Statcom Report of Elctrical

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    Chapter I

    INTRODUCTION

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    1. Introduction

    1.1. Introduction

    The modern power distribution network is constantly being faced with an

    ever-growing load demand. Distribution networks experience distinct change from a low

    to high load level everyday. Electric load growth and higher regional power transfers in a

    largely interconnected network becoming more complex and less secure power system

    operation. Power generation and transmission facilities are unable to meet these new

    demands.

    any loads at various distribution ends like domestic utilities !computers!

    process industries! ad"ustable speed drives! printers microprocessor based e#uipments etc.

    have become intolerant to voltage fluctuations! harmonic content and interruptions.

    $rowth of electronic loads has made the #uality of power supply a critical issue. There

    fore numerous problems have to be attended in monitoring the operation of such a

    system! like voltage fluctuations! power losses! etc. Power system engineers facing these

    challenges to operate the system in more a flexible.

    Electrical power losses in distribution systems correspond to about %&' of

    total losses in electric power systems. These electrical losses can be considerably reduced

    through the installation and control of reactive support e#uipments! such as capacitor

    banks! reducing reactive currents in distribution feeders and so on.

    (onventional solutions for solving distribution network problems! like

    tap-changing transformers to control the voltage along feeders are no longer viable!

    because the distribution network will be changed from a passive network into an active

    network and thus the voltage profile is not predictable any more. )ne of the most severe

    problems faced by distribution networks operators is voltage drop along distributionfeeders! which is caused by real and reactive power flow. *oltage control is a difficult

    task because voltages are strongly influenced by random load fluctuations.

    *oltage profile can be improved and power losses can be considerably

    reduced by installing (ustom Power Devices or (ontrollers at suitable location. These

    controllers which are also named Distribution +lexible ,( Transmission ystem D-

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    +,(T0 13 are a new generation of power electronics-based e#uipment aimed at

    enhancing the reliability and #uality of power flows in low-voltage distribution networks.

    (ustom power is formally defined as the employment of power electronic

    or static controllers in distribution systems rated up to /4 k* for the purpose of supplying

    a level of reliability or P5 that is needed by electric power customers who are sensitive to

    power variations. (ustom power devices or controllers 12-/3 include static switches!

    inverters! converters! in"ection transformers! master-control modules and energy-storage

    modules that have the ability to perform current-interruption and voltage-regulation

    functions with in a distribution system.

    (ustom Power Devices is classified into three categories by their structures such as

    Dynamic *oltage 6estorer D*60! Distribution T,T() DT,T()0 and olid-

    tate 7reaker 70. 8n the present paper D-T,T()! a member of (ustom power

    controllers family! is considered.

    The D-T,T() is a shunt-connected! solid-state switching power

    converter that provides flexible voltage control at the point of connection to the utility

    distribution feeder for power #uality P50 improvements and also exchanges both active

    and reactive power current0 193 with the distribution system by varying the amplitude

    and phase angle of the converter.

    ince this device is utili:ed in steady-state condition for long term!because of limited capacity of energy storage system! it cannot in"ect active power to the

    system for long term. Therefore! a suitable model for D-T,T() has been proposed

    in load flow program! which is applicable in large distribution systems.

    The effects of D-T,T() on voltage improvement at other nodes are considered and

    the optimum location of D-T,T() in the distribution network is determined.

    8n the proposed method D-T,T() is considered in modified load flow

    computations. +urther the optimal location is identified to place D-T,T() for the

    purpose of loss reduction and voltage improvement.

    ;oad flow is an important method for analysis! operation and planning

    studies of any power system in a steady-state condition. 8n this paper an efficient method

    for node and line identification utili:ed in load flow has been proposed.

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    The load flow method 1 , feeder is a conductor which connects the substation to the area where

    power is to be distributed .$enerally tappings are taken from the feeders! so that current

    remains same through out .The main consideration in the design of feeder is the current

    carrying capacity.

    b0 Distributor> , distributor is a conductor from which tappings are taken from supply to

    the consumers. ?hile designing the distributor! voltage drop along its length is the main

    consideration.

    c0 ervice main> , service main is generally a small cable which connects the distributor

    to the consumers terminals.

    The a.c.distribution system is classified in to Primary distribution system!

    econdary distribution system.

