F.5
Date Code 20080918 Instruction Manual SEL-749M Relay
Motor Thermal Element
The Basic Thermal Element
To properly account for the heating effects of the negative-sequence current,
calculate the negative-sequence rotor resistance. The rotor has slip with
respect to the stator negative-sequence current. To determine the value of the
negative-sequence slip as a function of positive-sequence slip, S, observe that
negative-sequence stator currents cause counter-rotating magnetic poles on the
inside face of the stator. When rotor speed is zero, the counter-rotating poles
induce fundamental frequency currents in the rotor: negative-sequence slip
equals positive-sequence slip, S. When the rotor is spinning at near
synchronous speed, the counter-rotating magnetic poles induce approximately
double-frequency currents in the rotor: negative-sequence slip equals twice
the fundamental frequency.
Based on these observations, negative-sequence slip equals (2–S). Substituting
this value for S in Equation F.3, calculate negative-sequence rotor resistance,
R
r–
.
Equation F.4
To obtain factors expressing the relative heating effect of positive- and
negative-sequence current, divide Equation F.3 and Equation F.4 by R
0
. For
the locked rotor case (slip, S = 1).
Equation F.5
When the motor is running (S ≈ 0), the positive-sequence heating factor, K
1
, is
solved as shown in Equation F.6.
Equation F.6
The negative-sequence heating factor, K
2
, at S ≈ 0 is solved as shown in
Equation F.7.
Equation F.7
To summarize, based on the assumption that the locked-rotor rotor resistance
is three times the running rotor resistance:
➤ The heating factor of positive-sequence current, K
1
, when the
motor is running is 1 per unit.
➤ The heating factor of negative-sequence current, K
2
, when the
motor is running is 5 per unit.
➤ Both K
1
and K
2
are 3 per unit when the rotor is locked.
The differences in the positive- and negative-sequence heating factors
immediately suggest that the thermal element should have two models
representing motor starting and running. The SEL-749M Relay thermal
element automatically selects the appropriate model to use based on the
measured sum of the positive-sequence current and the negative-sequence
where:
R
1
= Positive-sequence rotor resistance at slip S = 1
R
0
= Positive-sequence rotor resistance at slip S = 0
R
r-
R
1
R
0
–()2S–()• R
0
+=
R
r+
R
0
--------
S1=
R
r-
R
0
-------
S1=
R
1
R
0
------3===
1
R
r+
R
0
--------
S0=
=
R
0
R
0
------1==
K
2
R
r-
R
0
-------
S0=
2
R
1
R
0
------
⎝⎠
⎛⎞
• 1–5==
⎝⎠
⎜⎟
⎛⎞
=
Courtesy of NationalSwitchgear.com
To Next Page
