(notes for students)power engineering - 7 distribution

8/21/2019 (Notes for Students)Power Engineering - 7 Distribution

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Dr Houssem Rafik El Hana Bouchekara 1

Introduction To Power

Engineering

Dr : Houssem Rafik El Hana

BOUCHEKARA 2010/2011 1431/1432

KINGDOM OF SAUDI ARABIAMinistry Of High Education

Umm Al-Qura UniversityCollege of Engineering & Islamic Architecture

Department Of Electrical Engineering


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1 ELECTRIC POWER DISTRIBUTION ................................................................................... 3

1.1 INTRODUCTION .............................................................. ................................................. 3

1.2 TYPES OF DISTRIBUTION SYSTEMS ........................................................... ........................... 5

1.3 PRIMARY DISTRIBUTION ................................................................................... ................ 6

1.3.1 Radial Systems ....................................................................................................... 6

1.3.2 Loop or Ring Systems............................................................................................. 8

1.3.2.1 Open Loop .................................................................................................................... 8

1.3.2.2 Closed Loop .................................................................................................................. 9

1.3.3 Primary Network Systems ..................................................................................... 9

1.3.4 Secondary Distribution ........................................................................................ 11

1.3.4.1 Individual Transformer—Single Service ..................................................................... 11

1.3.4.2 Common Secondary Main .......................................................................................... 12

1.3.4.3 Banked Secondaries ................................................................................................... 12

1.3.4.4 Secondary Networks .................................................................................................. 13

1.3.5 Voltages ............................................................................................................... 15

1.4 DIFFERENCES BETWEEN EUROPEAN AND NORTH AMERICAN SYSTEMS ..................................... 16

2 LOAD CHARACTERISTICS ............................................................................................. 19

2.1 DEFINITIONS ........................................................ ......................................................... 20

2.2 INDIVIDUAL CUSTOMER LOAD .......................................... ............................................... 21

2.2.1 Demand ............................................................................................................... 21

2.2.2 Maximum Demand .............................................................................................. 22

2.2.3 Average Demand ................................................................................................. 22

2.2.4 Load Factor .......................................................................................................... 23

2.2.5 Distribution Transformer Loading ....................................................................... 23

2.2.6 Diversified Demand ............................................................................................. 24

2.2.7 Maximum Diversified Demand ............................................................................ 25

2.2.8 Load Duration Curve ............................................................................................ 25

2.2.9 Maximum Noncoincident Demand ...................................................................... 25

2.2.10 Diversity Factor.................................................................................................. 26

2.2.11 Demand Factor .................................................................................................. 27

2.2.12 Utilization Factor ............................................................................................... 27

2.2.13 Load Diversity .................................................................................................... 28

2.3 FEEDER LOAD ............................................................................................................... 28

2.3.1 Load Allocation .................................................................................................... 28

2.3.1.1 Application of Diversity Factors ................................................................................. 28

2.3.1.2 Load Survey ................................................................................................................ 29

2.3.1.3

Transformer Load Management ................................................................................ 32 2.3.1.4 Metered Feeder Maximum Demand ......................................................................... 33

2.3.1.5 What Method to Use? ................................................................................................ 34

2.3.2 Voltage-Drop Calculations Using Allocated Loads .............................................. 34

2.3.2.1 Application of Diversity Factors ................................................................................. 34

2.3.2.2 Load Allocation Based upon Transformer Ratings ...................... ..................... .......... 38


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1 ELECTRIC POWER DISTRIBUTION

1.1 INTRODUCTION

Once electrical power has been produced, it must be distributed to the locationwhere it is used. This chapter deals with electrical power distribution systems. This chapter

provides an overview of distribution systems. Figure 1 shows the electrical power systems

schematic sketch and the major topics of this chapter, Electrical Power Distribution.

Figure 1: The “vertical power system.” Power is produced at a few large generators (only one is shown) and

moved over a transmission system consisting of dozens, even hundreds of regional power lines (only one path

is shown). Once brought to the local community, it is reduced in voltage and shipped to neighborhoods, and to

the individual consumer, on a distribution system (only one of thousands of lines and customers is shown).

Some utilities perform all the functions shown, others only a portion.


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An electric distribution system, or distribution plant as it is sometimes called, is all of

that part of an electric power system between the bulk power source or sources and the

consumers’ service switches. The bulk power sources are located in or near the load area to

be served by the distribution system and may be either generating stations or power

substations supplied over transmission lines. Distribution systems can, in general, be divided

into six parts, namely, subtransmission circuits, distribution substations, distribution or

primary feeders, distribution transformers, secondary circuits or secondaries, and

consumers’ service connections and meters or consumers’ services. Figure 2 is a schematic

diagram of a typical distribution system showing these parts.

Figure 2: Typical distribution system showing component parts.

The subtransmission circuits extend from the bulk power source or sources to the

various distribution substations located in the load area. They may be radial circuits

connected to a bulk power source at only one end or loop and ring circuits connected to one

or more bulk power sources at both ends. The subtransmission circuits consist of

underground cable, aerial cable, or overhead open-wire conductors carried on poles, or

some combination of them.

Each distribution substation normally serves its own load area, which is a subdivision

of the area served by the distribution system. At the distribution substation thesubtransmission voltage is reduced for general distribution throughout the area. The

substation consists of one or more power-transformer banks together with the necessary

voltage regulating equipment, buses, and switchgear.

The area served by the distribution substation is also subdivided and each

subdivision is supplied by a distribution or primary feeder. The three-phase primary feeder

is usually run out from the low voltage bus of the substation to its load center where

it branches into threephase subfeeders and single-phase laterals. The primary feeders and

laterals may be either cable or openwire circuits, operated in most cases at 2400 or 4160

volts.


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Distribution transformers are ordinarily connected to each primary feeder and its

subfeeders and laterals. These transformers serve to step down from the distribution

voltage to the utilization voltage. Each transformer or bank of transformers supplies a

consumer or group of consumers over its secondary circuit. Each consumer is connected to

the secondary circuit through his service leads and meter. The secondaries and service

connections may be either cable or open-wire circuits.

Briefly, the problem of distribution is to design, construct, operate, and maintain a

distribution system that will supply agequate electric service to the load area under

consideration, both now and in the future, at the lowest possible cost. Unfortunately, no

one type of distribution system can be applied economically in all load areas, because of

differences in load densities, existing distribution plant, topography, and other local

conditions.