    Distribution substation>

    The distribution system is fed through distribution substation. Each

    substation normally serves its own load area! which is a subdivision of the area served by

    the distribution system. ,t the distribution substation the sub transmission voltage is

    reduced for general distribution throughout the area. The substation consists of one or

    more power transformers together with the necessary voltage regulating e#uipments!

    buses and switchgear. The substation designs are based on the consideration such as load

    density! high side voltage! low side voltage! reliability! voltage drop! cost and losses.

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    -;oads of power systems are divided into industrial! commercial and

    residential. ;arge industrial loads are served directly from the sub transmission network

    .mall industrial loads are served from the primary distribution network.

    (ommercial and residential loads consist largely of lighting! heating and

    cooling .These loads are independent of fre#uency and consume negligibly small amount

    of reactive power.

    The ratio of power utili:ed by the consumers of electric power to the

    power produced at generation stations must be high as possible. 8n other words the losses

    occurring in carrying electric power from the generator to the consumers must be kept at

    the minimum. These losses are called line losses or 826 losses in the line.

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    Distribution losses

    8t has been established that %&' of the total losses are occurring in the

    primary and secondary distribution system! while transmission and sub transmission lines

    account for only /&' of the total losses. There fore the primary and secondary

    distribution system must be properly planned to ensure losses within the acceptability

    limits.

    (a) Factors effecting distribution system losses

    +actors contributing to the increase in the line losses in the primary and

    secondary distribution system are +eeder length! 8nade#uate si:e of conductor! ;ocation

    of distribution transformer! Cse of over rated distribution transformers! ;ow voltages!

    ;ow power factor and Poor workman ship in fittings.

    (b) Methods for reduction of line losses

    The following methods are adopted for reduction of distribution system

    losses are (onstriction of new substation! 6einforcement of the feeder! 6eactive power

    compensation! A* distribution system! $rading of conductor! Csing shunt compensation

    techni#ues! +eeder reconfiguration and D$ unit placement.

    Distribution power losses can be considerably reduced by installing

    (ustom Power Devices or (ontrollers at suitable location. These controllers which are

    also named Distribution +lexible ,( Transmission ystem D-+,(T0 are a new

    generation of power electronics-based e#uipment aimed at enhancing the reliability and

    #uality of power flows in low-voltage distribution networks. 0. D-+,(T mean +,(T

    +lexible ,( Transmission ystems0 Aingorani! FF/0 that are diverted to distribution

    systems.

    1.3. oltage Im!ro"ement #echni$ues

    To improve the power #uality some devices need to be installed at a

    suitable locations. These devices are called custom power devices! which make sure that

    customers get pre specified #uality and reliability of supply the compensating devices

    compensate a load! i.e.! its power factor! unbalance conditions or improve the power

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    #uality of supplied voltage! etc. some of power #uality improvement techni#ues are given

    as below.

    1.3.1. Shunt %a!acitors

    6egulation of the power factor to increase the transmission capability and reduce

    transmission losses. hunt capacitors are primarily used to improve the power factor in

    transmission and distribution network! resulting in improved voltage regulation! reduced

    network losses! and efficient capacity utili:ation. .8mproved transmission voltage

    regulation can be obtained during heavy power transfer conditions when the system

    consumes a large amount of reactive power that must be replaced by compensation.

    ,t the line surge impedance loading level! the shunt capacitor would decrease the

    line losses by more than /&'.8n distribution and industrial systems! it is common to use

    shunt capacitors to compensate for the highly inductive loads! thus achieving reduced

    delivery system losses and network voltage drop.

    &enefits

    8mproved power factor

    6educed transmission losses

    8ncreased transmission capability

    .8mproved voltage control 8mproved power #uality

    'ther !!lication

    Aarmonic filters

    1.3.2. Shunt eactors

    The primary purpose of the shunt reactor is to compensate for capacitive charging

    voltage! a phenomenon getting prominent for increasing line voltage. ;ong high voltage

    transmission lines and relatively short cable lines since a power cable high capacitance

    to earth0 generate a large amount of reactive power during light power transfer conditions

    which must be absorbed by compensation. )therwise! the receiving terminals of the

    transmission lines will exhibit a voltage rise voltages ., better fine tuning of the reactive

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    power can be made by the use of a tap changer in the shunt reactor .8t can be possible to

    vary the reactive power between

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    These filters consist of capacitor banks with suitable tuning reactors and damping

    resistors. +or small and medium si:e loads! active filters! based on power electronic

    converters with high switching fre#uency! may be a more attractive solution.

