Cascade Reservoirs Construction - SJEMR · 2020. 8. 28. · Cascade Reservoirs Construction ‐‐...

ScientificJournalofEconomicsandManagementResearchVolume2Issue08,2020

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CascadeReservoirsConstruction

‐‐ACost‐BenefitAnalysisof"NewKaribaDams"FeiGao1,*andXiaLi2

1SchoolofInsurance,CentralUniversityofFinanceandEconomics,Beijing102206,China2SchoolofManagement,ShanghaiUniversity,Shanghai200444,China

Abstract

Thispaper established theCost‐BenefitOptimizationModelof cascade reservoirs toprovide the most economic address selection planning. We applied the SimplifiedTriangleMethodforFloodRoutingtoestimatetheMaximumandminimumdischargeofeachdam,provided themanagementstrategies indifferentmonthsand locations forZRA.

Keywords

0‐1IntegralProgramming,Cost‐BenefitOptimization,Simulation.

1. Introduction

1.1. BackgroundJune2015,areportbytheInstituteofRiskManagementofSouthAfricaincludedawarningthattheKaribadamis in jeopardyofcollapsing.KaribaDam,oneofthe largestreservoirs intheworld,straddlingtheborderbetweenZambiaandZimbabwe,nourishesandprotectsmorethan31billionpeoplealongtheZambeziRiverandsuppliesnearlyhalfthenations’electricitywithitsnumberof6,400GWh.2015,waterlevelsatKaribaDamdroppedto12%ofthecapacity.Itsbase erodedbywater streams,whichnot jeopardizemore than3billionpeople’s lives,butreduce40%energygenerationintheareaofSouthAfrica[1].Tobemorespecific,levelsfellto477.25 meters above sea level from 482.83 meters a year earlier, causing a 49% hike inelectricityprices [2]. Inorder toprevent theworseningof levelsdrop,protectpeople fromdangerous,andrecoverorenhanceitscapacityofpowergeneration,threeoptionshadbeenproposed: 1)Repairing the existingKaribaDam, 2)Rebuilding the existingKaribaDam, 3)RemovingtheKaribaDamandreplacingitwithaseriesoftentotwentysmallerdamsalongtheZambeziRiver.Theaimoffirsttwooptionsistorecoverthecapacityofdam,andthethirdoneisraisedbythepurposeoflargerenergygenerationandadditionalbufferseventhereisanextremecondition.IRMSAandtheWorldBankhadgivenabudgetoffirsttwooptions,andthethirdoneisestimatedbycost‐benefitoptimizationmodelofcascadereservoirs.Accordingtothecostsandbenefitsanalysisaswellasrisksandopportunitiesanalysis,theabilitytofund‐raisingshouldbegiventhepriority.OurtaskistoprovideadetailedanalysisofOption3).ThisnewsystemofdamsshouldhavethesameoverallwatermanagementcapabilitiesastheexistingKaribaDam.OuranalysissupportsarecommendationastothenumberandplacementofthenewdamsalongtheZambeziRiver.What’smore,wedevelopedastrategyformodulatingthewaterflowthroughournewmultipledam system that provides a reasonable balance between safety and costs. In addition toaddressingknownorpredictednormalwatercycles,weprovidedguidanceforextremewaterthatexplainsandjustifiestheactionsthatshouldbetakentoproperlyhandleemergencywaterflowsituations.Ourrecommendedstrategyincludesinformationthelocationsandlengthsof


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timethatdifferentareasoftheZambeziRivershouldbeexposedtothemostdetrimentaleffectsoftheextremeconditions.

1.2. GeneralAssumptionsThewaterstoragecapacityofthereservoirisequaltothemaximumamountofwateritcanprovide.Thebenefitsofbuildingareservoirareonlyincludedfiveparts:powergeneration,irrigationbenefits,watersupply,floodcontrolbenefitsandincomeinrecreation.Thecostofbuildingareservoirisonlyincludedfiveparts:constructionofdams,constructionof power stations, costs of maintenance, cost of populationmigration, and loss during theconstruction.Regardlessoftheusagetimeofthedam,costsandbenefitsarecurrent.Withoutconsideringthenumberofthespillwaygatesandswitchstateinthesesmallreservoirs.