In studying any load area, the entire distribution or delivery system from the bulk

power source-which may be one or more generating stations or power substations, to the

consumers should be considered as a unit. This includes subtransmission-distribution

substations, Primary feeders, distribution transformers, secondaries, and services. All of

these parts are interrelated and should be considered as a whole so that money saved in

one part of the distribution system will not be more’ than offset by a resulting increase

elsewhere in the system.

For different load areas, or even different parts of the same load area, the most

effective distribution system will often take different forms. Certain principles and features,

however, are common to almost all of these systems. The distribution system should

provide service with a minimum voltage variation and a minimum of interruption. Service

interruptions should be of short duration and affect a small number of consumers. The

overall system cost-including construction, operation, and maintenance of the system-

should be as low as possible consistent with the quality of service required in the load area.

The system should be flexible, to allow its being expanded in small increments, so as to meet

changing load conditions with a minimum amount of modification and expense. This

flexibility permits keeping the system capacity close to actual load requirements and thus

permits the most effective use of system investment. It also largely eliminates the need for

predicting the location and magnitudes of future loads. Therefore, long-range distribution

planning, which is at best based on scientific guesses, can be greatly reduced.

1.2 T YPES OF DISTRIBUTION S YSTEMS

Electric power distribution is the portion of the power delivery infrastructure that

takes the electricity from the highly meshed, high-voltage transmission circuits and delivers

it to customers. It can be divided into two subdivisions:

1. Primary distribution, which carries the load at higher than utilization voltages

from the substation (or other source) to the point where the voltage is

stepped down to the value at which the energy is utilized by the consumer.

Primary distribution lines are “medium-voltage” circuits.

2.

Secondary distribution, which includes that part of the system operating atutilization voltages, up to the meter at the consumer’s premises.


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1.3 PRIMARY DISTRIBUTION

Primary distribution systems include three basic types:

1. Radial systems, including duplicate and throwover systems

2. Loop systems, including both open and closed loops

3. Primary network systems

1.3.1 RADIAL S YSTEMS

The radial-type system is the simplest and the one most commonly used. It

comprises separate feeders or circuits “radiating” out of the substation or source, each

feeder usually serving a given area. The feeder may be considered as consisting of a main or

trunk portion from which there radiate spurs or laterals to which distribution transformers

are connected, as illustrated in Figure 3.

The spurs or laterals are usually connected to the primary main through fuses, so

that a fault on the lateral will not cause an interruption to the entire feeder. Should the fuse

fail to clear the line, or should a fault develop on the feeder main, the circuit breaker back at

the substation or source will open and the entire feeder will be de-energized.

To hold down the extent and duration of interruptions, provisions are made to

sectionalize the feeder so that unfaulted portions may be reenergized as quickly as practical.

To maximize such re-energization, emergency ties to adjacent feeders are incorporated in

the design and construction; thus each part of a feeder not in trouble can be tied to an

adjacent feeder. Often spare capacity is provided for in the feeders to prevent overload

when parts of an adjacent feeder in trouble are connected to them. In many cases, there

may be enough diversity between loads on adjacent feeders to require no extra capacity to

be installed for these emergencies.

Supply to hospitals, military establishments, and other sensitive consumers may not

be capable of tolerating any long interruption. In such cases, a second feeder (or additional

feeders) may be provided, sometimes located along a separate route, to provide another,

separate alternative source of supply. Switching from the normal to the alternative feeder

may be accomplished by a throwover switching arrangement (which may be a circuit

breaker) that may be operated manually or automatically. In many cases, two separate

circuit breakers, one on each feeder, with electrical interlocks (to prevent connecting a good

feeder to the one in trouble), are employed with automatic throwover control by relays. See

Figure 4.


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(a)

(b)

(c)

Figure 3: Primary feeder schematic diagram showing trunk or main feeds and laterals or spurs.


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Figure 4: Schematic diagram of alternate feed-throwover arrangement for critical consumers.

1.3.2 LOOP OR RING S YSTEMS

Another means of restricting the duration of interruption employs feeders designed

as loops, which essentially provide a two-way primary feed for critical consumers. Here,

should the supply from one direction fail, the entire load of the feeder may be carried from

the other end, but sufficient spare capacity must be provided in the feeder. This type ofsystem may be operated with the loop normally open or with the loop normally closed.

Figure 5: A ring power distribution system.

1.3.2.1 Open Loop

In the open-loop system, the several sections of the feeder are connected together

through disconnecting devices, with the loads connected to the several sections, and both

ends of the feeder connected to the supply. At a predetermined point in the feeder, the

disconnecting device is intentionally left open. Essentially, this constitutes two feeders

whose ends are separated by a disconnecting device, which may be a fuse, switch, or circuit

breaker. See Figure 6.

In the event of a fault, the section of the primary on which the fault occurs can be

disconnected at both its ends and service reestablished to the unfaulted portions by closing

the loop at the point where it is normally left open, and reclosing the breaker at the

substation (or supply source) on the other, unfaulted portion of the feeder.

Such loops are not normally closed, since a fault would cause the breakers (or fuses)

at both ends to open, leaving the entire feeder de-energized and no knowledge of where the

fault has occurred. The disconnecting devices between sections are manually operated and

may be relatively inexpensive fuses, cutouts, or switches.


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Figure 6: Open-loop circuit schematic diagram.

1.3.2.2 Closed Loop

Where a greater degree of reliability is desired, the feeder may be operated as a

closed loop. Here, the disconnecting devices are usually the more expensive circuit breakers.

The breakers are actuated by relays, which operate to open only the circuit breakers on each

end of the faulted section, leaving the remaining portion of the entire feeder energized.

In many instances, proper relay operation can only be achieved by means of pilot

wires which run from circuit breaker to circuit breaker and are costly to install and maintain;

in some instances these pilot wires may be rented telephone circuits. See Figure 7.

To hold down costs, circuit breakers may be installed only between certain sections

of the feeder loop, and ordinary, less expensive disconnecting devices installed between the

intermediate sections. A fault will then de-energize several sections of the loop; when the

fault is located, the disconnecting devices on both ends of the faulted section may be

opened and the unfaulted sections reenergized by closing the proper circuit breakers.

