Power factor

[mbrooke]

What determines low power factor or more precisely why some loads have varying power factor compared to others? Say I had an inductor. The current lags by 90*, and no other load. My power factor would be zero, correct? But if I add a resistor in parellel drawing equal current my power factor would be 50%? And if I add a capacitor of equal current (in parallel) my power factor is 100%? Does this accurately represent what goes on in most loads being a mixture of capacitance, inductance and resistance hence VA?

 

[Ingenieur]

What determines low power factor or more precisely why some loads have varying power factor compared to others? Say I had an inductor. The current lags by 90*, and no other load. My power factor would be zero, correct? But if I add a resistor in parellel drawing equal current my power factor would be 50%? And if I add a capacitor of equal current (in parallel) my power factor is 100%? Does this accurately represent what goes on in most loads being a mixture of capacitance, inductance and resistance hence VA?

pretty much
let's look at it in series, math is easier
R = 1 ohm
Xl = 1 ohm
Xc = 1 ohm

X = reactance
Xl = j 2 Pi f L or j Xl
Xc = 1 / ( j 2 Pi f C) or -j Xc
j = sqrt (-1)
f = system frequency
Pi = 3.14159..., not apple

let Zeq be total ckt impedance
if R: Zeq = R
if R and Xl: Zeq = R + jXl
if R, Xl and Xc: Zeq = R + jXl +(-jXc) or R + j(Xl -Xc)
so if Xc = Xl the reactive portion cancels

PF = cos (arctan ((Xl-Xc)/R))
so if (Xl - Xc) = 0 PF=1
as the ratio varies so does the PF
it can be leading/lagging or positive/negative depending on convention
Xl > Xc is usually considered lagging/negative, absorbs reactive power
Xc > Xl is usually considered leading/positive, supplies reactive power
although it actually is an exchange

the net power factor is the sum of the R, L and C values
so a lot of L, a little C with mostly R will drop it below 1 (lagging)

 

[mbrooke]

pretty much
let's look at it in series, math is easier
R = 1 ohm
Xl = 1 ohm
Xc = 1 ohm

X = reactance
Xl = j 2 Pi f L or j Xl
Xc = 1 / ( j 2 Pi f C) or -j Xc
j = sqrt (-1)
f = system frequency
Pi = 3.14159..., not apple

let Zeq be total ckt impedance
if R: Zeq = R
if R and Xl: Zeq = R + jXl
if R, Xl and Xc: Zeq = R + jXl +(-jXc) or R + j(Xl -Xc)
so if Xc = Xl the reactive portion cancels

PF = cos (arctan ((Xl-Xc)/R))
so if (Xl - Xc) = 0 PF=1
as the ratio varies so does the PF
it can be leading/lagging or positive/negative depending on convention
Xl > Xc is usually considered lagging/negative, absorbs reactive power
Xc > Xl is usually considered leading/positive, supplies reactive power
although it actually is an exchange

the net power factor is the sum of the R, L and C values
so a lot of L, a little C with mostly R will drop it below 1 (lagging)

Awesome incite, thank

But how does on go about net power factor? Consider an HID lamp with a reactive ballast. Its essentially a resistor in series with a reactor, yet the power factor can vary all over the place.

 

[mbrooke]

Also, in your series example, Im thinking a capacitive coupled voltage transformer? The reactor cancels the capacitor (eliminates phase shift) but the two in series still limit current/voltage?

Further, a capacitor generates vars and a reactor absorbs them in common power system terms? Where does a generator stand? If often see 3 phase generators with something like 0.85 power factor lagging.

 

[Besoeker]

If often see 3 phase generators with something like 0.85 power factor lagging.

That, in my experience, is often related to the prime nover. A 100kVA generator may be rated at that at 0.8PF. The prime mover may thus be rated at 80kW.

 

[mbrooke]

That, in my experience, is often related to the prime nover. A 100kVA generator may be rated at that at 0.8PF. The prime mover may thus be rated at 80kW.

Is this because current is flowing through the generator coils, but its not actually putting resistance on the prime mover?

 

[GoldDigger]

Is this because current is flowing through the generator coils, but its not actually putting resistance on the prime mover?

You got it exactly.
In fact it is "pushing and pulling" the prime mover every half cycle but averaging out to zero with a single phase generator but not even doing that for three phase when the reactive load is balanced.

And depending on the excitation and regulation scheme the output may not be stable if you go worse than .8 inductive or go capacitive at all. At less than full output it will tolerate a heavier inductive power factor.

Since the actual PF of the current from a generator is dependent entirely on the load, I like to think of the generator as *accepting* a power factor of .8 rather than *having* a power factor of .8.

 

[mbrooke]

You got it exactly.
In fact it is "pushing and pulling" the prime mover every half cycle but averaging out to zero with a single phase generator but not even doing that for three phase when the reactive load is balanced.

And depending on the excitation and regulation scheme the output may not be stable if you go worse than .8 inductive or go capacitive at all. At less than full output it will tolerate a heavier inductive power factor.

Since the actual PF of the current from a generator is dependent entirely on the load, I like to think of the generator as *accepting* a power factor of .8 rather than *having* a power factor of .8.

