T2 Load Characterstics

8/12/2019 T2 Load Characterstics

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Loads and Load Duration

2.0 Introduction

Unlike transmission systems, distribution systems are directly connected to loads. As

a result, the nature of the load often has a large influence on operational and planningdecisions concerning the distribution system.

Loads are characterized into the following customer classes:o Residentialo Commercialo Industrialo Agricultural (rural commercial)

Customer class loads are normally assessed at the feeder, substation, region, orsystem level, and at this level, end-users of a given class tend to use electrical energy

in much the same manner.

2.1 Load curves The load curve is a plot of load (or load per end-user) variation as a function of time

for a defined group of end-users.

The end-user grouping may be by electrical proximity, e.g., by feeder, substation,

region, or system level. Alternatively, it may be by end-user class.

Daily, weekly, monthly, and yearly load curves are commonly developed and used in

order to gain insight into the usage behavior of a group of end-users.

Fig. 1 shows a daily load curve for a single residential end-user. The multiplicity of

high peaks is due to the intermittent operation of large appliances such as

refrigerators, air conditioners, and stoves, where the highest peaks are a result ofsimultaneous operation of such devices.

Fig. 1: Daily load curve for single residential end-user [1]



Fig. 1 is not very useful for understanding the usage behavior of residential end-users

as a class. To do this, we develop a load curve for multiple residential end-users. To

provide a basis for comparison, we plot the load per end-user rather than the totalload. Fig. 2 illustrates daily load curves for 2, 5, 20, and 100 end-users, respectively.

24-hour demand curve for Customer # 1 and 2

24-hour demand curve for Customer # 3 and 4

Fig. 2: Daily load curves for groups of end-users [1]

We observe the smoothing effect on the curves. We also observe the peak load per

end-user decreases as the number of end-users in the group increases. This is because

at any given moment, some end-users will incur a peak while others do not, so that

the average load at any given moment will always be less than the highest individual

peaks for that moment.

This aggregation of load curves across multiple end-users is done for each of thedifferent end-user classes, except the load curves are given in terms of percent of

peak rather than load per end-user.

Fig. 3 illustrates such load curves for the various end-user classes, including a

“miscellaneous” class (mainly sales to other utilities) and also the aggregation of

these class-specific load curves into a system load curve.



Fig. 3: Class-specific load curves and system load curve

Some observations from Fig. 3 follow:

1. Urban and rural residential loads

- Have three peaks: once at 8 am, once at noon, and once at 6 pm,

- Have two valleys, once at 5 am and once at 3 pm,

- Differ in that the urban load does not fall off so steeply after 7 pm.

2. Commercial loads (rural and urban) peak at about 11 am, dip slightly at noon, and

then are rise slightly until about 5 pm after which they drop sharply.3. The industrial load curves are similar to the commercial except that the valley’s

only dip to about 50% of peak rather than 20% in the case of commercial. This is

the case since many industrial end-users operate 24 hours a day.

2.2 Load duration curves

It is often of interest to know the percent of time that the load in a system, flowing

through a substation, or flowing on a feeder exceeds some particular level.

For example, we might determine that at 90% of peak, the losses are unacceptably

large for the existing amount of voltage switched capacitors. Purchasing and

installing more voltage switched capacitors would solve the problem. This may be a

good investment if the load exceeds 90% of peak for more than 5% of the time.

Otherwise, it is not a good investment. So how do we tell the % of time the load

exceeds a particular value?

One tool for doing this is the so-called load duration curve, which is formed as

follows.



Consider that we have obtained, either through historical data or through forecasting,

a plot of the load vs. time for a period T, as shown in Fig. 4 below.

L o a d ( M

W )

Time T

Fig. 4: Load curve (load vs. time)

Of course, the data characterizing Fig. 4 will be discrete, as illustrated in Fig. 5.

L o a d ( M W )

Time T

Fig. 5: Discretized Load Curve

We now divide the load range into intervals, as shown in Fig. 6.

