A monte carlo method for multi area generation system reliability assessment

Area load uncertainty, correlation between area loads and generating unit derated states have been considered.. These sensitivity indices can provide information about which tie line or

R Billinton Power Systems Research Group University of Saskatchewan Saskatoon, Sask., Canada Department of Electrical mgineering

ABSTRACT: Considerable attention has been devoted to

multi-area generating system reliability assessment in

recent years [l-81 Most of proposed methods are based

on a combination of the generation capacity state

enumeration technique and the network flow (maximum

flowminimum cut) algorithm This paper presents a new

method for multi-area generation system reliability

assessment

It is based on direct sampling of generating unit

states, the clustering technique and the correlative

normal distribution sampling technique of the load

states A linear programming model is used to

minimize the total load curtailment Area load

uncertainty, correlation between area loads and

generating unit derated states have been considered

Incorporation of these factors does not create a

significant increase in computing time Sensitivity

indices of both system and each area to area

generation and tie line capacities can be calculated

These indices provide important information regarding

which tie line or which area generating capacity

should be reinforced from the overall system and each

area point of view Calculation results of a four-area

system are given to demonstrate the effectiveness of

the method

1N Most electric power companies operate as members

of an interconnected power system because of the

mutual benefits associated with interconnected

operation and planning Considerable attention

therefore has been devoted to multi-area system

reliability assessment in recent years (1-81 Most of

proposed methods are based on a combination of the

generation capacity state enumeration technique and

the network flow (maximum flow-minimum cut) algorithm

In order to reduce computational requirements in state

enumeration, some state space decomposition approaches

have been developed [1,3,4] These approaches can

prate effective in decreasing CPU time The

effectiveness of these approaches is reduced, however,

in those cases associated with a large unacceptable

set of states (infeasible range) This can easily

occur in interconnected system studies involving

relatively small individual system reserve margins

where a wide range of units or unit derated state

models are involved In order to limit the number of

states, a large rounding increment is required with

attendent loss of accuracy In order to combat this,

a large unacceptable set may be created Another

92 WM 141-2 PWRS

by the IEEE Power System Engineering Committee of

the IEEE Power Engineering Society for presentation

at the IEEE/PES 1992 Winter Meeting, New York, New

York, January 26 - 30, 1992 Manuscript submitted

August 15, 1991; made available for printing

December 3, 1991

A paper recommended and approved

W Li Area Transmission Planning Department System Planning Division Vancower, B.C., Canada B.C Hydro

problem involving computational effort is haw to deal with the detail associated with the annual load model The clustering technique utilized in Reference 5

provides a powerful approach €or aggregating load points and reducing the computation time It can also

be used to approximately capture the correlation between area loads in a cluster mean value sense This paper presents a new method for multi-area generation system reliability assessment A computer program named MASMOR (Multi-Area System Monte Carlo based Reliability evaluation) has been developed at the University of Saskatchewan based on this method

It has the following features: (1) The method is based

on direct sampling of generating unit states The generation capacity state model is not required and therefore no truncating and rounding errors are created Operational strategies of generating units can also be introduced ( 2 ) Area load uncertainty can

be considered using a normal distribution sampling technique When area load uncertainty is incorporated, correlation between area loads can be simulated more accurately by combining the clustering technique and a correlation sampling technique compared to the single clustering technique ( 3 ) A linear programing model

is used to minimize the total load curtailment while satisfying tie line capacity limits

The WEE sensitivity indices of both overall system and each area to area generation and tie line capacities can be calculated using this approach Reference 4 illustrates a procedure which can be utilized to calculate the sensitivity of the overall system An area may represent an individual utility

or even jointly owned generation and therefore area sensitivity indices are potentially useful These sensitivity indices can provide information about which tie line or which area generation capacity should be reinforced from both an overall system and each area point of view,

GFNERATING UNIT STATE SAMPLING The behaviour of each generating unit in each area can be simulated by a uniformly distributed randcnn number sequence in [0,1] In the case of a two state representation, let Si denote the state of the ith generating unit and FORi be its forced outage rate A uniformly distributed random number x is drawn in [Of11 ,

