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

Guide for electrical design engineers

Power Po wer Quali Qualitty Zbigniew Hanzelka AGH-University of Science & Technology

Mitigation of voltage unbalance U 12 U 1 I 23=I C I 12 I 1=I 12-I 31

U 23 I 31=I L

U 3 U 2 I 2=I 23-I 12 I 3=I 31-I 23

U 31

P o w e r Q u a l i t y

Power Quality http://www.leonardo-energy.org

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 (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 busbars o phase voltage U , supplied rom three-phase symmetrical system. COMPENSATOR (K)

I 1K I1 E1

I 3 K

U1 U

E2

2

U3

E3 I3

I 1A

SYMETRIC LOAD (S)

I 3A

ASYMETRIC LOAD LOA D (A)

Fig. 1. Diagram of the analysed node Since the system o electromotive orces (E (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 1 = Z 2 = Z 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 symmetrizatio n

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, Similarly, when connecting two singleelement loads, the level o unbalance does not depend on which voltages the loads are connected. However, when these loads will have a dierent 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.

2

Mitigation of voltage unbalance http://www.leonardo-energy.org

EXAMPLE 1 For the system of three loads on nominal voltage 380 V and powers, respectively: P1 = 7.22 kW, Q 1 = 7.22 kVAR (ind.); P2 = 7.22 kW, Q2 = 7.22 kVAR (cap.); P 3 = 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. fac tor. ________________________ From the load active and reactive power the elements of its equivalent admittance can be determined, i.e.: the Q P susceptance (B = 2 ) and conductance (G = 2 ) (Fig. 2). U U

Y Load ( P, Q )

UN

UN

B

G

Fig. 2. The load (P - active power, power, Q - reactive power) and its equivalent admittance Hence: Y 1 A = G1 A + jB1A =

P 1

Q1

7.22 kW

U

U

(380 V )

Y 2 A = G2 A + jB2 A = Y 3 A = G3 A + jB3 A =

− j 2

P 2 2

U

P 3 2

U

= 2

+ j

Q2 2

U

+ j

Q3 2

U

= =

− j 2

7.22 kW (380 V )

(380 V )

2

= (0.005− j 0.05)S

2

(380 V )

+ j

2

7.22 kW

7.22 kVAR

+ j

7.22 kVAR 2

(380 V ) 0 kVAR (380 V )2

= (0.005 + j 0.05)S

= 0.1S

Variant 1 – Loads connected as in Fig. 3: 1

Y31A

I 1A

Y12 A

Y 12 A = Y 1A Y 23 A = Y 2 A

2

I 2A

Y 31 A = Y 3 A

Y23 A

I 31A

3

I 3A

I 23 A

Fig. 3. Variant 1 of load connection

The current unbalance factor:

k I % =

I (2 ) I (1)

100% =

a2 Y 12 A +Y 23 A + aY 31A Y 12 A +Y 23 A +Y 31A 1

a = exp( j1200 ) =− + j 2

3

3 2

100% = 68.3%

1

a2 = exp( j1200 ) =− − j 2

3 2

Power Quality http://www.leonardo-energy.org Three-wire network voltages

] V [ s e g a t l o V

Three-wire network currents

400

40

300

30

200

20

100

10 ] A [ s t n e r r u C

0

0

-100

-10

-200

-20

-300

-30

-400

-40

0

0.01

0.02

0.03

0.04

0.05 Time [s]

0.06

0.07

0.08

0.09

0.1

0

0. 01

0.02

0. 03

0. 04

0. 05

0. 06

0. 07

0. 08

0. 09

0.1

Time [s]

Fig. 4. Voltage waveforms: Example 1 – Variant 1

Fig. 5. Current waveforms: Example 1 – Variant 1

See Figures 4 and 5. Y 12 A = Y 1A

Variant II -

The current unbalance actor:

Y 23 A = Y 3 A

k I % =

I (2 ) I (1)

100% =

Y 31 A = Y 2 A

a2 Y 12 A +Y 23 A + aY 31A Y 12 A +Y 23 A +Y 31A

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). Three-wire network currents 40

