Voltage Regulators Rural Networks

8/11/2019 Voltage Regulators Rural Networks

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HIGH-EFFICIENCY VOLTAGE REGULATOR FOR

RURAL NETWORKS

ABSTRACT

This paper presents a high-efficiency voltage regulator, which combines robustness, low

costs and easy maintenance without power electronics components. Power quality is the

combination of voltage quality and current quality. Quality of supply is a combination of voltage

quality and the non-technical aspects of the interaction from the power network to its customers.

These characteristics make it suitable for rural networks, where investments and operational cost

in power quality improvement are limited. The regulator consists of a multi winding reduced-

power transformer, and provides serial voltage compensation.

This paper presents a new voltage regulator that fulfills the rural networks needs: high efficiency,

robustness, easy maintenance and low cost. ection !! presents the design of the voltage

regulator, describing its power circuit and control system. ome practical considerations

regarding the design of the voltage regulator are presented in ection !!!. "nd finally, ection !#

presents the operation e$perience data of voltage regulators installed in the distribution network.

%ifferent voltage compensation steps are obtained by modifying the connection and the

polarity between the primary and secondary windings. The transformer design has been

optimi&ed to obtain a high-efficiency and low-cost regulator. "n automatic controller monitors

the output voltage and sets the optimal compensation step. "t present more than '(( units of the

voltage regulator are in operation.

)$perimental records for the operation of installed voltage regulators have shown their

reliability, high efficiency, and their capacity to improve power quality in rural networks.


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I. INTRODUCTION

L*+-duration voltage variation undervoltage and overvoltage is a central issue in

distribution network power quality. upply voltage and power quality are regulated by certain

standards, such as the )uropean )+ /(01( 203 or the "merican "+! 45'-0 263. These standards

are complemented in each country or state by specific codes and rules 273. The )uropean )+

/(01( stipulates that the ma$imum voltage amplitude variation accepted is 0(8, while the

"merican "+! 45'-0 defines a normal operating range of 06( # /8. +ational rules usually

define more restrictive voltage ranges9 for instance, the panish rule for voltage quality 2'3 sets

the ma$imum variation of the voltage at the load connection point at 67( # 8. The value of

voltage amplitude is an important quality issue, because loads are designed to work correctly

within a specific voltage range. everal problems in domestic and industrial equipment areassociated with long duration undervoltages, such as malfunctioning in relays and contactors,

incandescent lighting dim, switch-off of discharge lighting, failure of nonlinear loads e.g.,

computer power supplies, and torque reduction in induction machines. *n the other hand, long

duration overvoltages usually result in the overheating of loads motors and transformers, and

hence a reduction in their e$pected durability. ;ow voltage rural distribution networks compared

with urban networks are more susceptible to long-term voltage variations, due to the dispersed

configuration of customers. #oltage variations in rural areas are usually associated with long

distances between the loads and the distribution transformer. +owadays, the integration of non-

controllable dispersed generation in these networks is a new potential source of voltage variation

problems. To minimi&e long-term voltage variations in rural networks, distribution companies

have traditionally performed different actions: 0 tap change control in the main distribution

transformer9 6 installation of compensation equipment, such as capacitor banks, voltage

regulators, boosters, or auto-boosters9 and 7 as a last resort, because it is the most e$pensive

alternative, the distribution company upgrades the low voltage network increasing the line

capability, or changing the network rated voltage 2/3. !n rural areas, the ratio of contracted

power per connection point is much smaller than for urban areas9 therefore, investments to solve

specific voltage problems are limited. !n this situation, the use of compensation equipment such

as voltage regulators becomes an interesting alternative.


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different options for solving voltage problems. 4onsequently the cost-efficiency of voltage

regulators is also a key issue. 4urrently, there are different technologies for voltage regulators

both in commercial devices and in the literature: tap-switching, ferroresonant, and electronic 213.

The most advanced commercial voltage regulators are based on power electronics and provide

accurate voltage output. +owadays there are few approaches to voltage regulators in rural

networks 23=20(39 moreover these approaches still do not completely cover the needs of rural

distribution networks. This paper presents a new voltage regulator that fulfills the rural networks

needs: high efficiency, robustness, easy maintenance and low cost. ection !! presents the design

of the voltage regulator, describing its power circuit and control system. ome practical

considerations regarding the design of the voltage regulator are presented in ection !!!. "nd

finally, ection !# presents the operation e$perience data of voltage regulators installed in the

distribution network.

Power disri!"io# $o#ro%

Distribution SystemElectrical power is transmitted by high voltage transmission lines from

sending end substation to receiving end substation. At the receiving end

substation, the voltage is stepped down to a lower value (say 66kV or 33kV

or kV!. "he secondary transmission system transfers power from this

receiving end substation to secondary sub#station. A secondary substation

consists of two or more power transformers together with voltage regulating

e$uipments, buses and switchgear. At the secondary substation voltage is

stepped down to kV. "he portion of the power network between a

secondary substation and consumers is known as distribution system. "he

distribution

system can be classified into primary and secondary system. %ome large

consumers are given high voltage supply from the receiving end substations

or secondary substation.

"he area served by a secondary substation can be subdivided into a number

of sub# areas. Each sub area has its primary and secondary distribution

system. "he primary distribution system consists of main feeders and


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laterals. "he main feeder runs from the low voltage bus of the secondary

substation and acts as the main source of supply to sub# feeders, laterals or

direct connected distribution transformers. "he lateral is supplied by the

main feeder and e&tends through the load area with connection to

distribution transformers. "he distribution transformers are located at

convenient places in the load area. "hey may be located in specially

constructed enclosures or may be pole mounted. "he distribution

transformers for a large multi storied building may be located within the

building itself. At the distribution transformer, the voltage is stepped down to

'V and power is fed into the secondary distribution systems. "he

secondary ' distribution system consists of distributors which are laid along

the road sides. "he service connections to consumers are tapped off from

the distributors. "he main feeders, laterals and distributors may consist of

overhead lines or cables or both. "he distributors are 3# phase, ' wire

circuits, the neutral wire being necessary to supply the single phase loads.

)ost of the residential

and commercial consumers are given single phase supply. %ome large

residential and commercial consumer uses 3#phase power supply. "he

service connections of consumer are known as service mains.

"he consumer receives power from the distribution system. "he main part of

distribution system

includes*#

. +eceiving substation.

. %ub# transmission lines.

3. -istribution substation located nearer to the load centre.

'. %econdary circuits on the V side of the distribution transformer.

/. %ervice mains.

Power Flow


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0or distribution system the power flow analysis is a very important and

fundamental tool. 1ts results play the ma2or role during the operational

stages of any system for its control and economic schedule, as well as during

e&pansion and design stages. "he purpose of any load flow analysis is to

compute precise steady#state voltages and voltage angles of all buses in the

network, the real and reactive power flows into every line and transformer,

under the assumption

of known generation and load.

