differential protection function block description - · pdf file1.8 example for the setting...

Differential protection function block description

Document ID: PRELIMINARY VERSION

Budapest, October 2009

Differential protection

PRELIMINARY VERSION 2/48

User’s manual version information

Version Date Modification Compiled by

Preliminary 30.10.2009. Preliminary version, without technical information Petri

18.06.2010 Technical information added Petri



CONTENTS 1 Differential protection function .............................................................................................4

1.1 Structure of the differential protection algorithm ..........................................................4

1.2 The vector shift compensation (Vector group) .............................................................7 1.2.1 Principle of transformation to the D side ...............................................................7 1.2.2 Mathematical modeling of the current transformer’s vector group connection .....7 1.2.3 The matrix equations ............................................................................................8 1.2.4 Operation with the zero sequence current in case of phase-to-ground fault on the delta side .................................................................................................................... 10 1.2.5 The principal scheme of the vector group compensation .................................. 11

1.3 Harmonic analysis of the differential currents (Diff basic harm.), (Diff 2. harm.), (Diff

5. harm.)............................................................................................................................... 13 1.3.1 The principle of calculation ................................................................................ 13 1.3.2 The principal scheme of the harmonic analysis ................................................. 14

1.4 The harmonic restraint decision (2. harmonic restraint) and (5. harmonic restraint)

15 1.4.1 The principle of the restraint decision ................................................................ 15 1.4.2 The principal scheme of the harmonic restraint decision .................................. 16

1.5 The current magnitude calculation (Current magnitude) .......................................... 19 1.5.1 The principle of the current magnitude calculation ............................................ 19 1.5.2 The principal scheme of the current magnitude calculation .............................. 19

1.6 The evaluation of the differential characteristics (Differential characteristics) . 21 1.6.1 The principle of the differential characteristics................................................... 21 1.6.2 The unrestricted differential function .................................................................. 22 1.6.3 The principal scheme of the evaluation of differential characteristics ............... 24

1.7 The decision logic (Decision logic) ........................................................................... 26 1.7.1 The principle of the decision logic ...................................................................... 26 1.7.2 The principal scheme of the decision logic ........................................................ 26

1.8 Example for the setting calculation in the Protecta differential protection ................ 29 1.8.1 Data for the calculation ...................................................................................... 29 1.8.2 The setting parameters: ..................................................................................... 29

1.9 Technical summary ................................................................................................... 30 1.9.1 Technical data .................................................................................................... 30 1.9.2 The measured values ........................................................................................ 30 1.9.3 The parameters of the differential protection function ....................................... 30 1.9.4 The binary output status signals ........................................................................ 32 1.9.5 Binary input signal .............................................................................................. 32 1.9.6 The function block .............................................................................................. 33

2 Appendix: .......................................................................................................................... 34

2.1 Current distribution inside the Y/d transformers ........................................................ 34 2.1.1 Three-phase fault (or normal load state) ........................................................... 34 2.1.2 Phase-to-phase fault on the Y side .................................................................... 36 2.1.3 Phase-to-phase fault at the delta side ............................................................... 37 2.1.4 Single phase external fault at the Y side ........................................................... 38 2.1.5 Single phase fault at the delta side .................................................................... 40

2.2 Checking the setting example ................................................................................... 44 2.2.1 Checking in case of symmetrical rated load currents ........................................ 44 2.2.2 Checking for Y side external phase-to-phase fault ............................................ 45 2.2.3 Checking for D side external phase-to-phase fault ............................................ 46 2.2.4 Checking for Y side external phase-to-ground fault .......................................... 47



1 Differential protection function The differential protection function provides main protection for transformers, generators or large motors, but it can also be applied for overhead lines and cables of solidly grounded networks or for the protection of any combination of the aforementioned protected objects. Version DIF87_3w can be applied to protect three-winding transformers. The simpler version DIF87_2w does not process analogue inputs from the tertiary side. This chapter describes the three-winding transformer version but it also refers to necessary changes in application with transformers of two sides only.

1.1 Structure of the differential protection algorithm Fig.1-1 shows the structure of the differential protection (DIF87_3w) algorithm.

Figure 1-1 Structure of the differential protection algorithm

IprimL1

Vector Group Diff

base harm.

DIF87_3w

Binary

outputs

Measured values

Parameters

IprimL2

IprimL3

IsecL1

IsecL2

IsecL3

ItercL1

ItercL2

ItercL3

Diff

2. harm

Diff

5. harm

2. harm. restraint

5. harm.

restraint

Decision

logic

Current magnitude

Differential characteristics

Status signal



The inputs are

the sampled values of three primary phase currents,

the sampled values of three secondary phase currents,

the sampled values of three tertiary phase currents (in DIF87_3w version only) ,

parameters

status signal.

The outputs are

the binary output status signals,

the measured values for displaying. The software modules of the differential protection function:

Vector group

This module compensates the phase shift and turns ratio of the transformer. The results of this calculation are the “sampled values” of the phase-shifted phase currents for all three (two) sides of the transformer and those of the three differential currents.

Diff base harm.

This module calculates the basic Fourier components of the three differential currents. These results are needed for the high-speed differential current decision and for the second and fifth harmonic restraint calculation.

Diff 2. harm.

This module calculates the second harmonic Fourier components of the three differential currents. These results are needed for the second harmonic restraint decision.

Diff 5. harm.

This module calculates the fifth harmonic Fourier components of the three differential currents. These results are needed for the fifth harmonic restraint decision.

2. harm. restraint.

The differential current can be high during the transients of transformer energizing, due to the current distortion caused by the transformer iron core asymmetric saturation. In this case, the second harmonic content of the differential current is applied in this module to disable the operation of the differential protection function. The result of this calculation is needed for the decision logic.

5. harm. restraint.

The differential current can be high if the transformer is over-excited by a connected generator, due to the current distortion caused by the transformer iron core symmetric saturation. In this case, the fifth harmonic content of the differential current is applied in this module to disable the operation of the differential protection function. The result of this calculation is needed for the decision logic.

Current magnitude

This module calculates the magnitude of the phase-shifted phase currents and that of the differential currents. The result of this calculation is needed for the evaluation of differential characteristics.


This module performs the necessary calculations for the evaluation of the “percentage differential characteristics”. The result of this calculation is needed for the decision logic.



Decision logic

The decision logic module decides if the differential current of the individual phases is above the characteristic curve of the differential protection function. This curve is the function of the restraint current, which is calculated based on the magnitude of the phase-shifted phase currents. This module calculates the second and fifth harmonic ratios of the differential current relative to the basic harmonic content. The result can restrain the operation of the differential protection function. The high-speed overcurrent protection function based on the differential currents is also performed in this module. The following description explains the details of the individual components.



