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. Section II presents the design of the voltage

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

regarding the design of the voltage regulator are presented in Section III. And finally, Section IV

presents the operation experience data of voltage regulators installed in the distribution network.

Different voltage compensation steps are obtained by modifying the connection and the

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

optimized to obtain a high-efficiency and low-cost regulator. An automatic controller monitors

the output voltage and sets the optimal compensation step. At present more than 400 units of the

voltage regulator are in operation.

Experimental records for the operation of installed voltage regulators have shown their

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

I. INTRODUCTION

LONG-duration voltage variation (undervoltage and overvoltage) is a central issue in

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

standards, such as the European EN 50160 [1] or the American ANSI C84-1 [2]. These standards

are complemented in each country or state by specific codes and rules [3]. The European EN

50160 stipulates that the maximum voltage amplitude variation accepted is 10%, while the

American ANSI C84-1 defines a normal operating range of 120 V 5%. National rules usually

define more restrictive voltage ranges; for instance, the Spanish rule for voltage quality [4] sets

the maximum variation of the voltage at the load connection point at 230 V 7%. The value of

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

within a specific voltage range. Several problems in domestic and industrial equipment are

associated 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. On the other hand, long

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

hence a reduction in their expected durability. Low voltage rural distribution networks compared

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

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

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

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

problems. To minimize long-term voltage variations in rural networks, distribution companies

have traditionally performed different actions: 1) tap change control in the main distribution

transformer; 2) installation of compensation equipment, such as capacitor banks, voltage

regulators, boosters, or auto-boosters; and 3) as a last resort, because it is the most expensive

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

capability, or changing the network rated voltage) [5]. In rural areas, the ratio of contracted

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

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

as voltage regulators becomes an interesting alternative. Moreover, the distribution company also

takes into account the operation and maintenance costs and the energy losses resulting from the

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

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

both in commercial devices and in the literature: tap-switching, ferroresonant, and electronic [6].

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

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

networks [7]–[10]; 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. Section II presents the design

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

considerations regarding the design of the voltage regulator are presented in Section III. And

finally, Section IV presents the operation experience data of voltage regulators installed in the

distribution network.

Power distribution control

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 11kV). The 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

equipments, buses and switchgear. At the secondary substation voltage is

stepped down to 11kV. The portion of the power network between a

secondary substation and consumers is known as distribution system. The

distribution

system can be classified into primary and secondary system. Some large

consumers are given high voltage supply from the receiving end substations

or secondary substation.

The 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. The primary distribution system consists of main feeders and

laterals. The 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. The lateral is supplied by the

main feeder and extends through the load area with connection to

distribution transformers. The distribution transformers are located at

convenient places in the load area. They may be located in specially

constructed enclosures or may be pole mounted. The 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

400V and power is fed into the secondary distribution systems. The

secondary 14 distribution system consists of distributors which are laid along

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

distributors. The main feeders, laterals and distributors may consist of

overhead lines or cables or both. The distributors are 3- phase, 4 wire

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

Most of the residential

and commercial consumers are given single phase supply. Some large

residential and commercial consumer uses 3-phase power supply. The

service connections of consumer are known as service mains.

The consumer receives power from the distribution system. The main part of

distribution system

includes:-

1. Receiving substation.

2. Sub- transmission lines.

3. Distribution substation located nearer to the load centre.

4. Secondary circuits on the LV side of the distribution transformer.

5. Service mains.

Power Flow

For distribution system the power flow analysis is a very important and

fundamental tool. Its results play the major role during the operational

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

expansion and design stages. The 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.

During 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 Gauss-Siedel (bus impedance matrix),

Newton-Raphson’s (NR) and its decoupled versions. Nowadays, many

improvements have been added to all these methods involving assumptions

and approximations of the transmission lines and bus data, based on real

systems conditions.

The Fast Decoupled Power Flow Method (FDPFM) is one of these improved

methods, which was based on a simplification of the Newton-Raphson’s

method and reported by Stott and Alsac in 1974. This method due to its

calculations simplifications, fast convergence and reliable results became the

most widely used method in load flow analysis. However, FDPFM for some

cases, where high R/X ratios or heavy loading (Low Voltage) at some buses

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

developments have been made to overcome these convergence obstacles.

Some of them targeted the convergence of systems with high R/X ratios,

others those with low voltage buses. Though many efforts and elaborations

have been achieved in order to improve the FDPFM, this method can still

attract many researchers, especially when computers and simulations are

becoming more developed and are now able to handle and analyze large size

system.

Objectives of Radial Distribution System:-1. Planning, modernization and automation.

2. To provide service connection to various urban, rural and industrial

consumer in the allocated area.

3. Maximum security of supply and minimum duration of interruption.

4. Safety of consumers, utility personnel.

5. To provide electricity of accepted quality in terms of :-

(a) Balanced three phase supply.

(b) Good power factor.

(c) Voltage flicker within permissible limits.

(d) Less voltage dips.

(e) Minimum interruption in power supply.

Advantages of Radial Distribution System:-

(a) Radial distribution system is easiest and cheapest to build.

(b) The maintenance is easy.

