Referring to below...
Part 1. This measurement will NOT give just the resistive part of the
source impedance. Let Rs = source resistance, Xs = source inductive
reactance, and Rl = load resistance, Xc = test capacitor reactance (=
1/2piFC), F = 50 or 60 Hz, and Voc = open circuit voltage. The magnitude of
the voltage with a resistive load will be:
Vloaded = Voc × magnitude[Rl / (Rs + Rl + jXs)].
Clearly the reactive component will affect the measured voltage when
loaded.
Part 2. In this case, Vloaded = Voc × magnitude[-jXc/(Rs + jXs - jXc)].
Clearly, the resistive part has an effect on the voltage with a capacitive
load. The proposed phase measurement will simply measure the phase shift
between the current and voltage in the capacitor, and tells nothing about
the phase of the power line voltage source.
As I previously stated, since in this measurement the phase of the power
line current relative to the open circuit voltage is not available (only
voltage magnitudes are available), a capacitor and inductor must be used to
make the measurement.
Here are the details-
Measured voltage with capacitive load (Vc):
Vc = Voc × magnitude[-jXc/(Rs + j(Xs - Xc)] =Voc × Xc/sqrt[Rs² + (Xs -
Xc)²].
Rearranging:
Vc × sqrt[Rs² + (Xs - Xc)²] = Voc × Xc.
Squaring both sides, and expanding the (Xs - Xc)² term:
Vc² × (Rs² +Xs² - 2XsXc + Xc²) = Voc² × Xc². (Equation #1)
Measured voltage Vl with inductive load Xl:
Vl = Vc = Voc × magnitude[jXl/(Rs + j(Xs + Xl)] =Voc × Xl/sqrt[Rs² +
(Xs + Xl)²].
Rearranging:
Vl × sqrt[Rs² + (Xs + Xl)²] = Voc × Xl.
Squaring both sides and expanding the (Xs + Xl)² term:
Vl² × (Rs² +Xs² + 2XsXl + Xl²) = Voc² × Xl². (Equation #2)
Now multiply both sides of Equation #1 by Vl²/Vc²:
(Vl²/Vc²) × Vc² × (Rs² +Xs² - 2XsXc + Xc²) =(Vl²/Vc²) × Voc² × Xc²
Which is then:
Vl² × (Rs² +Xs² - 2XsXc + Xc²) =(Vl²/Vc²) × Voc² × Xc². (Equation #3)
Subtracting Equation #3 from Equation #2 yields:
Vl² × [2Xs × (Xl +Xc) +Xl² - Xc²] = Voc² × [Xl² - (Vl²/Vc²) × Xc²].
All the values in the above equation are known except for Xs, so Xs can be
found. Once the source reactance Xs is known, its value can be substituted
into either Equation #1 or Equation #2 and the value of Rs can be
determined.
Sorry for the long winded answer, and I hope all the math is correct.
One more comment: A measurement with a resistive load doesn't help. When
compared to Equation #1 or Equation #2, the equivalent equation has terms
in Rs², Rs, and Xs. If this equation is scaled and subtracted from Equation
#1 or Equation #2, one ends up with a single equation with two unknowns (Rs
and Xs) which cannot be solved.
Don Borowski
Schweitzer Engineering Labs
Pullman, WA
"Spencer, David H" <david.spen...@usa.xerox.com>@majordomo.ieee.org on
10/30/2002 08:57:00 AM
Please respond to "Spencer, David H" <david.spen...@usa.xerox.com>
Sent by: owner-emc-p...@majordomo.ieee.org
To: emc-p...@majordomo.ieee.org
cc:
Subject: RE: Measuring AC Line Impedance
Follow up............................
Having just completed an ton of work on this using input I got around here
(thanks to Don Borowski, Patrick Lawler, Joe Randolph and John Woodgate).
I believe we have characterized the AC mains of our facility.
As a sanity check/ technical check can any one comment on process.
Part one
1)Open circuit voltage measured.
2)Resistive load placed in circuit.
3) Voltage drop and current measured.
4) Voltage drop divided by current provides resistance component of AC
mains.
Part 2
1) Open circuit voltage measured.
2)Reactive load placed in circuit (approximately 120uF!)
3) Voltage change (increase really) and current measured (phase angle was
recorded to back check math vectorialy).