Figure 7: Closed-loop circuit.

1.3.3 PRIMARY NETWORK S YSTEMS

Although economic studies indicated that under some conditions the primary

network may be less expensive and more reliable than some variations of the radial system,

relatively few primary network systems have been put into actual operation and only a few

still remain in service.


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(b) Network distribution systems. Sectionalizing devices on feeders not shown.

(b) Network distribution systems .

Figure 8: Primary network.

This system is formed by tying together primary mains ordinarily found in radial

systems to form a mesh or grid. The grid is supplied by a number of power transformers

supplied in turn from subtransmission and transmission lines at higher voltages. A circuit

breaker between the transformer and grid, controlled by reverse-current and automatic

reclosing relays, protects the primary network from feeding fault current through thetransformer when faults occur on the supply subtransmission or transmission lines. Faults on


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sections of the primaries constituting the grid are isolated by circuit breakers and fuses. See

Figure 8.

This type of system eliminates the conventional substation and long primary trunk

feeders, replacing them with a greater number of “unit” substations strategically placed

throughout the network. The additional sites necessary are often difficult to obtain.Moreover, difficulty is experienced in maintaining proper operation of the voltage regulators

(where they exist) on the primary feeders when interconnected.

1.3.4 SECONDARY DISTRIBUTION

Secondary distribution systems operate at relatively low utilization voltages and, like

primary systems, involve considerations of service reliability and voltage regulation. The

secondary system may be of four general types:

1. An individual transformer for each consumer; i.e., a single service from each

transformer.

2. A common secondary main associated with one transformer from which a group

of consumers is supplied.

3. A continuous secondary main associated with two or more transformers,

connected to the same primary feeder, from which a group of consumers is supplied. This is

sometimes known as banking of transformer secondaries.

4. A continuous secondary main or grid fed by a number of transformers, connected

to two or more primary feeders, from which a large group of consumers is supplied. This is

known as a low-voltage or secondary network.

Each of these types has its application to which it is particularly suited.

1.3.4.1 Individual Transformer — Single Service

Individual-transformer service is applicable to certain loads that are more or less

isolated, such as in rural areas where consumers are far apart and long secondary mains are

impractical, or where a particular consumer has an extraordinarily large or unusual load

even though situated among a number of ordinary consumers.

In this type of system, the cost of the several transformers and the sum of power

losses in the units may be greater (for comparative purposes) than those for onetransformer supplying a group of consumers from its associated secondary main. The

diversity among consumers’ loads and demands permits a transformer of smaller c apacity

than the capacity of the sum of the individual transformers to be installed. On the other

hand, the cost and losses in the secondary main are obviated, as is also the voltage drop in

the main. Where low voltage may be undesirable for a particular consumer, it may be well to

apply this type of service to the one consumer. Refer to Figure 9.


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Figure 9: Single-service secondary supply.

1.3.4.2 Common Secondary Main

Perhaps the most common type of secondary system in use employs a common

secondary main. It takes advantage of diversity between consumers’ loads and demands, as

indicated above. Moreover, the larger transformer can accommodate starting currents of

motors with less resulting voltage dip than would be the case with small individualtransformers. See Figure 10.

In many instances, the secondary mains installed are more or less continuous, but

cut into sections insulated from each other as conditions require. As loads change or

increase, the position of these division points may be readily changed, sometimes holding

off the need to install additional transformer capacity. Also, additional separate sections can

be created and a new transformer installed to serve as load or voltage conditions require.

Figure 10: Common-secondary-main supply.

1.3.4.3 Banked Secondaries

The secondary system employing banked secondaries is not very commonly used,

although such installations exist and are usually limited to overhead systems.

This type of system may be viewed as a single-feeder low-voltage network, and the

secondary may be a long section or grid to which the transformers are connected. Fuses or

automatic circuit breakers located between the transformer and secondary main serve to

clear the transformer from the bank in case of failure of the transformer. Fuses may also be

placed in the secondary main between transformer banks. See Figure 11.

Some advantages claimed for this type of system include uninterrupted service,

though perhaps with a reduction in voltage, should a transformer fail; better distribution of


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load among transformers; better normal voltage conditions resulting from such load

distribution; an ability to accommodate load increases by changing only one or some of the

transformers, or by installing a new transformer at some intermediate location without

disturbing the existing arrangement; the possibility that diversity between demands on

adjacent transformers will reduce the total transformer load; more capacity available for

inrush currents that may cause flicker; and more capacity as well to burn secondary faults

clear.

Figure 11: Banked secondary supply.

Some disadvantages associated with this type of system are as follows: should one

transformer fail, the additional loads imposed on adjacent units may cause them to fail, and

in turn their loads would cause still other transformers to fail (this is known as cascading) ;

the transformers banked must have very nearly the same impedance and other

characteristics, or the loads will not be distributed equitably among them; and sufficient

reserve capacity must be provided to carry emergency loads safely, obviating the savings

possible from the diversity of the demands on the several transformers.

Banked secondaries, while providing for failure of transformers, do not provide

against faults on the primary main or feeder. Further, a hazard on any transformer

disconnected for any reason may result from a back feed if the secondary energizes the

primary (which may have been considered safe).

1.3.4.4 Secondary Networks

Secondary networks at present provide the highest degree of service reliability and

serve areas of high load density, where revenues justify their cost and where this kind of

reliability is imperative. In some instances, a single consumer may be supplied from this type

of system by what are known as spot networks.

In general, the secondary network is created by connecting together the secondary

mains fed from transformers supplied by two or more primary feeders. Automatically

operated circuit breakers in the secondary connection between the transformer and the

secondary mains, known as network protectors, serve to disconnect the transformer from

the network when its primary feeder is de-energized; this prevents a back feed from the

secondary into the primary feeder. This is especially important for safety when the primaryfeeder is de-energized from fault or other cause. The circuit breaker or protector is backed


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up by a fuse so that, should the protector fail to operate, the fuse will blow and disconnect

the transformer from the secondary mains. See Figure 12.

Figure 12: Low-voltage secondary network.

