# Power factor

#### Ingenieur

##### Senior Member
45 deg from the reactor? Or does the phase angle change with the resistor?
R = 1 ohm (or 1/0 deg)
Xl = 1j ohm (or 1/90 deg) = j 2 Pi (60) L so L = 2.65 mH (assuming a f of 60 Hz)
in parallel

Zeq = 1 (1J) / (1 + 1j) = (1/90 deg) / (1.414/45 deg) = 0.707/45 deg = 0.707 + 0.707j
PF = cos(45) = 0.707

#### Smart \$

##### Esteemed Member
a squared + b squared= c squared?
Yep... good ol' Pythagoras.

And Power Factor is the cosine of the angle formed by "a" and "c", which is mathematically a ÷ c.

If "a" is one unit, "c" is 1.4142 units (the square root of 2) when "b" is also one unit. Then 1 ÷ 1.4142 = 0.7071... your power factor.

#### mivey

##### Senior Member
V1rms = Vrms / sqrt(1 = (THDv /100)^2)
I1rms = Irms / sqrt(1 = (THDi /100)^2).
Typo fix:

V1rms = Vrms / sqrt(1 + (THDv /100)^2)
I1rms = Irms / sqrt(1 + (THDi /100)^2)

#### mivey

##### Senior Member
45 deg from the reactor? Or does the phase angle change with the resistor?
It is a function of both the resistance and reactance. They pull in different directions. It is not that one pulls and the other doesn't.

#### mbrooke

##### Senior Member
It is a function of both the resistance and reactance. They pull in different directions. It is not that one pulls and the other doesn't.

Ok, so one is drawing current at 90*, but as you start to introduce a linear source, some of that 90* current goes towards the linear source shifting it to say 45*? Or is it that both a 0* and 90* current wave exist?

#### Ingenieur

##### Senior Member
Ok, so one is drawing current at 90*, but as you start to introduce a linear source, some of that 90* current goes towards the linear source shifting it to say 45*? Or is it that both a 0* and 90* current wave exist?
all 3 exist
R 0 deg
L 90 deg
source composite 45 deg

think of the V ph being constant 0
the L affects i thru it, lags 90 deg
R has no affect
the source supplies the vector sum
which again divides as above across the loads

#### mbrooke

##### Senior Member
all 3 exist
R 0 deg
L 90 deg
source composite 45 deg

think of the V ph being constant 0
the L affects i thru it, lags 90 deg
R has no affect
the source supplies the vector sum
But the R has a current draw... What do you mean by composite though. I mean, if I could "see" the current and voltage.

#### mivey

##### Senior Member
Ok, so one is drawing current at 90*, but as you start to introduce a linear source, some of that 90* current goes towards the linear source shifting it to say 45*? Or is it that both a 0* and 90* current wave exist?
No. All of the 90d current flows in the inductor. All of the 0d current flow in the resistor. There is no 90d or 0d current in the main pipe as its flow has been modified to a composite flow at 45d. But it is not about the current. Think of the current as an indicator of what is happening in the AC system.

The thinking you are having is the result of bad fundamentals that you need to unlearn. I have preached that here before but some think that it does not matter what you tell somebody in the beginning as it is just an analogy. Now we get to the part where it matters and someone has created a stumbling block for you that you now must overcome. There is no reason to use incorrect fundamentals. Soapbox off.

So here goes. I should spend more time thinking about this response to make it precise but for a start: Stuff does not flow to the AC loads in currents like delivering water down a pipe. You can't deliver blue and yellow water as each spigot would get green water. The AC system is about delivering energy, not current so forget current as it is the sideshow. The energy flows to the load in waves. The energy flows in a medium made up of electric fields and magnetic fields. The current is an indicator of what is going on with the magnetic field. The voltage is an indicator of what is going on with the electric field. Think about that for a start. Field theory is a much better way to look at the system.

For any nay-sayers you can teach fundamentals of field theory starting at an elementary level. It is not complicated unless you have to unlearn bad fundamentals. A good reason to keep fundamentals straight and why it does matter. That soapbox is still hanging around.

Got to go.

#### Open Neutral

##### Senior Member
One question I have never resolved in my head is this:

Thanks to Tesla, I suppose, we leave in an inductive world. The usual issue is how much Xc to add to get the power factor more palatable.
What is the {practical} consequence of the other case, i.e. you have too much Xc in the picture?

The obvious case is when you've added enough capacitors errr.. synchronous converters, but then oops, the 3000 HP mumblewonker shuts down. Now your pf is {say} .8 but the other way.

The issues then?

#### mbrooke

##### Senior Member
No. All of the 90d current flows in the inductor. All of the 0d current flow in the resistor. There is no 90d or 0d current in the main pipe as its flow has been modified to a composite flow at 45d. But it is not about the current. Think of the current as an indicator of what is happening in the AC system.
But correct me though, as the inductor discharges energy (electrons) into the system it somehow shifts the wave because its adding electrons?

The thinking you are having is the result of bad fundamentals that you need to unlearn. I have preached that here before but some think that it does not matter what you tell somebody in the beginning as it is just an analogy. Now we get to the part where it matters and someone has created a stumbling block for you that you now must overcome. There is no reason to use incorrect fundamentals. Soapbox off.