T

10

9

8

7

6

5

4

3

2

1

0

L o a d ( M W )

Time

Fig. 6: Load range divided into intervals



11

10

9

8

7

65

4

3

2

1

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Probability(Load > L)

L ( M W )

Fig. 7: CDF with axes switched

If the horizontal axis is scaled by the time duration of the interval over which the

original load data was taken, T, we obtain the load duration curve.

This curve provides the number of time intervals that the load equals, or exceeds,

a given load level. For example, if the original load data had been taken over a

day, then the load duration curve would show the number of hours out of that year

for which the load could be expected to equal or exceed a given load level,

11109

87

654

3

210

2.4 4.8 7.2 9.6 12.0 14.4 16.8 19.2 21.6 24.0

Number of hours that Load > L

L ( M W )

Fig. 8: Load duration curve

Load duration curves are useful in that they provide guidance for judging different

alternatives. In our example of unacceptable losses at loads exceeding 90%, we

see from Fig. 8 that this situation occurs for 1.2 hours/day (or 5% of the time).



Chapter 2

Load Characteristics

Basic Definitions

Demand

The demand of an installation or system is the load at the receiving

terminals averaged over a specified interval of time. Measured in kW, kVA,

kA or A

Demand IntervalIt is the period over which the load is averaged. This selected period may

be 15 min, 30 min, 1 hr, or even longer, denoted as t Δ . Of course, theremay be situations where the 15-and 30-min demands are identical

Maximum DemandThe maximum demand of an installation or system is the greatest of all

demands which have occurred during the specified period of time.

Diversified demand (or coincident demand) It is the demand of the composite group, as a whole, of somewhat unrelated

loads over a specified period of time.

Noncoincident Demand The sum of the demands of a group of loads with no restrictions on the

interval to which each demand is applicable

Demand Factor It is the ratio of the maximum demand of a system to the total connected

load of the system. Therefore, the demand factor (DF) is

demand connected total

demands DF

.max≅



7

Connected LoadIt is the sum of the continuous ratings of the load-consuming apparatus

connected to the system or any part thereof.

Utilization FactorIt is the ratio of the maximum demand of a system to the rated capacity of

the system. Therefore, the utilization factor (Fu) is

Systemtheof Capacity Rated

demand F u

.max≅

Plant FactorIt is the ratio of the total actual energy produced or served over a designated

period of time to the energy that would have been produced or served if the

plant (or unit) had operated continuously at maximum rating. It is also

known as the capacity factor or the use factor . Therefore,

T rating plant

T served or produced energyactual

factor Plant ×

×

= max

It is mostly used in generation studies. For example,

T rating plant

generationannualactual factor Plant Annual

×=

max

Or

8760max ×=

rating plant

generationenergyannualactual

Load FactorIt is the ratio of the average load over a designated period of time to the

peak load occurring on that period. Therefore, the load factor FLD is



8

load peak

load averageF LD ≅

T load peak

T load averageF LD

×

×≅

T load peak

served units

×≅

Where T = time, in days, weeks, months, or years. The longer the period Tis the smaller the resultant factor.

8760factorloadAnnual

×=

load peak annual

energyannualtotal

Diversity factor

It is the ratio of the sum of the individual maximum demands of the varioussubdivisions of a system to the maximum demand of the whole system.

Therefore, the diversity factor FD is

demand coincident

demandsindividualof sumF D

max

max=

Or

g

n

D D

D D D DF

++++=

...321

Or



g

n

i

i

D D

D

F

∑=

=1

Where

Di = maximum demand of load i, disregarding time of occurrence

demand ent noncoincid class

peak groupsystemof timeat demand classcwhere Dc D i

n

i

iigmax

)(

1

=×=∑=

= Coincident maximum demand of group of n loads

The diversity factor can be equal to or greater than 1.0.

