IEEE Transactions on Reliability Volume 43 Issue 1 1994 [Doi 10.1109%2F24.285133] Sallam, A.a.;...

8/12/2019 IEEE Transactions on Reliability Volume 43 Issue 1 1994 [Doi 10.1109%2F24.285133] Sallam, A.a.; Desouky, M.;

1/7

170 IEEE TRANSACTIONS ON RELIABILXN, VOL. 43, NO. 1,1994 MARCH

Shunt Capacitor Effect on Electrical Distribution System Reliability

Abdelhay A. Sallam, Member IEEE

Mohamed Desouky

Hussien Desouky

Universityof Suez Canal Port Said

University of Suez Canal Port Said

University of Tanta, Tanta

Key WO Reliability improvement, Shunt capacitor,Distribution system, State-space method

Reader i d sGeneral purpose: Demonstrate a reliability-prediction modelSpecial math needed for explanation: Probability theorySj&al math needed to use r e s u h SameResults useful to: Reliability & power analysts

Summary & Conclusions To improve the security &reliability of a distribution system, as much power as feasible mustgo through a given transmission Line. This c n be achieved by usingshunt capacitors as compensators. These shunt capacitive compen-sators improve the load arrying capability of the h e y controll-ing the reactive power flow. Consequently, the capacitor existencec n not be ignored in evaluating system reliability. The paper a pplies the state-space method to calculate the reliability indices forcompensated & uncompensated systems with different successcriteria. The importance of using shunt capacitors to improve thelevel of distribution system reliability is illustrated in addition tot h e i r ~ ~ a s r e a e t i v e p o w e r c o n t r o l l e r s . u r p ,based on a Markov process, is applied to a numerical example,and indicates that system reliability is improved when usingshuntcapacitors.

1. INTRODUCTION

The main function of a power system is to feed the loadswith electrical energy as economically & reliably as feasible.The power system satisfies t h i s function, subjected to opera-tional constraints such as busbar voltage violation, power fac-tor change, and frequency variation. The power system c n bedivided into 3 subsystems: generation, transmission, anddistribution. The distribution system is responsible for transferof electrical energy from nodes (substations) to load points. Theanalysis of distribution systems is very complex because of itsdependance on the other two subsystems. So, the distributionsystem is analyzed as a separate entity [l].

Distribution system reliability is defined as the ability toprovide adequate electrical energy to the loads, with an accep-table continuity & quality [2,3]. System reliability can be sub-divided into two basic aspects [4,5]:

System adequacy which relates to the presence of sufficientfacilities withiq the system to satisfy the customer load re-quirements for static system conditions.

System security which involves the ability of the system torespond suitably to disturbances arising within the system,eg generator or transformer failure. The redundancy of linesis one of the methods to keep the security of the distributionsystem at a specific level when line interruptions occur.+

The distribution network is usually compensated by eitherseries or shunt capacitors as an effective &-economic& tool.Series capacitors increase the maximum power limit while shuntcapacitors have several effects:

reduce lagging component of circuit current,increase voltage level at the load and power factor of source

improve voltage regulation if the capacitoi units are proper-

reduce direct & reactive power loss in the system,decrease kVA loading on source generators and circuits to

relieve an over-loaded condition or release capacity for ad-ditional load growth.

Additional kW loading may be placed on the generators, vzreduce demand kVA where power is purchased,

reduce investment in system facilities per kW of load sup-

Therefore, the transmission & distribution system at somenodes or load points can be connected with shunt capacitors tocontrol the reactive power, aiming to:

reduce system losses,restore the stability margin,improve supply quality [6].

These capacitors can be used to increase the system securitylevel by increasing the loadability of uninterrupted lines. Shuntcapacitors, therefore, play the same role as redundant lines, viz,both of them increase system security.

This paper evaluates the reliability of the distributionsystem with shunt compensation, using the state-space method[7], indicating the effective role of the shunt capacitors. Thismethod uses & calculates state probabilities, state frequencies,and state durations. A numerical example demonstrates a con-siderable improvement in the reliability indices of the distribu-tion network when using shunt capacitors.

generators,

ly switched,

plied.

Notation

ps, p~ts, tFp i , tiA p [failure, repair] rate

, leq equivalent [failure, repair] ratef system frequency

i tienumberi.

probability of [success, failure]duration of [success, failure][probability, duration time] of state i

0018-9529/94/ 4.00 01994IEEE


2/7

SALLAM ET AL: SHUNTCAPACITOR EFFECT ON ELECTRICAL DISTRIBUTION SYSTEM RELIABILITY 171

Other, standard notation is given in Information for Readers& Authors at the rear of each issue.

