The Negative Branch Impedance in the Transformer Sequence Circuit Model

Elmo Price

ABB Inc. Krzysztof Kulasek

ABB Inc. Gary Kobet

Tennessee Valley Authority

Introduction The neutral (to ground) or delta tertiary current in transformers with high and low voltage wye-grounded windings and a delta tertiary winding is usually used to provide a sensitive polarizing quantity for legacy discrete directional relays or microprocessor functions to determine correct fault direction on transmission lines. A common assumption is that the polarizing current, either neutral current, IN, and delta current, IY0, as shown in figure 1(a) is always in the same direction regardless of the fault location being on the high (H) or low (X) voltage side. However, incorrect directional relay (function) operations have occurred due to the reversal of the polarizing current obtained from either of the two locations. The current reversal is the result of transformer design characteristics that produce a negative or very small positive branch impedance value in its equivalent circuit model – usually the low voltage. Refer to figure 1(b). This paper will address the development and effect of the sequence circuit model on polarizing current reversals and the aspects of transformer design that affect it. Also, a review of transformer characteristics and their application from two utilities is provided to identify potential application issues and their mitigation.

Y1

H1

X1

X3

H2

H3 Y3

Y2

X2

XX

IN

IY0

C S

ZH0 (+/-) ZX0

ZY0

(a) Autotransformer with delta tertiary (b) Zero sequence circuit

IC0

H0 X0

N

N

IY0

*

*

* Polarizing Current

Figure 1. Expected current direction in an autotransformer and its zero sequence

model for a ground fault on the high or low voltage side

Leakage impedance First it is important to have a fundamental understanding of leakage impedance between transformer windings. Leakage impedance is directly related to leakage flux. Leakage flux is that part of the total flux that is produced by energizing a winding that does not link the other winding. This is illustrated rather simply in figure 2(a) where φL is the leakage flux produced when the primary P winding is energized and

does not link (flow through the center of) the secondary S winding. Figure 2(b) illustrates the leakage flux where the primary and secondary are wound concentrically.

NSEP ES

φPS - links primary and secondary coils

φL - leakage

φL - leakage

NP

(a) Leakage flux illustration

CORE

PrimaryPrimary Secondary Secondary

φL - leakage

(b) Leakage flux between concentric windings

Figure 2. Leakage flux

Since the amount of flux in the secondary winding (the winding not directly energized in this case) is smaller than that in the primary winding there will be a smaller percent voltage induced into the secondary winding. Percent (leakage) impedance between two windings represents the induced voltage difference (drop) between the two windings. Figures 3 and 4 show the main parameters that influence the leakage impedance between windings where the windings are circular and wound concentrically on the core. This would be typical of core form construction. Shell form construction will be constructed differently, but equally as complex. The parameters include, but are not limited to, the winding diameters, winding heights, winding radial build, winding turns, the duct space between windings, the winding’s placement relative to the core and the winding connections. The following approximate formula is provided to illustrate how the relative winding-to-winding impedances change with the transformer geometry [2] using the H – X impedance as an example. Where:

W

HXXH

hdtt

*1KR π++−= - Rogowski factor

DH, DX, DY - Mean winding diameters tH, tX, tY - Radial build of the winding dHX, dXY, dHY - Duct space between windings hW – Winding height (or average winding height in case there are not equal) e – volt-per-turn NI = N1 I1 = N2 I2 – mmf (ampere-turns) at the reference current of winding of the pair f – Frequency

The above equation shows the impedance calculated for the H-X windings. Other impedances for a 3 winding transformer (X-Y and H-Y) can be calculated as well using the dimensions as per figure 3.

(1) ]%[ K* )3

(*2

*****10*48.2 R

6HX

XHXH

WHX dttDD

heINfZ +

++= −

2

Y

NT

YCORE

X HX

NSNP

DY

DX

DH

H – Primary windingNH – Primary winding turnsDH – Primary winding mean diameter

X – Secondary windingNX –Secondary winding turnsDX – Secondary winding mean diameter

Y – Tertiary windingNY – Tertiary winding turnsDY –Tertiary winding mean diameter

h – Winding heightdHX, dHY, dXY – Duct space between windingstH, tX, tY – Winding radial build

