How to size a correct DBR and cables?
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# Thread: How to size a correct DBR and cables?

1. Plastic
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## How to size a correct DBR and cables?

Hello,

I'm sizing a motor control system. While trying to select a correct DBR I received some recommendation from a supplier. The recommended DBR is very different from the minimal requirements coming from my calculations. I'm also confused by the method of calculation specified by Rockwell (PowerFlex Dynamic Braking Resistor Calculator - Rockwell Automation Publication PFLEX-AT001L-EN-P - September 2017).I would be very thankful for your comments and advises.

The motor is 150 HP, 1200 RPM, 447TC FRAME, 460/3/60HZ.
- The selected VFD is PowerFlex 753 AC Drive, with Embedded I/O, Air Cooled, AC Input with Precharge, no DC Terminals, Open Type, 302 Amps, 250HP ND, 200HP HD, 480 VAC, 3 PH, Frame 7.
- Total inertia of the load is 84 kg/m2.
- Max.speed 1200 rpm.
- Min.speed 0 rpm.
- Deceleration time - 11 sec.
The specified VFD has a DC bus regulation voltage of 790 V and Minimum brake resistance of 2.4 Ohm.

According to Rockwell method of calculation, the peak braking power for 11 sec. deceleration time is 120.6 kW. Based on this, the Maximum allowable resistance satisfying the DC bus regulation voltage of 790 V is 5.2 Ohm. The required joule rating of the resistance in order to stay this power (120.6 kW) during this time (11 sec.) must be at least 663.2 kW*sec. Once again, I did the calculation according to the Rockwell manual mentioned above.

The supplier proposed me a resistance with the following characteristics:
5.07 Ohm, 15.7 kW, 294 kW*sec. With this proposed resistance, I'm noting several problems regarding this offer:
1. The joule rating, 294 kW*sec, is much lower than required, 663.2 kW*sec, which means that the resistance will not be able to dissipate the heat, it will basically burn out.
2. The proposed resistance will be overloaded during about 9.5 seconds of 11 seconds of the deceleration time. The load will count about up to 768% of the rated power of the resistance descending linearly during the deceleration time. I have a doubt about the ability of the proposed resistance to stay this rate of overloading.

Am I right in my calculations and conclusions?

Finally, I wondered, according to which value should I specify the size of the cables to for the DBR. If I calculate it as a ration of DC bus regulation voltage of 790 V divided by the resistance of 5.07 ohm, it will result to 155.8 A, which means that I have to use 2 AWG single wire cable.

Is it correct calculation?

Any advice or recommendations would be appreciated.

Thanks.

2. Cast Iron
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Some one will be along with better answers but here are my thoughts. Regarding wire size, the wire size calculated is for a continuous load. I am sure a smaller wire could be run since the amperage is the peak current and will go to zero in 11 seconds. You could calculate using the average current for 11 seconds and determine the power dissipated in the wire and using the thermal mass of the wire calculate temperature rise. Then keep the wire at a temp less than the ratings of the terminals and insulation. One could also look at the size of the wires going to the terminals in the VFD.

A similar exercise is needed for the resistors assuming they have a heatsink or any specs for thermal mass. If so then one would also need a peak current spec on the resistors to be safe. Might also need max temp spec of the resistor and thermal resistance to do a complete analysis.

I only have experience designing a brake resistor for a 10hp VFD. It was easier to just use a brute force conservative design than to over think it. However at your power level over design becomes expensive.

Best of luck.

3. You don't specify how many times per minute (or hour) you are going to need to stop the load - this weighs heavily into the duty cycle rating that you need to keep in mind when selecting the resistor. Is this a normal stop? Will you require more aggressive E-Stop deceleration rates?

I have developed a spreadsheet for this kind of work and based on 4 different methods for calculating (Rockwell, Siemens, Control-Techniques, ABB) the following are the most conservative mix of design parameters.

• your peak braking power at beginning of deceleration is 162HP / 120.5kW (mechanical)
• if doing this stop every 5 minutes - your average braking resistor heat generation is 4kW
• Minimum calculated DB resistance should be around 5.2 Ohms by my calculations

In reality your actual DB Resistor bank resistance should be less than 5.2 Ohms with some margin . . . as the resistors heat up, invariably the resistance goes up as well and you don't want to be on the ragged edge. So pick a resistance value between the minimum allowed by the drive (2.4 Ohms) and that required (5.2 Ohms) and something you can live with as far as DB Resistor bank instantaneous current goes. Something between 3 and 4 ohms would be ideal. Just realize that your peak power dump will be 790V/Ohms with a PWM wave form - this defines your peak current, however, it does not define your peak power dissipation as the PWM waveform and the thermal time constant of the resistor will come into play and actual peak thermal power dissipation will be less than the peak mechanical power (120.5 kW in this case.) . . . the resistor spreads the power dissipation out in accordance with its thermal time constant.