0 (up state) if x 3 FoRi

1 (down state) if 0 4 x < M R i

In the situation in which generating unit derated states are considered, let PDRi be the probability of the derated state of the ith generating unit,

if x 3 PDRi + FoRi

if PDRi 4 x < PDRi + FoRi ( 2 )

The above sampling technique can be easily extended to include multi-derated generating unit states

2 (derated state) if 0 d x < PDRi

After all the generating unit states in each area

are determined by sampling, a generation capacity

level for the area can be obtained A similar sampling

technique can be used to select the tie line states in

a multi-area system

LQAD MODEL The load model involves two phases In the first

step, the 8760 hourly load points representing a year

are grouped into several clusters and the mean values

of the load points for each area in each cluster are

obtained by the K-means algorithm In the second step,

the area load uncertainty and correlation can be

incorporated by a normal distribution sampling

technique and a correlation sampling technique

The K-Means Algorithm 191

The K-means algorithm can be stated as follows :

(1) Select initial values of cluster means Mij

where i and j denote cluster i and area j

(2) Calculate Euclidean distances from each

hourly load point to each cluster mean by

(3)

where Dki denotes the Euclidean distance from

the kth load point to the ith cluster mean,

L the kth load value in the jth area and N

is the number of areas

Re-group the pints by assigning them to the

nearest cluster and calculate the new cluster

means by

kj

( 3 )

where Ni is the number of load points in the

ith cluster and IC denotes the set of the

load points in the ith cluster

( 4 ) Repeat steps (2) and (3) until all cluster

The cluster means are then used as the load levels

for each area in each cluster Each load level

represents Ni load points in the relative cluster in a

mean value sense Correlation between mean values of

area load points in each cluster is captured in the

K-mean algorithm Since it reflects correlative

relation between cluster means, the captured

correlation is approximate After reliability indices

for each cluster are calculated, annual reliability

indices can be obtained by weighting the indices for

each cluster by (Ni/8760)

means maintain unchanged between iterations

Area Load Uncertainty And Correlation

Load uncertainty always exists in an actual parer

system and it has long been recognized that load

uncertainty can have a great impact in reliability

evaluation of a single area generation system and a

composite system [lo-111

Load uncertainty can be modeled using a normal

distribution and therefore it is necessary to draw

normally distributed random numbers in order to

simulate area load uncertainty A normal distribution

has two parameters: mean value and standard deviation

The mean values are the cluster means obtained by the

K-mean algorithm and the standard deviation is

assigned according to the perceived load forecast

uncertainty, such as 5% to 10% This paper utilizes the tabulating technique of normal distribution sampling presented in Reference 11 to create normally distributed random numbers

If all the area loads are completely dependent, the cluster means of all the area loads are the same for each cluster In this case, only one normally distributed random number is required for each cluster

in order to determine the load states of all areas If all area loads are not completely dependent but some

are correlated, it is necessary to generate a normally distributed random vector for each cluster, in which each component corresponds to the load state of a particular area and whose components satisfy the correlation between the load points of different areas

in the same cluster The correlation can be expressed

by a correlation coefficient The correlation matrix corresponding to the ith cluster can be calculated as follows

According to the statistical definitions of variance, the covariance and the correlation coefficient, the elements of the correlation matrix corresponding to area n and area m for the ith cluster

is

The covariance matrix C corresponding to the correlation matrix p can be obtained by

2'

where U is the standard deviation for the ith area load dertainty usually, the same standard deviation

is assumed for all area loads In this case, Equation

(6) is simply written as

2

After the covariance matrix C between area loads for each cluster is obtained, a load correlation sampling technique [ll] can be used to simulate area load uncertainty and correlation The basic steps are summarized in the following:

(1) Calculate the area load covariance matrix according to Equations ( 5 ) and (6) from information obtained by the K-means algorithm

(2) Draw a N dimensional normally distributed random vector G whose components are independent of each other and each component has a mean of zero and a variance of unity, where N is the number of areas

