Modeling of phase-shift zigzag transformers in ATP

Modeling of phase-shift zigzag transformers in ATP Hans Kr. Høidalen, NTNU, Norway

Roald Sporild, ABB, Norway

Electrical Power Engineering O.S. Bragstadspl. 2F N-7491 Trondheim, Norway Tel: 73594225 / Fax: 73594279 [email protected]

Automation Technologies Division P.O.Box 6540 Rodeløkka N-0501 Oslo, Norway Tel: 22872547 / Fax: 22352811 [email protected]

Abstract - In large industry production facilities, twelve pulse rectifier units are often used for the conversion to DC-current. In order to improve the harmonic signature from the plant versus the grid, several transformer units are internally phase-displaced by means of combined couplings involving Z-arrangement. A new transformer model for these facilities has been developed in ATP and implemented in ATPDraw. The paper describes the theory for this phase-displacement and how the transformers are specified in ATP. Keywords: Saturable transformer, harmonics, phase-shift, zigzag, test report, ATPDraw.

1 Introduction In the power supply to large industrial plants involving AC-DC converters, power quality is a problem. The current on the AC-side contains harmonics of the order k⋅n±1, where k is the number of pulses in the rectifying bridge and n=1, 2… Filters on the high voltage AC side are expensive and alternative solutions are often beneficial. When several AC-DC converters are installed in parallel, power transformers with different phase-shifts can be used to cancel out the harmonic currents. In a particular industrial plant in Sunndalsøra-Norway five 12-pulse AC-DC converters are installed in parallel with phase shifts -12, -6, 0, +6, and +12, which results in an equivalent 60-pulse system. A zigzag coupling on the primary side and two secondary sides with 30 degrees internal phase shift supplying a 12-pulse rectifying bridge is investigated in this paper. The modeling of zigzag transformers with the saturable transformer components in ATP [1] is reported in [2]. In that paper the more normal zigzag transformer with two equal winding parts resulting in 30 degrees phase shift is investigated. In the present paper the analysis in [2] is extended in the case of an arbitrary phase shift of and degrees based on [3].

2

Modeling of zigzag winding

This section outlines how to model a zigzag winding compatible with the saturable transformer model in EMTP. The short circuit and magnetizing characteristics are handled

along with the zero-sequence behaviour. Two basic zigzag couplings are used for negative and positive phase shifts as shown in fig. 1. Phase + UzA

- U y+

B

I

Phase A

II

B

Leg

III

C

Z

Leg I II III

C

Y

- U y+

+ Uz-

Z

Y

a) Negative phase shift b) Positive phase shift Fig. 1 Investigated zigzag couplings. For negative phase shifts the zigzag winding of phase A consists of one part on leg I and one part on leg III in the opposite direction. The total voltage of phase A is shown in fig. 2. I

Uy I

Uy 60-α

Uz

60-α

UA

UA

Uz α

α

III

II

III

II

a) Negative phase shift b) Positive phase shift Fig. 2 Voltages of the zigzag winding of phase A. The absolute values of the phase voltages of each winding part are n=

Uy Uz

=

sin(α) sin(60 − α)

(1)

| U z |=

|UA | cos(α ) + n ⋅ cos(60 − α )

(2)

| U y |=

| U A | ⋅n cos(α ) + n ⋅ cos(60 − α )

(3)

with α equal to the absolute value of the phase shift. The voltage vectors are Uz =

UA 1 + n ⋅ ∠ − 60 o

Uy =

U A ⋅ n∠ − 60 o 1 + n ⋅ ∠ − 60 o

and

The same equations apply to the positive phase shift case.

(4) (5)

The winding resistance, the leakage inductance, and the magnetizing impedance of the total zigzag winding are now divided in two parts as illustrated to fig. 3. Phase A

Rz

Lz

Phase A + Uz -

Ry

N

Im

Leg I

Iz

Ly

Phase B -

U y ∠120

Lmy

I m ∠ − 120o

+ a) Short circuit

Leg I

Iy

Leg III

o

+ Uz -

Lmz

Uy +

b) Open circuit

Fig. 3 Distribution of the short-circuit and open-circuit impedances. Positive sequence, negative phase shift. The total short-circuit resistance and inductance as obtainable from measurements are R = R z + R y and L = L z + L y respectively as shown in fig. 3a). The winding resistance is proportional to the number of windings turns while the leakage inductance is proportional to the square of this number. Since the winding voltages Uz and Uy are proportional to the number of turns this gives R y = n ⋅ R z and L y = n 2 ⋅ L z . As a result Rz = Lz =