4) Voltage change divided by current provides reactive component of AC
mains.
As a side note, I also connected an isolation transformer as the reactive
load, the reactive numbers were very very close.
The resistive number + reactive number then make up the AC line impedance
for this site: Ztest if you will.
My two remaining questions:
Is this method of characterizing the AC line impedance valid (is there
something I'm missing)?
Based on my knowledge of these values, and their ratio to the reference
impedance(s) specified in EN61000-3-3 and EN61000-3-11, I should be able to
calculate and correlate the measured Dmax, Pst, et. al...to the limits
specified in those standards.
(REFERENCE section 6.1.3 of EN61000-3-11), using our existing AC mains.
Any comments or input would be welcome.
Thanks
Regards
David Spencer
Xerox Corp.
-----Original Message-----
From: John Woodgate [mailto:j...@jmwa.demon.co.uk]
Sent: Thursday, September 19, 2002 11:56 AM
To: emc-p...@majordomo.ieee.org
Subject: Re: Measuring AC Line Impedance
I read in !emc-pstc that Spencer, David H <david.spen...@usa.xerox.com>
wrote (in <052106A55179D611B34300096BB02E3F8B1D@USAMCMS4>) about
'Measuring AC Line Impedance' on Thu, 19 Sep 2002:
>Is anyone familiar with a method to measure and calculate those values.
The
>generic values I have for short circuit condition (which include 4 wires
in
>a magnetic conduit) come out higher than my measured values, and those do
>not include the motor generator source.
Put a large capacitor (mains voltage rated) across the mains and measure
the voltage change; it may actually increase. You need about 50 uF to
get a decent change on 120 V 60 Hz mains. With that result and the one
with the resistive load, you can calculate the source impedance as an R
and L in series.
I'd be interested to learn the result.
--
Regards, John Woodgate, OOO - Own Opinions Only.
http://www.jmwa.demon.co.uk
Interested in professional sound reinforcement and distribution? Then go to
http://www.isce.org.uk
PLEASE do NOT copy news posts to me by E-MAIL!
-------------------------------------------
This message is from the IEEE EMC Society Product Safety
Technical Committee emc-pstc discussion list.
Visit our web site at: http://www.ewh.ieee.org/soc/emcs/pstc/
To cancel your subscription, send mail to:
majord...@ieee.org
with the single line:
unsubscribe emc-pstc
For help, send mail to the list administrators:
Ron Pickard: emc-p...@hypercom.com
Dave Heald: davehe...@attbi.com
For policy questions, send mail to:
Richard Nute: ri...@ieee.org
Jim Bacher: j.bac...@ieee.org
All emc-pstc postings are archived and searchable on the web at:
http://ieeepstc.mindcruiser.com/
Click on "browse" and then "emc-pstc mailing list"
-------------------------------------------
This message is from the IEEE EMC Society Product Safety
Technical Committee emc-pstc discussion list.
Visit our web site at: http://www.ewh.ieee.org/soc/emcs/pstc/
To cancel your subscription, send mail to:
majord...@ieee.org
with the single line:
unsubscribe emc-pstc
For help, send mail to the list administrators:
Ron Pickard: emc-p...@hypercom.com
Dave Heald: davehe...@attbi.com
For policy questions, send mail to:
Richard Nute: ri...@ieee.org
Jim Bacher: j.bac...@ieee.org
All emc-pstc postings are archived and searchable on the web at:
http://ieeepstc.mindcruiser.com/
Click on "browse" and then "emc-pstc mailing list"
-------------------------------------------
This message is from the IEEE EMC Society Product Safety
Technical Committee emc-pstc discussion list.
Visit our web site at: http://www.ewh.ieee.org/soc/emcs/pstc/
To cancel your subscription, send mail to:
majord...@ieee.org
with the single line:
unsubscribe emc-pstc
For help, send mail to the list administrators:
Ron Pickard: emc-p...@hypercom.com
Dave Heald: davehe...@attbi.com
For policy questions, send mail to:
Richard Nute: ri...@ieee.org
Jim Bacher: j.bac...@ieee.org
All emc-pstc postings are archived and searchable on the web at:
http://ieeepstc.mindcruiser.com/
Click on "browse" and then "emc-pstc mailing list"
