1_Programacion binaria

8/6/2019 1_Programacion binaria

1/7

218 IEEE Transactions on Power Delivery, Vol. 13, No. 1,January 1998ptimized Distribution Protection Using Binary Programming

F. Soudi K. TomsovicSchool bf Electrical Engineering and Computer Science

Washington State UniversityPullman, WA 99 16 4

[email protected]

Abstract 1The fundamental goal of an electric utility is to serve itscustomers with a reliable and low cost power supply. Thisgoal has led to a number of standard protection engineeringpractices that ensure adequate service; however, withderegulation of the utility industry and increasedcompetitive pressures, there is a desire to further improveservice reliability and reduce costs. In this vein, this workproposes a binary programming optimization to identifytype and location of the protective devices on a distributionfeeder. The proposed algorithm uses engineering heudisticsto minimize computational time. Numerical exampleshighlight the proposed approach.Keywords: Distribution reliability, distribution systems,integer programming, linear programming, protectiondesign.

The fundamental goal of an electric utility has always beento serve its customers with a reliable and low cost powersupply. Traditionally, the acceptable level of reliability andcosts has been determined to a great extent by utility boardsand similar commissions. Those guidelines have led to anumber of standard protection engineering practices toensure adequate service; however, with the deregulation ofthe utility industry and increased competitive pressures,there is a desire to further improve service reliability andreduce costs. These pressures require a fundamentalimprovement in the assessment of, and design for,reliability. In this vein, this paper formulates a binaryprogramming problem to identify type and location of the

PE-639-PWRD-0-03-1997 A paper recommended and approved bythe IEEE Transmission and Distribution Committee of the IEEE PowerEngineering Society for publication in the IEEE Transactions on PowerDelivety. Manuscript submitted October 8, 1996; made available forprinting March 26, 1997.

protective devices on a distribution feeder. The objectiveof the optimization is to minimize the specific reliability.measures that are impacted by protection device locationwhile ensuring that all utility guidelines are satisfied.The change in the electric utility industry creates a need fora complete costbenefit analysis of every expense, to definenew indices for evaluating distribution reliability. Sincedistribution circuit contribute over 90% towards customeroutage and supply unavailability [1-21, addressingdistribution reliability is of paramount importance. Therehave been numerous studies for predicting the costbenefitratio associated with distribution feeder reliability [3-41.The interruption energy assessment rate (IEAR) linkscustomer outage cost to the service reliability indices inorder to incorporate such costs in the reliability costbenefitformulation [3]. In [4], it was proposed to select the mostcost effective reliability improvement project based on thecomparing the ratio of the various project costs to theassociated changes in the reliability indices. These projectsincluded replacing cables, installing protective devices, andother preventive or remedial actions. The System AverageIntenuption Frequency Index (SAIFI)and System AverageInterruption Duration Index (SAIDZ)were used in that work.In [ 5 ] , the author developed a new analytical reliabilityassessment method (Hierarchical Markov Modeling) whichfinds the expected annual interruption frequency and theexpected annual interruption duration for each customerexperience. A new measure of reliability was developedwhich includes both utility and customer costs referred as,the Total Cost of Reliability (TCR). The protection systemdesign was optimized based on these measures.Utilities can improve distribution system reliability eitherthrough preventive measures or by appropriate remedialactions in response to a disturbance. Preventive measuresinclude tree trimming on a regular basis, constructiondesign modification, e.g., lightning arresters to preventflashover, anmal guards, and so on. Remedial actionscapabilities include those provided by protective deviceresponse, fault locators and other sensors, and variousdistribution automation functions.From a customer point of view an outage can be classifiedas momentary or permanent. A momentary outage usuallylasts less than a few minutes, but a permanent outage