(c) It is widely used in sparsely populated areas.

Drawback of Radial Distribution System:-

(a) The end of the distributor nearest to the feeding point will be heavily

loaded.

(b) The consumers are dependent on a single feeder and single distributor.

Therefore, 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) The consumers at the distant end of the distributor would be subjected to

serious voltage fluctuations when the load on the distributor

The single line diagram of a typical low tension distribution system.History of Distribution System

In the early days of electricity distribution, direct current DC generators were

connected to loads

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

same voltage because there was no way of changing DC voltage levels,

other than inefficient motor-generator sets. Low DC voltages were used (on

the order of 100 volts) since that was a practical voltage for

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

voltage also required less insulation to be safely distributed within buildings.

The losses in a cable are proportional to the square 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. To reduce the current and copper required

for a given quantity of

power transmitted would require a higher transmission voltage, but no

convenient efficient method existed to change the voltage level of DC power

circuits. To keep losses to an economically practical level the Edison DC

system needed thick cables and local generators.

Modern Distribution System

The 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 equipment are used among the

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

leaves the sub-station in a primary circuit, usually with all three phases. The

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

because of the shape of a "Y".) The Wye configuration includes 3 phases

(represented by the three outer parts of the "Y") and a neutral (represented

by the centre of the "Y".) The neutral is grounded both at the substation and

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

delta. This method is older and less common. Delta is so named because of

the shape of the Greek letter delta, a triangle. Delta has only 3 phases and

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

(phase to phase), while in Wye there are two voltages, between two phases

and between a phase and 27 neutral (phase to neutral). Wye primary is safer

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

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

breaker tripping similar to a household fused cut-out system. In delta, if a

phase makes connection to ground it will continue to function normally. It

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

cut-outs will open the circuit. The voltage for this configuration is usually

4800 volts.

Requirement of Distribution system

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

supply within the

requirements of various types of consumers. Some of the requirements of a

good distribution

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

Proper Voltage:

One important requirement of a distribution system is that voltage

variations at consumers’ terminals should be as low as possible. The changes

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

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

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

cause failure of other appliances. Therefore, a good distribution system

should ensure that the voltage variations at consumers’ terminals are within

permissible limits. The statutory limit of voltage variations is +10% of the

rated value at the consumers’ terminals. Thus, if the declared voltage is 230

V, then the highest voltage of the consumer should not exceed 244 V while

the lowest voltage of the consumer should not be less than 216 V.

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

require from time to time. For example, 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. This necessitates that operating staff must continuously study

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

known schedules.

Reliability:

Modern industry is almost dependent on electric power for its operation. Homes and office

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

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

absolutely reliable. However, the reliability can be improved to a considerable extent by (a)

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

reserve facilities.

Classification of Distribution System

A distribution system may be classified according to:

(i) Nature of current:

According to nature of current, distribution system may be classified as (a) d.c. distribution

system and (b) a.c. distribution system. Now-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) Type of construction:

According 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

5 to 10 times cheaper than the equivalent underground system. In general, the underground

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

laws.

(iii) Scheme of connection:

According to scheme of connection, the distribution system may be classified as (a) radial

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

advantages and disadvantages.

Radial Distribution System

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 fixed before power can be restored. The figure of

Radial Distribution System is shown as :-

Radial Distribution System

In this system, separate feeders radiate from a single sub-station and feed

the distributors at one end only. Figure (a) shows a single line diagram of a

radial system for d.c. Distribution where a feeder OC supplies a distributor

AB at point A. Obviously, the distributors are fed at one point only i.e. point A

in this case. Figure (b) shows a single line diagram of radial system for a.c.

distribution. The radial system is employed only when power is generated at

low voltage and the sub-station is located at the centre of load. This is the

simplest distribution circuit and has the lowest initial cost.

Single Line Diagram of Radial Distribution System

Node Radial Distribution Network:-

Objectives of Radial Distribution System:-1. Planning, modernization and automation.

2. To provide service connection to various urban, rural and industrial

consumer in the allocated area.

3. Maximum security of supply and minimum duration of interruption.

4. Safety of consumers, utility personnel.

5. To provide electricity of accepted quality in terms of :-

(a) Balanced three phase supply.

(b) Good power factor.

(c) Voltage flicker within permissible limits.

(d) Less voltage dips.

(e) Minimum interruption in power supply.

Advantages of Radial Distribution System:-

(a) Radial distribution system is easiest and cheapest to build.

(b) The maintenance is easy.

(c) It is widely used in sparsely populated areas.

Drawback of Radial Distribution System:-

(a) The end of the distributor nearest to the feeding point will be heavily

loaded.

(b) The consumers are dependent on a single feeder and single distributor.

Therefore, 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) The consumers at the distant end of the distributor would be subjected to

serious voltage fluctuations when the load on the distributor

MODELINOGF DISTRIBUTIOSYNS TEMCOMPONENTS

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

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

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

This equation is obtained after Kron's reduction. It takes care of the effects of the neutral or

ground. At each bus i, the complex power S, is given by,

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

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

THREE-PHASE DISTRIBUTION LO AD FLOW ANALY.S.I S

Most of the distribution'systems are. radial in nature with a single voltage source. This special

property of the distribution system is used to derive various formulations. Different iterative

methods similar to Gauss-Seidel method are discussed in this paper. In this section, the

algorithms for these methods are given.