-uring the second half of the twentieth century, and after the large

technological developments in the fields of digital computers and high#level

programming languages, many methods for solving the load flow problem

have been developed, such as auss#%iedel (bus impedance matri&!,

4ewton#+aphson5s (4+! and its decoupled versions. 4owadays, many

improvements have been added to all these methods involving assumptions

and appro&imations of the transmission lines and bus data, based on real

systems conditions.

"he 0ast -ecoupled ower 0low )ethod (0-0)! is one of these improved

methods, which was based on a simplification of the 4ewton#+aphson5s

method and reported by %tott and Alsac in 78'. "his method due to its

calculations simplifications, fast convergence and reliable results became the

most widely used method in load flow analysis. 9owever, 0-0) for some

cases, where high +:; ratios or heavy loading (ow Voltage! at some buses

are present, does not converge well. 0or these cases, many efforts and

developments have been made to overcome these convergence obstacles.

%ome of them targeted the convergence of systems with high +:; ratios,

others those with low voltage buses. "hough many efforts and elaborations

have been achieved in order to improve the 0-0), this method can still

attract many researchers, especially when computers and simulations are

becoming more developed and are now able to handle and analy


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Objectives of Radial Distribution System:-. lanning, moderni


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!e single line diagram of a ty"ical low tension distribution system#$istory of Distribution System

1n the early days of electricity distribution, direct current -> generators were

connected to loads

at the same voltage. "he generation, transmission and loads had to be of the

same voltage because there was no way of changing -> voltage levels,

other than inefficient motor#generator sets. ow -> voltages were used (on

the order of volts! since that was a practical voltage for

incandescent lamps, which were then the primary electrical load. "he low

voltage also re$uired less insulation to be safely distributed within buildings.

"he losses in a cable are proportional to the s$uare of the current, the length

of the cable, and the

resistivity of the material, and are inversely proportional to cross#sectional

area. Early transmission networks were already using copper, which is one of

the best economically feasible

conductors for this application. "o reduce the current and copper re$uired

for a given $uantity of


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power transmitted would re$uire a higher transmission voltage, but no

convenient efficient method e&isted to change the voltage level of -> power

circuits. "o keep losses to an economically practical level the Edison ->

system needed thick cables and local generators.

%odern Distribution System

"he modern distribution system begins as the primary circuit leaves the sub#

station and ends as the secondary service enters the customer?s meter

socket. A variety of methods, materials, and e$uipment are used among the

various utility companies, but the end result is similar. 0irst, the energy

leaves the sub#station in a primary circuit, usually with all three phases. "he

most common type of primary is known as a &ye configuration (so named

because of the shape of a @@.! "he Bye configuration includes 3 phases

(represented by the three outer parts of the @@! and a neutral (represented

by the centre of the @@.! "he neutral is grounded both at the substation and

at every power pole. "he other type of primary configuration is known as

delta. "his method is older and less common. -elta is so named because of

the shape of the reek letter delta, a triangle. -elta has only 3 phases and

no neutral. 1n delta there is only a single voltage, between two phases

(phase to phase!, while in Bye there are two voltages, between two phases

and between a phase and 8 neutral (phase to neutral!. Bye primary is safer

because if one phase becomes grounded, that is, makes connection to the

ground through a person, tree, or other ob2ect, it should trip out the circuit

breaker tripping similar to a household fused cut#out system. 1n delta, if a

phase makes connection to ground it will continue to function normally. 1t

takes two or three phases to make connection to ground before the fused

cut#outs will open the circuit. "he voltage for this configuration is usually

'C volts.


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Re'uirement of Distribution system

A considerable amount of effort is necessary to maintain an electric power

supply within the

re$uirements of various types of consumers. %ome of the re$uirements of agood distribution

system are* proper voltage, availability of power on demand, and reliabilit

Pro"er (oltage:

Dne important re$uirement of a distribution system is that voltage

variations at consumers5 terminals should be as low as possible. "he changes

in voltage are generally caused due to the variation of load on the system.

ow voltage causes loss of revenue, inefficient lighting and possible burning

out of motors. 9igh voltage causes lamps to burn out permanently and may

cause failure of other appliances. "herefore, a good distribution system

should ensure that the voltage variations at consumers5 terminals are within

permissible limits. "he statutory limit of voltage variations is F of the

rated value at the consumers5 terminals. "hus, if the declared voltage is 3

V, then the highest voltage of the consumer should not e&ceed '' V while

the lowest voltage of the consumer should not be less than 6 V.

Availability of Power Demand:ower must be available to the consumers in any amount that they may

re$uire from time to time. 0or e&ample, motors may be started or shut down,

lights may be turned on or off, without advance warning to the electric

supply company. As electrical energy cannot be stored, therefore, the

distribution system must be capable of supplying load demands of the

consumers. "his necessitates that operating staff must continuously study

load patterns to predict in advance those ma2or load changes that follow the

known schedules.

Reliability:


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omes and office

buildings are lighted, heated, cooled and ventilated by electric power. This calls for reliable

service. ?nfortunately electric power, like everything else that is man-made, can never be

absolutely reliable. >owever, the reliability can be improved to a considerable e$tent by a

inter-connected system, b reliable automatic control system and c providing additional

reserve facilities.

C%&ssi'i$&io# o' Disri!"io# S(se)

" distribution system may be classified according to:

*i+ N&"re o' $"rre#, "ccording to nature of current, distribution system may be classified as a d.c. distribution

system and b a.c. distribution system. +ow-a-days a.c. system is universally adopted for

distribution of electric power as it is simpler and more economical than direct current method.

*ii+ T(e o' $o#sr"$io#,

"ccording to type of construction, distribution system may be classified as a overhead system

and b underground system. The overhead system is generally employed for distribution as it is

/ to 0( times cheaper than the equivalent underground system. !n general, the underground

system is used at places where overhead construction is impracticable or prohibited by the local

laws.

*iii+ S$e)e o' $o##e$io#,

"ccording to scheme of connection, the distribution system may be classified as a radial

system, b ring main system and c inter-connected system. )ach scheme has its own

advantages and disadvantages.


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R&di&% Disri!"io# S(se)

A radial system has only one power source for a group of customers. A power

failure, shortcircuit, or a downed power line would interrupt power in the

entire line which must be fi&ed before power can be restored. "he figure of

+adial -istribution %ystem is shown as *#

Radial Distribution System

1n this system, separate feeders radiate from a single sub#station and feed

the distributors at one end only. 0igure (a! shows a single line diagram of a

radial system for d.c. -istribution where a feeder D> supplies a distributor

A= at point A. Dbviously, the distributors are fed at one point only i.e. point A

in this case. 0igure (b! shows a single line diagram of radial system for a.c.

distribution. "he radial system is employed only when power is generated at

low voltage and the sub#station is located at the centre of load. "his is the

simplest distribution circuit and has the lowest initial cost.


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Single )ine Diagram of Radial Distribution System

*ode Radial Distribution *etwork:-

Objectives of Radial Distribution System:-. lanning, moderni


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3. )a&imum security of supply and minimum duration of interruption.