    &enefits

    Eliminates harmonics

    8mproved power factor

    6educe transmission losses

    8ncreased transmission capability

    8mproved voltage control

    8mproved power factor

    'ther a!!lications

    hunt capacitors

    1.3.+. Static ar %om!ensator

    tatic var compensators are used in transmission and distribution network mainly

    providing dynamic voltage support in response to systems disturbances and balancing the

    reactive power demand of large and fluctuating industrial loads. , static var compensator

    is capable of both generating and absorbing variable reactive power continuously as

    opposed to discrete values of fixed and switched shunt capacitors or reactors.?ith continuously variable reactive power supply! the voltage at the svc bus may be

    maintained smoothly over a wide range of active power transfer or system loading

    conditions. This entails the reduction of network losses and prevention of ade#uate power

    #uality to the electric energy end users.

    tatic var compensators are mainly used to perform voltage and reactive power

    regulation. Aowever! when properly placed and controlled! tatic *ar (ompensators can

    also effectively counteract system oscillations. , tatic *ar (ompensator! in effect! has

    the ability to increase the damping factor typically by -2 ? per var installed0 on a

    bulky power system witch is experiencing power oscillators.

    tatic *ar (ompensator *(0 is used most fre#uently for compensation of

    disturbances generated by the Electrical ,rc +urnaces E,+0 with a well-designed tatic

    *ar (ompensator *(0! disturbances such as flicker from the E,+ are mitigated

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    +licker! the random. The random voltage variations can also be disturbing to other

    process e#uipment fed from the same grid. The proper mitigation of flicker is therefore a

    matter of power #uality improvement as well as an improvement to human environment.

    &enefits,

    8ncreased power transfer capability

    ,dditional flexibility in grid operation

    8mproved grid voltage stability

    8mproved grid voltage control

    8mproved power factor

    'ther a!!lications,

    Power oscillation damping

    Power #uality +licker itigation! *oltage! 7alancing0

    $rid voltage support

    1.3.-. S##%'M

    tatic (ompensator! when connected to the grid! can provide dynamic voltage

    support in response to system disturbances and balance the reactive power demand of

    large and fluctuating industrial loads. , tatic (ompensator is capable of both generating

    and absorbing variable reactive power continuously as opposed to discrete values of fixed

    and switched shunt capacitors or reactors. ?ith continuously variable reactive power

    supply! the voltage at the tatic (ompensator bus may be maintained smoothly over a

    wide range of system operation conditions .This entails reduction of network losses and

    provision of sufficient power #uality to the electric energy end- users.

    tatic (ompensator uses voltage source converters to improve furnace

    productivity similar to a traditional tatic *ar (ompensator while offering superior

    voltage flicker mitigation due to fast response time. imilar to tatic *ar (ompensator!

    the tatic (ompensator can elegantly be used to restore voltage and current balance in the

    grid! and to mitigate voltage fluctuations generated by the traction loads.

    &enefits

    8ncreased power transfer capability

    ,dditional flexibility in grid operation

    8mproved grid voltage stability

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    8mproved grid voltage control

    8mproved power factor

    Eliminated flicker

    Aarmonic filtering

    *oltage balancing

    Power factor correction

    +urnaceBmill process productivity improvement

    'ther !!lications

    Power #uality+licker mitigation! *oltage balancing0

    $rid voltage support

    1.3.. Dynamic "oltage estorer

    8t is a series compensating device. 8t is used for protecting a sensitive load that is

    connected downstream from sagBswell etc. 8t can also regulate the bus voltage at the load

    terminal.

    1.3./. Static %urrent 0imiter (S%0)

    8t limits a fault current by #uickly inserting a series inductance in the fault path.

    1.3.. Static %ircuit &reaer

    8t breaks a faulted circuit much faster than a mechanical circuit breaker.

    1.3.1. Static #ransfer S4itch (S#S)

    8t is connected in the bus tie position when a sensitive load is supplied between

    two feeders. 8t protects the load by #uickly transferring it from the faulty feeder from the

    healthy feeder.

    1.3.11. 5nified Po4er 6uality %onditioner (5P6%)

    This device! like the Cnified Power +low (ontroller CP+(0 consists of two

    voltage inverters. The capabilities of this device are still unexplored .Aowever it can

    simultaneously perform the tasks of Distribution tatic (ompensator and Dynamic

    *oltage 6estorer.