0885-8977/98/$10.00 0 1997 IEEE


2/7

219requires repair and may be of several hours duration. On apermanent outage due to a fault, either a fuse blows or afterseveral unsuccessful automatic reclosings an automaticsectionalizing device lockouts. Historically, momentaryfaults have been ignored both since they did not result in areduction in energy supply and since utility commissionsdid not require momehtary fault reports. Still, it is worthnoting that todays electronic loads, such as, VCRs, digitalclocks, microwaves and computers, are very sensitive tomomentary faults. With the increase of these loads,customers have become less tolerant of such faults.Therefore, any reliability evaluation should include bothpermanent outages as well as momentary outages. This isincluded in the overall formulation of this work, but forbrevity only permanent outages are shown in thedevelopment.Today, most utilities !nave developed guidelines that givestep by step procedures to select protective devices forspecific applications. The number and types of protectivedevices to be installed on a particular feeder will dependupon the system impedance, the size and type of the load,the configuration of th e circuit, and the exposure to hazardswhich may causes autages. Since these guidelines arelimited in scope, engineering judgment still plays a majorrole in order to achieve a low cost and an acceptable level ofservice reliability. This paper proposes a more systematicapproach.

2. DISTRIBUTIONPROTECTIONThis section presents background information on thedistribution problem o F interest.2.1 Network structurleDistribution networks can be classified as either radial, spotor secondary. Radial systems are the most common and thefocus of this study. Radial networks may consist of bothoverhead and underground lines using either a three wire orfour wire scheme. On a four wire system, a ground neutralwire is run alongside the three phases, whereas on a threewire system, the neutral remains grounded at the substation.Laterals branching from the main three phase feeder can besingle phase, two phase or three phase. In addition, mostutilities design a system so two radial networks can pick upneighboring loads by tie switches during scheduled orunscheduled outages.2.2 Protection devicesIn general, protection of a distribution system consists of acircuit breaker at the substation with line reclosers,sectionalizers, interrupters and fuses along the main feeders

and on the laterals. These protective devices must satisfy thefollowing objectives:0 preventing safety hazards to the public by removing a

fault circuit from the network.preventing or minimizing damage to equipment byclearing an abnormal condition.

0 improving service reliability by removing a smallsection of the circuit for a given fault.

A feeder circuit breaker located at the substation and itsprotection scheme consists of phase, ground and automaticreclosing relays. A circuit breaker has fault interruption andautomatic reclosing capabilities. A line recloser has faultsensing, fault interrupting, and automatic reclosingcapability similar to those of a circuit breaker located at thesubstation. Importantly, line reclosers have the capability ofautomatically testing a line downstream from the recloser.The automatic scheme can be set to test energize the lineonce or twice at very high speed with several additionaltests at a lower speed. The high speed tests are designed toenable the line recloser to check for a temporary faultwithout blowing load side fuses, thereby avoiding anyunnecessary permanent outage for the customersdownstream of the fuse. This capability is called a fusesaving scheme. An interrupter is similar to a line recloser,except that it does, not have automatic reclosing capability.A sectionalizer is a device designed to isolate automaticallya faulted line section after sensing the fault and waiting for apre determined number of operations of a upstream breakeror line recloser. A sectionalizer does not have faultinterruption or automatic reclosing capability, but can beused to switch load currents that fall within its continuouscurrent rating.A fuse is a low cost automatic sectionalizing device. It hasfault sensing and interruption capabilities, but obviouslylacks automatic reclosing capability so that momentaryfaults are treated the same as permanent faults. Asmentioned earlier, problems with momentary faults cansometimes be addressed by using a fuse saving scheme. Afuse saving scheme allows a breaker or a line recloser toclear momentary faults before the fuse blows and thus,allows the fuse to operate only for permanent faults.2.3 Protection designType and location of a distribution protective devices hasbeen largely left to engineering judgment with limitedguidelines. In general, a circuit breaker with phase andground relays is installed at the substation. Line reclosersare installed on the main overhead feeder and on heavilyloaded or long laterals. Due to cost limitations, only alimited number of these devices are installed on any given


3/7

220feeder. A typical feeder may have as many as three to sixrecloser locations. Location of these devices variesdepending on the utility practices and the feederconfiguration [6-71. Some utilities break the feeder intoper section) and others may use the number of connectedcustomers (typically, about 50 0 customers per section) ordistance to break the feeder into sections. Intempters areused similar to line reclosers, except that they are used forunderground circuits.Sectionalizers are overhead line devices which must be usedin conjunction with a line recloser or a breaker. If there is alocation for which a line recloser should be installed but,coordination can not be achieved (with load and source sideprotection devices) then a sectionalizer can be used instead.

