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Figure C.3 – Phase to phase fault (LL)
IEC 60255-121:2014 © IEC 2014
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Calculation of mean, median and mode
The mean is the arithmetic average of a set of values, or distribution. The mean is calculated
by adding up the collected data and dividing by the total number of data points.
The median is the middle number of the sampled data. The median number of a finite list of
data can be found by arranging all the data from the lowest to the highest and picking the
middle sample. If there is an even number of observations then the median takes the average
of the two middle values.
The mode of a data sample is the element that occurs most often in the collection. Where
several values occur with the same frequency then the mode can be represented by more
than one value.
The distance protection function operate time is measured over ten samples:
34 ms, 31 ms, 35 ms, 31 ms, 43 ms, 31 ms, 38 ms, 39 ms, 48 ms, 31 ms
The mean is calculated as:
48 ms + 39 ms + 31ms + 35 ms + 38 ms + 31ms + 31ms + 31ms + 43 ms + 34 ms
= 36,1 ms
The median is calculated as follows.
Arranging the data in order the average of the 5
and 6 data point is 34,5 ms.
31ms, 31ms, 31ms, 31ms, 34ms, 35ms, 38ms, 39ms, 43ms, 48ms.
The mode is calculated as the most frequent data point which in this case is 31 ms.
Therefore the data presented for the distance protection functions operate time would be:
mean operate time 36,1 ms,
median operate time 34,5 ms,
mode operate time 31 ms.
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IEC 60255-121:2014 © IEC 2014
CT saturation and influence on the performance of distance relays
Clause 5 states that the relay manufacturers shall specify CT requirements necessary for
correct operation of the distance protection. It also specifies how the CT requirements shall
be expressed and the fault cases and conditions that shall be considered and fulfilled. This
informative annex gives the background and informs about CT saturation and the influence on
the performance of distance relays.
Saturation of CTs will give both amplitude and phase errors in the secondary current.
Sometimes saturation also can cause false secondary zero sequence currents. The errors can
cause different incorrect operations of distance protection relays. Failure to operate,
unacceptable delayed operation and unacceptable underreach can be classified as lack of
dependability. Unwanted operations due to incorrect directionality or unacceptable overreach
can be classified as lack of security.
AC saturation of a CT is caused by a symmetrical AC current with no DC component present.
AC saturation will cause a permanent reduction of the secondary current and the measured
impedance will be larger than the actual impedance. Therefore, AC saturation may cause a
failure to operate.
DC offset in the primary current will increase the risk of CT saturation but the saturation
caused by DC component alone will never cause a failure to operate. The secondary current
will recover with a speed depending on the primary DC time constant and the reduction of the
DC component of the primary current. If the protection fails to trip before saturation, the
saturation caused by DC component will cause an unwanted additional time delay that is
dependent on the primary time constant. Phase errors due to CT saturation will turn the
current phasor counter clockwise. This and other consequences of CT saturation can cause
overreach and risk of unwanted operations. The phase error due to CT saturation together
with other measuring errors can also cause wrong directional indication with the risk of
unwanted operations for reverse faults.
Remanence or remaining flux in the CT core influences the time to saturation. When there is
no DC offset, the remanence will only affect the first half cycle of the current waveform. If the
fault current has a DC offset, the remanence will impact the first moment when the CT will
saturate and the time to saturation can be decreased. The saturated secondary current has
the same characteristics as the saturation caused by DC component without any remanence.
This means that the presence of remanence increases the risk of unwanted operations and
unwanted additional time delays. It is important to be aware that remanence in itself will not
cause a failure to operate.
