# What is Power factor: Definition and 126 Discussions

In electrical engineering, the power factor of an AC power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit, and is a dimensionless number in the closed interval of −1 to 1. A power factor of less than one indicates the voltage and current are not in phase, reducing the average product of the two. Real power is the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of RMS current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power. A negative power factor occurs when the device (which is normally the load) generates power, which then flows back towards the source.
In an electric power system, a load with a low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The higher currents increase the energy lost in the distribution system, and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor.
Power-factor correction increases the power factor of a load, improving efficiency for the distribution system to which it is attached. Linear loads with low power factor (such as induction motors) can be corrected with a passive network of capacitors or inductors. Non-linear loads, such as rectifiers, distort the current drawn from the system. In such cases, active or passive power factor correction may be used to counteract the distortion and raise the power factor. The devices for correction of the power factor may be at a central substation, spread out over a distribution system, or built into power-consuming equipment.

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1. ### Alternator run at zero power factor lagging

Hello, I'm wondering if it's possible to make an alternator run at zero power factor lagging (purely inductive). I was researching this topic and apparently by shorting the leads of the alternator the output will become fully reactive. Yet I've attempted this on a small scale and the most I can...
2. ### Sizing an Isolation Transformer for a DC Power Supply

Good afternoon, How should an upstream isolation transformer be sized for a dc power supply? For example, if we have a power supply with the following specs: Input Voltage: 120 VAC Input Current: 2 Amps Inrush Current: 22 Amps Efficiency: 90% Power Factor: 0.55 Output Voltage: 24 VDC Output...
3. ### Power factor of a retrofitted LED unit in a fluorescent fitting

A poster on another forum has fitted a large number of 230V 50Hz 24W nominal LED tubes, apparently designed to be plugged straight into the old fluorescent fittings. He has found, by clamp meter measurement, that the new LED lights appear to be consuming 80W, not the claimed 24W. A number of...
4. ### Power factor of motor with VSD?

If I have a motor with a full load power factor of 0.8 and starting power factor of 0.3 and I install a VSD to run it with a datasheet power factor of 0.95, will the power factor during starting be 0.3 or 0.95? And at full load? Cheers!
5. ### Adjusting the Power Factor of an RLC circuit

a) An inductor should be added because that would cancel out the lag of the voltage with the current so that P = IV is at a maximum since V is ahead of I in an inductor b) ##cos(\phi) = \frac{R}{Z}##, ##R = Zcos(\phi) = 60\times 0.5 = 30 ohms## ##X_l - X_c = \sqrt{Z^2 - R^2} = \sqrt{60^2 -...
6. ### AC Drift Velocity: Understand Reactive Power & Movement of Electrons

Hi All I hope this topic makes sense for this forum and somebody can help me to understand. This is what I understand (please allow numerical approximations): 1. Electrons move in a conductor at a speed anywhere near the speed of light. 2. Electrons gain actual velocity (drift) only when...

8. ### Engineering Power Triangle and Power factor

Induction motors: pf = 0.8 triangle: θ = arccos(0.8) = 36.86 degrees Pa = 500/0.8 = 625 VA Pr = sqrt(625^2-500^2) = 375 VAR Synchronous motors: pf = 0.707 triangle: θ = arccos(0.707) = 45 degrees Pa = 500/0.707 = 707 VA Pr = sqrt(707^2-500^2) = 499.85 VAR I am uncertain of how I can...
9. ### Voltage regulation in transformers at unity power factor

So I've done part a) Primary current = 200000/415=481.9 Cos θ = -0.8 Sin θ = 0.6 Reg=(481.9 ( 0.014*-0.8 + 0.057*0.6))/415 = 0.0267 Reg% = 2.67% Part b I simply used the same equation but for secondary: @ unity p.f., cos θ =1, sin θ = 0 secondary current = 200000/11000 = 18.18...
10. ### What is the power factor in a series circuit?