1.2 The vector shift compensation (Vector group) The three-phase power transformers transform the primary current to the secondary side according to the turns ratio and the vector group of the transformers. The Y (star), D (delta) or Z (zig-zag) connection of the three phase coils on the primary and secondary sides causes the vector shift of the currents. The conventional electromechanical or static electronic devices of the differential protection compensate the vector shift with the appropriate connection of the current transformer coils. The numerical differential protection function applies matrix transformation of the directly measured currents of one side of the transformer to match them with the currents of the other side. In Protecta’s transformer differential protection the „Vector_group” software module calculates the matrix transformation and turns ratio matching. In this case, the target of the matrix transformation is the delta (D) side.

1.2.1 Principle of transformation to the D side The conventional electromechanical or static electronic devices of the differential protection compensate the vector shift with the appropriate connection of the current transformer coils. The principle is that the Y-connected current transformers on the delta side of the transformer do not shift the currents flowing out of the transformer. The delta-connected current transformers on the Y side of the transformer, however, result in a phase shift. This means that the Y-side currents are shifted according to the vector group of the transformer to match the delta-side currents. Additionally, the delta connection of the current transformers eliminates the zero sequence current component flowing on the grounded Y side of the transformer. As no zero sequence current can be detected on the delta side, this compensation is essential for the correct operation of the differential protection. If a phase-to-ground fault occurs on the Y side of the transformer, then zero sequence current flows on the grounded Y side while no out-flowing zero sequence current can be detected on the delta side. Without the elimination of the zero sequence current component, the differential protection generates a trip command in case of an external ground fault. If, however, the connection group of the current transformers on the Y side is delta, no zero sequence current flows out of the group. Thus the problem of zero sequence current elimination in case of an external ground fault is solved.

1.2.2 Mathematical modeling of the current transformer’s vector group connection

The numerical differential protection function applies numerical matrix transformation for modeling the delta connection of the current transformers. In practice, it means cyclical subtraction of the phase currents. In the vector shift compensation the sampled rst currents of the primary side (I1r, I1s, I1t) and those of the secondary side ((I2r, I2s, I2t)) are transformed to (RSTshift) values of both sides respectively, using matrix transformation. The method of transformation is defined by the „Code” parameter identifying the transformer vector group connection.



1.2.3 The matrix equations

The table below summarizes the method of transformation, broken down by the connection group of the transformers with two voltage levels. The tertiary side, if any – related to the primary – is processed similarly:

Tr. Conn. Group.

Code Transformation of the primary side currents

Transformation of the secondary side currents

Dy1 00

tI

sI

rI

TshitftI

SshitftI

RshitftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshitftI

SshitftI

RshitftI

2

2

2

101

110

011

3

1

2

2

2

Dy5 01

tI

sI

rI

TshitftI

SshitftI

RshitftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshitftI

SshitftI

RshitftI

2

2

2

110

011

101

3

1

2

2

2

Dy7 02

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshiftI

SshiftI

RshiftI

2

2

2

101

110

011

3

1

2

2

2

Dy11 03

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshiftI

SshiftI

RshiftI

2

2

2

110

011

101

3

1

2

2

2

Dd0 04

tI

sI

rI

TshitftI

SshitftI

RshitftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshitftI

SshitftI

RshitftI

2

2

2

100

010

001

2

2

2

Dd6 05

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshiftI

SshiftI

RshiftI

2

2

2

100

010

001

2

2

2

Dz0 06

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshifI

SshifI

RshiftI

2

2

2

211

121

112

3

1

2

2

2

Dz2 07

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshifI

SshifI

RshiftI

2

2

2

112

211

121

3

1

2

2

2

Dz4 08

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshifI

SshifI

RshiftI

2

2

2

121

112

211

3

1

2

2

2

Dz6 09

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshifI

SshifI

RshiftI

2

2

2

211

121

112

3

1

2

2

2



Dz8 10

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshifI

SshifI

RshiftI

2

2

2

112

211

121

3

1

2

2

2

Dz10 11

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

100

010

001

1

1

1

tI

sI

rI

TshifI

SshifI

RshiftI

2

2

2

121

112

211

3

1

2

2

2

Yy0 12

tI

sI

rI

TshitftI

SshitftI

RshitftI

1

1

1

110

011

101

3

1

1

1

1

tI

sI

rI

TshitftI

SshitftI

RshitftI

2

2

2

110

011

101

3

1

2

2

2

Yy6 13

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

110

011

101

3

1

1

1

1

tI

sI

rI

TshiftI

SshiftI

RshiftI

2

2

2

110

011

101

3

1

2

2

2

Yd1 14

tI

sI

rI

TshitftI

SshitftI

RshitftI

1

1

1

110

011

101

3

1

1

1

1

tI

sI

rI

TshitftI

SshitftI

RshitftI

2

2

2

100

010

001

2

2

2

Yd5 15

tI

sI

rI

TshitftI

SshitftI

RshitftI

1

1

1

101

110

011

3

1

1

1

1

tI

sI

rI

TshitftI

SshitftI

RshitftI

2

2

2

100

010

001

2

2

2

Yd7 16

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

110

011

101

3

1

1

1

1

tI

sI

rI

TshiftI

SshiftI

RshiftI

2

2

2

100

010

001

2

2

2

Yd11 17

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

101

110

011

3

1

1

1

1

tI

sI

rI

TshiftI

SshiftI

RshiftI

2

2

2

100

010

001

2

2

2

Yz1 18

tI

sI

rI

TshitftI

SshitftI

RshitftI

1

1

1

110

011

101

3

1

1

1

1

tI

sI

rI

TshifI

SshifI

RshiftI

2

2

2

211

121

112

3

1

2

2

2

Yz5 19

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

101

110

011

3

1

1

1

1

tI

sI

rI

TshifI

SshifI

RshiftI

2

2

2

211

121

112

3

1

2

2

2

Yz7 20

tI

sI

rI

TshitftI

SshitftI

RshitftI

1

1

1

110

011

101

3

1

1

1

1

tI

sI

rI

TshifI

SshifI

RshiftI

2

2

2

211

121

112

3

1

2

2

2

Yz11 21

tI

sI

rI

TshiftI

SshiftI

RshiftI

1

1

1

101

110

011

3

1

1

1

1

tI

sI

rI

TshifI

SshifI

RshiftI

2

2

2

211

121

112

3

1

2

2

2

Table 1-1 Vector shift compensation with transformation to the delta side



The differential currents are calculated using the (RSTshift) values and the DIF87_TRPr_IPar (TR primary) and DIF87_TRSec_IPar (TR secondary) parameters, defined by the turns ratio of the transformer and that of the current transformers, resulting in the currents marked with an apostrophe (’). The tertiary side is processed similarly. (The positive direction of the currents is flowing IN on both sides.)

TshiftI

SshiftI

RshiftI

ondaryTRTshiftI

SshiftI

RshiftI

primaryTRTshiftI

SshiftI

RshiftI

TshiftI

SshiftI

RshiftI

IdT

IdS

IdR

2

2

2

sec_

100

1

1

1

_

100

'2

'2

'2

'1

'1

'1

The current measuring software modules process these momentary values of the differential currents and calculate values that are proportional to the RMS values.