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    1.*. 0iterature Sur"ey

    +rom literature there exist several control strategies which are usually

    based on mathematical approach. Plenty of work has been dedicated to applying the

    mathematical optimi:ation techni#ues for system planning. 7efore the emergence of

    +,(T devices! early research on planning reactive power compensation has employed

    linear programming 1F3! discrete programming 1&3! parameter sensitivity 13! nonlinear

    programming 123! etc. o far! with the development of computer technology and

    optimi:ation theory! more and more sophisticated models recently have been established

    for +,(T devices allocation problems.

    , method of applying shunt capacitors for voltage control and peak loss

    reduction is discussed 1/3. The concept is extended to the optimi:ation of total monetary

    savings due to both peak loss and energy loss reductions. , computer program is

    developed to aid engineers in the application of such a method. 8n 193! a successful

    attempt was made to solve the problem using the dynamic programming approach. This

    optimi:ation techni#ue has eliminated the previously mentioned problems of optimum

    number and standard bank si:e. The method! however! was capable of dealing with the

    fixed type of capacitors only.8n 1

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    The D-T,T() distribution static compensator0 with fast response is

    an effective solution for improving the power #uality of distribution systems. The

    dynamic compensation of D-T,T() in &B&.9 k* distribution system is simulated

    with atlab! which proves the superiority and feasibility of D-T,T().

    8t is also #uite interesting to note that the 7harat Aeavy Electric ;imited

    7AE;0! 8ndia was successful in developing distribution scale T,T() also known as

    D-T,T() which has successfully been installed in industry. The worlds first

    commercial T,T() J4& *,!

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    1.+. Sco!e of the Pro7ect

    8n this pro"ect! the structure and principle of operation! implementation of

    Distribution tatic ynchronous (ompensator are discussed. ,nd the Proposed method

    for modeling D-T,T() is considered in modified load flow computations. +urther

    the optimal location is identified to place D-T,T() for the purpose of loss reduction

    and voltage improvement and program is done.

    uch device is employed to provide continuous voltage regulation using controlled

    converter. The advantage of this type of compensator over conventional *(Ls is the

    improved speed of response. This speed of response means that such a device is ideally

    suited to application with a rapidly varying load.

    Two standard distribution systems consisting of 8EEE-< and 8EEE-2F

    buses are considered and the D-T,T() model is applied to load flow and

    corresponding results are also presented and are compared.

    .

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    solid state current limiter (;0! solid state breaker 70! and solid

    state transfer switch T0. The compensating devices compensate a load! i.e. its power

    factor! unbalance conditions or improve the power #uality of supplied voltage! etc. These

    devices are either connected in shunt or in series or a combination of both. This class of

    devices includes the distribution static compensator D-T,T()0! dynamic voltagerestorer D*60! and unified power #uality conditioner CP5(0 123. ,mong compensating

    devices! a Dynamic *oltage 6estorer can deal with voltage sags and swells which are

    considered to have a severe impact on manufacturing places such as semiconductors and

    plastic products! food processing places and paper mills.

    (ustom Power Devices is classified into three categories by their

    structures such as Dynamic *oltage 6estorer D*60! Distribution T,T()

    DT,T()0 and olid-tate 7reaker 70. Two of the devices DT,T() and the

    D*6 share a similar architecture. 7oth are based on the voltage source converter. D*6 is

    connected in series with the line where as DT,T() is in shunt with the line across

    the load. ,mong these devices! the main purpose of D*6 that in"ects voltage in series

    with a distribution feeder is reducing the effect of short-term voltage sags! dips! swells

    and momentary interruptions.

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    The proposed system has a function of generating and absorbing voltage

    by self-charging control techni#ue. This system has three states> 0 normal operation! 20

    charging operation and /0 recharging operation. The paper discusses control issues and

    the proposed control algorithm. The proposed control techni#ue is applied to

    DT,T() for protecting voltage sags! swell and momentary interruption.

    2.3. Family %ustom Po4er De"ices, 8

    The family of emerging power electronic devices being offered to achieve

    these (ustom Power 12-/3 ob"ectives includes>

    (a) Distribution Static %om!ensator (D8S##%'M) to protect the distribution system

    from the effects of a polluting! e.g. fluctuating! voltage sags! swells! transients or

    harmonics non-linear harmonics producing0! and load.

    (b) Dynamic oltage estorer (D) to protect a critical load from disturbances! e.g.

    sags! swells! transients or harmonics! originating on the interconnected transmission or

    distribution system.

    (c) Solid8State &reaer (SS&) to provide power #uality improvement through

    instantaneous current interruption thereby protecting sensitive loads from disturbances

    that conventional electromechanical breaker cannot eliminate.