1.3. NotationsTableThefollowingtableprovidesmeaningsofimportantnotationsusedinourmodels.

Table1:NotationsTableSymbols Meanings Unitai Ifbuildadam at No.ipoint,ai=1; ifnot,ai =0

Vi WaterstoragecapacityofNo.ireservoir m3

iPo PopulationaroundNo.iarea Qi Water‐carryingcapacityattheoutletofNo.idam m3/s

Benefits

Ei ElectricenergyproductionbyNo.ipowerstation $Hi DifferentheightbetweenNo.ipointandNo.i+1point m

Coefficientofelectricityconversionfromwater Gi IrrigationcapacitybyNo.ireservoir $

ii ProbabilityoftypeifloodingatNo.iarea Ui Incomeofurbanwatersupply $

Cost

Bi CostofconstructionofNo.idam $

Si CostofconstructionofNo.ipowerstation $

Mi CostofmaintenanceofNo.idam $

Hi Costofpopulationmigration $

Li LossduringtheconstructionofNo.idam $

λ Coefficientoftotalcosts

γ Coefficientofannuity

2. DamSiteSelectionProject

Inordertoselectthebesteconomicplanfordamconstruction,wechooseoutasmanydamsaswecan,thenuse0‐1IntegerProgrammingtodeterminethespecificpointstoconstruct.Itisworthtopayattentionthatnoteverydamwouldbebuiltfinally,andtheeconomicfactoristhemostimportanttoconsider.

2.1. SelectionofStartPointandEndPointThe 2,574‐kilometre‐long River of Zambezi River flows through eastern Angola, along theborder between Zambia and Zimbabwe to Mozambique. There are two main sources ofhydroelectricpowerontheriver,theKaribaDamforZambiaandZimbabweandtheCahora


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BassaDamforMozambiqueandSouthAfrica.InordertoprotectthesovereigntyandintegrityofKaribaDamandsubstitutetheroleofit,thelocationofthesesmallerdamsmustnotcrossthe border between Zambia andAngola (Theblack line in Figure 1), and it is nomeans tobeyondtheentryofthelatterReservoir.Thus,weselecttheStartPointatthenationalborderatthepointofChavuma,andtheEndPointattheentryofCahoraBassaLake(Tworedstartsonthemap).

Figure1:PotentialDamLocation

2.2. PrinciplesofDamSiteFordecades,potentialhydropowerprojectsanddamshadtakenagreatdealofresearchforscientists and academics. They think, locations of those rivers of big dropping variance isbenefitforpowergeneration(AsmarkedontherightofPictureone)[4],andfloodingareasmustbeprotectedbydamsorothermeans.Finally,weselectedthepotentialsitesfordamsasmanyaspossible,whichmetatleastoneconditionoffollows:1.Highdroppingvarianceofriver;2.Locatedatfloodingandrainyareas;3.Rapidorhurrywaterflowsthroughthepoint;4.Locatedatthebranchoftheriver,whichisnarrowatitsentry.

2.3. MarkPointsontheMapAlong the chosen‐distance‐river, about 1200 kilometers, wemarked 22 points on themapwhichmeetsatleastonecondition,especiallyatthelocationofVictoriaFall(No.12),BatokaGorge (No.13),Devils Gorge (No.14) andMuptaGorge (No. 20). And a description of thesepointsasfollowing:

Table2:DescriptionofpotentialDamSite

Pointnumber Description

No.1toNo.5 Situatedneargeologicfaults,inareaspotentiallyvulnerabletoflooding.

No.1,No.6,No.7,No.8,No.9,No.12 Markedaswaterfallsorrapids,whichwouldgenerategreatpotentialenergy.

No.10,No.15,No18,No.19,No.21 LocatedatthebranchofZambeziRiver

No.13,No.14,No.20 Formedasfast‐flowinggorgesnaturally,whichwouldbeusedaspowerstations.

No.11,No.16,No17,No.22 Situatedatthemiddleoftwokindsoflandscapes,creatingabigdifferenceinheight.


