THE PHYSICS OF... POWER

[Carultch]

Active power is active power. It's as simple as that.

There are also other terms that include the word "power" that are not active power. Any of these terms use the short-hand "power" when the clarifier is dropped. Arguing that one term is or isn't "power" hinges on the definition used and is kinda pointless. But carry on if you must.

Power is the rate at which energy is converted between forms, or transferred from one system to another.

With real power, there is energy transferred from a source to a load.
With reactive power, there is energy transferred as capacitors charge/discharge, and as inductors accelerate their magnetic field.
With apparent power, this is simply a mathematical product of a special time "average" of Volts, and a special time "average" of Amps, that would seem to indicate power transmitted, until you realize that the Volts and Amps are not synchornized.

 

[jtinge]

THE PHYSICS OF... POWER

pf is ratio of beer to mug size.

You're right. Pf=kw/kVA. Thanks for the correction.

 

[dionysius]

I'll join in as well. Otherwise you have a DC component as was said earlier by others.

Count me in also. In math the imaginary number plane is resorted to to describe reactance. As a mental gymnastic exercise just cogitate on Euler's almost metaphysical identity with the RHS transposed and let me know what you see because it shows that imaginary numbers are equated to real numbers which is completely counter intuitive:

(e ** i * Pi ) + 1 = 0

 

[Carultch]

Count me in also. In math the imaginary number plane is resorted to to describe reactance. As a mental gymnastic exercise just cogitate on Euler's almost metaphysical identity with the RHS transposed and let me know what you see because it shows that imaginary numbers are equated to real numbers which is completely counter intuitive:

(e ** i * Pi ) + 1 = 0

It's not that imaginary numbers are equal to real numbers, it's that they are quantities within the same mathematical system of numbers, that we just aren't immediately aware of.

Gauss said that it was a very counterproductive choice of words to call them imaginary. He said that it would be better if we had called them direct numbers (positive real), inverse numbers (negative real), and lateral numbers (imaginary). I wonder what he would've wanted to call complex numbers, the sum imaginary and real.

Here's an introductory explanation to why e^(i*pi) = -1, even though those three numbers, e, i, and pi, all seem to have nothing to do with one another.
https://www.youtube.com/watch?v=Yi3bT-82O5s

 

[dionysius]

It's not that imaginary numbers are equal to real numbers, it's that they are quantities within the same mathematical system of numbers, that we just aren't immediately aware of.

Gauss said that it was a very counterproductive choice of words to call them imaginary. He said that it would be better if we had called them direct numbers (positive real), inverse numbers (negative real), and lateral numbers (imaginary). I wonder what he would've wanted to call complex numbers, the sum imaginary and real.

Here's an introductory explanation to why e^(i*pi) = -1, even though those three numbers, e, i, and pi, all seem to have nothing to do with one another.
https://www.youtube.com/watch?v=Yi3bT-82O5s

The difficulty arises since we are 3D beings in multi-dimensional space.

 

[Carultch]

The difficulty arises since we are 3D beings in multi-dimensional space.

Oops! Wrong link. Correction:
https://www.youtube.com/watch?v=-dhHrg-KbJ0

 

[FionaZuppa]

can you take the last 4 pages and normalize all the jargon using unit power of watt or J/sec

 

[Besoeker]

can you take the last 4 pages and normalize all the jargon using unit power of watt or J/sec

Common sense ain't as common as it's purported to be................

 

[Carultch]

can you take the last 4 pages and normalize all the jargon using unit power of watt or J/sec

There is real power that is measured in Watts, or Joules per second, which is energy transferred from source to load. This is what you get if you accumulate current * voltage at every instant throughout the cycle.

When the cycle of current is not synchronized with the cycle of voltage, and you multiply an "average" of each together, you don't get the actual power in Watts. Instead you get the apparent power, which we measure in Volt-Amperes instead of Watts. This is useful to know, because it affects the sizing of transmission and distribution equipment.

The nominal voltages and currents you usually see in the electrical industry are a special kind of time "average" called a root mean square. I'll leave it to you to read up on what that really is, and why we use it. The basic idea is that it is an equivalent DC voltage or current that would transmit the same power to a pure resistive load.

 

[jtinge]

When the cycle of current is not synchronized with the cycle of voltage, and you multiply an "average" of each together, you don't get the actual power in Watts. Instead you get the apparent power, which we measure in Volt-Amperes instead of Watts. This is useful to know, because it affects the sizing of transmission and distribution equipment.

Or beer mugs....

 

[Ingenieur]

V_(V) = E_(J) / Q_(C)
So
volt = joule / coulomb
ampere = coulomb / second
volt ampere or va
= joule / coulomb x coulomb / second = joule / second
= watt
hmmmm a unit of power
so S is power, as is Q

 

[FionaZuppa]

There is real power that is measured in Watts, or Joules per second, which is energy transferred from source to load. This is what you get if you accumulate current * voltage at every instant throughout the cycle.

if you had a load where voltage lagged current by 180 degrees would you have any power?

i recall similar chatter in another thread talking about how poco bills their kWh, different billing methods will show different bill even though power was the same.

