= −
. / .
. / . V
CalculatethepercentvoltagedroptothesecondaryoftransformerT3�
Usethesecondaryvoltagereferredtothehighside:
V
V V
drop= 1 V− T3 ⋅ = − ⋅ =
1
100 2400 2326 11
2400 . 100 3 0789. %
2.4.2.2 Load Allocation Based upon Transformer Ratings
Whenonlytheratingsofthedistributiontransformersareknown,thefeeder
canbeallocatedbaseduponthemetereddemandandthetransformerkVA
ratings� This method was discussed in Section 2�3�3� Example 2�4 demon-stratesthismethod�
Example 2.4
ForthesystemofExample2�1,assumethevoltageatN1is2400V,and
compute the secondary voltages on the three transformers, allocating
theloadsbaseduponthetransformerratings�Assumethatthemetered
kWdemandatN1is92�9kW�
Theimpedancesofthelinesegmentsandtransformersarethesame
asinExample2�3�
Assume the load power factor is 0�9 lagging, and compute the kVA
demandatN1fromthemetereddemand:
S12 92 9 1 j
0 9 0 9 92 9 45 0 103 2 25 84
= . − = + =
. /cos ( . ) . . . / . kVA
CalculatetheAF:
AF=
+ + =
103 2 25 84
25 37 5 50. / . 0 9175 25 84
. . / .
Allocatetheloadstoeachtransformer:
ST1=AF kVA⋅ T1=( .0 9175 25 84 25 20 6/ . )⋅ = . +j10 0. kVA
ST2=AF kVA⋅ T2=( .0 9175 25 84 37 5 31 0/ . )⋅ . = . +j15 0. kVA ST3=AF kVA⋅ T3=( .0 9175 25 84 50 41 3/ . )⋅ = . +j20 0. kVA
Calculatethelineflows:
S12=ST1+ST2+ST3=92 9. +j45 0. kVA
S23=ST2+ST3=72 3. +j35kVA
S34=ST3=41 3. +j20 0. kVA
Usingthesevaluesoflineflowsandflowsintotransformers,theproce-dure for computing the transformer secondary voltages is exactly the
sameasinExample2�3�Whenthisprocedureisfollowed,thenodeand
secondarytransformervoltagesare
V2=2378 1 0 4. / .− V VlowT1=234 0 0 6. / .− V
V3=2376 4 0 4. / .− V VlowT2=233 7 0 8. / .− V
V4=2374 9 0 5. / .− V VlowT3=233 5 0 9. / .− V Thepercentvoltagedropforthiscaseis
V V V
drop V T
= −
⋅ = − ⋅ =
1 3
1
100 2400 2334 8
2400 . 100 2 7179. %
2.5 Summary
Thischapterhasdemonstratedthenatureoftheloadsonadistributionfeeder�
Thereisagreatdiversitybetweenindividualcustomerdemands,butasthe
demandismonitoredonlinesegmentsworkingbacktowardthesubstation,
theeffectofthediversitybetweendemandsbecomesveryslight�Itwasshown
that the effect of diversity between customer demands must be taken into
account when the demand on a distribution transformer is computed� The
effectofdiversityforshortlateralscanbetakenintoaccountindetermining
themaximumflowonthelateral�FortheDFsofTable2�2,itwasshownthat
whenthenumberofcustomersexceeds70,theeffectofdiversityhaspretty
much disappeared� This is evidenced by the fact that the DF has become
almostconstantasthenumberofcustomersapproached70�Itmustbeunder-stoodthatthenumber70willapplyonlytotheDFsofTable2�2�Ifautilityis
goingtouseDFs,thenthatutilitymustperformacomprehensiveloadsurvey
inordertodevelopthetableofDFsthatapplytothatparticularsystem�
Examples2�3and2�4showthatthefinalnodeandtransformervoltages
areapproximatelythesame�Thereisverylittledifferencebetweenthevolt-ageswhentheloadswereallocatedusingtheDFsandwhentheloadswere
allocatedbaseduponthetransformerkVAratings�
Problems
2.1 Showninthefollowingtablearethe15minkWdemandsforfourcus-tomers between the hours of 17:00 and 21:00� A 25kVA single-phase
transformerservesthefourcustomers�
Time
Customer #1 (kW)
Customer #2 (kW)
Customer #3 (kW)
Customer #4 (kW)
17:00 8�81 4�96 11�04 1�44
17:15 2�12 3�16 7�04 1�62
17:30 9�48 7�08 7�68 2�46
17:45 7�16 5�08 6�08 0�84
18:00 6�04 3�12 4�32 1�12
18:15 9�88 6�56 5�12 2�24
18:30 4�68 6�88 6�56 1�12
18:45 5�12 3�84 8�48 2�24
19:00 10�44 4�44 4�12 1�12
19:15 3�72 8�52 3�68 0�96
19:30 8�72 4�52 0�32 2�56
19:45 10�84 2�92 3�04 1�28
20:00 6�96 2�08 2�72 1�92
20:15 6�62 1�48 3�24 1�12
20:30 7�04 2�33 4�16 1�76
20:45 6�69 1�89 4�96 2�72
21:00 1�88 1�64 4�32 2�41
a� Foreachofthecustomersdeterminethefollowing:
1� Maximum15minkWdemand
2� Average15minkWdemand
3� TotalkWhusageinthetimeperiod
4� Loadfactor
b� Forthe25kVAtransformerdeterminethefollowing:
1� Maximum15mindiversifieddemand
2� Maximum15minnoncoincidentdemand
3� Utilizationfactor(assumeunitypowerfactor)
4� Diversityfactor
5� Loaddiversity
c� Plottheloaddurationcurveforthetransformer�
2.2 TwotransformerseachservingfourcustomersareshowninFigure 2�13�
ThefollowingtablegivesthetimeintervalandkVAdemandofthe
fourcustomerdemandsduringthepeakloadperiodoftheyear�Assume
apowerfactorof0�9lagging�
Time #1 #2 #3 #4 #5 #6 #7 #8
3:00–3:30 10 0 10 5 15 10 50 30
3:30–4:00 20 25 15 20 25 20 30 40
4:00–4:30 5 30 30 15 10 30 10 10
4:30–5:00 0 10 20 10 13 40 25 50
5:00–5:30 15 5 5 25 30 30 15 5
5:30–6:00 15 15 10 10 5 20 30 25
6:00–6:30 5 25 25 15 10 10 30 25
6:30–7:00 10 50 15 30 15 5 10 30
a� Foreachtransformerdeterminethefollowing:
1� 30minmaximumkVAdemand
2� NoncoincidentmaximumkVAdemand
3� Loadfactor
4� Diversityfactor
5� Suggestedtransformerrating(50,75,100,167)
6� Utilizationfactor
7� Energy(kWh)duringthe4hperiod
b� Determine the maximum diversified 30min kVA demand at
the “tap�”
2.3 Two single-phase transformers serving 12 customers are shown in
Figure2�14�
The15minkWdemandsforthe12customersbetweenthehoursof
5:00p�m�and9:00p�m�aregivenattheendofthisproblem�Assume
a load power factor of 0�95 lagging� The impedance of the lines are
z = 0�306 +j0�6272Ω/mile�ThevoltageatnodeN1is2500/0V�
#3 #4
#1 #2 #5 #6 #7 #8
Tap
FIGURE 2.13
SystemforProblem2�2�
Transformerratings:
T1: 25kVA 2400–240V Zpu=0�018/40 T2: 37�5kVA 2400–240V Zpu=0�020/50
a� DeterminethemaximumkWdemandforeachcustomer�
b� DeterminetheaveragekWdemandforeachcustomer�
c� DeterminethekWhconsumedbyeachcustomerinthistimeperiod�
d� Determinetheloadfactorforeachcustomer�
e� Determinethemaximumdiversifieddemandforeachtransformer�
f� Determine the maximum noncoincident demand for each
transformer�
g� Determinetheutilizationfactor(assume1�0powerfactor)foreach
transformer�
h� DeterminetheDFoftheloadforeachtransformer�
i� DeterminethemaximumdiversifieddemandatnodeN1�
j� Computethesecondaryvoltageforeachtransformertakingdiversity
intoaccount�
Transformer#1:25kVA
Time #1 (kW) #2 (kW) #3 (kW) #4 (kW) #5 (kW)
05:00 2�13 0�19 4�11 8�68 0�39
05:15 2�09 0�52 4�11 9�26 0�36
05:30 2�15 0�24 4�24 8�55 0�43
05:45 2�52 1�80 4�04 9�09 0�33
06:00 3�25 0�69 4�22 9�34 0�46
06:15 3�26 0�24 4�27 8�22 0�34
T1 T2
N1 N2 N3
1 2 3 4 5 6 7 8 9 10 11 12
2500 ft 5000 ft
FIGURE 2.14
CircuitforProblem2�3�
(continued)
Time #1 (kW) #2 (kW) #3 (kW) #4 (kW) #5 (kW)