2. PROBLEM FORMULATION

Reliability indices are calculated for a distribution system

with and without shunt capacitors, viz compensated and un-compensated systems. Figure 1 shows the ties representingthe s-independent paths which connect the supply with one ofmany electric distribution load points. These ties have, ingeneral, different loading conditions, and each tie contains ashunt capacitor. The size of these capacitors is determinedoriginally in the system subjected to minimizing the reactivepower flow or increasing the line capability. When an inter-ruption occurs at any tie, the shunt capacitors for the uninter-rupted ties are switched on. So, the interrupted kVA can be com-pensated partially or completely. These capacitors increase theloadability of the uninterrupted ties, as shown in figure 2.

Figure 1. Distribution System with Shun t Capacitors[compensated system]

I -i

m b won .auno upJCit

L m d b i u r adding xpcit rs

h l b

Figure2. Effectof Shunt Capacitor on Tie Loadability

Figure 2 illustrates the effects of shunt capacitors onthe loadability. oa represents the load kVA at power factorf. Angle f is decreased to to improve the power factorat constant load kVA, ob = oa. This improvement canbe obtained by inserting shunt capacitors feeding the systemwith reactive power cb kVAR. This increases transmittedactive power by ef kW while load carrying capability isincreased by ac kVA. If the power factor is improved tounity (f=O), the maximum increase in both active power(eg kw) and load rating (ad kVA) is obtained. This maximumincrease of tie loadability requires adding shunt capacitorsproviding the system with the total required reactive powerdg kVAR.

For an integrated power system, the loadability increasecan be computed by load-flow techniques. Accordingly, thesystem reliability is assessed by calculating:

probability of success,probability of failure,durations of success & failure.

3. SOLUTION TECHNIQUE

The problem is modeled as a Markov process. Systemreliability is evaluated by describing the states and transitionsbetween them. A system state represents a particular condition.

. ta t . 3

3.1 Example 1

A system with 2 ties and 2 components is describedby the state-space diagram in figure 3. The system can bein 1 of 4 states:

0: working with 2 ties in-service3: failed with 2 ties out-service1,2: 1 tie in-service.

This is a homogeneous Markov process. The transition inten-sity matrix [A] is:


3/7

172

[AI =

Fromstate

0

1

23

To state0 1 2 3

-(A,+A2) A1 A2 0

P1 +2+Pl> 0 A2

P2 0 -(A,+ ) A1

0 P2 P1 --(PI+ )

Multiplying [A] by the vector of state probabilities:

lpl = [Po + P1 + P2 + P31

gives:

- A,+A2)Po + PlP1 + P2P2 + 0 = 0

Alp - (A2+1(1)Pl + 0 + PSP3 = 0

A 2 P 2 + A , + P2)p2 + PlP3 = 0

0 + b p i + h p 2 - ( P I + P ~ ) P ~ 0

IEEE TRANSACTIONS ON RELIABILITY, VOL. 3, NO. 1, 1994 MARCH

fi = A 2 P l ( ~ I + ) / D

h = AlA2(Pl+P2)/D

If the system contained 4 ties, it would be described by 16 states.The states can be defined as success or failure according to the

To simplify the calculations, the state-space diagram isreduced to an equivalentlcombined success state S and anequivalentlcombined failure state F; s e e figure 4.

(1) failure criterion.

2)

bFigure4. State-Space Diagram with2 Equivalent/Combined

(3) States

The transition intensity matrix is [8]:

S F

[AI =These 4 equations are independent; one can be om it td an d isreplaced by:

Po + P1 + P2 + P3 = 1 (4) 3.2 General Solution Steps

The solution is:

PO = ( P ~ P ~ ) / D

t3 = 1/(Pl+P2)The frequencies are:

1. Define the criteria for system success2. Define all system states for each criterion3. Based on the above criteria, derive the anticipated system

states; analyze the success criteria; and calculate the loadabili-ty increase of each tie when inserting the compensators. Classifythe states as success or failure. The state-space is partitionedinto success S and failure F domains as in figure 5 .

