load characteristics

1

Load Characteristics &

Load Metrics

Outlines♦ Introduction♦ Classifications of loads

– Residential loads– Industrial loads– Commercial loads– Agricultural loads

♦ Load characteristics – Basic Definitions– Load factors

♦ Application of load characteristics♦ Load Modeling♦ Mechanical Load Characteristics

2

Introduction

♦ Utilization?♦ It is the “end result” of the generation, transmission,

and distribution of electric power. ♦ The energy carried by the transmission and distribution

system is turned into useful work, light, heat, or a combination of these items at the utilization point.

Block diagram representation of a power system:

3

Introduction♦ Importance of Utilization!♦ Understanding and characterizing the utilization of

electric power is critical for proper planning and operation of power systems.

♦ Improper characterization of utilization can result of over or under building of power system facilities and stressing of system equipment beyond design capabilities.

4

Loads♦ The term load refers to a device or collection of

devices that draw energy from the power system.♦ Individual loads (devices) range from small light bulbs

to large induction motors or arc furnaces. ♦ The term load is often somewhat arbitrarily applied:

– used to describe a specific device;– referred to an entire facility and – used to describe the lumped power requirements of power

system components and connected utilization devices downstream of a specific point in large scale system studies.

5

6

Classifications of Loads♦ Loads classifications differ according to the

purpose and the manner for which the classification is developed. They are characterized in two different ways:

♦ Devices:–Types:

Lighting Motor Heating Electronic

–Device characterization of loads is important when assessing load behavior under abnormal conditions, either transient or steady-state, because the various devices behave differently under such conditions.

7

Classifications of Loads, cont’d♦ End user classes (Customer Class):

– Most common– Types:

– Residential– Commercial– Agricultural (rural commercial)– Industrial

– Customer classification is more appropriate when assessing usage behavior. Such behavior is normally assessed at the feeder, substation, region, or system level, and at this level, end-users of a given class tend to use electrical energy in much the same manner. This is the orientation we will take in this module.

8

Residential Load

♦ The highest type of loads from the point of view of the number of contributing customers and the revenue for the total number of customers.

♦ Divided into two main types, namely; Urban-Suburban and Rural loads.

♦ Rural areas are characterized by having the lightest load densities, therefore large areas have to be involved in load densities determinations.

♦ Urban areas have higher load densities and thus smaller subdivisions will be sufficient to reveal the load density.

9

Commercial Load

♦

10

Industrial Load

♦ They are treated as points of concentrated loads.

♦ Divided into two main types, namely; Small plants and Large plants.

♦ They have a wide range of variations in their load magnitudes.

11

Load Density Ranges

Area Type Load Density (KVA / Mile2) Calculation Remarks

Low density - rural residential areas 10 – 300 From 1 farm @ 10 KVA to 150 farms @2 KVA average / farm (300 KVA).

Medium density - suburban residentialareas 300 – 1200 20 % home saturation on 70 x 100 ft2

plots with 0.5 – 2 KVA / house.

High density - urban residential areas 1200 – 4800 80 % home saturation on 70 x 100 ft2

plots with 0.5 – 2 KVA / house.

Extra high density residential areas 1.5*104 – 2*104 High home saturation percentage withheating and air conditioning.

Commercial areas 1*104 – 3*105

Areas covering ranges of smallshopping centers and commercialareas up to downtown commercialareas of large cities.

Other Load Classifications The previous load classes represent the most

commonly used classification of loads. However, this is not the only classification

available. There are other classifications for the electric load

that depend on the manner or the purpose forwhich the classification originated.

Moreover, classifications according to combinedpurposes also exist.

Other Load Classifications

14

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.

Types of Load Curves Chronological Load Curve:

– Load against time during daily hours.– Its shape depends on type of load

(i) The area under the load curve represents the energy generated in the period considered.

(ii) The area under the curve divided by the total number of hours gives the average load on the power station.