30

20

10 ] A [ s t n e r r u C

0

-10

-20

-30

-40 0

0. 01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0. 09

0. 1

Time [s]

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 uniorm 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, thereore 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 zerosequence components are present. The symmetrizator (K) is connected in parallel to the asymmetric load (A) (Fig. (Fig. 1). The symmetrizator causes the currents I 1K , I 2K , I 3K , which adding to the load currents I 1A , I 2A , I 3A, result in the balanced system o the source currents I 1 , I 2 , I 3, according to the equation: I1 = I1 A + I 1K

I 2 = I 2 A + I 2K = a2 I 1

I 3 = I 3 A + I 3K = aI 1

4

(7)


As the currents drawn rom the network orm a balanced system, thereore the negative-sequence and zero-sequence components are equal zero: 1 I ( 0 ) = (I 1 + I 2 + I 3 ) = 0 3

1 I ( 2 ) = ( I 1 + a I 2 + a2 I 3 ) = 0 3

(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 ph ase-to-phase voltages. The impedances Z 12 A , Z 23A , Z 31A Z 1A , Z 2A Z 3A (or admittances Y 12 A , Y 23A , Y 31A Y1A , Y 2A Y 3A ), which in the diagram represent the actual load, can be unctions o time.

1

2

3

Z 12 A (Y 12 A )

0

Z 1 A (Y 2 A )

Z 23 A (Y 23 A )

Z 2 A (Y 2 A )

Z 31 A (Y 31A )

Z 3 A (Y 3 A )

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 dierent 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 positivesequence symmetrical component (reactive power compensation or the undamental requency) and o the zerosequence 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 A( 2 ) + I (K 2 ) = 0

I A( 0 ) + I (K 0 ) = 0

Im I A(1) + I (K 1) = I 0

(9)

where: I (A0 ) , I (A1) , I (A2 ) , I (K0 ) , I (K1) , I (K 2 ) are symmetrical components o the asymmetric load and compensator (index (K)) currents, respectively or the zero- (0), positive- (1) and negative-sequence component; ImI A(1) denotes the reactive part o the positive-sequence o the load current component (imaginary part in complex numbers notation); I 0 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.

5


For the load as in Fig. 4, the relations, describing the values o the negativen egative- and zero-sequence symmetrical components can be written as ollows (according to (8)):

⎡1 ⎤ Y 1A + aY 2 A + a2 Y 3A ) − (a2 Y 12A +Y 23A + aY31 A ) ⎥ ( ⎣3 ⎦

I (A2 ) = U⎢ I (A0 ) =

(10a)

U

Y 1A + a2 Y 2 A + aY 3A ) ( 3

(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 B1K B2K , B3K , connected to the phase-to-neutral voltages and B12K B23K , B31K , connected to the phase-to-phase 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 useul 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). 1

I 1 A

Y 2 A

2

I 2 A

Y 1 A

3

I 3 A

Y 3 A I N

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

EXAMPLE 2 U1 = 220 V

U 2 = a2 220 V

U 3 = a220 V

I1 A = U1Y 2 A = 220⋅( 0.05 + j 0, 05) = (11+ j11) A I 2 A = U 2 Y 1A = (−15.02 026 − j 4. 02 026) A I 3 A = U 3 Y 3 A = (−11− j19.05 052) A The current in neutral conductor: I N = 3I ( 0 ) = I1A + I 2 A + I 3A = (−15.026 − j 26.026) A where I ( 0 ) is the current zero-sequence symmetrical component. The negative-sequence symmetrical component: 1 I (A2 ) = ( I1A + a2 I 2 A + aI 3A ) = (1. 34 342 + j 2. 32 325) A 3

6


The positive-sequence symmetrical component:

1 I (A1) = ( I1A + aI 2 A + a2 I 3 A ) =14.667 667A 3 k I % =

The current unbalance actor:

I A( 2 )

100% = 50%

I A(1)

1

I 1

I 1 A

Y 2 A

I 2

I 2 A

Y 1 A

2

3

I 3

I 3 A

B1K

B 2 K

Y 3 A

I N

Fig. 6. The elimination of the zero-sequence component (EXAMPLE 2) Supply network c urren urrents ts

