G. Ziegler. Digital Differential Protection
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G. Ziegler, 10/2005 page28
Differential Protection Symposium
Belo HorizonteNovember 2005
Digital Differential Protection
Measuring Technique
Gerhard Ziegler
G. Ziegler, 10/2005 page29
Differential Protection Symposium
Belo HorizonteNovember 2005
a: feeder, b: generator, c: substation, d: primary winding of CT, e: secondary winding of CT, f: earth or
return conductor, g: pilot wire, h: relay windings, i: circuit breakers, k,l: movable and fixed relay
contacts, m: circuit, n: battery, o: electromagnetic device with armature p.
Merzand Price differential protection
Patent dated 1904
G. Ziegler, 10/2005 page30
Differential Protection Symposium
Belo HorizonteNovember 2005
Schutzobjekt
I
1
I
2
∆i
i
1
i
2
Electro-mechanical differential protection
based on induction relay
G. Ziegler, 10/2005 page31
Differential Protection Symposium
Belo HorizonteNovember 2005
Electro-mechanical differential protection
Rectifier bridge comparator with moving coil relay
Protection
object
I
1
I
2
i
1
i
2
(
)
21
Re
IIkI
s
−⋅=
21
III
Op
+=
s
I
Re
Op
I
s
I
Op
IΔI
Re
−=
I
∆
+
NS
G. Ziegler, 10/2005 page32
Differential Protection Symposium
Belo HorizonteNovember 2005
Differential protection
Analogstatic measuring circuit
21
III
Op
+
=
Protection
object
I
1
I
2
i
1
i
2
(
)
21
Re
IIkI
s
−
⋅
=
S
R
s
I ⋅
Re
S
R
Op
I ⋅
R
S
R
S
V1
V2
V3
U
Ref
G. Ziegler, 10/2005 page33
Differential Protection Symposium
Belo HorizonteNovember 2005
CPU
RAM
ROM
A
D
1
n
IL1
IL2
IL3
IE
UL1
UL2
UL3
UE
a.s.o.
0.67 ms (18 degr. el.)
1.2 kHz
clock
S & H
MUX
MIFilter
Processorsystem
Digital differential protection
Measuring value acquisition and processing
G. Ziegler, 10/2005 page34
Differential Protection Symposium
Belo HorizonteNovember 2005
I
=
I
I
RMS
0
n
Digital protection:
Measurement based on momentary values
2
ˆ
)
2
1
( cos
ˆ
I
RMS
I
n
I
I
=
∆⋅
−
=
=
ϕ
when n sampled values exceed the
pick-up limit I
=
∆T
samp.
corresponds to ∆ϕ ( 60Hz: 0.67 ms = 18
O
el.)
O
A
f
N
f
samp
T 360
.
⋅=∆⋅=∆ ωϕ
G. Ziegler, 10/2005 page35
Differential Protection Symposium
Belo HorizonteNovember 2005
18
O
= 1 ms (50 Hz)
= 0.67 ms (60 Hz)
trip
restrain
B
I
A
II
B
I
A
II
+=Σ
+=∆
:quantity gRestrainin
:quantity Operating
∆I
∆I>
ΣI
1
2
3
4
5
7
8
6
0
9
10
1
2
3
4
5
6
7
8
9
10
0
I
A
I
B
∆I
∆I
Digital differential protection:
Measurement based on momentary values
G. Ziegler, 10/2005 page36
Differential Protection Symposium
Belo HorizonteNovember 2005
n
i
2
sin
⋅
π
n
i
2
cos
⋅
π
C(k)S(k)
(k)
j
I
I
I
⋅
+
=
S(k)
I
C(k)
I
j
)(k
I
)( ink
i
+−
k-n
0 1 2 . . .n
ϕ
i
C(k)
I
S(k)
I
k
Discrete Fourier-Transformation (Principle)
Correlate
Correlate
Correlate:
Multiply samples and
add for one cycle
G. Ziegler, 10/2005 page37
Differential Protection Symposium
Belo HorizonteNovember 2005
)(
∑
⋅⋅⋅=
n
S
iΔnωsin
2
t
N
I
)(
∑
⋅⋅⋅
+
+
=
n
NO
C
iΔtnωcos
2
i
2
i
2
N
I
∆t
i
0
i
1
i
2
i
N
n
012N
012N
3 . . . .
3 . . .
Discrete Fourier-Transformation (calculation formulae)
i
3
n=1
N-1
n=1
N-1