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PICList Thread
'[EE] AC current sensing'
2005\07\05@230654 by Martin K

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I just had an idea on a way to measure AC current. The idea is to take a
small resistor .01 ohms and put it in series with the AC load. To
isolate this from the AC line one could use a surplus 600 ohm tel.
transformer. The benefit of this would be that the parts are very
inexpensive versus a dedicated current transformer. A clamp-on style is
not desirable in this application. Any thoughts?
--
Martin K
http://wwia.org/

2005\07\05@233242 by Charles Craft

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Depends on if you want UL cert down the road.
Not being directly in the current path makes life a little easier.

{Original Message removed}

2005\07\05@234945 by Vitaliy

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>I just had an idea on a way to measure AC current. The idea is to take a
> small resistor .01 ohms and put it in series with the AC load. To
> isolate this from the AC line one could use a surplus 600 ohm tel.
> transformer. The benefit of this would be that the parts are very
> inexpensive versus a dedicated current transformer. A clamp-on style is
> not desirable in this application. Any thoughts?
> --
> Martin K

Many years ago I saw a design where the author used a coil wound on a
ferrite ring that was placed around the current-carrying wire. Or is this
the same thing that you referred to as "a dedicated current transformer"?

Best regards,

Vitaliy

2005\07\06@000744 by Chen Xiao Fan

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What is the problem with this design regarding UL? Is it the problem with
the transformer? Does it need to be UL recognized or better UL listed?

{Original Message removed}

2005\07\06@002554 by Chen Xiao Fan

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What is the application here? I think one needs to know the range
of the AC current, the accuracy requirement, the allowed phase shift
in order to decide which current sensing element to be used here.

The three most common sensor technologies today are the low resistance
current shunt, the current transformer (CT), and the Hall effect sensor.
Personally I have used LEM (http://www.lemusa.com) Hall Effect sensor
(they have CT as well) and like them. They have both voltage sensor and
current sensor. Of course they are not really cheap but you can get some
free samples.

Regards,
Xiaofan

{Original Message removed}

2005\07\06@080028 by olin piclist

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Martin K wrote:
> I just had an idea on a way to measure AC current. The idea is to take a
> small resistor .01 ohms and put it in series with the AC load. To
> isolate this from the AC line one could use a surplus 600 ohm tel.
> transformer. The benefit of this would be that the parts are very
> inexpensive versus a dedicated current transformer. A clamp-on style is
> not desirable in this application. Any thoughts?

Should work.  Just make sure the transformer primary/secondary isolation is
rated for the peak AC line voltage plus some margin.


*****************************************************************
Embed Inc, embedded system specialists in Littleton Massachusetts
(978) 742-9014, http://www.embedinc.com

2005\07\06@083307 by Charles Linquist

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Martin K wrote:
> I just had an idea on a way to measure AC current. The idea is to take a
> small resistor .01 ohms and put it in series with the AC load. To
> isolate this from the AC line one could use a surplus 600 ohm tel.
> transformer. The benefit of this would be that the parts are very
> inexpensive versus a dedicated current transformer. A clamp-on style is
> not desirable in this application. Any thoughts?


Allegro hall-effect work well.

http://www.allegromicro.com/

They are lossless and have total isolation.  Of all the approaches, I
have tried, hall-effect sensors are generally the most practical.

Charles Linquist

2005\07\06@112304 by Dwayne Reid

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At 09:06 PM 7/5/2005, Martin K wrote:
>I just had an idea on a way to measure AC current. The idea is to take a
>small resistor .01 ohms and put it in series with the AC load. To
>isolate this from the AC line one could use a surplus 600 ohm tel.
>transformer. The benefit of this would be that the parts are very
>inexpensive versus a dedicated current transformer. A clamp-on style is
>not desirable in this application. Any thoughts?

Two thoughts:

1) most telco transformers do not work well at frequencies less than 200
Hz.  In your case, the source impedance is very low which does extend the
frequency response downwards - somewhat.  You would have to try it and see.

2) most telco or audio transformers do not have adequate primary to
secondary voltage isolation ratings.  This is a safety hazard.

The solution to both these problems is simple: wind your own primary around
the existing windings.  Use sufficiently heavy wire that will carry the
entire load current - this eliminates the need for the low value
resistor.  Make sure the primary winding has adequate insulation ratings.

