distribution system modeling and analysis - the nature of loads

The nature of loads

Contents

1

2

3

4

5

Relationship Between Load and Loss Factors

Distribution Transformer Loading

Individual Customer Load

Definitions

Feeder Load

What is load?

The answer to that question depends upon what type of an analysis is desired. For example, the steady-state analysis (power-flow study) of a transmission system will require a different definition of load than that used in the analysis of a secondary in a distribution feeder.

What is load?

The problem is that the load on a power system is constantly changing. The closer you are to the customer, the more pronounced will be the ever-changing load. There is no such thing as a “steady-state” load.

Definitions - Demand

Load averaged over a specific period of time.

Load can be kW, KVAR, kVA, or A.

Must include the time interval.

Example:Example:The 15-minute kW The 15-minute kW

demand is 100 demand is 100 kW.kW.

Definitions – Maximum Demand

Greatest of all demands that occur during a specific time.

Must include demand interval, period, and units.

Example:Example:The 15-minute The 15-minute Maximum kW Maximum kW

demand for the demand for the week was 100 kW.week was 100 kW.

Definitions – Average Demand

The average of the demands overa specified period (day, week,

month, etc.)


Example:Example:The 15-minute The 15-minute

average kW average kW demand for the demand for the

month was 350 kW.month was 350 kW.

Definitions – Diversified Demand

Sum of demands imposed by a group of loads over a particular

period.


Example:Example:The 15-minute The 15-minute diversified kW diversified kW demand in the demand in the

period ending at period ending at 9:30 was 200 kW.9:30 was 200 kW.

Definitions – Max. Diversified Demand

Maximum of the sum of demands imposed by a group of loads over a

particular period.


Example:Example:The 15-minute max. The 15-minute max.

diversified kW diversified kW demand for a week demand for a week

was 500 kW.was 500 kW.

Definitions – Max. Noncoincident Demand

For a group of loads, the sum of theindividual maximum demands withoutany restriction that they occur at the

same time.


Example:Example:The maximum The maximum

noncoincident 15-noncoincident 15-minute kW demand minute kW demand for a week was 700 for a week was 700

kW.kW.

DefinitionsDemand Factor

Ratio of maximum demand to connected load.

Utilization Factor Ratio of maximum demand to rated

capacity.Diversity Factor

Ratio of the maximum noncoincident demand to the maximum diversified demand.

Definitions

Load Factor Ratio of the average demand of any

individual customer or group of customers over a period to the maximum demand over the same period.

Load Diversity Difference between maximum non-

coincident demand and the maximum diversified demand.

Individual Customer Load – Demand Interval

Demand Interval It is the period over which the load is

averaged. This selected Δt period may be 15 min, 30 min, 1 hr, or even longer. Of course, there may be situations where the 15- and 30-min demands are identical.

Individual Customer Load - Demand

Demand Load averaged over a specific period of time. The demand of an installation or system is

the load at the receiving terminals averaged over a specified interval of time.

In order to define the load, demand curve is broken into equal time.

For example, in Figure 1 the selected time interval is 15 minutes.

The straight lines represent the average load in a time interval.


The shorter the time interval, the more accurate will be the value of the load.

The average value of the load in an interval is defined as the 15-minute kW demand.

6:15 6:30

1.0

2.0

3.0

4.0

5.0

6.0

15 M

inut

e kW

Dem

and

6:45

Time of Day

Instantaneous

Fig. 1 Customer demand curve


The 24-hour 15-minute kW demand value for a customer is shown in Figure 2.

0

5

10

15

00:15 02:45 05:15 07:45 10:15 12:45 15:15 17:45 20:15 22:45

Time of Day

kW D

eman

d

Fig. 2 24-hour demand curve.

Individual Customer Load – Max. Demand

Maximum Demand Greatest of all demands that occur during a

specific time. During the 24-hour period (Fig. 2), there is a

great variation in the demand. The greatest of these is the 15-minute

maximum kW demand. For this customer the 15-mimute maximum

kW demand occurs at 11:45 and has a value of 12.68 kW.

Individual Customer Load – Average Demand

Average Demand The average of the demands over a

specified period.

During the 24-hour period, energy (kWh) will be consumed. The energy in kWh used during each 15-minute time interval is computed by

hour4

1demandkWmin15kWh

Hours

energyTotalDemandAverage

Individual Customer Load – Average Demand

The total energy consumed during the day is the summation of all of the 15-minute interval consumptions.