06:30 3�22 0�54 4�29 9�57 0�44
06:45 2�27 5�34 4�93 8�45 0�36
07:00 2�24 5�81 3�72 10�29 0�38
07:15 2�20 5�22 3�64 11�26 0�39
07:30 2�08 2�12 3�35 9�25 5�66
07:45 2�13 0�86 2�89 10�21 6�37
08:00 2�12 0�39 2�55 10�41 4�17
08:15 2�08 0�29 3�00 8�31 0�85
08:30 2�10 2�57 2�76 9�09 1�67
08:45 3�81 0�37 2�53 9�58 1�30
09:00 2�04 0�21 2�40 7�88 2�70
Transformer#2:37�5kVA
Time #6 (kW) #7 (kW) #8 (kW) #9 (kW) #10 (kW) #11 (kW) #12 (kW)
05:00 0�87 2�75 0�63 8�73 0�48 9�62 2�55
05:15 0�91 5�35 1�62 0�19 0�40 7�98 1�72
05:30 1�56 13�39 0�19 5�72 0�70 8�72 2�25
05:45 0�97 13�38 0�05 3�28 0�42 8�82 2�38
06:00 0�76 13�23 1�51 1�26 3�01 7�47 1�73
06:15 1�10 13�48 0�05 7�99 4�92 11�60 2�42
06:30 0�79 2�94 0�66 0�22 3�58 11�78 2�24
06:45 0�60 2�78 0�52 8�97 6�58 8�83 1�74
07:00 0�60 2�89 1�80 0�11 7�96 9�21 2�18
07:15 0�87 2�75 0�07 7�93 6�80 7�65 1�98
07:30 0�47 2�60 0�16 1�07 7�42 7�78 2�19
07:45 0�72 2�71 0�12 1�35 8�99 6�27 2�63
08:00 1�00 3�04 1�39 6�51 8�98 10�92 1�59
08:15 0�47 1�65 0�46 0�18 7�99 5�60 1�81
08:30 0�44 2�16 0�53 2�24 8�01 7�74 2�13
08:45 0�95 0�88 0�56 0�11 7�75 11�72 1�63
09:00 0�79 1�58 1�36 0�95 8�19 12�23 1�68
2.4 Onadifferentday,themetered15minkWdemandatnodeN1forthe
systemofProblem2�3is72�43kW�Assumeapowerfactorof0�95lagging�
Allocatethemetereddemandtoeachtransformerbaseduponthetrans-formerkVArating�Assumetheloadsareconstantcurrentandcompute
thesecondaryvoltageforeachtransformer�
2.5 Asingle-phaselateralservesfourtransformersasshowninFigure 2�15�
Assumethateachcustomer’smaximumdemandis15�5kW+j7�5kvar�
Theimpedanceofthesingle-phaselateralisz=0�4421+j0�3213Ω/1000ft�
Thefourtransformersareratedas
T1andT2:37�5kVA,2400–240V,Z=0�01+j0�03perunit T3andT4:50kVA,2400–240V,Z=0�015+j0�035perunit UsetheDFsfoundinTable2�2anddeterminethefollowing:
a� The 15min maximum diversified kW and kvar demands on each
transformer�
b� The15minmaximumdiversifiedkWandkvardemandsforeachline
section�
c� Ifthevoltageatnode1is2600/0V,determinethevoltageatnodes
2through9�Incalculatingthevoltages,takeintoaccountdiversity
usingtheanswersfrom(a)and(b)�
d� Usethe15minmaximumdiversifieddemandsatthelateraltap(sec- tions1–2)frompart(b)�Dividethesemaximumdemandsby18(num-berofcustomers)andassignthatasthe“instantaneousload”foreach
customer�Nowcalculatethevoltagesatallofthenodeslistedinpart
(c)usingtheinstantaneousloads�
e� Repeatpart(d)exceptassumetheloadsare“constantcurrent�”Todo
this,takethecurrentflowingfromnode1tonode2frompart(d)and
divideby18(numberofcustomers)andassignthatasthe“instanta-neousconstantcurrentload”foreachcustomer�Again,calculateall
ofthevoltages�
f� Takethemaximumdiversifieddemandfromnode1tonode2and
“allocate” that to each of the four transformers based upon their
kVAratings�Todothis,takethemaximumdiversifieddemandand
divideby175(totalkVAofthefourtransformers)�Nowmultiplyeach
transformerkVAratingbythatnumbertogivehowmuchofthetotal
diversifieddemandisbeingservedbyeachtransformer�Again,cal-culateallofthevoltages�
g� Computethepercentdifferencesinthevoltagesforparts(d)through
(f)ateachofthenodesusingpart(c)answerasthebase�
1 2 4 6 8
7 5
3 9
380 ft 470 ft 750 ft 820 ft
T1 T2 T3 T4
FIGURE 2.15
SystemforProblem2�5�
39