That makes sense. So the labelled PF is basically saying how the KW was derived taking PF into consideration?

 

[Ingenieur]

Also, in your series example, Im thinking a capacitive coupled voltage transformer? The reactor cancels the capacitor (eliminates phase shift) but the two in series still limit current/voltage?

Further, a capacitor generates vars and a reactor absorbs them in common power system terms? Where does a generator stand? If often see 3 phase generators with something like 0.85 power factor lagging.

yes
there still is voltage drop V drop because there is an Z
basic Z relationships
Xl or L as f increases so does Z
Xc or C as f increases Z goes down

a generator operates at a leading PF
the rating of 0.9 or whatever describes the KW/KVA rating at a specified PF (assumed lagging as most loads are)


but no real power

 

[Ingenieur]

Awesome incite, thank

But how does on go about net power factor? Consider an HID lamp with a reactive ballast. Its essentially a resistor in series with a reactor, yet the power factor can vary all over the place.

it may vary due to the L portion but should be fairly constant for a given F and L

 

[mbrooke]

yes
there still is voltage drop V drop because there is an Z
basic Z relationships
Xl or L as f increases so does Z
Xc or C as f increases Z goes down

a generator operates at a leading PF
the rating of 0.9 or whatever describes the KW/KVA rating at a specified PF (assumed lagging as most loads are)


but no real power

Can you go further in a generator producing leading power factor?

 

[Ingenieur]

Can you go further in a generator producing leading power factor?

in a motor the rotor (field) slips behind the stator (armature), positive slip, ie, is loaded or under drag, motor supplies power to the load
in a generator it leads, negative slip, being driven, or the driver (wind, diesel, turbine, etc) supplies the power to the generator
the difference is described by the rotor angle

if you have an R and net L system the reactive power must be supplied, it is supplied by the generator
utilities hate it
although it requires negligible fuel it does take up line capacity that they can't bill for lol

 

[mbrooke]

in a motor the rotor (field) slips behind the stator (armature), positive slip, ie, is loaded or under drag, motor supplies power to the load
in a generator it leads, negative slip, being driven, or the driver (wind, diesel, turbine, etc) supplies the power to the generator
the difference is described by the rotor angle

if you have an R and net L system the reactive power must be supplied, it is supplied by the generator
utilities hate it
although it requires negligible fuel it does take up line capacity that they can't bill for lol

But doesnt this change when generators are paralleled? For example increasing the voltage increases the VARs, and rotor angle dictates KW load the generator picks up?

 

[jumper]

Since the actual PF of the current from a generator is dependent entirely on the load, I like to think of the generator as *accepting* a power factor of .8 rather than *having* a power factor of .8.

Aw ya gotta post something like that and make me think.:rant:

J/K Goldy

Let me wrap my head around this later, with any luck I may understand it....maybe....we"ll see.

 

[mbrooke]

Aw ya gotta post something like that and make me think.:rant:

J/K Goldy

Let me wrap my head around this later, with any luck I may understand it....maybe....we"ll see.

Im in the same boat as you :lol::blink:

 

[jumper]

Im in the same boat as you :lol::blink:

Goldy, Bes, and Iggy have chimed in so far, this could be interesting and educational. Them fellers are quite smart and I like learning/understanding.

 

[Besoeker]

Goldy, Bes, and Iggy have chimed in so far, this could be interesting and educational. Them fellers are quite smart and I like learning/understanding.

Kind words if I may say so, sir.

Goldilocks is spot on as usual. It's the load that determines power factor.
The generator is usually rated in kVA. Since the voltage is fixed, the kVA tells you the maximum current you can draw from the generator.
The 0.8 PF tells you the maximum power in kW. (kW/kVA is PF).

 

[Ingenieur]

The Gent who said I have some smarts
please confirm with my wife

here's a data sheet for squirrel cage induction generator
50 Hz
3 pole pairs or 6 poles
the electrical speed is 120 x 50 / 6 = 1000 rpm
but note it's rated speed is 1007.2
and the slip is negative -0.0072
mech w = 1000 x (1 - (-0.0072)) = 1007.2
so mech > elec speed
a motor is the opposite, say 1800 vs 1760

in this case the pf is negative or leading
both the machine and load have a pf
the load will determine where the machine operates
I just learned a technique called a Parks transformation into the dq domain
basically converts the mess into DC components
much easier to manipulate and visualize

 

[Ingenieur]

Here's another way to look at it

a generator and a reactive load
since it is a loop Ig - Il = 0 or Ig = Il at any node
and Vg + Vl = 0 or Vg = -Vl for the loop
basic KVL / KCL
and Pg + Pl = 0 or Pg = -Pl or Vg Ig pfg = Vl Il pfl
substituting
-Vl Il pfg = Vl Il pfl
cancelling
-pfg = plf
same magnitude opposite sign or lead/lag
another way of expressing it the sum of pf's = 0

 

[mbrooke]

I will post more tomorrow, but page 44 and on has some really good examples:


https://books.google.com/books?id=4...ge&q=Power System Analysis and Design&f=false