(iii) The peak load indicated by the load curve represents the maximum demand

15

Chronological Load Curve, Cont’d

16

Types of Load Curves, cont’d

Load Duration Curve:– Arrangement of elements of chronological load curve in

descending order.– Depends on the number of working hours of each load

regardless when did it work– The area under load duration curve is equal to the area

under chronological load curve.

Typical chronological curve. Load duration curve

17

Load Duration Curve, Cont’d

♦ Some remarks from load duration curve and chronological load curve:

(i) The area under the load duration curve and the corresponding chronological load curve is equal and represents total energy delivered by the generating station.

(ii) The base load (Minimum load) in the load duration curve will operate for 24 hours.

(iii) Load duration curve gives a clear analysis of generating power economically. Proper selection of base load power plants and peak load power plants becomes easier.

(iv) From these curves the distribution of load between various generating units can also be predicted.

18

19

Daily Load Curve ♦ This figure 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

♦ The highest peaks are a result of simultaneous operation of large devices as refrigerators, air conditioners, and stoves.

20

Daily Load Curves, cont’d♦ To understanding the usage behavior of residential end-users as

a class, we develop a load curve for multiple residential end-users

daily load curves for groups of end-users

21

Daily Load Curves, cont’d

♦ We observe the curves become more smoother as the number of customers increases.

♦ 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 the different end-user classes, except the load curves are given in terms of percent of peak rather than load per end-user.

22

Daily Load Curves, cont’d♦ Load curves for the various end-user classes and also the

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

“miscellaneous” class (mainly sales to other

utilities)

23

Daily Load Curves, cont’d♦ Some observations from the previous figures:(i) 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.

(ii) Commercial loads (rural and urban):– Have a peak at about 11 am, dip slightly at noon, and then are rise

slightly until about 5 pm after which they drop sharply.(iii) 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.

(iv) The system load (solid line):– Has the same form as the residential curves but the peaks and

valleys are less pronounced due to the smoothing effect of the other load class curves.

24

Load Metrics

♦ There are a number of metrics used to capture the variability of loads. Some of them are mainly used in reference to a single end-user (or customer), and some of them are mainly used in reference to a substation transformer or a specific feeder.

25

Load Metrics- Individual Customer♦ There are several metrics commonly applied to individual

end-users or groups of end-users.1. Demand:

The demand of an installation or system is the load at the receiving terminals averaged over a specified interval of time, for example, the 15-minute demand was 4.8 kW.

2. Demand Interval:It is the period over which the load is averaged.

0

1

2

3

4

5

6

7

8

3.98 4 4.02 4.04 4.06 4.08 4.1 4.12 4.14 4.16

Time of Day

15 m

inut

es K

W D

eman

d

26

3. Maximum Demand:The maximum demand of an installation or system is the largest of all demands which have occurred during specified period of time.

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time of the Day

15-M

inut

e K

W D

eman

d

One hour

Customer 2Customer 1

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time of the Day

15-M

inut

e K

W D

eman

d

One hour

Load Metrics- Individual Customer

27

4. Average Demand:The energy in kWh used during each 15-minute time interval is computed by:

kWh = (15-min kW demand)*(1/4) hour The total energy consumed during the day is the summation of all of the 15-min interval consumptions.

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time of the Day

15-M

inut

e K

W D

eman

d

One hour

Average demand =4.9 kW

HoursEnergy TotalDemandKW Average

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time of the Day

15-M

inut

e K

W D

eman

d

One hour

Average demand =2.13 kW


0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Tim e of the D ay

15-M

inut

e K

W D

eman

d

One hour

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time of the D ay

15-M

inut

e K

W D

eman

dOne hour

28

5. Load Factor:It is the ratio of the average load over a designated period of time to the peak load occurring on that period.

FLF= 0.66

demandkW Max.demandkW Average)(Factor Load LDF


♦ It is clear that 1st customer’s load is more constant, whereas the 2nd customer’s load is more variable.

♦ Utilities sometimes penalize large industrial or commercial customers on their electric bill if the load factor is too low (to encourage them to improve their load factor ( FLD).