'. %afety of consumers, utility personnel.

/. "o provide electricity of accepted $uality in terms of *#

(a! =alanced three phase supply.

(b! ood power factor.

(c! Voltage flicker within permissible limits.

(d! ess voltage dips.

(e! )inimum interruption in power supply.

Advantages of Radial Distribution System:-

(a! +adial distribution system is easiest and cheapest to build.

(b! "he maintenance is easy.

(c! 1t is widely used in sparsely populated areas.

Drawback of Radial Distribution System:-

(a! "he end of the distributor nearest to the feeding point will be heavily

loaded.

(b! "he consumers are dependent on a single feeder and single distributor.

"herefore, any fault on the feeder or distributor cuts off supply to the

consumers who are on the side of the fault away from the sub#station.

(c! "he consumers at the distant end of the distributor would be sub2ected to

serious voltage fluctuations when the load on the distributor

/ODELINOGF DISTRIBUTIOSYNS TE/

CO/PONENTS


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The individual components of & distribution system are modeled by their mathematical

equivalents. The three-phase modeling of distribution system components is given . The series

impedance matri$ of a three-phase line section is given by equation

This equation is obtained after @ronAs reduction. !t takes care of the effects of the neutral or

ground. "t each bus i, the comple$ power S, is given by,

whereP:pe' and Q;," are the specified real and reactive powers respectively of bus i. The

equivalent current inBection at bus i for the kfh iteration is given as,

THREE-PHASE DISTRIBUTION LO AD FLOWANALY.S.I S


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and bus voltages are .dependent on each other, these quantities are required to be determined

iteratively. The swing bus is short-circuited while calculating the component of bus voltages due

to the current inBections.

The following steps are involved in this algorithm:

0. The bus voltages are assumed to have some initia0,value. The D-bus (Y,) is formed.A

6. The current inBections are computed by using equation 7 for which the recent values of bus

voltages are taken.

2. The voltage deviations (VD) due to current inBections are computed by the factori&ation of D-

bus,

f =[Y! [ VD]' '

4. The voltage deviations calculated in step 2 are superimposed on the no load bus voltage

(VNL)>. ence, the bus voltages are updatedAas. 3" = VNL + [ VD]' (5)

/. The convergence is checked. !f the method has not converged. then steps from to ' are

repeated.

. Modi#ied Gauss-Se2.dMethod

The implicit C-bus method described earlier requires the factori&ation of the full D-bus matri$,

adversely affecting the performance i# terms of speed. .>ence, a new method has been suggested

in 213 by blending the implicit C-bus method and the auss-eidel method to improve the

computational efficiency. Eor a distribution system with n buses, where P:peAand Qtpecare the

specified powemat bus i, the bus voltage for k'" iteration can be calculated by using the auss-

eidel method

as.


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The values of voltages used in the modified auss-eidel method are the most recently

computed values, whereas thevalues of voltages used in the implicit C-bus method are the


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Two matrices are developed, vi&. the bus inBection to branch current F!F4 matri$ and branch

current to bus voltage F4F# matri$. Fy . . using simple matri$ multiplication of these two

matrices, the Two developed matrices, F!F4 and F4F# are used to obtain the load flow

solution. The development of these two matrices is e$plained with reference to Eig. . The figure

shows a simple distribution system. !t has sub-station at its bus number !, and bus numbers to 1

are the load buses loadflowGsolution is obtained


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$. %o&&d-c&d *ubstitutio+

!n all the previous methods, the voltages at all the buses in the system are calculated in one step,

by using the matrices. !n forward-backward substitution, the @4; and @#; are applied at each.


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node and branch respectively. Fy solving these equations iteratively, the solution is obtained 2!.

The following steps involved in this method:

ptiml o&de&i+ o +odes:

+odes are renumbered according to source node - load node relationship to facilitate the

forward and backward substitution. Thus, a forward path is created from the source node to the

load node and a backward path is traced from the load node to the source node. The branch node

nearer to the source is called as the parent node and the other node is called as the child node.

!nitially, the flat voltage start is assumed.

c&d substitutio+:

This is used to calculate the current in each branch. The current in the last branch is equal to the

current inBection at the corresponding end node. The voltage values are kept constant. The

network is traced in the backward direction. The currents in all the other branches can be found

out by using @4; as given by the equation.

where I,, ("1).Ib (U,) and I, (ut) are the branch currents of line section m, and ib,, i" and

iLc are the equivalent current inBections at the child node (i) of branch m. M is the set of line

sections connected to mrhbranch at its child node (p is the number of a line section which is an

element of


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respectively. These values of the voltages are used for calculating the currents by backward

substitution in the ne$t iteration.

/hec for convergence:

The forward and backward substitutions are performed in each iteration of the load flow. The

voltage magnitudes at each bus in an iteration are compared with their values in the previous

iteration. !f the error is within the tolerance limit, the procedure is stopped. *therwise, the steps

of backward substitution, forward substitution and check for convergence are repeated

0. 1dde& 2eto& 3heo&4

The ladder network theory given in [9] is very much similar to the forward-backward

substitution method. Though the basic principle of both the methods is same, there are

differences in the steps of implementation. !n the ladder network theory, the optimal ordering of

nodes is done 'irs.!n the backward substitution, the node voltages are assumed to be equal o

some initial value in e 'irs iteration. Tecurrents in each branch are computed by @4; using

equation 66. !n addition to the branch currents, the node voltages are also computed by using

equation. Thus, the value of the swing bus voltage is &%so determined. This calculated value of

the swing bus voltage is compared with its specified value. !f the error is within the limit, thenthe load flow converges9 otherwise the forward substitution isperformed &s e$plained in the case

of forward-backward substitution method. Thus, in the ladder network theory, the !"s voltages

are calculated twice in the same iteration as compared to only once for the forward-backward

substitution method. .The convergence is checked in the ladder network theory by comparison

between the specified and calculated voltage values of the swing bus, whereas the difference

between the values of bus voltages at the present and previous iterations is considered for

convergence in the forward-backward substitution method.

Eorward sirbstitufion

This is used to calculate the voltage at each node starting from the child node of the first branch

by using @#;. The swing bus voltage is set to its specified value. The current in each branch is

held constant at the value obtained in the backward substitution. Thus, using the branch currents


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calculated in the backward substitution, the values of voltages are calculated by using the

equation,

Fast Decou"led Power Flow for Radial Distribution System

1n +adial -istribution %ystem, the large +:; ratio causes problems inconvergence of conventional load flow algorithm. "herefore for the betterconvergence some modified load flowmethods are used. 0or the purposes of power flow studies, we model a radialdistribution system as a network of buses connected by distribution lines,switches, or transformers to a voltage specified source bus. Each bus mayalso have a corresponding load, shunt capacitor, and:or co#generatorconnected to it. "he model can be represented by a radial interconnection ofcopies of the basic building block shown in 0igure '. the dotted lines fromthe co#generator, shunt capacitor, and load to ground are to indicate thatthese elements may be connected in an ungrounded delta#configuration.

