Electrical Engineering
Measurement of zero sequence impedance for three-winding transformers Using actual measurements rom a reputable transormer manuacturer, Er. Lee Wai Meng explains the required connection scheme and associated calculations.
Xos
As
Secondary
Xop
Ap
Primary
K
XoT
AT
Tetiary Bp
A three-winding transormer has the ollowing speciications: • Primary winding o 300 MVA, 230 kV, star connected with the neutral accessible, and connected to the local grid. • Secondary winding o 300 MVA, 132 kV, kV, star connected with the neutral accessible, and connected to the load o the consumer. ertiary winding o 90 MVA, 15.75 • kV,, delta c onnected, and not connected kV to any load. he sole purpose o the tertiary winding is to allow the low o zero sequence current during ault conditions. Model or zero sequence A three-winding transormer has zero sequence impedance or the primary, secondary,, and tertiary windings. secondary = zero sequence • X OP impedance o the primary winding • X = zero sequence OS impedance o the secondary winding • X = zero sequence O impedance o the tertiary winding he equivalent circuit or the zero sequence impedance is illustrated in Figure 1. It is important to recognise that point K in Figure 1 is a ictitious point and does not represent the neutral point o the transormer. he connection o the zero sequence impedance to the system is determined by imaginary switch A P, A S, A , BP, BS, and B. Switch A P, A S, or A will be closed i the winding is star connected and with the neutral connected to ground. Switch A P, A S, or A will be opened i the winding is star connected and with the neutral not connected to ground. Switch B P, BS, or B will be closed only i the winding is delta connected. 26 · THE SINGAPORE ENGINEER
BT
BS
Zero bus
Figure 1 - Zero sequence sequence impedance
Confguration o Windings
Status o Switch A P, A S, or A T
BP, BS, or BT
1) Delta
Open
Closed
2) Star with neutral connected to ground
Closed
Open
3) Star with neutral NO connected to ground
Open
Open
With the combinations o the switches in various open and closed states, the values o X OP, X OS and X O can be calculated rom measurements o injected voltage and induced current at the primary, secondary and and tertiary terminals o the transormers. Connection scheme In order to solve or the three unknowns (X OP, X OS and X O), at least three equations or three measurements are needed. Figures
2A to 5A show the connection schemes. Figures 2B to 5B show the zero sequence impedance diagram or the connection schemes in Figures 2A to 5A. Te test source can be connected either at the primary or secondary windings. windings. Te test source is a single phase AC source, and there is no need or a three phase AC source or the measurement o the zero sequence impedance. Te measurement o the positive sequence impedance will however require a three phase AC source.
Connection Scheme
Zero Sequence Impedance
Figure 2A
XOP + X O
Figure 3A
XOP +
Figure 4A
XOS + X O
Figure 5A
XOS +
Jan 2010
Electrical Engineering Tetiary
Tetiary
Primary
Secondary
Primary
Secondary
3Io
3Io
Io
Test Source, Vo
Io
Test Source, Vo
Xos XOT Xos + XOP
Figure 3A - Test source at Primary, XOP +
Figure 2A - Test source at Primary, XOP + XOT
Xos Ap
As
Secondary
Xop XOT
Test Source, Vo
AT
Tetiary Bp
BS
BT
Ap
Test Source, Vo
Xos
As
Secondary
XoT
AT
Tetiary
Xop
Bp
BS
BT
Zero bus
Zero bus
Figure 2B - Zero sequence impedance, X OP + XOT
XoS XOT XOS + XOT
Figure 3B - Zero sequence impedance, XOP +
Tetiary
Tetiary
Primary
Primary
Secondary
Secondary
3Io
Io
Test Source, Vo
3Io
Io
Test Source, Vo Figure 5A - Test source at Secondary, XOS +
XoT XOP XoT + XOP
Figure 4A - Test source at Secondary, XOS + XOT
Xos
As
Xop
Ap
Primary
Ap XOT
AT
Bp BT
BS
Tetiary
Test Source, Vo
Xos
As
XoT
AT
Xop
Primary Bp
BT
BS
Tetiary
Test Source, Vo
Zero bus
Zero bus
Figure 4B - Zero sequence impedance, Xos + X OT
Figure 5B - Zero sequence impedance, Xos +
XoT XOP XoT + XOP
THE SINGAPORE ENGINEER
Jan 2010 · 27