The number of primary feeders supplying a network is very important. With only two

feeders, only one feeder may be out of service at a time, and there must be sufficient spare

transformer capacity available so as not to overload the units remaining in service; thereforethis type of network is sometimes referred to as a single-contingency network.

Most networks are supplied from three or more primary feeders, where the network

can operate with the loss of two feeders and the spare transformer capacity can be

proportionately less. These are referred to as second-contingency networks.

Secondary mains not only should be so designed that they provide for an equitable

division of load between transformers and for good voltage regulation with all transformers

in service, but they also must do so when some of the transformers are no longer in service

when their primary feeders are de-energized. They must also be able to divide fault current

properly among the transformers, and must provide for burning faults clear at any pointwhile interrupting service to a minimum number of consumers; this often limits the size of


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secondary mains, usually to less than 500 cmil × 103, so that when additional secondary

main capacity is required, two or more smaller size conductors have to be paralleled. In

some networks, where insufficient fault current might cause long sections of secondary

mains to be destroyed before the fault is burned clear, sections of secondary mains are

fused at each end.

Because these networks may represent very large loads, their size and capacity may

have to be limited to such values as can be successfully handled by the generating or other

power sources should they become entirely de-energized for any reason. When they are de-

energized for any length of time, the inrush currents are very large, as diversity among

consumers may be lost, and this may be the limiting factor in restricting the size and

capacity of such networks.

1.3.5 VOLTAGES

For all types of service, primary voltages are becoming higher. Original feederprimary voltages of about 1000 V have climbed to nominal 2400, 4160, 7620, 13,800,

23,000, and 46,000 V. Moreover, primary feeders that originally operated as single-phase

and two-phase circuits are all now essentially three-phase circuits; even those originally

operated as delta ungrounded circuits are now converted to wye systems, with their neutral

common to the secondary neutral conductor and grounded.

Secondary voltages have changed from nominal 110/220 V singlephase values to

those now operating at 120/240 V single-phase and 120/208 or 120/240 V for three-phase

circuits, the 120-V utilization being applied to lighting and small-motor loads while the 208-

and 240-V three-phase values are applied to larger-motor loads. More recently, secondary

systems have employed utilization voltage values of 277 and 480 V, with fluorescent lighting

operating single-phase at 277 V and larger motors operating at a three-phase 480 V. To

supply some lighting and small motors single-phase at 120 V, autotransformers of small

capacity are employed to step down the 277 V to 120 V.

Secondary voltages and connections will be explored further in discussing

transformers and transformer connections.

Note: Voltage levels are defined internationally, as follows:

Low voltage: up to 1000 V

Medium voltage: above 1000 V up to 36 kV

High voltage: above 36 kV

Supply standards variation between continents by two general standards have

emerged as the dominant ones:

In Europe

IEC governs supply standards

The frequency is 50 Hz and LV voltage is 230/400 V

In North America


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IEEE/ANSI governs supply standards

The frequency is 60 Hz and the LV voltage is 110/190 V.

1.4 DIFFERENCES BETWEEN EUROPEAN AND NORTH AMERICAN

S YSTEMS

Distribution systems around the world have evolved into different forms. The two

main designs are North American and European. This book deals mainly with North

American distribution practices; for more information on European systems. For both forms,

hardware is much the same: conductors, cables, insulators, arresters, regulators, andtransformers are very similar. Both systems are radial, and voltages and power carrying

capabilities are similar. The main differences are in layouts, configurations, and applications.


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Figure 13: North American versus European distribution layouts.

Figure 13 compares the two systems. Relative to North American designs, European

systems have larger transformers and more customers per transformer. Most European

transformers are three-phase and on the order of 300 to 1000 kVA, much larger than typical

North American 25- or 50-kVA single-phase units.

Secondary voltages have motivated many of the differences in distribution systems.

North America has standardized on a 120/240-V secondary system; on these, voltage drop

constrains how far utilities can run secondaries, typically no more than 250 ft. In European

designs, higher secondary voltages allow secondaries to stretch to almost 1 mi. European

secondaries are largely three-phase and most European countries have a standard

secondary voltage of 220, 230, or 240 V, twice the North American standard. With twice the

voltage, a circuit feeding the same load can reach four times the distance. And because

three-phase secondaries can reach over twice the length of a single-phase secondary,

overall, a European secondary can reach eight times the length of an American secondary

for a given load and voltage drop. Although it is rare, some European utilities supply rural

areas with single-phase taps made of two phases with single-phase transformers connected

phase to phase.

In the European design, secondaries are used much like primary laterals in the North

American design. In European designs, the primary is not tapped frequently, and primary-


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level fuses are not used as much. European utilities also do not use reclosing as religiously as

North American utilities.

Some of the differences in designs center around the differences in loads and

infrastructure. In Europe, the roads and buildings were already in place when the electrical

system was developed, so the design had to “fit in.” Secondary is often attached tobuildings. In North America, many of the roads and electrical circuits were developed at the

same time. Also, in Europe houses are packed together more and are smaller than houses in

America.

Each type of system has its advantages. Some of the major difference between

systems are the following:

Cost — The European system is generally more expensive than the North

American system, but there are so many variables that it is hard to compare

them on a one-to-one basis. For the types of loads and layouts in Europe,

the European system fits quite well. European primary equipment isgenerally more expensive, especially for areas that can be served by single-

phase circuits.

Flexibility — The North American system has a more flexible primary design,

and the European system has a more flexible secondary design. For urban

systems, the European system can take advantage of the flexible secondary;

for example, transformers can be sited more conveniently. For rural systems

and areas where load is spread out, the North American primary system is

more flexible. The North American primary is slightly better suited for

picking up new load and for circuit upgrades and extensions.

Safety — The multigrounded neutral of the North American primary system

provides many safety benefits; protection can more reliably clear faults, and

the neutral acts as a physical barrier, as well as helping to prevent dangerous

touch voltages during faults. The European system has the advantage that

high-impedance faults are easier to detect.

Reliability — Generally, North American designs result in fewer customer

interruptions. Some researchers simulated the performance of the two

designs for a hypothetical area and found that the average frequency of

interruptions was over 35% higher on the European system. Although

European systems have less primary, almost all of it is on the main feederbackbone; loss of the main feeder results in an interruption for all customers

on the circuit. European systems need more switches and other gear to

maintain the same level of reliability.