%ince a given branch may be single#phase, two#phase, or three#phase. "hebasic building block of radial distribution systemis shown on the ne&t pageas*#

Figure

!e +asic +uilding +lock of Radial Distribution System#

Dne of the key concepts behind our formulation is that the voltage andcurrent at one bus can be


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e&pressed as a function of the voltage and current at the ne&t bus. 1f we let

the e$uations GH as

"he branch update function GH is given below as*

Bhere Wk is a vector containing the real and imaginary parts of the voltagesand currents at bus

k#"he function gk is determined by the sub#laterals attached at bus k aswell as the models fordistribution lines, switches, transformers, loads, shunt capacitors, and co#generators. 0rom Vk wecan compute the currents in2ected by the loads, shunt capacitors, and co#generators. iven Ik , and the currents Ij in2ected into sub#laterals branching off from bus k, weapply I> at bus k tocaculate current GH given as*#

BhereAk is the set of buses ad2acent to bus k on sub#laterals.0rom the following e$uation (C!, we can solve for the voltage and current atthe primary giventhe voltage and current at the secondary GH as*#

"herefore by solving e$uation (8! , we get


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%o that by using this method we get the converged value easily and fastthan the other ordinarymethods.

1n mathematics, an incidence matri.is a matri&that shows the relationshipbetween two classes of ob2ects. 1f the first class isXand the second is Y, the matri&has one row for each element ofXand one column for each element of Y. "he entryin rowxand columnyis ifxandyare related (called incidentin this conte&t!and if they are not. "here are variationsJ see below.

Gr& eor(

U#dire$ed d dire$ed 3r&s

"n undirected graph
http://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Matrix_(mathematics)http://en.wikipedia.org/wiki/Mathematics


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!n graph theoryan undirected graphGhas two kinds of incidence matri$: unoriented and

oriented. The i#$ide#$e )&ri4or "#orie#ed i#$ide#$e )&ri4 of Gis apH qmatri$bij,

wherepand qare the numbers of verticesand edgesrespectively, such that bijI 0 if the verte$ viand edgexjare incident and ( otherwise.

Eor e$ample the incidence matri$ of the undirected graph shown on the right is a matri$consisting of ' rows corresponding to the four vertices and ' columns corresponding to the

four edges:

The i#$ide#$e )&ri4of a directed graphDis apH qmatri$ 2bij3 wherepand qare the number

of vertices and edges respectively, such that bijI J 0 if the edgexjleaves verte$ vi, 0 if it enters

verte$ viand ( otherwise. +ote that many authors use the opposite sign convention.

"n orie#ed i#$ide#$e )&ri4of an undirected graph Gis the incidence matri$, in the sense ofdirected graphs, of any orientation of G. That is, in the column of edge e, there is one K0 in the

row corresponding to one verte$ of eand one J0 in the row corresponding to the other verte$ of

e, and all other rows have (. "ll oriented incidence matrices of Gdiffer only by negating someset of columns. !n many uses, this is an insignificant difference, so one can speak of !eoriented

incidence matri$, even though that is technically incorrect.

The oriented or unoriented incidence matri$ of a graph Gis related to theadBacency matri$of its

line graphLG by the following theorem:

whereLG is the adBacency matri$ of the line graph of G,#G is the incidence matri$, and$qis the identity matri$of dimension q.

The @irchhoff matri$is obtained from the oriented incidence matri$MG by the formula

MGMG%.

The integral cycle spaceof a graph is equal to the null spaceof its oriented incidence matri$,

viewed as a matri$ over the integersor realor comple$ numbers. The binary cycle space is thenull space of its oriented or unoriented incidence matri$, viewed as a matri$ over the two-

element field.

Si3#ed d !idire$ed 3r&s

The incidence matri$ of a signed graphis a generali&ation of the oriented incidence matri$. !t is

the incidence matri$ of anybidirected graphthat orients the given signed graph. The column of apositive edge has a K0 in the row corresponding to one endpoint and a J0 in the row

corresponding to the other endpoint, Bust like an edge in an ordinary unsigned graph. Thecolumn of a negative edge has either a K0 or a J0 in both rows. The line graph and @irchhoff

matri$ properties generali&e to signed graphs.

/"%i3r&s
http://en.wikipedia.org/wiki/Graph_theoryhttp://en.wikipedia.org/wiki/Undirected_graphhttp://en.wikipedia.org/wiki/Undirected_graphhttp://en.wikipedia.org/wiki/Matrix_(math)http://en.wikipedia.org/wiki/Vertex_(graph_theory)http://en.wikipedia.org/wiki/Edge_(graph_theory)http://en.wikipedia.org/wiki/Edge_(graph_theory)http://en.wikipedia.org/wiki/Directed_graphhttp://en.wikipedia.org/wiki/Adjacency_matrixhttp://en.wikipedia.org/wiki/Adjacency_matrixhttp://en.wikipedia.org/wiki/Line_graphhttp://en.wikipedia.org/wiki/Line_graphhttp://en.wikipedia.org/wiki/Identity_matrixhttp://en.wikipedia.org/wiki/Identity_matrixhttp://en.wikipedia.org/wiki/Kirchhoff_matrixhttp://en.wikipedia.org/wiki/Kirchhoff_matrixhttp://en.wikipedia.org/wiki/Cycle_spacehttp://en.wikipedia.org/wiki/Cycle_spacehttp://en.wikipedia.org/wiki/Null_spacehttp://en.wikipedia.org/wiki/Null_spacehttp://en.wikipedia.org/wiki/Integershttp://en.wikipedia.org/wiki/Integershttp://en.wikipedia.org/wiki/Real_numbershttp://en.wikipedia.org/wiki/Real_numbershttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Field_(mathematics)http://en.wikipedia.org/wiki/Signed_graphhttp://en.wikipedia.org/wiki/Bidirected_graphhttp://en.wikipedia.org/wiki/Multigraphhttp://en.wikipedia.org/wiki/Graph_theoryhttp://en.wikipedia.org/wiki/Undirected_graphhttp://en.wikipedia.org/wiki/Matrix_(math)http://en.wikipedia.org/wiki/Vertex_(graph_theory)http://en.wikipedia.org/wiki/Edge_(graph_theory)http://en.wikipedia.org/wiki/Directed_graphhttp://en.wikipedia.org/wiki/Adjacency_matrixhttp://en.wikipedia.org/wiki/Line_graphhttp://en.wikipedia.org/wiki/Identity_matrixhttp://en.wikipedia.org/wiki/Kirchhoff_matrixhttp://en.wikipedia.org/wiki/Cycle_spacehttp://en.wikipedia.org/wiki/Null_spacehttp://en.wikipedia.org/wiki/Integershttp://en.wikipedia.org/wiki/Real_numbershttp://en.wikipedia.org/wiki/Complex_numbershttp://en.wikipedia.org/wiki/Field_(mathematics)http://en.wikipedia.org/wiki/Signed_graphhttp://en.wikipedia.org/wiki/Bidirected_graphhttp://en.wikipedia.org/wiki/Multigraph


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The definitions of incidence matri$ apply to graphs withloopsand multiple edges.The column

of an oriented incidence matri$ that corresponds to a loop is all &ero, unless the graph is signed

and the loop is negative9 then the column is all &ero e$cept for L6 in the row of its incidentverte$.