H1

Y1

H

Y2X0

H0

X1

Y

NT

YCORE

X HX

NSNP

DY

DX

DH

H1

Y1

SH

Y2H0X0

X1

SeriesCommon

(a) Conventional YYD three winding (b) Autotransformer YYD

h

dXY dHX

dHY

tHtY tX

Figure 3. Parameters affecting leakage impedance between windings

YCORE

X

H1

Y1

H

H0X0

X1

SeriesCommon

YCORE

H1Y1

H

H0X0

X1

SeriesCommon

YCORE

X

H1Y1

H

H0X0

X1

SeriesCommon

Y2Y2

X

Y2

(a) Configuration 1Tertiary next to core

(b) Configuration 2Tertiary between series and common winding

(c) Configuration 3Tertiary outside of series winding

Figure 4. Placement of tertiary winding

Equation (1) can be also used to calculate the impedance of an autotransformer. In that case we should enter N * I either for the common or the series winding. The calculated impedance H-X is on the basis of the equivalent power, not the rated (through) power. However, in system studies we have to refer to the rated power and therefore, this impedance must be multiplied by the reduction factor R which is equal to (VH – VX)/ VH. Impedance X-Y can be calculated directly from the equation (1). However, when calculating the H-Y impedance for an autotransformer winding arrangement as per fig. 3b one has to take into consideration that the current will flow in the series and common winding (see fig. 6 b) and therefore the total ampere-turns have to be considered with the equivalent H and X winding dimensions.

The calculation of winding-to-winding leakage impedance becomes increasingly difficult with additional windings and their relative placement (for example, with the tertiary Y winding located between H and L (fig. 4 b) windings). This task is generally left to the manufacturers using FEM (finite element method) design programs for the magnetic field calculations.

3

When working on a new transformer design or running a system study engineers have to consider transformer and network impedances when calculating short circuit currents and forces. Symmetrical and unsymmetrical fault cases must be evaluated to find the maximum mechanical and thermal stress for the design. The method of the symmetrical components is used to calculate short circuit current. It is described in several publications including the Electrical Transmission and Distribution Reference Book [1]. The paragraph above described how the positive sequence impedance for a transformer can be calculated. The negative sequence is equal to the positive. The calculations of the zero sequence impedance of a transformer are more complex and cannot be represented by simplified formulas. In general the following factors must be considered: transformer construction (shell or core type), type of the core (three or five legs), windings connections, presence of the neutral terminal (YN), and existence of a delta connected winding. When zero-sequence current flows in only one winding of a phase (e.g. the secondary winding in the Y-YN connection) without corresponding balancing ampere-turns in another winding, a flux in all three phase legs will be generated that have equal amplitude and the same phase angle. The return path for this flux will depend on the transformer core construction. Three single-phase units, three-phase shell form and three-phase five-legged core form units (see fig. 5, a, c and d) offer a low reluctance return path through the core, and therefore, the zero sequence impedance will be high. The values will be of the order of the magnetizing branch impedance. For a three-phase three-legged design (see fig. 5(b)) with a wye-wye connection the zero sequence flux saturates the top and bottom core yokes forcing a return path of the flux outside of the core. The flux in this case will have a relatively high reluctance path, and therefore a low zero sequence impedance. However, this impedance is usually 5 to 10 times greater than the positive sequence leakage impedance between winding [2]. This order of magnitude is due to the effect of the tank that can be regarded as a short-circuited delta connected winding for the circulation of zero sequence currents. The zero-sequence impedances in these cases are influenced by the degree of saturation in the core and, therefore, will vary with the zero-sequence currents.

When zero-sequence currents can flow through two windings per phase, with equal and opposite ampere-turns (D-YN connection), the transformer zero-sequence impedance approaches the positive sequence leakage impedance between those two windings. Analysis of that with different winding connections is given in reference [2].

The zero sequence impedance, and therefore its relation/ratio to positive sequence impedance, varies greatly depending on:

• Winding arrangement • Winding connection - wye or delta • Winding location relative to core and other windings • Whether LV windings are vertically stacked • Transformer core construction

The above factors cause the Z0/Z1 ratio to vary in value between a minimum of around 0.35 to nearly 1.0. When working on the short circuit calculations of a power transformer the designer has to calculate the zero sequence impedance with good accuracy. Using a factor may lead to wrong calculation of the current and under or overestimate the SC currents. Since the forces are proportional to the square of the current it is an important factor in the design evaluation. It is equally important for the protection engineer to have accurate winding-to-winding zero sequence impedances rather than depending on factors.