1.2.4 Operation with the zero sequence current in case of a phase-to-ground fault on the delta side

On the secondary side of a high voltage /medium voltage transformer which is connected in delta on the medium voltage side, an additional neutral grounding transformer is applied. Between the neutral point of this grounding transformer and the ground either a grounding resistor is connected to limit the single phase-to-ground fault currents below 100 A (in some cases 200 A only), or a Petersen coil is applied here, which limits the single-phase fault currents to a small value of a few Amps. In these cases, there are two locations for the current transformers on the delta side to supply the differential protection. In one case, the neutral grounding transformer is located inside the protected zone of the differential protection (In Fig. 2-7 and 2-8 of the Appendix it is location ”Z”), in the other case the neutral grounding transformer is outside the protected zone (In Fig. 2-7 and 2-8 of the Appendix, this is the application of the current transformers at location „Y”). If the neutral grounding transformer is in the protected zone, then the current distribution depends on the location of the supplying generator, as it is shown in Figures 2-7 and 2-8 of the Appendix. In these cases, for the correct operation of the differential protection (if the operating characteristic lines are set to be sensitive) the subtraction of the zero sequence current is needed. This additional transformation „moves” the measuring location to the point („Y”) where no zero sequence current can flow, so these transformed currents do not include the zero sequence current of the neutral grounding transformer.



1.2.5 The schema of the vector group compensation Figure 1-2 shows the principal scheme of the vector shift compensation.

Figure 1-2 Schema of the vector shift compensation.

The inputs are the sampled values of:

the three phase currents of the primary side (IprimL1, IprimL2, IprimL3)

the three phase currents of the secondary side (IsecL1, IsecL2, IsecL3)

the three phase currents of the tertiary side (ItercL1, ItercL2, ItercL3 in version DIF87_3w only)

parameters for vector shift and turns ratio compensation.

IprimL1

Vector Group

Parameters

IprimL2

IprimL3

IsecL1

IsecL2

IsecL3

ItercL1

ItercL2

ItercL3

IdR

IdS

IdT

I1Rshift’1

I1Sshift’

I1Tshift’

I2Rshift’

I2Sshift’

I2Tshift’

I3Rshift’

I3Sshift’ I3Tshift’



Enumerated parameters for the vector shift compensation:

Parameter name Title Selection range Default

Parameter to select connection group of the transformer coils in primary-secondary relation:

DIF87_VGrSec_EPar_ Pri-Sec VGroup*

Dy1,Dy5,Dy7,Dy11,Dd0,Dd6,Dz0,Dz2,Dz4,Dz6,Dz8,Dz10,Yy0,Yy6,Yd1,Yd5,Yd7,Yd11,Yz1,Yz5,Yz7,Yz11

Dd0


DIF87_VGrTer_EPar_ Pri-Ter VGroup*


Dd0

Table 1-2 Enumerated parameters for the vector shift compensation

* If the connection of the primary winding in the primary-secondary and primary-tertiary relations is selected in contradiction, the protection function is automatically disabled and the function generates a warning signal. Boolean parameter for the vector shift compensation:

Parameter name Title Default Explanation

DIF87_0Seq_BPar_ ZeroSequ.Elimination True See Chapter 1.2.4

Table 1-3 The Boolean parameter for the vector shift compensation

Integer parameters for the turns ratio compensation:

Parameter name Title Unit Min Max Step Default

Parameters for the current magnitude compensation:

DIF87_TRPr_IPar_ TR Primary comp. % 20 500 1 100

DIF87_TRSec_IPar_ TR Secondary comp. % 20 500 1 100

DIF87_TRTer_IPar_ TR Tertiary comp. % 20 500 1 100

Table 1-4 Integer parameters for the vector shift compensation

The outputs are the “sampled values” of the phase-shifted currents:

The differential currents after phase-shift,

IdT

IdS

IdR

The primary currents after phase-shift,

'1

'1

'1

TshiftI

SshiftI

RshiftI

The secondary currents after phase-shift,

'2

'2

'2

TshiftI

SshiftI

RshiftI

The tertiary currents after phase-shift (in version DIF87_3w only).



1.3 Harmonic analysis of the differential currents (Diff

basic harm.), (Diff 2. harm.), (Diff 5. harm.)

1.3.1 The principle of calculation The differential current can be high during the transients of transformer energizing due to the current distortion caused by the transformer iron core asymmetrical saturation. In this case, the second harmonic content of the differential current is applied to disable the operation of the differential protection function. The differential current can be high in case of the over-excitation of the transformer due to the current distortion caused by the transformer iron core symmetrical saturation. In this case, the fifth harmonic content of the differential current is applied to disable the operation of the differential protection function. The harmonic analysis block of modules consists of three individual software modules.

Diff base harm.

This module calculates the basic Fourier components of the three differential currents. These results are needed for the high-speed differential current decision and for the second and fifth harmonic restraint calculation.

Diff 2. harm.

This module calculates the second harmonic Fourier components of the three differential currents. These results are needed for the second harmonic restraint decision.

Diff 5. harm.

This module calculates the fifth harmonic Fourier components of the three differential currents. These results are needed for the fifth harmonic restraint decision.



1.3.2 The schema of the harmonic analysis

Figure 1-3 shows the structure of the harmonic analysis.

Figure 1-3 Principal scheme of the harmonic analysis.

The inputs are the “sampled values” of the differential currents, based on the phase-

shifted currents:

The differential currents after phase-shift

IdT

IdS

IdR

The outputs are the basic, the second and the fifth harmonic Fourier components of

the differential currents:

The basic harmonic Fourier components of the differential currents

IdTF

IdSF

IdRF

1

1

1

The second harmonic Fourier components of the differential currents

IdTF

IdSF

IdRF

2

2

2

The fifth harmonic Fourier components of the differential currents

IdTF

IdSF

IdRF

5

5

5

These values are processed by the software modules 2. harmonic restraint and

5. harmonic restraint

Diff base harm.

Diff 2. harm

Diff 5. harm

IdR

IdS

IdT

F1IdR

F1IdS

F1IdT

F2IdR2

FI2dS

FI2dT

FI5dR

FI5dS

FI5dT



1.4 The harmonic restraint decision (2. harmonic

restraint) and (5. harmonic restraint)

1.4.1 The principle of the restraint decision The differential current can be high during transformer energizing due to the current distortion caused by the transformer iron core asymmetrical saturation. In this case, the second harmonic content of the differential current is applied to disable the operation of the differential protection function. The differential current can be high in case of the over-excitation of the transformer due to the current distortion caused by the transformer iron core symmetrical saturation. In this case, the fifth harmonic content of the differential current is applied to disable the operation of the differential protection function. The harmonic analysis block of modules consists of two sub-blocks, one for the second harmonic decision and one for the fifth harmonic decision. Each sub-block includes three individual software modules for the phases. The software modules evaluate the harmonic content relative to the basic harmonic component of the differential currents and compare the result with the parameter values set for the second and fifth harmonic. If the content is high, then the assigned status signal is set to “true” value. If the duration of the active status is at least 25 ms, then the resetting of the status signal is delayed by an additional 15 ms.