wherecomponent i and ri is the outage time of component i.A recent survey [9 ] indicates that the majority of the utilitiesuse customer based indices to evaluate their servicereliability, with the most commonly used indices given asSystem Average Interruption Frequency Index (SAIFI),System Average Interruption Duration Index (SAIDI),Customer Average Interruption Duration Index (CAIDI) ,Average Service Availability Index (ASAI ) and MomentaryAverage Interruption Frequency Index (MAIFI).

is the set of components whose failure results in ansections based On the connected load (mical1y, 3- 5 MVA at the given load point, A i is the failure rate of

2.5 Distribution reliability and Protective DevicesFuses are used on both overhead and underground circuits.A fuse is low cost but comes at the great disadvantage of along restoration time due to fuse replacement and becauseit treats momentary faults the same as permanent faults. Atmany utilities, economic considerations require a fuse to beinstalled on any lateral three or more spans long. Also, it isimportant to insure that fuses will coordinate with sourceand load side protective devices. Miscoordination betweenthese devices may cause a fuse to blow for a fault outside itsprotection zone which will delay identifying the troublesection and hence increase outage duration.2.4 ~ i ~ t ~ ~ b ~ t i o neliability measure s

An important goal in designing and operating a distributionsystem is achieving and maintaining an acceptable level ofservice reliability. In this section, we discuss the effects ofautomatic, manual or remotely controlled line sectionalizingdevices in SAIFI, SAIDI, CAIDI, ASAI and MAIFI indiceswhich is summarized in Table 1.

X X X XX X XX X X

AutomaticManualRemote

A variety of reliability indices for a distribution system havebeen defined [S-91. These indices can be divided into threecategories. (X indicates an impact)

Table I : The reliability impacts of sectionalizing devices

e Single load point indices.0 Customer orientated indices.S Load orientated indices.Single load point indices which provide service reliabilitydata from an individual customer viewpoint, are the averagefailure rate A,,

nA, = C A i (1)i= l

Automatic line sectionalizing devices such as line reclosers,intempters, sectionalizers and fuses will reduce the totalnumber of customers affected for a single outage byautomatically isolating the faulted section. They also reducethe frequency of outages for customers on the source side ofthese devices, and reduce the duration of outages byexpediting the task of locating the faulted feeder section. Intheory, the more automatic devices installed on adistribution feeder the better the service reliability. Still,there are some application limitations, such as, coordination

the average outage duration r s ,n ai y; .i= lr, =7 between devices and the cost of the installation,maintenance and operation. Also, three phase linesectionalizing devices with automatic reclosing capabilitiesmay worsen the MAIFI index.(2)2 ii= l Manual line sectionalizing devices, such as switches anddisconnects, will reduce the duration of interruption bv

and the average annual outage duration U,, allowing faulted line sections to be manually isolated andpermit service to be restored to customers on unfaulted


4/7


5/7

222The following basic assumptions are used in the calculationof the SAIFI index which are representative of presentpractices.

The feeder is operated as a radial feeder but can beconnected as a loop through a normally open switch.The number and type of customers are known for eachindividual section.Failure rate for a line section includes connectedequipment failure rates.Multiple faults are not considered and all failures arerepaired before the next fault occurs.All laterals have been assigned to be one of the threepre-defied categories.A breaker is located at the substation and no fuses areallowed to be installed on the main feeder.