The demand factor is:

demand connected total

demands DF

max≅

Or

Maximum demand = total connected demand x DF

The diversity factor can also be given as

g

n

i

ii

D D

DF TCD

F

∑=

×

=1

Where TCDi = Total Connected Demand of group, or class, i load

DFi = Demand Factor of group, or class, i load

Coincidence Factor

It is the ratio of the maximum coincident total demand of a group ofconsumers 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. Therefore, the coincidence factor (FC ) is

demandsindividualof sumdemand coincident F c

maxmax≅

Thus, the coincidence factor is the reciprocal of diversity factor; that is,

∑=

=n

ii

g

c

D

DF

1



Primary Feeder Load Data

Time

Load, kW

Street

lightingResidential Commercial

Total

Demand

12 A.M 100 200 200 500

1 100 200 200 500

2 100 200 200 500

3 100 200 200 500

4 100 200 200 500

5 100 200 200 500

6 100 200 200 500

7 100 300 200600

8 0 400 300 700

9 0 500 500 1000

10 0 500 1000 1500

11 0 500 1000 1500

12 noon 0 500 1000 1500

1 0 500 1000 1500

2 0 500 1200 1700

3 0 500 1200 17004 0 500 1200 1700

5 0 600 1200 1800

6 100 700 800 1600

7 100 800 400 1300

8 100 1000 400 1500

9 100 1000 400 1500

10 100 800 200 1100

11 100 600 200 90012 P.M. 100 300 200 600





Load DiversityIt is the difference between the sum of the peaks of two or more individual

loads and the peak of the combined load. Therefore, the load diversity (LD)

is

∑=

−≅n

i

gi D D LD1

)(

Contribution FactorDefines Ci as the contribution factor of the i

th load to the group maximum

demand. It is given in per unit of the individual maximum demand of the ith

load. Therefore,

nn332211g D cDcD cDcD ×…+×+×+×=

Substituting

∑=

=n

1i

i

g

c

D

DF

Or

∑

∑

=

=

×

=n

i

i

n

i

ii

C

D

Dc

F

1

1



Loss FactorIt is the ratio of the average power loss to the peak-load power loss during a

specified period of time. Therefore, the loss factor (FLS) is

load peak at loss power

loss power averageF LS ≅

Here is an approximate formula to relate the loss factor to the load factor:

2

7.03.0 LD LD LS F F F += Where

FLS = loss factor, pu

FLD = load factor, pu.

Plotting the Load Duration Curve

The load duration curve is the plot of load demand v.s. the period or time

for which the load persists on the system. Usually the duration of the load isexpressed as percentage of the total time.

Example #1:

Draw the daily load duration curve for certain substation that has the

following demand data during 24 hours.

Period 0 to

7

7 to

9

9 to

11

11 to

13

13 to

16

16 to

22

22 to

24

Load in

(MW)

20 100 45 70 40 85 30

The following Table helps drawing the required curve:

1- Build a Table that has 3 columns and number of rows equal to the

number of the periods in your given data.2- The first column contains the load demand in a descending order.



3- The second column contains the total time for which each load

persists.

4- The third column contains the percentage of each load duration or

period to the total time.

5- Draw the curve according to the firs column (on the vertical axis) and

the second column (on the horizontal axis).

6- Then you may approximate your curve following the ordinary

methods of curve fitting.

As follows:

Load demand in

(MW)

Duration of the load

in (hrs)

Duration of the load

in (% of the total time)

100 2 8.33

85 2+6=8 33.30

70 8+2=10 41.67

45 10+2=12 50.00

40 12+3=15 62.50

30 15+2=17 70.83

20 17+7=24 100.00Daily Load Duration Curve

0

20

40

60

80

100

120

8.33 33.3 41.67 50 62.5 70 100

% Time

L o a d i n

( M W )



Load factor

The ratio of the average demand over a time interval to the maximum

demand over the same time interval.

peak

avg

LD

P

PF =

The load factor always falls between 0 and 1. It indicates how peaked the

load curve is.