1.4.2 The principal scheme of the harmonic restraint decision

Figure 1-4 Principal scheme of the harmonic restraint decision

The inputs are the basic, the second and the fifth harmonic Fourier components of the

differential currents:

The basic harmonic Fourier components of the differential currents

IdTF

IdSF

IdRF

1

1

1

The second harmonic Fourier components of the differential currents

IdTF

IdSF

IdRF

2

2

2

The fifth harmonic Fourier components of the differential currents

IdTF

IdSF

IdRF

5

5

5

The outputs of the modules are the status signals for each phase and for the second and fifth harmonics separately, indicating the restraint status caused by high harmonic contents.

F1IdR

F1IdS

F1IdT

F2IdR2

FI2dS

FI2dT

F5IdR

F5IdS

F5IdT

2.harm restr. L1

2.harm restr. L2

2.harm restr. L3

5.harm restr. L1

5.harm restr. L2

5.harm restr. L3

Para meters

2. harmonic restraint decision

5. harmonic restraint decision



Figure 1-5 Logic schema of the harmonic restraint decision.

The logic schema is repeated for the second (n=2) and fifth (n=5) harmonic restraint decision for all three phases separately (x=L1, L2, L3). First the ratio of the harmonic and the base harmonic is calculated, and this ratio is compared to the parameter setting (second and fifth separately). If the ratio is high, the restraint signal is generated immediately and a timer is started at the same time. If the 25 ms delay is over and during the running time the ratio was continuously high, then a drop-off timer is started, which extends the duration of the restraint signal. The decisions of the phases are connected in an OR gate to result in general second or fifth harmonic restraint status signals. The binary output status signals of the harmonic restraint decision function are listed in Table 1-5.

Binary output signals Signal title Explanation

Second harmonic restraint signals

DIF87_2HBlkL1_GrI 2.Harm Restr. L1 Restraint in phase L1 caused by high second harmonic content in the differential current



DIF87_2HBlk_GrI 2.Harm Restr. Restraint caused by high second harmonic content in any of the differential currents

Fifth harmonic restraint signals

DIF87_5HBlkL1_GrI 5.harm Restr. L1 Restraint in phase L1 caused by high fifth harmonic content in the differential current



DIF87_5HBlk_GrI 5.Harm Restr. Restraint caused by high fifth harmonic content in any of the differential currents

Table 1-5 Binary output status signals of the harmonic restraint decision function

F1Idx

FnIdx2

DIFF87_2HBlkL1GrI_ DIFF87_2HBlkL2GrI_ DIFF87_2HBlkL3GrI_ DIFF87_5HBlkL1GrI_ DIFF87_5HBlkL2GrI_ DIFF87_5HBlkL3GrI_

Parameters

Ratio

25ms

t t

15ms

OR

0.2

&



Integer parameters of the harmonic restraint decision function are listed in Table 1-6.


Parameter of the second harmonic restraint:

DIF87_2HRat_IPar_ 2. Harm. Ratio % 5 50 1 15

Parameter of the fifth harmonic restraint:

DIF87_5HRat_IPar_ 5. Harm. Ratio % 5 50 1 25

Table 1-6 Integer parameters of the harmonic restraint decision function



1.5 The current magnitude calculation (Current

magnitude)

1.5.1 The principle of the current magnitude calculation The module, which evaluates the differential characteristics, compares the magnitudes of the differential currents and those of the restraint currents. The current magnitudes are needed for this calculation. These magnitudes are calculated in this module.

1.5.2 The principal scheme of the current magnitude calculation

Figure 1-6 Principal scheme of the current magnitude calculation.

IdR

IdS

IdT

I1Rshift’1

I1Sshift’

I1Tshift’

I2Rshift’

I2Sshift’

I2Tshift’

I3Rshift’

I3Sshift’ I3Tshift’

Id

I1 shift

I2 shift

I3 shift

M_IdR

M_IdS

M_IdT

M_I1Rshift’

M_I1Sshift’

M_I1Tshift’

M_I2Rshift’

M_I2Sshift’

M_I2Tshift’

M_I3Rshift’

M_I3Sshift’ M_I3Tshift’



The inputs are the “sampled values” of the phase-shifted currents:

The differential currents after phase-shift,

IdT

IdS

IdR

The primary currents after phase-shift,

'1

'1

'1

TshiftI

SshiftI

RshiftI

The secondary currents after phase-shift,

'2

'2

'2

TshiftI

SshiftI

RshiftI

The tertiary currents after phase-shift (in version DIF87_3w only).

'3

'3

'3

TshiftI

SshiftI

RshiftI

The outputs are the magnitudes of the calculated currents

The magnitudes of the differential currents after phase-shift,

IdTM

IdSM

IdRM

_

_

_

The magnitudes of the primary currents after phase-shift,

'1_

'1_

'1_

TshiftIM

SshiftIM

RshiftIM

The magnitudes of the secondary currents after phase-shift,

'2_

'2_

'2_

TshiftIM

SshiftIM

RshiftIM

The magnitudes of the tertiary currents after phase-shift

(in version DIF87_3w only)

'3_

'3_

'3_

TshiftIM

SshiftIM

RshiftIM



1.6 The evaluation of the differential characteristics

(Differential characteristics)

1.6.1 The principle of the differential characteristics This module evaluates the differential characteristics. It compares the magnitudes of the differential currents and those of the restraint currents. The restraint currents are calculated using the following formulas:

2

''3_'2_'1__

RshiftIMRshiftIMRshiftIMIresRM

2

''3_'2_'1__

SshiftIMSshiftIMSshiftIMIresSM

2

''3_'2_'1__

TshiftIMTshiftIMTshiftIMIresTM

Based on these values (generally denoted as “Ires”) and the values of the differential current magnitudes (generally denoted as “Id”), the differential protection characteristics are shown in Figure 1-7.

Figure 1-7 The differential protection characteristics

Additionally, separate status signals are set to “true” value if the differential currents in the individual phases are above the limit set by the dedicated parameter (see “Unrestricted differential function”).

Ires

Slope=DIF87_f2_IPar_

DIF87_f3_IPar_

DIF87_f1_IPar_

Slope=const=2

Id



Integer parameters


Base sensitivity:

DIF87_f1_IPar_ Base sensitivity % 10 50 1 20

Slope of the second section of the characteristics:

DIF87_f2_IPar_ 2nd part of TripChar - 10 50 1 20

Slope of the third section of the characteristics:

DIF87_f3_IPar_ 3rd part of TripChar - 200 2000 1 200

Table 1-7 Integer parameters of the differential protection characteristics



DIF87_L1St_GrI_i Start L1

This internal status is true if the differential current in phase R at the restraint current is above the characteristic lines


This internal status is true if the differential current in phase S at the restraint current is above the characteristic lines


This internal status is true if the differential current in phase T at the restraint current is above the characteristic lines

Table 1-8 Binary output status signals of the differential protection characteristics

1.6.2 The unrestricted differential function If the calculated differential current is very high, then the differential characteristic is not considered anymore because the separate status signals for the phases are set to “true” value if the differential currents in the individual phases are above the limit defined by parameter setting. The decisions of the phases are connected in an OR gate to result in the general start status signal. Integer parameter of the unrestricted differential function is shown in Table 1-9.


