Download KB019

KILOVAR
Date
May 1991
GREENWOOD, SOUTH CAROLINA
Issue
19
Capacitor Tank Rupture Curve Coordination
When capacitors are being evaluated for purchase, frequently the only consideration
given to various designs is the initial cost - even though capacitors do differ in a
wide variety of technical parameters. The most significant variation is in terms of
safety characteristics. How a capacitor behaves during fault events has a serious
impact on safety considerations. Many progressive utilities today are including
safety characteristics as part of their purchase evaluations. One key procedure in
this process is understanding how to compare different capacitors' tank rupture
curves.
Fuse Curve Coordination
Fuse curve coordination is the single most critical factor in evaluating the safety
of a capacitor installation and one quite frequently overlooked. To ensure
coordination, the maximum clear TCC curve for the fuse link must coordinate with the
tank rupture curve of the capacitor. This coordination is necessary to insure that
the fuse will clear the circuit prior to tank rupture occurring. The fuse's maximum
clear TCC must fall to the left of the tank rupture TCC curve at and below the level
of available fault current. The time between the fuse's maximum clear curve and the
capacitor's tank rupture curve is called the coordination margin. This is calculated
at the fault current level in question.
Note that when a capacitor unit fails it will eventually fail to a short circuit.
The fault current flowing through the shorted capacitor is what must be evaluated.
In general:
o
For grounded wye pole mounted racks or single series group substation banks,
the fault current is the line to ground short circuit current at the location
of the installation.
o
For ungrounded wye pole mounted banks the fault current is limited by the
impedance of the good capacitors in the other phases and is equal to three
times the capacitor bank's normal current. Therefore a bank which normally
draws 80 amps, will draw 240 amps during a failure event. On the surface i t
may appear that ungrounded wye banks are safer due to the lower current drawn
during faults, however the long period of time it takes the fuse to operate
may result in the loss of coordination with the low end of the capacitor's
tank rupture curve. In addition, the capacitors in the other phases are now
energized at line-to-line voltage. Should the fuse clear slowly, the extended
time of operation at this voltage may result in additional unit failures.
o
In single series group ungrounded wye substation installations,the fault
current flowing through the failed capacitor is equal to three times the
current normally flowing through the entire bank. Therefore a unit which draws
only 30 amps but installed in a bank that draws 450 amps, upon failure the
unit will see 1350 amps.
Post Office Box 1224. Greenwood. SC 29648
o
For all other bank configurations
the fault current is dependant upon
the bank configuration and must be
calculated.
Tank Rupture Curve Types
Tank rupture curves available from
manufacturers may be probabilistic or
definite in nature. Definite tank rupture
curves indicate that there is minimal
likelihood of capacitor case rupture if a
fuse or protective device falls anywhere
to the left of the curve. See Figure 1.
This type of curve is exhibited by
capacitor
designs
that
have
very
consistent
faulted
impedance
characteristics. Depending
upon
the
manufacturer of the capacitor, the user
may find that a single curve or a family
of curves must be employed to properly
represent the rupture characteristics of
all voltage and Kvar size capacitor units.
Achieving safe coordination with this type
of tank rupture curve is generally simple
and reliable. Even minimal coordination
margins are usually considered acceptable.
Figure 1
Definite Tank Rupture Curve
Manufacturers of capacitors that exhibit
probability type tank rupture curves
usually supply 10% probability curves,
though 50% curves are available and should
be obtained from the manufacturer. A
probability curve indicates that rupture
may occur at a time-current level to the
left of the curve according to the
probability percentage associated with
that curve. Therefore a 10% curve
signifies that there exists a 10% chance
of not achieving coordination when using
that curve. For this reason obtaining the
largest coordination margins possible when
using
probability curves is highly
advantageous. See Figure 2.
Comparison of the 10% curve with the 50%
curve should be performed to ascertain the
degree of spread associated with the
underlying data. Though this process is
often cumbersome, it must be done to
ensure that the safety of an installation
is completely understood. When this spread
of data is examined, it frequently becomes
clear that it is not possible to achieve
an acceptable degree of confidence that
coordination will be achieved. It is not
recommended
to use capacitors
with
probability curves unless an appropriate
analysis confirms that coordination can be
achieved with an acceptable confidence
factor.
