Page 8-2
Effective 10/02For more information visit: www.cutler-hammer.eaton.comIL17562BH04
Use phasor analysis to determine the sequence currents from physical
phase current phasors.
Any 3 phase ac current without external
ground or neutral return path can be represented by the addition of I
1
and I
2
phasors in each phase. For an example, refer to the unbal-
anced motor currents of Figure 8.3. In this case, the three phase
currents in the motor are I
A
, I
B
, and I
C
. Note that I
B
and I
C
are of about
the same magnitude as I
A
, yet are noticeably displaced in phase
position. This is an example of a serious negative-sequence condition
which is threatening to the rotor, yet is not reflected in the current
magnitudes alone.
To calculate the positive sequence component in phase A, rotate the
phase B current phasor 120 degrees in the positive direction and the
phase C phasor 240 degrees in the positive direction. Refer to Figure
8.4. The formula for I
A1
is:
I
A1
= I
A
+ (I
B
Ð120°) +( I
c
Ð240°)
3
Note that these are phasor (vector) operations with a phasor result.
The positive sequence phasors in phases B and C have the same
magnitude as the phase A positive sequence phasor, but lag the phase
A component by exactly 120 and 240 degrees respectively. This
balanced set of phasors drives the motor’s useful work.
To calculate the negative sequence component in phase A, rotate the
phase B current phasor 120 degrees in the negative direction and the
phase C phasor 240 degrees in the negative direction. Refer to Figure
8.5. The formula for I
A2
is:
I
A2
= I
A
+ (I
B
Ð-120°) + (I
c
Ð- 240°)
3
The negative sequence phasors in phases B and C have the same
magnitude as the phase A positive sequence phasor, but lead the phase
A component by exactly 120 and 240 degrees respectively. This
balanced set of phasors represents the net effect of magnitude or phase
unbalance and only heats the rotor.
Certain harmonics in the phase currents produce torques in the rotor,
just like positive and negative sequence currents. In particular, the 7
th
and 13
th
and certain higher harmonics act like positive sequence. The
5
th
, 11
th
, and certain other higher harmonics act like negative sequence.
This can also influence motor performance and heating. The MP-3000
sequence calculations also capture these harmonic currents and
include their effect in the thermal modeling.
Prior to the use of a microprocessor in a multifunction motor protection
relay, there was no reasonable way of modeling the total heating
effects of the positive and negative sequence components on a
continuous basis. Therefore, oversimplified assumptions were used
with available relays. This resulted both in nuisance tripping and in
motor burnouts or life reduction. The MP-3000 uses a unique, patented
calculation for determining these values from current samples and
modeling their effects. The effective current squared, as used in the
calculation for rotor heating, is:
I
2
=
I
1
2
+
kI
2
2
Here
1
2
2
is weighted by k because of the disproportionate heating
caused by the negative sequence current component. The effects of
both the positive and negative sequence currents are accurately taken
into account. Their combined effect is incorporated into a rotor
protection algorithm that effectively keeps track of the temperature of
the rotor.
It is not necessary to pick an arbitrary phase unbalance setting to trip
the motor, although such an unbalance trip function is additionally
included in the relay to speed up tripping without heating for grossly
unbalanced conditions. As long as the combined effect of the positive
and negative sequence currents does not approach the motor damage
curve, the MP-3000 will allow the motor to run.
8.2.3 Thermal Bucket
The MP-3000 models heating as the filling of a thermal reservoir or
accumulating bucket whose size is determined by the thermal capacity
of the motor. This capacity is calculated in the relay from motor
nameplate constants. The filling is proportional to effective I
2
over
time, where effective I
2
includes the disproportionate heating effect of
negative-sequence currents. Cooling is also modeled as draining of
the bucket. The loss of equilibrium between heating and cooling leads
to an eventual thermal trip. The thermal bucket filling in percent can be
observed continuously on the MP-3000 display, via data communica-
tions, or via the 4-20 mA transducer output.
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