A. Implicit Z-bus Method

The implicit Z-bus method is the most commonly used method 151. The method works on the

principle of superposition as applied to the system bus voltages. According to the principle of

superposition, only one type of source is considered at a time for the calculation of bus voltages.

An iterative procedure is used in this method. Initially, all the bus voltages are assumed to be

equal to the swing bus voltage (only swing bus is considered as the source in the system with all

the current injections at load buses taken as zero). In the next step, since the current injections

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 injections.

The following steps are involved in this algorithm:

1. The bus voltages are assumed to have some initia1,value. The Y-bus (Y,) is formed.'

2. The current injections are computed by using equation 3 for which the recent values of bus

voltages are taken.

3. The voltage deviations (VD) due to current injections are computed by the factorization of Y-

bus,

f = [YB] [ VD]' (4)

4. The voltage deviations calculated in step 3 are superimposed on the no load bus voltage

(VNL)H. ence, the bus voltages are updated'as. 3" = VNL + [ VD]' (5)

5. The convergence is checked. If the method has not converged. then steps from 2 to 4 are

repeated.

B. ModiJied Gauss-Se2.d Method

The implicit Z-bus method described earlier requires the factorization of the full Y-bus matrix,

adversely affecting the performance in terms of speed. .Hence, a new method has been suggested

in [6] by blending the implicit Z-bus method and the Gauss-Seidel method to improve the

computational efficiency. For a distribution system with n buses, where P:pe'and Qtpec are the

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

Seidel method

as.

The values of voltages used in the modified Gauss-Seidel method are the most recently

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

Two matrices are developed, viz. the bus injection to branch current (BIBC) matrix and branch

current to bus voltage (BCBV) matrix. By . . using simple matrix multiplication of these two

matrices, the Two developed matrices, BIBC and BCBV are used to obtain the load flow

solution. The development of these two matrices is explained with reference to Fig. . The figure

shows a simple distribution system. It has sub-station at its bus number I, and bus numbers 2 to 6

are the load buses loadflow‘solution is obtained

D. Forward-Backward Substitution

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

by using the matrices. In forward-backward substitution, the KCL and KVL are applied at each.

node and branch respectively. By solving these equations iteratively, the solution is obtained [SI.

The following steps involved in this method:

Optimal ordering of nodes: Nodes 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.

Initially, the flat voltage start is assumed.

Backward substitution:

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

current injection 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 KCL as given by the equation.

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

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

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

element of M).

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

substitution in the next iteration.

Check 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. If the error is within the tolerance limit, the procedure is stopped. Otherwise, the steps

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

E. Ladder Network Theory

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. In the ladder network theory, the optimal ordering of

nodes is done first. In the backward substitution, the node voltages are assumed to be equal to

some initial value in the first iteration. The currents in each branch are computed by KCL using

equation 22. In addition to the branch currents, the node voltages are also computed by using

equation. Thus, the value of the swing bus voltage is also determined. This calculated value of

the swing bus voltage is compared with its specified value. If the error is within the limit, then

the load flow converges; otherwise the forward substitution is performed as explained in the case

of forward-backward substitution method. Thus, in the ladder network theory, the bus 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.

Forward sirbstitufion

This is used to calculate the voltage at each node (starting from the child node of the first branch) by using KVL. 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

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

Fast Decoupled Power Flow for Radial Distribution System

In Radial Distribution System, the large R/X ratio causes problems in convergence of conventional load flow algorithm. Therefore for the better convergence some modified load flowmethods are used. For the purposes of power flow studies, we model a radial distribution system as a network of buses connected by distribution lines, switches, or transformers to a voltage specified source bus. Each bus may also have a corresponding load, shunt capacitor, and/or co-generator connected to it. The model can be represented by a radial interconnection of copies of the basic building block shown in Figure 4.2 the dotted lines from the co-generator, shunt capacitor, and load to ground are to indicate that these elements may be connected in an ungrounded delta-configuration. Since a given branch may be single-phase, two-phase, or three-phase. The basic building block of radial distribution systemis shown on the next page as:-

Figure

The Basic Building Block of Radial Distribution System.

One of the key concepts behind our formulation is that the voltage and current at one bus can be

expressed as a function of the voltage and current at the next bus. If we let

the equations [1] as

The branch update function [1] is given below as:

Where Wk is a vector containing the real and imaginary parts of the voltages and currents at busk. The function gk is determined by the sub-laterals attached at bus k as well as the models fordistribution lines, switches, transformers, loads, shunt capacitors, and co-generators. From Vk wecan compute the currents injected by the loads, shunt capacitors, and co-generators. Given Ik + 1and the currents Ij injected into sub-laterals branching off from bus k, we apply KCL at bus k tocaculate current [1] given as:-

Where Ak is the set of buses adjacent to bus k on sub-laterals.From the following equation (28), we can solve for the voltage and current at the primary giventhe voltage and current at the secondary [1] as:-

Therefore by solving equation (27) , we get

So that by using this method we get the converged value easily and fast than the other ordinarymethods.