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3. Cost‐BenefitOptimizationModelofSmallerDams

3.1. Cost‐benefitOptimizationModelofCascadeReservoirsSincethereareseveralfactorsdecidingwhethertobuildadamatthe22candidatelocations,factorsaredividedintotwoaspects,namelycostandbenefitfactorsforpreliminaryanalysis.Ourtask istobuildanoptimalcost‐benefitsystemofsmallerdamsonthebasisofdynamicfactors,thenchoosecertaindams(between10to20)tocomeintooperation.

Figure2:BenefitsandCostsofBuildingSmallerDams3.1.1. BenefitModelofSmallerDamsThebenefitmodel istomeasuretheearningofeachsmallerdamintheselectedregionandcalculatetotalearnings.Wedecidetoselectfourparts:powergenerationcapacityofcascadereservoirs,irrigationbenefits,urbanwatersupplybenefitsandthefloodcontrolbenefitasthebasisofthecalculationofbenefitsofsmallerdams.(1)TherevenueestimatemodelofgeneratingelectricofgradientreservoirsWithin the scopeof the electricity supply, the electric energydemandedbyeach electricitysectorneedstobeintegratedtodescribethechangesofelectricityusedfordaysandhours.Annualloaddiagram:thegraphrepresentingthechangeofelectricityusedforeachmonthinayear.Loadfigurecommonlyusesdailymax(N )min(N)loadchangecurveanddaily(ormonthly)averageloadchangecurve.[5]

Figure3:Theannualloaddiagram

Theelectricityloadchartisprepared,thenbasedonthepartthathydropowerstationshouldbeas,theelectricitythathydroelectricplantsshouldgeneratecanbedetermined,throughtheformulaforoutput:


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iii HQN (1) ——waterdensity(=1000kg/ 3m )

iQ ——powerflow,unit 3m /s

iH ——drop,unitm

N——output,unitkgfm/sInengineering,thecommonlyusedunitforNiskilowatt(kw),1kw=102kgfm/s,then

QHQHN 80.9102

1000 (2)

i

i

i H

N

H

NQ

80.9

1

1000

102 ii (3)

TheelectricityHydropowerstationgenerateisalsorelatedtotheefficiencyoftheturbineandgenerator,asaresult,theactualformulaforprocessingis

QHQHN EW 9.8i (4)

N——output,unitkw ——the combination of efficiency coefficient and unit conversion constant, 7.5‐8.8 asoften.[6]Ei——ElectricenergyproductionbyNo.ipowerstationMW,unit$

Pw——Priceofeachmegawattofpower,unitkw/$Sothedirecteconomicbenefitsbroughtbygeneratingelectricityis

PwQHEi (5)

(2)EstimationModelofAgriculturalIrrigationWater

Figure4:DistributionofUrbanWaterSupply

The appropriate moisture retention of crops not only rely on the effective supply ofprecipitationintheatmospherebutalsoneedtobeprovidedfromthefarmlandconservancymeasurestoaddwater,whichiscalledagriculturalirrigationwater.Makesurethesystemofallkindsofagriculture[7],ifgivenirrigatedareaandthepercentofplantedareaofallkindsofagriculture,theamountofirrigationwaterandirrigationtimecanbegotten.Aboveall,irrigationincomeforNo.iis

gi PVG i2 (6)

iG ——IrrigationcapacitybyNo.ireservoirunit$


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i2V ——WatersuppliesofNo.ipointinirrigation,unit 3m

gP ——Productionoffarmland,unit$/ 3m

(3)EstimateModelofUrbanWaterSupplyAssumptionThewatersupplyoftheNo.itothetownisequaltothesumofthecivilwatersupplyandtheindustrialwatersupplywithintheresponsibleurbanarea.

uPoV i ii1 D (7)

iV1 ——WatersuppliesofNo.ireservoirintown,unit 3m

iD ——IndustrialwaterconsumptionofNo.i,unit 3m

iPo ——PopulationofNo.ipoint,unitperson

u ——AveragewaterconsumptioninZambianwatershed,unit 3m /year

iU ——Incomeofurbanwatersupply,unit$

Pr ——Priceofurbanwater,unit$/ 3m Thenextstepistocalculatethetotalrevenueoftownwatersupply:

Pr1i iVU (8)