Some of the cheapie audio transformers from Mouser have just enough room
for a single layer primary of #18 triple-layer Kapton-insulated magnet wire.

dwayne

--
Dwayne Reid   <spam_OUTdwaynerTakeThisOuTspamplanet.eon.net>
Trinity Electronics Systems Ltd    Edmonton, AB, CANADA
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2005\07\07@024807 by Chen Xiao Fan

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William Koon of Analog Devices has written a good general article
"Current sensing for energy metering" which compares current shunt,
CT, Hall-effect sensor and Rogowski Coil. I think CT is the most
commonly used. However if you are doing applications like PFC
(power factor correction) or APF (active power filtering), then
Hall Effect sensor is the best bet because of its outstanding
frequency response.

Regards,
Xiaofan

-----Original Message-----
From: Chen Xiao Fan
Sent: Wednesday, July 06, 2005 12:26 PM
To: 'Microcontroller discussion list - Public.'
Subject: RE: [EE] AC current sensing

What is the application here? I think one needs to know the range
of the AC current, the accuracy requirement, the allowed phase shift
in order to decide which current sensing element to be used here.

2005\07\07@034217 by ardhuru

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On a related subject, though not a direct answer to your query, do check up
the neat software at  http://www.dazyweblabs.com

Lets you measure the power consumption of any load, using the input on your
sound card!

They also give the schematic of the simple hardware required to run this.

I ran into problems aquiring a current transformer, so I was wondering if as
per Vitaly's suggestion a home made ferrite ring wound transformer would
work.

Regards,

Anand.

{Original Message removed}

2005\07\07@040438 by Chen Xiao Fan

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Cheak out "Rogowski coil". It is lower in cost than CT and Hall Effect
sensor. You need a analog or digital integrator after it though.

>From William Koon's paper:
"A simple Rogowski coil is an inductor which has mutual inductance with the
conductor carrying the primary current. Rogowski coil is typically made
from aircore coil so in theory there is no hysteresis, saturation, or
non-linearity."

-----Original Message-----
From: .....ardhuruKILLspamspam@spam@vsnl.com
Sent: Thursday, July 07, 2005 3:41 PM
...
I ran into problems aquiring a current transformer, so I was wondering if as
per Vitaly's suggestion a home made ferrite ring wound transformer would
work.
Regards,
Anand.

2005\07\07@084538 by vasile surducan

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On 7/6/05, Olin Lathrop <olin_piclistspamKILLspamembedinc.com> wrote:
> Martin K wrote:
> > I just had an idea on a way to measure AC current. The idea is to take a
> > small resistor .01 ohms and put it in series with the AC load. To
> > isolate this from the AC line one could use a surplus 600 ohm tel.
> > transformer. The benefit of this would be that the parts are very
> > inexpensive versus a dedicated current transformer. A clamp-on style is
> > not desirable in this application. Any thoughts?
>
> Should work.  Just make sure the transformer primary/secondary isolation is
> rated for the peak AC line voltage plus some margin.

 The input informations are insufficient to affirm that will work.
Everything depends about the current value. On 0.01 ohm, 1A load will
produce 10mV. Far insufficient  to assure a linear conversion through
this kind of transformer at small load currents.
 Second, the telephone transformers are not usualy designed for
500Vac isolation (316V peak for 220V AC) , smaller on 125V ac systems.

Vasile

2005\07\07@103917 by S Bakaletz

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Allegro MicroSystems makes a Hall effects current sensor and shunt in one
package ACS750 family.
Jeff Bachiochi wrote a good article on using the chip
http://www.circuitcellar.com/magazine/164toc.htm


2005\07\07@150833 by Alvaro Deibe Diaz

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You can check out this one, too:

http://www.gmw.com/electric_current/Sentron/CSA-1.html

Hall effect, SMD, Galvanic isolation, AC/DC current sensing, linear
response, great sensitivity, and reasonably priced (this is what they claim,
of course).

{Quote hidden}

> -

2005\07\07@160227 by Peter

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On Thu, 7 Jul 2005, Chen Xiao Fan wrote:

> William Koon of Analog Devices has written a good general article
> "Current sensing for energy metering" which compares current shunt,
> CT, Hall-effect sensor and Rogowski Coil. I think CT is the most
> commonly used. However if you are doing applications like PFC
> (power factor correction) or APF (active power filtering), then
> Hall Effect sensor is the best bet because of its outstanding
> frequency response.