FLF= 0.29

29

6. Demand Factor:It is defined as follows:

♦ The total connected load is the sum of the ratings of all the electrical devices at the customer location.

♦ The demand factor gives an indication of the percentage of electrical devices that are ON when the maximum demand occurs.

load connected Totaldemand Maximum(DF)Factor Demand


30

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time of the Day

15-M

inut

e K

W D

eman

d

One hour

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time of the Day

15-M

inut

e K

W D

eman

d

One hour

0

1

2

3

4

5

6

7

8

9

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time of the Day

15-M

inut

e K

W D

eman

d

One hour

Customer 1 Customer 2 Customer 3

Energy usage 24.5 17.5 10.67

Max kW demand

7.5 7.8 7.2

Time of max demand

1:15 1:45 4:30

Average kW demand

4.93 3.5 2.14

Load factor 0.66 0.45 0.29

Customer # 1 Customer # 3

Customer # 2

Load Metrics-Distribution Transformer

31

♦ The following terminology is applied to customer group metrics or transformer loading metrics, but not usually to individual end-users.

1. Diversified (Coincident) Demand:It is the sum of demands imposed by a group of loads (customers) over a specific period of time .

♦ N.B. In the previous slide, the summation of the three loads is the diversified demand for the transformer and it is shown below.

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time of the Day

15-M

inut

e K

W D

eman

d

One hour


Note that how the demand curve is beginning to smooth out

20‐Jan‐12 32

2. Maximum Diversified Demand:

It is the maximum value in the diversified demand curve. ♦ Note that it is not the sum of individual maximum demands nor it

occurs at the same time of individual maximum demand.

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time of the Day

15-M

inut

e K

W D

eman

d

One hour

Maximum diversified

demand


18.2 kW

33

3. Maximum Non-coincident Demand:It is the sum of the individual customer 15-minutes maximum kW demands.

For the previous example:Max. non-coincident demand = 7.8 + 7.5 + 7.2 = 22.5 kW

4. Diversity Factor:It can be defined according to the following formula:

24.12.185.22

demand ddiversifie Maximumdemand coincident-non MaximumFactorDiversity DF

So, by knowing the diversity factor and the maximum demand of each load, the maximum diversified demand of a group of customers can be computed.


34

♦ The diversity factor can be mathematically written as:

g

n

ii

g

nD D

D

DDDDF

121 ..

demand ddiversifie Maximumdemand coincident-non Maximum

But, the demand factor for individual customer is given by:

demand connected Totaldemand Maximumfactor Demand DF

DFTCDDF load connected Totaldemand Maximum

g

n

iii

D D

DFTCDF

1


35

♦ The diversity factor will be different as the number of customers increases till it reaches a saturation level as shown in the figure below:

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25 30 35

Number of Customers

Div

ersi

ty fa

ctor


36

5. Utilization Factor:It gives an indication of how well the capacity of the transformer is being utilized.

RatingkVA r TransformeDemandKVA Maximum)(Factor n Utilizatio uF

6. Load Diversity:It is the difference between the non-coincident maximum demand and the maximum diversified demand.

g

n

ii DDLD

1


37

Example: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?

Utilization Factor- Example

Components with high utilization factors (close to or greater than 1) may need to be replaced or reinforced in the near future.

061.1550

3.583550

9.0/525Factorn Utilizatio

38

7. Contribution Factor (ci)It is defined as the contribution of the ith load to the group maximum diversified demand.

nng DcDcDcD ...2211

demand maximum coincident-non Classpeak system of at time demand Class

ic


n

ii

nnC

D

DcDcDcF

1

2211 ...

n

ii

gC

D

DF

1

or,

9. Loss Factor:It is the ratio of the average power loss to the peak power loss during a specified period of time.

loadpeakatlosspowerlosspower average)(Factor Loss LSF

39

The feeder is connected to more than one transformer.

The load that a feeder serves will display a smoothed out demand curve as shown below.

