Guide for electrical design engineers - Chapter 5 : Mitigation of voltage unbalance

8/14/2019 Guide for electrical design engineers - Chapter 5 : Mitigation of voltage unbalance

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Guide for electrical design engineers

Zbigniew HanzelkaAGH-University of Science & Technology

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rQuality

Power Quality

Mitigation of voltage unbalance

U12

U23

U31

U2

U3

U1

I23=IC

I31=IL

I12

I1=I12-I31

I2=I23-I12

I3=I31-I23


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http://www.leonardo-energy.org

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1. Introduction

When the limit values o unbalance actor, specifed in standards are exceeded, the use o symmetrizatin systems

is required. A symmetrizator should not cause signifcant active power losses during operation; it implies that the

symmetrization process shall be carried out by means o reactive elements (LC) or using active methods (power

electronic systems).

2. Symmetrization of the load currents

The urther analysis, using the method o symmetrical components, concerns the system node in the confguration

as in Figure 1. An asymmetrical load (A), symmetrical load (S) and compensator (K) are connected to substation bus-

bars o phase voltage U, supplied rom three-phase symmetrical system.

AI 3AI 1

KI 3KI 1

3E

1E

3U

2U

1U

COMPENSATOR

(K)

SYMETRIC

LOAD

(S)

ASYMETRIC

LOAD (A)

1I

3I

2E

Fig. 1. Diagram of the analysed node

Since the system o electromotive orces (E) and the supply line are symmetrical, it is assumed that the voltage

unbalance at the load terminals is caused by the asymmetry o the load currents. It means that, i the asymmetry

o the load currents is eliminated, the voltages at the point o the load connection orm the symmetrical three-phase

system. This is the case o the supply system protection, and the loads connected to it, against the asymmetry caused

by asymmetrical currents o the load (A) and resulting asymmetrical voltage drops across the equivalent impedances

o supply system (on assumption identical in all phases: Z Z Z 1 2 3= = ).

An obvious conclusion rom Figure 1 is that the voltage unbalance at PCC, caused by the load asymmetry, can be mitigated

by reduction o the phase equivalent impedances (short-circuit impedances) i.e. by increasing the short-circuit capacity at

the point o load connection, what in practice means connecting the load to the point o the system o higher voltage.

3. The natural symmetrization The frst and the most basic operation o the symmetrization process is the arrangement o the actual load

connections between the system phases, in such a way that the current unbalance actor (and hence the voltage

unbalance actor) was the smallest possible value. In case o connecting a single load to the network, the level

o unbalance (measured by the current unbalance actor or zero- or negative-sequence component) does not depend

on phase-to-phase or phase-to-neutral voltage, where the load is connected. Similarly, when connecting two single-

element loads, the level o unbalance does not depend on which voltages the loads are connected. However, when

these loads will have a dierent character then, in terms o the natural symmetrization (i.e. the symmetrization,

which does not require any additional elements), it is important to take into account the character o the loads and

phase angles o the voltages they are connected to.


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EXAMPLE 1

For the system of three loads on nominal voltage 380 V and powers, respectively: P1

= 7.22 kW, Q1

= 7.22 kVAR (ind.);

P2

= 7.22 kW, Q2

= 7.22 kVAR (cap.); P3

= 7.22 kW, Q3

= 0 delta-connected, supplied from three-phase 3x380/220V

network, determine the arrangement of their connections to the network phases, ensuring minimum value of the

current unbalance factor.________________________

From the load active and reactive power the elements of its equivalent admittance can be determined, i.e.: the

susceptance (B =Q

U2) and conductance (G =

P

U2) (Fig. 2).

GB

Load

(P, Q) U NUN

Y

Fig. 2. The load (P - active power, Q - reactive power) and its equivalent admittance

Hence:

Y G jBP

Uj

Q

U

kW

Vj

kVAR

VA A A1 1 1

1

2

1

2 2 2

7 22

380

7 22

3800= + = = =

.