If the total energy consumed during the period by customer is 58.96 kWh, then the 15-minute average kW demand is computed by

kW..

Hours

energyTotalDemandAverage 462

24

9658

Individual Customer Load – Load Factor

Load Factor Ratio of the average demand of any

individual customer or group of customers over a period to the maximum demand over the same period.

The ratio of the average load (or average demand) over a designated period of time to the peak load (or maximum demand) occurring on that period.


Therefore, the load factor FLD is

In Figure 2, the load factor can be found by

Load factor gives an indication of how well the utility’s facilities are being utilized.

demnadkWminMaximum

demnadkWminAverage

loadpeak

loadaverageFLD

15

15

19406812

462.

.

.

loadpeak

loadaverageFLD


From the utility’s standpoint, the optimal load factor would be 1.0, since the system has to be designed to handle the maximum demand.

Sometimes utility companies will encourage industrial customers to improve their load factors. One method of encouragement is to penalize the customer on the electric bill for having a low power factor.


By energy, the load factor can be expressed as

For the annual factor, it can be expressed as

Tloadpeak

TloadaverageFLD

where T = time, in days (24), weeks (168), months (730), or years (8760).

8760loadpeakAnnual

energyannualTotalfactorloadAnnual


A distribution transformer will provide service to one or more customers. Each customer will have a demand curve similar to Figure 2.

For example, there are four customers connected to the same distribution transformer. The load curves for the four customers show that each customer has his unique loading characteristic.


Cust. #1 Cust. #2 Cust. #3 Cust. #4

Energy Usage (kWh) 58.57 36.46 95.64 42.75

Maximum kW Demand 6.18 6.82 4.93 7.05

Time of Max. kW Demand 13:15 11:30 6:45 20:30

Average kW Demand

Load Factor DemandMaximum

DemandAverage

2.44 1.52 3.98 1.78

0.40 0.22 0.81 0.25

Time

Energy

Diversified Demand

Diversified Demand (Coincident Demand) It is the demand of the composite group, as a

whole, of somewhat unrelated loads over a specified period of time.

It is assumed that one distribution trans-former serves four customers discussed previously. The sum of the four 15-minute kW demands for each time interval is the diversified demand for the group in that time interval.

Diversified Demand

Customer #1

0

5

10

15

Time of Day

kW

De

ma

nd

Maximum demand = 13.1 kW Customer #2

0

5

10

Time of Day

kW

De

ma

nd

Maximum demand = 8.5 kW

Customer #3

0

5

10

15

Time of Day

kW

De

ma

nd

Maximum demand = 11.5 kW Customer #4

0

2

4

6

0:1

5

2:0

0

3:4

5

5:3

0

7:1

5

9:0

0

10

:45

12

:30

14

:15

16

:00

17

:45

19

:30

21

:15

23

:00

Time of Day

kW

De

ma

nd

Maximum demand = 5.7 kW

15-mimute Max. Diversity Demand

Fig. 3 24-hour demand curve

Maximum Diversified Demand

The importance of the maximum diversified demand is the maximum sum of the contributions of the individual demands to the diversified demand over a specific time interval.

Note that this maximum demand does not occur at the same time as any one of the individual demands, nor is this maximum demand the sum of the individual maximum demands.

Load Duration Curve

A load duration curve can be developed for the transformer serving the four customers. Sorting in descending order, the kW demand of the transformer develops the load duration curve.

The load duration curve plots the 15-minute kW demand versus the percent of time.

The curve can be used to determine whether a transformer needs to be replaced due to an over-loading condition.

Load Duration Curve

For example, the load duration curve shows the transformer operates with a 15-mimute kW demand of 20 kW or greater 15% of the time.

Fig. 4 Transformer load duration curve.

Demand factor

The demand factor can be defined for an individual customer.

The definition is The ratio of the maximum demand to the

total connected load. Therefore, the demand factor (DF) can be expressed as

The demand factor is usually less than 1.0. It is an indicator of the simultaneous

operation of the total connected load.

demandconncetedtotal

demandmaximumDF

Demand factor

For example the 15-minute maximum kW demand of

Customer #1 was found to be 6.18 kW. The total connected load will be the sum of

the ratings of all of the electrical devices at the customer’s location.