R 1+ n L

∧

1 + n2

∧

R⋅n 1+ n L ⋅ n2 Ly = 1 + n2

(6)

Ry =

(7)

The total magnetizing impedance as obtainable from measurements is Z m = U A / I m . According to fig. 3b) the magnetizing current in the two winding parts is Im =

Uz + Iz Z mz

∧ − I m ∠ − 120 o =

−U y Z my

+ Iy

(8)

When the transformer is unloaded I z + I y ⋅ n = 0 . From this (8) can be reformulated as I m ⋅ (1 − n∠ − 120 o ) =

Uy Uz −n⋅ Z mz Z my

(9)

Inserting (4) and (5) into (9) gives after some manipulation Im =

UA 1 + n + n2

 1 n 2 ∠ − 60 o ⋅ −  Z mz Z my 

   

(10)

The magnetizing inductance is proportional to the square of the number of windings, Lmy = n 2 ⋅ Lmz . If the magnetizing impedance is assumed to be purely inductive the total measurable appearant magnetizing inductance is Lm = U A /( jωI m ) , where UA is the phase voltage. The absolute value is taken since a phase shift in the magnetizing current will be

introduced in the zigzag winding. From (10) the magnetizing inductances in each winding part are obtained Lm ⋅ | 1 − ∠ − 60 o | Lm = 2 1+ n + n 1 + n + n2 2 L ⋅n = m 1 + n + n2

Lmz =

(11)

Lmy

(12)

In the saturable transformer model in EMTP a magnetizing branch is added to the primary winding only. In this case Zmy in (10) must be set to zero. This results in = LEMTP mz

Lm 1 + n + n2

(13)

The zero sequence reluctance can similarly to the magnetizing inductance be found from fig. 3b). In this case the current I 0 = I m in phase B on leg I is equal in amplitude, but opposite in phase to the current in phase A. This also applies to voltages across the two winding parts, so that U y 0 = −n ⋅ U z 0 and U z 0 + U y 0 = U A . The relationship I z 0 + I y 0 ⋅ n = 0 is still valid. This gives I0 =

U z0 + I z0 Z 0z

∧ − I0 =

− U y0 Z0y

+ I y 0 ⇒ I 0 (1 − n) =

U A0  1 n2 ⋅ + 1 − n  Z 0 z Z 0 y

   

(14)

The zero sequence impedance is mostly inductive and for a 3-leg core mostly linear. The zero sequence inductance is proportional to the square of the number of windings. This gives L0 z =

U A0 2 ⋅ ω ⋅ I 0 (1 − n )2

∧

L0 y =

U A0 2 ⋅ n2 ⋅ ω ⋅ I 0 (1 − n )2

(15)

The saturable transformer component in EMTP supports only a zero-sequence reluctance in the primary winding. In this case Z0y is zero and LEMTP = 0z

U A0

ω ⋅ I0

⋅

1

(1 − n )2

(16)

The reluctance specified in EMTP is R0 = U 2 / 3L0 where U is the voltage across the winding where the reluctance is connected. This gives R0 =

ω ⋅ I 0 ⋅ U A0 U z20 = EMTP 3 3 ⋅ L0 z

(17)

3. ATPDraw implementation A new component called SATTRAFO is introduced in ATPDraw from version 4.0. This is a general 3-phase saturable transformer component with 2 or 3 windings. The component completely replaces the old GENTRAFO and that component is automatically replaced by SATTRAFO when loading an older circuit. The new SATTRAFO component supports all phase shifts between Y- and D- windings (not just Y, Dlead, Dlag, Y180 as in GENTRAFO) as well as Autotransformers and zigzag windings. For a zigzag winding the user can specify the phase shift and degrees and the voltage and short circuit impedance distribution is automatically calculated by ATPDraw according to (2), (3), (6), and (7). The phase shift is specified related to a Y-winding. The two couplings in fig. 1 are used dependent on the sign of the phase shift. ATPDraw does not recalculate the magnetizing branch and zero sequence reluctance. This must be done manually by the user according to (13) and (17). The

internal 3-phase node of the zigzag winding is given a name Txxxx where the number xxxx is the incremented transformer number. Several zigzag windings are supported in a single transformer. The dialog box of the new SATTRAFO component is shown in fig. 4.

