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dkriley
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Join Date: Aug 2008
Location: Chicago, IL USA
Posts: 120
Good Answers: 2

Mathematical Equation for Power Factor of 1 in Single-Phase Motor

10/08/2008 1:42 PM

Goal:

How do I calculate the inductance (Xi) in a single-phase motor so I can add the appropriate capacitance (Xc) to null the reactance (Z) in my circuit to and get true resistance (R)?

Strategy:

120Vac 60Hz Supply. 1/70hp 0.6amp motor nameplate. Using a meter that measures inductance; I measured the motor stator as (35mH) resistance (13ohm). Using induction and phasor (polar) equations, I came up with 1uF to cancel the reactance in the circuit.

Implement:

Bench test supply current 0.6A, load current 0.6A without capacitance (1uF).

Bench test supply current 0.6A, load current 0.6A with capacitance (1uF).

Evaluate:

But, when I replaced the (1uF) capacitor with (10uF);

Bench test supply current 0.3A, load current 0.6A.

Excellent improvement. Supply current halved.

Sleepless in Illinois:

Can anyone inlighten me on an equation?
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RVZ717
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United States - Member - USA! Hobbies - Musician - Sound Man Engineering Fields - Mechanical Engineering - More than a Hobby Technical Fields - Technical Writing - New Member

Join Date: Oct 2008
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#1

Re: Mathematical Equation for Power Factor of 1 in Single-Phase Motor

10/08/2008 4:34 PM

http://www.allaboutcircuits.com/vol_2/chpt_11/3.html has your answer, and can give it in a better format than i can on this thread.

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Anonymous Poster
#2

Re: Mathematical Equation for Power Factor of 1 in Single-Phase Motor

10/08/2008 5:14 PM

The answer is 102uF.
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RVZ717
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#3
In reply to #2

Re: Mathematical Equation for Power Factor of 1 in Single-Phase Motor

10/08/2008 5:28 PM

Funny, I get exactly double that @ 204uF. Could you show the equation you used, i would like to see where i went wrong.

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Anonymous Poster
#4
In reply to #3

Re: Mathematical Equation for Power Factor of 1 in Single-Phase Motor

10/08/2008 5:43 PM

I just calculated the impedance of a capacitor in parallel with a resistor and inductor:

Zc // (Zl+Zr)

And then calculated what the capacitor should be to get an impedance that is strictly resistive. It was basically:

1/(jwL + R) + jwC

It's messy so I'm not ruling out that I may have made a mistake instead of you.
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Isti80
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#5
In reply to #3

Re: Mathematical Equation for Power Factor of 1 in Single-Phase Motor

10/09/2008 4:41 AM

Same here, I must have got something wrong.

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kayems
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Join Date: Jun 2008
Posts: 24
#6

Re: Mathematical Equation for Power Factor of 1 in Single-Phase Motor

10/09/2008 5:48 AM

True power 1/70hp Ptrue = 10.657w Voltage V = 120V Inductive Current IL = 0.6A Apparent power Papp = 72 VA  Papp = V*IL Power Factor cos ø = 0.148  cos ø = Ptrue / Papp Reactive power Preact = 71.2var  Papp^2= Preact^2+Ptrue^2 Capacitive Reactance XC = 202.23 Ω XC = V^2 / Preact Capacitance C = 13.124μF C = 1/2*pi*f*XC Capacitive Current IC = 0.6A  Ic = V/ Xc Supply Current Is = 0.3A  1/Is = 1/IL+1/IC
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kayems
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Join Date: Jun 2008
Posts: 24
#7
In reply to #6

Re: Mathematical Equation for Power Factor of 1 in Single-Phase Motor

10/09/2008 5:50 AM

bear with me, i dont know why it is appearing like this...
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Anonymous Poster (2); Isti80 (1); kayems (2); RVZ717 (2)

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