# Comparison of energy storage density of inductive and capacitive systems

In the paper A Review of Short Pulse Generator Technology by John Mankowski (IEEE Transactions on Plasma Science, Vol. 28, No. 1, 2000, pp 102-108) I found that "energy density of inductive storage systems is two orders of magnitude greater than that of capacitive systems". The author first showed equations for energy density:

Then he claimed to choose "reasonable" parameters:

Could anyone please explain why these parameters are reasonable. Is this really a valid comparison?

• Homework question? If not, where is this question actually coming from? – jonk Oct 9 '17 at 16:36
• @jonk. No homework at all. I am curious about the comparison given by the author. – space bobcat Oct 9 '17 at 16:38
• I would question whether or not the "balance of plant" (BOP) is considered in the calculation. Also, the storage time will strongly influence the design of a complete storage system. In an inductive system, the BOP may include a chilling system for superconductivity. In both systems the BOP would include the charging and discharging control systems. – Charles Cowie Oct 9 '17 at 16:39
• Your last line(s) don't look like simple curiousity to me, which usually has attached to it some related thoughts within the curious mind that have occurred from reading such papers. It certainly happens that way with me. But I'll take you at your word. – jonk Oct 9 '17 at 16:41
• I think supercapacitors are more like 10^7, not 10^5, including the BOP. So in short - no, he's short changing them. Edit: Though I see the date is 2000. So maybe he was more accurate, 10^5 would be about right for an electrolytic, and good supercaps are newish. – Jack B Oct 9 '17 at 16:42

## Abstract

Today's ultrafast, pulse generators are capable of producing high-voltage pulses, (>1 kV), with fast, leading-edge rise times, (<1 ns). A review of generator implementation methods is presented that includes a detailed discussion of the various circuit designs and a list of commercially available high-voltage pulse generators. All of these generators are capable of rise times less than a few ns and voltages greater than several hundred volts. Finally, a brief description of the three primary switch types, reed, spark gap, and solid state is presented

I have used equipment like this in the power industry and it looks realistic to me.

A certain amount of energy must be stored in order to dump it into a variable industry load or device under test (DUT). Think large like substation or distribution components or plasma generators.

His conclusion is that inductive energy storage has much higher density.

The article was comparing all the commercial HiV generators available that store energy to dump into large commercial electric industry components for stress testing for lightning industry standard tests. ie. rise time< 1ns >200kV and high currents up to 50kA.

High T materials use a hybrid of hard iron core and silicate dielectric particles. Something like silica nanocomposite (RhB–Fe3O4/MnO2/SiO2/KCC-1)

This discussed finer details of high T cores at 30kHz with material and geometry improvements, but no actual values. (their trade secrets) http://global-sei.com/technology/tr/bn80/pdf/80-20.pdf

One has to examine the materials used in each design to assign a relative constant compared to air. The requirements are cost, size, quality of insulation, leakage, voltage breakdown>50kV/mm, contaminations that induce partial discharge, saturation levels of new ferromagnetic materials (10T).

Plastic has a dielectric constant around 2, transformer oil is ~ 4. Cold rolled grain Oriented Steel (CRGOS) has a B max around 6T and hybrid materials are ~ 10T.

Old equipment I have used to test up to 200kV for < 5 MVA transformers occupied 5m x10m floor space and was 80's technology.

• It used a 5 Hp motors to drive a leather friction flywheel machine design for HV testing . This is turn charged up 19" racks of polystyrene capacitors in parallel with a remote voltage sensor for a regulated output. This in turn was wired in a machine working as a Marx Generator (multiplier) with 1kW low R Resistors the size of shock absorbers to control the waveform rise and tail time determined also by the load capacitance. The machine had a remote control motorized gap and inductive spark trigger to calibrate the voltage and energy stored.

Here my rise time was limited due to the primitive 300MHz scope to 1 ns but no problem, I expect it could be 100ps.