    (d) Solid8State #ransfer S4itch (SS#S) to instantaneously transfer sensitive loads froma disturbance on the normal feed to the undisturbed alternate feed.

    2.3.1. Distribution Static %om!ensator (D8S##%'M)

    The D-T,T() is a solid-state dc to ac switching power converter that

    consists of a three-phase! voltage-source forced air-cooled inverter. 8n its basic form! the

    D-T,T() in"ects a voltage in phase with the system voltage! thus providing voltage

    support and regulation of *,6 flow.

    The D-T,T() can also be used to reduce the level of harmonics on a

    line. 7ecause the D-T,T() continuously checks the line waveform with respect to a

    reference ,( signal! it always provides the correct amount of harmonic compensation.

    7y a similar argument! the D-T,T() is also suitable for reducing the impact of

    voltage transients. The amount of load that can be supported is determined by the *,

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    rating of the inverters! and the length of time that the load can be maintained by the

    amount of energy storage provided.

    The D-T,T() is available in ratings from 2 to & *, in modular 2-

    *, increments. These are similar in performance to *(. Csing only capacitors or

    inductors or batteries! these devices can draw B supply both leading and lagging currents.

    They have a very good response time and are more suitable for special industrial loads

    like arc furnaces.

    2.3.2. #he Dynamic oltage estorer (D)

    The D*6 is a solid-state dc to ac switching power converter that in"ects a

    set of three single-phase ac output voltages in series with the distribution feeder and in

    synchronism with the voltages of the distribution system. 7y in"ecting voltages of

    controllable amplitude! phase angle and fre#uency harmonic0 into the distribution feeder

    in instantaneous real time via a series in"ection transformer! the D*6 can MrestoreM the

    utility of voltage at its load-side terminals when the #uality of the source-side terminal

    voltage is significantly out of specification for sensitive load e#uipment. The reactive

    power exchanged between the D*6 and the distribution system is internally generated by

    the D*6 without any ac passive reactive components! i.e. reactors and capacitors. +or

    large variations deep sags0 in the source voltage! the D*6 supplies partial power to theload from a rechargeable energy source attached to the D*6 dc terminal. The D*6 is

    available in ratings from 2 to & *, in modular 2-*, increments.

    The D*6 is capable of generating and absorbing the voltage

    independently controllable real and reactive power. 8t consists of three-phase voltage

    source inverter! in"ection transformer! D( ;8GN and 6ectifier for charging the D( ;8GN

    or 7attery. ,s you know! 6ectifier is generating the harmonic problem in distribution

    lines. 6ectifier or devices for charging D( ;8GN is useless in this proposed system by

    their structure.

    2.3.3. Solid8State 9Instantaneous9 %urrent Interru!tion

    (urrent interruption technology! utili:ing high power olid-tate

    7reakers 70! to solve most of the distribution system problems that result in voltage

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    sags! swells! and power outages. ?hen combined with a current limiting reactor or

    resistor! the 7 can rapidly insert the current limiting device into the distribution line to

    prevent excessive fault current from developing from sources of high short circuit

    capacity! e.g. multi-sourced distribution substations. ,t the power levels associated with

    a solid-state

    switch composed of $T)s and a solid-state switch using (6s in series with a current

    limiting reactor or resistor. The $T) switch is the main circuit breaker used to clear

    source-side faults. 8t is rated for the maximum normal line current! but not rated for fault

    currents. 8t is normally closed and conducts current uninhibited until the magnitude of the

    current reaches a pre-set level at which point it opens rapidly interrupting the current

    flow.

    2.3.*. Solid8State 9Instantaneous9 0oad #ransfer

    8ntroducing a line of olid-tate Transfer witches capable of providing

    uninterruptible power to critical distribution-served customers. olid-state! fast acting

    sub-cycle0 breakers can instantaneously transfer sensitive loads from a normal supply

    that experiences a disturbance to an alternate supply that is unaffected by the disturbance.The alternate supply may be another utility primary distribution feeder or a standby

    power supply operated from an integral energy storage system. 8n this application! the

    7 acts as an extremely fast conventional transfer switch that allows the restoration of

    power of specified #uality to the load within B9 cycle.

    The T consists of two three-phase 7@s! each with independent

    control. The status of the three individual phase switches in each 7 will be individually

    monitored! evaluated! and reported by continuous real-time switch control and

    protections circuits. The operation of the two 7@s will be co-ordinates by the transfer

    switch control circuit that monitors the line conditions of the normal and alternate power

    sources and initiates the load transfer in accordance with operator selectable criteria.

