Installation manual
GEO Direct PWM Amplifiers – Preliminary Documentation
24 System Wiring
Where:
J is the total system inertia (including motor) in lbftsec
2
ω is the velocity of the motor in Radians per Second
e
L
is the stored energy, in Joules (watt-seconds), of the load
Energy Loss in Transmission
The energy loss in the transmission of the energy occurs in two distinctive areas. First, the motor’s
resistance burns energy in simple watts. Second the mechanical gearing, bearings, and linkages present a
frictional loss. The motor’s resistive losses can be calculated for a linear deceleration profile as follows:
d
t*
phase
r*i
2
3
xr
e =
Where:
i is the current used during deceleration in amperes
r
phase
is the motor’s resistance phase-to-phase in ohms
t
d
is the time duration of the deceleration profile in seconds
e
xr
is the lost energy in Joules (watt-seconds)
The mechanical transmission energy losses can be calculated as follows:
d
ta*
friction
T*i678.0
xm
e
ω
=
Where:
T
friction
is the total friction in lbftsec
2
ω is the velocity of the motor in Radians per Second
e
xm
is the mechanical energy loss in Joules (watt-seconds)
t
d
is the time duration of the deceleration profile in seconds
Energy Stored in the Drive
Not all regenerative energy is spent in the resistive dump process. The drive has bus capacitors capable of
storing some of the returned energy. This energy storage is calculated using the following equation:
(
)
2
2
v
2
1
vc
2
1
c
e −=
Where:
C is the total bus capacitance in the drive in Farads
V
1
is the Bus Voltage at which Regen turns on
V
2
is the nominal bus voltage
e
c
is the energy stored in Joules (Watt-Seconds)
Need for Regen Resistor
Any energy that is not lost in the transmission of the energy and cannot be stored by the bus capacitors
must be dumped by the Regen circuits into the regen resistor. The following equation summarizes the
energy flow:
c
e
xm
e
xr
e
1
e
excess
e −−−=
Phrase this slightly differently and it can be stated that if e
excess
is less than or equal to 0 there is no need to
use an external Regen Resistor.