Fig. 4 ATPDraw dialog box of the new SATTRAFO component. The data specified in fig. 4 will produce an ATP-file as shown below: TRANSFORMER THREE PHASE TX0001 25.2 TRANSFORMER T1A 1.E11 1. 1.28 9999 Z1A 1Z1A T0002C -.0084.103215.6797 2 T0002A -.0014.00279.93446 3D2A D2C .00061 .0174 .693 4Y3A .0002.00585 .4 TRANSFORMER T1A T1B 1Z1B T0002A Z1B 2 T0002B 3D2B D2A 4Y3B TRANSFORMER T1A T1C 1Z1C T0002B 2 T0002C Z1C 3D2C D2B 4Y3C

0

D2A Y3A D2B Y3B D2C Y3C

4. Case study This section outlines in details how to model a 3-winding transformer based on the test report and the result of using it to supply a 12-pulse rectifying bridge.

4.1 Test report Coupling: Rated power: Rated primary voltage: Rated secondary voltage: Rated tertiary voltage: Rated frequency: Open circuit current: Short circuit impedance 1-2: Short circuit impedance 1-3: Short circuit impedance 2-3: Phase shift Z (ref. 3):

ZN0d11y 24.8 MVA 10.735 kV 693 V 693 V 50 Hz 0.0056 pu 0.0084 + j0.1015 pu 0.0084 + j0.1015 pu 0.0210 + j0.1887 pu -7.5 deg.

This will result in the standard per unit equivalent circuit for the short circuit impedances 1

Z1

Z2

2

Z1 = ( Z12 + Z13 − Z 23 ) / 2 = −0.0021 + j 0.00715 [ pu ] Z 2 = ( Z12 + Z 23 − Z13 ) / 2 = 0.0105 + j 0.0944 [ pu ]

Z3

3

Z 3 = ( Z13 + Z 23 − Z12 ) / 2 = 0.0105 + j 0.0944 [ pu ]

Fig. 5 Per unit equivalent circuit 4.2 Winding 1, zigzag The zigzag winding 1 is further split in Z and Y parts with n =

sin(7.5o ) = 0.165 . sin(60 − 7.5o )

The total winding voltage is U A = 10.735 / 3 kV = 6.2 kV The voltages across each winding part are calculated by ATPDraw from (2) and (3): U 1z =

10.735 / 3 kV = 5.68 kV cos(7.5 ) + 0.165 ⋅ cos(60 o − 7.5o ) o

U 1 y = 5.68 kV ⋅ 0.165 = 0.934 kV

(18) (19)

The short circuit impedance is

Z1 = (− 0.0021 + j 0.00715) ⋅ (10.735 kV )2 / 24.8 MVA = −0.00976 + j 0.0332 [Ω]

The individual resistance and inductance in each winding part is calculated by ATPDraw from (6) and (7): 1 [Ω] = - 8.4 [mΩ] 1 + 0.165 0.165 R1 y = −0.00976 ⋅ [Ω] = - 1.4 [mΩ] 1 + 0.165 0.0332 1 L1z = ⋅ [H] = 0.103 [mH] 2π ⋅ 50 1 + 0.1652 0.0332 0.1652 L1 y = ⋅ [H] = 2.79 [ µH] 2π ⋅ 50 1 + 0.1652 R1z = −0.00976 ⋅

(20)

(21)

If the HV winding 1 is chosen as the primary winding, the magnetizing branch will be added to the first winding part (Z) of the zigzag winding. This is probably not a good choice, and alternatively the magnetizing branch should be added to the low-voltage Y-coupled winding.

This could be done externally or by choosing winding 3 as the primary. The magnetizing branch added to winding 1 should be calculated from (13). The measured inductance is Lm =

1/ 3 pu = 0.328 pu = 0.368 ⋅ (10.735 kV )2 / 24.8 MVA = 1.52 [H] 2π ⋅ 50 ⋅ 0.0056

and the inductance that should be added to winding 1Z in EMTP: = LEMTP mz

Lm 1 + n + n2

= 1.28 [H]

If a measurement of the zero sequence impedance is missing a reasonable assumption for this particular transformer is to set it to 2/3 of the positive sequence magnetizing current. Further, the zero sequence inductance added in EMTP is one half of the real value according to (15) and (16). This gives R0 =