In mathematics, an incidence matrix is a matrix that shows the relationship between two classes of objects. If the first class is X and the second is Y, the matrix has one row for each element of X and one column for each element of Y. The entry in row x and column y is 1 if x and y are related (called incident in this context) and 0 if they are not. There are variations; see below.

Graph theory

Undirected and directed graphs

An undirected graph

In graph theory an undirected graph G has two kinds of incidence matrix: unoriented and oriented. The incidence matrix (or unoriented incidence matrix) of G is a p × q matrix (bij), where p and q are the numbers of vertices and edges respectively, such that bij = 1 if the vertex vi and edge xj are incident and 0 otherwise.

For example the incidence matrix of the undirected graph shown on the right is a matrix consisting of 4 rows (corresponding to the four vertices) and 4 columns (corresponding to the four edges):

The incidence matrix of a directed graph D is a p × q matrix [bij] where p and q are the number of vertices and edges respectively, such that bij = − 1 if the edge xj leaves vertex vi, 1 if it enters vertex vi and 0 otherwise. (Note that many authors use the opposite sign convention.)

An oriented incidence matrix of an undirected graph G is the incidence matrix, in the sense of directed graphs, of any orientation of G. That is, in the column of edge e, there is one +1 in the row corresponding to one vertex of e and one −1 in the row corresponding to the other vertex of e, and all other rows have 0. All oriented incidence matrices of G differ only by negating some set of columns. In many uses, this is an insignificant difference, so one can speak of the oriented incidence matrix, even though that is technically incorrect.

The oriented or unoriented incidence matrix of a graph G is related to the adjacency matrix of its line graph L(G) by the following theorem:

where A(L(G)) is the adjacency matrix of the line graph of G, B(G) is the incidence matrix, and Iq

is the identity matrix of dimension q.

The Kirchhoff matrix is obtained from the oriented incidence matrix M(G) by the formula

M(G)M(G)T.

The integral cycle space of a graph is equal to the null space of its oriented incidence matrix, viewed as a matrix over the integers or real or complex numbers. The binary cycle space is the null space of its oriented or unoriented incidence matrix, viewed as a matrix over the two-element field.

Signed and bidirected graphs

The incidence matrix of a signed graph is a generalization of the oriented incidence matrix. It is the incidence matrix of any bidirected graph that orients the given signed graph. The column of a positive edge has a +1 in the row corresponding to one endpoint and a −1 in the row corresponding to the other endpoint, just like an edge in an ordinary (unsigned) graph. The column of a negative edge has either a +1 or a −1 in both rows. The line graph and Kirchhoff matrix properties generalize to signed graphs.

Multigraphs

The definitions of incidence matrix apply to graphs with loops and multiple edges. The column of an oriented incidence matrix that corresponds to a loop is all zero, unless the graph is signed and the loop is negative; then the column is all zero except for ±2 in the row of its incident vertex.

Hypergraphs

Because the edges of ordinary graphs can only have two vertices (one at each end), the row of an incidence matrix for graphs can only have two non-zero entries. By contrast, a hypergraph can have multiple vertices assigned to one edge; thus, the general case describes a hypergraph.

Incidence structures

The incidence matrix of an incidence structure C is a p × q matrix [bij], where p and q are the number of points and lines respectively, such that bij = 1 if the point pi and line Lj are incident and 0 otherwise. In this case the incidence matrix is also a biadjacency matrix of the Levi graph of the structure. As there is a hypergraph for every Levi graph, and vice-versa, the incidence matrix of an incidence structure describes a hypergraph.

Finite geometries

An important example is a finite geometry. For instance, in a finite plane, X is the set of points and Y is the set of lines. In a finite geometry of higher dimension, X could be the set of points and Y could be the set of subspaces of dimension one less than the dimension of Y; or X could be the set of all subspaces of one dimension d and Y the set of all subspaces of another dimension e.

Block designs

Another example is a block design. Here X is a finite set of "points" and Y is a class of subsets of X, called "blocks", subject to rules that depend on the type of design. The incidence matrix is an important tool in the theory of block designs. For instance, it is used to prove the fundamental theorem of symmetric 2-designs, that the number of blocks equals the number of points.

Create graphs from an incidence matrix

Description

graph.incidence creates a bipartite igraph graph from an incidence matrix.

Usage

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

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

Arguments

incidence The input incidence matrix. It can also be a sparse matrix from the Matrix package.

directed Logical scalar, whether to create a directed graph.

mode A character constant, defines the direction of the edges in directed graphs, ignored for undirected graphs. If ‘out’, then edges go from vertices of the first kind (corresponding to rows in the incidence matrix) to vertices of the second kind (columns in the incidence matrix). If ‘in’, then the opposite direction is used. If ‘all’ or ‘total’, then mutual edges are created.

multiple Logical scalar, specifies how to interpret the matrix elements. See details below.

weighted This argument specifies whether to create a weighted graph from the incidence matrix. If it is NULL then an unweighted graph is created and the multiple argument is used to determine the edges of the graph. If it is a character constant then for every non-zero matrix entry an edge is created and the value of the entry is added as an edge attribute named by the weighted argument. If it is TRUE then a weighted graph is created and the name of the edge attribute will be ‘weight’.

add.names A character constant, NA or NULL. graph.incidence can add the row and column names of the incidence matrix as vertex attributes. If this argument is NULL (the default) and the incidence matrix has both row and column names, then these are added as the ‘name’ vertex attribute. If you want a different vertex attribute for this, then give the name of the attributes as a character string. If this argument is NA, then no vertex attributes (other than type) will be added.