Lastly as far as Resistor rating in kW goes - you need more capacity than your average dissipation requires - if you need to stop every 5 minutes, your average dissipation is 4kW which is tiny compared to your peak load. Generally I pick the greater of the average kW (4kW in this case) and the Peak kW / 10 (which is 12kW in this case) . . . so 12kW should be fine in this case (again, assuming you need to stop every 5 minutes). This depends somewhat on what kind of resistor you are using and what the thermal time constant is - generally wire wound ceramic DB resistors have time constants measured in 10's of seconds and this provides a lot of peak power overload capacity that can be to your advantage (again, as long as you have a reasonable duty cycle / time between stops).

Spec your stopping frequency and answer questions about the E-Stop versus normal stop and lets see how things look.

4. Plastic
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Originally Posted by motion guru
You don't specify how many times per minute (or hour) you are going to need to stop the load - this weighs heavily into the duty cycle rating that you need to keep in mind when selecting the resistor. Is this a normal stop? Will you require more aggressive E-Stop deceleration rates?

I have developed a spreadsheet for this kind of work and based on 4 different methods for calculating (Rockwell, Siemens, Control-Techniques, ABB) the following are the most conservative mix of design parameters.

• your peak braking power at beginning of deceleration is 162HP / 120.5kW (mechanical)
• if doing this stop every 5 minutes - your average braking resistor heat generation is 4kW
• Minimum calculated DB resistance should be around 5.2 Ohms by my calculations

In reality your actual DB Resistor bank resistance should be less than 5.2 Ohms with some margin . . . as the resistors heat up, invariably the resistance goes up as well and you don't want to be on the ragged edge. So pick a resistance value between the minimum allowed by the drive (2.4 Ohms) and that required (5.2 Ohms) and something you can live with as far as DB Resistor bank instantaneous current goes. Something between 3 and 4 ohms would be ideal. Just realize that your peak power dump will be 790V/Ohms with a PWM wave form - this defines your peak current, however, it does not define your peak power dissipation as the PWM waveform and the thermal time constant of the resistor will come into play and actual peak thermal power dissipation will be less than the peak mechanical power (120.5 kW in this case.) . . . the resistor spreads the power dissipation out in accordance with its thermal time constant.

Lastly as far as Resistor rating in kW goes - you need more capacity than your average dissipation requires - if you need to stop every 5 minutes, your average dissipation is 4kW which is tiny compared to your peak load. Generally I pick the greater of the average kW (4kW in this case) and the Peak kW / 10 (which is 12kW in this case) . . . so 12kW should be fine in this case (again, assuming you need to stop every 5 minutes). This depends somewhat on what kind of resistor you are using and what the thermal time constant is - generally wire wound ceramic DB resistors have time constants measured in 10's of seconds and this provides a lot of peak power overload capacity that can be to your advantage (again, as long as you have a reasonable duty cycle / time between stops).

Spec your stopping frequency and answer questions about the E-Stop versus normal stop and lets see how things look.
Thanks for the explication.

I assumed the duty cycle of 10 minutes. It is not ES case. It's supposed just to decrease time delays between runs.

I would like to understand some fundamental thing - why the average power is taken in comparison to the resistor rated power. I mean, the resistor rated power is the power that the resistor dissipates according to the Ohm's law P=I*V=V^2/R, where P is (mechanical power)*(motor efficiency)-(other loses), I and V are RMS values of the PWM wave regenerated by the P. I'm agreed that due to the factors like parasitic values in the resistor, efficiency of the motor, non-sinusoidal form of PWM etc., the power developed on the resistor is less than the applied mechanical power, but as I see it is still minor. The most of the power coming out to the resistor will be still close to the mechanical power. Actually, the expression for calculation of the maximum DBR value for 11 sec of deceleration used by Rockwell confirms it - it takes the sqrt of peack braking power which is mechanical power divided by DC bus regulation voltage (790 V). Even with small duty cycle, the proposed DBR (5.07 Ohm, 15.7 kW, 294 kW*sec) will still be subject to load of some hundreds percent during about 9 sec (with 11 sec of deceleration time). That means that the resistance must stay these 9 seconds in a power decreasing from the peak of 120.5kW to the rated power of the resistor, 15.7 kW. Does it?

What is confusing in taking the average power dissipated by the DBR is that it is taken as an average over motor on/off cycle. In my mind, according to electrical laws it must be calculated based on PWM voltage waveform duty cycle, though even then the power developed on the DBR will be too high for the proposed DBR.

Thanks