I thought it was the Rogowski coil that gave the outstanding frequency
response ?

Peter

2005\07\07@160530 by Peter

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On Thu, 7 Jul 2005 ardhuruspamspam_OUTvsnl.com wrote:

{Quote hidden}

You can use a small mains transformer with the secondary in parallel
with a shunt which is in series with the mains circuit. E.g. 0.1 ohm
shunt and 10A load = 1V across the shunt (and 10W!) and 12V out from a
120:12V transformer. The error should be small once you calibrate it in
your circuit.

Peter

2005\07\07@201845 by Chen Xiao Fan

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No. If you read the article you will know that Rogowski coil
will not work very well at high frequency (say a few KHz). It
is okay for the energy meter application that the author
was addressing but not for the PFC and APF application.

I was involved in a project of 1kW 3-phase multilevel universal
PFC/APF/VAR-compensator (based on One-Cycle Control) research
project and we used LEM exclusively for the phase current measurement
and the switching frequency is more than 50kHz.

Regards,
Xiaofan


{Original Message removed}

2005\07\08@050236 by Michael Rigby-Jones

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{Quote hidden}

A previous company I worked for use Rogowski coils for measuring the harmonic content in electric locomotive traction current.  That went up to 10's of kHz.  As the Rogowski coil has no core to cause losses I'd have though it's high frequency response would be far superior to a standard current transformer.

Regards

Mike

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2005\07\08@052153 by Chen Xiao Fan

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Yes it is much better than the standard current transformer. However
at least from the paper that it is not so good as the Hall Effect
sensor. I think it is because of the principle and the
integrator. The LEM sensors work at more than 100KHz.

Maybe your previous company has quite a good implementation of
the integrator. Anyway I have not used the Rogowski myself.

Regards,
Xiaofan

-----Original Message-----
From: Michael Rigby-Jones
Sent: Friday, July 08, 2005 5:02 PM

A previous company I worked for use Rogowski coils for measuring the
harmonic content in electric locomotive traction current.  That went
up to 10's of kHz.  As the Rogowski coil has no core to cause losses
I'd have though it's high frequency response would be far superior to
a standard current transformer.

Regards

Mike

2005\07\08@052804 by Michael Rigby-Jones

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>-----Original Message-----
>From: RemoveMEpiclist-bouncesTakeThisOuTspammit.edu [spamBeGonepiclist-bouncesspamBeGonespammit.edu]
>Sent: 08 July 2005 10:22
>To: 'Microcontroller discussion list - Public.'
>Subject: RE: [EE] AC current sensing
>
>
>Yes it is much better than the standard current transformer.
>However at least from the paper that it is not so good as the
>Hall Effect sensor. I think it is because of the principle and
>the integrator. The LEM sensors work at more than 100KHz.
>
>Maybe your previous company has quite a good implementation of
>the integrator. Anyway I have not used the Rogowski myself.
>

Quite possibly, I was never really involved but I do know it had several plug in analog cards and DSP based processor card.

Regards

Mike

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2005\07\08@122736 by alan smith

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These are nice parts...BUT....not sure how well they work with AC.  I have samples of these, as at one time was planning on putting them on a board but size and current requirements kept me from using them.

Alvaro Deibe Diaz <TakeThisOuTadeibeEraseMEspamspam_OUTudc.es> wrote:You can check out this one, too:

http://www.gmw.com/electric_current/Sentron/CSA-1.html

Hall effect, SMD, Galvanic isolation, AC/DC current sensing, linear
response, great sensitivity, and reasonably priced (this is what they claim,
of course).

{Quote hidden}

> -

2005\07\08@132352 by Peter

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On Fri, 8 Jul 2005, Chen Xiao Fan wrote:

> No. If you read the article you will know that Rogowski coil
> will not work very well at high frequency (say a few KHz). It
> is okay for the energy meter application that the author
> was addressing but not for the PFC and APF application.
>
> I was involved in a project of 1kW 3-phase multilevel universal
> PFC/APF/VAR-compensator (based on One-Cycle Control) research
> project and we used LEM exclusively for the phase current measurement
> and the switching frequency is more than 50kHz.

