8.1 OVERVIEW
The next step in the process is the removal of any decaying offset from each phase current measurement. This is done
using a digital simulation of the so-called "mimic circuit", which is based on the differential equation of the inductive circuit
which generates the offset. Next, phaselets are computed by each L90 relay for each phase from the outputs of the mimic
calculation, and transmitted to the other relay terminals. Also, the sum of the squares of the raw data samples is computed
for each phase, and transmitted with the phaselets.
At the receiving relay, the received phaselets are combined into phasors. Also, ground current is reconstructed from phase
information. An elliptical restraint region is computed by combining sources of measurement error. In addition to the
restraint region, a separate disturbance detector is used to enhance security.
The possibility of a fault is indicated by the detection of a disturbance as well as the sum of the current phasors falling out-
side of the elliptical restraint region. The statistical distance from the phasor to the restraint region is an indication of the
severity of the fault. To provide speed of response that is commensurate with fault severity, the distance is filtered. For mild
faults, filtering improves measurement precision at the expense of a slight delay, on the order of one cycle. Severe faults
are detected within a single phaselet.
Whenever the sum of phasors falls within the elliptical restraint region, the system assumes there is no fault, and uses
whatever information is available for fine adjustment of the clocks.
The inductive behavior of power system transmission lines gives rise to decaying exponential offsets during transient con-
ditions, which could lead to errors and interfere with the determination of how well measured current fits a sinewave.
The current signals are pre-filtered using an improved digital MIMIC filter. The filter removes effectively the DC compo-
nent(s) guaranteeing transient overshoot below 2% regardless of the initial magnitude and time constant of the dc compo-
nent(s). The filter has significantly better filtering properties for higher frequencies as compared with a classical MIMIC filter.
This was possible without introducing any significant phase delay thanks to the high sampling rate used by the relay. The
output of the MIMIC calculation is the input for the phaselet computation. The MIMIC computation is applied to the data
samples for each phase at each terminal. The equation shown is for one phase at one terminal.
Phaselets are partial sums in the computation for fitting a sine function to measured samples. Each slave computes phase-
lets for each phase current and transmits phaselet information to the master for conversion into phasors. Phaselets enable
the efficient computation of phasors over sample windows that are not restricted to an integer multiple of a half cycle at the
power system frequency. Determining the fundamental power system frequency component of current data samples by
minimizing the sum of the squares of the errors gives rise to the first frequency component of the Discrete Fourier Trans-
form (DFT). In the case of a data window that is a multiple of a half cycle, the computation is simply sine and cosine
weighted sums of the data samples. In the case of a window that is not a multiple of a half-cycle, there is an additional cor-
rection that results from the sine and cosine functions not being orthogonal over such a window. However, the computation
can be expressed as a two by two matrix multiplication of the sine and cosine weighted sums.
Phaselets and sum of squares are computed for each phase at each terminal from the output of the mimic computations as
follows:
8
(
Re Phaselet
(
Im Phaselet
PartialSumOfSquares
where: Re(Phaselet
p
Im(Phaselet
p
PartialSumOfSquares
p = phaselet index: there are N / P phaselets per cycle
P = number of phaselets per cycle
Imimic
= k th sample of the mimic output, taken N samples per cycle
k
8-2
⋅
p P
2π
∑
)
=
cos
------
p
N
⋅
k
p P P
1
=
–
+
⋅
p P
2π
------ k 1
∑
)
⋅
sin
=
–
p
N
⋅
k
p P P
1
=
–
+
⋅
p P
∑
Imimic
=
p
k
⋅
k
=
p P P
–
+
1
) = real component of the p th phaselet
) = imaginary component of the p th phaselet
= the p th partial sum of squares
p
L90 Line Differential Relay
8.1.3 REMOVAL OF DECAYING OFFSET
k 1
⋅
⋅
–
-- -
Imimic
k
2
⋅
Imimic
–
-- -
k
2
2
8 THEORY OF OPERATION
8.1.4 PHASELET COMPUTATION
GE Power Management
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