I calculated in the following and got the correct answer. However, I wonder whether this way is correct or not. Thanks! PR / Pavg = Irms^2 * R / Irms^2*Z = 15 /33.36 = 0.45
11. ### Engineering Calculating Power Factor in an AC circuit, given voltage and current

My attempt at solving this question: I realized my attempt is wrong however I just don't know how to proceed in the first step. How can I calculate the phase shift? and find Voltage and Current in phasor form??If I know that, then I can use power factor formula: pf=Pav/V*I
12. ### Engineering RLC Series Network: Impedance, Current, Power Factor, Phasor Diagram

Hello. I have completed the following question. My answer: i) Circuit Impedance Reactance = XL = 2 x pi x F x L = 2 x pi x 50 x 0.15 = 47.12 Ohms Reactance of Capacitor = XC = 1/2 x pi x F x C...
13. ### A 50 kW load operates from a 60 Hz 10 kV rms line with a power factor of 60% lagging -- Determine the capacitance that must be placed in parallel

Please can you have a look at the file at point me in the right direction if I'm wrong. Thank you
14. ### Is Replacing a 25 kVAr Unit with Two 12.5 kVAr Units More Efficient?

Hi all, The power factor correction unit for one of the buildings that I am working on needs maintenance. The service report recommends replacing the existing 25 kVAr unit with 2 x 12.5 kVAr units as "the demand on your site according to the data supplied shows us that at most there is only...
15. ### How to make the power factor of induction motors be a leading power factor?

Hi guys, This month onwards our power distributor says that we only get powerfactor incentive when only we make the powerfactor leading and in between 0.95 and 1. Our industry fully consists of induction motor and compensative capacitors are provided but this month onwards we have to keep the...
16. ### Having difficulty increasing my load power factor above 0.95

I have an inductive load (120 volts AC at 0.5 amps AC at 60 Hz, 0.9 power factor before correction) that is a connected to the grid. I have been trying to increase the power factor above 0.95, but no matter how much I tune the power factor correction capacitors I cannot increase the power factor...
17. ### Parallel Capacitance - Power Factor Question

Homework Statement A 50 kW load operates from a 60 Hz 10 kV rms line with a power factor of 60% lagging. Determine the capacitance that must be placed in parallel with the load to achieve a 90% lagging power factor. The Attempt at a Solution For Z at 0.6pf S=P/pf = 50000/0.6 = 83333.33VA I =...
18. ### How to correct for a Leading Power Factor (kVArh)

Hi guys, We have a industrial connection of 225 kW. Our industry consists mostly of Induction motors and runs in night shift mostly. So we use capacitor banks for lower factor correction. And so far we have maintained 0.995-0.999 pf (sometimes even 1) over the years. Previously, the power...
19. ### Calculating 208V load, purpose of sqrt(3) and power factor?

Hi all, a pretty simple question. I want to be able to calculate the load on a 100amp 3 phase service. As an example if I have 9 lighting fixtures that are rated @ 11 amps 208v each (auto ranging 200-240v actually but service will be 3 phase so 208v ish) Putting evenly across each leg x,y,z...
20. ### Why is a capacitor a generator of lagging reactive power?

An ideal capacitor has power factor of zero degree leading as current leads the voltage in capacitor.But it also means that capacitor is generator of lagging reactive power.What does that mean.How does it do so.Capacitor is used for reactive power generation at inductive load sites.
21. ### Relation between power factor and phase angle

Homework Statement apparently your effective power is V_maxI_max * cos(x) where x is the phase angle. So I must consider only real power Homework Equations power = VI current = I sin(wt) The Attempt at a Solution Let impedence be = e^ix . I'll write current as Ie^i(wt) consideronly the real...
22. ### Find the Capacitance when given the Power Factor

Homework Statement w = 1 rad/s power factor is 0.8 lag Homework Equations Using Phasor we can do The Attempt at a Solution Since pf = 0.8 lag. I source lags V source by 36.87 degrees. Vc is voltage across Capacitor = Voltage across ( Resistor + inductor) Solving this I get C = 0.5 But book...
23. ### AC synchronous motor power factor

Is it true that AC synchronous motors (the ones with the DC slip rings and excitation current running into rotor poles) have a power factor of 1.0 when they run in synchronous mode? Would that be because with sufficient rotor DC current he rotating AC magnetic field is precisely counterbalanced...
24. W