4

φ0

(a) Three single phase cores

φ0 φ0φ0

(b) Three phase three legged core form

φ0

B

φ0

I0A I0

C I0

3I0

3I0

BA CI0 I0 I0

(c) Three phase five legged core form

φ0 φ0φ0

3I0

BA I0CI0 I0

φ0

φ0

φ0

(d) Three phase shell form

A

B

CI0

I0

I0

3I0

Figure 5. Zero sequence flux path for different transformer core constructions

Impedance testing Impedance testing of a transformer is addressed in IEEE Standard C57.12.90 – 2010, Section 9. Testing measures the positive and zero sequence impedances between any two windings. Zero sequence testing is essential when an accurate transformer model is needed for ground fault studies and polarization current requirements. Basically, positive sequence impedance is measured between windings by applying a voltage to one winding and shorting the other winding being tested. All other windings are left open. The voltage is increased until the winding’s nominal rated current is flowing. Since the current is at 100% of rated the measured voltage in % of rated voltage is equal to the % impedance between the two windings. The losses are also measured to give the real (resistance) part of the impedance. Resistance, however, will not be considered further in this paper. The basic test connections for a single-phase three winding conventional and autotransformer are shown in figure 6.

Y

XH Y

X

H

Y

XH

Y

XH

ZHX ZXYZHY

IX

IYIY

IX

Y

X

H Y

X

H

IY IY

ZHX ZXYZHY

(a) Conventional transformer (b) Autotransformer

VT

VT

ITIT

Figure 6. Test connections for a single-phase three winding YYD conventional and autotransformer

Single phase units do not require zero sequence testing as the positive and zero sequence impedances are equal. This is also generally true for three phase shell form designs and core form designs with more than three legs. Zero sequence testing is warranted for three legged core designs with or without a delta

5

winding. Test connections for a three-phase YYD autotransformer with a delta tertiary winding are shown in figure 7. These tests will provide the transformer’s positive and zero sequence impedances.

Zero sequence testing will include the effect of the tank [acting as a buried tertiary winding]. Testing the zero sequence impedance between windings of a three-phase transformer uses a single phase voltage source and the connections of figures 7(c) and 7(d). Also, not shown, is the test connection for ZXY0 where in figure 7(d) the test voltage is applied to the X terminals of the common winding and the H terminals are left open.

The C57.12.90 standard provides the connections and equations to determine the zero sequence T branch model. The difference between the positive and zero sequence impedances is the effect of the core and tank design on zero sequence flux.

Y1H1

X1

X3

H2

Y3

Y2

X2

C SN

I=0

VH1-H2

Y1

H1X1

X3

H2

Y3

Y2

X2

C SN

3IH0

IY0VH0

IH0

IH0

IH0

(a) Three-phase autotransformer ZHX1 positive sequence test

(c) Three-phase autotransformer ZHX0 zero sequence test

VT

IT

H3

H3

Y1

H1X1

X3

H2

Y3

Y2

X2

C SN

3IH0

IY0VH0

IH0

IH0

IH0

(d) Three-phase autotransformer ZHY0 zero sequence test

H3

Common winding X terminals shorted and grounded.

Common winding X terminals open circuited.

Y1H1

X1

X3

H2

Y3

Y2

X2

C SN

IY1

IY2

IY3

VH1-H2

(b) Three-phase autotransformer ZHY1 positive sequence test (accessible delta tertiary winding connections)

VT

IT

H3

IX1IX2

IX3

Figure 7. Three-phase positive and zero sequence impedance tests

6

The effect of tertiary winding placement There are multiple types of transformers where particular application and system conditions set the ratings, working conditions and unit application; substation, distribution and network tie autotransformers. The most common in the USA and in Canada for HV transmission lines are autotransformers. The electrical characteristics of an autotransformer or any other three winding YYD transformer are generally represented in system analysis by an equivalent circuit “T” diagram as shown in figure 8(b). When impedances ZHX, ZHY and ZXY of figure 8(a) are known equivalent ZH, ZX and ZY of figure 8(b) are calculated using equations 2 – 4 where all impedances are expressed in percent or per unit on the same reference power (MVA base).