Calculate the low triangular matrix A by the following equations

( 3 )

c,

II

2 4 i-1 k-1 Aii 0 (Cii - L Aik)

j-1

k-1

Aij * (Cij - E Aik Ajk)/Ajj

( 4 ) Create a N dimension correlative normally

distributed random vector R by

where B is a mean value vector whose

components are the cluster means Both area

load uncertainty and the correlation defined

by matrix C are included in the random vector

R

LINEAR PROGRAMMING MODEL FOR MULTI-AREA SYSTEMS

After the area generation capacity levels, area

load states and tie line states are selected by the

described sampling techniques: it is necessary to

evaluate the reliability indices of the selected

multi-area system state All areas can be divided into

two sets of supporting and supported areas In the

supporting set, the available area generation capacity

is larger than the area load A "generator variable"

is defined for each area in the supporting set The

u p r limit of each "generator variable" is the

difference between the available area generation

capacity and the area load In the supported set, the

available area generation capacity is smaller than the

area load A "required load" is defined for each area

in the supported set, which equals the difference

between the area load and the available area

generation capacity A "fictitious generator variable"

is also defined for each area in the supported set

When the "required load" at each area can not be

completely satisfied due to the insufficient total

available generation capacity in the supporting set

generator variables" can provide the unsatisfied parts

of the "required load" such that power balance in each

area is always guaranteed Essentially, the

"fictitious generator variables" are load curtailment

variables in the supported areas and therefore the

upper limit of each "fictitious generator variable" is

assigned as the relative "required load"

The "generator variables", the "fictitious

generator variables", the "required loads" and tie

lines constitute a new small "generation-transmission"

system The basic objective is to minimize the total

load curtailment while satisfying the power balance at

each node (area) and upper limits of the tie line

capacities, the "generator variables" and the

"fictitious generator variables" The following

linear programming model can be used for this purpose:

i m

s.t E TP + GPi = 0

j +i 3

E TP + GFi = DPi (i€ND)

j +i 3

where GPi and GFi denote the "generator variables" and

the "fictitious generator variables" at the ith node

respectively; j+i'* indicates that j belongs to the

line set in which all lines are connected to node i;

TP is the tie line power on line j and it is positive

when entering into node i and negative when issuing I

from node i; DPi is the "required load" at the ith node; SPi is the upper limit of the ith "generator variable"; is the capacity limit of the jth tie

line; NG, ND and NT are the sets of the "generator variables", the "fictitious generator variables" and tie lines respectively; ai is the weighting factor for the ith "fictitious generator variable"

There is a wide variety of possible supporting policies in multi-area generation system reliability assessment One of advantages of a linear programming model such as that described is that variable supporting policies can be easily incorporated Four supporting policies of priority order, priority order plus path order, shortest distance and proportional principle have been incorporated into the "OR computer program A priority order supporting policy

is used in this paper This can be considered by assigning different values of weighting factors ai The supported area with the first priority has a maximum value of ail the supported area in the next priority has a second maximum value of ai, etc These values of ai are specified in terms of their relative magnitudes and therefore it is easy to select these values

Another advantage of the linear programming model

is that the LOEE sensitivity indices of both system and area to area generations and tie line capacities can be calculated It should be noted that it is not possible to obtain the area sensitivity indices merely

by using the concept of dual variables Calculation of the area sensitivity indices can be explained intuitively as follows For a standard linear programming problem

min cTx

s.t AX = b

x 3 0 its optimal and feasible solution can be expressed by

X,, = B b where B is the optimal basis at the optimal and feasible solution and is the basic variable subvector B will maintainkchanged if the right-hand term b has a sufficiently small change Therefore

(18) this means

J

where ~i~ is an element of B - ~

Equation (19) indicates that the elements in the optimal basis are the sensitivities of the basic variables to the elements in the right-hand term of constraints Area sensitivity indices to area generations and tie line capacities can be therefore obtained by solving the linear programming model expressed by Equations (12) - (17)