( )

.

( )( .005 0 05j S. )

Y G jBP

Uj

Q

U

kW

Vj

kVAR

VA A A2 2 2

2

2

2

2 2 2

7 22

380

7 22

3800= + = + = + =

.

( )

.

( )( .005 0 05+j S. )

Y G jB PU

jQU

kWV

j kVARV

SA A A3 3 33

2

3

2 2 27 22

380

0

3800 1= + = + = + =.

( ) ( ).

Variant 1 Loads connected as in Fig. 3:

Y YA A12 1=

Y YA A23 2=

Y YA A31 3=

Fig. 3. Variant 1 of load connection

The current unbalance factor: kI

I

a Y Y aY

Y Y YI

A A A

A A A

%

( )

( )% % . %= =

+ +

+ +=

2

1

212 23 31

12 23 31

100 100 68 3

a j j= = +exp( )120 12

32

0

a j j2 0120 12

32

= = exp( )

1

2

3

AY12

AY23

AY31

AI1

AI2

AI3

AI 31

AI23


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0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

-400

-300

-200

-100

0

100

200

300

400 Three-wire network voltages

Time [s]

Voltages[V

]

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

-40

-30

-20

-10

0

10

20

30

40

Three-wire network currents

Time [s]

Currents[A]

Fig. 4. Voltage waveforms: Example 1 Variant 1 Fig. 5. Current waveforms: Example 1 Variant 1

See Figures 4 and 5.

Variant II - Y YA A12 1=

Y YA A23 3=

Y YA A31 2=

The current unbalance actor: kI

I

a Y Y aY

Y Y YI

A A A

A A A

%

( )

( )% % . %= =

+ +

+ +=

2

1

2

12 23 31

12 23 31

100 100 18 3

This is the minimal value o the current unbalance actor, which can be obtained connecting the impedances

to phase-to-phase voltages in various confgurations. This confguration has been taken or urther considerations (Fig. 6).

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

-40

-30

-20

-10

0

10

20

30

40

Three-wire network currents

Time [s]

Currents[A]

Fig. 6. Waveforms of currents: Example 1 Variant 2

In cases, where the negative component cannot be su ciently reduced solely by means o the more uniorm

distribution o the loads between phases, compensators are used. The purpose o the compensation systems is usually

the elimination or mitigation o the negative- and zero-sequence component o currents at the point o connection

o asymmetric load. Such process is called symmetrization.

4. Compensator/symmetrizator

In the three wire MV systems, usually operated as the isolated neutral point or compensated systems, asymmetrical

loads are connected on phase-to-phase voltages. In such case, there is no zero-sequence component o currents,

thereore the symmetrization resolves into elimination or mitigation o the negative-sequence component. The

LV systems are typically our-wire networks, with grounded neutral point, thus the negative-sequence and zero-

sequence components are present. The symmetrizator (K) is connected in parallel to the asymmetric load (A) (Fig. 1).

The symmetrizator causes the currents I1K

, I2K

, I3K

, which adding to the load currents I1A

, I2A

, I3A

, result in the balanced

system o the source currents I1, I

2, I

3, according to the equation:

I I IA K1 1 1= + I I I a I A K2 2 22

1= + = I I I aI A K3 3 3 1= + = (7)

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As the currents drawn rom the network orm a balanced system, thereore the negative-sequence and zero-sequence

components are equal zero:

I I aI a I ( ) ( )2 1 22

3

1

3

0= + + = I I I I ( ) ( )0 1 2 31

3

0= + + = (8)

The load to be balanced can be represented in general as a circuit o six elements in the star/delta connection (Fig. 4),

where individual elements are connected to phase-to-neutral, as well as to phase-to-phase voltages. The impedances

Z Z Z Z Z Z A A A A A A12 23 31 1 2 3, , , (or admittances Y Y Y Y Y Y A A A A A A12 23 31 1 2 3, , , ), which in the diagram represent the actual

load, can be unctions o time.