ZH

H X

H X

Y

ZHX

ZHY ZXY

Y

ZY

ZX

(a) Three winding transformer sequence circuit model with winding-to-winding impedances as tested

(b) Three winding transformer sequence circuit equivalent T model

Figure 8. Equivalent T diagram for an autotransformer

𝑍𝑍𝐻𝐻 =𝑍𝑍𝐻𝐻𝐻𝐻 + 𝑍𝑍𝐻𝐻𝐻𝐻 − 𝑍𝑍𝐻𝐻𝐻𝐻

2 (2)

𝑍𝑍𝐻𝐻 =𝑍𝑍𝐻𝐻𝐻𝐻 + 𝑍𝑍𝐻𝐻𝐻𝐻 − 𝑍𝑍𝐻𝐻𝐻𝐻

2 (3)

𝑍𝑍𝐻𝐻 =𝑍𝑍𝐻𝐻𝐻𝐻 + 𝑍𝑍𝐻𝐻𝐻𝐻 − 𝑍𝑍𝐻𝐻𝐻𝐻

2 (4)

Unless all impedances between different systems are listed in the transformer specification a designer can choose to put the delta connected winding in three different relative positions in relation to the high and low voltage winding as presented in figure 4. The selection is based on the optimized production cost and loss evaluation. Generally this is configuration 1 of figure 4(a), which is guided primarily by insulation requirements. In some applications, however, it could be beneficial to have the tertiary (Y) winding as the outermost and wind the main low (X) and high (H) voltage coils with smaller diameters as shown in configuration 3 of figure 4(c). This is often feasible for transformers with a high H/X turns ratio such as 260/72 kV or 345/34.5 kV because it will reduce copper weight and load losses in the main windings and offset the cost of insulation. Such high turns ratio applications with an outer tertiary winding are being used with wind farm and other small generation utilities.

With the same reference power the impedance between windings is a function of the geometry as was explained earlier when discussing equation (1). Figures 3 and 4 also give a visual explanation of the dimensions and tertiary placement. When looking at the winding configuration 1 of figure 4(a) we can

7

see that the impedances based on the distance between windings that ZHX and ZXY are smaller than ZHY, at the same time ZHX + ZXY is very close in value to ZHY being slightly larger or smaller due to the variance in other parameters. Using the equation (3) above for this winding configuration we can see that in the equivalent T diagram low voltage impedance, ZX, may have a small negative value with the right parameter values. It will be a similar situation for the configuration 3 of figure 4(c) where the impedances ZHX + ZHY < ZHY is possible using equation (2). In case it is required to have all positive branch impedances in the T diagram, winding configuration 2 of figure 4(b) can be used. This cannot be changed by adding a reactor in the tertiary winding (to limit current during faults) since this will simultaneously increase impedances 𝑍𝑍𝐻𝐻𝐻𝐻 and 𝑍𝑍𝐻𝐻𝐻𝐻 .

In order to illustrate the change in the impedances, short circuit zero sequence currents and other transformer design criteria, the authors selected a 280 MVA 161.7/69 kV autotransformer with a 56.6 MVA 13.8 kV buried tertiary winding. Analysis included the 3 winding configurations per figure 4. Fault currents were calculated using IEEE 57.12.00-2010 with Z0/Z1=1 for the HV and LV systems. The equivalent sequence network used is shown in figure 9.

ZHS1

ZHS2

ZH1

Positive

Negative

ZHS0

Zero

ZX1

ZY1

ZH1 ZX1

ZY1

ZH0 ZX0

ZY0

Y

Y

X

X

X

Y IX0 IH0

IY0

1.0 pu

IH1

IH2

IX1

IX2

ZLS1

ZLS2

ZLS0

H

H

H

1.0 pu

Sequence circuit interconnection for fault on high voltage (H) side

Sequence circuit interconnection for fault on low voltage (X) side

Figure 9. Sequence network interconnection for analysis

Results are shown in tables 1 and 2. Analysis shows that there are zero sequence current reversals in the tertiary and common windings for configurations 1 and 3. It is also shown that with positive tertiary current a reversal in the common winding can still occur.

Table 1. 280 MVA Autotransformer - impedances for different winding arrangements.

Winding configuration Positive sequence Impedance Positive sequence impedance

8

H - X H - Y X - Y H X Y 1 Core-TV-LV-HV 10.6 29.0 14.4 12.6 -2.00 16.4 2 Core-LV-TV-HV 10.2 8.4 11.4 3.6 6.6 4.8 3 Core-LV-HVR-HV-TV 10.4 39.7 70.3 -10.1 20.5 49.8 All impedances are in % on 0.6*280 MVA base at rated winding voltage. ZBase = kV2/MVA, ZΩ = ZBase x Z%/100 HVR - regulating winding

Table 2. 280 MVA Autotransformer – Zero sequence currents for single Φ-G ground fault on HV and LV