I do agree to some extent, but you also have to keep in mind the audience. When teaching to high school or people in their first year of college, remotely grasping true theoretical or metaphysical ideas is next to impossible for the average student, even many who would otherwise be considered bright or gifted simply because its well beyond any frame of reference they have access to. Both because the brain is still developing at that age and the fact in our daily lives we always encounter things we can verify with our 5 senses. Explaining something beyond the 5 senses obeying rules differing from those we are familiar with needs a starting point, and analogies are imo a perfect way to bridge known reality with theory. You need a reference to do so. Perhaps not perfect, but in order to "get it" one needs to start some place. Otherwise in the end a person just ends up parroting something they were never able to grasp. Yes I agree at some point you "unlearn" analogies but I would say that is part of a person's evolution of knowledge much like a child plays with toys and eventually out grows them. While those toys may not reflect the real world, the primitive skills learned playing with a toy crane eventually holds the foundation to the far more complicated skills (and psychological) comfort into operating a real one.

Look at it like this. When Mike Holt was explaining branch feeder AFCIs, he brought up how a capacitor was used to time the device. Of course, capacitors were more common then quartz crystals in timing everything down to windshield wipers. Trying to start off with the rate of charge vs discharge to trigger a triac or the like is to big of a jump. However when he explained it was like sew saw with a weight at one end and a jar of water in the other with a hole in it, and that if you can fill the jar faster then water is leaving the hole it will over come the weight; the rudimentary concept of how a capacitor is used for timing begins to click even though there is no such taking place within the circuit on any level. Another example is relativity. While Space Time is all around us, imagining its relation to gravity or time dilation is tricky. The math proves it, but before a physics student "gets it" its often best to take a trampoline, draw equal lines on it, and then place a bowling ball in the center. Add a golf ball to the edge swirling around the side to show orbit as a bonus. Once that happens, while not 100% anatonically or dimensionally correct, it provides the bridge between observable day to day reality and something into the realm going beyond perception.

While I am highly critical of education, IMHO analogies are a powerful tool in the classroom. Perhaps I am biased, but analogies have helped me a great deal when learning anything new. Ditto to relation or tying to past courses.

So here goes. I should spend more time thinking about this response to make it precise but for a start: Stuff does not flow to the AC loads in currents like delivering water down a pipe. You can't deliver blue and yellow water as each spigot would get green water. The AC system is about delivering energy, not current so forget current as it is the sideshow. The energy flows to the load in waves. The energy flows in a medium made up of electric fields and magnetic fields.
Correct me if I am wrong, but aren't electric and magnetic fields the byproduct of electrons jumping from atoms to atoms? And for give me, (this is really wild and probably stupid, Im just guessing :lol but when those electrons are in free space during the jump, they effect space-time producing the phenomenon that we see?

The current is an indicator of what is going on with the magnetic field. The voltage is an indicator of what is going on with the electric field. Think about that for a start. Field theory is a much better way to look at the system.

I may need help here. Field theory is not something I ever touched in depth, and I do agree the analogy no longer holds but I am up for it.

For any nay-sayers you can teach fundamentals of field theory starting at an elementary level. It is not complicated unless you have to unlearn bad fundamentals. A good reason to keep fundamentals straight and why it does matter. That soapbox is still hanging around.

Got to go.
I don't mind, speak your mind, very eye opening

#### Ingenieur

##### Senior Member
But the R has a current draw... What do you mean by composite though. I mean, if I could "see" the current and voltage.
the i and v thru R are in phase
composite = made up of the R and L components
google phase shift and many graphical examples will be available

#### Ingenieur

##### Senior Member
V = L di/dt
when i is at a peak the slope/derivative is 0 so v is zero (crossing zero)
in other words as you go earlier in time v peaks first and i lags 1/4 cycle or 90 deg

i = C dv/dt
when v is at a peak the slope/derivative is 0 so i is zero (crossing zero)
in other words as you go earlier in time i peaks first and v lags by 1/4 cycle or 90 deg

there is a reason calc and trig are taught before EM field, linear circuits, etc
it allows you to conceptualize
as english is the 'language' of history, etc
math is the 'language' of EE/physics/etc

#### mbrooke

##### Senior Member
Ok, thanks, that is helping me understand. Any graphed examples or oscilloscope examples? I want to Google Phase shift, but as always with Google you have no idea if the information is correct.

#### Sahib

##### Senior Member
45 deg from the reactor? Or does the phase angle change with the resistor?
You can change the phase angle either by changing the resistance or the inductance or even both.

#### Besoeker

##### Senior Member
Ok, thanks, that is helping me understand. Any graphed examples or oscilloscope examples? I want to Google Phase shift, but as always with Google you have no idea if the information is correct.
Here's one I prepared earlier:

#### mbrooke

##### Senior Member
Why doesnt the power wave appear to be a sign wave?

#### Besoeker

##### Senior Member
Why doesnt the power wave appear to be a sign wave?
It is but at twice the frequency of the fundamental.

#### mbrooke

##### Senior Member
It is but at twice the frequency of the fundamental.
Twice? :dunce: Or is it just the way its measured (counted twice in one cycle)?

#### Besoeker

##### Senior Member
Twice? :dunce: Or is it just the way its measured (counted twice in one cycle)?
The current and voltage both go through a cycle. When both are positive at the same time you get positive power. When both are negative at the same time you get positive power. That happens twice per cycle. Hence double the fundamental frequency.

#### Ingenieur

##### Senior Member
It is twice the fundamental freq
and offset positive

sin(2x) = 2sin(x)cos(x)