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U transformer core and rogowski coil questions

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Dosinski

Wed Dec 21 2011, 12:51AM

Registered Member #2680 Joined: Wed Feb 10 2010, 09:23PM
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Posts: 45

I have been trying to find information regarding information on how much power a rogowski coil can draw from the wire passing through it and also how much power a U-core can draw from a cable running through it. Unfortunately, I can find very little imformation on both considering that U-cores are almost never used by themselves because of inefficiencies and rogowski coils are only really used for measuring current. I'm trying to get about half a watt of power or more. The cables I'm trying to get power from have a few kV on them

I have considered using a current transformer, but I can't use split-core transformers or something that encircles the entire cable (for one reason or another). The thing I am struggling with the most is finding out how effective a current transformer is in the shape of a U. I didn't take any courses on transformers yet so I can't get a grasp on the equations>_<

All I can find on rogowski coils is that they are used for measuing current through a wire, but I haven't seen any information on how much power they can draw.

Patrick

Wed Dec 21 2011, 02:02AM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

I think you need to take a first derviative of the returned wave, but Rogowski's are kinda special , i tried tobuid one awhile ago but was not successful.

let me check jim lux's site...

Steve Conner

Wed Dec 21 2011, 07:59AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

First thing to check is whether the cable has just one conductor inside, or whether it has two with current flowing in opposite directions. If the latter, you're stuffed, as the magnetic fields cancel.

Now, power. When a CT is placed on a cable, it looks like an inductance in series with the load current. The inductance is roughly that of a 1 turn winding on your core, and hopefully you can calculate that for an open U core. If not I guess you can measure it by making a test winding on the core you're going to use.

The power you can extract follows from the reactance of the inductor, and the maximum power transfer theorem. When CTs are used for measurement, a burden resistor much smaller than the reactance is used, to ensure an accurate result, but that means the CT extracts far less power than it is capable of.

I'd be very surprised if you couldn't get half a watt from some big power cable, assuming it's a single core and there is current in it. If a straight winding on your CT didn't work, then tuning it to resonate at the power frequency would boost the output considerably. But don't blame me if it explodes!

Sulaiman

Wed Dec 21 2011, 12:33PM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

If the cable is not armoured/shielded and carrying ac at kV
then you may be able to tap off power by capacitive coupling,
a few inches of self-adhesive copper tape (or similar, Al foil etc.) should pick up the E-field of the nearest conductor in the cable.
But I'd expect an eht power cable to be armoured/shielded.

Dosinski

Wed Dec 21 2011, 12:34PM

Registered Member #2680 Joined: Wed Feb 10 2010, 09:23PM
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Posts: 45

Yes, the cables I'm looking at are just single conductor cables. Though my particular question is if U-core transformers would be sufficient in getting power from the cable instead of CTs.

edit: @Sulaiman: I looked at capacitive coupling, but I'm a bit worried that shielding will reduce the power to nothing :/

klugesmith

Wed Dec 21 2011, 09:17PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Yes, what Badgerhedron Man and Sulaiman said, assuming your goal is to harvest energy by -magnetic- coupling. We can help you with the basics of transformer calculations, if you haven't taken that course yet.

If for whatever reason you can't close a ferrous core around the victim conductor, a core that is almost closed is better than none. And better than an open or closed, nonferrous Rogowski coil core. (the RC doesn't lose much from being open, but has much less flux to work with).

But... the design depends only on the frequency and current, not the voltage on the victim conductor. To get 1/2 watt from a wire carrying 1 amp at mains frequency would require a substantial weight of iron, even in a closed core. (Need enough flux for at least 1/2 volt per turn). An open-core design might be reasonably feasible if you could count on 100 amps whenever you need to harvest energy. Give us some ideas of current, volume, weight, and cost limits. Do you require a fixed core gap wide enough to fit around the insulated victim conductor?

Dosinski

Wed Dec 21 2011, 11:34PM

Registered Member #2680 Joined: Wed Feb 10 2010, 09:23PM
Location:
Posts: 45

Yeah, I'm specifly looking at a U-core with an air gap large enough to allow the wire to be placed in, which has made finding any information difficult :/
The frequency is 50 Hz. The maximum cable diameter I'm looking at is 3.45 inches. The minimum amount of power is half a watt when there is 50A flowing through the cable.
So the transformer window is be around 3.5-3.6 inches. And the core material will be laminated silicon steel. That's about all I could figure out on my own (which isn't much).

klugesmith

Thu Dec 22 2011, 08:09AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

Wow, that's a pretty thick cable. Are you trying to hang an instrument on a power transmission line? I ran some numbers & this looks pretty cumbersome. Perhaps you should reconsider capacitive coupling.

Here is one comprehensive online tutorial about transformers:

Anyone else care to sanity-check the results below?

1) With 50 amps RMS in the primary, we need to burden it with a voltage drop of at least 10 mV to extract 1/2 watt.

2) With a perfect core material and 3.5-inch (0.089 m) air gap, H is 562 A/m; multiplying by u0 gives B (RMS) of 0.7 mT (7 gauss).

3) To induce 0.01 volt/turn at 50 Hz, you need that flux density in an area of at least .045 m^2 (70 in^2). You are going to have to line up many big U-cores to get that much area.

4) CT's, just like regular power transformers, normally want the magnetizing ampere-turns to be much less than the operating (power-transferring) primary and secondary ampere-turns. How about 5 amps? For that, our flux density would be 10x less and area 10x greater. The magnetic hardness of regular transformer steel might become a problem.

5) Maybe a Rogowski coil would be less impractical, because of the savings in iron. Maximum H around the 28 cm circumference of the cable is 180 A/m, good for B of 2.2 gauss (0.22 mT) RMS. A Rogowski coil turn developing 10 mV would need an area of 0.14 m^2, for example a rectangle extending 2 cm radially outward from the cable surface and 7 meters along the cable. 100 turns like that would give you 1 volt open circuit;
actually less because the 2.2 gauss value applies only at the inside edge of each turn.

Still want to pursue this?
Or think harder about how to get a split core to close around the primary?

Steve Conner

Thu Dec 22 2011, 10:51AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Kluge, that seems sane, but I think if the whole thing were resonated to 50Hz by putting a capacitor across the secondary, the answer would get Q times better.

Unfortunately, I guess it would be the loaded Q.

Dr. Slack

Thu Dec 22 2011, 02:32PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Is it really going to be so hard to slap an I across the end of the U (I guess if the cable is hard flush against the wall then yes).

Just as resonating it would make it get Q times better, going down to a 0.5mm airgap from 3" would gain you two orders of magnitude. Every time you halve the airgap, you will double the power you can extract from the cable (by doubling the series inductance it sees and so the voltage drop at the current clamp). Until the gap becomes very small, << 1mm, it will still be the gap limiting you rather than the iron permeability.

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