SC Case Winding configuration

HV (kA) LV (kA) TV (kA) Line Series

winding Line Common

winding Line Winding

1φ fault on HV

1 -1.558 -1.558 3.734 -2.176 0.00 -0.24 2 -2.804 -2.804 2.42 0.384 0.00 11.93 3 -3.51 -3.51 5.69 -2.183 0.00 7.271

1φ fault on LV

1 1.82 1.82 -7.69 5.87 0.00 9.844 2 1.132 1.132 -4.957 3.826 0.00 6.625 3 2.64 2.64 -5.01 2.365 0.00 -3.53

The effect of the negative branch impedance on current polarization All of the measured winding-to-winding impedances in table 1 above will be positive. One of the branch impedances, however, is likely to be negative unless design constraints are imposed. With winding configuration 1 being the usual case, ZHY will be the largest of the three branch impedances, possibly causing ZY to be negative. In Figure 10(a), k0 represents the per-unit current that flows in the ZX leg with 1.0 per unit of current flowing to the point of discontinuity (for example a ground fault) on the high-voltage system. This distribution factor is very important in identifying whether or not neutral or tertiary current in the transformer is a reliable polarizing quantity. ZS0 is the source impedance for the low voltage system. With one per-unit current flowing in the high voltage winding, for a ground fault on the high-voltage system, k0 per-unit current flows in the low voltage system and 1- k0 flows to ground through the common and tertiary windings. Translating per unit current to amperes, in figure 10(b) with one ampere of zero sequence current in the high voltage winding of an autotransformer, there will be k0VH/VX amperes of zero sequence current in the low voltage system, 1 - k0VH/VX amperes of zero sequence current will flow to ground through the common winding and (1 - k0)VH/VY amperes will circulate in the delta tertiary winding. For the conventional three winding transformer of figure 10(c) the currents have the same high and low side ct primary distribution, the ct secondary neutral current sum and tertiary current are proportional to (1 – k0) provided the neutral cts have the ratios as indicated. Therefore, the neutral sum of a conventional transformer does not have the same limitations as an autotransformer neutral.

9

ZX0X

1-k0

1.0 pu

k0 =

HZH0

ZY0

ZLS0

X

H

Y

ZY0ZX0 + ZLS0+ ZY0

k0VH/VX

1.0

(1 - k0)VH/VY

3(1 - k0VH/VX)

*Polarizing Current

(b) Relative ampere values in autotransformer

(a) Zero sequence circuit of a three winding transformer (values in perunit)

k0

Tertiary current reverses if k0 > 1

*

*

3(1 - k0)*

(1 - k0)VH/VY

*Polarizing Current

*

H1.0

Y

X

k0VH/VX

(c) Relative ampere values in three winding transformer

VH/VX:1 1:1

Figure 10. Zero sequence current reversal in the delta tertiary and common windings

The summary of requirements for correct operation (no current reversal) for a fault on the high voltage side is:

• From figure 9 𝑘𝑘0𝑥𝑥 = 𝑍𝑍𝑌𝑌0𝑍𝑍𝑋𝑋0+𝑍𝑍𝐿𝐿𝐿𝐿0+𝑍𝑍𝑌𝑌0

(5)

• Delta 𝑘𝑘0𝑥𝑥 < 1 (6) • Neutral 𝑘𝑘0𝑥𝑥 < 𝑉𝑉𝐻𝐻/𝑉𝑉𝐻𝐻 (7)

Equations for correct operation for a fault on the low side are derived similarly as:

• 𝑘𝑘0ℎ = 𝑍𝑍𝑌𝑌0𝑍𝑍𝐻𝐻0+𝑍𝑍𝐻𝐻𝐿𝐿0+𝑍𝑍𝑌𝑌0

(8)

• Delta 𝑘𝑘0ℎ < 1 (9) • Neutral 𝑘𝑘0ℎ < 𝑉𝑉𝐻𝐻/𝑉𝑉𝐻𝐻 (10)

Usually there are no issues for faults on the low side of the transformer (equations 8 – 10). Most transformer designs will not usually result in a negative ZHO branch and therefore k0h will be less than 1. However, it was shown in tables 1 and 2 that a unit such as configuration 3 (winding placement from the core: X, H and Y) could result in k0h of equation (9) not being satisfied and the delta tertiary winding current reverses. On the other hand the neutral current would most likely always be a good polarizing source.