(4)EstimationmodeloffloodcontrolbenefitThefrequencyandgradeofthefloodoccurredintherepresentativeyearofeachpotentialdampointarefound,andthemathematicalmodelisusedtosimulatethefrequencyofthefloodinotheryearsduringtheoperationperiodofthesystem,andthencalculatetheexpectedvalue.[8]

iitiD iF (9)

iF ——AvoidabledamagebenefitsfromNo.idam,unit$

ii ——ProbabilityoftypeifloodingatNo.idam

itD ——Lossoftypeiflooding,unit$(5)Calculatethetotalbenefitsofsmallerdams

)(Tb22

1iiiii

iFUGEa

(10)

Tb——Totalearningsofdams,unit$3.1.2. CostModelofSmallerDamsInthismodel,costsaremeasuredintermsofmoneyandcurrencyperyear,andacoefficientofannuity, ,isintroducedintoequations.Morespecifically,thetotalcostsaredividedintofiveparts:Constructionfeesofdams,Construction feesofpowerstations,Costsofmaintenance,Costofpopulationmigration,andLossduringtheconstruction.

Figure5:ComponentsofTotalCost


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Thesumofvaluesoffivefactorsstandsforthetotalcostsofeachdam.AccordingthereportbytheInstituteofRiskManagementofSouthAfrica,thedamsmustbeusedformorethan100years,thusthetotalcostsshouldbesetasidefor100yearsandwesuppose asaaveragerate.

iiiiiiiii VLHMVSVBiC Po (11)

iC ——TotalcostsofNo.idam)(Bi iV ——CostofconstructionofNo.idam

)(Si iV ——CostofconstructionofNo.ipowerstation

iM ——CostofmaintenanceofNo.idam

iPoiH —— Costofpopulationmigration

)(Li iV ——LossduringtheconstructionofNo.idam

——Coefficientofannuity

Andthecostofwholeconstructioncanbemeasuredas:

22

1

n

ii iCaTC (12)

Inordertoestimatethecostsaccuratelyandactually,acoefficientoftotalcosts,λ,isintroducedas a coefficient tomeasure the cost ofwater storageof reservoirperm3. we consider thecoefficientλisrelatedtowaterstorageofreservoir,andusethefollowingdatastoconstructaregressionequationaboutTotalCostandWaterStorage.WefindtensetsofdataofTotalCostandWaterStorageaboutthedamsin10years.

Table3:DatasofTotalCostandWaterStorageaboutthedamsin10years

NameofDam ThreeGorges Shuibuya Goupitan Longtan Pubugou

TotalCost $2.7×1010 $1.3×109 $8.7×108 $5.1×109 $1.05×107

WaterStorage 3.93×1010m3 4.58×109m3 6.45×109m3 2.73×1010m3 5.17×106m3

NameofDam Hongjiadu Tankeng Wawushan Dongping Baishuikeng

TotalCost $1.85×108 $9.58×108 $3.1×108 $1.34×108 $5.09×107

WaterStorage 4.92×109m3 3.53×109m3 5.84×108m3 3.36×108m3 2.46×108m3

ApplyingthemethodofmathematicalregressionanalysiswithSPSS,oneregressionequationwasgivenout.

3925- 1018.11069.3-31.092.54 XXXY (13)


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Figure6:Fitting‐figuresofrelationbetweenTotalCostandWaterStoragetestforequalityperformedbySPSS,andtheresultsofitasfollows:

Table4:ModelSummaryandParameterEstimates

DependentVariable:TotalCost

EquationModelSummary ParameterEstimates

RSquare F df1 df2 Sig. Constant b1 b2 b3

Linear .796 31.133 1 8 .001 ‐1247.102 .555

Quadratic .958 78.946 2 7 .000 1405.901 ‐.590 3.069E‐5

Cubic .999 1763.314 3 6 .000 54.920 .312 ‐3.693E‐5 1.182E‐9

Power .845 43.461 1 8 .000 1.432 .785

Growth .695 18.267 1 8 .003 4.945 .000

Exponential .695 18.267 1 8 .003 140.434 .000

Logistic .695 18.267 1 8 .003 .007 1.000

TheindependentvariableisWaterStorage.