Maximum coincident demand

The maximum coincident demand for a time interval is the maximum of the

sum of the demands imposed by a group of loads over that time interval.

The maximum coincident demand is also called the peak demand. We will

use P peak to represent this.

The difference between maximum demand and maximum coincidentdemand is that the former refers to a single load and the latter to a group of

loads.

Consider sub X that supplies 5 feeders. At 17:15-17:30, the demand on each

feeder was

Example 1:

F1 F2 F3 F4 F5

F1: 120 kW

F2: 80 kWF3: 100 kW

F4: 110 kW

F5: 90 kW

Total: 500 kW

If this was the maximum total loading for the day at this substation, we

would say that “The maximum coincident demand seen at Sub X for

Monday occurred between 17:15 and 17:30 and was 500 kW, i.e., Monday’s

peak demand at Sub X was 500 kW.”

Maximum non-coincident demand

The sum of maximum demands on the individual groups over a time

interval, without restriction that the maximum demands occur at the same

time. We will use Pncpeak to represent this.

16



Example 1:

Consider sub X again.

Feeder 1 sees its daily peak at 16:45-17:00 and it is 150kW.

Feeder 2 sees its daily peak at 18:00-18:15 and it is 150 kW.

Feeder 3 sees its daily peak at 16:30-16:45 and it is 110 kW.

Feeders 4 and 5 all see their daily peak between 17:15 and 17:30 and are

110 kW and 90 kW, respectively.

F1 F2 F3 F4 F5

Summarizing,

F1 peak : 150 kW

F2 peak : 150 kW

F3 peak : 110 kW

F4 peak : 110 kW

F5 peak : 90 kW

Total: 610 kW

The total is 610 kW. So we would say that “The maximum noncoincident

demand seen at Sub X was 610 kW.”

Note: the maximum non-coincident demand is always larger than the

maximum coincident demand, and comparing the two provides an

indication of the extent to which diversification of usage is helping to reduce

the peak for the load group.

Load diversity

Load diversity is the difference between the noncoincident maximum

demand and the coincident maximum demand. In the above example, the

load diversity is 110 kW.

LD = Pncpeak - P peak =610 -

Demand Factor

The demand factor DF k for device or group k is the ratio of the maximum

coincident demand P peak,k to the total connected load for device k .

k

k peak k

L

P DF ,=

The total connected load Lk for device k is the sum of the ratings of all load

components.

17



The total connected load Lk is an upper bound for the non-coincident

maximum demand:

- Total connected load depends only on connected equipment.

- Non-coincident maximum demand depends on how equipment is

operated.

Note that 0<DFk <1.0.

So what does a small demand factor mean?

Lots of load but peak is small, therefore load operates

nonsimultaneously.

What does large demand factor mean?

Peak is close to total connected load therefore most of load operates

simultaneously.

Utilization factor

Utilization factor for device k , UF k , is often computed for transformers or

feeders. It is the ratio of the maximum coincident kVA demand on the

component to the rating of the component:

k

k peak

Uk Rating

PF

,=

The utilization factor provides an indication of how well the component is

being utilized.

Example 3:

Consider that a transformer serving five feeders is rated 550kVA and that

the maximum coincident demand on the transformer for the year is 525kW

at a power factor of 0.9. What is the utilization factor?

061.1

550

3.583

550

9.0/525===U F

Components with high utilization factors (close to or greater than 1) may

need to be replaced or reinforced in the near future.

18



Diversity factor

The diversity factor for device or group k , F Dk , is the ratio of the maximum

noncoincident demand to the maximum coincident demand:

k peak

k ncpeak

Dk P

P

F ,

,=

If we know the diversity factor, and we know the maximum noncoincident

demand (from each customer’s bill), we may compute the maximum

coincident demand from

Dk

k ncpeak

k peak

F

PP

,

, =

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T2 Load Characterstics