Assume that this total comes to 35 kW, then

1766.035

18.6

LoadConnectedTotal

DemandMaximumFactorDemand

Connected Load

The sum of the continuous ratings of the load-consuming apparatus connected to the system. Or, the sum of the ratings of the electricity consuming apparatus connected to a generating system.

That is, the electric load (in watts), if all apparatus and equipment connected to the system are energized simultaneously.

Noncoincident demand Noncoincident demand

The demands of a group loads are with no restrictions on the interval.

Maximum Noncoincident Demand The 15-minute maximum noncoincident kW

demand for the day is the sum of the individual customer 15-minute maximum kW demands.

For the transformer, the sum of the individual maximum is

kW8387551158113 .....DemandentNoncoincidMaximum

Diversity Factor

It is the ratio of the sum of the individual maximum demands of the various sub-divisions of a system to the maximum demand of the whole system.

That is, diversity factor is the ratio of the maximum noncoincident demand of a group of customers to the maximum diversified demand of the group.

Diversity Factor

Therefore, the diversity factor (FD) is

DemandCoincidentMaximum

DemandsentNoncoincidMaximum

DemandMaximumCoincident

DemandsMaximumIndividualofSumFD

g

n

1ii

g

n321D

D

D

D

DDDDF

Di = maximum demand of load i, dis- regarding time of occurrence.

Dg = D1+2+3+…+n

= coincident maximum demand of group of n loads.

Diversity Factor

From the definition of demand factor, we can obtain

DFTCDDemandConncetedTotalDemandMaximum

then,

g

in

1ii

g

n

1ii

D D

DFTCD

D

D

F

Diversity Factor

The diversity factor can be equal to or greater than 1.

The idea behind the diversity factor is that when the maximum demands of the customers are known, then the maximum diversified demand of a group of customers can be computed.

There will be a different value of the diversity factor for different numbers of customer.

Diversity Factor

Table 1 developed from a database is an example of the diversity factors for the number of customers ranging from one to 70.

N DF N DF N DF N DF N DF N DF N DF1 1.0 11 2.67 21 2.90 31 3.05 41 3.13 51 3.15 61 3.182 1.60 12 2.70 22 2.92 32 3.06 42 3.13 52 3.15 62 3.183 1.80 13 2.74 23 2.94 33 3.08 43 3.14 53 3.16 63 3.184 2.10 14 2.78 24 2.96 34 3.09 44 3.14 54 3.16 64 3.195 2.20 15 2.80 25 2.98 35 3.10 45 3.14 55 3.16 65 3.196 2.30 16 2.82 26 3.00 36 3.10 46 3.14 56 3.17 66 3.197 2.40 17 2.84 27 3.01 37 3.11 47 3.15 57 3.17 67 3.198 2.55 18 2.86 28 3.02 38 3.12 48 3.15 58 3.17 68 3.199 2.60 19 2.88 29 3.04 39 3.12 49 3.15 59 3.18 69 3.2010 2.65 20 2.90 30 3.05 40 3.13 50 3.15 60 3.18 70 3.20

Table 1 Diversity Factor

Diversity Factor

A graph of the diversity factors is shown in Figure 8.

0

0.5

1

1.5

2

2.5

3

3.5

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Number of Customers

Div

ersi

ty F

acto

rs

Fig. 5 Diversity Factor

Diversity Factor

Note in Table 2.2 and Figure 2.8 that the value of the diversity factor basically leveled out when the number of customers reached 70.

This is an important observation because it means that as viewed from the substation, the maximum diversified demand of a feeder can be predicted by computing the total noncoincident maximum demand of all of the customers served by the feeder and dividing by 3.2.

Utilization Factor

It is the ratio of the maximum demand of a system to the rated capacity of the system. Therefore,

The utilization factor gives an indication of how well the capacity of an electrical device is being utilized. For transformer, it can be expressed as

capacitysystemrated

t)(coincidendemandmaximumFu

Utilization Factor

For example

The transformer serving four loads is rated 15 kVA. Using the 16.16 kW maximum diversified demand and assuming a power factor of 0.9. Find the utilization factor.

ratingkVArtransforme

demandkVAmaximumrtransformeofFu

Utilization Factor

961790

1616.

.

.

FactorPower

demandkWMaximumratingkVArTransforme

197115

9617.