High-speed differential protection current level:

DIF87_HCurr_IPar_ Unrestrained I-Diff % 800 2500 1 800

Table 1-9 The integer parameters of the unrestricted differential protection

characteristics




Unrestricted decision

DIF87_UnRL1St_GrI_i Start L1 unrestr. This internal status is true if the differential current in phase R is above the high current setting



DIF87_UnRGenSt_GrI General start unrestr. This status is true if in any of the phases the differential current is above the high current setting

Table 1-10 The binary output status signals of the unrestricted differential protection

characteristics



1.6.3 The principal scheme of the evaluation of differential characteristics

Figure 1-8 Schema of evaluation of differential protection characteristics

The inputs are the magnitudes of the calculated currents:

The magnitudes of the differential currents after phase-shift,

IdTM

IdSM

IdRM

_

_

_

The magnitudes of the primary currents after phase-shift,

'1_

'1_

'1_

TshiftIM

SshiftIM

RshiftIM

The magnitudes of the secondary currents after phase-shift,

'2_

'2_

'2_

TshiftIM

SshiftIM

RshiftIM

The magnitudes of the tertiary currents after phase-shift

(in version DIF87_3w only)

'3_

'3_

'3_

TshiftIM

SshiftIM

RshiftIM

M_IdR

M_IdS

M_IdT

M_I1Rshift’

M_I1Sshift’

M_I1Tshift’

M_I2Rshift’

M_I2Sshift’

M_I2Tshift’

M_I3Rshift’

M_I3Sshift’ M_I3Tshift’

Start L1

Start L2

Start L3

UnRestr.Start L1

UnRestr.Start L2

UnRestr.Start L3



Parameters





DIF87_L1St_GrI_ Start L1 This status is true if the differential current in phase R at the restraint current is above the characteristic lines

DIF87_L2St_GrI_ Start L2 This status is true if the differential current in phase S at the restraint current is above the characteristic lines

DIF87_L3St_GrI_ Start L3 This status is true if the differential current in phase T at the restraint current is above the characteristic lines


DIF87_UnRL1St_GrI Start L1 unrestr. This status is true if the differential current in phase R is above the high current setting



Table 1-11 The binary output status signals of the unrestricted differential protection

characteristics



1.7 The decision logic (Decision logic)

1.7.1 The principle of the decision logic

The decision logic combines the following binary signals:

Start signals of the differential characteristic module

Unrestricted start signals of the differential characteristic module

Harmonic restraint signals of the 2nd harmonic restraint decision

Harmonic restraint signals of the 5th harmonic restraint decision

Disabling status signals defined by the user applying the graphic equation editor DIF87_Blk_GrO

1.7.2 The schema of the decision logic

The inputs are the calculated status signals of the Differential characteristics and Unrestricted

differential modules, those of the 2.harmonic restraint and 5.harmonic restraint modules and

binary input parameters.

Binary input signals Signal title Explanation


DIF87_L1St_GrI_i Start L1 This internal status is true if the differential current in phase R at the restraint current is above the characteristic lines

DIF87_L2St_GrI_i Start L2 This internal status is true if the differential current in phase S at the restraint current is above the characteristic lines

DIF87_L3St_GrI_i Start L3 This internal status is true if the differential current in phase T at the restraint current is above the characteristic lines





Second harmonic restraint signals


DIF87_2HBlk L2_GrI 2.Harm Restr. L2 Restraint in phase L2 caused by high second harmonic content in the differential current


Fifth harmonic restraint signals

DIF87_5HBlkL1_GrI 5.Harm Restr. L1 Restraint in phase L1 caused by high fifth harmonic content in the differential current



Table 1-12 The binary input status signals of the decision logic



Blocking input signal The differential protection function has a binary input signal, which serves the purpose of disabling the function. The conditions of disabling are defined by the user applying the graphic equation editor for the signal DIF87_Blk_GrO.

Binary input signal Explanation

DIF87_Blk_GrO Output status of a graphic equation defined by the user to disable the differential protection function.

Table 1-13 The blocking input status signals of the decision logic

These input status signals are processed by the decision logic to generate additional status signals, but at the same time they are output signals as well. The binary output signals are listed in Table 1-14 below.



DIF87_L1St_GrI_ Start L1

This status is true if the differential current in phase R at the restraint current is above the characteristic lines and the function is not blocked


This status is true if the differential current in phase S at the restraint current is above the characteristic lines and the function is not blocked


This status is true if the differential current in phase T at the restraint current is above the characteristic lines and the function is not blocked


DIF87_UnRL1St_GrI_ Start L1 unrestr. This status is true if the differential current in phase R is above the high current setting and the function is not blocked



Harmonic blocking



DIF87_HarmBlk_GrI_ HarmBlk This status is true if either the second or the fifth harmonic in any of the phases blocks the output

Table 1-14 The binary output status signals of the differential protection

characteristics

These signals are processed by the trip logic of the device.



Figure 1-9 The logic schema of the differential protection function

DIF87_L1St_GrI_i

DIF87_L2St_GrI_i

DIF87_L3St_GrI_i

DIF87_UnRL1St_GrI_i

DIF87_UnRL1St_GrI_i

DIF87_UnRL1St_GrI_i

DIF87_2HBlkL1_GrI_

DIF87_2HBlkL2_GrI_

DIF87_2HBlkL3_GrI_

DIF87_5HBlkL1_GrI_

DIF87_5HBlkL2_GrI_

DIF87_5HBlkL3_GrI_

DIF87_5HBlkL3_GrI_

OR

OR

DIF87_L1St_GrI_

OR

AND

AND

AND

AND

AND

AND

OR

OR

DIF87_L2St_GrI_

DIF87_L3St_GrI_

DIF87_GenSt_GrI_

DIF87_UnRL1St_GrI_

DIF87_UnRL2St_GrI_

DIF87_UnRL3St_GrI_

DIF87_UnRGenSt_GrI_

DIF87_HarmBlk_GrI_

NOT

NOT



1.8 Example for the setting calculation in the Protecta differential protection

1.8.1 Data for the calculation

As an example, the transformer data:

Sn = 125 MVA U1/U2 = 132/11.5 kV/kV Yd11

Current transformer:

CT1 600/1 A/A CT2 6000/1 A/A

Rated currents of the transformer:

I1np = 546 A On the secondary side of the CT I1n = 0.91 A I2np = 6275 A On the secondary side of the CTI2n = 1.05 A

1.8.2 The setting parameters:

TR primary = 91 %

(This is a free choice, giving the primary side current transformer’s current, as a percentage of the rated current of the CT.)