Afaik Rogowski coils are used to measure and scope the pulses in kA and
nanosecond ranges. A Rogowski coil can be configured as an unshielded
untwisted pair transmission line, terminated properly, and wound
edgewise on the conductor to be analyzed. The result is more or less
like a directional coupler with several windings. Afaik it has no upper
frequency limit at all.

Peter

2005\07\08@142902 by Alvaro Deibe Diaz

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I'm planning to use one of this sensors to monitor the current of an AC
motor. 33A max current spected (220V). Current carrying track on the
opposite side of the PCB. This should give us proper galvanic isolation,
enough track width and acceptable sensitivity. Time will tell the goodness
of the sensor...

Alan smith wrote:

{Quote hidden}

2005\07\09@185824 by Martin Klingensmith

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Chen Xiao Fan wrote:

>What is the problem with this design regarding UL? Is it the problem with
>the transformer? Does it need to be UL recognized or better UL listed?
>
>  
>
I've decided that one of the Allegro sensors is probably the best thing
to use. I should have figured, I have a couple sitting right here but I
didn't think about them as I have as of now only used them for DC
applications [though I realize they work just fine for AC or DC]

The application is an AC load analyzer/meter including PFC metering and
energy/power calculations.
I'm planning on using an 18F1220 but I fear the ADC may not be fast
enough to measure a signal having a bad PF [watch the current through a
CFL sometime for fun]
I do believe the rest of the '1220 should be plenty fast considering it
runs at 40MHz and has a hardware multiply.
I'm open to any comments/criticism.

--
Martin Klingensmith

2005\07\09@210508 by David P Harris

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Michael Rigby-Jones wrote:

>A previous company I worked for use Rogowski coils for measuring the harmonic content in electric locomotive traction current.  That went up to 10's of kHz.  As the Rogowski coil has no core to cause losses I'd have though it's high frequency response would be far superior to a standard current transformer.
>
>  
>
Can you describe how to make a Rogowski coil?
David


2005\07\10@222803 by Chen Xiao Fan

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I agree with you that 18F1220 has too weak ADC. dsPICs have faster
ADCs. Silabs C8051Fxxx has much better ADC performance. Maybe you
can look at that as well. Keil offers free 4K C compiler for
it.

What do you mean by PFC metering? Does it mean to measure the power
factor and THD? Then perhaps a DSP is the way to go. Please have a
look at TMS320F2407 or better with an external fast ADC.

For energy metering, Microchip has an application note based on
a 16F873A.

We have HP 6811A AC power source/analyzer and I like it. But it
is quite expensive.

On a side note, IR has finally come out the new PFC control IC based
on the patented one-cycle control of Dr K.M. Smedley of University
of California at Irvine. It is quite an interesting IC to look at
if you are interested in low power PFC applications.

Regards,
Xiaofan

{Original Message removed}

2005\07\11@002230 by Chen Xiao Fan

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The IC I mentioned is IR uPFC controller IR1150. It is a small
SOIC-8 power factor correction controller suitable for 75W to
3KW application. Originally I think they have a more ambitious
chip development (to integrated the power MOSFET inside) but
somehow it is very difficult to isolate the high power part (600V)
and the low power part (5V or <15V) of the IC. I am not so sure
whether they still has the plan. Anyway this IC is a serious
competitor to TI/Unitrode's dominant PFC IC.

For those who are interested, please refer to the following
website: http://www.irf.com/acdc.

Regards,
Xiaofan

-----Original Message-----
From: Chen Xiao Fan
Sent: Monday, July 11, 2005 10:28 AM
...
On a side note, IR has finally come out the new PFC control IC based
on the patented one-cycle control of Dr K.M. Smedley of University
of California at Irvine. It is quite an interesting IC to look at
if you are interested in low power PFC applications.

2005\07\11@042843 by Michael Rigby-Jones

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{Quote hidden}

I don't know any details as we bought them from a small manufacturer (this was ~9 years ago).  The ones we used has a solid plastic (PTFE possibly) toroidal core.  I belive they are wound simmilarly to a normal toroidal coil, but the wires have to both exit at the same "end" of the coil, i.e. one of the wires is routed back to the start of the coil underneath all the windings.  We also had a flexible coil with a break in it, so it could be wrapped around conductors without breaking a circuit, and it had it's own battery powered integrator so it could be plugged into a normal DMM for current measurement.  IIRC the winding of the coils was critical for it's performance, the turns had to be very evenly spaced other with output would vary if the current carrying conductor was moved within the toroid.