H(er3r&s

Fecause the edges of ordinary graphs can only have two vertices one at each end, the row of an

incidence matri$ for graphs can only have two non-&ero entries. Fy contrast, a hypergraphcanhave multiple vertices assigned to one edge9 thus, the general case describes a hypergraph.

I#$ide#$e sr"$"res

The i#$ide#$e )&ri4of an incidence structure&is apH qmatri$ 2bij3, wherepand qare the

number of oi#sand %i#esrespectively, such that bijI 0 if the pointpiand lineLjare incident

and ( otherwise. !n this case the incidence matri$ is also abiadBacency matri$of the ;evi graph

of the structure. "s there is a hypergraphfor every ;evi graph, and vicevers, the incidencematri$ of an incidence structure describes a hypergraph.

Fi#ie 3eo)eries

"n important e$ample is a finite geometry. Eor instance, in a finite plane,is the set of pointsand *is the set of lines. !n a finite geometry of higher dimension,could be the set of points

and *could be the set of subspaces of dimension one less than the dimension of *9 orcould be

the set of all subspaces of one dimension +and *the set of all subspaces of another dimension e.

B%o$5 desi3#s

"nother e$ample is ablock design.>ereis a finite set of MpointsM and *is a class of subsets of

, called MblocksM, subBect to rules that depend on the type of design. The incidence matri$ is an

important tool in the theory of block designs. Eor instance, it is used to prove the fundamental

theorem of symmetric 6-designs, that the number of blocks equals the number of points.

Cre&e 3r&s 'ro) i#$ide#$e )&ri4

Des$riio#

graph.incidencecreates a bipartite igraph graph from an incidence matri$.

Us&3e

graph.incidence(incidence, directed = FALSE, mode = c("all",

"out",
http://en.wikipedia.org/wiki/Loop_(graph_theory)http://en.wikipedia.org/wiki/Loop_(graph_theory)http://en.wikipedia.org/wiki/Multiple_edgeshttp://en.wikipedia.org/wiki/Multiple_edgeshttp://en.wikipedia.org/wiki/Hypergraphhttp://en.wikipedia.org/wiki/Incidence_structurehttp://en.wikipedia.org/wiki/Biadjacency_matrixhttp://en.wikipedia.org/wiki/Biadjacency_matrixhttp://en.wikipedia.org/wiki/Biadjacency_matrixhttp://en.wikipedia.org/wiki/Levi_graphhttp://en.wikipedia.org/wiki/Hypergraphhttp://en.wikipedia.org/wiki/Finite_geometryhttp://en.wikipedia.org/wiki/Block_designhttp://en.wikipedia.org/wiki/Block_designhttp://en.wikipedia.org/wiki/Loop_(graph_theory)http://en.wikipedia.org/wiki/Multiple_edgeshttp://en.wikipedia.org/wiki/Hypergraphhttp://en.wikipedia.org/wiki/Incidence_structurehttp://en.wikipedia.org/wiki/Biadjacency_matrixhttp://en.wikipedia.org/wiki/Levi_graphhttp://en.wikipedia.org/wiki/Hypergraphhttp://en.wikipedia.org/wiki/Finite_geometryhttp://en.wikipedia.org/wiki/Block_design


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"in", "total"), multiple = FALSE, weighted = NULL, add.names

= NULL)

Ar3")e#s

incidence"he input incidence matri&. 1t can also be a sparse matri& fromthe atri!package.

directed ogical scalar, whether to create a directed graph.

mode A character constant, defines the direction of the edges in

directed graphs, ignored for undirected graphs. 1f Kout5, then edges

go from vertices of the first kind (corresponding to rows in the

incidence matri&! to vertices of the second kind (columns in the

incidence matri&!. 1f Kin5, then the opposite direction is used. 1f

Kall5 or Ktotal5, then mutual edges are created.

multiple ogical scalar, specifies how to interpret the matri& elements. %ee

details below.

weighted "his argument specifies whether to create a weighted graph from

the incidence matri&. 1f it is NULLthen an unweighted graph is

created and the multipleargument is used to determine the edges

of the graph. 1f it is a character constant then for every non#


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Taken purely abstract, plytpes are described by their surtpial ele!ents plus therelati"e incidences. The !st basic #ay t gi"e thse incidences are $-%-!atrices #ith% !eaning &incident& and $ &nt&. 'ut already the easiest plytpes #uld ask r huge!atrices. This is the entrance r sy!!etry, the sy!!etry the plytpe itsel. likesurtpial ele!ents n# can be classed tgether "ia sy!!etrical e*ui"alence, and the

incidence relatin #ill be gi"en r the classes instead. This reduces the size the!atri cnsiderably. The diagnal ele!ents these reduced !atrices #ill gi"e the ttalcunt ele!ents each the respecti"e e*ui"alence classes. The nn-diagnalele!ents (n,!) #ill pr"ide the nu!bers incident surtpes class ! #ith any the ele!ents class n. The subdiagnal parts the r#s thus still describe thesurtpial ele!ent classes. The superdiagnal parts the r#s describe theiren"irn!ental aspacts, i.e. "erte igures, edge igures etc.

Regular plytpes are bund t pr"ide a single class surtpes per di!ensin, but ingeneral there #ill be !re sy!!etry-ine*ui"alent ele!ents the sa!e di!ensinality.Therere it is cn"eniant t display the di!ensinal brders as #ell as a superi!psed

guiding grid. erte-transiti"ity r instance can be read r! an incidence !atridirectly, as thse plytpes sh# up nly a single "erte class.

/ere as an ea!ple the incidence !atri the truncated cube is gi"en. The Dynkindiagra!s the relati"e classes are pr"ided in additin in rnt the r#s.

01

. . . $$ %&$ % ' $ ' %

. ! . $$ % $ %& * $ ' '

. . ! $$ % $ * '% $ + %

o! . $$ $ +$ - *. !&! $$ -$ & &$ *

This matri$ shows that there are 6' vertices, all having the same symmetry upper-left element.

The lowest two rows show that the 6-dimensional elements have 7 or 5 vertices lower-leftblock and therefore are triangles or octagons.The rightmost entries of the first row show further

that at each verte$ 0 such triangle and 6 octagons are incident.Eurther there are 6 types of edges,

the upper one is incident to 0 triangle and 0 octagon, the other one is incident to 6 octagons only.
http://www.orchidpalms.com/polyhedra/uniform/14.wrl


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The middle block of the bottom two rows shows that the triangle will have all edges of the first

type clearly, but the octagons do use edges of both types alternatingly. "ltogether there are 5

triangles and 1 octagons lower-right block.