    The T can be provided with either (6 or $T) switches depending

    upon the specific load transfer speed re#uirements. T voltage and current ratings are

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    being developed for 9.= to /9.< k* and /&& to 2&& ystem protection practices are

    accommodated in the T available control modes depending upon the critical load

    re#uirements and utility preferencesBpractices.

    8n this pro"ect report D-T,T()! a member of (ustom power

    controllers family! is considered.

    2.9 Distribution T,T()

    2.*.1. Introduction

    Distribution T,T() D-T,T()0 is utili:ed to compensate power

    #uality problems and also it can #uickly regulate its susceptance to provide dynamic

    reactive compensation and regulate the bus voltages in the power system.The D-T,T() is a shunt-connected! solid-state switching power

    converter that provides flexible voltage control at the point of connection to the utility

    distribution feeder for power #uality P50 improvements such as unbalanced load!

    voltage sag! voltage fluctuation and voltage unbalance and also exchanges both active

    and reactive power current0 1=3 with the distribution system by varying the amplitude

    and phase angle of the converter.

    2.*.2. oltage source con"erters (S%)

    , voltage-source converter is a power electronic device! which can

    generate a sinusoidal voltage with any re#uired magnitude! fre#uency and phase angle.

    *oltage source converters are widely used in ad"ustable-speed drives! but can also be

    used to mitigate voltage dips. The *( is used to either completely replace the voltage or

    to in"ect the Omissing voltageL. The Omissing voltageL is the difference between the

    nominal voltage and the actual. The converter is normally based on some kind of energy

    storage! which will supply the converter with a D( voltage. The solid-state electronics in

    the converter is then switched to get the desired output voltage. Gormally the *( is not

    only used for voltage dip mitigation! but also for other power #uality issues! e.g. flicker

    and harmonics.

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    *oltage source converters are of two typeLs vi:. series voltage controller and

    shunt voltage controller. Aowever D-T,T() belongs to the shunt voltage controller.

    8n this pro"ect! the D-T,T() is used to regulate voltage at the connecting bus.

    2.*.3. Structure and Princi!le of '!eration

    (a) Structure

    $eneral structure of D-T,T() is similar to T,T()! which is

    schematically shown in fig.! consists of energy storage device! voltage source converter!

    a coupling transformer connected in shunt to the distribution network through a coupling

    transformer.

    Fig 2.1, chematic diagram of a D-T,T()

    Csing a converter! the devices appear as fully synchronous sources which

    are capable of absorbing and in"ecting reactive power on an electricity system at

    distribution voltages.

    8n this model! D-T,T() is capable of in"ecting active power in

    addition to reactive power. ince this device is utili:ed in steady-state condition for long

    term! because of limited capacity of energy storage system! it cannot in"ect active power

    to the system for long term for voltage regulation purpose.

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    Therefore! for the steady-state application! D-T,T() consists of a

    small D( capacitor and a voltage source converter and the steady-state power exchange

    between D-T,T() and the ac system is reactive power.

    7ut! there are several factors that must be considered when designing the

    D-T,T() and associated control circuits. 8n relation to the power circuit the

    following issues are of ma"or importance>

    D( link capacitor si:e

    (oupling transformer reactance and transformation ratio

    )utput filters e#uipment

    Fig 2.2, chematic diagram of a D-T,T()! only reactive power exchange.

    The *( connected in shunt with the ac system provides a multifunctional

    topology which can be used for up to three #uite distinct purposes>

    . *oltage regulation and compensation of reactive power

    2. (orrection of power factor and

    /. Elimination of current harmonics.

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    Q ending and receiving bus voltages

    Q Power angles between two buses

    Q eries impedances of the transmission line connecting the two buses.

    (onsider a single line diagram of two buses of a radial distribution system

    as shown in +ig./.! the number of branches nb and the number of buses t are related

    through t R nbS.

    *k *

    8;iP;kS"5;k P;S"5;

    Fig 3.1, ingle line diagram of two buses of a distribution system.

    ?here 6 and K are resistance and reactance of the branch. P;k and 5;k are the

    active and reactive powers of node k. 8;i is the current flowing in the line. ubscript O;L in

    P; and Q; refers to the load connected at th

    bus.

    8nitially! a flat voltage p.u0 of all the nodes is assumed and load currents and

    charging currents of all the loads are computed using E#s. /.0 and /.20 respectively.

    The load current of node k is

    ILk.k0 =

    PLk

    k 0 j QLk

    k 0