Load Metrics- Feeder Load

40

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

Load Metrics- Feeder Load

41

Example 1

Determine the following:a) For each transformer find the 15-minute non-coincident maximum kW

demandb) The 15-minute diversified kW demandc) The 15-minute maximum kVA diversified demand for each transformer

assuming power factor = 0.9d) Repeat parts a and b for each line segment.

N FD N FD

1 1 11 2.67

2 1.6 12 2.7

3 1.8 13 2.74

4 2.1 14 2.78

5 2.2 15 2.8

6 2.3 16 2.82

7 2.4 17 2.84

8 2.55 18 2.86

9 2.6 19 2.88

1 2.65 20 2.9

42

Example 1, Solution

T1:Non-coincidence max kW demand = 12.4+13.4+16.1+12.9+11.9 = 66.7 kW

T2:Non-coincidence max kW demand = 12.9+13.8+14.2+16.3+14.3+17 = 81.6 kW

kW 3.302.27.66

5for max demand Div. Max.

factorDiversitycoincidentNon

kW 5.353.26.81



T3:Non-coincidence max kW demand = 17+15.1+16.7+18.3+17.3+16.1+17 = 117.5 kW

kW 0.494.25.117



43

Example 1, Solution

kVA 6.339.03.30 demand .kVA Max. T1



The maximum non-coincident kW demand is the sum of the maximum demands of all 18 customers.

Segment N1-N2

Non-coincident max. demand: 66.7+81.6+117.5 = 265.5 kW

kW 8.9286.2

8.26518for

max demand Div. Max.

factorDiversity

coincidentNon

44

Example 1, Solution

The line sees 13 customers. The maximum non-coincident kW demand will be

Segment N2-N3

Non-coincident max. demand: 81.6+117.5 = 199.1 kW

kW 6.7274.2

1.19913for

max demand Div. Max.

factorDiversity

coincidentNon

Segment N3-N4

The line segment sees the same non-coincident demand and diversified demand as that of transformer T3.

45

Example 2

There are six residential customers connected to a distribution transformer as shown below. Assume that the connected load is 9 kW per house and that the demand factor and diversity factor are 0.65 and 1.1 respectively. Determine the following:a)The diversified demand on the distribution transformer.b)The needed rating of the transformer if the power factor is 0.85 lagging and available standard transformer ratings are 10, 25, 35, 50 and 100 kVA.

46

Example 2, solution

D

n

iii

g F

DFTCDD

1The diversified demand

kW 9.311.1

65.096

1

i

gD

The kVA rating will be: kVAkVA 5.3785.09.31

To avoid any overloading of the transformer the closest transformer will be the 50 kVA.

47

Example 3

For the following data find the following:

a) The class contribution factors for each of the three load classes.

b) The diversity factor for the primary feeder.

c) The diversified maximum demand of the load group.

d) The coincident factor of the load group.

48

Example 3, solution

For better visualization to the load, the summation of the three loads is added as shown below

49

Example 3, solution

demand maximum coincident-non classpeak system of at time demand class

ic

0kW 100

kW 0streetc

6.0kW 1000kW 600

lresidentiac

0.1kW 1200kW 1200

commercialc

a) The class contribution is defined as:

50

Example 3, solution

b) The diversity factor is defined as:g

n

ii

D D

DF

1

nng DcDcDcD ...2211

As previously defined, the maximum diversified demand is defined as follows:

278.112000.110006.01000

12001000100

1

1

n

iii

n

ii

D

Dc

DF

51

Example 3, solution

c) The maximum diversified demand

kW 1800...2211 nng DcDcDcD

Also this can be shown from the previous figure.

d) Coincidence factor :

7825.0278.111

D

C FF

52

Application of Load Characteristics

♦ There are two main types of applications to load characteristics in distribution systems;

– Loss evaluation– Load estimation.