Two relations on these numbers are generally valid. The one is the equation

!Nn,nO!Nn,mI!Nm,nO!Nm,m. This is true whether incident representants of those classes ofsubpolytopes do e$ist or not, as in the latter case the corresponding non-diagonal elements are

both &ero. The other observation is, and this derives right from the diagrammatic representation

of the (-0-matri$, the so called >asse diagram, that this diagram read top-down instead ofbottom-up would describe the dual abstract polytope. The same is even true for the reduced

matrices, where the matri$ of the dual polytope can be read off by Bust rotating the matri$ half

way around an a$is orthogonal to the writing plane, thereby interchanging counts of vertices and

facets, or dualising the numbers of the verte$ figures into those of facets and vice versa. Eurther-on to each of the subdiagonal parts of the rows, the superdiagonal parts of the rows, and the

diagonal itself, the )uler formula might be applied9 but appropriate e$tensions like genus,

density etc. would have to be considered.

+ote that the same polytope might be a fi$-element under different symmetry groups. Thus there

could be different reduced incidence matrices, all describing the same polytope. )specially theidentity map, taken as reducing symmetry, would reproduce the (-0-matri$. *n the other hand

incidence matrices Bust like >asse diagrams only depend on the structure of the abstract

polytope. That is, different isomorph realisations of it would have the same incidence matri$. Eorinstance a conve$ polygon n abstractly can not be distinguished from the polygram nRd as

long there are no incidences of different types.

POWER 6UALITY

The contemporary container crane industry, like many other industry segments, is often

enamored by the bells and whistles, colorful diagnostic displays, high speed performance, and

levels of automation that can be achieved. "lthough these features and their indirectly related

computer based enhancements are key issues to an efficient terminal operation, we must not

forget the foundation upon which we are building. Power quality is the mortar which bonds the

foundation blocks. Power quality also affects terminal operating economics, crane reliability, our

environment, and initial investment in power distribution systems to support new crane

installations. To quote the utility company newsletter which accompanied the last monthly issue

of my home utility billing: G?sing electricity wisely is a good environmental and business

practice which saves you money, reduces emissions from generating plants, and conserves our


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natural resources.S "s we are all aware, container crane performance requirements continue to

increase at an astounding rate. +e$t generation container cranes, already in the bidding process,

will require average power demands of 0/(( to 6((( k = almost double the total average

demand three years ago. The rapid increase in power demand levels, an increase in container

crane population, 4U converter crane drive retrofits and the large "4 and %4 drives needed to

power and control these cranes will increase awareness of the power quality issue in the very

near future.

P*)U Q?";!TD PU*F;)


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greater k#" demand burden on the utility or engine-alternator power source. ;ow power factor

loads can also affect the voltage stability which can ultimately result in detrimental effects on the

life of sensitive electronic equipment or even intermittent malfunction. #oltage transients created

by %4 drive 4U line notching, "4 drive voltage chopping, and high frequency harmonic

voltages and currents are all significant sources of noise and disturbance to sensitive electronic

equipment

!t has been our e$perience that end users often do not associate power quality problems

with 4ontainer cranes, either because they are totally unaware of such issues or there was no

economic 4onsequence if power quality was not addressed. Fefore the advent of solid-state

power supplies, Power factor was reasonable, and harmonic current inBection was minimal. +ot

until the crane Population multiplied, power demands per crane increased, and static power

conversion became the way of life, did power quality issues begin to emerge. )ven as harmonic

distortion and power Eactor issues surfaced, no one was really prepared. )ven today, crane

builders and electrical drive ystem vendors avoid the issue during competitive bidding for new

cranes. Uather than focus on "wareness and understanding of the potential issues, the power

quality issue is intentionally or unintentionally ignored. Power quality problem solutions are

available. "lthough the solutions are not free, in most cases, they do represent a good return on

investment. >owever, if power quality is not specified, it most likely will not be delivered.

Power quality can be improved through:

V Power factor correction,

V >armonic filtering,

V pecial line notch filtering,

V Transient voltage surge suppression,

V Proper earthing systems.

!n most cases, the person specifying andRor buying a container crane may not be fully

aware of the potential power quality issues. !f this article accomplishes nothing else, we would

hope to provide that awareness.


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!n many cases, those involved with specification and procurement of container cranes

may not be cogni&ant of such issues, do not pay the utility billings, or consider it someone elseSs

concern. "s a result, container crane specifications may not include definitive power quality

criteria such as power factor correction andRor harmonic filtering. "lso, many of those

specifications which do require power quality equipment do not properly define the criteria.

)arly in the process of preparing the crane specification:

V 4onsult with the utility company to determine regulatory or contract requirements that must be

satisfied, if any.

V 4onsult with the electrical drive suppliers and determine the power quality profiles that can be

e$pected based on the drive si&es and technologies proposed for the specific proBect.

V )valuate the economics of power quality correction not only on the present situation, but

consider the impact of future utility deregulation and the future development plans for the

terminal.

T>) F)+)E!T *E P*)U Q?";!TD

Power quality in the container terminal environment impacts the economics of the terminal

operation, affects reliability of the terminal equipment, and affects other consumers served by the

same utility service. )ach of these concerns is e$plored in the following paragraphs.

0. )conomic !mpact

The economic impact of power quality is the foremost incentive to container terminal operators.

)conomic impact can be significant and manifest itself in several ways:

a. Power Eactor Penalties

owever, their service contract


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with the Port may still require that a minimum power factor over a defined demand period be

met. The utility company may not continuously monitor power factor or k#"U usage and reflect

them in the monthly utility billings9 however, they do reserve the right to monitor the Port

service at any time. !f the power factor criteria set forth in the service contract are not met, the

user may be penali&ed, or required to take corrective actions at the userSs e$pense. *ne utility

company, which supplies power service to several east coast container terminals in the ?",

does not reflect power factor penalties in their monthly billings, however, their service contract

with the terminal reads as follows:

GThe average power factor under operating conditions of customerSs load at the point

where service is metered shall be not less than 5/8. !f below 5/8, the customer may be required

to furnish, install and maintain at its e$pense corrective apparatus which will increase the Power

factor of the entire installation to not less than 5/8. The customer shall ensure that no e$cessive

harmonics or transients are introduced on to the 2utility3 system. This may require special power

conditioning equipment or filters. The !))) td. /0W-0WW6 is used as a guide in %etermining

appropriate design requirements.S

The Port or terminal operations personnel, who are responsible for maintaining container

cranes, or specifying new container crane equipment, should be aware of these requirements.

?tility deregulation will most likely force utilities to enforce requirements such as the e$ample

above. Terminal operators who do not deal with penalty issues today may be faced with some

rather severe penalties in the future. " sound, future terminal growth plan should include

contingencies for addressing the possible economic impact of utility deregulation.

b. ystem ;osses

>armonic currents and low power factor created by nonlinear loads, not only result in

possible power factor penalties, but also increase the power losses in the distribution system.