### What is the role of cosφ in calculating power in LRC series circuits?

Homework Statement With just about any problem asking for "rate at which source is delivering electrical energy to the circuit" or "find the power of the circuit" in a LRC circuit, I get that you have to calculate for the average power. But the multiple equations confuse me - sometimes in...
25. W

### What circuit element should be placed in series to raise power factor?

Homework Statement A series circuit has an impedance of and a power factor of 0.720 at 50.0 Hz. The source voltage lags the current. What circuit element, an inductor or a capacitor, should be placed in series with the circuit to raise its power factor? Homework Equations cosΦ=R/Z...
26. ### Is There a Standard Power Factor Convention for Voltage and Current Angles?

Homework Statement Is there a power factor convention when it comes to the angles of a given current and voltage? In one class I learned that PF = cos(θ_V - θ_I) but in another the professor claims (I still think he is wrong) the convention for that class is PF=cos(θ_I - θ_V). Here is a...
27. ### How to Calculate Total Power Factor in a Parallel AC Circuit?

Homework Statement I am given this circuit: One of the questions is to find the total power factor of this installation. The other questions involving current and such, I have solved. Homework EquationsThe Attempt at a Solution I am able to find the power of each Z1 and Z2, by multiplying...
28. ### Power factor of ideal transformer

Can anyone explain why the power factor of an ideal transformer cos (phi) is equal to 1?? A simple ideal transformer is formed of 2 ideal coils. The power factor of an ideal coil is 0 since phase difference between the current and the applied voltage is - π/2. Then how can the power factor of...
29. ### Correcting power factor without affecting active power.......

When correcting power factor without affecting active power, wouldn't the current and voltage of the system have to change due to Active power =VrmsIrmscos(theta), where cos(theta) is the power factor?
30. ### What is tangent of power factor angle for an alternator?

My book had these two solved examples that gave contradictory replies. The power output of an alternator is 100 kW. Now if the tangent of pf angle is 0.8 lagging, the KVAR rating must be -80KVAR. I drew phasor and got this. I took it that since tangent is negative. Now tangent is opposite...
31. ### Power Factor Correction (open leg on a floating wye)

We had a switch fail to close on the A phase of a floating wye connected capacitor bank. The C phase fuse was found to be bad and was replaced, however the B phase fuse then blew. The bad switch was then found and replaced. After that the system operated normally. The contractor said the...
32. ### Power factor correction (capacitor in parallel with inductive load)

Why we must install capacitor in parallel to inductive load? Why not install it in series?
33. ### Good beginner's resources for power factors and grids

I am doing a BSEE and going power side. I am also applying for scholarships and bursaries, and would like to be able to talk specifically about power factors. More than this though, I want to understand it. Most of what I've found so far is very specialized and technical. What good resources...
34. ### Induction motors and power factor

Hi all, I have a 1 HP capacitor start motor (old, c.1950) that runs an air compressor in my little workshop. When it's running, the lights in the shop and the whole house dim and brighten rhythmically, at about 5 Hz. This, of course, is related to the compression cycles of the compressor, but...
35. ### Maximum power factor of three phase receiver

Homework Statement Given symmetric three phase system (see attachment) of phase voltages with angular frequency \omega=100 rad/s, R=5\omega L=100\Omega. Find capacitance of capacitor C such that power factor of three phase receiver has maximum value. Homework Equations Power factor is given by...
36. ### Power Factor Correction for a small 60W AC Induction motor

Hello, I have a light AC fan, that I wish to correct its power factor. According to my measurements, it has around 0.7 LAG power factor. Here are my digital measurements: Vsupply = 204VAC I(load) = 0.237Amps phi = 43 , pf = 0.7 LAG My target power factor (pf) is to be 0.85 , and to...
37. ### Three-phase power factor correction

Hello. I have a doubt regarding the following problem: 1. Homework Statement Calculate capacitors' capacity to rephase (cos(φF) = 1) the load ZL Homework Equations The formula to calculate capacity in this case is: CY = P(tan(φi) - tan(φF))/ωVrms2 or CΔ = P(tan(φi) - tan(φF))/3ωVrms2...
38. ### How does a Synchronous condenser shift the phase