Power quality — Generally, European systems have fewer voltage sags and

momentary interruptions. On a European system, less primary exposure

should translate into fewer momentary interruptions compared to a North

American system that uses fuse saving. The three-wire European system

helps protect against sags from line-to-ground faults. A squirrel across a

bushing (from line to ground) causes a relatively high impedance fault path

that does not sag the voltage much compared to a bolted fault on a well-


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grounded system. Even if a phase conductor faults to a low-impedance

return path (such as a well-grounded secondary neutral), the delta – wye

customer transformers provide better immunity to voltage sags, especially if

the substation transformer is grounded through a resistor or reactor.

Aesthetics — Having less primary, the European system has an aesthetic

advantage: the secondary is easier to underground or to blend in. For

underground systems, fewer transformer locations and longer secondary

reach make siting easier.

Theft — The flexibility of the European secondary system makes power

much easier to steal. Developing countries especially have this problem.

Secondaries are often strung along or on top of buildings; this easy access

does not require great skill to attach into.

Outside of Europe and North America, both systems are used, and usage typically

follows colonial patterns with European practices being more widely used. Some regions of

the world have mixed distribution systems, using bits of North American and bits of

European practices. The worst mixture is 120-V secondaries with European-style primaries;

the low-voltage secondary has limited reach along with the more expensive European

primary arrangement.

Higher secondary voltages have been explored (but not implemented) for North

American systems to gain flexibility. Higher secondary voltages allow extensive use of

secondary, which makes undergrounding easier and reduces costs. Westinghouse engineers

contended that both 240/480-V three-wire single-phase and 265/460-V four-wire

threephase secondaries provide cost advantages over a similar 120/240-V threewire

secondary (Lawrence and Griscom, 1956; Lokay and Zimmerman, 1956). Higher secondaryvoltages do not force higher utilization voltages; a small transformer at each house converts

240 or 265 V to 120 V for lighting and standard outlet use (air conditioners and major

appliances can be served directly without the extra transformation). More recently,

Bergeron et al. (2000) outline a vision of a distribution system where primary-level

distribution voltage is stepped down to an extensive 600-V, three-phase secondary system.

At each house, an electronic transformer converts 600 V to 120/240 V.

2 LOAD CHARACTERISTICS In the planning of an electrical distribution system, as in any other enterprise, it is

necessary to know three basic things:

1. The quantity of the product or service desired (per unit of time)

2. The quality of the product or service desired

3. The location of the market and the individual consumers

Logically, then, it would be well to begin with the basic building blocks, the individual

consumers, and then determine efficient means of supplying their wants, individually and

collectively.


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2.1 DEFINITIONS

The load that an individual customer or a group of customers presents to the

distribution system is constantly changing. Every time a light bulb or an electrical appliance

is switched on or off, the load seen by the distribution feeder changes. In order to describe

the changing load, the following terms are defined:

1.

Demand

• Load averaged over a specific period of time.

• Load can be kW, kvar, kVA, or A.

• Must include the time interval.

•

Example: the 15-minute kW demand is 100 kW.

2.

Maximum Demand

•

Greatest of all demands that occur during a specific time

• Must include demand interval, period, and units

• Example: the 15-minute maximum kW demand for the week was 150 kW

3.

Average Demand

•

The average of the demands over a specified period (day, week, month, etc.)


• Example: the 15-minute average kW demand for the month was

350 kW

4.

Diversified Demand

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


• Example: the 15-minute diversified kW demand in the period ending at 9:30

was 200 kW

5. Maximum Diversified Demand

•

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

particular period


•

Example: the 15-minute maximum diversified kW demand for the week was

500 kW

6.

Maximum Noncoincident Demand

•

For a group of loads, the sum of the individual maximum demands without

any restriction that they occur at the same time

•

Must include demand interval, period, and units


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•

Example: the maximum noncoincident 15-minute kW demand for the week

was 700 kW

7.

Demand Factor

• Ratio of maximum demand to connected load

8. Utilization Factor

• Ratio of the maximum demand to rated capacity

9.

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

10.

Diversity Factor

•

Ratio of the maximum noncoincident demand to the maximum diversified

demand

11.

Load Diversity

• Difference between maximum noncoincident demand and the maximum

diversified demand

2.2 INDIVIDUAL CUSTOMER LOAD

Figure 14 illustrates how the instantaneous kW load of a customer changes during

two 15-minute intervals.

2.2.1 DEMAND

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

Figure 14 the selected time interval is 15 minutes. In each interval the average value of the

demand is determined. In Figure 14 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. This

process is very similar to numerical integration. The average value of the load in an interval

is defined as the 15-minute kW demand .

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

curve is developed from a spreadsheet that gives the 15-minute kW demand for a period of24 hours.


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Figure 14: Customer demand curve.

Figure 15: 24-hour demand curve for Customer #1.

2.2.2 MAXIMUM DEMAND

The demand curve shown in Figure 15 represents a typical residential customer.

Each bar depicts the 15-minute kW demand. Note that during the 24-hour period there is a

great variation in the demand. This particular customer has three periods in which the kW

demand exceeds 6.0 kW. The greatest of these is the 15-minute maximum kW demand .

For this customer the 15-minute maximum kW demand occurs at 13:15 and has a

value of 6.18 kW.

2.2.3 AVERAGE DEMAND

During the 24-hour period, energy (kWh) will be consumed. The energy in kWh used

during each 15-minute time interval is computed by:

( 1)

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

interval consumptions. From the spreadsheet, the total energy consumed during the period

by Customer #1 is 58.96 kWh. The 15-minute average kW demand is computed by:


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( 2)

2.2.4 LOAD FACTOR

“Load factor” is a term that is often used when describing a load. It is defined as the

ratio of the average demand to the maximum demand. In many ways load factor gives an

indication of how well the utility’s facilities are being utilized. From the utility’s standpoint,

the optimal load factor would be 1.00 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 load factor.

For Customer #1 in Figure 15 the load factor is computed to be

( 3)

2.2.5 DISTRIBUTION TRANSFORMER LOADING

A distribution transformer will provide service to one or more customers. Each

customer will have a demand curve similar to that in Figure 15. However, the peaks and

valleys and maximum demands will be different for each customer. Figure 16,Figure 17and

Figure 18give the demand curves for the three additional customers connected to the same

distribution transformer. The load curves for the four customers show that each customer

has his unique loading characteristic. The customers’ individual maximum kW demand

occurs at different times of the day. Customer #3 is the only one who will have a high load

factor. A summary of individual loads is given in Table 1. These four customers demonstrate

that there is great diversity among their loads.