TR secondary = 105 % (This is a direct consequence of selecting TR primary; this is the current of the secondary side current transformer related to the rated current of the CT.) The code value of the transformer’s connection group (see Table 1-1) (Yd11):

Code = 17



1.9 Technical summary

1.9.1 Technical data

Function

Accuracy

Operating characteristic Dual slope + unrestrained section

Unrestrained differential < 3%

Base sensitivity <2%

Reset ratio 0.95

Operate time, restrained <35 ms

Reset time, restrained <40 ms

Operate time, unrestrained <20 ms

Reset time, unrestrained <40 ms

1.9.2 The measured values

The measured values of the differential protection function.

Measured value Dim. Explanation

Idiff. L1 In % The calculated differential current in phase L1 (after vector group compensation)



Ibias L1 In % The calculated restraint current in phase L1 (after vector group compensation)



Table 1-15 The measured analogue values of the differential protection function

Remark: The evaluated basic harmonic values of the measured input phase currents (without vector group compensation) help the commissioning of the differential protection function. These evaluations, however, are performed by an independent software measuring module; therefore, this chapter does not cover the description of these measurements.

1.9.3 The parameters of the differential protection function The parameters of the differential protection function are explained in the following tables. Enumerated parameters for the differential protection function:

Parameter name Title Selection range Default

Parameter to enable the differential protection function:

DIF87_Op_EPar_ Operation Off,On On


DIF87_VGrSec_EPar_ Pri-Sec VGroup*


Dd0


DIF87_VGrTer_EPar_ Pri-Ter VGroup*


Dd0

Table 1-16 The enumerated parameters of the differential protection function



* If the connection of the primary winding in the primary-secondary and primary-tertiary relations is selected in contradiction, then the protection function is automatically disabled and the function generates a warning signal. Boolean parameter for the differential protection function:

Parameter name Title Default Explanation

DIF87_0Seq_BPar_ ZeroSequ.Elimination True See Chapter 1.2.4

Table 1-17 The Boolean parameters of the differential protection function

Integer parameters


Parameters for the current magnitude compensation:

DIF87_TRPr_IPar_ TR Primary comp. % 20 500 1 100

DIF87_TRSec_IPar_ TR Secondary comp. % 20 500 1 100

DIF87_TRTer_IPar_ TR Tertiary comp. % 20 200 1 100

Parameter of the second harmonic restraint:

DIF87_2HRat_IPar_ 2nd Harm. Ratio % 5 50 1 15

Parameter of the fifth harmonic restraint:

DIF87_5HRat_IPar_ 5th Harm. Ratio % 5 50 1 25

Parameters of the percentage characteristic curve:

Base sensitivity:

DIF87_f1_IPar_ Base sensitivity % 10 50 1 20

Slope of the second section of the characteristics:

DIF87_f2_IPar_ 2. part of TripChar - 10 50 1 20

Slope of the third section of the characteristics:

DIF87_f3_IPar_ 3. part of TripChar - 200 2000 1 200

High-speed differential protection current level:

DIF87_HCurr_IPar_ Unrestrained I-Diff % 800 2500 1 800

Table 1-18 The integer parameters of the differential protection function

Floating point parameters The differential protection function does not have floating point parameters. Timer parameters The differential protection function does not have timers.



1.9.4 Binary output status signals

The binary output status signals of the differential protection function.


Restrained differential protection function

DIF87_L1St_GrI_ Start L1 Start of the restrained differential protection function in phase L1 (after vector group compensation)



DIF87_GenSt_GrI General Start General start of the restrained differential protection function

Unrestrained differential protection function

DIF87_UnRL1St_GrI_ Start L1 unrestr. Start of the unrestrained differential protection function in phase L1 (after vector group compensation)



DIF87_UnRGenSt_GrI_ General Start unrestr General start of the unrestrained differential protection function

Harmonic blocking



Table 1-19 The binary output status signals of the differential protection function

1.9.5 Binary input signal

The differential protection function has a binary input signal, which serves the purpose of disabling the function. The conditions of disabling are defined by the user applying the graphic equation editor.

Binary input signal Explanation

DIF87_Blk_GrO Output status of a graphic equation defined by the user to disable the differential protection function.

Table 1-20 The binary input signal of the differential protection function



1.9.6 The function block

The function blocks of the differential protection function for transformers with two or three voltage levels are shown in Figure 1-10. This block shows all binary input and output status signals that are applicable in the graphic equation editor.

Figure 1-10 The function block of the differential protection function



2 Appendix:

2.1 Current distribution inside the Y/d transformers For the explanation, the following positive directions are applied:

Fig. A2-1

Positive directions

2.1.1 Three-phase fault (or normal load state)

The figure below shows the current distribution inside the transformers in case of three-phase fault or at normal, symmetrical load state:

Currents in case of normal load (or three-phase fault)

Fig. A2-2

In this figure, k is the current ratio. The positive directions are supposed to be directed out of the transformer on both sides, as it is assumed by the differential protection. (If the directions suppose currents flowing through the transformer, then

I2R input = kI/√3(1-a2)

This indicates that the connection group of this transformer is Yd11.)

K L l k

I

+ +

I

r

TR

t

S

s

a2*I1Rinput*k/√3

I1Rinput I2Rinput

I1Rinput*k/√3

a*I1Rinput

I2Tinput

a2*I1Rinput

I2Sinput

a*I1Rinput*k/√3

R



Here the primary currents form a symmetrical system:

a

aI

TinputI

SinputI

RinputI2

1

1

1

1

The secondary currents can be seen in the figure (please note the division factor √3 in the effective turns ratio):

)1(

)(

)1(

3

1*

2

2

22

2

a

aa

a

Ik

TinputI

SinputI

RinputI



2.1.2 Phase-to-phase fault on the Y side Assume I current on the primary Y side between phases S and T.

Currents inside the transformer at ST fault on the Y side

Fig. A2-3

In this figure, k is the current ratio. The Y-side currents are:

1

1

0

1

1

1

I

TinputI

SinputI

RinputI

The delta-side currents can be seen in this figure:

1

2

1

*3

1*

2

2

2

Ik

TinputI

SinputI

RinputI

r

TR

t

S

s

I*k/√3

0 I*k/√3

0

-I

I*k/√3

-2* I*k/√3

-I*k/√3

R

I



2.1.3 Phase-to-phase fault on the delta side

Assume I current on the secondary delta side between phases “s” and “t”. .