RSquareofCubicisthelargest,indicatingthatthefitisthebest.AndtheSigvalueis0.000(Thenormallevelis0.05),lessthanthesignificancelevel,sowecanrejectthenullhypothesis,thatthecurvefittingisbetter.Consideringthedetrimentalaffectofextremeconditiontodams,suchasfloodingsandstorms,a2%increaseshouldbeaddedtoitsoriginalcosts[2].AndcorrecttheCostFunctionlikethis:

%21iViC (14)

iV ——Coefficientoftotalcosts

iC ——CorrectthecostofNo.idam


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3.2. RelatedDatasSimulationSincetheriver’srelateddatasareunkownorunstatistical,weusearandomsimulationmodeltosimulate22setsofdatasofthesedams,accordingtothekonwndatasofVaictoriaFallsandKaribaDaminyears.

Figure7:Simulationdata’swithMATLAB

Andgiveoutthesedatasintable:Table5:SimulationdatasofStorage,FolwsandHeight

NumWaterStorage

(m3)

Flows

(m3/s)

Height

(m)Num

WaterStorage

(m3)

Flows

(m3/s)

Height

(m)

1 103.2 263.9 30.4 12 100 490.1 32.6

2 138.4 339.3 38.9 13 90.4 565.5 37.6

3 76 414.7 36.8 14 105.6 640.9 40.1

4 51.2 527.8 32.5 15 125.6 640.9 35.3

5 65.6 603.2 28.9 16 139.2 678.6 32.4

6 109.6 716.3 39.6 17 142.4 640.9 31.7

7 116 678.6 35.7 18 124 603.2 35.9

8 124.8 678.6 43.2 19 110.4 716.3 34.9

9 126.4 640.9 38.9 20 113.6 640.9 40.9

10 114.4 603.2 42.3 21 99.2 678.6 45.7

11 132 527.8 39.6 22 125.6 527.8 47.9

3.3. 0‐1IntegerProgramminginDeterminingDamSitesInthismodel,whetherthedamcanbebuilthasnotbeendecided.Andweassumethatthereisacoefficienttoshowifthedambeconstructed.Thecostsofthedamwouldbeincludedifitwouldbebuilt,whichwouldbemultipliedbyanumberof1,whiletheothersituationwouldbemultipliedbythenumberof0.Thentheplanthatleadtomaximumbenefitwouldbeselected.


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Atfirst,introduce0‐1variables:

bulitnot is dam No.i ,0

built is dam No.i ,1ia ,(15)

Inordertomaintainthepowergenerationandirrigationcapacityatoriginallevels,objectivefunctionandconstraintsarelisted:

22

1

maxn

iiii CBaTcTb (16)

1or 0

..22

1

22

1

i

originali

n

ii

n

ioriginalii

a

EEa

VVa

ts

Consideringbenefitandcostfactorsmentionedabove,writeprogramswithMatlab,accordingtotheobjectivefunctionandconstraints,toidentifythemosteconomicconstructionplan,thenselectthespecificsites.

Figure8:SitesSelectionProgramflow

RuntheProgram,andlistselectionresultsasfollows:

Figure9:SitesSelectionResults


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Finally,weselecttobuild17damsalongZambeziRiver,theyare:No.2,No.6,No.7,No.8,No.9,No.10,No.11,No13,No.14,No.15,No.16,No.17,No.18,No.19,No.20,No.21,No.22.

Figure10:SitesSelectionMap

4. MaximumandMinimumDischargeofDamsunderExtremeConditions

4.1. TheMethodofCalculatingtheMaximumEmissionofFloodHypothesis: In the state of small watershed and small reservoir without considering thenumberofthespillwaygatesandswitchstateConception:Flooddetentioncapacity:ThemaximumamountoffloodthatcanbeaccommodatedFloodstoragecapacity:ThemaximumamountoffloodthatcanstoreSupposingthattheflowofstorageandoutboundflowaresimplifiedastriangular,sothetotalfloodstorageis:

TmQ2

1W (17)

Figure11:SimplifiedTriangleMethodforFloodRouting

Asforpicturea,themaximumdischargeflowofthereservoirfromthedamheightis:

)1(qW

VQ mmm

(18)

mQ ——peakdischarge


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mV ——flooddetentioncapacity

T——flooddurationAsforpictureb,thestartinglevelofthereservoirisbelowtheweircrestelevation,butthetimeoffillingtothecrestelevationislessthanthatofthefloodpeak,sothetotalfloodstorageis:

WTTVWV

Q

s

mm

m

11

)1(q

(19)

sV —— floodstoragecapacityThetwoequationsareestablishedfromthepointviewofwaterbalance[4].