53

Loss Evaluation♦ During a specified interval, assume the load is

“a” for time t1, “b” for time t2, and “c” for time t3.The average load (demand) is

321

321

ttttctbtaPav

♦ The demand loss is then calculated as

2

321

3212,

ttttctbtakPkP avavLS

where: k is the proportionality constant

20‐Jan‐12 54

The Relationship Between the Load and Loss Factors

♦ Consider the following primary feeder connected to a variable load

2max PP

PPF avav

LD

2,

,

max,

,

LS

avLS

LS

avLSLS P

PPP

F

♦ load factor and loss factors for this dailyload curve are:

♦ Assume also that the load is characterized by the following arbitrarily and idealdaily load curve

55

2max PP

PPF avav

LD

2,

,

max,

,

LS

avLS

LS

avLSLS P

PPP

F

TtTPtPPav)(12

TPtTPtPFLD

2

12 )(T

tTPP

TtFLD

)(

2

1

But

Also,

It can be shown that: TtT

PP

TtF

LS

LSLS

)(

2,

1,

The Relationship Between the Load and Loss Factors, cont’d

56

211, PkPLS

TtT

PP

TtFLS

)(2

2

1

The copper losses are the function of the associated loads:2

22, PkPLS

Using the above equations, the load factor can be related to the loss factor for three different cases:a) Off-peak load is zerob) Very short lasting peakc) Load is steady


57

a) Off-peak load is zero:

01, LSP 01 Pand

TtFF LSLD

b) Very short lasting peak:

0t and 1T

tT

2LDLS FF


58

c) Load is steady Tt

In this case the difference between the peak load and the off-peak load is negligible. An example for such load is a petrochemical plant.

LDLS FF

Therefore, in general, the loss factor cannot be determined from load factor. However, limiting values of the relation can be found.

F2LD FLS FLD


So, the value of the loss factor is:

59

Buller and Woodrow developed an approximate formula to relate the loss factor with the load factor:

27.03.0 LDLDLS FFF

For rural areas the formula has been modified as follows:

284.016.0 LDLDLS FFF


Both FLD and FLS are in per unit

Load Estimation♦ Step 1: Determine the total number of appliances by

multiplying the total number of customers by the per unit saturation.

♦ Step 2: From the curve in the Maximum diversified 30 min demand characteristics figure, obtain the corresponding diversified demand per customer for the given number of customers.

♦ Step 3: The maximum demand is obtained by multiplying the demand found in step 2 by the total number of appliances.

♦ Step 4: The contribution of this type of load to the group maximum demand is obtained by multiplying the resultant value from step 3 by the corresponding hourly variation factor found in the Hourly variation factor table.

60

Maximum Diversified 30 Min Demand Characteristics Of Various Modern Residential Loads Figure *

61

Maximum Diversified 30 Min Demand Characteristics of Various Modern Residential Loads Figure *

a = clothes dryer; b = off-peak water heater, "off-peak" load; c = water heater, uncontrolled, interlocked elements; d = range; e = lighting and miscellaneous appliances; f = 0.5-hp room coolers; g = off-peak water heater, "on-peak" load, upper element uncontrolled;h = oil burner; i = home freezer; j = refrigerator; k = central air-conditioning, including heat-pump cooling, 5 hp heat pump (4-ton air conditioner); l = house heating, including heat-pump-heating-connected load of 15 kW unit-type resistance heating or 5-hp heat pump.

* C.E. Arvidson, “Diversified Demand Method of Estimating Residential Distribution Transformer Loads”, Edison Electr. Inst. Bull., Vol.8, October 1940, pp 469-479.

62

Hourly Variation Factor Table *

63

Hourly Variation Factor Table *

* = Load cycle and Maximum diversified demand are dependent on outside temperature, dwelling construction and insulation among other factors.

† = Load cycle and maximum diversified demands are dependent on tank size, and heater element rating: values shown apply to 52-gal tank, 1500 and 1000 W elements.

‡ = Load cycle is dependent on schedule of Water heater restriction.

§ = Hourly variation factor is dependent on living habits of individuals: in a particular area, values may be different from those shown.

