,t. On the basis of this result,

determine the sub CG1 output change. Further, if

contingencies belonging

to

the sub target2

exist,

the sub

CG2

output

change is

zero.

The mathematical

expressions are as follows.

MI

O

V j E SCGZ

(12)

Pm,.-= p +

w

Vi

SCGl

(13)

P,,... = P AP = P ,

Q j

E SCGZ 14)

where CCTs,c,,Ds the CCT of the sub targetl computed

using the DEEAC, and Pmi,nw(resp. P,j,nm) is the

output of i th (resp. j-th) machine after the

rescheduling.

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2 Compute the sensitivity of the CC T of the m ain target

. with respect to the main CG

output,

and estimate the

main CG output limit corresponding to CCT=f,,. On the

basis of this result, determine the main CG output

change. The m athematical expressions are as follows.

MainCG

p.,.._ = PA + M h

Vh

E MCG

(16)

where

CCTm,c,D

s the CCT of the main target, that is

usually (when passing through

I

n Fig.2) computed

using the DEEAC, but that has to be computed by the

time-domain method when the main target is in B i.e.

passing through ln Fig.2. And Pmh,., is the output

of h-th machine after the rescheduling.

3 Use 6 , t , ) , rotor angle at F I . ~ . btained by the

Taylor series expansion, when identifying which

machines belong to the critical machines group for the

computation of the CCT of the main target. At first,

classify all the machines except the main CG, the sub

CG l and the sub CG2 into PO and NE. The

PO

is the

group of the m achines whose

rotor

angles

in

the Center

Of Angle ( 'CO N) reference frame at Ff are positive

(the number of its elements is

Np),

and the NE is

negative (the number of

its

elements is NnJ . Their

rescheduling amounts are determined as follows.

Urn cAc (17)

kMCC

SubCGI

PO

SubCG2 NE

All the groups of the machines are compared in

Table 1.

Output

change

Decrease Decrease Decrease

Constant

Increase

4. Simulation

In order to investigate the validity of the proposed

method, we demonstrate it using the 9-machine 20-bus

system

6]

as shown in Fig.3 where all the generators are

modeled as simplified models and all the loads are

represented as constant impedance loads. We consider

0

-0 s

the

fault locations. The stability scenario

is

described in the beginning of the previous chapter. Set

tc,=0.20s,

and t,,'=tc,+0.05s=0.25s. Her e we do not chang e

the output of generator 1 and 2, because they are operated

in the rated values. Since generator 5 and 6, 8 and

9

are

connected on the same bus, their behaviors are almost the

same. Then we consider the generators belong to the sam e

group.

At first, the

result

of the contingency ranking using

the DEEAC is shown in Table2 where 'CCT (TDS)'

means the CCT computed by the time-domain simulation

only to check the accuracy of the ranking and thus these

need not to be computed for the actual operation.

Comparing CCT(D EEA C) with CCT(T DS) to the ranking

result, the ranking

is

proved

to

be accurate enough.

As shown in Tablel, A is composed of

0

nd

@,

and

B

is of

@, 0

and

0.

he

0

egarded as

the severest contingency is actually unstable on the basis

of the result of the checking, and thus

0

s the main

target

and

G5

and G6 is the main CG. The

0 hat

is

another contingency belonging

to

A and whose CG is

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different from the main

CG

is actually unstable too, and

thus

@

is the sub target

I

and

G

and

G9

is the sub CGI

,

Su b target2 and sub CG2

are

not found in this case.

The result of the screening is shown in Tahle3, and

the generation rescheduling is performed using this result.

Table2 Ranking result (initial condition)

Table 3 Screening result (initial condition)

Generator

I

2

3

4

5

6

7

8

9

0 t - h , [rad1

Belonging group

1.2972 Fixed

0.0710 Fixed

-0.0885 NE

-0.0640 PO

-0.1716

Main CG

-0.2 677 Main CG

-0.2046 PO

-0.

330 Sub CGI

-0.0970 Sub C G l

Fault

location

apm8,9

CCT (DEEAC) Check

CG ategory

Is1

Where P is the sum of the output of G8 and

G9.

Then using the ratio of capacities, we determine the

output changes of G and G9.

0 1 0,190 3 Unstable 8,9(Su bCG I)

AP9 =- c9 AJ

- mm q-0 . 043)

=

-0.032

C C, ' 555.55+1666.66

Sub targetl

The output of G8 and G9 after the rescheduling is

computed using

(1

3 )

(29)

ns,,,er Pm8 AP, = 0.42 + -

0.01 I ) =

0.409

Pmg n-

P AP, = 1.25+ - 0 . 0 3 2 ) = 1.218

Next, As is the case with sub targetl, using the CCT

sensitivity of the a ( t h e main target) compute the output

change

Of

G5 and G 6 using

15),

ap,,,,

Where Pms bs the sum

of

output of G5 and

G 6

Therefore, the output changes of G5 and

G6

( 3 1 )

D5 =c

1666 66

x -0.088) =

-0.066

C,

+C,

AJ5 6= 555.55+1666.66

-0.088) =

-0.022

p6=c 555.55

C,+C, AJ5 6 =555.55+1666.66

Therefore, the

sum of

the output changes of

PO

is

computed using

21).

-

33.3333 x

{ -

0.088)+

- 0.044))

(34)

3 . 3333+33 . 3333

=-0 . 119

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The sum

of

NE

is

computed using (22).

M”*=

-bpm

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