Economic Analysis of power system in.ppt

Economic analysis

1. 6/19/2024 AKM/Distribution 1
Animportantfactorofthedistributioninvestoristhevalueof
assetinvestedanditsrecoveryovertime
Therequiredinvestmentdonotoccuratoncebutneededasthework
progress.
Similarlythereturnalsooccurasthetimepasses
ARupeetodayismorevaluablethanaRupeetomorrow
Thenetinvestmentinanyyearisthedifferenceininvestmentand
return(positiveornegative)
Soforthepropereconomicanalysis;
Firstrequiredtopreparescheduleplanmentioninghowtheoverall
projectwillprogressasafunctionoftime(Timeschedule)
Thenforthatamountofworkhowmuchinvestmentwillrequirewhen.
Yearlyreturnafterthisinvestment
Economic Analysis

2. 6/19/2024 AKM/Distribution 2
Disbursement schedule Exampleyear Capital
investment
Operational
investment
Return Net investment
1
2
3
May be for
some initial
year
4
5
6

19
20

Includes
Input Energy
cost
O&M cost
Taxes

May be after
some initial
year

3. 6/19/2024 AKM/Distribution 3
Present Value
Centraltothefinancialandeconomicevaluationprocess.
Presentvaluingwillbecarriedoutthroughdiscountingnextperiod’s
financialoutlay(F
1)toitspresentvaluethroughmultiplyingitbya
discountfactor.
Discountfactororpresentworthfactorisafunctionofthediscountrate()
whichistherewardthatinvestorsdemandforacceptingadelayed
payment.
ARupeetodayismorevaluablethanaRupeetomorrow
AnUtilityexpectstogainapremiumonhisinvestmentwithdueapproval
oftheregulatorduetothefollowingthreefactors:
-inflation
-risktaking
-expectationofarealreturn.
expectstoregainhismoney,plusareturnwhichtallieswiththemarketand
hisestimationofthesethreefactors.

4. 6/19/2024 AKM/Distribution 4
Presentvalue(PV)=discountfactor×F1
whereDiscountfactor=1÷(1+)
Withadiscountrate(expectedrateofreturn)oftenpercent
annually,thediscountfactorforthefirstyearsfinancialoutlay
willbe1/(1+0.1)=0.909
MaterializingRs22,000afteroneyearwillbeequalto
0.909×Rs22000=Rs20,000today.
Outlayatyear2willhavetobemultipliedby1/(1+)
2
Discountfactorinyearnisequalto1/(1+)
n
Presentvalue=F
n×discountfactor
n=F
n×[1/(1+)
n
]
$100occurringafterfiveyears,withadiscountrateof10%
willhave a presentvalueequalto
$100×[1/(1+0.1)
5
]=$62.092today.
$100occurringafter30yearswillbeequalto
$100×[1/(1+0.1)
30
]=$5.731today

5. 6/19/2024 AKM/Distribution 5
Cash Flows
Cashflowisthedifferencebetweenmoneyreceivedandmoney
paid.
Eachyear’sfuturecashflowcanbediscountedtoitspresent
valuebydividingitbythediscountfactorforthatyear.
extendedstreamofcashflowsM
0,M
1,M
2…M
noccurringat
years0,1,2…,nhasapresentvalueof:
InthespecialcaseofM
1=M
2==M
n=M  









N
n
n
n
n MMMM
MPV
 1111
2
21
0  



N
n
MPV
1
1

6. 6/19/2024 AKM/Distribution 6
Example
Consideradistributionnetworkprojectinvolvingan
investmentof$50,000atthebeginningofeachyearoverfour
years,startingtoday,withadiscountfactorofeightpercent,its
presentvalueis   












32
3
08.01
1
08.01
1
08.01
1
11050PV
= 50 ×103 (1+0.926+0.857+0.794) = $ 178850

7. 6/19/2024 AKM/Distribution 7
Future and Past Valuing
Futurevaluing(FV)ofapresentvalue(PV)meansthat
thebaseyearhasbeenmovedintothefuturebynyears
PVisoccurringnowat–nyearsfromthenewbaseyear.
Theuniversaldiscount(compound)factorismaintained,
withnegativenvalue,
FV=PV×[1/(1+)
-n
]=PV(1+)
n
Forpastvaluing,thebaseyearhasbeenmovedintothe
pastbynyears.
ThepastvaluewillequalPV×[1/(1+)
n
].