* C.E. Arvidson, “Diversified Demand Method of Estimating Residential Distribution Transformer Loads”, Edison Electr. Inst. Bull., Vol.8, October 1940, pp 469-479.

64

65

Load Models♦ Load models are traditionally classified into

two broad categories, Static models Dynamic models

♦ In performing power system analysis such as power flow and stability simulation studies, models must be developed for all pertinent system components, including generating stations, transmission and distribution equipment, and load devices.

♦ Improper modeling could be very costly.

66

Static Load Models ♦ These models express the active and reactive powers, at any

instant of time, as a function of the bus voltage magnitude and frequency.

♦ Static load models are used in both static and dynamic load components.

♦ The static load is modeled as an exponential function of voltage

67

Dynamic Load Models ♦ Studies of inter area oscillations, voltage stability, and long term

stability often require load dynamic to be modeled. ♦ Difference or differential equations can be used to represent

such models

68

Dynamic Load Models, cont’d

69

Types of Static and Dynamic Load Models ♦ The following terminology is commonly used in

describing different types of static and dynamic load models.

- Constant impedance load model is a static load model where the power varies directly with the square of the voltage magnitude. It may also be called a constant admittance load model.

- Constant current load model is a static load model where the power varies directly with the voltage magnitude.

- Constant power load model is a static load model where the power does not vary with changes in voltage magnitude. It may also be called constant MVA load model.

70

Simple Static Load Models Representations

71

Hybrid Load Models Representations

72

Types of Static and Dynamic Load Models, cont’d

- Polynomial load model is a static load model that represents the power relationship to voltage magnitude as a polynomial equation, usually in the following form:

- The parameters of this model are the coefficients (a1 to a6) and the power factor of the load. This model is sometimes referred to as the “ZIP” model, since it consists of the sum of constant impedance (Z), constant current (I), and constant power (P) terms.

- Po and Qo are the real and reactive power consumed by the load at nominal voltage respectively.

73


- Exponential load model is a static load model that represents the power relationship to voltage as an exponential equation, usually in the following form:

Note that by setting these exponents to 0, 1, or 2, the load can be represented by constant power, constant current or constant impedance models, respectively. Other exponents can be used to represent the aggregate effect of different types of load components. Exponents greater than 2 or less than 0 may be appropriate for some types of loads.

74

Comparison of Exponential and Polynomial Models

♦ Both models provide good representation around rated or nominal voltage.

♦ The accuracy of the exponential form deteriorates when voltage significantly exceeds its nominal value, particularly with exponents (α) greater than 1.0.

♦ The accuracy of the polynomial form deteriorates when the voltage falls significantly below its nominal value when the coefficient a1 is non zero.

♦ A nonzero a1 coefficient represents some portion of the load as constant power.

♦ A scheme often used in practice is to use the polynomial form, but switch to the exponential form when the voltage falls below a predetermined value.

75


- Frequency-dependent load model is a static load model that includes frequency dependence. This is usually represented by multiplying either a polynomial or exponential load model by a factor of the following form:

where f is the frequency of the bus voltage, fo is the rated frequency, af is the frequency sensitivity parameter of the model.

76

Load Modeling Technique

♦ There are two approaches in load modeling, a)The component based approach, which models

the load on the basis of familiarity with static and dynamic behavior of all the individual loads and load components of a particular load bus; and

b)The measurement based approach, which uses system identification to estimate a proper model and its parameters.

77

Component-Based Approach

♦ It is a “bottom-up” approach in that the different load component types comprising load are identified.

♦ Each load component type is tested to determine the relationship between real and reactive power requirements versus applied voltage and frequency.

♦ A load model, typically in polynomial or exponential form, is then developed from the respective test data.

♦ The range of validity of each model is directly related to the range over which the component was tested.

78

Component-Based Approach (Cont.)

♦ The load model is expressed in a per-unit basis (i.e., normalized with respect to rated power, rated voltage, rated frequency, rated torque if applicable, and base temperature if applicable).

