03. digital current differential protection · - the line charging current •fault condition: i 1...

A New ApproachA New Approach

to to

Current Differential ProtectionCurrent Differential Protection

forfor

Transmission LinesTransmission Lines

2

CURRENT DIFFERENTIAL MODELCURRENT DIFFERENTIAL MODELCURRENT DIFFERENTIAL MODEL

I1

I2

Ic

2

Ic

2

•Normal Condition: I1 + I

2 = I

C - the line charging current

•Fault Condition: I1 + I

2 = I

C

•Can be done on a per phase basis

Current Differential Protection for Transmission Lines

3

PERCENT RESTRAINT

CHARACTERISTIC

PERCENT RESTRAINTPERCENT RESTRAINT

CHARACTERISTICCHARACTERISTIC

k*[ | I1 | + | I2 | ]

| I1 + I2 |

OPERATE

RESTRAINT

IMIN

K1


4Current Differential Protection for Transmission Lines

v t V t

VrealN

Vkk

N

VimagN

Vkk

N

peak

k

N

k

N

( ) cos( )

( ) [ cos( )]

( ) [ sin( )]

= • +

= • • • •∑

= • − • • •∑

=

−

=

−

ω φ

π

π

22

22

0

1

0

1

Discrete Fourier TransformDiscrete Fourier Transform

5

W1W2

W1

W2

One cycle sliding Fourier

window on fault waveform

Magnitude Response of One Cycle

Sliding Fourier Window

TRADITIONAL ONE CYCLE FOURIERTRADITIONAL ONE CYCLE FOURIER


6

W1

W2

W1

W2

One cycle sliding Fourier

window on fault waveform

Magnitude Response of Dynamic

Fourier Window

W3

Fault

Detection

VARIABLE FOURIER WINDOWVARIABLE FOURIER WINDOW

W2


7

Phaselet al C X

Phaselet aginary S X

Where

p kk p P P

p P

k

pk p P P

p P

k k

Re

Im

:

= ∑ ⋅

= −∑ ⋅

=

= ⋅ − +

⋅

= ⋅ − +

⋅1

1

C , S Sine and Cosine Coefficients

p = phaselet index: there are N / P phaselets per cycle

P = the number of samples per phaselet

X = kth sample of the input signal

k k

k

PHASELET CALCULATIONPHASELET CALCULATION


8

PHASOR CALCULATIONPHASOR CALCULATION

Phasor al

Phasor aginary

T nW T n W

T n W T n W

PhaseletSum al

PhaseletSum aginary

n

n

RR RI

IR II

n

n

Re

Im

( , ) ( , )

( , ) ( , )

Re

Im

=

•

Phaselets are converted to phasors by the following:

Where:

PhaseletSum al Phaselet aln p

p nW

P

n

Re Re=

= − +

∑1

PhaseletSum aginary Phaselet aginaryn p

p nW

P

n

Im Im= ∑= − +1

n = Phasor index; W = Window size in samples


9

Time Domain:

Sampled Data:

Time Domain:

Sampled Data:

IZ t I t Rd

dtI t L( ) ( ) ( ( ))= • + •

IZ kI k I k

RI k I k

L( )( ( ) ( )) ( ( ) ( ))+ = + + • + + − •δ δ δ

δ2 2

MIMIC ALGORITHMMIMIC ALGORITHM


10

DUAL SLOPE PERCENT RESTRAINTDUAL SLOPE PERCENT RESTRAINT

k*[ | I1 | + | I2 | ]

| I1 + I2 |

OPERATE

RESTRAINT

K1

K2Dynamic

Restraint


11

σ = − • + •∑=x X PL X PLi R R I I

i

N2

1

( )