Just googled and found the company we used http://homepage.ntlworld.com/rocoil/ .  They weren't cheap though!

Regards

Mike

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2005\07\11@231405 by Martin K

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Chen Xiao Fan wrote:
> I agree with you that 18F1220 has too weak ADC. dsPICs have faster
> ADCs. Silabs C8051Fxxx has much better ADC performance. Maybe you
> can look at that as well. Keil offers free 4K C compiler for
> it.
>
> What do you mean by PFC metering? Does it mean to measure the power
> factor and THD? Then perhaps a DSP is the way to go. Please have a
> look at TMS320F2407 or better with an external fast ADC.
>

Yes I should have said "PF analyzing" as PF correction metering makes no
sense. I'm not sure how to actually analyze the PF from a piecewise
signal, that is part of what I am researching.


> For energy metering, Microchip has an application note based on
> a 16F873A.

Basic energy metering would be fairly simple IMO.

> On a side note, IR has finally come out the new PFC control IC based
> on the patented one-cycle control of Dr K.M. Smedley of University
> of California at Irvine. It is quite an interesting IC to look at
> if you are interested in low power PFC applications.
>
> Regards,
> Xiaofan

Is it just for low power? I thought it was for up to 4kW, if we were
looking at the same chip. Very interesting indeed that only one inductor
and a shunt resistor is needed now.

I've also been wondering if it is possible to make a flyback PFC for a
specific application I have in mind. It seems as though it should work
keeping in mind that the energy is transferred in the off time for both
the boost and flyback topologies.

--
Martin K
http://wwia.org/

2005\07\12@020319 by Chen Xiao Fan

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Maybe FFT is the way to go for PF analyzing. There must be some
experts in this list on how to do discrete FFT.

I am not so sure that we are looking at the same chip since
IR1150 is specified for 75W to 3KW+ and it needs an external
power MOSFET (or IGBT) to work. Maybe you were looking at the
old chip with built-in power MOSFET. The chip never comes out.

3KW is "low power" and 240VAC is "low voltage" for electric power
engineering. :) I normally do not want to deal with anything above
1kW and 253VAC and I think I will not have to do that any more. My
universal AC/DC power supply design now consumes only 0.7W and does
not need any power factor correction. Anyway, I think typical PFC
application above 3kW will need require significant considerations
of the protection of the components.

It is okay to be used in flyback PFC applications. Low power
flyback PFC works in discontinuous conduction mode (DCM). One cycle
control typically works in continuous conduction mode (CCM). Still
the efficiency will not be as good as boost PFC. Single stage PFC
is still not so good as 2-stage boost PFC + DC-DC converter in
terms of efficiency.

The best paper for one-cycle control of single-phase PFC
is the following. BTW, Dr Lai is now with Intersil.

[1] Z. Lai, Keyue Smedley. "A Family of Power Factor
Correction Controllers". APEC '97. New York. IEEE 1997.

It also appears in IEEE Transactions on Power Electronics,
Volume: 13 , Issue: 3, May 1998, Pages:501 - 510

The beauty of one-cycle control is that it scales very well.
It works for single-phase PFC/APF. IMHO IR is too late to
come out this IC to capture the market from others like TI.

It also works for 3-phase PFC/APF. It will also works for
high power multi-level PFC/APF. Let's wait to see some
companies come out with 3-phase PFC control IC with
one-cycle control.

Regards,
Xiaofan

{Original Message removed}

2005\07\12@085603 by olin piclist

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Chen Xiao Fan wrote:
> Maybe FFT is the way to go for PF analyzing.

FFT would not be very useful.  You are looking for relative phase
relationship between two signals, not the spectra of the signals separately.

Think of the case where the voltage is a pure sine and you have three
different loads, resistive, capacitive, and inductive.  If the magnitude of
the load currents are the same, an FFT will give the same result in all
cases even though one has a power factor of 1 and the other two of 0.

To compute power factor, compute the RMS voltage and current, and the actual
power.  Power factor is the ratio of the true power divided by the product
of the RMS voltage and current.  You can see that this can be at most 1,
which is what you get only with a resistive load.  The extremes are pure
capacitive and inductive loads where the delivered power is 0 and the power
factor therefore is 0.  Technically an active load could produce negative
power factors, but this means the load is actually delivering power back to
the AC line.