.

ratingkVArTransforme

demandkVAMaximumfactornUtilizatio

Load Diversity

Load diversity is defined as the difference between the noncoincident maximum demand and the maximum diversified demand.

For the transformer, the load diversity is represented as

demandddiversifieMax.-demandentnoncoincidMax.DiversityLoad

Load Diversity

It is the difference between the sum of the peaks of two or more individual loads and the peak of the combined load.

Then, the load diversity (LD) is

gDD

demandddiversifieMax.-demandentnoncoincidMax.LD

n

1ii

Coincidence Factor It is the ratio of the maximum coincident total

demand of a group of consumers to the sum of the maximum power demands of individual consumers comprising the group both taken at the same point of supply for the same time.

The coincidence factor (FC) is

Dn

ii

g

C

FD

D

demandsmaximumindividualofsum

demandmaximumcoincidentF

1

1

Contribution Factor

It is defined as the contribution factor of the ith load to the group maximum demand. Therefore,

nng DDDDD cccc 332211

n

ii

n

iii

n

ii

nnC

D

Dc

D

DcDcDcDcF

1

1

1

332211

demandmaximumentnoncoincidclass

peakgroup.,e.isystemoftimeatdemandclassci

where ci is called contribution factor.

Contribution Factor

Special case

Case 1： n321 DDDD , then

n

c

nD

cDF

n

1ii

n

1ii

C

That is, the coincident factor is equal to the average contribution factor.

Contribution Factor

Case 2： n321 cccc , then

c

c

n

i

n

ii

1i

1C

D

D

F

That is, the coincident factor is equal to the contribution factor.

Example 1

Problem 2.3

Example 2

There are six residential customers connected to a distribution transformer. The connected load is 9 kW for each house, and the demand factor and diversity factor for the group of six houses have been decided as 0.65 and 1.10, respectively. Determine the diversified demand of the group of six houses on the distribution transformer.

Example 3

Assume that example 2 has a system peak of 3000kW per phase and a copper loss of 0.5 percent at the system peak. Determine the following： The copper loss of the feeder in kilowatts per

phase. The total copper losses of the feeder in

kilowatts per three-phase.

Example 4

Assume that annual peak load of a primary feeder is 2000 kW, at which the power loss, i.e., total copper loss, or , is 80 kW per three-phase. Assuming an annual loss factor of 0.15, determine: The average annual power loss. The total annual energy loss due to the

copper losses of the feeder circuits.

RI2

Example 5

Assume that there are two primary feeders supplied by one transformer. One of the feeders supplies an industrial load which occurs primarily between 8 am and 11 pm, with a peak of 2000kW at 2 pm. The other one feeds residential loads which occur mainly between 6 am and 12 pm, with a peak of 2000kW at 9 pm. Determine the following: (System peak load is 3000kW at 7 pm.) The diversity factor of the load connected to the

transformer. The load diversity of the load connected to

transformer. The coincidence factor of the load connected to

transformer.

Example 5

Industrialload

Residentialload

Reserved forFuture loads

PrimaryFeeder

TransmissionLine

DistributionTransformer

1000

2000

3000

2 4 6 8 10 12Noon

2 4 6 8 10 1212A.M.

Industrialload peak

Residentialload peak

Systempeak load

Example 6

Use the data shown in Table 2. Note that the peak occurs at 5 P.M. Determine the following: The class contribution factors for each of the

three load classes. The diversity factor for the primary feeder. The diversified maximum demand of the load

group. The coincidence factor of the load group.

TimeLoad , kW

Street Lighting Residential Commercial

1 100 200 200

2 100 200 200

3 100 200 200

4 100 200 200

5 100 200 200

6 100 200 200

7 100 300 200

8 0 400 300

9 0 500 500

10 0 500 1000

11 0 500 1000

12 noon 0 500 1000

1 0 500 1000

2 0 500 1200

3 0 500 1200

4 0 500 1200

5 0 600 1200

6 100 700 800

7 100 800 400

8 100 1000 400

9 100 1000 400

10 100 800 200

11 100 600 200

12 A.M. 100 300 200

Example 7

Assume a substation supplied an annual peak load of 3500 kW. The total annual energy supplied to the primary feeder circuits is 10,000,000 kWh. The peak demand occurs in July or August and is due to air-conditioning load. Find the annual average power demand. Find the annual load factor.