2
Figure 2
10% and 50%Tank Rupture Curves
For a 100 Kvar Capacitor
Coordination Using Probability Based Curves
Probability based tank rupture curves are developed when the spread of the
underlying rupture test data indicates that there is too much variation that can
properly be accounted for by using a definite curve. When developing the curves, a
sample of capacitors is tested to rupture at a given current level. The so called
10% curve is drawn so that only 10% of the time-to-rupture values are less than the
time value used to draw the curve. The 10% curve is actually a curve representing a
probability of 0.90 that the time-to-rupture is equal to or greater than the time
indicated on the curve.
We can solve for the standard deviation, σ, of the underlying data via the following
formula:
the time to rupture at the current value of interest
for the 10% curve
Where:
the time to rupture at the current value of interest
for the 50% curve
Using this data, one can calculate the time associated with any probability as
follows:
t
P
.50
Where:
the value from Table 1 that corresponds to the
confidence factor desired
Confidence
Factor
.9000
.9100
.9200
.9300
.9400
.9500
.9600
.9700
.9800
.9900
.9950
.9990
.9999
Z
1.28
1.34
1.41
1.48
1.55
1.64
1.75
1.88
2.05
2.33
2.58
3.09
3.72
Table 1
Z Values for Normal Distribution
Probabilities
(i.e. Confidence Factors)
Figure 3
100 Kvar Probability Tank Rupture Curves
with 25T M a x i m u m Clear Curve
Example of Coordination
For example, in Figure 3, three curves are drawn; the maximum clear curve for a 25T
fuse link, the 10% capacitor rupture curve for a 100 kVAr capacitor, and the 50%
curve for the 100 kVAr capacitor. The fault current level to be analyzed is 2000
amps. Table 2 summarizes the coordination margins at 50% and 10% taken directly from
the curves, as well as a 5% and 1.6% values calculated using equations ( A ) and (B).
Time for
Probability
50% Data
10% Data
5% Calculated
1.6% Calculated
Confidence
Factor
.500
.900
.950
.984
Fuse
Operation
.026 sec
.026 sec
.026 sec
.026 sec
Coordination
Margin
Rupture
.086 sec
.050 sec
.040 sec
.026 sec
.060 sec (3.6 cycles)
.024 sec (1.4 cycles)
.016 sec (.84 cycles)
0 - Coordination Lost
Table 2
Comparison of Coordination Margins for Various
Probabilities of Rupture
Understanding the calculated values may be easier if they are visualized as having
been read off of a new curve that was created. Therefore the margins for the 5% data
can be considered to have been obtained from a "5% curve". From Table 2 it may be
observed that as the probability of rupture goes down (and therefore the confidence
of not having a rupture goes up), the coordination margin decreases. This is part of
the difficulty in using probability curves; achieving coordination with the
published curve often gives a false sense of security. In this example, all
coordination margin is lost with a "1.6% curve". This means that if a given
application required better than a 98.4% likelihood of no rupture upon failure, this
unit and or fuse combination must be rejected.
Conclusions
When evaluating a capacitor unit's suitability for a given installation in terms of
safety from rupture, the following should be observed:
1.
The tank rupture curves should be obtained from the manufacturers during
the design stage. If the curves are probability in nature, then both the
10% and 50% curves should be obtained.
2.
The desired coordination margin and confidence level should be
ascertained to achieve the required level of safety at the installation
site.
3.
The coordination margins at the fault current level in question should
be evaluated. Any capacitor unit not exhibiting a sufficient
coordination margin should be eliminated from consideration.
4.
On capacitors with
probability curve is
margin based on the
value should be used
probability tank rupture curves, if the 10%
not sufficient to assure safety, a new coordination
desired probability should be calculated and this
for evaluation.
Bulletin KB019 - April 1991
Copyright 1991 Cooper Power Systems
File Reference: 230
I