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Table 1: Individual Customer Load Characteristics.

2.2.6 DIVERSIFIED DEMAND

It is assumed that the same distribution transformer serves the four customers

discussed previously. The sum of the four 15 kW demands for each time interval is the

diversified demand for the group in that time interval, and, in this case, the distributiontransformer. The 15-minute diversified kW demand of the transformer for the day is shown in

Figure 19. Note how the demand curve is beginning to smooth out. There are not as many

significant changes as in some of the individual customer curves.


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Figure 19: Transformer diversified demand curve.

2.2.7 MAXIMUM DIVERSIFIED DEMAND

The transformer demand curve of Figure 19 demonstrates how the combined

customer loads begin to smooth out the extreme changes of the individual loads. For thetransformer, the 15-minute kW demand exceeds 16 kW twice. The greater of these is the

15-minute maximum diversified kW demand of the transformer. It occurs at 17:30 and has a

value of 16.16 kW. 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.

2.2.8 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 shown in Figure 20. The load duration curve plots the 15-minute kW

demand versus the percent of time the transformer operates at or above the specific kW

demand. For example, the load duration curve shows the transformer operates with a 15-

minute kW demand of 12 kW or greater 22% of the time. This curve can be used to

determine whether a transformer needs to be replaced due to an overloading condition.

2.2.9 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 in question, the

sum of the individual maximums is

( 4)


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Figure 20: Transformer load duration curve.

2.2.10 DIVERSITY FACTOR

By definition, diversity factor is the ratio of the maximum noncoincident demand of

a group of customers to the maximum diversified demand of the group. With reference tothe transformer serving four customers, the diversity factor for the four customers would

be:

( 5)

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

customers. The value computed above would apply for four customers. If there are five

customers, then a load survey would have to be set up to determine the diversity factor forfive customers. This process would have to be repeated for all practical numbers of

customers. Table 2 is an example of the diversity factors for the number of customers

ranging from one to 70. The table was developed from a different database than the four

customers discussed previously.

Table 2: Diversity Factors


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A graph of the diversity factors is shown in Figure 21. Note in and Figure 21 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, at least for the system from which these

diversity factors were determined, that the diversity factor will remain constant at 3.20 from

70 customers up. In other words, 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.

Figure 21: Diversity factors.

2.2.11 DEMAND FACTOR

The demand factor can be defined for an individual customer. For example, the 15-

minute maximum kW demand of Customer #1 was found to be 6.18 kW. In order to

determine the demand factor, the total connected load of the customer needs to be known.

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, the demand factor is

computed to be

( 6)

The demand factor gives an indication of the percentage of electrical devices that

are on when the maximum demand occurs. The demand factor can be computed for an

individual customer but not for a distribution transformer or the total feeder.

2.2.12 UTILIZATION FACTOR

The utilization factor gives an indication of how well the capacity of an electrical

device is being utilized. For example, the transformer serving the four loads is rated 15 kVA.

Using the 16.16-kW maximum diversified demand and assuming a power factor of 0.9, the

15-minute maximum kVA demand on the transformer is computed by dividing the 16.16-kW

maximum kW demand by the power factor, and would be 17.96 kVA. The utilization factor is

computed to be

( 7)


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2.2.13 LOAD DIVERSITY

Load diversity is defined as the difference between the noncoincident maximum

demand and the maximum diversified demand. For the transformer in question, the load

diversity is computed to be

− ( 8)

2.3 FEEDER LOAD

The load that a feeder serves will display a smoothed-out demand curve as shown in

Figure 22 The feeder demand curve does not display any of the abrupt changes in demand of

an individual customer demand curve or the semi-abrupt changes in the demand curve of a

transformer. The simple explanation for this is that with several hundred customers served

by the feeder, the odds are good that as one customer is turning off a light bulb another

customer will be turning a light bulb on. The feeder load therefore does not experience a

jump as would be seen in the individual customer’s demand curve.

2.3.1 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. When this is the case, the load allocated to each transformer needs

to be determined.

Figure 22: Feeder demand curve.

2.3.1.1 Application of Diversity Factors

The definition of the diversity factor (DF) is the ratio of the maximum noncoincident

demand to the maximum diversified demand. Diversity factors are shown in Table 2. When

such a table 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; that is, the

maximum diversified demand can be computed by:


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( 9)

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

2.3.1.2 Load SurveyMany 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. Such

a load survey requires the installation of a demand meter at each customer’s location. The

meter can be the same type used to develop the demand curves previously discussed, or it

can be a simple meter that only records the maximum demand during the period. 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. The plot of points for 15 customers, along with

the resulting equation derived from a linear regression algorithm, is shown in Figure 23. The

straight-line equation derived is

⋅ ( 10)

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 groups of customers is metered. This will involve

selecting a series of locations where demand meters can be placed that will record the

maximum demand for groups of customers ranging from at least 2 to 70. At each meterlocation the maximum demand of all downstream customers must also be known. With that

data, the diversity factor can be computed for the given number of downstream customers.

Example 1:

A single-phase lateral provides service to three distribution transformers as shown in

Figure 24. 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-minute maximum kW demand is given by the equation:

⋅

The kWh consumed by Customer #1 is 1523 kWh. The 15-minute maximum kW

demand for Customer #1 is then computed as:

⋅

The results of this calculation for the remainder of the customers is summarized

below by transformer.


30/48


Figure 23: kW demand vs. kWh for residential customers.

Figure 24: Single-phase lateral.

Determine for each transformer the 15-minute noncoincident maximum kW

demand and, using the Table of Diversity Factors in Table 2, determine the 15-minute

maximum diversified kW demand.


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Determine the 15-minute noncoincident maximum kW demand and 15-minute

maximum diversified kW demand for each of the line segments.


32/48


Example 1 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. For example, 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 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

was 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. At the timethat 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. There will be an infinite amount of combinations of line flow down N1-N2 and

through transformer T1 that will produce the maximum diversified demand of 72.6 kW on

line N2-N3.