CASE STUDIES The Test System

The four-area system shown in Figure 1 is considered as the test system

Figure 1 The four-area generation system

Area 1 is the basic IEEE Reliability Test System

(RTS) [12] The annual peak load of the RTS is 2850 FlW

and its generator data (32 generating units) can be

found in Reference 12 Area 2, 3 and 4 are three

modified RTS's The modifications are as follows:

Area 2: Three 197 MW generators are removed and the

annual peak load is reduced to 2280 MW

Area 3: One 800 MW generator with FOR=O.18 is added

and the annual peak load is increased to

3575 Mw

Area 4: One 800 MW generator with FOR=O.18 and one

600 MW generator with FOR=0.15 are added

and the annual peak load is increased to

4180 MW

The tie line data are given in Table 1

Table 1 The Tie Line Data

From Area No I Capacity ( M W ) I FOR 1

1 - 3 I 200 I 0.0005 1

_ _ _ I

The annual load curve data for the RTS (8736

hourly load points in percentage of the annual peak

load) are given in Reference 12 When the area loads

are considered to be completely dependent, the same

annual load curve data of the RTS are applied to the

four areas When correlation between area loads (non-

completely dependent) is considered, the area load

curve in Area 1 remains unchanged and the area load

curves in Area 2, 3 and 4 were obtained by displacing

the hourly load values of Area 2 ahead by four hours,

those of Area 3 ahead by two hours and those of Area 4

backwards by two hours respectively

In order to include generating unit derated

states, the 350 MW and the two 400 Mw generators were

derated to 50% capacity with the derated state

probabilities given in Reference 10 The state

probabilities of the derated models are such that the

derating-adjusted two-state model data is identical to

that given in Reference 12

The specified supported priority order is : Area 4

-Area 3 -Area 2 -Area 1

LOLE And LOEE Indices

Eight cases were studied The convergence criterion of the simulation is that the coefficient of variation for the system LOEE is less than 0.05 The studies were done on a computer VAX-6330 The results for these studies are shown in Tables 2-5

completely dependent area loads, no load uncertainty and no generating unit derated states

Case 2: correlation between area loads, no load

uncertainty and no generating unit derated states

Case 3: completely dependent area loads, load

uncertainty (5% standard deviation) and

no generating unit derated states Case 4: correlation between area loads, load

uncertainty (5% standard deviation) and

no generating unit derated states Cases 5 to 8 basically correspond to Cases 1 to 4

respectively with the difference that derated states

of 50% capacity for the 350 MW and the two 400 MW

generators in each area are included

Case 1:

Table 2 LOLE Indices for Cases 1 to 4 (in hrsmac)

I Case 1 I Case 2 I Case 3 I Case 4 I

I

I

I Area 1 I 0.51999 I 0.18562 I 1.50711 I 0.56825 I

1 Area 2 I 0.65723 1 0.28788 I 1.29675 1 0.54931 1

I Area 3 1 4.67838 I 3.25331 I 6.82495 I 4.67462 I

1 Area 4 1 6.71499 1 5.64925 I 9.92413 1 8.16069 1

1 System 9.04900 I 17.12834 I 13.33456 I

I(minutes) 1 2.43 1 3.42 1 2.28 I 3.62 1

I I I

I 11.69466 I

I ( (I ( -_ I - I I

Table 3 W E E Indices for Cases 1 to 4 (in HWhmar)

I I Case 1 1 Case 2 I Case 3 I Case 4 1

I Area 1 I 48.533301 11.275011 212.627901 61.233461

I Area 2 I 73.920731 18.025581 162.838291 32.225051

I Area 3 I 736.581121 388.3348111222.51611I 648.877621

I Area 4 )1309.93604~1064.93188~1972.32385~1501.68359~

I System ~2168.97144~1482.5677513570.30713~2244.02026~

_l-l _

Table 4 LOLE Indices for Cases 5 to 8 (in hrsmar)