4.2. EstimationoftheMinimumExpectationEmissionundertheConstraintBenefit

Intheseasonofwatershortage,therearetwomainsourcesofwaterconsumptioninreservoirs,oneistomeetpowergenerationneedsthroughthedrainage,theotheristomeettheareaofirrigation and urban water supply minimum requirements through the remaining waterstoragereservoir.Restrictions:

)(qV 12i ii VV ;

iV2i2V ;iV1i1V ; tQq (20)

Whentheequalsignisestablished,minimumemissions minq canbegotten

iV ——waterstoragecapacityofreservoirduringdryseason,unit 3m

i2V ——thesupplyofirrigationwaterduringdryseason,unit 3m

i1V ——thewatersupplyofthetown,unit 3m

t——thetotaltimeofpowergenerationundernormalconditions,units

minq ——theminimumexpecteddischarge

5. DemonstrationAnalysisofDamDischargeinExtremeCondition

SelectNo.12damtoanalyzewhich locatednearVictoriaFallsof17dams,andestimate themaximum expected discharges and the minimum expected discharges under the extremeconditions. Then the suggestionswere given. The analysis of other dam points of thinkingprocessissimilar,sodonotrepeathere.

Figure12:TheMaximumExpectedDischargeandtheMinimumExpectedDischargeofDifferentDams


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5.1. TheMaximumExpectedDischargesofNo.12According to the averagemonthlywater flow data in the yearwhich is representative, themonthwithmeanflowexceeding1000 s/m3 isthefloodseason.FortheNo.12dam,FebruarytoJuneisusuallythefloodseason.Accordingtothehistoricaldata,Marchhasthelargestflow,andtheflowis8720 s/m3 .

Table6:ZambeziRiverMonthlyAverageFlowsatVictoriaFalls(1907‐2008)

Ascanbeseenfromtheabovetable,

mQ =8720 s/m3.

011301120003024606087202

1W 3m ,

Suppose39

12m m103V , From the flood control calculation of the maximum discharge’s method can be seen, themaximumdischargeflowofReservoiriis

4862)01130112000

1051(8720q

9

m12

s/m3.

Asforthemaximumdischarges,dependingonthedurationofitsflooddischarge.

TW 4862max

maxW ——Themaximumdischarges

T ——The duration of flood dischargeWhenthemaximumdischargesareequaltothetotalamountoffloodstorage,thetimerequiredis

542

T12

mq

Wdays.

5.2. TheMinimumExpectedDischargesofNo.12Wewillestimatetheminimumexpecteddischargeof theNo.12damundertheconditionofbenefitconstraint.Step1DeterminethemonthlyenergydemandfortheNo.12jurisdiction.Ascanbeseenfromtheabovefigure,thedemandforelectricityintheKalibaareaisnotaffectedbytheseasons.Asatotalof17smalldamsarebuilt,theaveragemonthlydemandforpowerinthesmalldamjurisdictionis10765kW.Suppose,

12N 10765kW.

Step2calculatetheminimumdischargesrequiredtomeettheenergyrequirementsAsknows,


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12H =20.6m,

Set =8.0,

Then

s/m65H

NQ 3

12

1212

,

Sot65tQq 12min

Theminimumdischargesarerelatedtothetimeofpowergeneration,inonemonth,

30246060t 259200s,Then

minq =1684800003m

6. Recommendation

6.1. ProposalontheNumberandPlacementoftheNewDamsFor the construction of smaller dams in the Zambezi River Basin, not only to meet theconstructionofthefeasibilityoftheconditions,butalsoshouldconsiderthebenefitsandthecostssothatthedifferencereachanoptimalvalue.