♦ A composite load is approximated by combining appropriate load model types in certain proportions based on load survey information. The resulting composition is referred to as a “load window.”

79

Component-Based Approach (Cont.)

i) 1-ph Central Air Conditioner load

TVTVVVQTVTVTVp

**455.1*839.0*422.5*543.0*664.0315.0**900.0*388.2*07.2*9507.0*4311.00.1

232

22

ii) 3-ph Central Air Conditioner load

TVTVTVQTVTVTVp

**597.0*199.0*81.5*058.0*37.2695.0**154.0*188.0*005.1*487.0*269.00.1

22

22

iii) Freezer

432

432

*0995*293*276.427*269.038.1*380*6.133*616.12*32.10.1

VVVVQVVVVp

The following are examples for component load models, which are constructed based on measurements conducted by EPRI

where: ΔV is the voltage difference and ΔT is the temperature deference

80

Measurement Approach

♦ It is a “top-down” approach in that measurements are taken at either a substation level, feeder level, some load aggregation point along a feeder, or at some individual load point.

♦ Variation of frequency for this type of measurement is not usually performed unless special test arrangements can be made.

♦ Voltage is varied using a suitable means and the measured real and reactive power consumption recorded.

♦ Statistical methods are then used to determine load models. ♦ A load survey may be necessary to classify the models derived

in this manner. ♦ The range of validity for this approach is directly related to the

realistic range over which the tests can be conducted without damage to customers’ equipment.

81

Devices Contributing to Modeling Difficulties

♦ Protective relays are notoriously difficult to model.

♦ The entire load of a substation can be tripped off line or the load on one of its distribution feeders can be tripped off line as a result of protective relay operations.

♦ At the utilization level, motors on air conditioner units and motors in many other residential, commercial, and industrial applications contain thermal and/or over-current relays whose operational behavior is difficult to predict.

Protective Relays

82

Thermostatically Controlled Loads♦ Air conditioning units, space heaters, water heaters, refrigerators,

and freezers are all controlled by thermostatic devices.

♦ The effects of such devices are especially troublesome to model when a distribution load is reenergized after an extended outage (cold-load pickup).

♦ The effect of such devices to cold-load pickup characteristics can be significant.

Devices Contributing to Modeling Difficulties, cont’d

83

Voltage Regulation Devices♦ Voltage regulators, voltage controlled capacitor

banks, and automatic LTCs on transformers exhibit time-dependent effects.

♦ These devices are present at both the bulk power and distribution system levels.


84

Discharge Lamps (Mercury Vapor, Sodium Vapor, and Fluorescent Lamps)♦ These devices exhibit time-dependent characteristics

upon restart, after being extinguished by a low-voltage condition, usually about 70% to 80% of rated voltage.


Mechanical LoadCharacteristics

85

Nature of Mechanical load♦ The nature of the mechanical load has to be examined before

selecting an electrical drive (motor). ♦ The drive should be able to meet the output torque at

different speeds. ♦ To ensure proper choice of motor for a given drive, the

matching of speed-torque characteristic is to be ensured for both motor and load.

♦ When there is a decrease in speed, the motor torque should be more than the load torque and for an increase in speed the motor torque must be less than the load torque.

♦ This figure shows the relationship in which the load torque TL1 gives a stable operating point, while the load torque curve TL2 results in unstable condition.

86

Types of Mechanical Loads (Load Torques)

♦ Load can be classified under two categories:(1) Active or potential load torque:

This type of load is due to the forces of gravity, compression or tension in a spring or in any elastic body. It is also known as potential load as it is associated to the change in the potential energy of various elements of an electrical drive system. They may be positive or negative depending upon whether they aid or oppose the motion of the drive.

Examples:♦ Hoists, elevators, lifts and railway locomotives on gradients etc.

(2) Passive load torque:These are due to friction, cutting and deformation of inelastic body. These torques always oppose the motion of drive and change their sign when the direction of rotation of the drive is changed.