Example 8

Use the data given in Example 7 and suppose that a new load of 100 kW with 100 percent annual load factor is supplied from the substation. The investment cost, or capacity cost, of the power system upstream, i.e., toward the generator, from the substation is $3.00/kW per month. Assume that the energy delivered to these primary feeders is $0.03/kWh. Find the new annual load factor on the substation. Find the total annual cost to the utility to serve this

load.


Assume that the primary feeder shown in Figure 6 is connected to a variable load.

Figure 7 shows an arbitrary and idealized load curve.

PLS1

P1

Fig. 6 The primary feeder.


Fig. 7 Idealized load curve.


Assume that the off-peak loss is PLS,1 at some off-peak load P1 and that the peak loss is PLS,2 at some off-peak load P2. The load factor is

From Figure 7, we can obtain

2P

P

P

PF av

max

avLD

T

tTPtPPav

12

Substituting this equation into the previous one.


TP

tTPtPFLD

2

12

or

T

tT

P

P

T

tFLD

2

1

The loss factor is

From Figure 9, we also can obtain


2,LS

av,LS

max,LS

av,LSLS P

P

P

PF

where PLS,av = average power loss.PLS,max = maximum power loss.PLS,2 = peak loss at peak load.

T

tTPtPP ,LS,LS

av,LS

12

Then, the loss factor can be expressed as

The copper losses are the function of the associated loads.


TP

tTPtPF

,LS

,LS,LSLS

2

12

wherePLS,1 = off-peak loss at off-peak load.t = peak load duration.T-t = off-peak load duration.

211 PkP ,LS 2

22 PkP ,LS and

Thus, the loss factor can be expressed as


TPk

tTPktPkFLS

22

21

22

or

T

tT

P

P

T

tFLS

2

2

1

The load factor can be related to loss factor for three different cases: Case 1: Off-peak load is zero,

That is, the load factor is equal to the loss factor and they are equal to the t/T constant.

T

tT

P

P

T

tFLS

2

2

1 T

tT

P

P

T

tFLD

2

1


i.e. 01 ,LSP , since P1=0.

T

tFF LSLD

Case 2: Very short lasting peak, that is . Then,

That is, the value of the loss factor approaches the value of the load factor squared.


0t

01.T

tT

2LDLS FF Therefore,

Case 3: Load is steady. That is, . It means the difference between peak load and off-peak load is negligible. Thus,


Tt

1

2

1

2

1

T

TT

P

P

T

T

T

tT

P

P

T

tFLD

1

2

2

12

2

1

T

TT

P

P

T

T

T

tT

P

P

T

tFLS

LDLS FF

That is, the value of the loss factor approaches the value of the load factor.

Therefore, in general, the relationship between loss factor and load factor can be shown as

An approximate formula to relate the loss factor to the load factor as

LDLSLD FFF 2


27030 LDLDLS F.F.F 28020 LDLDLS F.F.F (T. P.C)

Feeder Load

The load that a feeder serves will display a smoothed demand curve as shown in Figure 8.

The feeder demand curve does not display any of the abrupt changes in demand of an individual customer demand curve.

The simple explanation for this is that the feeder serves with several hundred customers, and one customer is turning off a light bulb, then another customer will be turning a light bulb on.

Feeder Load

Fig. 8 Feeder demand curve.

Feeder Total

0

5000

10000

15000

0:1

5

2:1

5

4:1

5

6:1

5

8:1

5

10

:15

12

:15

14

:15

16

:15

18

:15

20

:15

22

:15

Time of Day

kW

De

ma

nd

Load Allocation

In the analysis of a distribution feeder load, data will have to be specified.

The data provided will depend upon how detailed the feeder is to be modeled, and the availability of customer load data.

The most comprehensive model of a feeder will represent every distribution transformer. Then, the load allocated to each transformer needs to be determined.

Application of Diversity Factors

The definition of the diversity factor (DF) is the ratio of the maximum noncoincident demand to the maximum diversified demand.

When diversity factor is available, then it is possible to determine the maximum diversified demand of a group of customers such as those served by a distribution transformer.

Application of Diversity Factors

That is, the maximum diversified demand can be computed by:

This maximum diversified demand becomes the allocated load for the transformer.

nDF

DemandentNoncoincidMaximumDemandddiversifieMaximum

Load Survey

Many times the maximum demand of individual customers will be known, either from metering or from a knowledge of the energy (kWh) consumed by the customer.