Supply network c urrents [A]

[A]

40

40

20

20

0

0

-20

-20

-40

-40 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

current in neutral conductor [A]

0.1 [s]

0. 01 01

0. 02 02

0. 03 03

0. 04 04

0. 05 05

0. 06 06

0. 07 07

0. 08 08

0. 09 09

0. 1 [s]

0. 08 08

0. 09 09

0. 1 [s]

current in neutral conductor [A] 0.02

40

0.01

20

0

0

-0.01

-20 -40

0

-0.02 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1 [s]

Fig. 7. Waveforms of currents currents:: EXAMPLE 2 – before the elimination of zero-se zero-sequence quence component

0

0. 01 01

0. 02 02

0. 03 03

0. 04 04

0. 05 05

0. 06 06

0. 07 07

Fig. 8. Waveforms of currents currents:: EXAMPLE 2 – after the elimination of zero-s zero-sequence equence component

The elimination o the current zero-sequence component is perormed by means o the two-element symmetrizator in the example confguration as in Fig. 6.

Supply network currents: I1 = U1(Y 2 A + jB1K )

I 2 = U 2 (Y 1 A + jB2K )

I 3 = U 3 Y 3 A

The condition or the current in neutral conductor to become zero takes orm: I1 + I 2 + I 3 = 0 Hence: Reactive part o neutral current:

Im( I1 + I 2 + I 3 ) = 0

Active part o neutral current:

Re( I1 + I 2 + I 3 ) = 0

and

Substituting the numerical values: 0.05 - 0.0683 + 0.866B2K - 0.05 = 0

and

0.05 + B1K – 0.0183 – 0.5B2K + 0.0866 = 0

7


Hence:

B1K =−0.0789 0789S

B2K = 0.0789 0789S

Y Σ1 = Y 2 A + jB1K =( 0. 05 05 − j 0. 02 0289)S Y Σ2 = Y 1 + jB2K = ( 0. 05 05 + j 0. 02 0289)S Y Σ3 = Y 3 + jB jB3K = 0.1S I1 = U1Y Σ1 = 220⋅( 0.005 − j 0.0289) = (11− j 6. 358) A I 2 = U 2 Y Σ2 = ( 0.00 006 − j12.70 705) A I 3 = U 3 Y Σ3 = (−11+ j19. 05 052) A I1 + I 2 + I 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 compensation and symmetrizatio sy mmetrization n o the admittance Y 23A

B12K

= −B12 A + −

B23K =

B31K

G12 A

= −

3 G12 A 3

G23 A 3

+

+ −B23 A +

+

compensation and symmetrization o the admittance Y 12A

G23 A 3

compensation o the reactive part o the load admittances

G31A 3 G31 A 3

+ B0 = −B12 A + B0 +

+ B0 = −B23 A + B0 +

+ −B31 A + B0 = −B31 A + B0 +

compensation and symmetrization o the admittance Y 31A

G31 A − G23 A 3 G31 A − G23 A 3 G31 A − G23 A 3

(11)

symmetrization symmetrizatio n o the load

In practice, the susceptances o a static compensator perorm both processes simultaneously, that means symmetrization 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. 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 Y 12A compensation o the imaginary part is achieved through parallel connection o a susceptance (-B (-B12) ollowed by symmetrization o the remaining part o such a single interphase load by connecting the symmetrizing susceptances respectively: (G (G12A / 3 ) or the voltage U 12 and (-G (-G12A / 3 ) or the voltage U 31. The compensation process o 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.