*****************************************************************
Embed Inc, embedded system specialists in Littleton Massachusetts
(978) 742-9014, http://www.embedinc.com

2005\07\12@103239 by Martin K

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Olin Lathrop wrote:
{Quote hidden}

So calculating the power factor could be done quite easily on an 18F
however THD would require a FFT to calculate the sum of powers at
frequencies above the fundamental.

--
Martin K
http://wwia.org/

2005\07\12@123855 by olin piclist

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Martin K wrote:
> So calculating the power factor could be done quite easily on an 18F
> however THD would require a FFT to calculate the sum of powers at
> frequencies above the fundamental.

Calculating power factor should be possible on a 18F since its mostly a few
multiplies per sample.  Calculating total harmonic distortion doesn't
require a FFT, although that's one way.  You don't need to know the full
spectrum to calculate THD, only how much power is in the fundamental and how
much everywhere else.  There are simpler ways of doing that than a FFT.


*****************************************************************
Embed Inc, embedded system specialists in Littleton Massachusetts
(978) 742-9014, http://www.embedinc.com

2005\07\12@134312 by Martin K

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Olin Lathrop wrote:
> Martin K wrote:
>
>> So calculating the power factor could be done quite easily on an 18F
>> however THD would require a FFT to calculate the sum of powers at
>> frequencies above the fundamental.
>
>
> Calculating power factor should be possible on a 18F since its mostly a few
> multiplies per sample.  Calculating total harmonic distortion doesn't
> require a FFT, although that's one way.  You don't need to know the full
> spectrum to calculate THD, only how much power is in the fundamental and
> how
> much everywhere else.  There are simpler ways of doing that than a FFT.

The only way I can think of would be to high pass filter the
current/voltage signals and then figure out the total power of that
signal [>60Hz] sound reasonable? It seems like it gives you the "power
here, power everywhere else" data.
A digital IIR/FIR filter would have a better result but probably take
much more computation.

--
Martin K
http://wwia.org/

2005\07\12@143901 by olin piclist

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Martin K wrote:
> The only way I can think of would be to high pass filter the
> current/voltage signals and then figure out the total power of that
> signal [>60Hz] sound reasonable? It seems like it gives you the "power
> here, power everywhere else" data.

That's going to be tricky since a simple high pass filter will still pass
significant fundamental at the level that THD is often measured.  You need
to find the power in everything except the fundamental down to a fraction of
a percent to be useful in most applications.


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2005\07\12@204636 by Chen Xiao Fan

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I think Olin's correct that power factor should be able
to be measured using an 18F. THD is a bit tricky and I think those
power analyzers /high end scopes are using FFT. However if
we can measure the power factor and the displacement factor,
then we can get the distortion factor and thus the THD. So
the question is how to effectively measure the displacement
factor, which is the phase difference between the fundamental
voltage and fundamental current.

For those who are a bit interested but confused about the various
jargons:

1) power factor =(average power) / ((rms voltage)*(rms current))
2) THD = total harmonic distortion

3) If the voltage is pure sine wave, then we have the following formula.
(power factor) = (distortion factor) * (displacement factor)
(displacement factor) =cos (phase angle between fundamental of i and v)
(distortion factor) =(rms fundamental current) / (rms current)
(distortion factor) = 1/sqrt(1 + (THD)^2))

Normally the phase voltage is pretty okay in USA and most part
of the world with only a bit flat top on the peak so one can assume
it to be sinusoidal (the THD of the voltage is typically <5%).

Or it is better that you check Robert W. Erickson's lecture notes
on University of Colorado website or his book "Fundamentals of
Power Electronics", 2nd ed.

Regards,
Xiaofan

{Original Message removed}

2005\07\21@145626 by alan smith

picon face
Take a look at the ADI demo board schematics on how they do front end filtering using the ADE7758 and others in the family

Martin K <RemoveMEmartin-distlistsTakeThisOuTspamspamnnytech.net> wrote:

Olin Lathrop wrote:
{Quote hidden}

The only way I can think of would be to high pass filter the
current/voltage signals and then figure out the total power of that
signal [>60Hz] sound reasonable? It seems like it gives you the "power
here, power everywhere else" data.
A digital IIR/FIR filter would have a better result but probably take
much more computation.

--
Martin K
http://wwia.org/

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