Some utility companies will perform a load survey of similar customers in order to determine the relationship between the energy consumption in kWh and the maximum kW demand.

Load Survey

At the end of the survey period the maximum demand vs. kWh for each customer can be plotted on a common graph.

Linear regression is used to determine the equation of a straight line that gives the kW demand as a function of kWh.

For example, the straight-line equation can be expressed as

Load Survey

kWh0.0050140.1058demandkWMax.

400 600 800 1000 1200 1400 1600 1800 20000

2

4

6

8

10

12

Energy (kWh)

15 M

inut

e M

axim

um k

W D

eman

d (k

W)

10.5

1.9

kWi

kW1i

2000500 kWhi

Load Survey

Knowing the maximum demand for each customer is the first step in developing a table of diversity factors as shown in Table 2.

The next step is to perform a load survey where the maximum diversified demand of group of customer is metered.

This will involve selecting a series of location where demand meters can be placed.

Load Survey

The meters will record the maximum demand for groups of customers ranging from at least 2 to 70.

At each meter location the maximum demand of all downstream customer must also be known.

With that data, the diversity factor can be computered for the given number of downstream customers.

Load Survey

The first step Knowing the maximum demand for each

customer. The results can use to find “Maximum

Noncoincident demand”.

The second step The maximum diversified demand of groups

of customer is metered. The results are used to obtain “Maximum

diversified demand”

Load Survey

The third step By the previous data, the diversity factor

can be computered.

DemandddiversifieMaximum

DemandentNoncoincidMaximumDFn

Example 9

A single-phase lateral provides service to three distribution transformer as shown in Figure 9.

T1 T2 T3

N1 N2 N3 N4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Fig. 9 Single-phase lateral.

Example 9

The energy in kWh consumed by each customer during a month is known. A load survey has been conducted for customers in this class, and it has been found that the customer 15-mimute maximum kW demand is given by the equation

kWh008020kWdemand ..

Example 9

Customer #1 #2 #3 #4 #5

kWh 1523 1645 1984 1590 1456

kW 12.4 13.4 16.1 12.9 11.9

Customer #6 #7 #8 #9 #10 #11

kWh 1235 1587 1698 1745 2015 1765

kW 10.1 12.9 13.8 14.2 16.3 14.3

Customer #12 #13 #14 #15 #16 #17 #18

kWh 2098 1856 2058 2265 2135 1985 2103

kW 17.0 15.1 16.7 18.3 17.3 16.1 17.0

T1

T2

T3

Example 9

Determine for each transformer the 15-mimute noncoincident maximum kW demand and, using the Table 2 (Diversity Factor), determine the 15-mimute maximum diversified kW demand.

Determine the 15-mimute noncoincident maximum kW demand and 15-minute maximum diversified kW demand for each of the line segments.

Example 9

Discussing This Example demonstrates that Kirchhoff’s

current law (KCL) is not obeyed when the maximum diversified demands are used as the load flowing through the line segments and through the transformers.

At node N1 the maximum diversified demand flowing down the line segment N1-N2 is 92.8 kW, and the maximum diversified demand flowing through transformer T1 is 30.3 kW.

KCL is obeyed or not?

Why?

Example 9

KCL would then predict that the maximum diversified demand flowing down line segment N2-N3 would be the difference of these, or 62.5 kW.

However, the calculations for the maximum diversified demand in that segment were computed to be 72.6 kW.

The explanation is that the maximum diversified demands for the line segments and transformers don’t necessarily occur at the same time.

Example 9

At the time that line segment N2-N3 is experiencing its maximum diversified demand, line segment N1-N2 and transformer T1 are not at their maximum values.

All that can be said is that, at the time segment N2-N3 is experiencing its maximum diversified demand, the difference between the actual demand on line segment N1-N2 and the demand of transformer T1 will be 72.6 kW, not 62.5 kW.

Transformer Load Management

The transformer load management program relates the maximum diversified demand of a distribution transformer to the total kWh supplied by the transformer during a specific month.

The usual relationship is the equation of a straight line. Such an equation is determined from a load survey.


This type of load survey meters the maximum demand on the transformer in addition to the total energy in kWh of all of the customers connected to the transformer.

A transformer load management program is used by utilities to determine the loading on distribution transformers.


The program is primarily used to determine when a distribution transformer needs to be changed out due to a projected overloading condition.