)( 1212 AAYZ

)( 21 AAYZ

)( 2323 AA YZ )( 22 AA YZ

)( 3131 AA YZ )( 33 AA YZ

1 3 02

Fig. 4. General diagram of the three-phase unbalanced load

To establish the rules o compensation and symmetrization, the values o specifed impedances should be assumed

constant, and generally dierent rom each other. This does not exclude considerations on their variability in time.These impedances can be regarded as a representation o the time-varying load, but only in the specifc, selected

instants o time the sampling instants. The set o such constant values o impedances represents the load at discrete

instants o time.

The compensation o asymmetric load will be understood as the compensation o reactive part o the positive-

sequence symmetrical component (reactive power compensation or the undamental requency) and o the zero-

sequence component (or three-phase, our-wire systems) and negative-sequence component or the undamental

requency. Among various possible methods, the inductive-capacitive systems are o particular importance. Their

practical applications are certain solutions o static ollow-up compensators.

5. The compensator/symmetrizator parameters

The symmetrization and compensation o the undamental harmonic reactive current is a process, which in practice

consists in connecting in parallel to the asymmetric load the asymmetric reactive elements (reactors, capacitors)

o such values as to ulfl the conditions (9):

I IA K( ) ( )2 2 0+ = I IA K

( ) ( )0 0 0+ = Im ( ) ( )I I IA K1 1

0+ = (9)

where: I I IA A A( ) ( ) ( ), ,0 1 2 , I I IK K K

( ) ( ) ( ), ,0 1 2 are symmetrical components o the asymmetric load and compensator (index (K))

currents, respectively or the zero- (0), positive- (1) and negative-sequence component; Im ( )IA1 denotes the reactive

part o the positive-sequence o the load current component (imaginary part in complex numbers notation); I0

is the value o reactive current, which is the measure o the load non-compensating level permitted in the supply

conditions by electrical power supplier. Thus, according to the presented notation, the processes o the reactive

current compensation and symmetrization (or the zero-sequence and negative-sequence component) have been

separated.



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For the load as in Fig. 4, the relations, describing the values o the negative- and zero-sequence symmetrical

components can be written as ollows (according to (8)):

I U Y aY a Y a Y Y aY A A A A A A A( )2

1 22

32

12 23 31

1

3= + +( ) + +( )

(10a)

IU

Y a Y aY A A A A( )0

12

2 33= + +( ) (10b)

I the expressions (10) are not identically equal zero, and the asymmetry level is inadmissibly high, the load symmetrization

is needed and can be made by connecting a symmetrization-compensating device with elements B B BK K K1 2 3, , connected

to the phase-to-neutral voltages and B B BK K K12 23 31, , connected to the phase-to-phase voltages. The problem resolves into

fnding the compensating susceptances, which in connection with the admittances to be compensated will constitute

a symmetric load. The relations, where the parameters o symmetrizator/compensator are expressed as a unction

o the equivalent impedances (admittances) o the load to be compensated/symmetrized, will be presented urther in

this paper. This is particularly useul when designing a symmetrizator. The symmetrizator parameters can be expressed

as a unction o other quantities, which describe a compensated load, i.e.: the current symmetrical components, values

o phase currents or powers, instantaneous values o phase voltages and currents, etc.

6. Symmetrization of a star-connected load with neutral conductor elimination of the zero-sequence symmetrical component

In this case the process o compensation comprises o two stages. The frst one concerns the elimination o the

zero-sequence symmetrical component elimination o the current in neutral conductor. The confguration in Fig. 5

has been taken or urther considerations; it is distinguished by the minimum value o the current unbalance actor

(the values o elements as in the EXAMPLE 1).