The SAIFI index for a distribution feeder is defined as

where N i is the number of customers in section i, NT is thetotal number of customers on the feeder. The numerator of(6) can be broken down into the contributions from themain feeder and each lateral as

a+R+1q=l

where a is the number of category three laterals, p is thenumber of category two laterals, and the first term, q = l , isthe contribution from the main feeder. The requiredcalculation for each main feeder or lateral g is

i=l i=I

where q n s the number of the possible locations on the mainfeeder or lateral, Aqi is the permanent failure rate and yq iis the temporary failure rate for section i of y, respectively,and N q j is the number of customers for section j of yincluding all laterals connected to that section. Note, if thereis a three phase device at location qk , then the variable

X q k l = 0, and Otherwise X q k l = 1. Here, the subscript 1 isused to represent a three phase device and the subscript 2represents a fuse. These counter intuitive definitions for thevariables x are used to simplify equation (8). Since themain feeder requires a three phase device at the substationand fuses are not permitted (8 ) reduces to

The calculation for the category two laterals can also begreatly simplified since a fuse will be installed at the tap andno other protective device will be installed on the lateral.Thus,

A , =? ( A q i+yq i ) ? Nq i q a + 2 ..a + p + l (10)i=l i=l

Notice, that (IO) is constant for a given feeder since theprotection has been already determined. In this way,minimizing

Z = CAqq=l

is equivalent to minimizing the SAIFI index.The constraints for this problem are coordination, designand application limitations, costs, and those due to thereduction of the non-linear binary programming problem toa zero-one linear programming problem. These are detailedin the following.3.2.1 CoordinationIf coordination between two protective devices at locationsk and can not be achieved, then a constraint must be added.For the coordination between two three phase devices,

for two single phase devices,X 4 k 2 +xg2 2 1 (13)

and for a combination of these

where n q k l and x d l represent possible locations for a threephase device, X g k 2 and x d 2 represent possible locations fora fuse at locations gk and qj respectively.


6/7

3.2.2 D esign and ap plicationFor category three laterals, a three phase device or a singlephase device must be installed at the tap points, so

xq l l + x q I 2= 1 , for q ~ ( 2..a+ l ) (15)For any other locations only one type of the protectivedevice may be installed, so

x q i , + x q i 2 2 1 , i ~ ( 2. . q n } and q ~ ( 2..a+ ) (16)If at a location qi , due to a physical or other limitation, onlya three phase device is allowed, then

or if only a single phase device is allowed, thenX q i 1 = I

must be added as a constraint. If a fuse is installed atlocation qi, then a three phase device will not be allowed forany possible location on the load side of the fuse, so

xgi2 + ~ ~ ( ~ + l ) ~I , ~ { i..qn -1) andq E(2 .. .a+ l } (19)

3.2.3 Cost limitationsDue to cost limitations:, there may be a limited number ofthree phase (20) and single phase (21) devices allowed, so

q=Ii=l q=lwhere g, is the number of the available three phase devicesfor the entire feeder and g , is the number of the availablesingle phase devices for the category three laterals.4. TEST CASEConsider the simple overhead radial system shown in Fig. 3with seven possible protective device locations. Thepermanent and temporary failure rates, the number ofcustomers and averagf; connected load to each section are

~

shown in Table 2.

223

Fig. 3 Simple 7-load point radial systemIn this example, the goal is to minimize the SAIFI index byidentifying the type and location of protective devices. Thefollowing constraints are enforced:

There are only two line reclosers available.There is no limitation on the number of the fuses whichcan be installed.A proper coordination between line reclosers inlocations #13 and #14 is not possible.A fuse can not be installed on the main feeder.A fuse or a line recloser must be installed on all taps.There will be a breaker in location #11.All laterals are category three.

The above translate into a total of 15 constraints in theproposed formulation. Then the objective of this problem isto minimize

After reducing to binary programming and removing theconstants, then the objective reduces to

Section11121314213141

Rqi V Y ~ ) Yqi U?Y~ ) Nqi ( c ~ ~ t . ) qi (KVA)1 oo 2.00 300 12000.75 1.75 250 5502.25 5.50 125 2002.00 4.75 200 4500.25 0.75 20 301 oo 2.00 50 1000.50 2.50 10 15