The results of the program can also be used to allocate loads to transformers for feeder analysis purposes.

Because the utility will have in the billing database the kWh consumed by each customer every month.


As long as the utility knows which customers are connected to each transformer by using the developed equation, the maximum diversified demand (allocated load) on each transformer on a feeder can be determined for each billing period.

Metered Feeder Maximum Demand

The major disadvantage of allocating load using the diversity factors is that most utilities will not have a table of diversity factors. The process of developing such a table is generally not cost effective.

The major disadvantage of the transformer load management method is that a database is required that specifies which transformer serve which customer.


Allocating load based upon the metered readings in the substation requires the least amount of data.

Most feeders will have metering in the substation that will, at minimum, give either the total three-phase maximum diversified kW or kVA demand and/or the maximum current per phase.


The kVA ratings of all distribution transformers are always known for a feeder. The metered readings can be allocated to each transformer based upon the transformer rating.

An “allocation factor” (AF) can be determined based upon the metered three-phase kW or kVA demand and the total connected distribution transformer kVA


The allocated load per transformer is then determined by

The transformer demand will be either kW or kVA depending upon the metered quantity.

totalkVA

DemandMeteredAF

Where metered demand can be either kW or kVA, andkVAtotal = sum of the kVA ratings of all distribution transformers.

rtransformekVAAFdemandrTransforme


When the kW or kVA is metered by phase, the load can be allocated by phase where it will be necessary to know the phasing of each distribution transformer.

When the maximum current per phase is metered, the load allocated to each distribution transformer can be done by assuming nominal voltage at the substation and then computing the resulting kVA.

Example 10

Assume that the metered maximum diversified kW demand for the system of Example 9 is 92.8 kW. Allocate this load according to the kVA ratings of the three transformers.

51125053725kVA total ..

kW/kVA824905112

892

AF

..

.

kVA

demandMetered

total

Example 10

The allocated kW for each transformer becomes

T1： kW62202582490kW1 ..

T2： kW933053782490kW2 ...

T3： kW24415082490kW3 ..

What Method to Use?

Four different methods have been presented for allocating load to distribution transformers: Application of diversity factors. Load survey. Transformer load management. Metered feeder maximum demand.

Which method to use depends upon the purposeof the analysis.

What Method to Use?

If the purpose is to determine as closely as possible the maximum demand on a distribution transformer, then either the diversity factor or the transformer load management method can be used.

Neither of these methods should be employed when the analysis of the total feeder is to be performed.

What Method to Use?

The problem is that using those methods will result in a much larger maximum diversified demand at the substation than actually exists.

When the total feeder is to be analyzed, the only method that gives good results is that of allocating load based upon the kVA ratings of the transformers, that is, allocation factor.

Voltage-Drop Calculation Using Allocation Loads

The various voltage drops will be computed using the loads allocated by two of the methods in the following examples. (Diversity factor and allocation factor)

For these studies it is assumed that the allocated loads will be modeled as constant real power and reactive power.

Application of Diversity Factor

The loads allocated to a line segment or a distribution transformer using diversity factors are a function of the total number of customers down stream from the line segment or distribution transformer.

With a knowledge of the allocated loads flowing in the line segments and through the transformers and the impedances, the voltage drops can be computed.

Example 11

For the system of Example 9, assume the voltage at N1 is 2400 volts. Compute the secondary voltages on the three transformers and calculate the percent voltage drop to the secondary of transformer T3 using the diversity factor. Assume that the power factor of the loads is

0.9 lagging. The impedance of the lines are:

mile/.j. 6030z

Example 11

The ratings of the transformers are

T1 : 25kVA, 2400-240 volts,

T2 : 37.5kVA, 2400-240 volts,

T3 : 50kVA, 2400-240 volts,

%.Z 4591 %.Z 5002

%.Z 4081

T1 T2 T3

N1 N2 N3 N4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

5000’ 500’ 750’

Example 12

For the system of Example 9, assume the voltage at N1 is 2400 volts and compute the secondary voltages on the three transformers, allocating the loads based upon the transformer ratings. Assume that the metered kW demand at N1 is 92.9 kW. The impedances of the line segments and transformers are the same as in Example 11. Assume the load power factor is 0.9 lagging.

distribution system modeling and analysis - the nature of loads

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maximum diversified

maximum noncoincident

demand curve

average load

everchanging load

specific period of time

minute maximum

particular period