Analyzing the values for a high voltage fault (equations 5 – 7) we reach some very important conclusions; the common neutral of a wye-delta-wye three winding transformer or the neutral of a wye-wye autotransformer with a delta tertiary will supply a reliable polarizing current only if k0 < VX/VH. If it were greater than the ratio VX/VH, the direction of the polarizing current to the relay would be in the opposite direction to that shown in figure 10(b or c). This is unacceptable because this current should always be up the neutral when there is current flow to a ground fault on the low voltage wye system. Also, keep in mind that k0 may even be greater than VX/VH for small positive values of the low side impedance ZLS0 + ZX0 causing a neutral polarizing current reversal.

The delta winding of such a transformer is virtually always a reliable polarizing source unless the net impedance to the system is not positive. For example, if the quantity ZLS0 + ZX0 is negative, the current inside the delta would not be suitable as a polarizing source.

When using polarizing current one must stay aware of the application’s sensitivity to decreasing source impedance with system configuration changes. As systems grow and become more interconnected, the

10

short circuit capacity increases and thus reduces the high and low voltage source impedances to the transformer. A previously installed application, which operated correctly, may misoperate due to the subsequent system changes.

Field data analysis Autotransformer application impedance data from two utilities can be found in Appendix A. Table 3 summarizes the data.

Table 3. Summary of autotransformer application data Utility A Utility B Both Total units in survey 57 28 85 # (%) with negative high side branch impedance 0 0 0

# (%) with negative low side branch impedance 42 (72%) 17 (61%) 60 (71%) # (%) not suitable for tertiary current polarization, k0 > 1 1 (2%) 0 1 (1%) # (%) not suitable for neutral current polarization, k0 > VX/VH 38 (67%) 10 (36%) 48(56%)

The study of the utility applications suggests that autotransformers are designed, unless otherwise specified, with their winding configuration build from core, Y-X-H as shown in figure 4(a), such that negative low voltage branch impedance in the auto transformer equivalent circuit is rather common occurring in 60% to 75% of transmission voltage level autotransformers. These negative impedances are generally small enough such that the low voltage source impedance overcomes the effect of the transformer’s negative low voltage branch impedance making the use of the delta tertiary suitable for most applications – 99% of the applications studied here. However, 71% of these are subject to the possibility of decreasing source impedances due to system changes. In 56% of the cases studied the transformer’s neutral current is not suitable as a polarizing source. These numbers will vary with transformer design and likewise from utility to utility that use them.

A review of each utility’s applications the following:

Utility A • Most applications involving newer technology used voltage polarizing • Tertiary current polarizing was used mostly for legacy products where available • Neutral current polarizing was not used

Utility B • Most applications involving newer technology used voltage polarizing • Tertiary current polarizing was used where available mostly for legacy products and newer

products where dual polarization (using both voltage and current) was desired. • Polarizing current derived from high and low voltage line ct connections was used in one

application (figure 12(c)). • Neutral current polarizing was used in some cases where tertiary current was not available and

there were no application issues.

While this study was limited to autotransformers it should be noted that conventional full winding transformers are subject to delta tertiary current reversals and the criteria of equations 6 and 9 still apply.

11

Mitigation

Use Delta Tertiary Current Where applications of neutral current polarization are not reliable and a current transformer (ct) is available in the unloaded delta tertiary winding (or 3 cts in a loaded tertiary) then it would be possible to change current polarization sources.

*

*

*Polarizing Current

(a) Buried or non-loaded delta tertiary winding (b) Loaded delta tertiary winding

LOAD

Figure 11. Connection of delta tertiary current transformers

X

H

Y

3k0

1.0

(1 - k0)VH/VY

IN = 3(1 - k0VH/VX)

(a) Polarizing with neutral and low voltage cts

*S

C

k0VH/VX

IP = 3(1 - k0)

3

3VX/VH

C/(S+C)= VX/VH Aux ct

X

H

Y1.0

(1 - k0)VH/VY

IN = 3(1 - k0VH/VX)

*

k0VH/VX

3k0

VH/VX

3IP = 3(1 - k0)

(c) Polarizing with high and low voltage cts

VH/VX

VH/VX

1

1

INS = 3(VX/VH - k0)

X

H

Y1.0

(1 - k0)VH/VY

IN = 3(1 - k0VH/VX)

(b) Polarizing with neutral and high voltage cts

*S

C

k0VH/VX

IP = 3(1 - k0)

C/(S+C)= VX/VH Aux ct

VH/VX

1

1

3k0VH/VX

3

3k03

INS = 3(1 - k0VH/VX)