AY

1

1

AY

2

2

AY

3

3

NI

AI1

AI2

AI3

Fig. 5. Three-phase four-wire network - star-connected load

EXAMPLE 2

U V1 220= U a V2 2 220= U a V3 220=

I U Y j j AA A1 1 2 220 0 05 0 05 11 11= = + = +( . , ) ( )

I U Y j AA A2 2 1 15 026 4 026= = ( . . )

I U Y j AA A3 3 3 11 19 052= = ( . )

The current in neutral conductor: I I I I I j AN A A A= = + + = 3 15 026 26 0260

1 2 3( ) ( . . )

where I

( )0

is the current zero-sequence symmetrical component. The negative-sequence symmetrical component:

I I a I aI j AA A A A( ) ( ) ( . . )2 1

22 3

1

31 342 2 325= + + = +

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The positive-sequence symmetrical component: I I aI a I AA A A A( ) ( ) .1 1 2

23

1

314 667= + + =

The current unbalance actor: k

I

II

A

A%

( )

( ) % %= =

2

1 100 50

AY

1

1

AY

2

2

AY

3

3

NI

AI1

AI

2

3I

KB1 KB 2

1I

2I

AI

3

Fig. 6. The elimination of the zero-sequence component (EXAMPLE 2)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

-40

-20

0

20

40Supply network c urrents

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-40

-20

0

20

40current in neutral conductor

[A]

[A]

[s]

[s]

0 0. 01 0. 02 0. 03 0. 04 0. 05 0. 06 0. 07 0. 08 0. 09 0. 1-40

-20

0

20

40Supply network c urrents

0 0. 01 0. 02 0. 03 0. 04 0. 05 0. 06 0. 07 0. 08 0. 09 0. 1-0.02

-0.01

0

0.01

0.02current in neutral conductor

[A]

[A]

[s]

[s]

Fig. 7. Waveforms of currents: EXAMPLE 2 before Fig. 8. Waveforms of currents: EXAMPLE 2 after

the elimination of zero-sequence component the elimination of zero-sequence component

The elimination o the current zero-sequence component is perormed by means o the two-element symmetrizator

in the example confguration as in Fig. 6.

Supply network currents:

I U Y jBA K1 1 2 1= +( ) I U Y jBA K2 2 1 2= +( ) I U Y A3 3 3=

The condition or the current in neutral conductor to become zero takes orm:

I I I1 2 3 0+ + =

Hence:

Reactive part o neutral current: Im( I I I1 2 3 0+ + =) and

Active part o neutral current: Re( I I I1 2 3 0+ + =)Substituting the numerical values:

0.05 - 0.0683 + 0.866B2K

- 0.05 = 0 and 0.05 + B1K

0.0183 0.5B2K

+ 0.0866 = 0



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Hence: B SK1 0 0789= . B SK2 0 0789= .

Y Y jB j SA K1 2 1 0 05 0 0289= + = ( . . )

Y Y jB j SK2 1 2 0 05 0 0289= + = +( . . )

Y Y jB SK3 3 3 0 1= + = .I U Y j j A1 1 1 220 0 005 0 0289 11 6 358= = = ( . . ) ( . )

I U Y j A2 2 2 0 006 12 705= = ( . . )

I U Y j A3 3 3 11 19 052= = + ( . )

I I I1 2 3 0+ +

The current zero-sequence component has been eliminated (Fig. 8).

7. Symmetrization a three-wire load

7.1. Symmetrization of a delta-connected load

B BG G

B B BG G

B G

K AA A

AA A

K A

12 1223 31

0 12 031 23

23 12

3 3 3

3

= + + + = + +

= + BB G B B B G G

BG G

B

A A A A A

KA A

A

23 31 0 23 0 31 23

3112 23

31

3 3

3 3

+ + = + +

= + + + BB B BG G

AA A

0 31 031 23

3= + +

In practice, the susceptances o a static compensator perorm both processes simultaneously, that meanssymmetrization and reactive current compensation and then the resulting values o the susceptance are defned

by (11), where B0

represents the permissible level o non-compensation. As it results rom (11), the three susceptances

that are necessary or reactive current compensation and symmetrization can be expressed through real and

imaginary components o the load admittance. The frst elements o the right side o the relation (11) represent

the components o the compensation susceptances, necessary or the compensation o the imaginary part o the

adequate load admittance. The second element represents the components o the compensator that are necessary

or the symmetrization o the real parts o the load admittance. These relations clearly indicate that the process

o compensation can also be treated as an activity concerning each o the interphase load admittances separately.