Incidence Matrices

by Dr Richard Klitzing

(reproduced with permission)

Taken purely abstract, polytopes are described by their surtopial elements plus the relative incidences. The most basic way to give those incidences are 0-1-matrices with

1 meaning "incident" and 0 "not". But already the easiest polytopes would ask for huge matrices. This is the entrance for symmetry, the symmetry of the polytope itself. Alike surtopial elements now can be classed together via symmetrical equivalence, and the incidence relation will be given for the classes instead. This reduces the size of the matrix considerably. The diagonal elements of these reduced matrices will give the total count of elements of each of the respective equivalence classes. The non-diagonal elements I_(n,m) will provide the numbers of incident surtopes of class m with any of the elements of class n. The subdiagonal parts of the rows thus still describe the surtopial element classes. The superdiagonal parts of the rows describe their environmental aspacts, i.e. vertex figures, edge figures etc.

Regular polytopes are bound to provide a single class of surtopes per dimension, but in general there will be more symmetry-inequivalent elements of the same dimensionality. Therefore it is conveniant to display the dimensional borders as well as a superimposed guiding grid. Vertex-transitivity for instance can be read off from an incidence matrix directly, as those polytopes show up only a single vertex class.

Here as an example the incidence matrix of the truncated cube is given. The Dynkin diagrams of the relative classes are provided in addition in front of the rows.

o3x4x

. . . || 24 |  2  1 | 1 2------++----+-------+----. x . ||  2 | 24  * | 1 1. . x ||  2 |  * 12 | 0 2------++----+-------+----o3x . ||  3 |  3  0 | 8 *. x4x ||  8 |  4  4 | * 6

This matrix shows that there are 24 vertices, all having the same symmetry (upper-left element). The lowest two rows show that the 2-dimensional elements have 3 or 8 vertices (lower-left block) and therefore are triangles or octagons. The rightmost entries of the first row show further that at each vertex 1 such triangle and 2 octagons are incident. Further there are 2 types of edges, the upper one is incident to 1 triangle and 1 octagon, the other one is incident to 2 octagons only. 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). Altogether there are 8

triangles and 6 octagons (lower-right block).

Two relations on these numbers are generally valid. The one is the equation I_(n,n)*I_(n,m)=I_(m,n)*I_(m,m). This is true whether incident representants of those classes of subpolytopes do exist or not, as in the latter case the corresponding non-diagonal elements are both zero. The other observation is, and this derives right from the diagrammatic representation of the 0-1-matrix, the so called Hasse diagram, that this diagram read top-down instead of bottom-up would describe the dual abstract polytope. The same is even true for the reduced matrices, where the matrix of the dual polytope can be read off by just rotating the matrix half way around an axis orthogonal to the writing plane, thereby interchanging counts of vertices and facets, or dualising the numbers of the vertex figures into those of facets and vice versa. Further-on to each of the subdiagonal parts of the rows, the superdiagonal parts of the rows, and the diagonal itself, the Euler formula might be applied; but appropriate extensions like genus, density etc. would have to be considered.

Note that the same polytope might be a fix-element under different symmetry groups. Thus there could be different (reduced) incidence matrices, all describing the same polytope. Especially the identity map, taken as reducing symmetry, would reproduce the 0-1-matrix. On the other hand incidence matrices just like Hasse diagrams only depend on the structure of the abstract polytope. That is, different isomorph realisations of it would have the same incidence matrix. For instance a convex polygon {n} abstractly can not be distinguished from the polygram {n/d} as long there are no incidences of different types.

POWER QUALITY

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. Although 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: ‘Using electricity wisely is a good environmental and business

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

natural resources.’ As we are all aware, container crane performance requirements continue to

increase at an astounding rate. Next generation container cranes, already in the bidding process,

will require average power demands of 1500 to 2000 kW – almost double the total average

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

crane population, SCR converter crane drive retrofits and the large AC and DC drives needed to

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

near future.

POWER QUALITY PROBLEMS

For the purpose of this article, we shall define power quality problems as:

‘Any power problem that results in failure or mis operation of customer equipment, manifests

itself as an economic burden to the user, or produces negative impacts on the environment.’