Currents inside the transformer at “st” fault on the delta side

Fig. A2-4

In this figure, k is the current ratio. The secondary currents are:

1

1

0

2

2

2

I

TinputI

SinputI

RinputI

These are distributed in the delta assuming a 2/3 : 1/3 distribution factor. Thus, the primary Y-side currents can be seen in this figure:

2

1

1

*3

1*

1

1

1

Ik

TinputI

SinputI

RinputI

r

TR

t

S

s

-1/3*I

-1/3*I*√3/k 0

-1/3*I

2/3*I*√3/k

-I

-1/3*I*√3/k

I

2/3*I

R



2.1.4 Single-phase external fault on the Y side A) Assume I fault current in phase R in case of a solidly grounded neutral. No power supply is assumed on the delta side:

Currents inside the transformer at a single-phase fault on the Y side (Bauch effect)

Fig. A2-5

In this figure, k is the current ratio. The primary Y-side currents are:

1

1

1

1

1

1

I

TinputI

SinputI

RinputI

On the delta side, there are no currents flowing out of the transformer:

0

0

0

2

2

2

I

TinputI

SinputI

RinputI

r

TR

t

S

s

I*k/√3

I 0

I*k/√3

I

0

I

0

I*k/√3

R



B) Assume I fault current on the Y side in phase R in case of a solidly grounded neutral. Assume the power supply on the delta side:

Currents inside the transformer at a single-phase fault on the Y side, supply on the delta side

Fig. A2-6

In this figure, k is the current ratio. The primary Y-side currents are:

0

0

1

1

1

1

I

TinputI

SinputI

RinputI

The delta-side currents can be seen in this figure:

1

0

1

*3

1*

2

2

2

Ik

TinputI

SinputI

RinputI

r

TR

t

S

s

0

I - I*k/√3

I*k/√3

0

I*k/√3

0

0

0

R



2.1.5 Single-phase fault on the delta side

The delta side is usually applied at medium voltage levels. If a high/medium voltage transformer with delta secondary is used, then a separate neutral grounding transformer is applied for neutral grounding (Petersen or grounding resistance). The impedance between the neutral point and the ground suppresses the fault current below 100 A (perhaps 200 A), the Petersen coil allows only a few Amperes. On the delta side there are two locations for the current transformers supplying the differential protection. In one case the neutral grounding transformer is within the protected zone (see figure below, current transformers at location „Z”). The other possibility is for the neutral grounding transformer to be excluded from the protected zone (see figure below, current transformers at location „Y”).

2.1.5.1 Power supply on the Y side

As the zero sequence current component of the delta side can influence the behavior of the differential protection (sensitive setting), this chapter analyses the current distribution in case of a single-phase-to-ground fault on the delta side.

Current distribution at external single-phase-to-ground fault, Y-side power supply

Fig. A2-7

I√3/k

X

r

TR t

S

s

1

R

I√3/k

I√3/k -I√3/k

I√3/k

1

I√3/k

2I

-I

-I I

I

3I

3I

Y Z

2I 3I

CT positve direction Real current direction



For the current distribution an external „r” phase fault is assumed, and at the fault location the current is Ir = 3Io. The arrows indicating the real currents can be constructed at this starting point. Based on the figure above, with positive directions out of the transformer the currents in the CT-s are: On the Y side (location X in Fig. 2-7):

0

1

1

/3

1

1

1

kI

TinputI

SinputI

RinputI

The delta-side currents at location „Y”:

1

1

2

2

2

2

I

TinputI

SinputI

RinputI

If the current is measured at location „Z”, then the node - which has to satisfy Kirchhoff’s node law – is extended by the neutral grounding transformer but the current flowing between the neutral point and the ground in not measured and not added to the current summation. This current is the 3Io zero sequence component, which can be calculated as the sum of the phase currents. At location „Z” the zero sequence component has no other path to flow but the neutral grounding transformer. The delta-side currents at location „Z”:

0

0

3

'2

'2

'2

I

TinputI

SinputI

RinputI

In this case, the zero sequence current is I. If the vector group compensation is for the delta side, then the transformation does not change this current; on the high-voltage side, however, there is no zero sequence component. In any event, the transformation would filter this component out. In practice, this zero sequence current component is always below the rated current of the transformer but if the differential protection is set to sensitive or a relay test set is applied mechanically without any logic control this can result in the faulty operation of the differential protection in case of an external fault. To avoid such faulty operation, there is a binary parameter in the differential protection the effect of which is to subtract the zero sequence current component from the phase currents if required:

1

1

2

1

1

1

0

0

3

20'2

20'2

20'2

2

2

2

III

ITinputI

ISinputI

IRinputI

TinputI

SinputI

RinputI

This means that based on the currents of the CT-s located at „Z”, the current that could be measured at location „Y” is calculated. NOTE: This zero sequence current subtraction could also be applied without any consequences to current transformers at location „Y” because in case of external faults, no



zero sequence current can be detected at this location. In case of an internal fault, however, this decreases the faulty phase current by 2/3. This could worsen the sensitivity of the differential protection in the event of high-impedance internal faults. The subtraction of the zero sequence current in the case of measurement at location „Y” can be disabled using the aforementioned binary parameter.

2.1.5.2 Power supply on the delta side

If a transformer connects distributed generators on a medium voltage network with neutral grounding, a possible state of operation can be that the transformer is disconnected on the high-voltage Y side. No current can flow on the Y side and if the differential protection measures the currents on the medium voltage side at location „Z” (Fig. 2-8), then in case of a sensitive setting of the characteristic lines or at testing, the differential protection can generate a faulty trip command. The current distribution is shown in Fig. 2-8 below:

Current distribution in case of a delta-side single-phase fault, supply on the delta side

Fig. A2-8

X

r

TR t

S

s

R

3I

Y

CT „+” direction Real current

G

G

G

Z

I

I I I

I I

I

I

I 2I

I

I

3I



In this case no current is detected at the point „X” (CB open):

0

0

0

1

1

1

TinputI

SinputI

RinputI

The measured currents at „Z” can be seen in the figure:

1

1

1

'2

'2

'2

I

TinputI

SinputI

RinputI

To avoid mal-operation (trip) in the event of an external fault, a binary parameter is applied the effect of which is to subtract the zero sequence current on the delta side:

0

0

0

1

1

1

1

1

1

20'2

20'2

20'2

2

2

2

II

ITinputI

ISinputI

IRinputI

TinputI

SinputI

RinputI

It means that based on the currents of the CT-s located at „Z”, the current, that could be measured at location „Y” is calculated. The faulty trip is avoided by this transformation.



2.2 Checking the setting example

2.2.1 Checking in case of symmetrical rated load currents

For checking, the positive directions defined in the Appendix are applied:

Based on Fig. A2-2 of the Appendix, the primary currents are:

a

anpI

TinputI

SinputI

RinputI2

1

600

1*1

1

1

1

The transformed values of the primary side (See Table 1-1):

)1(

)(

)1(

00183.0*13

1

1

1

1

)1(

)(

)1(

_

100*

600

1*1

3

1

1

1

1

101

110

011

3

1

_

100

1

1

1

2

2

2

2

a

aa

a

npI

TshiftI

SshiftI

RshiftI

a

aa

a

primaryTRnpI

TinputI

SinputI

RinputI

primaryTRTshiftI

SshiftI

RshiftI

The secondary currents are illustrated in Fig. A2-2 of the Appendix (please note the division by √3 as defined by the turns ratio):

)1(

)(

)1(

6000

1*

3

1*

5.11

132*1

2

2

22

2

a

aa

a

npI

RinputI

RinputI

RinputI

The secondary currents are transformed by the unit matrix (see Table 1-1). It means that only the turns ratio is considered:

)1(

)(

)1(

00182.0*13

1

2

2

2

)1(

)(

)1(

*6000

1*

3

1*

5.11

132*1*

sec_

100

2

2

2

2

2

2

2

a

aa

a

npI

TshiftI

SshiftI

RshiftI

a

aa

a

npIondaryTR

TshiftI

SshiftI

RshiftI

These currents are the same (with the round-off error of 0.5%) as the primary transformed currents but multiplied by „-1”. As the differential currents are the sum of the shifted phase currents, these all result zero; the differential protection is balanced.