(5)

Figure5. Partitionof the State-Space into Success, S, andFailure, F Domains

4. Solve the state-space model for steady-state state prob-abilities pi i E F and pj 0 E S).

5 . Reduce the dimension of the state-transition matrix bycombining all the states in the subset S, and the states in the

(8)


4/7

SALLAM ET AL: SHUNT CAPACITOR EFFECT ON ELECTRICAL DISTRIBUTION SYSTEM RELIABILITY

subset F. The probability of system failure p~ is the probabilityof state F:

TABLE1Reliability Data[9]

P F = P ii E F

6. System failure frequency, f F , is the frequency of F:

(9)A r

Component (failurelyear) (hourslfailure)

i E F j S

7. The mean duration of system failure, tp

The main steps of the problem solution for B specificcriterion are illustrated by the flow chart in figure 6.

Given distribution system data

Choose the load point, i

Deduc e the po ssible ties for thechosen distribution point

Calculate the loadabilityof each tie,for uncompensated and compensated systems

Apply state-space method and follbwthe

general pro cedure to get the reliabilityindices ps, p ~ ,s t~

Figure 6. Flow chart of General Solution

4. TEST SYSTEM'

~

173

The technique is applied to the reliability indices for theelectrical distribution network in figure 1. The number of ties

n = 4. The steps of the solution according to figure 6 are:1. The reliability data for the system are in table 1.

'The number of signifcant f igures is not intended o imply any ac-curacy in the estimates, but to illustrate the arithmetic.

13.8 kV circuit breakerscable terminations at 13.8 kVdisconnected switchestransformers

switchgear bus:(connected to 2 CBs)(connected to 4 CBs)3-phase cablekmfUSeS

manual switches

distribution transformerone kVAR capacitor

supply

0.00360.00180.00610.0030

0.00680.01360.12830.0023o.Ooo10.0050.0040.00162

2.125.0

3.6130.0

26.826.8

1.091 . 12.0

12.01.853.6

2. The reliability indices for the ties feeding the load pointin figure 1 are in table 2.

TABLE2Reliability Indices for Ties Feedingthe Load

Tie No. System A c r~

r Compensated 0.5153 0.1819 5.496Uncompensated 0.4554 0.1636 6.112

Uncompensated 0.4872 0.1585 6.311

3 Compensated 0.5624 0.2164 4.622Uncompensated 0.4295 0.1801 5.551

4 Compensated 0.6111 0.2072 4.8126

2 Compensated 0.5785 0.1829 5.467

Uncompensated 0.4523 0.1726 5.793

3. Let the full load at the load point be 500 kVA deliveredthrough its ties with loading conditions:

Tie no. kVA p.f. (lag) kW

1 5 0.80 42 100 0.85 853 150 0.88 1324 200 0.90 180

The power diagram is illustrated in figure 2, the increase inloadability of ties T I , T2, T3, T4 gainst the compensator sizecan be evaluated as in table 3.

4. The following 3 criteria for success are to be examined.The power X f full load) delivered to the load point must be:

a. 100, b. 70, c. 50.

5 . The state-space method is implemented as follows:


5/7

174 E E E TRANSACTIONS ON RELIABILITY, VOL.43, NO. 1, 1994 MARCH

TABLE 3Loadab ility Increase of Ties vs Compensator Size

Loadabilityincrease

Compeyto r size AkVAIUkVATie No. p.f. (AkVAR) (AkW) (AkVA)

410

1 0.8 152337

612

2 0.85 182262

620

3 0.88 284082

1428

4 0.90 426098

2 2.54 5.06 7.58 10.0

10 12.5

2 2.355 5.887 8.248 9.41

15 17.65

4 4.558 9.1

12 13.616 18.218 20.5

4 4.448 8.89

12 13.3316 17.7820 22.22

a20304674

612182262

413.318.626.654.6

7 O14.021.030.049.0

i. The continuity of load (%cont), epresents the fractionalincrease in the power delivered to the load point due to shuntcapacitor insertion. It is calculated by (12).

So we can decide that t h i s state is a failure for success-criter iodl and a success for the other two success-criteria.4

Similarly, the other states can be evaluated and tabulated;see tables 4 & 5 for uncompensated and compensated systems,respectively.