When applied to the container crane industry, the power issues which degrade power quality

include:

• Power Factor

• Harmonic Distortion

• Voltage Transients

• Voltage Sags or Dips

• Voltage Swells

The AC and DC variable speed drives utilized on board container cranes are significant

contributors to total harmonic current and voltage distortion. Whereas SCR phase control creates

the desirable average power factor, DC SCR drives operate at less than this. In addition, line

notching occurs when SCR’s commutate, creating transient peak recovery voltages that can be 3

to 4 times the nominal line voltage depending upon the system impedance and the size of the

drives. The frequency and severity of these power system disturbances varies with the speed of

the drive. Harmonic current injection by AC and DC drives will be highest when the drives are

operating at slow speeds. Power factor will be lowest when DC drives are operating at slow

speeds or during initial acceleration and deceleration periods, increasing to its maximum value

when the SCR’s are phased on to produce rated or base speed. Above base speed, the power

factor essentially remains constant. Unfortunately, container cranes can spend considerable time

at low speeds as the operator attempts to spot and land containers. Poor power factor places a

greater kVA demand burden on the utility or engine-alternator power source. Low 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. Voltage transients created

by DC drive SCR line notching, AC drive voltage chopping, and high frequency harmonic

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

equipment

It has been our experience that end users often do not associate power quality problems

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

economic Consequence if power quality was not addressed. Before the advent of solid-state

power supplies, Power factor was reasonable, and harmonic current injection was minimal. Not

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. Even as harmonic

distortion and power Factor issues surfaced, no one was really prepared. Even today, crane

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

cranes. Rather than focus on Awareness and understanding of the potential issues, the power

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

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

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

Power quality can be improved through:

• Power factor correction,

• Harmonic filtering,

• Special line notch filtering,

• Transient voltage surge suppression,

• Proper earthing systems.

In most cases, the person specifying and/or buying a container crane may not be fully

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

hope to provide that awareness.

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

may not be cognizant of such issues, do not pay the utility billings, or consider it someone else’s

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

criteria such as power factor correction and/or harmonic filtering. Also, many of those

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

Early in the process of preparing the crane specification:

• Consult with the utility company to determine regulatory or contract requirements that must be

satisfied, if any.

• Consult with the electrical drive suppliers and determine the power quality profiles that can be

expected based on the drive sizes and technologies proposed for the specific project.

• Evaluate 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.

THE BENEFITS OF POWER QUALITY

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. Each of these concerns is explored in the following paragraphs.

1. Economic Impact

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

Economic impact can be significant and manifest itself in several ways:

a. Power Factor Penalties

Many utility companies invoke penalties for low power factor on monthly billings. There

is no industry standard followed by utility companies. Methods of metering and calculating

power factor penalties vary from one utility company to the next. Some utility companies

actually meter kVAR usage and establish a fixed rate times the number of kVAR-hours

consumed. Other utility companies monitor kVAR demands and calculate power factor. If the

power factor falls below a fixed limit value over a demand period, a penalty is billed in the form

of an adjustment to the peak demand charges. A number of utility companies servicing container

terminal equipment do not yet invoke power factor penalties. However, their service contract

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 kVAR usage and reflect

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

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

user may be penalized, or required to take corrective actions at the user’s expense. One utility

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

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

with the terminal reads as follows:

‘The average power factor under operating conditions of customer’s load at the point

where service is metered shall be not less than 85%. If below 85%, the customer may be required

to furnish, install and maintain at its expense corrective apparatus which will increase the Power

factor of the entire installation to not less than 85%. The customer shall ensure that no excessive

harmonics or transients are introduced on to the [utility] system. This may require special power

conditioning equipment or filters. The IEEE Std. 519-1992 is used as a guide in Determining

appropriate design requirements.’

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.

Utility deregulation will most likely force utilities to enforce requirements such as the example

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

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

contingencies for addressing the possible economic impact of utility deregulation.

b. System Losses

Harmonic 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. Container cranes are significant contributors to harmonic currents and low

power factor. Based on the typical demands of today’s high speed container cranes, correction of

power factor

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

converts to a 6 to 10% reduction in the monthly utility billing. For most of the larger terminals,

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

c. Power Service Initial Capital Investments

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

modification of systems for terminal capacity upgrades, involves high cost, specialized, high and

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

collector bars, etc. must be sized based on the kVA demand. Thus cost of the equipment is

directly related to the total kVA demand. As the relationship above indicates, kVA demand is

inversely proportional to the overall power factor, i.e. a lower power factor demands higher kVA

for the same kW load. Container cranes are one of the most significant users of power in the

terminal. Since container cranes with DC, 6 pulse, SCR drives operate at relatively low power

factor, the total kVA 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. In the absence of power quality corrective equipment, transformers are larger,

switchgear current ratings must be higher, feeder cable copper sizes are larger, collector system

and cable reel cables must be larger, etc. Consequently, 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.

2. Equipment Reliability

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

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

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

can induce harmonics, the same phenomena which create harmonic current injection in DC SCR

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.

3. Power System Adequacy

When considering the installation of additional cranes to an existing 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

existing power distribution systems to which new or relocated cranes are to be connected. In

other words, addition of power quality equipment may render a workable scenario on an existing

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

without high risk of problems.

4. Environment

No issue might be as important as the effect of power quality on our environment.

