Inexpensive power factor correction

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A 12 uF recycled motor run cap on the same extension cord as a 61 W fan
raised its power factor from 0.69 to 0.98, with an audible spark. A series
choke with 18/2 lamp cord ($31 for 250' at Home Depot) wound on a square
varnished steel coathanger core might limit the switch inrush current.

R. Clarke's nice web page on magnetism

http://www.ee.surrey.ac.uk/Workshop/advice/coils/terms.html#efarea

says magnetic flux Phi = IL/N = 0.04/N webers, and the max flux density
B = Phi/Ae = 1.6 teslas, to avoid saturating steel, so NAe = 0.04/1.6
= 0.025 = NPir^2, for a core cross section of radius r, and L = 0.004
= Mu0MurN^2r^2/Le henrys, where Le is the core perimeter in meters...

10 PI=4*ATN(1)'powfac
20 V=120'load voltage (rms)
30 P=61'load power (watts)
40 PF=.69'uncorrected power factor
50 XC=V^2*PF/(P*SQR(1-PF^2))'reactance (ohms)
60 C=1/(377*XC)'ideal PF correction capacitor (farads)
70 PRINT V,P,PF,1000000!*C
80 CS=12'standard cap value (microfarads)
90 C=CS/1000000!'standard cap value (farads)
100 IC=V*377*C'cap current (amps)
110 IMAX=20*P/V'peak cap current (amps)
120 DT=V*SQR(2)*C/IMAX'charging time (seconds)
130 L=V*SQR(2)*DT/IMAX'series inductance (henrys)
140 FRES=1/(2*PI*SQR(L*C))'resonant frequency (hertz)
150 PRINT CS,IMAX,L,FRES/60
170 MU0=PI*.0000004'free-space permeability
180 MUR=200'relative steel permeability
190 MU=MU0*MUR'absolute steel permeability
200 B=1.6'allowable max flux density (teslas)
210 NR2=IMAX*L/B/PI'Nr^2 constant
220 N2R2=4*L/MU/PI'n^2r^2 constant
230 WA=.1*.1/(39.37^2)'wire area (m^2)
240 NL=50'initial number of turns
250 R=SQR(NR2/NL)'core radius (m)
260 E=2*R+SQR(NL*WA)'square core edge (m)
270 N=N2R2/NR2*E'iterate
280 IF ABS(N-NL)>.1 THEN NL=N:GOTO 250
290 N=2*INT(N/2+.5)'round to even number
300 WIRELENGTH=3.281*PI*N*R'bifilar wirelength (feet)
310 PRINT N/2,WIRELENGTH
320 ECORE=39.37*E'core edge (inches)
330 RCORE=39.37*R'core radius (inches)
340 PRINT ECORE,RCORE
350 VCORE=4*ECORE*PI*RCORE^2'core volume (in^3)
360 LCOAT=36'coathanger length (inches)
370 DCOAT=.07'coathanger diameter (inches)
380 VCOAT=LCOAT*PI*DCOAT^2/4'coathanger volume (in^3)
390 NCOAT=INT(VCORE/VCOAT+.5)'number of coathangers
400 PRINT LCOAT,DCOAT,NCOAT

volts watts Power factor ideal PF cap (uF)

120 61 .69 11.78694

standard peak current inductance 60 Hz
PF cap (uF) (A) (H) harmonic

12 10.16667 3.343618E-03 13.2425

wire turns length

53 8.751237 feet

core edge radius

1.657399 in .3153355 in

coathanger
length diam number

36 in .07 in 15

Nick

 

[Andrew Burgess]

A 12 uF recycled motor run cap on the same extension cord as a 61 W fan
raised its power factor from 0.69 to 0.98, with an audible spark. A series
choke with 18/2 lamp cord ($31 for 250' at Home Depot) wound on a square
varnished steel coathanger core might limit the switch inrush current.

You probably know but didn't mention that you must split the
zip cord and wind each wire in opposite directions around
the coat hanger so the magnetic fields add and you get an
inductor.

 

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You probably know but didn't mention that you must split the zip cord and
wind each wire in opposite directions around the coat hanger so the magnetic
fields add and you get an inductor.

I shoulda mentioned my plan to leave the cord unsplit, but reconnect
the pair in series, with the end of one wire going to the beginning
of the other.

Mr. Clarke has another web site. He writes

My ignorance of the magnetic properties of coathangers
is almost total

However, 200 sounds as good as any other value.

Working back from a 1.8" diameter core of 0.36" radius gives an
inductance of 0.398 mH and a flux density of 1.60 T, so it looks like
you're on the right lines.

As I remark at
http://www.ee.surrey.ac.uk/Workshop/advice/coils/index.html

trial and error ... sorry, iteration, is the way to go. You are in
a somewhat different position since you are able to choose arbitrary
dimensions for your core, but the nice BASIC program is as good an
approach as any...

Nick

 

[Andrew Burgess]

I shoulda mentioned my plan to leave the cord unsplit, but reconnect
the pair in series, with the end of one wire going to the beginning
of the other.

Hmmm. Doesn't solve the problem, the current runs in opposite
directions so the fields cancel. That's how you make a
non-inductive resistor ;-)

I make something similar out of zip cord extension cords,
splitting the wire but not cutting it, wrapped in opposite
directions around a piece of water pipe, to act as a
blocking inductor for X-10 signals. Works but boy does it
humm when set on something made of steel!

 

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Hmmm. Doesn't solve the problem, the current runs in opposite directions...

It does?

Nick

 

[Andrew Burgess]

It does?

Maybe I'm not picturing it right. The current runs down the
left half, through your splice, then up the right half?

Like a twisted pair without the twist?

Or waitaminute.. left wire, A and B ends, right wire, A and
B ends. Are you connecting left-A to right-B? I was
picturing left-A to right-A...

 

[[email protected]]

... left wire, A and B ends, right wire, A and B ends. Are you connecting
left-A to right-B?

Yes. So current enters left B and exits left A,
then enters right B and exits right A...

Nick