I Case 5 1 Case 0 i Case 7 I Case 8 1

I

I Area 1 I 0.16263 1 0.04125 1 0.80329 I 0.27450 I

1 Area 2 I 0.54225 I 0.28788 I 1.08667 I 0.45581 1

1 Area 3 I 2.15711 1 1.08688 I 3.77542 I 2.21619 1

I Area 4 1 3.17558 1 2.49638 I 5.13854 I 4.34513 I

1 System I 5.73323 I 3.85050 I 9.31079 I 6.97538 I

((minutes) I 3.26 I 5.35 I 3.03 1 5.37 I

I CPU tlme 1 I

-

Table 5 LOEE Indices for Cases 5 to 8 (in MWhmar)

I

I -

1 Area 1

1 Area 2

I Area 3

I Area 4

I System

Case 5 I Case 6 1 Case 7 I case 8 I

18.53292) 2.434861 115.816981 26.667501 53.778731 18.941401 133.968721 29.95026) 298.260931 106.248811 608.011411 262.732941 532.648561 391.914% l1010.176451 694.656491 903.221311 519.53979~1867.97363~1014.00714~

-

-

It can be seen from these results that the indices

in the cases of completely dependent area loads are

larger than those in the cases of correlation between

area loads under the same other conditions that load

uncertainty and/or generating unit derated states are

considered or not considered Area load uncertainty

can have a great inpact on the calculated reliability

indices and always provides a more pessimistic

appraisal of multi-area system reliability

Utilization of derated state models for large capacity

generating units provides more optimistic estimation

of multi-area system reliability compared to the

utilization of a derating-adjusted testate model It

is therefore advisable to consider all the factors

existing in an actual power system such as correlation

between area loads, area load uncertainty and

generating unit derated states in multi-area system

reliability evaluation

In the results shown in Tables 2-5, there is an

apparent anomaly in the comparison between Case 2 and

Case 6 These two cases are identical except for the

fact that Case 6 includes the derated state models

The LOLE and LOEE in Area 2 do not decrease, as one

might expect, in Case 6 when compared with Case 2

This is due to the fact that Area 2 has a relatively

large reserve of 23.4% (compared to Area 4 with

14.9%) The effect of including a derated state model

in this case is relatively small and is masked by the

residual uncertainty associated with Monte Carlo

simulation

Sensitivity Indices

The method presented in this paper has been used

to calculate both system and area LOEE sensitivity

indices to area generations and tie line capacities in

various cases Additional CPU time is required when

the sensitivity indices are calculated The WEE

sensitivity indices for Cases 1 to 4 are listed in

Tables 6 to 9 It should be noted that Area No or system in the first column corresponds to incremental

variations of LOEE in the sensitivity indices while

Area No or Line No in the first row corresponds to incremental variations of area generations or tie line capacities

It can be seen from these results that although the values of the sensitivity indices are different in the various cases considering completely dependent area loads or correlation between area loads, area load uncertainty or no load uncertainty and generating unit derated states or derating-adjusted two-state models of generating units, their ranking orders in these cases are basically the same On the other hand, the ranking orders of the sensitivity indices for the overall system and each area are different From the overall system point of view, the best choice is to reinforce Tie-line 4, followed by Tie-line 6 and the

generating capacity in Area 4 From an Area 4 point of view, the best choice is to reinforce the generating capacity in Area 4, followed by Tie-lines 6 and 2 From an Area 3 point of view, the best choice is to

reinforce the generating capacity in Area 3, followed

by Tie-lines 3 and 5 From an Area 2 point of view, the best choice is to reinforce the generating capacity in Area 2, followed by Tie-lines 1 and 3

From an Area 1 point of view, the best choice is to reinforce the generating capacity in Area 1, followed

by Tie-lines 1 and 2 Increasing the generating

capacity of each area naturally has the greatest impact on improving the reliability of each area itself It is interesting to note that for the overall system, the first choice should be to reinforce two tie lines instead of increasing the generating capacity of the multi-area system

coNcLusIoNs

A new method for multi-area generation system Table 6 UXE Sensitivity Indices of System and Area to Area Generation and Tie Line Capacities in Case 1 (in rwh/year,+w)

I I Area 1 I Area 2 I Area 3 I Area 4 1 Line 1 I Line 2 I Line 3 I Line 4 I Line 5 I Line 6 I