Electrical Engineering Measurement results Te measurement results in the table on the right have been obtained rom a reputable transormer vendor or an installation at a customer’s acility in Jurong Island. For the connection scheme in Figure 2A, the impedance recorded by the test source will be (10950 / 424) or 25.8 ohm. Te equivalent zero sequence impedance will be (3 x 25.8) or 77.5 ohm per phase or X OP + X O = 77.5 ohm per phase. o convert the ohm per phase to the equivalent % value, the base impedance at the primary winding must be calculated, and this is equal to (230 x 230) / 300 or 176 ohm. Te % impedance value will be (77.5 / 176) or 44%. Te calculations or Figure 3A are similar to that or Figure 2A because the test source is connected at the primary winding. For the connection scheme in Figure 4A, the impedance recorded by the test source will be (2610 / 1034) or 2.5 ohm. Te equivalent zero sequence impedance will be 3 x 2.5 or 7.5 ohm per phase or X OS + X O = 7.5 ohm per phase. o convert the ohm per phase to the equivalent % value, the base impedance at the secondary winding must be calculated, and this is equal to (132 x 132) / 300 or 58 ohm. Te % impedance value will be (7.5 / 58) or 13%. Te calculations or Figure 5A are similar to that or Figure 4A because the test source is connected at the secondary winding. Calculation results From the measurement results, we have the ollowing: X OP + X O= 44% X OP + X OS + X O= X OS +
=
13%
=
7%
26%
Connection Scheme
Measured Measured Voltage in kV Current in Ampere
Calculated Impedance in ohm per phase
Calculated Impedance in %
Figure 2A
10.95
424
77.5
44
Figure 3A
10.19
676
45.2
26
Figure 4A
2.61
1034
7.5
13
Figure 5A
1.52
1027
4.4
7
Te base values are 300 MVA, 230 kV or 300 MVA, 132 kV
o zero sequence impedance are across the physical terminals o the primary, secondary, and tertiary windings. Tese physical values o zero sequence impedance are X O_PS = X OP + X OS = 27% X O_P = X OP + X O = 33% X O_S = X OS + X O = 13% Zero sequence impedance Te measurement o the zero sequence impedance or transormers is seldom done or small transormers, and is done only or large transormers. It is common to assume that the zero sequence impedance o the transormer is equal to the positive sequence impedance which is the transormer leakage impedance. Te exceptions to this are the three phase transormers with three limbs or the core. Tis type o construction does not provide the return path or the zero sequence fux through the core o the three limbs. Te return path or the zero sequence fux is through the metal body o the transormer tank. Tereore the zero sequence impedance will not be equal to the positive sequence impedance, and typical values are 85% to 90% o the positive sequence impedance. Single phase to ground ault Te single phase to ground ault will depend on the positive, negative, and zero sequence impedance.
Solving the equations, we will have X OP = 29% X OS = - 2% X O = 15%
Single Phase to Ground Phase =
X OP, X OS and X O, are ctitious zero sequence impedances and hence may have negative values. Te physical values 28 · THE SINGAPORE ENGINEER
Jan 2010
=
where Vo is the pre-ault phase to neutral voltage X 1 is the positive sequence impedance X 2 is the negative sequence impedance X 0 is the zero sequence impedance I F is the three phase ault current In most applications, X 1 = X 2 and hence the single phase to ground ault current will be o the three phase ault current, where K = When X = X 1, the single phase O to ground ault current equals the three phase ault current. • When X is less than X , the single O 1 phase to ground ault current is more than the three phase ault current. • When X is greater than X , the O 1 single phase to ground ault current is less than the three phase ault current. •
hereore measurement o the zero sequence impedance o a transormer is important when the transormer is o large MVA size because o the possibility that the single phase to ground ault current is greater than the three phase ault current.
[Er. Lee Wai Meng is Principal Consultant/Director of J.M. Pang & Seah (Pte) Ltd, an electrical and mechanical consultancy. A Singapore-registered professional engineer, he has a 230 kV switching licence from Energy Market Authority (EMA)].