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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
Current Differential Protection for Transmission Lines
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
Current Differential Protection for Transmission Lines
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
Current Differential Protection for Transmission Lines
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
Current Differential Protection for Transmission Lines
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
Current Differential Protection for Transmission Lines
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
Current Differential Protection for Transmission Lines
10
DUAL SLOPE PERCENT RESTRAINTDUAL SLOPE PERCENT RESTRAINT
k*[ | I1 | + | I2 | ]
| I1 + I2 |
OPERATE
RESTRAINT
K1
K2Dynamic
Restraint
Current Differential Protection for Transmission Lines
11
σ = − • + •∑=x X PL X PLi R R I I
i
N2
1
( )
“GOODNESS OF FIT” CALCULATION“GOODNESS OF FIT” CALCULATION
Current Differential Protection for Transmission Lines
12
PERCENT RESTRAINT CHARACTERISTIC
ON THE COMPLEX PLANE
PERCENT RESTRAINT CHARACTERISTIC
ON THE COMPLEX PLANE
REAL
IMAG
K1·IrIop
OPERATE
REGION
Current Differential Protection for Transmission Lines
13
ADAPTIVE RESTRAINT CHARACTERISTICON THE COMPLEX PLANE
ADAPTIVE RESTRAINT CHARACTERISTICON THE COMPLEX PLANE
REAL
IMAG
Iop
OPERATE
REGION
STEADY STATE
RESTRAINT
DYNAMIC
RESTRAINT
Current Differential Protection for Transmission Lines
14
ELLIPTICAL RESTRAINT
CHARACTERISTIC
ELLIPTICAL RESTRAINT
CHARACTERISTIC
REAL
IMAG
Iop
OPERATE
REGION
DYNAMIC
ELLIPTICAL
RESTRAINT TRADITIONAL
CIRCULAR
RESTRAINTSTEADY STATE
CIRCULAR
RESTRAINT
Current Differential Protection for Transmission Lines
15
Time synchronization Internet “Ping-Pong”Time synchronization Internet “Ping-Pong”
Current Differential Protection for Transmission Lines
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.
Current Differential Protection for Transmission Lines
17
Differential Path Delay CorrectionDifferential Path Delay Correction
Current Differential Protection for Transmission Lines
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
Current Differential Protection for Transmission Lines
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
Current Differential Protection for Transmission Lines
Redundant communications with Hot Standby
on 2 terminal applications:
Relay 1 Relay 2
Communication link #1
Communication link #2
20
Communications ArchitectureCommunications Architecture
Current Differential Protection for Transmission Lines
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
Communications ArchitectureCommunications Architecture
Current Differential Protection for Transmission Lines
• 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
22Current Differential Protection for Transmission Lines
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
Current Differential Protection for Transmission Lines
24Current Differential Protection for Transmission Lines
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
Current Differential Protection for Transmission Lines