E.g. or the load Y12A

compensation o the imaginary part is achieved through parallel connection o a susceptance (-B12

)

ollowed by symmetrization o the remaining part o such a single interphase load by connecting the symmetrizing

susceptances respectively: (G12A/ 3 ) or the voltage U12 and (-G12A/ 3 ) or the voltage U31. The compensation processo such a load with its indication diagrams has been presented in Fig. 9. For a symmetric system o supply voltages

o positive sequence, such a circuit is equivalent to three star-connected resistors, each o them having a conductance

G12

.

compensationand symmetrization

o the admittanceY

23A

compensationo the reactive part othe load admittances


o the admittanceY

12A


o the admittanceY

31A

symmetrization o the load

(11)

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The above considerations illustrate the well known Steinmetz rule o symmetrization, according to which any single-

phase active load (or active-reactive one, ater its equivalent susceptance has been compensated), connected e.g.

between phases 1-2 (Fig. 9), can be symmetrized by means o reactive elements LCo such values, that the currents

ulfl the relations (12).

I I I A23 31 1213

= = (12)

The obtained relations (11) transorm any three-phase asymmetric load into the symmetric, resistive or resistive-

inductive load with a defned level o reactive current. For a symmetric system o supply voltages o positive sequences

the generated circuit is equivalent (or B0

= 0) to three, star connected resistors, each having a conductance value

G = G12A

+ G23A

+ G31A

.

The condition or the compensator elements selection can also be expressed as a unction o the phase reactive

powers o an asymmetric load:

Q Q Q Q Q Q QA K A K A K 1 1 2 2 3 3 0+ = + = + = (12)

Q1A

, Q2A

, Q3A

- the load phase reactive powers,

Q1K

, Q2K

, Q3K

- the compensator phase reactive powers,

Q0

- assumed non-compensating level.

For the compensator delta-connected elements, the interphase reactive powers can be determined with respect to

the load phase reactive powers, according to the relations:

Q Q Q Q Q

Q Q Q Q Q

Q Q Q Q

K A A A

K A A A

K A A A

12 1 2 3 0

23 1 2 3 0

31 1 2 3

= + +

=+ +

= + +QQ0

(13)

I3

I12

I23=IC

I2

I1

1

2

3

I31=IL

3

12G

C =

3

112

G

L

I3 = 0

I2

I1

1

2

3

I12G12

(a) (b)



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U12

U23

U31

U2

U3

U1

I23=IC

I31=IL

I12

I1=I12-I31

I2=I23-I12

I3=I31-I23

(c)

Fig. 9. (a) A single-phase system before the symmetrization;

(b) single-phase system with the symmetrizator;

(c) phasor diagram, which illustrates the process of symmetrization

EXAMPLE 3

For the loads confguration as in the EXAMPLE 1 Variant II, susceptances o the delta-connected symmetrizator/

compensator are:

B B G G SK A A A12 12 23 311

30 0211= =( ) .

B B G G SK A A A23 23 31 121

30= =( )

B B G G SK A A A31 31 12 231

30 0211= =( ) .

The sign + preceding the susceptance denotes its capacitive character, the sign - the inductive character.

The capacitance o the capacitor connected between phases 1-2 is determined rom the relation:

CB

f

S

HzFK

K12

12

2

0 0211

2 5067 2= =

..

