Capacitor-balancing resistor sizing

[willDavidson]

TL;DR

how do you properly size balancing resistors?

I understand that when sizing balancing resistors you should consider the power rating of the resistors. The resistance and power rating has to be high enough so that they do not overheat. Even with a large enough power rating, I know that they will effect your overall efficiency since that's just power loss. How do you appropriately size them though? If you have two series resistors, why not place like 2 series 5 MEG resistors across them? Or even higher?

 

[Baluncore]

1. Allocate voltage to the series capacitors in proportion to the reciprocal of each capacitance.
2. Specify the balancing current required and available, that will flow through all balancing resistors.
3. Maintain a constant RC product = time constant, for all parallel pairs of R and C in the series chain.
4. Check the power rating of each resistor is sufficient.
5. Check the voltage ratings of each resistors is sufficient.
6. Examine what happens when tolerance of any component varies over the range expected.

 

[DaveE]

Specify the balancing current required

This is the heart of the question. Unfortunately, in my experience, it is extremely difficult to get this answer in any general sense. Much depends on the capacitor technology and the manufacturer's characterization and specification of their parts. You may find a leakage current specification on the data sheet, if so, this is what you use to choose the resistors. It's not an uncommon specification for good manufacturers of electrolytic caps, since leakage is a know issue with those technologies. For film caps it is much more difficult, since a well designed and built film cap should have no leakage. Unfortunately a robust design still needs to be tolerant of less than perfect parts.

In practice many engineers guess, or size the resistors based on how large, hot, or inefficient their design can tolerate. Others use "rules of thumb" passed down often with little justification. What I would do is call the application engineers at good capacitor manufacturers and talk with them about this, after you have read the datasheets and application notes thoroughly (yes, every footnote, everything!). This is a case where you get what you pay for; often that is a good QC program, thorough characterization of components, and customer support. Unfortunately, people (designers or component manufacturers) will have to compete with manufacturers that cut corners, so a lot of this kind of support is going away.

If you want to do more research, you can look up the Mil-Specs for the capacitor type, but then you either have to buy Mil grade parts, or translate Mil quality into commercial parts.

 

[willDavidson]

Thanks for the in depth explanations. What does it mean to specify the balancing current required? How does it relate to leakage current? I'll be using film caps but I'm still curious in general for all caps how to size them.

 

[Baluncore]

What does it mean to specify the balancing current required?

The balancing current must be large compared to the maximum capacitor leakage current, otherwise it could be out of balance due to leakage current. Capacitor voltages could deviate from those expected, which may then exceed the capacitor voltage rating.

At the start, I would make the balancing current ten times the maximum possible leakage current and de-rate the capacitors to 80% of their quoted voltage. If the capacitor string is subjected to sudden current demands you may need to check the capacitance tolerance.

In effect you are making two parallel potential dividers. One composed of resistors for the DC and low frequencies, the other composed of capacitors for the higher frequencies and spikes.
The time constant you select for your RC elements will determine the power dissipated in the balancing resistors, and the recovery time from voltage deviations due to capacitance tolerance.

By keeping all the time constants close you are balancing the AC and the DC voltages.

 

[DaveE]

Thanks for the in depth explanations. What does it mean to specify the balancing current required? How does it relate to leakage current? I'll be using film caps but I'm still curious in general for all caps how to size them.

Once you have an idea of the worst case leakage currents (that would be a minimum on one cap and a maximum leakage on the other). Then it is a simple resistive divider problem. The difference in leakage current has to flow through your balancing resistor network to determine the ratio of voltages on the caps. You can model leakage as a current source if you are using worst case analysis, or as a parallel resistor if you want a more realistic dynamical model.

 

[DaveE]

Also, if you do get a leakage current spec for your film caps, recognize that this value was chosen by the manufacturer as a screening value for their production. i.e. they can't sell a cap that exceeds their in house limit which will be a little less than the spec. This means they have an incentive to set a loose spec. Most if not all caps will be much better than what they specify. Engineers rarely choose their caps based on this number, so they don't have much incentive to make it sound as good as they likely are. How you actually use this for moderate reliability designs is a mystery to me. Hi-rel designs use the specification, cheap consumer products do whatever they want, if they worry about it at all, the in between case is confusing.

As an aside, I had a friend that was consulting for a big consumer manufacturer of computer mice. They thought that an IC that specified a pull-up resistor on an unused input was too conservative, and they think resistors are expensive. So they did a "small" production run of 100,000 units without the resistor to see if they could delete it.

 

[willDavidson]

If I cannot find the leakage current specification, how would I go about selecting the balancing resistors then? It doesn't seem like it would be feasible to select the balancing resistors after measuring the capacitors. But going on that, would I apply a voltage simply measure the decrease in voltage to determine the parallel resistance and from there get leakage current?

I found a capacitor online that provides the insulation resistance. I've attached a pic here, but I'm not sure how to even use it.

 

[willDavidson]

That's for your answers. I just though about this and let me rephrase this. I didn't realize that there was anything more to it than putting large resistors in series/parallel with capacitors to distribute the voltage evenly. I didn't know it had anything to do with leakage current. I'm still not sue exactly how to design around that parameter, but first I guess I should figure out my leakage current. That should not be a problem as I already have a few of the capacitors that I'll be using.