Table 2 Reliability data for system of Fig.3


7/7

224

21,31,41 13,14 4.5121,31,41 12,14 3.5621,31,41 12,13 4.6921,31,41 12 3.2721,31,41 13 3.6621 31 41 14 3.3

where * is the optimal solution found by algorithm fo r caseI , an d * * is or case 2.Table 3 SAIFI fo r Fig. 1 systemThe optimal solution for this problem was found using acommercial mixed integer linear programming package andis seen to be example 7 in Table 3. This solutionrecommends installing line reclosers at locations 12 and 13,and fuses at locations 21, 31, and 41. Note that the SAIFZindex is smaller for example 5, but due to the coordinationproblem, violates the specified constraints. Next, theproblem was modified to allow only one line recloser. Theoptimal solution is 3.56 intermptionslcustomer year,example 3, which is around 4% less than example 6 withtwo line reclosers. These simple examples clearly indicatethat selecting proper locations to install protective devicescan greatly enhance their effectiveness.

5. CONCLUSIONThis paper proposes a binary programming technique toimprove the effectiveness of distribution protective design.The technique identifies type and location of the protectivedevices on a distribution feeder based on the objective ofminimizing the SAIFI. Future work is focusing oncomputational issues, and addressing tradeoffs between loadand customer based reliability indices as well as temporaryand permanent fault considerations.

6. REFERENCESL.Goel and R.N.Allan, Evaluation of InterruptedEnergy Assessment Rates in Distribution System, IEEETransactions on Power Systems, Vol. 6, No. 4, Oct.1991, pp. 1876-1882.R.N.Allan and E.N.Dialynas, I.R.Homer, Modeling andEvaluating the Reliability of Distribution Systems,VoLPAS-98, No. 2, Nov./Dec. 1979, pp.436-444.ZEEE Transactions on Power Apparatws Systems,

L.GoeP and R.Billinton, Determination of ReliabilityWorth for Distribution System Planning, IEEETransactions on Power Delively, Vol. 9, No. 3, July1994, pp. 1577-1583.

4. W.F.Horton, SGoldberg and R.A.Hartwel1, ACostiBenefit Analysis in Feeder Reliability Studies,IEEE Transactions on Power Systems, Vo1.4, No.1, Jan.1989, pp. 446-452.

5 . R.E.Brown, Reliability Assessment and DesignOptimization in Electric Power Distribution Systems,Ph.D. Dissertation. University of Washington, 1996.

6. J.G.Tine and D.A.Walder, Improved DistributionSystem Reliability at Northeast Uti1ities:A CaseHistory, IEEE Transactions on Power D elivey , Vol. 8,No. 2, April 1993, pp. 689-696.

7. C.M.Warren, The Effect of Reducing MomentaryOutages on Distribution Reliability Indices,Proceedings of the, IEEE T&D Conference, Dallas,Texas, Sept. 22 - 27 1991, pp. 698-703.

8. R.Billinton and R.N.Allan, Reliability Evaluation ofPower Systems, New York: Plenum Press, 1984, pp.2 10-239.

9. IEEE Working Group on System Design, Trial UseGuide for Electric Power Distribution ReliabilityIndices, Report P1366, Draft #14.

10.C. McMillan, Mathematical Programming, John Wiley& Sons, New York, 1970,pp. 334-362.

BIOGRAPHIESFarajollah Soudi received his B.S. and M.S. in ElectricalEngineering in 1982 and 1984 from Northem ArizonaUniversity and Arizona State university, respectively. From1984 to 1994, he worked for PG&E, and his last positionwas a senior protection engineer. Since 1994 he has beenworking as a consultant and pursuing his Ph.D. degree atWashington State University. He is registered ProfessionalEngineer in the State of California and a member of TauBeta Pi.Kevin Tomsovic received the B.S. from Michigan Tech.University, Houghton, in 1982, and the M.S. and Ph.D.degrees from University of Washington, Seattle, in 1984and 1987, respectively, all in Electrical Engineering. He hasheld positions at McDonnell Douglas, IBM, and MITLincoln Laboratory. Visiting university positions haveincluded Boston University, National Cheng KungUniversity, National Sun Yat-Sen University and the RoyalInstitute of Technology in Stockholm. Currently, he is anassociate professor at Washington State University. Hisresearch interests include expert system and fuzzy setapplications to power system control and security.

1_Programacion binaria

Documents

Transcript of 1_Programacion binaria