The inductance o the reactor connected between phases 3-1 is determined rom the relation:

LfB Hz S

mHKK

3131

1

2

1

2 50 0 0211150= =

.

The load and compensator are shown in Fig. 10. Ater connecting the compensator/symmetrizator:

I I I j A j A1 12 31043 89 0 001 43 89 0* * * ( . . ) . exp( )= = +

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I I I j A j A2 23 12021 945 37 988 43 87 120* * * ( . . ) . exp( )= =

I I I j A j 3 31 23021 945 37 987 43 87 120* * * ( . . ) . exp( )= = +

The phase currents of supply network constitute the three-phase symmetrical system.

AI12

AY23

KB

23

AY12 K

B12

AY31 K

B31

1

2

3

*

1I

*

2I

*

3I I

*

31I

*

31

*

12I

AI23

AI31

Fig. 10. Delta-connected asymmetric load with the symmetrizator

0 0.01 0.02 0. 03 0.04 0.05 0.06 0.07 0. 08 0. 09 0.1-400

-300

-200

-100

0

100

200

300

400

Three-wire network voltages

Time [s]

Voltages[V]

0 0. 01 0.02 0.03 0.04 0.05 0. 06 0.07 0. 08 0.09 0. 1-80

-60

-40

-20

0

20

40

60

80 Three-wire network currents

Time [s]

Currents[A]

Fig. 11. Voltage and current waveforms (EXAMPLE 3)



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7.2. Star-connected asymmetrical load

The symmetrization o a star-connected load is analysed ater star-to-delta transormation. Further procedure o the

symmetrizator parameters selection is analogical as in section 7.1.

8. Static compensatorsReactive power static compensators are widely used in transmission and distribution systems, cooperating with

medium and large power, rapidly variable loads, which are the most disturbing or the electric power system. Static

compensators can perorm various tasks, such as compensation o the undamental component reactive power,

symmetrization and mitigation o voltage fuctuations (ficker). Also some active lters congurations have a capability

o symmetrization.

8.1. Static VAR compensators

The purpose o a compensator (with control and measuring system) is to measure adequate electric quantities

o the load and generate in the compensator such currents, that the resultant load: compensator compensated load,

as seen rom the supply network, was symmetrical, and the undamental harmonic reactive current drawn rom thenetwork did not exceed the value permitted in the supply conditions.

Generally, static compensators are the systems, which comprise reactors and/or capacitors controlled by means

o semiconductor circuits.

They can be treated as the values o susceptances, controlled according to the needs o compensation/symmetrization.

Thyristors in these systems are used as switches or phase-controlled elements. In practice various solutions

o compensators are applied. Among the most oten used compensators is the FC/TCR compensator with xed

capacitor and controlled (variable) reactor current.

8.1.1. Compensator/symmetrizator FC/TCR

So-called FC/TCR circuits are the most commonly used static VAr compensators/stabilizers in industry. They arecomposed o a Fixed Capacitor (FC) connected in parallel to a Thyristor-Controlled-Reactor (TCR). FC is most commonly

a passive lter, ltering the harmonic/harmonics o a load and/or o the TCR. This solution is an example o the indirect

compensation method in which the sum o the basic (1) TCR current harmonic ITCR(1)

and the load reactive current

IO(1)

is constant, and equals the FC current IFC(1)

(Fig. 12a). The TCR current waveorm or three sampled control

angles is shown in Figure 12b (single-phase circuit). The control angle (with respect to the positive voltage zero-

crossing) and the basic current harmonic o TCR can vary in each supply voltage hal-cycle, within the range o values

( , )

2

.