• "Cold rolled grain Oriented Steel (CRGOS) has a B max around 6T and hybrid materials are ~ 10T". At what frequency? What would it be at 5 kHz and 10 kHz? Nanosecond pulse generators that I have used can go up to 100 kHz. Thanks for still coping with me and updating your answer. – space bobcat Oct 9 '17 at 18:39
• It would seem the article lists the equipment and the researcher did his homework. I have not read the article, just the abstract. – Tony Stewart Sunnyskyguy EE75 Oct 9 '17 at 18:42
• What probe did you use for taking this waveform if it isn't a secret? – space bobcat Oct 9 '17 at 18:42
• I used a piece of wire around the ground return cable to act as a current probe into the best quality coax into a 50 ohm termination. I also compared with a 10:1 scope probe which had more resonance. so the power pulse was ~11V^2/50R~ 6W ( low power signal) – Tony Stewart Sunnyskyguy EE75 Oct 9 '17 at 18:44
• Oh, I see. I wanted to know if you have read it but didn't think that it'd be appropriate to ask. The article doesn't list actual equipment. It overviews common ways to generate high-voltage pulses. No specific equipment is shown. It only demonstrates outlines of approaches (for example, the author briefly mentions drift step recovery diodes, provides an example of a diagram, and keeps going toward the next method). My question is still about the given values. How appropriate are they? 10T is not going to be 10T at higher frequencies. Correct? The author says nothing about pulse frequency. – space bobcat Oct 9 '17 at 18:50

He seems to be selling capacitors short

A quick look on google suggests that supercaps come in around 6Wh/L, converting to SI units, that's $2\times10^7$W/m³. So much better than his calculation, and all the more so because that's not the energy stored in the field, it includes the volume of the electrodes etc.

His figure for energy stored in a magnet seems reasonable. For high fields, you saturate magnetic materials and they no longer give much benefit, so choosing $\mu_0$ seems reasonable, and 10T is acheiveable at a reasonable price point. 20T can also be had, but is more expensive and only increases the end result by a factor of 4. It is also worth noting that the "Balance of Plant" required to support a superconducting magnet is a lot larger than that required for a capacitor, so the all-included figure will be worse.

As for why the author said that, well, we don't know, but it could be that:

• Supercaps were newer, less effective, and/or less well known 17 years ago. I haven't looked into their history to check.
• He just pulled out some numbers that looked reasonable, by looking up breakdown voltage and $\varepsilon$ for some common dielectrics.
• He was intentionally ignoring supercaps for the same reason he was ignoring 20T magnets: because they are (or were) hard or expensive to get right.
• He was intentionally trying to make magnetic storage look good. Bad form, yes, but it happens. Even in top journals. It is especially common in discussion sections which don't have the same expectations of rigour that the actual results being reported do.
• [Edited in]: He is not doing a general comparison, but comparing energy storage techniques for a specific job. And there is some reason that supercaps are not suitable for the specific task at hand.
• unfortunately this answer is totally wrong because these high K parts cannot be used to generate the voltages and rise times needed for the equipment being evaluated. The context of the article is evaluating all COmmercial testers with <1ns >200kV rating for lightning load dump tests. – Tony Stewart Sunnyskyguy EE75 Oct 9 '17 at 17:16
• I don't have access to the article, and assumed that we were talking about long term storage. Hence also talking about superconducting magnets. – Jack B Oct 9 '17 at 17:17
• that's ok , your assumptions were not given were wrong – Tony Stewart Sunnyskyguy EE75 Oct 9 '17 at 17:19
• @TonyStewart.EEsince'75, thanks for your input. I don't think that the context was evaluating all commercial testers with "1ns rise time 200kV for lightning load dump tests". Why 200kV? Why lightning load dump tests? From the context of the journal itself, the generators that go through comparison would be used for something like corona plasma or DBD plasma generation. Could you expand why these high K parts couldn't work for fast rise times? – space bobcat Oct 9 '17 at 17:25
• I put the abstract in my correct answer. It does not and can not use high K caps which have leakage many orders of magnitude higher than required. – Tony Stewart Sunnyskyguy EE75 Oct 9 '17 at 17:27