2.3.1.3 Transformer Load Management

A transformer load management program is used by utilities to determine the

loading on distribution transformers based upon a knowledge of the kWh supplied by the

transformer during a peak loading month. 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.

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.

With the information available from several sample transformers, a curve similar to that

shown in Figure 2.10 can be developed, and the constants of the straight-line equation can

be computed. This method has an advantage 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.


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2.3.1.4 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 transformers serve whichcustomers. Again, this database is not always available.

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 during a month.

The kVA ratings of all distribution transformers is 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.

( 11)

where Metered demand can be either kW or kVA, and kVAtotal = sum of the kVA

ratings of all distribution transformers

The allocated load per transformer is then determined by:

⋅ ( 12)

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

When the kW or kVA is metered by phase, then 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. The load allocation will now follow the same procedure as outlined above. If

there is no metered information on the reactive power or power factor of the feeder, a

power factor will have to be assumed for each transformer load.

Modern substations will have microprocessor-based metering that will provide kW,

kvar, kVA, power factor, and current per phase. With this data, the reactive power can also

be allocated. Since the metered data at the substation will include losses, an iterative

process will have to be followed so that the allocated load plus losses will equal the metered

readings.

Example 2:

Assume that the metered maximum diversified kW demand for the system of

Example 1 is 92.9 kW. Allocate this load according to the kVA ratings of the three

transformers.

Solution:


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2.3.1.5 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 purpose of the analysis. 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. 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 beanalyzed, the only method that gives good results is that of allocating load based upon the

kVA ratings of the transformers.

2.3.2 VOLTAGE-DROP CALCULATIONS USING ALLOCATED LOADS

The voltage drops down line segments and through distribution transformers are of

interest to the distribution engineer. Four different methods of allocating loads have been

presented. The various voltage drops will be computed using the loads allocated by two of

the methods in the following examples.

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

2.3.2.1 Application of Diversity Factors

The loads allocated to a line segment or a distribution transformer using diversity

factors are a function of the total number of customers downstream from the line segment

or distribution transformer. The application of the diversity factors was demonstrated in

Example 2.1. 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. The

assumption is that the allocated loads will be constant real power and reactive power.


35/48


In order to avoid an iterative solution, the voltage at the source is assumed and the

voltage drops calculated from that point to the last transformer.

Example 3 demonstrates how the method of load allocation using diversity factors is

applied. The same system and allocated loads from Example 1 are used.

Example 3:

For the system of Example 2.1, assume the voltage at N1 is 2400 volts and compute

the secondary voltages on the three transformers using the diversity factors. The system of

Example 2.1, including segment distances, is shown in Figure 2.12.

Assume that the power factor of the loads is 0.9 lagging.

The impedance of the lines are: z = 0.3 + j 0.6 Ω/mile

The ratings of the transformers are

−

−

−

Figure 25: Single-phase lateral with distances.

Solution:

From Example 1 the maximum diversified kW demands were computed. Using the

0.9 lagging power factor, the maximum diversified kW and kVA demands for the line

segments and transformers are


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37/48



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2.3.2.2 Load Allocation Based upon Transformer Ratings

When only the ratings of the distribution transformers are known, the feeder can be

allocated based upon the metered demand and the transformer kVA ratings. This method

was discussed in Section 2.3.3. Example 4 demonstrates this method.

Example 4:

For the system of Example 1, 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.

Solution:

The impedances of the line segments and transformers are the same as in Example

3. Assume the load power factor is 0.9 lagging; compute the kVA demand at N1 from the

metered demand:


39/48



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Example 5:

Shown below are the 15-minute kW demands for four customers between the hours

of 17:00 and 21:00. A 25-kVA single-phase transformer serves the four customers.

1. For each of the customers determine:

(a) Maximum 15-minute kW demand

(b)

Average 15-minute kW demand

(c) Total kWh usage in the time period

(d) Load factor

2.

For the 25-kVA transformer determine:

(a) Maximum 15-minute diversified demand

(b) Maximum 15-minute noncoincident demand

(c)

Utilization factor (assume unity power factor)

(d) Diversity factor

(e) Load diversity

3.

Plot the load duration curve for the transformer

Example 6:

Two transformers each serving four customers are shown in Figure 26.

Figure 26: system for this example.


41/48


The following table gives the time interval and kVA demand of the four customer

demands during the peak load period of the year. Assume a power factor of 0.9 lagging.

1. For each transformer determine the following:

(a)

30-minute maximum kVA demand

(b)

Noncoincident maximum kVA demand

(c) Load factor

(d) Diversity factor

(e)

Suggested transformer rating (50, 75, 100, 167)

(f) Utilization factor

(g) Energy (kWh) during the 4-hour period

2.

Determine the maximum diversified 30-minute kVA demand at the Tap

Example 7:

Two single-phase transformers serving 12 customers are shown in Figure 27.


The 15-minute kW demands for the 12 customers between the hours of 5:00 p.m.

and 9:00 p.m. are given in the tables that follow. Assume a load power factor of 0.95 lagging.

The impedance of the lines are z = 0.306 + j 0.6272 Ω/mile. The voltage at node N1 is 2500 V.

Transformer ratings:

−

−


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1.

Determine the maximum kW demand for each customer.

2. Determine the average kW demand for each customer.

3.

Determine the kWH consumed by each customer in this time period.

4. Determine the load factor for each customer.

5. Determine the maximum diversified demand for each transformer.

6.

Determine the maximum noncoincident demand for each transformer.

7.

Determine the utilization factor (assume 1.0 power factor) for each transformer.

8. Determine the diversity factor of the load for each transformer.

9.

Determine the maximum diversified demand at Node N1.

10.

Compute the secondary voltage for each transformer, taking diversity intoaccount.


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Example 8:

A single-phase lateral serves four transformers as shown in Figure 28.


Example 9:

Assume that each customer’s maximum demand is 15.5 kW + j 7.5 kvar. The

impedance of the single-phase lateral is z=0.4421+ j 0.3213Ω/1000 ft. The four transformers

are rated as:

T1 and T2: 37.5 kVA, 2400-240 V,

Z =0.01+ j 0.03 per-unit

T3 and T4: 50 kVA, 2400-240 V,

Z =0.015+ j 0.035 per-unit

Use the diversity factors found in Table 2 and determine:

(1)

The 15-minute maximum diversified kW and kvar demands on each

transformer.