With the increase o the angle the undamental harmonic o the reactor current decreases, what is tantamount to

the increase o its equivalent inductive reactance or this harmonic and to the decrease in the undamental harmonic

reactive power, drawn by the reactor. The undamental harmonic o the reactor current is expressed by the ormula:

I UB I I I

TCR K K FC m

( ) ( ) ( )( ) ( ) ( ) sin ( )1 1 13 2 2 = = = [ ] (14)

where: control angle o the switch T thyristors, IFC(1)

capacitor current, ITCR(1)

() reactor current (undamental

harmonic), Im

- the reactor current amplitude or =

2. Thyristor are ully conducting or = /2. B

Kis the controlled

susceptance o the TCR step, its value is controlled by changing the conduction angle o thyristors. The resultant

compensator current ik(t) is the sum o the capacitor and reactor currents:

i t i t i t k FC TCR( ) ( ) ( )= + (15)

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I the current in the reactor branch is equal zero ( = ), then the compensator eeds reactive power to the supply

network and its current has a capacitive character. When thyristors are ully conducting, and the reactor power

is greater than the capacitor power, the compensator draws reactive power and its current has an inductive character.

The compensator current is controlled rom IFCmax

to ITCRmax

in a continuous manner. The disadvantage o this system

is generation o the current harmonics, which results rom the phase control o thyristor switch (Fig. 12c).

In the three-phase conguration (Fig. 13a) the single-phase TCRs (as in Fig. 12) are delta-connected in parallel with

xed capacitors; together they constitute a triangle o equivalent phase-to-phase susceptances or the supply network

(Fig. 13b). Their values vary independently and continuously as a result o changes in the control angles (12

, 23

, 31

). This

way, the circuit implements the Steinmetz procedure in order to compensate and symmetrize the three-phase load.

Fig. 12. (a) Conceptual diagram;

(b) TCR current waveforms;

(c) harmonics amplitudes per unit of basic current component amplitude

I23L( 23)

23I23C

I31L( 31)

31I31C

I12L( 12)

12I12C

1

2

3

B12K

B23K

B31K

I12K

I23K

I31K

(a) (b)

Fig. 13. Diagram of FC/TCR static compensator



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8.1.2. TSC/TCR (Thyristor Switched Capacitor/ Thyristor Controlled Reactor)

In this confguration a capacitor bank is divided into the steps, switched by means o thyristor AC switches, according

to the compensation/symmetrization needs. Synchronization o the instant o switching with respect to the supply

voltage waveorm guarantees elimination o overvoltages and inrush currents, normally associated with capacitor

switching. Also reduced are the values o current high harmonics, as related to the FC/TCR structure o the samenominal power.

8.1.3. STATCOM

The newest solutions o compensating systems are the STATCOM devices, based on AC/DC converters. The STATCOM

compensator can be considered as a controlled voltage source (VSI inverter in IGBT or GTO technology) connected

to the power supply system through the reactors (Fig. 14), or as an inertialess, three-phase synchronous machine,

whose phase voltages their amplitude, phase and requency are independently controlled. The reactive power/

current ow is controlled by means o the voltage amplitude control. Due to the independent control in each phase o

the system, the compensator enables voltage symmetrization by elimination o the negative-sequence component.

The relationship between the values and phase angles o the supply network voltages (Ubus

) and the compensator

output voltages (UVSC) (beore and ater the reactor Xr Fig. 14) determines the value and character (inductive orcapacitive) o the compensator current (power). At the zero phase shit between voltages U

busand U

VSC, only reactive

current ows. When Ubus

< UVSC

the current is capacitive, or Ubus

> UVSC

the current is inductive (Fig. 15). This way the

compensator can be a source or a load o reactive power. The STATCOM compensators are characterized with the

ollowing basic eatures:

they can simultaneously perorm combine unctions o reactive power compensation, load symmetrization

and fltering o harmonics,

do not require use o passive components; their overall dimensions are several times smaller than those

o SVC compensators o analogical power,

compared to the TSC/TCR and FC/TCR system they have better dynamic properties,

due to the development in power electronics their prices show a declining tendency.