 

[GoldDigger]

if you had a load where voltage lagged current by 180 degrees would you have any power?

Such a "load" would more commonly be called a generator, and real energy would be moving, just in the opposite direction to what the energy flow would be if it were a load.
The power associated with this generator would be exactly the same as the power associated with an equivalent load, just with the opposite sign (direction).

 

[FionaZuppa]

Such a "load" would more commonly be called a generator, and real energy would be moving, just in the opposite direction to what the energy flow would be if it were a load.
The power associated with this generator would be exactly the same as the power associated with an equivalent load, just with the opposite sign (direction).

can you show me two time slices where the scalar power turns into vectors that have opposite signs?

 

[GoldDigger]

can you show me two time slices where the scalar power turns into vectors that have opposite signs?

That happens with a 90 degree offset. Starting at a voltage zero crossing, the integral over each 1/4 cycle of I(t)V(t)dt has the opposite sign from the preceding 1/4 cycle.
It does not turn into a vector with opposite sign, it is simply a scalar with opposite sign, which can be interpreted as power transferred in the opposite direction. When you add the positive and negative values the result is zero over a half (and therefore also over a full) cycle.

I suspect that you really meant to specify a 90 degree offset, but my answer addressed a 180 degree offset.

Like the people who say:"I really turned my life around 360 degrees."

 

[FionaZuppa]

That happens with a 90 degree offset. Starting at a voltage zero crossing, the integral over each 1/4 cycle of I(t)V(t)dt has the opposite sign from the preceding 1/4 cycle.
It does not turn into a vector with opposite sign, it is simply a scalar with opposite sign, which can be interpreted as power transferred in the opposite direction. When you add the positive and negative values the result is zero over a half (and therefore also over a full) cycle.

I suspect that you really meant to specify a 90 degree offset, but my answer addressed a 180 degree offset.

Like the people who say:"I really turned my life around 360 degrees."

scalars cant use the word "direction". if it has direction then its a vector :thumbsup:

next is, show me negative power, i say no such thing. the energy is transferred from generator to load, one direction only regardless of AC, the "power" is consumed on the load side.
why not just apply your equations as if I and V have passed through a full wave rectifier?

 

[wwhitney]

scalars cant use the word "direction". if it has direction then its a vector

Sure they can, positive or negative, i.e. direction in one dimension.

Cheers, Wayne

 

[wwhitney]

next is, show me negative power, i say no such thing.

P = I * V [instantaneously]
E_(a,b) = integral_(a,b) I * V [total energy transferred over the time interval from a to b]
P_(a,b) = E_(a,b) / (b - a) [average power over the time interval from a to b]

Say I = sin (t), and V = sin (t + pi/2) = cos (t) [pi/2 = 90 degrees in radians]

E_(a,b) = integral_(a,b) sin(t) cos(t)
= integral_(a,b) 1/2 sin(2t)
= - 1/2 cos(2t) |_(a,b)
= - 1/2 (cos(2b) - cos(2a))

Consider a few different intervals:

"1st" quarter cycle
E_(0, pi/2) = -1/2 (cos(pi) - cos(0)) = -1/2 (-1 - 1) = 1
P_(0, pi/2) = 2 / pi

Next quarter cycle
E_(pi/2, pi) = -1/2 (cos(2pi) - cos(pi)) = -1/2 (1 - (-1)) = -1
P_(pi/2, pi) = - 2 / pi

Half cycle
E_(0, pi) = E(0, pi/2) + E(pi/2, pi) = 0
P_(0, pi) = 0

Cheers, Wayne

 

[FionaZuppa]

Sure they can, positive or negative, i.e. direction in one dimension.

Cheers, Wayne

so then its a vector :?

next is, show me negative AND positive power between generator and load where the load is consuming 100kW

Wayne, you need to wrap the absolute math symbol around your answers :thumbsup:, no such thing as "-1" power, you cannot "negatively consume" energy.

your net power is not 1 + (-1) now is it, net power is |1|+|-1|

 

[wwhitney]

so then its a vector :?

Well, after the choice of a unit vector, a one dimensional vector space is "the same thing" as the scalar field. Not sure it is worth distinguishing in this case.

Wayne, you need to wrap the absolute math symbol around your answers :thumbsup:, no such thing as "-1" power, you cannot "negatively consume" energy.

Nope, you're mistaken. Once you choose a direction to represent positive power transfer (e.g. from the "generator" to the "load"), then negative power just means that energy is being transferred in the reverse direction, i.e. from the "load" to the "generator". Which occurs every other quarter cycle with a purely reactive load, so that the net energy transfer is 0.

Cheers, Wayne