(2) The 15-minute maximum diversified kW and kvar demands for each line

section.

(3)

If the voltage at node 1 is 2600 V, determine the voltage at nodes 2,3,4,5,6,7,8,

and 9. In calculating the voltages, take into account diversity using the answers

from (1) and (2) above.

(4)

Use the 15-minute maximum diversified demands at the lateral tap (Section 1-

2) from Part (2) above. Divide these maximum demands by 18 (number of

customers) and assign that as the “instantaneous load” for each customer. Nowcalculate the voltages at all of the nodes listed in Part (3) using the

instantaneous loads.

(5) Repeat Part (4) above, but assume the loads are “constant current.” To do this,

take the current flowing from node 1 to node 2 from Part (4) above, divide by

18 (number of customers), and assign that as the instantaneous constant

current load for each customer. Again, calculate all of the voltages.

(6)

Take the maximum diversified demand from node 1 to node 2 and allocate that

to each of the four transformers based upon their kVA ratings. To do this, take

the maximum diversified demand and divide by 175 (total kVA of the four

transformers). Now multiply each transformer kVA rating by that number to


44/48


give how much of the total diversified demand is being served by each

transformer. Again, calculate all of the voltages.

(7) Compute the percent differences in the voltages for Parts (4), (5), and (6) at

each of the nodes using the Part (3) answer as the base.

Example 10:

Given a 120-volt 15-ampere branch circuit supplies a load which consists of four

lamps. Each lamp draws 3 amperes of current from the source. The lamps are located at 10-

foot intervals from the power distribution panel. The resistance of 1000 feet of No. 14

copper wire is 2.57 ohms.

Find the voltage across lamp No 4.

Figure 29: Circuit for calculating the voltage drop in a branch circuit.

Solution:

a. The resistance of 1000 feet of No. 14 copper wire is 2.57 ohms.

Therefore, the resistance of 20 feet of wire is:

b. Calculate voltage drop VD No. 1. (R equals the resistance of 20feet of wire.)

Calculate load VL No. 1. (The source voltage minus VD No. 1.)


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c. Calculate voltage drop and load No. 2.

d. Calculate voltage drop and load No. 3.

e. Calculate voltage drop and load No. 4.

Notice that the voltage across lamp No. 4 is substantially reduced from the 120-voltsource value due to the voltage drop of the conductors. Also, notice that the resistances

used to calculate the voltage drops represented both wires (hot and neutral) of the branch

circuit. Ordinarily, 120-volt branch circuits do not extend more than 100 feet (30.48 meters)

from the power distribution panel. The preferred distance is 75 feet (22.86 meters). The

voltage drop in branch-circuit conductors can be reduced by making the circuit shorter in

length or by using larger conductors.

In residential electrical wiring design, the voltage drop in many branch circuits is

difficult to calculate since the lighting and portable appliance receptacles are placed on the

same branch circuits. Since portable appliances and “plug-in” lights are not used all of the

time, the voltage drop will vary according to the number of lights and appliances in use. This

problem is usually not encountered in an industrial or commercial wiring design for lights,

since the lighting units are usually larger and are permanently installed on the branch

circuits.

Example 11:

Given a single-phase 240-volt load in a factory is rated at 85 kilowatts. The feeders

(two hot lines) will be 260-foot lengths of RHW copper conductor. The maximum conductor

voltage drop allowed is 2%.

Find the feeder conductor size required.


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Solution:

Determine the feeder conductor size. The next larger size conductor is 400 MCM.

The 400 MCM RHW copper conductor will carry 335 amperes. This is less than the required

354.2 amperes, so use the next larger size, which is a 500 MCM conductor.

Example 12:

Given a 480-volt three-phase three-wire (delta) feeder circuit supplies a 45-kilowatt

balanced load to a commercial building. The load operates at a 0.75 power factor. The

feeder circuit (three hot lines) will be a 300-foot length of RH copper conductor. The

maximum voltage drop is 1%.

Find the feeder size required (based on the voltage drop of the circuit).

Solution:


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Determine the feeder conductor size. The closest and next larger conductor size is

No. 1 AWG. The No. 1 AWG RH copper conductor will carry 130 amperes, much more than

the required 72.25 amperes. Therefore, use No. 1 AWG RH copper conductors for the feeder

circuit.

Example 13: The single-phase distributor

A two-core, single-phase distributor, ABCD, is 640 m long, is fed at end A only, and

supplies loads at B, C, and D. the distance from A to B is 274.3 m, that from B to C is 274.3 m,

and that from C to D is 91.4 m. the distributor has a resistance of 0.2

and an inductive

reactance of 0.075, each per 914.4 m of single core. Calculate the voltage required at A so

that the voltage at D shall be 220 V when the loads are as follows:

60 A at 0.8 PF. lagging, at B;

50 A at 0.9 PF. lagging, at C;

30 A at unity PF., at D.

The distributor is represented by a single-line diagram in figure 1.5.

Example 14: Distributor fed from both ends


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Calculate the current distribution and the voltage at points B and C when the

distributor in example 1.3 is fed at both ends at 250 V, the load being unaltered.

In figure 1.6, the current fed in from end A is assumed to be A and the currents in

the other sections have been obtained using Kirchhoff’s first law.

Solution:

Hence the current distribution is as in figure 1.7.

Obviously, these currents are alternating, but the arrows are useful in that they

indicate the direction of energy flow. Also they show that B is the point of minimum

potential.

Example 15:

Calculate the current distribution when the distributor in example 1.4 is fed at end A

at 250 V and at end B at 245 V, the load being unaltered.

Example 16: Distribution networks

Calculate the current distribution when the two-core ring main represented by the

single-line diagram, figure 1.10, is fed at point A.

Solution:

The solution is the same as that for a distributor fed from both ends at the same potential.

See example 1-4.

Hence the current distribution is as shown in figure 1.11.

Example 17:

Calculate the current distribution when the two-core ring main represented by the

single-line diagram, figure 1.12, is fed at point A at 250 V. hence calculate the voltage at

each load point.

(notes for students)power engineering - 7 distribution

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