8 THEORY OF OPERATION
The computation of phaselets and sum of squares is basically a consolidation process. The phaselet sums are converted
into stationary phasors by multiplying by a precomputed matrix. Phaselets and partial sums of squares are computed and
time stamped at each relay and communicated to the remote relay terminals, where they are added and the matrix multipli-
cation is performed. Since the sampling clocks are synchronized, the time stamp is simply a sequence number.
The L90 uses an adaptive restraint in which the system uses measured statistical parameters to improve performance. In
particular, the system is able to adjust the restraint boundary dynamically to reflect measurement error. Also, in the peer to
peer architecture, fine adjustments are made to the sampling clocks to compensate for residual timing errors. Finally, the
data sampling frequency tracks the power system frequency to improve the accuracy of the phasors.
Adjustment of the restraint boundary is based on computing and adding all sources of current measurement error. (See
section on On-Line Estimate of Measurement Errors for sources and details of this calculation.) Each relay performs this
calculation from phaselets and sum of squares each time new information is available from remote terminals. The L90 relay
computes current phasor covariance parameters for all sources of measurement error for each phase of each terminal:
CRR = expected value of the square of the error in the real part of a phasor
CRI = CIR = expected value of the product of the errors in the real and imaginary parts
CII = expected value of the square of the error in the imaginary part of a phasor
Covariance parameters for each terminal are added together for each phase, and are used to establish an elliptical
restraint boundary for each phase.
Each L90 relay digital clock is phase synchronized to every other L90 relay clock and frequency synchronized to the power
system. Phase synchronization controls the uncertainty in phase angle measurements and frequency synchronization elim-
inates errors in phasor measurement when samples do not span one exact cycle.
A disturbance detection algorithm is used to enhance security and to improve transient response. Conditions for a distur-
bance include the magnitude of zero sequence current, the magnitude of negative sequence current, and changes in posi-
tive, negative, or zero sequence current. When a disturbance is detected, the phaselet computation is reset and fault
detection is enabled.
Normally, the sum of the current phasors from all terminals is zero for each phase at every terminal. A fault is detected for a
phase when the sum of the current phasors from each terminal for that phase falls outside of a dynamic elliptical restraint
boundary for that phase, based on a statistical analysis. The severity of the fault is computed from covariance parameters
and the sum of the current phasor for each phase as follows.
2
(
)
Severity
Re Phasor
=
(
+ Im Phasor
This equation is based on the covariance matrix and yields an elliptical restraint characteristic, as shown in Figure 8–3. The
elliptical area is the restraint region. When the covariance of the current measurements is small, the restraint region
shrinks.
When the covariance increases, the restraint region grows to reflect the uncertainty of the measurement. The computed
severity increases with the probability that the sum of the measured currents indicates a fault. With the exception of
"Restraint", all quantities are defined in previous sections. "Restraint" is a restraint multiplier, analogous to the slope setting
of traditional differential approaches, for adjusting the sensitivity of the relay. For most applications, a value of 1 is recom-
mended. Raising the restraint multiplier corresponds statistically to demanding a greater confidence interval, and has the
effect of decreasing sensitivity while lowering it is equivalent to relaxing the confidence interval and increases sensitivity.
Thus, the restraint multiplier is an application adjustment that is used to achieve the desired balance between sensitivity
and security.
GE Power Management
(
) Im Phasor
⋅
(
) 2
⋅
Re Phasor
–
2
2
)
⋅
⋅
,
–
18 Restraint
max C
RR
L90 Line Differential Relay
8.1.6 DISTURBANCE DETECTION
C
⋅
R 1
--------------------------------------
(
,
)
min C
C
RR
11
C
II
8.1 OVERVIEW
8.1.5 ADAPTIVE STRATEGY
8.1.7 FAULT DETECTION
8-3
8
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