I Area 1 I -0.51542 I -0.01747 I -0.10483 I -0.06989 I -0.34070 I -0.20966 I -0.08736 1 -0.00874 I -0.14851 1 -0.04368 1

I Area 2 I -0.00874 I -0.65520 1 -0.02621 1 -0.10483 I -0.55910 I -0.07862 I -0.55910 1 -0.06989 I -0.00874 I -0.45427 1

1 Area 3 1 -0.17472 1 -0.04368 I -4.67376 1 -0.54163 I -0.04368 1 -0.31450 1 -4.45536 j -3.69533 1 -4.17581 I -0.46301 I

I Area 4 I -0.06989 I -0.03494 I -0.06989 I -6.70925 I -0.06989 I -6.40349 I -0.11357 I -6.12394 I -0.00000 1 -6.61315 I

I S p t a I -0.76877 1 -0.75130 I -4.87469 I -7.42560 I -1.01338 I -7.00627 I -5.21539 I -9.89789 I -4.33306 I -7.57411 I

Table 7 UXE Sensitivity Indices of System and Area to Area Generation and Tie Line Capacities in Case 2 (in Whhear/llW)

I I Area 1 I Area 2 1 Area 3 1 Area 4 I Line 1 1 Line 2 I Line 3 I Line 4 I Line 5 1 Line 6 I

I Area 1 I -0.18346 1 -0.00000 I -0.06115 I -0.03494 1 -0.18346 I -0.07862 I -0.06115 I -0.01747 I -0.06115 I -0.03494 I

I Area 2 I -0.00000 I -0.27955 1 -0.00000 1 -0.03494 I -0.26208 I -0.03494 I -0.26208 I -0.03494 I -0.00000 I -0.21840 I

I Area 3 1 -0.09610 I -0.00000 I -3.24979 I -0.28829 I -0.00000 I -0.19219 1 -3.23232 1 -2.76931 1 -3.04886 1 -0.28829 1

I Area 4 I -0.03494 I -0.00000 I -0.00000 I -5.64346 I -0.00000 I -5.52115 1 -0.03494 I -5.46000 I -0.00000 1 -5.62598 I

I System I -0.31450 I -0.27955 1 -3.31094 I -6.00163 1 -0.44554 1 -5.82691 1 -3.59050 I -8.28173 I -3.11002 1 -6.16762 I

Table 8 UlEE Sensitivity Indices of System and Area to Area Generation and Tie Line Capacities in Case 3 (in twh/year/?w)

I I Area 1 1 Area 2

1-1 Area 1 I -1.50259 I -0.13104

1 Area 2 I -0.05242 1 -1.29293

I Area 3 I -0.45427 I -0.21840

I Area 4 1 -0.41059 I -0.33197

1 System I -2.41987 I -1.97434

Area 3 I Area 4 I Line 1

-0.31450 I -0.29702 I -0.86486 -0.13978 1 -0.28829 1 -0.83866 -6.82282 I -1.15315 1 -0.09610 -0.23587 I -9.92410 1 -0.17472 -7.51296 1-11.66256 1 -1.97434

Line i I Line 3 I Line 4 I Line 5

-0.47174 I -0.16598 I -0.12230 I -0.45427 -0.20093 I -0.76877 I -0.20966 1 -0.04368 -0.57658 I -5.87059 I -4.73491 I -5.36390 -8.80589 I -0.21840 I -8.63117 I -0.03494 -10.05514 1 -7.02374 1-13.69805 1 -5.89680

Line 6 I

-0.17472 I

-0.52416 I

-0.81245 I

-9.20774 I

-10.71907 1

I

Table 9 LOEE Sensitivity Indices of System and Area to Area Generation and Tie Line Capacities in Case 4 (in twh/year/W)

I I Area 1 I Area 2 1 Area 3 1 Area 4 1 Line 1 1 Line 2 1 Line 3 1 Line 4 I Line 5 1 Line 6 1

I Area 1 I -0.56784 I -0.00000 J -0.13104 1 -0.03494 I -0.53290 I -0.31450 I -0.13104 I -0.11357 I -0.34944 I -0.03494 I