TABLE 4Success & Failure States vs Success Criteria

[for the uncompensated system]~~~~~~~~~~~

Success criterionstage State Continuityno. probability ( cont.) 100 70 50

1 Po 100 S S S

2 P1 90.84 F S Spz 80.55 F S SP3 69.79 F F SP4 58.81 F F S

3 Pl2 71.40 F S SP31 49.65 F F FP14 60.94 F F SP23 50.34 F F SP24 39.40 F F FP 4 28.60 F F F

4 PlU 41.18 F F FP234 9.153 F F FP341 19.45 F F FP412 30.2 1 F F F

5 P1234 0.0 F F F

S = success state; F = failure state

TABLE 5Success & Failure States vs Success Criteria

[for the compensated system]96cont = 1

i = l , i j

Notation

i tie numberj interrupted tie numberkWi tie load z

AkW,AkWi,- maximum AkWi at unity power factor.

increase in kWi due to shunt capacitor insertion

Example

Let j = 2 , Akwi = 0.9 AkWi,-. Then

AkW1 = 0.9 AkWi,- = 0.9.10 = 9.0 kW

AkW3 = 0.9 AkW3,- = 0.9.18 = 16.2 kW

AkW4 = 0.9 AkW4,- = 0.9.20 = 18.0 kW.

The fraction of continuity for these conditions is:

%cont = (437 - 85.0 + 43.2)/437 = 90.43 of full load

Success criterion

Stage State Continuityno. probability ( cont.) 100 70 50

1 Po

2 P1P2

P3P4

3 Pl2P31PI4

P23P24P34

4 P123P234

P341P412

5 Pl234

100

10090.4379.1067.67

79.2367.3456.4556.5245.1333.75

45.3111.2122.5433.91

0.0

S

SFFF

FFFFFF

FFFF

F

S

SSSF

SSFFFF

FFFF

F

S

SSSS

SSSSFF

FFFF

F

ii. Using tables 4 5, the failure success states can bedefined in the state diagram:


6/7

175ALLAM ET AL: SHUNT CAPACITOR EFFECT ON ELECTRICAL DISTRIBUTION SYSTEM RELIABILITY

figure 7, for the success criterion {b (70 )},without & withcompensation, figures 8 9, respectively. From which, thesuccess states for the uncompensated system are:

Pot P1, P2l Pl2;

and for the compensated system are:

PO, P1, P2t P39 P123 P31.

The other states are failure states.

Figure7. States of the Load Supplied rom IndependentTies,Tl, T2, Tsl T4

' L - , -st.0. I

Figure 8. Partition of States into Success& Failure Domains[Uncompensated; Success criterion = 70 ]

Figure 9. Partition of States into Success& Failure Domains[Compensated; Success criterion = 7 0 ]

Figure 10. Reduced State-Diagram with2 Success & FailureStates[ X , * 2x2 + 2x3 + 6b; eq 2 ~ 2 2 ~ 36~41

The state transition matrix is:

From To statestate S F

The equations become:

Omit (15) and replace it by the solution of (13) & (14). Theresult for case b (compensated; success criterion = 70 ) s:

PF = 0.7142, p s = 0.2857

t~ = 0.5838, ts = 0.2835

Similarly, the reliability indices for all cases (uncompensatedcompensated) can be calculated. The results are in table 6 .

Table 6 indicates the improvement of reliability indices dueto capacitor insertion (capacitor effectiveness). For example,at 50 success criterion the success probability is increased by0.011, and the failure probability is decreased by the same

iii. The [A] derived from figure 7 consists of 16x16elements; thus 16 equations are solved to get the probabilitiesof al l individual states. To reduce the dimension of [A],somestates can be combined. Figure 10 is the reduced state-spacegraph- amount.


7/7

176 IEEE TRANSACTIONS ONRELIABILITY, OL. 3, NO. 1 1994 MARCH

REFERENCES

[l] R. Billinton, R.N. Allan, ReliabilityA t f h g e Electric PowerSystem, 1988; Kluwer AcademicPublishers.

[2] R. Billinton, Reliabdity assessmentof electric power systems, FirstSymp. Electric Power Systemsin Dcvcloping cowrrrics 1987 Mar, pp1-7; Riad Kingdom of Saudi Arabia.

[3] R. Billinton, R.N. Allan,Reliability Evaluation of Engineering Sys tem ,1984; Longman.

[4] J. Oteng-Adjei, R. Billinton, Evaluation ofinterrupted energy assess-ment rates in composite systems,ZEEE Power Sjs te m, PWRS-5, 1990

[5] L. Salvaderi,R. Billinton, A comparison between two fuedamentallydifferent approaches to composite systemreliabfity evaluation, IEEEPower Appamn*r/sLsrems, ol 12, 1985 Dec, pp 3486-3492.