Table7:ConstraintsonDamConstruction

Conditions Description

Constructionfeasibility

①notcrosstheborder

②highdroppingvarianceofriver

③Rapidorhurrywater lows

④Locatedat loodingandrainyareas

⑤Locatedatthebranchofnarrowriver

Cost‐Effectiveness

Benefits

①Powergeneration

②Constructionofpowerstations

③Irrigation

④Watersupply

⑤Avoidablelossin lood

⑥Incomeinrecreation

Costs

①Constructionofdams

②Costsofmaintenance

③Costofpopulationmigration

④Lossduringtheconstruction


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Finally,weselecttobuild17damsalongZambeziRiver,theyare:No.2,No.6,No.7,No.8,No.9,No.10,No.12,No13,No.14,No.15,No.16,No.17,No.18,No.19,No.20,No.21,No.22

6.2. RecommendationsonDamManagementduringtheFloodSeasonReservoirsplayamajorroleinfloodcontrolandwatersupplybycontrollingtheirdischarges.Thesizeofthedischargeisaffectedbytheobjectivefactorssuchasdamsite,damheight,flow,seasonandothersubjectivefactorssuchasurbanwatersupplydemand,irrigationdemandandpowergenerationdemand.Reasonablearrangementsfordischargesandthetimeofdischargeisimportanttothereservoirmanagement.6.2.1. ManagementoftheDamintheFloodingIn the flood season, the reservoirswith small capacity, low altitude, large flow, suffers thelargestadverseinfluences.Thelengthsofaffectedtimearetheentirefloodseason.Floodseasonatdifferentdamsitesisdifferent,sotheaffectedtimeisalsodifferent.Accordingtothehistoricaldata,whentheaverageflowismorethan1000m3/s,floodseasonisarriving.Thenmeasuresshouldbetakeninflooddischarge.For theNo.12dam, the floodseason is fromFebruary to June,and themaximumexpecteddischarges are most likely to occur in March. Therefore, during this period, the reservoirmanagementpersonnelshouldincreasedischargesaccordingtotheactualsituationinordertoavoidtheriskofburst.From2.3.2wecanseethatthemaximumexpecteddischargesisaffectedbythetimeofflooddischarge.Whenthefloodseasonlasts,themaximumexpecteddischargesinthismonthcanbelargerthanthatinthestorageflood.Forthenextmonth,thetimeofflooddischargeshouldbelongerthan54days.Whenthefloodseasonisabouttopass,themaximumexpecteddischargesforthemonthshouldbelessthanthestorageflood,inordertostorewaterforthedryseason,thetimeshouldbelessthan54days.6.2.2. DamManagementofDrySeasonUnderlong‐termlow‐waterconditions,thosereservoirswithsmallstoragecapacityandsmallwaterflowbuthighhydropowerdemandaremostadverselyaffected.Itsimpacttimeshouldbethedurationoftheentiredryseason.Accordingtothehistoricaldata,thattheaverageflowislessthan300m3/sinonemonthisthedryseason.Wheninthedryseason,reservoirstorageislow,thistimethewaterislikelytobedifficulttomeettherequirementsofwatersupply(urbanwaterandirrigationwater)anddrainagepowergeneration.When generating electricity as the first function of the reservoir, the minimum expecteddischarges must meet the demand for power generation (which can be calculated fromEquation 1), but at this time facing the shortage of water supply, the proposed treatmentmethod has two: Plan A increase the water storage capacity ahead of time; Plan B applyupstreamreservoirtoincreasedischarges.Whenthestorageofwatersupplyasthefirstfunctionofthereservoir,tomeettheurbanwaterand irrigationwater, the amountofwaterdischarge isnot enough tomeet thedemand forelectricitygeneration,atthistime,theproposedtreatmentmethodsare:PlanAincreasetheamountofwateraheadofschedule;PlanBtransferpowerfromotherplaces.Obviously, the cost of Plan B is expensive and the possibility of realization is unknown.Therefore,inordertopreventtheshortageofsupplyinthedryseason,watershouldbestoredinthefloodseason.