I've attached an example I found online discussing how to measure leakage current. It said the ammeter in series with the capacitor is usually used for low value capacitors typically 1uF or less. Mine are 6 uF so based on this I should use the parallel voltmeter configuration. The challenge I see here is I would need to measure dv/dt, right? I'll need the capacitance value too and even that could be off +/-10%. I guess that's not a big deal since it would just translate to an insulation resistance of +/-10% which should be considered in the design anyway. Do I use a large resistor sever Mohm to prevent it from discharging, or how do I size this resistor?

https://product.tdk.com/info/en/con...here are two basic ways,source (See Figure 2).

 

[DaveE]

I would need to measure dv/dt, right?

No. Leakage current is a DC measurement. Use a DC source that has dV/dt=0.

 

[Baluncore]

Mine are 6 uF so based on this I should use the parallel voltmeter configuration.

Why not let us know the manufacturer and model of the capacitors you plan to use?
We need their voltage rating, and the voltage you will apply to each.

 

[willDavidson]

I've drawn the circuit and equations that I think that I should use. Does this approach look correct?

Vs = source voltage
Rm = measurement resistance (external resistance used to measure voltage)
Rp = parallel resistance of capacitorOnce I get the leakage current, I'm not sure what to do next. I simply make the resistance or each balancing resistor ~10x lower than this value?

Why not let us know the manufacturer and model of the capacitors you plan to use?
We need their voltage rating, and the voltage you will apply to each.

I plan to use 4 series Vishay MKP1848C59010JP2 1.5 kV 9 uF capacitors found at the link below. I will be applying 1 kV across each.

https://www.digikey.com/en/products/detail/vishay-beyschlag-draloric-bc-components/MKP1848C59010JP2/5373200

 

[DaveE]

So, your circuit will have 4KV and store 18J of energy? Then it's time for me to quit.

I'm not comfortable doing remote (and free) consultation on potentially dangerous and/or difficult designs. This type of work should be done with the help of people with experience in this type of design, who are fully aware of all of the circumstances involved.

Good luck, be careful. Talk as much as possible to manufacturers of parts or subsystems that address this market. Be wary of advice via social media, we could be wrong, we could be unaware of other important considerations, we could be gone next month when you really need help.

Finally, IMO, you need to add a good dose of FMEA (failure modes and effects analysis) to you workload. What can go wrong, how will it happen, and what will happen as a consequence.

 

[willDavidson]

DaveE,

So, your circuit will have 4KV and store 18J of energy? Then it's time for me to quit.

I'm not comfortable doing remote (and free) consultation on potentially dangerous and/or difficult designs. This type of work should be done with the help of people with experience in this type of design, who are fully aware of all of the circumstances involved.

Thanks for your help so far then. As I stated from the first, I am not interested in finding the solution to this specific problem. I am interested in learning about voltage balancing for capacitors in general. That would apply to any voltage or energy level.

I appreciate your concern for safety. I'm not building a circuit in my basement so I do take proper safety precautions and this will not be just thrown together. I am also not relying on people here for all of the answers. The advice provided so far has been helpful. I'll continue to dig deeper. Thanks again.

Also, FEMA will be part of this. That will be time consuming, but it will not be skipped. Thanks again.

 

[willDavidson]

I'm not comfortable doing remote (and free) consultation

Sorry but I just wanted to add that I'm a student so there is no profit being made from this. I am not doing this for a company. I just wanted to mention that because you mentioned not being consulting for free. I just wanted to make sure you didn't think I'm getting paid as an engineer and using this for a commercial product.

 

[Tom.G]

Hi Will, I just looked at the datasheet you linked to and have a few comments.

The style capacitor you have in mind seems to be available for up to 1200Vdc max at 85C. If the maximum temperature does not exceed 70C, it can live with 1440Vdc. That is probably enough safety margin for a "build one of a kind" or "experimenter" design. For production or long-life, I would choose to use five of them in series instead of four. Each of those five would be 12uF, instead of 9uF, to give the same total capacitance.

To find the leakage current, the graph you supplied (from pg 13 of the data sheet) can be used. It gives the time constant of the capacitors versus temperature. The time constant is the product of capacitance in Farads and leakage resistance in Ohms, with the result expressed in seconds; 10,000 seconds at room temperature.

With Time=RxC, and knowing time and capacitance, you can find the leakage resistance; R=(T/C). You then have R=((1x10⁴)/(12x10^-6)).
If I did the math correctly, the leakage resistance of a 12uF cap is 833 MegOhms at room temperature.

Using the graph on pg 13, at 50C the resistance will be 90% of that or 750 MegOhms.

Using a factor 10 for leakage current, a resistive divider for balancing would then consist of a 75 Megohm resistor across each capacitor. Unfortunately 75 Megohm, 1KV resistors are quite rare and likely expensive. For a single build you would probably use three 22Meg and a 10Meg in series across each cap. Those are standard value resistors and are USD $0.41 each at digikey,
https://www.digikey.com/en/products/detail/yageo/HHV-50FR-52-22M/2813184

If you build the circuit on A PCB you should have a solder mask on the board at those voltages... and watch out for component spacing, you want an ample leakage path for kiloVolt circuits. Don't try to use one of those plastic prototype boards, you will get "brimstone and fire."

