118
NVA100X-D - Manual - 02 - 2016
FUNCTION CHARACTERISTICS
Thermal image - 49MG for motor or generator protection
Preface
The phase currents (true RMS) are used into an algorithm reproducing a thermal replica according
the IEC 60255-8 standard taking into account the Joule losses and the cooling effect due to the load
reduction; in this way the previous history and the overload are taken into account. The thermal pro-
tection keeps the information of the motor’s heating state due both to the variations of the load condi-
tions, which cause thermal accumulations, and to balanced and unbalanced overload currents.
The measurement of the thermal image by the total memory module therefore extends the protection
criterion in the various operating conditions that may thermally load the motor over the maximum
allowed temperature for continuous service:
long-lasting overloads,
too frequent starts and stops,
running on a voltage below the rated value,
too long starts,
mechanic faults.
Since in case of unbalanced input the heating due to the negative sequence component exceeds
that due to the positive sequence, the thermal image unit computes as well the heating contribute of
the unbalanced input current with an adjustable weighting factor
K
2
. The thermal protection can be
adapted to the different features of motors by setting the thermal heating T+ and cooling T- constants
( the T+ constant refers to motor running condition, while the T- constant, always higher than T+,
refers to stopped condition). These values must be declared by the manufacturer.
Furthermore an adjustable initial thermal image value may be preset (by means of ThySetter, binary
input or keyboard commands.
The trip element has an adjustable threshold; with 1.2 D
θ
B
setting (ie 1.2 times the overtemperature
corresponding to the nominal operation condition) the corresponding tripping current
I
B
is 1.1 since
the temperature rise is proportional to the square of the current.
The 49 element is provided with two further thresholds D
θ
AL1
and D
θ
AL2
, lower than the previous one.
These thresholds, both adjustable, provide an alarm signal to draw attention in the event of anoma-
lous heating, without switching off the motor. One of the above thresholds can be used to prevent
motor starting when heating approaches the trip conditions since the additional heating brought on
by the starting currents would cause the protection to operate.
Operation and settings
The thermal current used for thermal image calculation is:
I
th
= √[(max (
I
L1rms
,
I
L2rms
,
I
L3rms
))
2
+K
2
·I
2
2
]
where
I
L1rms
,
I
L2rms
,
I
L3rms
are the true RMS value of the phase currents on side L, computed tack-
ing account the contribution of the harmonics up to eleventh order.
where the negative and positive sequence currents are computed as:
I
1
=(
I
L1L
+e
j120°
·
I
L2L
+e
-j120°
·
I
L3L
)/3 and
I
2
=(
I
L1L
+e-
j120°
·
I
L2L
+e
+j120°
·
I
L3L
)/3
with e
-j120°
= -1/2-j√3/2, e
j120°
= -1/2+j√3/2.
Over the start of the motor, the thermal equivalent current counted for the thermal image is:
I
th
= {√[(max (
I
L1rms
,
I
L2rms
,
I
L3rms
))
2
+K
2
·I
2
2
]} /
K
ST
where
K
ST
is an adjustable parameter (1.0...3.0), that lowers the thermal equivalent current during the
start if the setting change mode is selected.
According to a single-body thermal model, the thermal image is based on the differential equation:
dD
θ
/dt + D
θ
/T+ = (
I
th
/
I
B
)
2
/T+
where D
θ
is the system thermal state as a percentage of base thermal capacity D
θ
B
corresponding
to the base current
I
B
[1]
and T+ is the heating thermal time constant
During the time that the motor stops running, when the equivalent thermal current goes down the
threshold 0.1
I
B
, the thermal image is computed as:
dD
θ
/dt + D
θ
/T- = 0, where T- is the cooling constant.
The operating characteristic (IEC 60255-8) is:
t
=T · ln{[(
I
th
/
I
B
)
2
-
Δθ
p
/
Δθ
B
)] / [(
I
th
/
I
B
)
2
-
Δθ
>/
Δθ
B
]}=T · ln{[(
I
th
/
I
B
)
2
- (
I
p
/
I
B
)
2
] / [(
I
th
/
I
B
)
2
-
Δθ
>/
Δθ
B
] =
T · ln{[(
I
th
/
I
B
)
2
-
p
2
] / [(
I
th
/
I
B
)
2
-
Δθ
>/
Δθ
B
]} [1], where:
t:
operating time,
ln: natural logarithm,
D
θ
p
and
I
p
are the thermal image and the corresponding equivalent thermal current before the
overload occurs,
p
=
I
p
/
I
B
=√(D
θ
p
/D
θ
B
: pre-load,
Δθ
>: threshold
Note 1 Assuming that the secondary rated current of the line CT’s equals the rated current of the relay, as usually happens, the I
B
value is the ratio
between the rated current of the protected component (line, transformer,...) and the primary rated current of the CT’s.
—
•
•
•
•
•
•
•
•
•
•
heat-cool.ai
T-
0. 3 6 [p.u.]
1
t
D
θ
[p.u.]
D
θ
[p.u.]
T+
0.6 3 [p.u.]
1
t
Heating and cooling time constants for the thermal image elements - 49
Heating
Cooling