[6] T.J.E. iller, ReactivePower Connol in Electnc Systems,1982; JohnWiley & Sons.

[7] J. Endrenyi, ReliabilityMotieiing in Electric Power Systems,1978; JohnWdey & Sons.

[8] M.L. chooman, probabilislic Reliability: An Engineering Apjmxch 1968;

[9] C.R. Heising, Examples of reliabilityand availability analysisof common low voltageindustri a powerdis t r i ion system, Znrhcrtrial ond Com-mercial Power Systems Technical Gnf, 1976 May, pp 90-104; IEEE ASCalif.

NOV,p~ 1317-1323.

McGraw-Hill.

AUTHORS

Prof. AbdelhaySallam; Dept. of Electrical Engineering; Univ.of Suez Canal;Port-Said, EGY PT.

Awelhrg. spllrm (M82) was born in ElmchallaElkubra,Egypt in 1946.He received the BS (1 7), MS (1972). and PhD 1976) from C airo Universi-ty Egypt. He has been employed with the Ministry of Industry. and the El-m s ~ ying and Finishing Co. , Dept. of Electrical Substations, ElmehallaElkubra, Egypt. In 1979 hepincd th Dep. f Electrical Engkwhg, U n i v h t yof Suw Canal as a Lecturer. From 1981-1983he was a visiting member ofstaff in the Dept. f Electrical & Electronics Eng., University of New CastleUponTyne,UK.Si1983heisworkingintheDept.ofElccbical~,

University of Suez Canal where.his now a Professor. He is a m a a b a o f I EEE

Dr. Mohamed Dcooulry; Dept. of ElectricalEngineering;Univ. of Suez Canal;Port-Said, EGYPT.

Mohpwd DeswLy was born in Ismailia Egypt in 1946. He receivedthe BS (1969) Assuit University, Egypt;MS 1975) Cairo University, Egypt;and PhD (1982)Collegeof Enghcaing, Zittau, Gcrmany.In 1970, he joinedthe Dcpt. of Elactrical Engineering, University of Maasoura, Egypt as aDemonstrator, then as an Asst Lecturer 1975)and as a Ledum 1982). Since1984he joined the Dept. of Electrical Engineering, University of SuezCanalwhere he is now an Asst Professor.

Dr. HusStinDesoulry;Dept. of E b d a l ngineaing; Univ. of Tan@ EGYPT.Hussehr DesouLy was born in Elmchalla Elkubra, Egypt in 1948. He

received the BS (1972) Alexandria University, Egypt;MS 1979) MansouraUniversity, Egypt; and PhD (1990) University of Suez Canal Egypt. He wasemployedwith the Electrical Authority.Gharbia. Egypt during 1973-1990.He

was with ESACOin Saudi Arabia in 1981-1985as an ElectricalEngineer. In1991 Aug. h e joined thc Dept. f Electrical Engineering, University of Tantawhere he is a Lecturer.

Manuscript TR91-199 received 1991 November 12; revised 1992 July 21.

IEEE Log Number 10636 4TRb

Our Past Editors

The early Editors of this Transactions created somethingout of nothing, and then perservered in keeping that fragilesomething alive and growing. They deserve a great deal of ourrecognition and t hanks We, the present Editorial Board andreaders of this Transactions, are pleased to recognize and thankour early Editors, as well as he more recent ones, by publishingtheir names here.

Some of the early history is clouded because he Editorsname was not published in ths Transactions until 1960. Anyonewho has information on the Editors in those early years, pleasewrite or call us so that we can complete this list.

?P. K. McElroyErnie J. BreidungW. . Lamb, Jr.John A. ConnorRalph A. EvansRichard A . KowalskiMyron A. Wilson

Past Editors1950-19541954-19581958-19601960-19641965- 19681969-19851986-19871988-1988

This Transactions was published aperiodically fromthe time it began in 1952through 1967. In 1968it was promotedto a quarterly. It became a bimonthly (except for February whenthe Proceedings of the Annual Reliubiliv& Maintainabiliv Sym-p s i w n were distributed) in 1973 and stayed that way until 1992

r l r rcbhen it became a quarterly again.

IEEE Transactions on Reliability Volume 43 Issue 1 1994 [Doi 10.1109%2F24.285133] Sallam, A.a.;...

Documents

Transcript of IEEE Transactions on Reliability Volume 43 Issue 1 1994 [Doi 10.1109%2F24.285133] Sallam, A.a.;...