7SR105 Rho Description of Operation
©2018 Siemens Protection Devices Chapter 1 Page 22 of 57
Section 3: Protection Functions
3.1 Thermal Protection
To prevent overheating of the motor thermal overload protection is used to remove the motor supply when a
nominated thermal state (
θ
) is reached.
The thermal overload function uses measured 3-phase true RMS current to estimate the thermal state of the
motor. The Thermal State (
θ
) is based on both past and present current levels.
θ
= 0% for unheated equipment,
and
θ
= 100% for maximum thermal state of equipment i.e. the trip threshold. For given current level, the Thermal
State will ramp up over time, dependent on the thermal time constant, until Thermal Equilibrium is reached when
Heating Effects of Current = Thermal Losses.
Thermal
State
TIME
100%
0%
Thermal Equilibrium
Trip
Overload
Figure 3.1-1 Thermal Overload Heating and Cooling Characteristic
The NPS component of unbalanced current has a greater heating effect on the motor than the PPS current
component. An NPS component can be included within an ‘equivalent thermal current’ (I
EQ
) used in the thermal
overload algorithm. The NPS weighting factor K can be used to increase overload protection sensitivity to NPS
current.
The thermal model accommodates both heating and cooling conditions with exponential curves as illustrated
below:
For the heating curve:
−
×
=
×
−
⋅
=
−
θ
τ
τ
I
I
I
e
EQ
EQ
t
2
2
2
θ
2
EQ
ln
t(mins)
or,
100%,
)
(1
I
I
θ
For the cooling curve:
F
F
θ
θ
ln
.
θ
θ
τ
τ
=
×
=
−
t
or
e
t
The time constant of the thermal protection is dependent on the operate state of the motor i.e. whether it is
starting, running or stopped. Three values of thermal time constant are used during the different states of motor
operation – see
Table 3-1
Application of Thermal Time Constants
Gn 49 TauH
(mins)
Heating Time Constant:
Used during normal motor running conditions and overloads.
Gn 49 TauS
(mins)
Starting Time Constant:
Multiple of heating time constant takes into consideration the
reduced cooling available when the motor is running up to full speed.
Gn 49 TauC
(mins)
Cooling Time Constant:
Multiple of heating time constant takes into consideration the
reduced rate of cooling of a stopped motor.
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