8


The above considerations illustrate the well known Steinmetz rule o symmetrization, according according to which any singlesingle phase active load (or active-reactive one, ater its equivalent susceptance has been compensated), connected e.g. between phases 1-2 (Fig. 9), can be symmetrized by means o reactive elements LC LC o o such values, that the currents ulfl the relations (12). I23 = I31 =

1 3

(12)

I 12 A

The obtained relations (11) transorm any three-phase asymmetric load into the symmetric, resistive or resistiveinductive 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: Q1A + Q1K = Q2 A + Q2K = Q3A + Q3K = Q 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: Q12K =−Q1A −Q2 A + Q3 A + Q0 Q23K =+Q1A −Q2 A − Q3A +Q0

(13)

Q31K =−Q1A + Q2 A − Q3A + Q0

I 1

I 1 1

1 I 12

G 12

I 12 I 2 I 31=I L 2

2

1  

I 2

 L  C

G 12

I 23=I C

=

3

I 3 = 0 3

3

I 3

(a)

(b)

9

G 12 3

Power Quality http://www.leonardo-energy.org U 12 U 1 I 23=I C I 12 I 1=I 12-I 31

U 23 I 31=I L

U 3 U 2 I 2=I 23-I 12 I 3=I 31-I 23

U 31

(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 symmetrizati symmetrization on

EXAMPLE 3 For the loads confguration as in the EXAMPLE 1 – Variant II, susceptances o the delta-connected symmetrizator/ compensator are: 1

B12K =−B12 A −

3

B23K =−B23 A − B31K =−B31A −

1 3 1 3

(G23A −G31 31A ) = 0.0211S (G31A −G12A ) = 0S (G12 A −G23 2 3A ) =−0.0211S

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: C 12 K =

B12 K 2 π f

=

0.0211S ≅ 67.2 μ F 2⋅ π ⋅50 Hz

The inductance o the reactor connected between phases 3-1 is determined rom the relation: L31K =

1 2 π fB31K

=

1 2⋅ π ⋅50 Hz ⋅0.0211S

≅150mH

The load and compensator are shown in Fig. 10. Ater connecting the compensator/symmetrizator: I1* = I 1*2 − I 3* 1 = ( 43.89 + j 0.001) A ≅ 43.89 exp( j 00 )A

10


I 2* = I *23 − I 1*2 = (−21.945 − j 37.988) A ≅ 43. 87exp(− j 1200 ) A I 3* = I *31 − I *23 = (−21.945 + j 37.987) A ≅ 43. 87exp( j1200 )

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

I 12 1

I 12 A

*

I 1

Y 12 A

I 31 A

B12 K

2 *

I 2

B 31K

Y 31 A

I 23 A B 23 K

Y 23 A

*

I 31

3 *

I 31

*

I 3

Fig. 10. Delta-connected asymmetric load with the symmetrizator Three-wire network voltages 400

300 200

100 ] V [ s e g a t l o V

0

-100

-200 -300

-400

0

0.01

0.02

0. 03 03

0.04

0.05 0.06 Time [s]

0.07

0. 08 08

0. 09 09

0.1

0. 08 08

0.09

0. 1

Three-wire network currents 80 60 40 20 ] A [ s t n e r r u C

0

-20 -40 -60 -80

0

0. 01 01

0.02

0.03

0.04

0.05 0. 06 06 Time [s]

0.07

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

11


Star-connected asymmetrical load

7.2.

The symmetrization o a star-connected load is analysed ater star-to-delta transormation. Further procedure o the symmetrizator parameters selection is analogical as in section 7.1.

Static compensators

8.

Reactive 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 perorm various tasks, such as compensation o the undamental component reactive power, symmetrization and mitigation o voltage fuctuations (ficker). Also some active lters congurations have a capability o symmetrization.

Static VAR compensators

8.1.

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 the network 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 oten used compensators is the FC/TCR compensator with xed capacitor and controlled (variable) reactor current.

8.1.1.

Compensator/symmetrizator Compensator/symmet rizator FC/TCR

So-called FC/TCR circuits are the most commonly used static VAr compensators/stabilizers in industry. They are composed 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 – I TCR(1) and the load reactive current – I O(1) is constant, and equals the FC current – I FC(1) (Fig. 12a). The TCR current waveorm or three sampled control angles α is shown in Figure 12b (single-phase circuit). The control angle (with respect to the positive voltage zerocrossing) and the basic current harmonic o TCR can vary in each supply voltage hal-cycle, within the range o values

π

α ∈(

, π ) . 2 With the increase o the angle α 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, power, drawn by the reactor. The undamental harmonic o the reactor current is expressed by the ormula:

ITCR(1) ( α ) = 3UBK = ( IK (1) − IFC( 1) ) =

I m

π

[2( π − α ) −sin 2( π − α )]

(14)

where: α – control angle o the switch T thyristors, I FC(1) – capacitor current, I TCR(1)(α) – reactor current (undamental harmonic), I m - the reactor current amplitude or α =

π

. Thyristor are ully conducting or α = π /2. BK is the controlled 2 susceptance o the TCR step, its value is controlled by changing the conduction angle o thyristors. The resultant compensator current i k (t) is the sum o the capacitor and reactor currents: ik (t ) = iFC ( t ) +i TCR (t )

(15)

12


I the current in the reactor branch is equal zero (α = π), 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 I FCmax to I TCRmax 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 conguration (Fig. 13a) the single-phase TCR’s (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 Their values vary independently and continuously as a result o changes in the control angles (α12, α23, α31). 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 waveform waveforms; s; (c) harmonics amplitudes per unit of basic current component amplitude 1

I 12K

I 12L (α 12)

B 12K

I 12C

α12

I 31K

I 31L ( α31)

2

I 31 31C C

α31

I 23L (α 23)

B 31K

I 23K

B 23K I 23C

α23

3

(a)

(b) Fig. 13. Diagram of FC/TCR static compensator

13


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 waveorm 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 same nominal 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 (U (U bus) and the compensator output voltages (U (U VSC) (beore and ater the reactor X r – Fig. 14) determines the value and character (inductive or capacitive) o the compensator current (power). At the zero phase shi t between voltages U bus and U VSC, only reactive current ows. When U bus < U VSC the current is capacitive, or U bus > U VSC 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 perorm 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, 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. i

i ux

ux u bus

i

u bus

u bus Xr

u vsc

LOAD

u vsc

u vsc

VSC

u bus < u vsc

Fig. 14. Schematic diagram o a compensator (VSC) connected to the supply network

u bus > u vsc

Fig. 15. Phasor diagrams or diferent relations between U bus and U VSC

Static series compensators

8.2.

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 - ΔU XSR , (X = 1, 2, 3) can be expressed as the sum o two three-phase systems, which execute two independent processes: -

Symmetrization.This unction is perormed by means means o 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 ( ΔU XS or x = 1, 2, 3) to the source voltages, the symmetric system o voltages is obtained at the point B (Fig. 16).

14


-

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 ( ΔU XR for x = 1, 2, 3), which guarantees an increase or reduction of the load voltages, according to the stabilization needs –Fig. 16.

Unbalanced Unbalan ced sys system tem of the supply networ networkk volta voltages ges

ΔU 1SR

ΔU 1S

U 1

U 2

ΔU 1R

ΔU 2SR

ΔU 2S

U 01

ΔU 2R

ΔU 3SR

U 3

SUPPLY NETWORK VOLTAGES

Balanced Balanc ed vol voltag tages es sys system tem wit with h controlled contro lled value valuess

ΔU 3S

U 02

ΔU 3R

U 03

COMPENSATOR

LOAD

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 th e supply line through three single-phase 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.

15

Power Quality http://www.leonardo-energy.org ΔU 1SR

ΔU

ΔU 3SR

Filters o the voltage symmetrical components (1)

U

(2)

U

rectifer (1)

Control system

( U ) reerence (2)

( U ) reerence

Fig. 17. The schematic diagram of series system of stabilizatio stabilization n symmetrization of the load voltage References 1.

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

2.

Engineering Recommendation Recommendation P29: Planning Planning limits or voltage voltage unbalance in the United United Kingdom. The Electricity Council (U.K.), 1989.

3.

Gyugyi L., Otto R.A., Putman T.H T.H.:.: Principles Principles and applications o static, thyristor-controlled thyristor-controlled shunt shunt compensators. compensators. IEEE Transactions Vol. PAS – 97, no 5, Sep./Oct. 1978.

4.

IEC 61000-2-1, 1990: Electromagnetic Electromagnetic compatibility-Part 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 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 power quality events.

9.

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

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

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16

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

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