8. 6/19/2024 AKM/Distribution 8
Annuity factor
Presentvaluingofastreamofequalcashflows,M
Ifwesubstitute‘a’forM/(1+)and‘x’for1/(1+)
PV=a(1+x+x
2
+…+x
n-1
) Equ.(1)
Multiplyingbothsidesby‘x’
xPV=a(x+x
2
+…+x
n
) Equ.(2)
Subtractingtheequation(2)from(1)
PV(1–x)=a(1–x
n
) Equ.(3) 
n
MMM
PV
 





111
2
 



n
MPV
1
1

9. 6/19/2024 AKM/Distribution 9
Substitutingfor‘a’and‘x’andthenmultiplyingbothsidesby
(1+)andrearranginggives:
Theexpressioninbracketsintheaboveequationistheannuity
factor,whichisthepresentvalueofanannuityof$1paidatthe
endofeachofnperiods,atadiscountrate
theannuityfactoristhesummationofalltheannualvaluesof
thediscountfactorsovertheperiod










n
MPV
1
11
Annuity factor =
PV = M ×Annuity factor 
N
factordiscount

10. 6/19/2024 AKM/Distribution 10
Capital recovery factor (CRF) or
equivalent annual cost
Anannuityfactorisameansofconvertingastreamofequal
annualvaluesintoapresentvalue,atagivendiscountrate
(interest)
Acapitalrecoveryfactor(CRF)performsthereverse
calculation
CRFistheamountofmoneytobepaidattheendofeachyear
torecover(amortise)theinvestmentatarateofdiscount,,
overnyears
Theequivalentannualcost,Mwillbethereciprocalof
equationofPVmentionedearliertorAnnuityfac
PV
M
= PV ×CRF

11. 6/19/2024 AKM/Distribution 11
equivalentannualcapitalcostofaninvestmentof$1million
overtenyears,atarateofinterestof12%isfactorAnnuity
CRF
1
 











n
1
11
1  











10
12.0112.0
1
12.0
1
1000000$
= $ 1000000 ×0. 17698 = $ 176 980 annually

12. 6/19/2024 AKM/Distribution 12
Cost Estimation
Forcalculationoftheprojectcostfirsttheunitcostsofeachof
thecomponentshavetobeassessed.Forexampleforanew
distributionsystemplanning;
UnitCostofSub-transmissionline.
Unit cost of 33/11 kV Substation (if any)
Unit cost of 11 kV Distribution
Unit Cost of Low Voltage Transmission
Unit cost of Distribution Transformer.
Unit cost for the Consumer Services.
Additional cost (e.g. unit cost of River-Crossing (if any))
Service connection cost
In addition to that the cost of 1 unit of Energy at Area substation
should also be known.
There are different methods to calculate this very popular is
LRMC

13. 6/19/2024 AKM/Distribution 13
Long Run Marginal Cost(LRMC)
IncaseofscenariobasedLRMCapproach,likelyleveland
locationofdemandandgenerationareforecastedareawise
foralongperiod(20–40years)withintervals(2-4years).
Theestimatedforecasteddemandandgenerationsarethan
includedinthebasesystem(present)andthenthe
requirementsfornewinvestmentsaredetermined.
Theaboveprocedureisrepeatedfor20-40years
Nextafuturecostisdevelopedforoverlongperiod(20-40
years)
Thesecostsarethandiscountedbacktothepresentvalue,
annuitisedanddividedbythedemandandgenerationsof
respectivezones.
Finalzonalpricesatdifferentvoltagescanbeobtained.

14. 6/19/2024 AKM/Distribution 14
Cost Estimation (contd)
Costestimationfornewextensionplancan
beperformedbyestimatingthequantities
underdifferentalternativeschemes
Forotherpurpose;forexamplelossreduction
thebasicprincipleissameonlyinthecost
estimationsslightlydifferspecifictothe
requirement.
CostDisbursementschedulecommoninall
planningprocedure

15. 6/19/2024 AKM/Distribution 15
Over all planning procedure
Exploretheviableoptions
Checkthetechnicalrequirements(e.g.Voltage
constraints,conductorcurrentcarryingcapacity,
reliabilityequipmentsetc.)
Shortouttheoptionsthatsatisfiestechnical
requirements
Preparethecostdisbursementschedule
Performeconomicanalysisandchoosetheoption
whichisbestfromeconomicalpointofview.
Economicindicator
For comparison of the various options PV, or annual
cost indicator may be used.
The economic feasibility of the project requires IRR
or B/C ratio.

16. 6/19/2024 AKM/Distribution 16
IRR
Given a time series of cash flows involved in a project, the
internal rate of return follows from the net present value as a
function of the rate of return.
A rate of return for which this function is zero is an internal
rate of return.
Example
Calculate the internal rate of return for
an investment of as shown in table
Solution:
We use an iterative solver to determine
the value of rthat solves the above equation:
The result from the numerical iteration is .
28.09 %
0
10




n
i
i
i
M
NPV

year Net
investment
0 -100
1 39
2 59
3 55
4 20