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

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

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

improve our air quality

Rural areas

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

terms "countryside" and "rural areas" are not synonyms: a "countryside" refers to rural areas that

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

About 91 percent of the rural population now earn salaried incomes, often in urban areas. The 10

percent who still produce resources generate 20 percent of the world’s coal, copper, and oil; 10

percent of its wheat, 20 percent of its meat, and 50 percent of its corn. The efficiency of these

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

operations

Voltage control

In those pre-digital MIDI days, synths used a different system to control themselves and each

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

that carried a voltage.

A voltage is just a measure of how much electrical 'push' 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 Volts.

In an analogue synth, voltages are used to control how much each module does what it´s

designed to do. Turn up the voltages to an amplifier, for example, and the sound gets louder. Do

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

Modulation sources - low-frequency oscillators, ADSRs, and so on - are cunningly designed

boxes that ramp voltages up and down automatically in predicted ways. Without them, You and

Your friends would have to turn knobs and dials by hand every time You hit a note. Most synths

use a standard voltage-control system. This defines a common one-volt-per-octave scale - in

other words, every time the control voltage goes up by one volt, the frequency of an oscillator

doubles. Turn up the voltage by 1/12th of a volt, and the pitch goes up by a semitone.

Consequently, a 4V signal would cause an oscillator to produce a pitch one octave higher than a

3V signal, and that´s the theory of one-volt-per-octave.

One fo the clever -and strange- things about analogue synthesis is that you can interchange

control voltage and audio lines, because there´s no practical difference between the two. An

audio signal is just a voltage that´s wobbling up and down particularly fast, but it´s still basically

a voltage, just like you´ll get from any module.

This means you can use the output of an oscillator to change the pitch of another, or of a filter, or

the gain of a amplifier (vca). This gives you acces to strange and unusual effects that you can´t

create any other way.   

Gate and Trigger

The gate signal told the synth that you had pressed a key. This voltage, usually in the 5V-10V

range, would remain constant as long as the key was held. As soon as the key was released, the

gate signal would stop (drop to OV), and the synth's envelope would immediately jump to its

release stage.

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

momentary (about 5ms) rather than continuous signal, and could not tell the synth to produce a

sound; it worked in conjunction with the gate. The trigger signal's purpose was to start the synth's

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

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

articulated. Without a trigger signal, a new note would sound using the current state of the

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

synths.

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

where the voltage jumped from OV to 10V then back down to OV. The other type, called an S-

trigger (or switch trigger), was used on Moog synthesizers. It consisted of a continuous gate-type

voltage that dropped to OV when a key was pressed. This voltage was used to control a switch

that produced a trigger when it closed in response to the voltage drop.

VOLTAGE REGULATOR PRINCIPLE OF OPERATION

The proposed voltage regulator provides discrete serial voltage compensation. Voltage is

compensated using tapswitching, which combines two regulation principles: voltage

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. Different compensation values can be obtained

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

contactors, with four poles each. An 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:

—Step voltage regulation: voltage is adjusted 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.

—Robustness: the voltage regulator will be usually placed outdoors, in dispersed locations, some

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

contactors are preferred to power electronics.

—Low cost: using serial voltage compensation instead of a full power converter reduces the

device size and cost, increasing the efficiency notably. Moreover, the higher reliability

reduces the maintenance costs. Section III in this paper presents a cost analysis of the voltage

regulator. The regulator is intended for the use in distribution networks, both indoors or

outdoors; for instance, pole mounted in overhead lines (Fig. 1). 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. Power Circuit

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

Fig. 2), with two primary windings and a secondary serial compensation winding. In addition,

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

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

the windings (see Table I). The selection of the adequate compensation step is performed by a

microprocessor-based control unit. The primary windings of the transformer P1 and P2 have the

same number of turns , and they are connected to the input voltage with contactor C1. The

primary windings can be parallel or series connected using contactor C2, so the effective number

of turns can be or 2 respectively. Each connection determines a certain voltage ratio, as indicated

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

can be series connected with the distribution network or bypassed using contactorC1. Finally, the

polarity of the magnetic coupling is set by contactor C3. The output voltage is then increased or

decreased depending on contactor C3. The output voltage can be formulated as the input voltage

plus the compensation voltage set by the regulator (1). 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:

— is the number of turns of windings P1 or P2;

— is the number of turns of winding S;

— is the connection constant, which can be 1 or 2 for parallel

and series connection respectively of P1 and P2. In 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 I. 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. Hence, 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. Given the design of the voltage regulator, the rated power of the

transformer is lower than the power that the voltage regulator can supply (2). The power

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

the transformer of a voltage regulator with 40-V compensation and 230-V rated voltage, will

have a rated power of 17% the maximum load that the voltage regulator can supply

B. Control System

The objective 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. In this situation, the device will be automatically

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

that consists of three modules (Fig. 3).

—The Measure Module registers voltage and current at the voltage regulator output. Every 32

cycles, average RMS voltage values are calculated, and these are used to decide if voltage

compensation is needed. For the sake of security, if the voltage exceeds the security range ( , )

the voltage regulator will be disconnected from the network.

—The Comparison Module compares the average value of a set of output voltage values with the

reference voltage range ( , ), and decides if a new compensation step is required.

