Re: Generator KVAR?
When I have two pretty sharp people explaining the error of my thinking, it really makes me re-think my reasoning.
I'm thinking we are looking at two different things. If I am translating correctly, most of your (plural) posts are dealing only with Real Power (P). The concept I am looking at is Complex Power, S = P + jQ
Here is what I'm hearing that is causing me difficultly:
1. Power is not a sinusoidal function.
2. Power is not the cross product of the V and I vectors.
3. Power is not a vector. It has only magnitude, no direction.
Here is my thinking:
Mathematics is (are?) the abstract techniques we use to model real phenomena. The model is not reality. For example, voltage is represented by a vector, current is represented by a vector. Vectors and vector math are abstract techniques we use to represent\describe\predict the V, I behavior.
Power triangles, Parallel law of addition, VIcos(theta), V X I, V (dot) I, complex numbers, polar coordinates, rectangular coordinates, matrices, power triangles - all methods of dealing with vectors, which we use to represent the behavior of reality.
Originally posted by rattus:
... The product of two sinusoids is not another sinusoid. The power wave for a resistive load is sin squared and looks something like full wave rectified DC. It is all positive and is certainly not sinusoidal. ...
I would tend not to agree. For the case of a resistive load, sin^2(x) = 1/2 - 1/2 cos(2x)
Yes, it?s all positive, but it is sinusoidal. Okay, it's co-sinusoidal. But if we wait 12.5ms, it will be sinusoidal
Originally posted by rattus:
... You drop the phase angle from the voltage and current phasors and you are left with the RMS magnitudes. Multiply these scalars together for apparent power. Throw in PF, another scalar, for real power. ...
Well, that would be called the "dot product" of the V, I vectors. Yes, the answer is a scalar. For a resistive load, this works well.
The Complex Power vector derived from V X I (cross product) also contains the same information. It can be represented in rectangular coordinates as S = P + jQ, where P is the projection of S on the real axis. It can also be represented in Polar Coordinates as (R, theta), where R = magnitude(S) and theta = the phase angle. And the power triangle mentioned in a previous post is just another method to handle the vector algebra.
The Complex Power vector also contains additional information. In particular the phase angle tells the reactive nature of the load.
Originally posted by rattus:
... You can add real and reactive power as you would add two vectors, but that does not make the sum a vector. ...
Why wouldn't it be a vector? This representation of the Complex Power vector has magnitude and direction.
Originally posted by rattus:
... The angle of the power triangle is arccos(PF); it is not the sum of the voltage and current angles. ...
I'm lost on this one. Yes, the power triangle angle is arcos(pf). But pf comes from the cos(theta) in the power triangle. And isn?t that the same angle as the angle between the V and I vectors.
Assuming only one generating source and the frame of reference is either the V vector direction or the I vector direction, then it seems the angle is the sum of the voltage and current vectors. As far as a power triangle not being a vector, okay, it is just another method of handling the vector algebra.
Originally posted by Bob:
quote: ... The problem is, for practical purposes, the "math" appears to be the same, so we attribute "vectorness" to power. But in "real life" there is no "relative change in position" for power as there is with current and voltage. (And don't try to make the argument of generation / consumption - it won't fly - you know the "vector" diagram isn't showing that)
I'm not sure what part of real life you are looking at.
As far as a "relative change in position", take the case on an industrial plant. One adds the real power to the reactive power. Convention is: positive real power (P) is to the right; positive reactive power (Q) is up and is defined as inductive; positive phase angle is anti-clockwise from the positive P axis.
In this case, the power company measures it, measures the phase angle, and it is close enough to real life that they will charge extra real dollars if the phase angle gets too large.
Now let?s take the case of two generating plants, feeding a common line. The only one I am familiar with is the one around here. The local generation is 120 MW. There is a 350 mile tie line to the "big city" generation - could be as much as 1000 MW. They sell power to us. In conversation with the transmission line guys, they talk about "loading the line with VARS? They could do that by either increasing the power angle at the far away plant or they could switch in capacitors along the line - VAR correction they call it. All consistent with vector operations, and vector algebra.
Humm ? I wonder if one can load the line with VARS from the close end, and still get the power to transfer from the far end. I?ll have to ask the transmission line guys next time I see them.
Originally posted by Bob:
quote:
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Originally posted by coulter
"Complex power looks like a vector to me."
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That is indeed the problem - it looks like one.
... The problem is, for practical purposes, the "math" appears to be the same, so we attribute "vectorness" to power.
... Apparent Power" and "Reactive Power" are pseudo-vectors created to make the math work.
Humm ... A "vector" is a mathematical abstract concept used to calculate/predict a real world phenomenon. A "pseudo-vector" is a mathematical abstract extension of a vector. (carl's definitions)
So, if I am translating you correctly, Complex Power looks like a vector and the vector math works, but it?s not a vector.
Well, okay, but if we are using an abstract concept and an extension of an abstract concept to describe a real world event, and the math works, accurately predicting the behavior of the phenomena, why not call it a vector.
carl