These losses are not visible as a separate item on your monthly utility billing, but you pay for

them each month. 4ontainer cranes are significant contributors to harmonic currents and low

power factor. Fased on the typical demands of todaySs high speed container cranes, correction of

power factor


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alone on a typical state of the art quay crane can result in a reduction of system losses that

converts to a 1 to 0(8 reduction in the monthly utility billing. Eor most of the larger terminals,

this is a significant annual saving in the cost of operation.

c. Power ervice !nitial 4apital !nvestments

The power distribution system design and installation for new terminals, as well as

modification of systems for terminal capacity upgrades, involves high cost, speciali&ed, high and

medium voltage equipment. Transformers, switchgear, feeder cables, cable reel trailing cables,

collector bars, etc. must be si&ed based on the k#" demand. Thus cost of the equipment is

directly related to the total k#" demand. "s the relationship above indicates, k#" demand is

inversely proportional to the overall power factor, i.e. a lower power factor demands higher k#"

for the same k load. 4ontainer cranes are one of the most significant users of power in the

terminal. ince container cranes with %4, 1 pulse, 4U drives operate at relatively low power

factor, the total k#" demand is significantly larger than would be the case if power factor

correction equipment were supplied on board each crane or at some common bus location in the

terminal. !n the absence of power quality corrective equipment, transformers are larger,

switchgear current ratings must be higher, feeder cable copper si&es are larger, collector system

and cable reel cables must be larger, etc. 4onsequently, the cost of the initial power distribution

system equipment for a system which does not address power quality will most likely be higher

than the same system which includes power quality equipment.

6. )quipment Ueliability

Poor power quality can affect machine or equipment reliability and reduce the life of

components. >armonics, voltage transients, and voltage system sags and swells are all power

quality problems and are all interdependent. >armonics affect power factor, voltage transients

can induce harmonics, the same phenomena which create harmonic current inBection in %4 4U

variable speed drives are responsible for poor power factor, and dynamically varying power

factor of the same drives can create voltage sags and swells. The effects of harmonic distortion,

harmonic currents, and line notch ringing can be mitigated using specially designed filters.

7. Power ystem "dequacy


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hen considering the installation of additional cranes to an e$isting power distribution system, a

power system analysis should be completed to determine the adequacy of the system to support

additional crane loads. Power quality corrective actions may be dictated due to inadequacy of

e$isting power distribution systems to which new or relocated cranes are to be connected. !n

other words, addition of power quality equipment may render a workable scenario on an e$isting

power distribution system, which would otherwise be inadequate to support additional cranes

without high risk of problems.

'. )nvironment

+o issue might be as important as the effect of power quality on our environment.

Ueduction in system losses and lower demands equate to a reduction in the consumption of our

natural nm resources and reduction in power plant emissions. !t is our responsibility as occupants

of this planet to encourage conservation of our natural resources and support measures which

improve our air quality

R"r&% &re&s

Uural areas are large and isolated areas of an open country with low population density. The

terms McountrysideM and Mrural areasM are not synonyms: a McountrysideM refers to rural areas that

are open. Eorest, wetlands, and other areas with a low population density are not a countryside.

"bout W0 percent of the rural population now earn salaried incomes, often in urban areas. The 0(

percent who still produce resources generate 6( percent of the worldSs coal,copper,and oil9 0(

percent of its wheat, 6( percent of its meat, and /( percent of its corn. The efficiency of these

farms is due in large part to the commerciali&ation of the farming industry, and not single family

operations

Vo%&3e $o#ro%

!n those pre-digital

other. !nstead of digital bits and bytes, information was passed between modules through wires

that carried a voltage.
http://en.wikipedia.org/wiki/Populationhttp://en.wikipedia.org/wiki/Populationhttp://en.wikipedia.org/wiki/Urban_areahttp://en.wikipedia.org/wiki/Coalhttp://en.wikipedia.org/wiki/Copperhttp://en.wikipedia.org/wiki/Copperhttp://en.wikipedia.org/wiki/Copperhttp://en.wikipedia.org/wiki/Oilhttp://en.wikipedia.org/wiki/Populationhttp://en.wikipedia.org/wiki/Urban_areahttp://en.wikipedia.org/wiki/Coalhttp://en.wikipedia.org/wiki/Copperhttp://en.wikipedia.org/wiki/Oil


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" voltage is Bust a measure of how much electrical ApushA a circuit has. Plug a voltage source -

like a battery, or synth module - into a circuit and it will push the electricity around so it starts

flowing. The amount of this push - you can think of it as electrical pressure - is measured in units

called #olts.

!n an analogue synth, voltages are used to control how much each module does what itXs

designed to do. Turn up the voltages to an amplifier, for e$ample, and the sound gets louder. %o

the same to an oscillator and its pitch pitch goes up. Try it with a filter and the filter opens.


39/52

The trigger signal also told the synth you were playing a note, but unlike a gate, it was a

momentary about /ms rather than continuous signal, and could not tell the synth to produce a

sound9 it worked in conBunction with the gate. The trigger signalAs purpose was to start the synthAs

envelope generators, thus articulating the attack of the note. henever the synth received a new

trigger, the envelope generators would be restarted, and the attack of that new note would be

articulated. ithout a trigger signal, a new note would sound using the current state of the

envelope generator - much the same as what hoppens in the AlegatoA mode found on modern

synths.

Triggers came in two varieties. The first, used by "UP instruments, was a momentary spike

where the voltage Bumped from *# to 0(# then back down to *#. The other type, called an -

trigger or switch trigger, was used on


40/52

ratio regulation and polarity selection. The voltage regulator has a transformer with two

independent primary windings, which is fed from the network, and a secondary

compensationwinding, which is serial connected. %ifferent compensation values can be obtained

by changing the connections between the primary and secondary windings, using three power

contactors, with four poles each. "n automatic controller measures the output voltage and selects

the optimal voltage compensation connection. The characteristics of the proposed design make it

suitable for the needs of rural distribution networks:

Yep vo-ge reg-ion: voltage is adBusted within the required quality range, and for

industrial or commercial applications in rural networks there is usually no need for an accurate

voltage regulation based on small steps or continuous regulation.

Y/obsness: the voltage regulator will be usually placed outdoors, in dispersed locations, some

of them with difficult access. Eor greater reliability and easy maintenance, electromechanical

contactors are preferred to power electronics.

YLo0 cos: using serial voltage compensation instead of a full power converter reduces the

device si&e and cost, increasing the efficiency notably.


41/52

outdoors9 for instance, pole mounted in overhead lines Eig. 0. The design proposed in this

paper can be used for one-phase and three-phase voltage regulators. This paper is focused on the

one-phase voltage regulator, including a description of its power circuit and the control system.