“GOODNESS OF FIT” CALCULATION“GOODNESS OF FIT” CALCULATION


12

PERCENT RESTRAINT CHARACTERISTIC

ON THE COMPLEX PLANE

PERCENT RESTRAINT CHARACTERISTIC

ON THE COMPLEX PLANE

REAL

IMAG

K1·IrIop

OPERATE

REGION


13

ADAPTIVE RESTRAINT CHARACTERISTICON THE COMPLEX PLANE

ADAPTIVE RESTRAINT CHARACTERISTICON THE COMPLEX PLANE

REAL

IMAG

Iop

OPERATE

REGION

STEADY STATE

RESTRAINT

DYNAMIC

RESTRAINT


14

ELLIPTICAL RESTRAINT

CHARACTERISTIC

ELLIPTICAL RESTRAINT

CHARACTERISTIC

REAL

IMAG

Iop

OPERATE

REGION

DYNAMIC

ELLIPTICAL

RESTRAINT TRADITIONAL

CIRCULAR

RESTRAINTSTEADY STATE

CIRCULAR

RESTRAINT


15

Time synchronization Internet “Ping-Pong”Time synchronization Internet “Ping-Pong”


Relay 1 Relay 2

time

t0

t1

t2

t3

tf

tr

Forwardtravel

time

Returntravel

time

Relayturn-around

time

tf = t

r =

t3

- t0 - (t

2 - t

1)

2

16

DIGITAL FLYWHEELDIGITAL FLYWHEEL

clock 1 clock 2

“Virtual Shaft”

ω ω

• Sample clocks set via a 32 bit equivalent counter

• Counter is set as a result of thousands of “Ping-Pong” messages

• If communications is lost, sample clocks continue to “free wheel”

Superior accuracy is obtained with the 32 bit counter. Long term

accuracy is only a function of the base crystal stability.


17

Differential Path Delay CorrectionDifferential Path Delay Correction


If tr = t

f, this “differential” time delay results in a

phase angle error in the measured phasor

2

θ

θ2

Communication path time differentialis corrected via current measurement

θ

18

Data Packet ComparisonData Packet Comparison


Address Control Time Tag Data CRC

Data from Relay #1

Address Control Time Tag Data CRC

Data from Relay #2

Note: Only data with identical

time tags are compared

19

Communications ArchitectureCommunications Architecture


Redundant communications with Hot Standby

on 2 terminal applications:

Relay 1 Relay 2

Communication link #1

Communication link #2

20



Relay 1

Relay 2 Relay 3

• Peer-to-Peer operation

• Each relay has sufficient information to make

an independent decision• Communication Redundancy

Current Phasors communicated

from each relay to every other

relay

21



• Master-Slave operation• At least one relay has sufficient information to make

an independent decision

• The deciding relay(s) sends a transfer-trip command

to all other relays

Relay 1

Relay 2 Relay 3

Relay 2

Data

Relay 3

Data

“Transfer Trip”

message


Relay 1

Relay 2 Relay 5

• Can support up to a 5 terminal line configuration with either Peer-to-Peeror Master/Slave or any combination thereof

Relay 3 Relay 4

Communications ArchitectureCommunications ArchitectureCommunications Architecture

23

Channel Bandwidth Tripping Data Packets Op. Time

kbps per cycle (cycle)

Dedicated Fiber 64 Single phase 2 3/4 - 1

(0 to 40kM)

RS-422 Sync. 64 Single phase 2 3/4 - 1

G.703 Sync. 64 Single phase 2 3/4 - 1

Note: The RS-422 and G.703 interfaces are designed to operate

over digital multiplexed communication channels

CHANNEL MEDUIM OPTIONSCHANNEL MEDUIM OPTIONS



I1 I2

x

Ic

2

Ic

2

IC = C dV/dt

• Corrects sample data before a phasor is computed

• Compensates all frequency components - not just the

fundamental

Capacitive Error Current CompensationCapacitiveCapacitive Error Current Compensation Error Current Compensation

25

• Enhanced Performance

• Time Synchronization

- Communication Path Delay Adjustment

- Differential Communication Path Delay

• Redundancy for Loss of Communications

• Flexible Communication Configurations

• Communications Media Options

SUMMARYSUMMARY


03. digital current differential protection · - the line charging current •fault condition: i 1...

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