Appendix G
129
Peak power regeneration occurs at the moment deceleration begins, when the velocity is
highest.
P
shaft( peak )
= 2πv
max
T
Not all of this peak power must be dissipated in the power resistor. Some of it will be
dissipated in the copper windings of the motor—these power losses are known as copper
losses.
P
copper
= I
2
R =
3
2
T
k
T
2
R
where
I = motor current, in amps (A)
R =line – to – line motor resistance, in ohms (Ω)
k
t
= motor torque constant, in newton meters per amp rms (Nm / A rms)
Power is also dissipated in the drive itself—these losses are known as drive losses. (Notice
that we use the absolute value of the torque.)
P
drive
= 52
T
k
T
The peak power dissipated in the regeneration resistor, then, is equal to the peak shaft power,
less copper and drive losses.
P
peak
= P
shaft
− P
copper
− P
drive
Substituting the values from the previous equations, we obtain the equation for calculating
peak power:
P
peak
= 2πv
max
T
()
−
3
2
T
k
T
2
R−52
T
k
T
Substitute values from your application into this equation.
• If P
peak
is less than the Peak Power Dissipation Rating, the internal resistor is adequate.
• If P
peak
is greater than the Peak Power Dissipation Rating, install an external resistor.
Calculating Average Power
Time plays a role in average power calculations. Total regenerated energy is equal to the area
of the triangle under the deceleration portion of the move profile. In the move profile shown
earlier, the time of deceleration is t
1
. Total energy, W, is therefore:
W
regen
=
1
2
height
()
base
()
=
1
2
2πv
max
T
()
t
1
During the deceleration time, copper losses and drive losses will dissipate some of the
regenerated energy. To determine how much energy these losses will dissipate, each of these
losses must be multiplied by the time t
1
:
W
copper
=
3
2
T
k
T
2
R
t
1
W
drive
= 52
T
k
T
t
1
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