Hi, So when you over-excite the rotor of a synchronous motor, or under-excite the rotor of a synchronous generator, how is the flux actually changing the power factor of the armature to leading? (something to do with the magnitude of the armature reaction flux vector?) That is to ask: by what...
39. ### Apparent power, true power, reactive power and power factor

I calculated the apparent power, true power, reactive power and power factor by using: S=VI S=17684.5 at an angle of 135 In rectangular, that's = -1261.83+j1261.83This is probably a stupid question, but I have S= 17684.5 P= - 1261.83 Q=1261.83 power factor = -0.707 In the marking...
40. ### Power Factor Correction: Capacitor Bank

Typically the power factor penalty that a utility charges is only for inductive lagging power factors or leading ones too? i.e. is the penalty for all PF differences from unity or only on the inductive side? e.g. Say I have a lot of motors which bring the PF down & I add a static capacitor...
41. ### Power Factor of an L-C-R curcuit

Homework Statement A series L-C-R circuit Comprises of a 250mH coil, 0.01 MFD capacitor and a 5W resistor. A dependent voltage defined by e = 2.5cos(80000t) is applied across it. Determine the power factor. [/B] Homework Equations Power Factor = cos(x) = R/Z Z = sqrt^[R^2 + (XL - XC)^2] The...
42. ### Need help proving an equation for power loss in a dielectric

Homework Statement 2. Homework Equations [/B] I am trying to prove the equation $$\frac{\bar{P}}{V}=\frac{1}{2}E_0^2\sigma_{AC}$$ which can be rewritten as  \begin{align} \frac{\bar{P}}{V} &= \frac{1}{2}E_0^2\sigma_{AC}\\ &=\frac{1}{2}E_0^2\ \omega\ \epsilon_0\ \epsilon^{''}_r\\...
43. ### Overall Power Factor of three motors for transformer voltage drop calculation

Hi Suppose I have three motors connected to a single busbar which is fed by a single transformer and suppose that the current into the busbar (i.e. the total current of the transformer secondary) is known. If I wish to calculate the transformer voltage drop the I will obviously need the load...
44. ### 3 Phase Induction Motor Full Load Power Factor

Hi, If the voltage, full load current and full load output power (kW) of a 3 phase induction motor are known, and the efficiency is assumed to be 90% (is this realistic), am I correct in thinking that the full load power factor can be approximated (due to assumed and not actual efficiency) as...
45. ### What is the impact of increased magnetizing current on transformer power factor?

In a transformer , we know that the no-load current has two components , one magnetizing component I0sinphiand other one is the winding loss component i.e. I0cosphi.. if the magntizing current increases in the transformer what is the effect on the power factor??
46. ### Design of Power Factor Correction Capacitor?

Hello... kindly help me out in designing of power capacitor to improve the power factor as the given load is 950 KWatt and power factor is 0.7, as i want to improve the power factor to 0.92 then what formula i should use to design the capacitor as the Voltage line to line are 400Volts
47. ### Need some help -- Power Factor Correction for a Motor

< Mentor Note -- thread moved to HH from the technical engineering forums, so no HH Template is shown > Hi there. I am wondering if someone can help me.. Below is a question and answer, I need help with IV . Where does the 0.51 and 0.28 come from? I've tried cos and sin and thitha but doesn't...
48. ### Why Do Transformers Operate Better at High Power Factor?

I have read that transformers operate on high power factor but I cannot get what is the reason behind it..?? I mean..what if we are having a low power factor..how is that going to affect the working of transformer??
49. ### Can Three Inductors in a Circuit Act Like a Capacitor?

Hyperthetically, say you had three inductors that each were ideal (90 deg lagging each) pf of zero. So there is a circuit with some current limited supply and you series these inductors up and excite the circuit. Is it going to look like a capacitor because the total angle is 270o like a...
50. ### Measuring Power Factor in AC Circuits

How can one measure power factor in AC circuit? http://www.cnktechlabs.com/index_files/cnkdevelopmentkit.htm