Figure 12. Delta tertiary polarizing current using neutral, high voltage and low voltage cts

As is sometimes the case tertiary cts may not have been provided. In such cases it is possible to obtain a secondary ct polarization current that is equal to the tertiary ct secondary current by using a combination

12

of the neutral, high voltage and low voltage cts. Three connection methods are shown in figure 12. These are polarizing with the neutral and sum of low voltage cts, polarizing with the neutral and sum of high voltage cts and polarizing with the sums of high and low voltage cts. An auxiliary current-balancing auto transformer is required for connections with the neutral ct. The neutral ct has the same ratio as the high or low voltage cts with which it is being used and the ct ratios are normalized with the high voltage ct ratio equal to 1 to simplify the expressions.

The ct schemes may be subject to incorrect operation if a fault occurs within the zone defined by the ct locations. It is expected that other protections, e.g. transformer differential and restricted earth fault, will have operated.

If tertiary current cannot be used based on the provided criteria then sequence voltage or current compensated sequence voltage is suggested.

Transformer Design The issue of polarizing current reversal can be eliminated through transformer design. Using configuration 2 of figure 4(b) is an example. In this case the tertiary is placed between the high and low voltage windings altering the tested winding-to-winding impedances and calculated branch impedances shown in table 1. With these impedances immunity to polarizing current reversal is guaranteed barring human connection errors. This can be validated by calculating k0 for both high and low voltage faults with source impedance set to zero (IHS0 = ILS0 = 0) and using equations 5 – 10. If both k0h and k0l values meet the criteria of the equations then there will never be issues.

Alternative Polarizing Methods The primary advantage of current polarization is that the quantity provides more sensitive directional control in those applications where measuring a polarizing voltage may be a problem. This is particularly true when polarizing voltage is measured near a strong ground source (small source impedance). Also, using polarizing current has been a long established with many utilities and is very much a part of their installed base where changing to alternative methods can be very expensive. In such cases frequent review of the application is warranted.

Zero and Negative sequence voltages are far more reliable polarization methods, and are indeed preferred, if sensitivity is not an issue. This is particularly true in applications where mutual coupling affects the reliability of both zero sequence voltage and current polarization methods and negative sequence voltage polarization has to be used. With the increased use of microprocessor technology methods have been developed to reliably compensate zero and negative sequence polarizing voltages with the respective line zero or negative sequence current to address sensitivity issues. One method is illustrated in figure 13. In figure 13(a) we see the zero sequence voltage profile for a forward fault. The zero (or negative) sequence voltage is highest at the fault location and reduces in value as the measurement moves back towards a source. The zero sequence voltage measured at relay A is the voltage drop across the source impedance and equal to –I0AZ0A. This quantity may not be a voltage sufficient for polarizing. Observe the voltage profile. By adding some line impedance voltage drop, –I0AkZ0L, to the measured quantity we get –I0A(Z0A + kZ0L), a quantity sufficient for polarization for detecting forward faults accurately. This is as if the voltage transformer was moved out on the transmission line by a distance k times line length. Now we must investigate how setting this compensation affects reverse faults. Observe the voltage profile on figure 13(b) for a reverse fault. Reliable polarizing for a reverse fault requires that (Z0L + Z0B) > kZ0L plus some margin to assure sufficient reverse fault voltage polarization. If the protected line, Z0L, is long (in impedance) and k is set less than 0.4 there is no problem.

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These methods vary from manufacturer to manufacturer, but all generally work the same. Applying this compensation usually eliminates the need for the transformer polarizing current for these applications.

REL A

Z0B

V0A = - I0AZ0A

REL BI0BI0A

V0k = - I0A(Z0A+kZ0L)

-V0

mZ0L (1-m)Z0LZ0A

A B

kZ0L

Fault Location- I0A(kZ0L)

V0(MAX)

Zero Sequence Voltage Distribution

REL A

Z0B

REL BI0B

I0A

-V0

Z0LZ0A

A B

Zero Sequence Voltage Distribution

I0B

V0(MAX) V0k = - I0B(Z0B+(1-k)Z0L)

I0B(kZ0L)

V0A = - I0B (Z0B+Z0L)

Fault Location

Fault Location

(a) Forward Fault

(b) Reverse Fault

X

X

Figure 13. Compensating zero sequence voltage with zero sequence line current

Conclusions and Recommendations The negative branch impedance of the transformer’s T branch model was investigated as to its effects on current reversals in the delta tertiary winding and transformer neutral. Along with the negative branch values small positive values allowed current reversals in the transformer’s neutral. Given the importance of accuracy the model should be developed with zero sequence impedances derived from zero sequence testing. It was also pointed out how transformer design affects the T branch model. Generally the negative or low impedance is on the low voltage side of the transformer model. However, different winding configurations can eliminate or even move the negative impedance to the high voltage side. The latter case being possible or even likely for transformers with high H/X turns ratios (e.g. 345/34.5/13.8 kV).