I Area 2 I -0.00000 I -0.54163 I -0.02621 I -0.10483 I -0.54163 I -0.10483 I -0.48922 I -0.07862 1 -0.02621 1 -0.37565 I

I Area 3 I -0.02621 I -0.00000 I -4.67376 I -0.19219 I -0.00000 1 -0.16598 I -4.50778 I -4.20202 I -4.48157 I -0.19219 I

1 Area 4 1 -0.05242 1 -0.02621 1 -0.02621 I -8.15942 I -0.02621 I -7.79251 1 -0.05242 1 -7.82746 I -0.00000 I -8.07206 I

I Sytm I -0.64646 1 -0.56784 I -4.85722 I -8.49139 I -1.10074 1 -8.37782 1 -5.18045 1-12.22166 I -4.85722 I -8.67485 I

reliability assessment is presented in this paper

This method is based on direct sampling of generating

unit states, the clustering technique and the

correlative normal distribution sampling technique of

load states and a linear programming model to minimize

the total load curtailment Area load uncertainty,

correlation between area loads and generating unit

derated states have been considered Incorporation of

these factors does not create a significant increase

in computing time Sensitivity indices of both system

and each area to area generations and tie line

capacities can be calculated These indices provide

information on which tie line or generating capacity

in which area should be reinforced first from the

overall system and each area point of view

The calculated results for a specific four-area

system indicate that considering correlation between

area loads and generating unit derated states can

produce an optimistic appraisal of multi-area

generation system adequacy while considering area load

uncertainty can provide a pessimistic appraisal The

actual factors which exist in an actual power system,

therefore, should be incorporated in a multi-area

generation system reliability assessment Although

consideration of these factors can lead to different

values for the sensitivity indices, their ranking

orders are basically the same

The ranking orders of the sensitivity indices for

the overall system and each area are, however,

different which indicates that a compromise between

areas and the overall system is required when

selecting a reinforcement plan based on the

sensitivity indices

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M.S Aldenderfer and R.K Blashfield, "Cluster

Analysis", Newbury Park, Sage Publications, 1984

[IO] R.N Allan, R Billinton and N.M.K AWel-Gawad,

"The IEEE Reliability Test System - Extension

to and Evaluation of the Generating System", IEEE Transactions on Power Systems, PWR-1, No 4,

1111 Li Wenywn and R Billinton, "Effect of Bus Load Uncertainty and Correlation in Composite System

Adequacy Evaluation" , IEEEDES 1991 Winter Meeting, 91-75-0, PWRS, New York, Feb 3-7,

1991

[I21 IEEE Conunittee Report, "IEEE Reliability Test

Nov 1986, pl-7

System", IEEE Transactions on PAS, Vol 98; 1979,

~2047-2054

BIOGRAPHIES

Billinton (F, 1978) came to Canada from Eng?a in 1952 Obtained B.Sc and M.Sc Degrees from the University of Manitoba and Ph.D and D.Sc Degrees from the University of Saskatchewan Worked for Manitoba Hydro in the System Planning and Production Divisions Joined the University of Saskatchewan in

1964 Formerly Head of the Department of Electrical Engineering Presently C.J MacKenzie Professor of Engineering and Associate Dean, Graduate Studies, Research and Extension of the College of Engineering Author of papers on Power System Analysis, Stability, Economic System Operation and Reliability Author or co-author of seven books on reliability Fellow of the IEEE, the EIC and the Royal Society of Canada and a Professional Engineer in the Province of Saskatchewan

G r a & t d TsingHua University Obtained M.Sc and Ph.D Degrees from Chongqing University Worked for the North-East Power Company of China in the Technical and Equipment Division and at the Electricit6 de France in the Research and Development Division, Chongqing University and University of Saskatchewan in the Electrical Engineering Department

He is-presently with the System Planning Division of B.C Hydro

Author of papers on Secure and Economic Operation, Optimization Techniques, Power System Planning and

Reliability Author of a book on secure and economic operation of power systems Senior member of the IEFZ and member of the Chinese Society of Electrical mgineering and the Sociitk des Electriciens et des Electroniciens de France