LOAD VSC

ubus

uvsc

Xr

i

ubus

ubus

ubus

ubus

uxux

uvsc u vsc

< uvsc

> uvsc

i i

Fig. 14. Schematic diagram o a compensator (VSC) Fig. 15. Phasor diagrams or diferent

connected to the supply network relations between Ubus

and UVSC

8.2. Static series compensators

The series compensator can be provided with an additional - aside rom the load voltage control - unction o

symmetrization. The concept o such a compensator and block diagram o the example design is shown in Fig. 16.

The series voltages applied to individual phases o the system - UXSR , (X = 1, 2, 3) can be expressed as the sum o twothree-phase systems, which execute two independent processes:

- Symmetrization. This unction is perormed by means o the three-phase system o series voltages, determined

on the basis o the measurement o negative-sequence component o load voltages. In result o adding

appropriate components o series voltages ( UXS or x = 1, 2, 3) to the source voltages, the symmetric systemo voltages is obtained at the point B (Fig. 16).

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- Stabilization of the voltage positive-sequence component value. For this purpose, to the source voltages

has to be added the symmetric system of series voltages ( UXR for x = 1, 2, 3), which guarantees an increaseor reduction of the load voltages, according to the stabilization needs Fig. 16.

U1

U1S U1R

U01

U1SR

U2 U2S U2R

U02

U2SR

U3 U3S U3R

U03

U3SR

COMPENSATOR

SUPPLYNETWORK

VOLTAGESLOAD

Balanced voltages system withcontrolled values

Unbalanced system of thesupply network voltages

Fig. 16. Procedure of symmetrization and control of the load voltages by means of the series compensator

The example of a practical system, shown in schematic diagram in Fig. 17, of comprises three single-phase dc/ac

PWM converters connected in series with the supply line through three single-phase transformers. The load voltages

are measured and used for determination of the symmetrical components and hence to the determination of the

converters switching patterns, which ensure obtaining the series voltages. It is also possible to employ a three-phase

inverter with asymmetrical switching functions in individual branches of the converter. The symmetrization and

control / regulation of the load voltage are then performed by means of controlling the amplitude and phase angle

of reference voltages.



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U(2)

U(1)

U1SR

U

U3SR

rectifer

Filters o thevoltagesymmetrical

components

Control

system

(U(1)

)reerence

(U(2)

)reerence

Fig. 17. The schematic diagram of series system of stabilization symmetrization of the load voltage

References

1. ANSI C84.1: 1995, American national standard or electric power systems and equipment voltage ratings.

2. Engineering Recommendation P29: Planning limits or voltage unbalance in the United Kingdom.

The Electricity Council (U.K.), 1989.

3. Gyugyi L., Otto R.A., Putman T.H.: Principles and applications o static, thyristor-controlled shunt compensators.

IEEE Transactions Vol. PAS 97, no 5, Sep./Oct. 1978.

4. IEC 61000-2-1, 1990: Electromagnetic compatibility-Part 2: Environment-Section 1: Description o the

environment - Electromagnetic environment or low-requency conducted disturbances and signalling in

public power supply systems.

5. IEC 61000-2-5, 1995: Electromagnetic compatibility-Part 2: Environment-Section 5: Classifcation

o electromagnetic environments.

6. IEC 1000-2-12, 1995:Electromagnetic compatibility-Part 2: Environment-Section 12: Compatibility levels or

low-requency conducted disturbances and signalling in public medium-voltage power systems.

7. IEC 61000-4-27, 2000: Electromagnetic compatibility Part 4-27: Testing and measurement techniques

Unbalance, immunity test.

8. IEEE P1159.1: Guide or recorder and data acquisition requirements or characterisation o power quality events.

9. Miller J. E.: Reactive power controlled in electric systems. John Willey & Sons 1982.

10. UIE Guide to quality o electrical supply or industrial installations. Part 4: Voltage unbalance. 1998.

Power Quality

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Guide for electrical design engineers - Chapter 5 : Mitigation of voltage unbalance