Example:♦ Fraction torque: it always acts in a direction opposite to that of

driving torque.87

Components of Load Torques

♦ Load torque can be divided into following components:1. Frictional torque (TF):

Friction will be present at the motor shaft and also in various moving parts of the load. TF is equivalent value of various friction torques referred to the motor shaft.

1. Windage torque (TW):Windage torque is due to wind and opposing the motor’s motion.

1. Torque required to do some useful mechanical work (TL):This torque depends upon particular application. It may be: Constant and independent of speed ;

Some function of speed;

Depend on the position or path followed by load;

Time variant or time-invariant;

Vary periodically and it may also depend on the load's mode of operation.

88

Classification of Mechanical Loads

♦ Mechanical loads can be broadly classified into load torque varying with speed and with time.

(A) Variation with speed:

(i) Constant load torque:The torque is independent of the speed and it is constant. Example:

– hoist is an example of load where torque is constant and independent of speed.

89

Classification of Mechanical Loads, cont’d♦ Mechanical loads can be broadly classified into load

torque varying with speed and with time.(A) Variation with speed:

(ii) Load torque varies linearly with speed: The torque is increased linearly with the speed. Example:

– hoist fluid friction where lubricant is used

90

Classification of Mechanical Loads, cont’d♦ Mechanical loads can be broadly classified into

load torque varying with speed and with time.(A) Variation with speed:

(iii) Load torque varies with square of speed : Examples:

– fans, compressors, centrifugal pumps, ship-propellers, coilers, etc.

91

Classification of Mechanical Loads, cont’d♦ Mechanical loads can be broadly classified into

load torque varying with speed and with time.(A) Variation with speed:

(iv) Load torque varies inversely with the speed : This occurs where deformation of material takes placeExamples:

– grinding and metal drawing etc.

92

Classification of Mechanical Loads, cont'd

(B) Variation with time:Depending upon the time for which load exists on a electric drive, the load torques can be classified as:

(i) Continuous and constant load:– Example: centrifugal pumps operating under same

condition for a long time.(ii) Continuous but variable loads:– Example: hoisting winches, conveyors etc .(iii) Short time intermittent loads:– Example: excavators, cranes and hoists etc.(iv) Pulsating loads:– Example: reciprocating pumps and textile looms, etc.(v) Impact loads: – Example: rolling mills, forging hammers, shearing

machines etc. Such machines have flywheel associated with them.

93

Characteristics of Different Types of Mechanical Loads

1. Lifting load: This involves lifting of some weight by a crane or hoist etc. In lifting of loads the torque required independent of speed.

2. Air and fluid friction: In these types of loads the torque changes with the square of speed such as in blowers, fans and water wheels etc. In this case Torque (speed)2 as shown in this figure

Torq

ue

94

Characteristics of Different Types of Mechanical Loads, cont'd3. Load due to friction: Whenever two surfaces move one over

the other on a shaft, rotates in a bearing or bush, an opposite face always acts at the surface. This force is called the frictional force. However this force can be decreases by the using a lubricant. When no lubricant is used friction is called dry friction, torque in that case is constant with speed. In fluid friction where a lubricant is used the torque is linearly proportional to speed as shown below

95

Characteristics of Different Types of Mechanical Loads, cont'd4. Deformation loads: Such types of loads occur in

crushing, grinding and metal drawing etc. In such cases torque is inversely proportional to the speed as shown in the following figure.

96

Characteristics of Different Types of Mechanical Loads, cont'd

5. Combined loads: a combination of two or more types of mechanical loads e.g. in a centrifugal pump the mechanical load consist mainly of a height head and velocity head. Height head means pump has to lift water from lower level to higher level against gravity. Therefore the torque required for this load will be constant and independent of speed. Velocity head means the load due to friction and therefore the torque required to overcome this load will be proportional to square of speed as shown below.

Torq

ue

Height HeadVe

loci

ty H

ead

Net

Cur

ve

97

load characteristics

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