The high remanence type CT (closed core) is the most commonly used type of CT and it can
contain relatively high levels of remaining flux. Even if the influence of remanence mostly has
not been considered in the CT dimensioning, the operational experiences have been good. If
the dimensioning of the CTs has considered only CT saturation without remanence, the
performance of the distance protection will be within specified limits as long as no remanence
occurs. However, if remanence in unfavourable direction occurs there is a risk that the CTs
will saturate faster than the required time to saturation and the relay will have an additional
time delay that is dependent on the fault current primary time constant of the actual fault
position. For most faults along a line the primary time constant is relatively small and any
additional time delay that may occur is mostly of no importance. In some applications the
primary time constant can be much larger and for close-in faults there may be a risk of
unacceptable additional time delay (lack of dependability). In such specific cases it may be
necessary to consider the remanence in dimensioning the CT.
IEC 60255-121:2014 © IEC 2014
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Remanence can also cause unwanted operations (lack of security) due to faster CT saturation
and overreach causing operations for faults on an adjacent busbar or for faults at the
beginning of adjacent lines. The risk of unwanted operations is higher on short lines but shall
generally be considered to be relatively small. Unwanted operations can also occur for
reverse faults on the busbar or for faults at the beginning of other lines in the station due to
remanence or remaining flux. The risk of these unwanted operations is also considered to be
small. In spite of this, an unwanted operation normally is considered as a more serious
incorrect operation than an unwanted additional time delay. Therefore, the security cases in
general have higher priority than the dependability cases if remanence or remaining flux is
Basically CT saturation can cause the following types of incorrect operations: unwanted
operations for close-in reverse and zone 1 faults and failure to operate or delayed operation
for close-in forward and zone 1 faults. Therefore, four main fault positions are relevant for
dimensioning the CTs and shall be considered to specify the CT requirements. The fault
positions are shown in Figure E.1: close-in reverse (fault 1), close-in forward (fault 2), zone 1
underreach (fault 3) and zone 1 overreach (fault 4).
Figure E.1 – Fault positions to be considered for specifying the CT requirements
Each CT has a fixed saturation e.m.f. that specifies most of the properties of a CT. The rated
equivalent limiting secondary e.m.f. E al is defined in Equation (E.1) as follows:
E al = K ssc . K td .I sr (R ct + R b )
K ssc = I psc /I pr
K ssc is the CT symmetrical short circuit current factor;
is the CT rated primary short circuit current;
is the CT rated primary current;
is the CT rated secondary current;
is the CT rated transient dimensioning factor;
is the CT secondary winding resistance;
is the CT rated resistive burden.
Clause 5 states that the CT requirements shall be specified as a rated equivalent limiting
secondary e.m.f. E al. The required rated equivalent limiting secondary E alreq depends on the
application and on the design of the relay. E alreq is defined in Equation (E.2) as follows:
E alreq = (I f /I pr ).K tot .I sr (R ct + R ba )
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IEC 60255-121:2014 © IEC 2014
is the maximum primary CT current for the considered fault case;
is the total over-dimensioning factor (including the transient dimensioning factor and
the remanence dimensioning factor); when K tot = 1 the CT will not saturate for a
continuous symmetrical fault current with the magnitude I f , if there is no remanent
is the total resistive burden, including the secondary wires and all relays in the
Distance relay applications require that CTs shall not saturate for a specific minimum time in
order to have correct relay operation for faults. The time to saturation for a CT is a function of
the transient dimensioning factor. The required saturation free time is dependent on the relay
design and can vary for different fault positions. In cases with different DC offset and also
different remanence the CT shall be over-dimensioned with the K tot factor to guarantee the
required saturation free time. The relay manufacturer shall specify the required K tot factors for
the specific distance relay and the different fault positions. For the specific application the
required rated equivalent limiting secondary e.m.f. E alreq can be calculated and the CTs can
In general distance protection requires longer saturation free time for detection of zone 1
faults than for detection of close-in faults and hence the over-dimensioning factor for zone 1
faults is larger than the over-dimensioning factor for close-in faults. As the relation between
fault current levels for close-in faults and zone 1 faults is dependent on the relation between
the source impedance and the length of the line, this relation also decides whether the closein fault or the zone 1 fault will give the over-dimensioning factor for each specific application.
This means that one of the four (fault 1 to 4) fault positions will decide the dimensioning for
each specific application and for all other fault positions there will be an additional CT margin.