A. Poe& /i&cuit

The power circuit of a one-phase voltage regulator consists of a multiwinding transformer see

Eig. 6, with two primary windings and a secondary serial compensation winding. !n addition,


42/52

three power contactors are used to connect the windings and the network. ith this design, five

different voltage ratios can be achieved in the transformer by changing the connection between

the windings see Table !. The selection of the adequate compensation step is performed by a

microprocessor-based control unit. The primary windings of the transformer P0 and P6 have the

same number of turns , and they are connected to the input voltage with contactor 40. The

primary windings can be parallel or series connected using contactor 46, so the effective number

of turns can be or 6 respectively. )ach connection determines a certain voltage ratio, as indicated

in Table !. The secondary winding of the transformer is the serial compensation winding, and

can be series connected with the distribution network or bypassed using contactor40. Einally, the

polarity of the magnetic coupling is set by contactor 47. The output voltage is then increased or

decreased depending on contactor 47. The output voltage can be formulated as the input voltage

plus the compensation voltage set by the regulator 0. The compensation voltage is given by the

ratio of the secondary winding turns and the primary winding turns , times

the voltage at the input of the device

where:

Y is the number of turns of windings P0 or P69

Y is the number of turns of winding 9

Y is the connection constant, which can be 0 or 6 for parallel

and series connection respectively of P0 and P6. !n addition this value will be positive for direct

winding coupling, and negative for inverse coupling of windings. The proposed design of the

voltage regulator has five different compensation steps can be achieved by changing the position

of the three contactors, as is shown in Table !. The standby mode of the voltage regulator is set

with the three contactors opened, and guarantees that the device is disconnected from the

distribution network. >ence, the secondary winding is short-circuited and input and output

voltages are the same, as . This stand-by mode protects loads connected to the voltage regulator

from any failure of the device. iven the design of the voltage regulator, the rated power of the

transformer is lower than the power that the voltage regulator can supply 6. The power

difference depends on the ratio between the compensation and the rated voltages. Eor instance,


43/52

the transformer of a voltage regulator with '(-# compensation and 67(-# rated voltage, will

have a rated power of 08 the ma$imum load that the voltage regulator can supply

. /o+t&ol *4stem

The obBective of the voltage regulator is to improve the line voltage whenever it can be achieved,

and to guarantee system security in the event of a failure of the voltage regulator or severe

contingency in the distribution network. !n this situation, the device will be automatically

disconnected from the network. Eor this purpose, the voltage regulator includes a control system

that consists of three modules Eig. 7.

Y%!e Mesre Mo+-e registers voltage and current at the voltage regulator output. )very 76

cycles, average U


44/52

voltage regulator corrects the voltage with two maneuvers, using steps ' and / path F-4-%.

II. DESIGN AND CONSTRUCTION, PRACTICAL CONSIDERATIONS

This section discusses various aspects of the construction of the voltage regulator, given the needto guarantee its correct and safe operation.

. %rns1ormer Design

" shell-type transformer has been selected for its hardness and its lower operation temperature,which makes it more appropriate for achieving greater efficiency in the functioning of the

voltage regulator. " software tool has been developed to analy&e the costs of different

transformer column designs. This tool analy&es the active material cost and the energy losses

cost of the transformer 2003. The cost analysis for a 67(R'(-# transformer is shown in Eig. /,

where different designs for the column length of the magnetic core are presented. The cost


45/52

calculation assumes the following prices: the steel lamination cost is )uros 7Rkg, the copper cost

is )uros 5./Rkg, and the energy losses for 1( ((( hours at )uros (.0Rkh. iven the results in

Eig. /, the optimal transformer design has a column length of W7 mm. Eor this design, total

transformer costs are )uros /55./6, which can be split into )uros 'W6.16 for energy losses and

)uros W/.W for active material cost. " detailed electro-magnetic analysis for the selected length

of the 67(R'(-# transformer has been performed with "+*ETSs


46/52


47/52

transformer has been designed with a low flu$ density in order to reduce the energy losses in the

steel laminations.

#. Vo-ge /e1erence /nge De1iniion

The reference voltage range will be defined usually in accordance with the quality

standards in each country. Eor instance, if voltage requirements at the load are 67( #

8, the proposed settings for the voltage regulator will be

, and . >owever, for certain voltage-sensitive applications, a reduced reference voltage range

may be required. !n this case, some adaptations in the design are required to avoid oscillations in

the compensation maneuvers. !f the control system step-ups because output voltage is below

the reference , the new compensated voltage

should always be lower than the reference voltage , to avoid oscillations. This constraint can be

formulated for each step c as follows:

The proposed design of the voltage regulator can be then adapted to a small-voltage reference

range. The values can be achieved by selecting the adequate winding turns of the primary

and secondary windings.

#. &ompension Mnevers eqence


48/52

"s defined in the previous section, a compensation maneuver changes the position of the

contactors of the device. The compensation maneuver starts with the disconnection of the

contactor 40. Then, contactors 46 and 47 are opened or closed depending on the compensation

step needed. This operation is performed off-load, which minimi&es possible transients and

e$tends the service life of contactors 46 and 47. "nd finally, 40 is closed, and a new

compensation step is obtained. )$perimental results for the compensation maneuver are shown

in Eig. 5, which shows voltage in the coil of contactor 40, and voltage in the primary winding,.

&. 0ic!ing &onro-

The reliability and e$pected life of the voltage regulator is mainly determined by the power

contactor 40, which operates on-load. ?nfavorable switching conditions will shorten the life

of the contactor, and some malfunctioning can occur when the contactor fails to open because

contactor contacts are welded or fails to close because contacts have lost their conducting

surface. Three improvements have been implemented in the design of the voltage regulator to

enhance the switching maneuver of contactor 40.

YTwo poles of contactor 40 are parallel connected to open the load current see Eig. 0. The

other two poles are series connected to open the rated voltage.

Y" capacitor is connected in the primary winding P0.

YThe 4ompensation


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D. 211icienc %es

The efficiency of a voltage regulator, whose technical data are enclosed in the Table !!, has been

tested. The tests have been carried out with a variable voltage source, in order to emulate the real

operation in a non-constant voltage network. "dBustable loads at power factor 0 and power factor

(.5 have been used to


51/52

charge the voltage regulator. The results of the efficiency tests are shown in Table !!! and Table

!#. "lthough the voltage regulator has '.78 total energy losses, its efficiency at any load is

remarkable. imilarly noteworthy is the fact that, due to its 7 ((( #" transformer, this voltage

regulator can manage apparent power at the output of up to 01 /(( #". !n short, the voltage

regulator design presented in this paper offers low cost and high efficiency.

REFERENCES

203 Z#oltage characteristics of electricity supplied by public distribution networks,[ in4roc.

&2N2L2&, Frussels, Felgium, 6((0.

263 "+! 45'.0 "merican +ational tandard for )lectric Power ystems and )quipmentY

#oltage Uatings 1( >& "merican +ational tandards !nstitute, 6((1.

273 U.


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20(3 *. . Elurscheim, 4o0er &irci #re6er %!eor n+ Design, ser. !)) Power )ngineering

eries. ;ondon, ?.@.: !)), 0W56.

20'3

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Voltage Regulators Rural Networks