Cheers,
Tom

 

[DaveE]

Sorry but I just wanted to add that I'm a student so there is no profit being made from this. I am not doing this for a company. I just wanted to mention that because you mentioned not being consulting for free. I just wanted to make sure you didn't think I'm getting paid as an engineer and using this for a commercial product.

It's not the free part that worries me in the least. I wouldn't be here if I cared about that. It's the difficult/dangerous part that worries me. I'm not sure we are really helping if you only get a part time, partly informed consultant. You may be better in the long run with people you have a deeper relationship with. I don't want to be responsible for making you think you have this design solved based on my partial involvement, limited to the questions you ask.

While getting good leakage current data can be very difficult; knowing what data you need, and knowing how to apply that to your circuit design are the easy part of these HV energy storage designs. There are normally many other issues related to reliability, performance, and safety that you will also need to address. In my experience these issues are much more complex than this thread.

 

[willDavidson]

Using the graph on pg 13, at 50C the resistance will be 90% of that or 750 MegOhms.

Using a factor 10 for leakage current, a resistive divider for balancing would then consist of a 75 Megohm resistor across each capacitor. Unfortunately 75 Megohm, 1KV resistors are quite rare and likely expensive. For a single build you would probably use three 22Meg and a 10Meg in series across each cap.

Hi Tom,
Thanks for the explanation, I understand how the chart works now. I just checked the numbers again and I think it's an order of magnitude lower or 83.3 MegOhm. Derating to 90% for temperature would be 75 MegOhm. Using a factor of 10 for leakage current, 7.5 MegOhm seems pretty achievable. Using the factor of 10 sets the maximum resistance criteria, right? Therefore, I could use something like a 2 MegOhm resistor sacrificing higher power loss on the resistors, right? Of course, I would want to make sure their power dissipation is well below their rated value for reliability purposes.

 

[Baluncore]

I plan to use 4 series Vishay MKP1848C59010JP2 1.5 kV 9 uF capacitors found at the link below. I will be applying 1 kV across each.

From the data sheet.
Insulation resistance; RC between leads, after 1 min > 10 000 s
R * 9 uF = 10k sec;
R = 10k / 9 uF;
R = 1G111
You should use a maximum of 100 Meg as the balancing resistance across each cap.

The Yageo HHV series resistor maximum value is 68 Meg.
1 kV / 68 Meg = 14.7 uA; → 14.7 mW
Now, verify the resistor power and voltage ratings are in spec.

 

[willDavidson]

You should use a maximum of 100 Meg as the balancing resistance across each cap.

The Yageo HHV series resistor maximum value is 68 Meg.
1 kV / 68 Meg = 14.7 uA; → 14.7 mW
Now, verify the resistor power and voltage ratings are in spec.

If I were to use like a 1 Meg resistor equivalent, that should provide better voltage balancing with the tradeoff of higher losses right? In that case I would just have to make sure the power rating was still fine. Other than the additional power loss, are there any other downsides to having a much lower resistance than the maximum value of 100 Meg? It seems the lower value would ensure proper operation under more extreme conditions such as higher voltage, higher operating temperature, and over the lifetime as leakage current increases.

 

[Baluncore]

It seems the lower value would ensure proper operation under more extreme conditions such as higher voltage, higher operating temperature, and over the lifetime as leakage current increases.

Calculate the margins. Don't just make changes because it seems like a good idea. That costs too much and reduces product lifetime.

The maximum resistor value is 10% of capacitor leakage resistance, because the component tolerances are about 10%. When the potential divider is subjected to changes in voltage, the matched time constant, RC, keeps the voltage divided evenly. If capacitors will have a greater, say 20% variation, then lower resistance must be needed. That is why you should always use R and C components from the same batches. They will age together.

By all means use 1 Meg resistors. High voltage resistors usually go open circuit with time. Higher currents do that faster. Again, make sure components are from the same batch so they all age together.

Getting the resistor wattage rating wrong, causes failure in the short term. The voltage specification is more subtle, it is critically important to the number of hours your product can be powered before the balancing ceases to function and it takes out a capacitor.

The balancing resistors also discharge the capacitors for safety. Lower value RC time constants do that faster. 68M * 9uF = 612 sec = 10 minutes. 1 Meg * 9 uF = 9 seconds.

Your power supply must generate the energy lost in balancing. Lower balancing R makes a hotter power supply with a shorter life. Careful calculation compounds savings in energy, mass and dollars.

The parallel resistors will be close to the capacitors on the PCB. The heat of the resistors will reduce the lifetime of the capacitors. Minimise that balancing heat. Keep the separation of each parallel R and C on the PCB similar, to maintain balanced thermal ageing.

 

[willDavidson]

Baluncore,

Thanks for the detailed explanation with so many factors to consider. I will take into account thermal considerations as well.