The following recommendations are made from the results of the investigation.

• Voltage polarization and impedance compensated voltage polarization are wise alternatives and are recommended as first choices.

• Reliable polarization current can generally always be obtained from the delta tertiary winding. There are a few exceptions where zero sequence source impedance is very small and does not allow its use. Also schemes involving the neutral and line cts are available to provide a proportional quantity when tertiary windings are not provided with cts. Each application should be reviewed with system changes.

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• Polarization current from the neutral ct is not generally reliable and, therefore, not recommended where alternatives are available. Using the neutral ct connected to line cts with an auxiliary transformer may very well be suitable.

• Accurate zero sequence testing is desired for development of the T branch model.

• The problem of negative branch impedances can be eliminated with the design of transformer winding configurations. The possible extra costs, first and evaluated, should be considered.

References [1] Electrical Transmission and Distribution Reference Book. ABB Inc. Raleigh, North Carolina. 1997.

[2] Giorgio Bertagnolli. Short Circuit Duty of Power Transformers. ABB Ltd. Zurich, Switzerland 2007

[3] Elmore, W., Price, E. “Polarization Fundamentals.” 27th Annual Western Protective Relay Conference. Spokane, Washington. October 24 – 26, 2000.

[4] Andrichak, J., Patel, S. “Polarizing Sources for Directional Ground Relays.” Publication GER3182A. GE power Management. Malvern, PA.

[4] IEEE Standard C57.12.00, 2010

[5] IEEE Standard C57.12.90, 2010

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Biographies

Elmo Price, PE Elmo is currently a Senior Consultant with ABB Inc. He received his BSEE degree in 1970 from Lamar State College of Technology and his MSEE degree in 1978 from the University of Pittsburgh. He began his career with Westinghouse in 1970 and worked in many engineering positions in various manufacturing divisions, and as a District Engineer located in New Orleans providing engineering support for Westinghouse power system products. With the consolidation of Westinghouse into ABB in 1988 Elmo assumed regional responsibility for product application for the Protective Relay Division. Since then he has worked in various technical management positions responsible for product management, product design, application support and relay schools. Elmo is a registered professional engineer and a Life Senior member of the IEEE. He is a member of the IEEE Power System Relay Committee and the Line Protection Subcommittee, serving as a contributing member to many working groups. He has two patents and has authored and presented numerous industry papers.

Krzysztof Kulasek Krzysztof is Vice President of Engineering for ABB Large and Medium Power Transformers in North America located in Varennes, QC, Canada. While working in the transformer business for more than 20 years he has been involved in new technology implementations in different factories as well as product and production process development. Krzysztof’s areas of expertise include: transformer optimization, insulation design, SC calculations, stray loss heating, process improvement and production optimization. While being part of the ABB global technical team he contributed to R&D projects, technology and quality improvement initiatives and new engineers training. He received his electrical engineering degree in 1993 at the Technical University of Lodz, Poland from the faculty of Electrical Machines and Transformers and has been an IEEE member since 2002.

Gary Kobet Gary is an Electrical Engineer (short-term planning) for the Tennessee Valley Authority (TVA) in Chattanooga, Tennessee. His responsibilities include machine and voltage stability studies for the operating horizon, developing operating guides, and disturbance analysis. Previously he worked in the System Protection department scoping relaying schemes for transmission and generation projects, as well as developing relay set point calculations. He has performed transient studies using EMTP for breaker TRV studies and switching surge overvoltages. Previously he worked as a field engineer and as power quality specialist. Mr. Kobet earned the B.S.E. (electrical) from the University of Alabama in Huntsville in 1989 and the M.S.E.E. from Mississippi State University in 1996. He is a member of the IEEE Power Engineering Society, CIGRE’, Eta Kappa Nu, Tau Beta Pi, and is a registered professional engineer in the state of Alabama. Presently he is serving on the NERC Geomagnetic Disturbance Task Force.

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Appendix A - Autotransformer Application Data

Utility A

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Utility A continued

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Utility B

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