U z20 3 ⋅ LEMTP 0z

≈ 2⋅

5.682 5.682 = = 25.2 [Ω] EMTP 1.28 2 ⋅ Lmz

4.3 Winding 2 and 3 The Delta- winding: The total winding voltage is U A2 = 0.693 kV The short circuit impedance is Z 2 = (0.0105 + j 0.0944 ) ⋅

(

)

2

3 ⋅ 0.693 kV / 24.8 MVA = 0.61 + j5.48 [mΩ]

R2=0.61 [mΩ] and L2=17.5 [µH]

The Wye- winding: The total winding voltage is U A3 = 0.693 / 3 = 0.4 kV The short circuit impedance is Z 3 = (0.0105 + j 0.0944 ) ⋅

(

)

2

3 ⋅ 0.4 kV / 24.8 MVA = 0.203 + j1.83 [mΩ]

R3=0.203 [mΩ] and L3=5.85 [µH]

4.4 Simulation of two parallel 12-pulse rectifying bridges This example is based on a practical situation in an industrial plant in Norway. Two “12pulse” rectifying bridges are installed in parallel as shown in fig. 6. The purpose is to show how the usage of phase-shift zig-zag transformers reduces the harmonic content of the current on the high-voltage (132 kV) side. Two situations are simulated and the harmonic contents calculated • without phase-shift between the two zig-zag transformers (0/0) • with a 15 deg. phase shift between the two (-7.5/7.5)

5 uH

Cable

HVBUS 132 kV

0.0265

Diode Zig-zag bridges trans form ers ZN0d11y0 10.7/0.693 kV

132/11.3 Regulation trans form ers 11.3/10.6 kV

22.2 m H

5 mF

Cable

5 uH

5 mF

0.0265

Fig. 6. Circuit in ATPDraw for simulation of two parallel 12-pulse rectifying bridges. 1000 100

400 [A] 300

Phase shifts zig-zag 0/0 -7.5/7.5

10

200

1

100

0.1 0

0.01

-100 -200

0.001

-300

0.0001

-400 0.080

0.084

0.088

0.092

0.096

Fig. 7a) Current on the 132 kV side.

[s] 0.100

1E-005 0

10

20

30

40

50

Fig. 7b) Harmonic content of fig. 7a).

Tab. 1. Numbers from fig. 7b). Obtained by PlotXY [4]. Harmonics 1 5 7 11 13 23 25 35 37 47 49 THD

Current [A] RMS Zig-zag: 0/0 Zig-zag:-7.5/+7.5 261.60 262.24 0.12843 0.079998 0.05890 0.029712 9.84720 0.000767 5.79000 0.000788 1.89680 1.549300 1.46000 1.219200 0.73766 0.000280 0.63500 0.000335 0.41233 0.368940 0.37700 0.331470 4.4835 % 0.77615 %

As seen from fig. 7b) the phase-shifting (-7.5/7.5 deg.) of the zig-zag transformers greatly reduces the harmonics of order 11-13 and 35-37. The two parallel rectifying bridge both of type 12-pulse thus become a 24-pulse system seen from the HV-side.

5. Conclusion Modelling of zig-zag transformers using the SATURABLE TRANSFORMER component in ATP is presented in this paper. General formulas for the ratios of voltage, resistance and leakage inductance between the two parts of a zig-zag winding are presented. A new component in ATPDraw called SATTRAFO handles the calculation of these ratios automatically and supports all phase shifts of Y, D and Z-coupled windings. An example shows how to establish a zig-zag coupled SATURABLE TRANSFORMER component in ATP based on the test report. A second example shows how two parallel 12pulse rectifying bridges become an equivalent 24-pulse system seen from the HV-side when a phase shift of 15 deg. is introduced between two zig-zag coupled transformers. The results confirm a considerable reduction in THD due to the phase-shift arrangement. This in turn contributes to a simplified and cheaper filter arrangement as compared to the ordinary 12-pulse converters. References [1] Alternative Transients Program (ATP) - Rule Book, Canadian/American EMTP User Group, 1987-1998. [2] P. Riedel: “Modelling of zigzag-transformers in the three-phase system”. [3] SIMSEN- Simulation Software for Power Networks, Electrical Drives and Hydraulic Systems, http://simsen.epfl.ch/ [4] Massimo Ceraolo: PloyXY- Plotting program for the ATP.