—The Compensation Module receives a step-change order from the Comparison Module and

opens or closes the three contactors to achieve a new compensation step in the voltage regulator.

A voltage compensation example is presented in Fig. 4, using a voltage regulator with a 40-V

secondary, and two 230-V primary windings. The reference voltage values, and , are in dash

lines, and the solid lines represent the theoretical relationship between the input and output

voltages for different compensation steps. In the example the initial voltage at the output is 220

V at point A, which is within the reference voltage range. Voltage suddenly decreases to 190 V

(point B). Then, the

voltage regulator corrects the voltage with two maneuvers, using steps 4 and 5 (path B-C-D).

II. DESIGN AND CONSTRUCTION: PRACTICAL CONSIDERATIONS

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

A. Transformer Design

A 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. A software tool has been developed to analyze the costs of different

transformer column designs. This tool analyzes the active material cost and the energy losses

cost of the transformer [11]. The cost analysis for a 230/40-V transformer is shown in Fig. 5,

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

calculation assumes the following prices: the steel lamination cost is Euros 3/kg, the copper cost

is Euros 8.5/kg, and the energy losses for 60 000 hours at Euros 0.1/kWh. Given the results in

Fig. 5, the optimal transformer design has a column length of 93 mm. For this design, total

transformer costs are Euros 588.52, which can be split into Euros 492.62 for energy losses and

Euros 95.9 for active material cost. A detailed electro-magnetic analysis for the selected length

of the 230/40-V transformer has been performed with ANSOFT’s

Maxwell Software [12]. This analysis corresponds to the operation at point D of the example

presented in Fig. 4, and voltages in the windings are shown in Fig. 6. The maximum flux density

distribution in the transformer for the voltage regulator is shown in Fig. 7. We observe that the

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

steel laminations.

B. Voltage Reference Range Definition

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

standards in each country. For instance, if voltage requirements at the load are 230 V

7%, the proposed settings for the voltage regulator will be

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

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

the compensation maneuvers. If 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.

B. Compensation Maneuvers Sequence

As 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 C1. Then, contactors C2 and C3 are opened or closed depending on the compensation

step needed. This operation is performed off-load, which minimizes possible transients and

extends the service life of contactors C2 and C3. And finally, C1 is closed, and a new

compensation step is obtained. Experimental results for the compensation maneuver are shown

in Fig. 8, which shows voltage in the coil of contactor C1, and voltage in the primary winding,.

C. Switching Control

The reliability and expected life of the voltage regulator is mainly determined by the power

contactor C1, which operates on-load. Unfavorable 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 C1.

—Two poles of contactor C1 are parallel connected to open the load current (see Fig. 1). The

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

—A capacitor is connected in the primary winding P1.

—The Compensation Module guarantees the switching of contactors to zero current crossing

[13].

D. Efficiency Test

The efficiency of a voltage regulator, whose technical data are enclosed in the Table II, 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. Adjustable loads at power factor 1 and power factor

0.8 have been used to

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

IV. Although the voltage regulator has 4.3% total energy losses, its efficiency at any load is

remarkable. Similarly noteworthy is the fact that, due to its 3 000 VA transformer, this voltage

regulator can manage apparent power at the output of up to 16 500 VA. In short, the voltage

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

REFERENCES

[1] “Voltage characteristics of electricity supplied by public distribution networks,” in Proc.

CENELEC, Brussels, Belgium, 2001.

[2] ANSI C84.1 American National Standard for Electric Power Systems and Equipment—

Voltage Ratings (60 Hz) American National Standards Institute, 2006.

[3] R. Malaman, J. Afonso, L. Lo Schiavo, A. Romero, C. Sepulveda, R. Vrolijk, and B.

Wharmby, Quality of Electricity Supply: Initial Benchmarking on Actual Levels, Standards and

Regulatory Strategies Council of European Energy Regulators (CEER), 2001.

[4] RD 1955/2000 de 1 de diciembre por el que se regulan las actividades de transporte,

distribución, comercialización, suministro y procedimientos de autorización de instalaciones de

energía eléctrica B.O.E., Dec. 27, 2000, Spain [Online]. Available: http://www.boe.es

[5] G. Salis and A. Safiagianni, “Economically optimization of a radial power network based on

voltage criterion,” Adv. Eng. Softw., vol. 22, no. 1, pp. 1–20, 1995.

[6] W. E. Kazibwe and M. H. Sendaula, Electric Power Quality Control Techniques. New York:

Van Nostrand Reinhold, 1993.

[7] D. H. Jang and G. H. Choe, “Step-up/down AC voltage regulator using transformer with tap

changer andPWMAC chopper,” IEEE Trans. Ind. Electron., vol. 45, no. 6, pp. 905–911, Dec.

1998.

[8] S. G. Peschel, A. Molden, and O. Tonello, “In-Line Buck/BoostVoltage Regulation Systems

and Apparatus,” U.S. Patent 5844402, Dec. 1998.

[9] B. Meyer, J. Serdyn, H. J. Beukes, and R. G. Stephen, “Stretching low-voltage electrification

networks by means of electronic voltage regulators,” in Proc. Power Engineering Society

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