Appendix A – DC Power Supply Design
05/2008
Danaher Motion
118
S200-VTS Product Manual
A.4
Bus Energy & Power Numerical Examples
The energy flows in the drive bus are:
In
- Motoring mechanical Motor losses (motor accelerates).
Out
- Regenerated mechanical energy – Motor losses (motor decelerates).
Out
- Regenerated motor inductive energy (disable or fault).
A.4.1
Min. External Bus Capacitance
Inductance in AKM motors mated to S200s can be as high as 5 mH (line-to-line). The inductive
energy stored in a 5 mH motor at 18 ARMS is calculated as:
E winding = 0.75 x Inductance line-to-line x I
RMS
x I
RMS
= 0.75 x 0.005 henry x 18
RMS
x 18
RMS
= 1.2 joules
The bus capacitor needed to absorb the regenerated energy (E
REGEN
) is sized using the general
rule that the energy stored in the capacitor be a minimum of 5 * E
REGEN
. This limits the voltage
increase on the bus due to regeneration to 10% of the DC value. Using this general rule to find
the minimum bus capacitance for the motor in the above example (for simplicity, ignore that a
fraction of regenerated inductive energy is dissipated in the motor):
E bus cap = 5 x 1.2 joules = 6 joules
E bus cap = 1/2 Cbus x DC voltage x DC voltage
Assume the bus DC voltage is 75 volts
Cbus = 2 x Ebus cap/(75 V x 75 V)
= 2 x 6 joules/(75 V x 75 V)
= 2,133 µF
The internal S200 bus capacitance is 200 µf, which is less than 10% of the required
capacitance for energy absorption.
A.4.2
Energy from Acceleration Time
The bus supply for a group of S200 drives must have enough total capacitance to handle brief,
high-current bus transient flows (positive and negative) a few milliseconds without excessive
bus voltage variation. The peak output power of a 6/18 ARMS DC S200 can be as high as 1.5
kW (1.5 kW = 18 ARMS x rt(2) x 60 V (emf + IR)). This is an energy flow of 3 joules for 2 ms or
15 joules for 10 ms.
Mechanical energy is estimated by considering the load to be pure inertia and measuring the
velocity transition times. A full torque acceleration or deceleration of an inertia load yields a
triangle power pulse with an energy (in joules) half of the peak power (in watts) multiplied by the
velocity ramp time (in seconds) from zero speed. Monitor the motor acceleration by mapping
velocity and torque to DAC monitor pins (J4-14, 15), and then looking at them with a scope. Set
DM1Map to VelFB and DM2Map to IFB. See the I/O Setting tab in S200Tools. At a peak power
flow to the shaft of 1 kW = (25 A x 40 V EMF), the energy delivered vs. acceleration time is:
5 ms
2.5 joules
10 ms
5.0 joules
15 ms
7.5 joules
A.4.3
Capacitor Energy Absorb/Deliver
The capacitor energy absorbed or delivered for a 5 V change from a 75 bias is:
3 joules for 8,000 µf
7 joules for 20,000 µf
16 joules for 45,000 µf
A.4.4
Bus DC Input Power
Bus input power can be estimated by adding motor shaft power and motor resistive winding
loss. The shaft power equation is:
Shaft power (watt) = Torque (N-m) x Speed (rad/sec)
where
rad/sec = rpm/60 x 2
π
The equation for motor resistive (heat) loss is:
Winding loss (watt) = 1.5 x R
line-to-line
x I
RMS
x I
RMS