2.2.2 Checking for Y-side external phase-to-phase fault Assume I fault current on the Y side of the transformer in phases S and T. According to Fig. A2-3 of the Appendix, the input currents from the primary side of the transformer:

1

1

0

**600

1

1

1

1

I

TinputI

SinputI

RinputI

Transforming these currents:

1

2

1

00183.0**3

1

1

1

1

1

2

1

_

100*

600

1**

3

1

1

1

1

101

110

011

*3

1

1

1

1

I

TshiftI

SshiftI

RshiftI

primaryTRI

TinputI

SinputI

RinputI

TshiftI

SshiftI

RshiftI

The input currents from the secondary side of the transformer can be seen in Fig. A2-3 of the Appendix:

1

2

1

**3

1*

5.11

132*

6000

1

2

2

2

I

TinputI

SinputI

RinputI

According to Table 1, these secondary-side currents are transformed with the unit matrix; therefore, only the turns ratio has to be considered:

1

2

1

00182.0*3

1

2

2

2

1

2

1

*6000

1*

3

1*

5.11

132**

sec_

100

2

2

2

I

TshiftI

SshiftI

RshiftI

IondaryTR

TshiftI

SshiftI

RshiftI

These currents are the same (with the round-off error of 0.5%) as the primary transformed currents but multiplied by „-1”. As the differential currents are the sum of the shifted phase currents, these all result zero; the differential protection is balanced. Please note the multiplication factor „2” in phase S. Its consequences will be analyzed in a separate chapter.



2.2.3 Checking for D-side external phase-to-phase fault Assume I fault current on the D side of the transformer in phases S and T. According to Fig. A2-4 of the Appendix, the input currents to the differential protection are:

1

1

0

**6000

1

2

2

2

I

TinputI

SinputI

RinputI

According to Table 1-1, these secondary side currents are transformed with the unit matrix, therefore, only the turns ratio has to be considered:

1

1

0

*10*1587.0

2

2

2

1

1

0

*6000

1*

sec_

100

2

2

2

3 I

TshiftI

SshiftI

RshiftI

IondaryTR

TshiftI

SshiftI

RshiftI

The input currents from the primary Y side can be seen on Fig. A2-4 of the Appendix:

2

1

1

3

1**3*

132

5.11*

600

1

1

1

1

I

TinputI

SinputI

RinputI

The transformation of these Y-side currents according to Table 1:

1

1

0

**10*1596.0

1

1

0

**132

5.11*3*

3

1*

1

100*

600

1

1

1

1

101

110

011

*3

1

1

1

1

3 I

IIbe

TinputI

SinputI

RinputI

TshiftI

SshiftI

RshiftI

1

1

0

*10*1596.0*

1

1

1

1

1

0

132

5.11*

_

100*

600

1**

3

1

1

1

1

101

110

011

*3

1

1

1

1

3I

TshiftI

SshiftI

RshiftI

primaryTRI

TinputI

SinputI

RinputI

TshiftI

SshiftI

RshiftI

These currents are the same (with a round-off error of. 0.5%) as the secondary transformed currents but multiplied by „-1”. As the differential currents are the sum of the shifted phase currents, these all result zero; the differential protection is balanced. Please note the multiplication factor „-1” and „1” in phases S and T, respectively. Its consequences will be analyzed in a separate chapter.



2.2.4 Checking for Y-side external phase-to-ground fault A) If the neutral point of the transformer is grounded, an R phase-to-ground primary I fault current can be supposed. Suppose additionally that no supply from the delta side can be expected. Based on Fig. A2-5 of the Appendix, the input currents from the Y side are:

1

1

1

**600

1

1

1

1

I

TinputI

SinputI

RinputI

The transformation of the primary currents according to Table 1:

0

0

0

0

0

0

_

100*

600

1**

3

1

1

1

1

101

110

011

*3

1

1

1

1

primaryTRI

TinputI

SinputI

RinputI

TshiftI

SshiftI

RshiftI

The secondary currents can be seen on Fig. A2-5 of the Appendix:

0

0

0

**3

1*

5.11

132*

6000

1

2

2

2

I

TinputI

SinputI

RinputI

Based on Table 1-1, these secondary currents are transformed with the unit matrix, so only the turns ratio is considered:

0

0

0

0

0

0

**3

1*

5.11

132*

6000

1*

2

100

2

2

2

IIbe

TshiftI

SshiftI

RshiftI

0

0

0

0

0

0

5.11

132*

_

100*

6000

1**

3

1

2

2

2

primaryTRI

TshiftI

SshiftI

RshiftI

Because of zero currents, the differential protection is stable. B) Now suppose I fault current in phase R on the external primary side of the transformer if the neutral is grounded. The fault is supplied in this case from the delta side: Based on Fig. A2-6 of the Appendix, the input currents from the primary side are:

0

0

1

**600

1

1

1

1

I

TinputI

SinputI

RinputI



The transformation of these primary currents:

1

0

1

00183.0**3

1

1

1

1

1

0

1

_

100*

600

1**

3

1

1

1

1

101

110

011

*3

1

1

1

1

I

TshiftI

SshiftI

RshiftI

primaryTRI

TinputI

SinputI

RinputI

TshiftI

SshiftI

RshiftI

The input currents from the delta side, based on Fig. A2-6 of the Appendix are:

1

0

1

**3

1*

5.11

132*

6000

1

2

2

2

I

TinputI

SinputI

RinputI

Based on Table 1-1, these secondary currents are transformed with the unit matrix, so only the turns ratio is considered:

1

0

1

**3

1*00182.0

1

0

1

**3

1*

5.11

132*

6000

1*

2

100

2

2

2

I

IIbe

TshiftI

SshiftI

RshiftI

1

0

1

00182.0*3

1

2

2

2

1

0

1

*6000

1*

3

1*

5.11

132**

sec_

100

2

2

2

I

TshiftI

SshiftI

RshiftI

IondaryTR

TshiftI

SshiftI

RshiftI

The currents are balanced; the differential protection does not generate a trip command.

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Texte tapé à la machine

MICROENER - 49 rue de l'Université 93160 Noisy le Grand France - +33 (0)1 48 15 09 09 - [email protected]

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differential protection function block description - · pdf file1.8 example for the setting...

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