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7. StrengthsvsWeakness

7.1. Strengths1)Solvetheproblemfromtheactualsituation.Infullconsiderationofcontours,topography,precipitationandotherfactorsundertheconditionsofchoicefordamsites.2)Abstractthepracticalproblems,withtheuseof0‐1planningmethodtosimulatethenumberandlocationofdams.3)Determinethenumberandlocationofdamsfromthecost‐benefitoptimizationpointofview4)Classificationdiscussion.Reasonablerecommendationsaregivenforthemaximumexpectedandminimumexpecteddischargesfordifferentregionsunderextremeconditions.5)Wheninsensitivityanalysisandmodificationofthemodel,wediscusseachparameter,theresultsshowthatourmodelparametershaveawiderangeofapplications.

7.2. Weaknesses1)This model takes into account too many factors, leading to the settlement process iscumbersome,thesolutionisdifficult.2)Oneofthemodelparameters(floodingtime)stillneedstobedeterminedexperimentallyandcannotbededucedfromtheexistingphysicalconstants.3)Forouremergencyguidanceproposal,onlysomekeydamsareconsidered,andthereisnospecificconsiderationforeachtypeofdam.

8. SensitivityAnalysis

In order to better guide the establishment of multi‐dam systems, the most benefits, weconducted a sensitivity analysis. Sensitivity analysis is particularly important if you areinvestinginaprojectthatmustbeconsideredforfeasibility.Themainpurposeofinvestmentsensitivityanalysisistorevealtheinfluenceofrelevantfactorsoninvestmentdecision‐makingevaluationindex,todeterminethesensitivefactorsandseizethemaincontradictions.Step 1 Select the sensitivity analysis indicator. Here, we use the cost‐benefit principle.Therefore,weselectnetincomeasthesensitivityanalysisindicator.Step2Calculatethetargetvalueofthetechnicalscheme.Normally,thevalueoftheeconomicbenefitevaluationindexinthenormalstateistakenasthetargetvalue.Step3SelectUncertainty.Wechoosethefactorwhichlargelyeffectthetargetvalue.Here,wemainlyselectthestoragecapacityastheuncertaintyfactor.Step4Calculatethedegreeofinfluenceofuncertainfactorsonanalysisindicators.Theprincipleofunivariatesensitivityanalysisisthatonlyoneuncertaintycanbechangedatatime.Step5Identifysensitivefactors,analyzeandtakemeasurestoimprovetheanti‐riskabilityoftechnicalsolutions.We take thestoragecapacityas theuncertainty factor, carrieson thesensitivityanalysis inMATLAB,obtainstheresult,likefigureasfollows:


ISSN:2688‐9323

244

Figure13:Sensitivityanalysiscurve

Throughtheaboveanalysis,wecanseethatwhenthetotalstoragecapacityincreasesby70‐80,thetotalbenefitisincreasing.Thereasonisthatsomedamsmaybeeconomicallyinefficient,so when increasing the storage capacity to a limit, then the economic benefits diminish.Therefore,thetotalstoragecapacityofthesesmalldamsshouldbeincreasedby70‐80istheeconomy.

References

[1] http://mgafrica.com/article/2016‐01‐20‐kariba‐dam‐drops‐to‐record‐low‐12‐and‐zimbabwe‐zambia‐stare‐at‐a‐nightmareKaribaDamDropstoRecordLow12%,andZimbabwe,ZambiaStareatANightmare.

[2] http://mp.weixin.qq.com/s? biz=MzIxMjA1MzQwOA==&mid=212151600&idx=1&sn=b919d6fa2287b23447b82b581e228312&3rd=MzA3MDU4NTYzMw==&scene=6KaribaDam JeopardizesCahoraBassaDamand3BillionPeople’sLivesandProperty.

[3] ImpactofTheFailureofTheKaribaDam‐TheInstituteofRiskManagementSouthAfrica,2015[4]ExistingandPotentialHydropowerProjectsonTheZambeziRiver.

[4] YeBingru.WaterUtilityCalculationandWaterResourcesPlanning,1995.[5] YangLong.StudyonHydroelectricPowerGenerationandPowerGenerationEfficiency,2014.[6] WuLi.ClassificationandFormulationofCropIrrigationSystem,2011.[7] Wang Guangjie.Calculation of Annual Average Flood Control Benefit for Monitoring System for

Chaihereservoir,2014.[8] PreliminaryDesignSpecificationforPowerStationofTalaDitch,2004.

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