One of the most interesting paragraphs I have ever read

[DejanC]

So in my studies of electrical engineering, I found some interesting information. During my research I found some interesting perspective from one of the legendary electrical engineers Charles Prometeus Steinmetz. He was the father of the phasor analysis of AC signals we still use today. A genius when it came to all things electrical engineering during his era.

He made a statement about oscillating currents which he defines in the attached paper. Please refer to the image for what is a profound statement on reactive power in the context of oscillating currents. What I find fascinating is the uniqueness of this phenomenon compared to any AC phenomenon as he mentions. We are always taught reactive power can not have any impact on real power, but here it shows a NEGATIVE energy component of the REAL power! It affects the REAL part of the impedance! Amazing? Or well known?

How can this be? How is this not mentioned regularly?

[ejeffrey]

I don't know the difference between an "oscillating current circuit" and an "alternating current circuit".  Without more context it's hard to say what this is all about.

[woofy]

I think it means at resonance, as opposed to any frequency. In these circumstances the impedance of a series LC can approach zero. In the same way a parallel LC  can be very high impedance.

[Just_another_Dave]

I don't know the difference between an "oscillating current circuit" and an "alternating current circuit".  Without more context it's hard to say what this is all about.

Could “oscillating current circuit” refer to an AC current with a DC offset that causes it to never change its sign?

Is any case, the behavior described in the text reminds me LC resonances

[DejanC]

Oscillating currents are described in the paper i attached in the original post. He clearly states this is something that doesn't occur in AC. Notice how the real part of the impedance has a contribution from the reactance! Incredible.

[DejanC]

Can no technical expert explain this? Please don't tell me Steinmetz was wrong...that is just foolish

[IanB]

The author is apparently talking about the analysis of LC resonant circuits.

In a series LC circuit, the impedance becomes zero at the resonant frequency.

When doing the mathematical analysis of this arrangement, there are some negative terms that cancel out positive terms, which is how a resulting impedance of zero can arise.

There is nothing mysterious about this, it is just mathematics.

And no, it does not affect the real part of the impedance. In a series RLC, circuit the impedance at the resonant frequency is R, and is minimized.

Sometimes old-fashioned language can be confusing to modern ears, since we are accustomed to different ways of expressing things.

[DejanC]

Two problems with the above post. First this is stated by Steinmetz who literally wrote textbooks on AC phenomenon. He was aware of LC resonances. He also specifically describes this phenomenon as something that does not happen on AC circuits. Finally, he shows in the expression of impedance that the reactancea counteract the resistance!

Please read carefully.

[IanB]

Two problems with the above post. First this is stated by Steinmetz who literally wrote textbooks on AC phenomenon. He was aware of LC resonances. He also specifically describes this phenomenon as something that does not happen on AC circuits. Finally, he shows in the expression of impedance that the reactancea counteract the resistance!

Please read carefully.

I just went to the trouble of downloading and reading the attached PDF. Let's quote the opening paragraphs:

Alternating currents have found very extensive application for light and power. Period and amplitude are constant in the alternating current.

A very important class are the currents of constant period, but geometrically varying amplitude, that is, currents in which the amplitude of each following wave bears to that of the preceding wave a constant ratio. Such currents consist of a series of waves of constant length, decreasing in amplitude, that is in strength, in constant proportion. They are called oscillating currents

The author is writing about isolated RLC resonant circuits. He specifically addresses underdamped systems where oscillations will continue once started. If you start oscillations in such a circuit, they will, in theory, continue forever since the amplitude decays to zero only after infinite time.

If you construct such a circuit where the resistance is zero, then in theory the oscillations will continue forever without decaying in amplitude, since the impedance of the LC portion is zero, and R is zero as given.

There cannot be a circuit where R > 0 and where oscillations continue forever without decay, since this would be a perpetual motion machine. If the text seems to imply this, it is because author's language is confusing. You have to read between the lines when interpreting the text.

For the best understanding, go through the whole chapter paragraph by paragraph, and do the mathematical derivation yourself on a notepad, so you see how each equation is derived.

[DejanC]

I don't see any mistake in his derivation, the only caveat is he is talking about apparent impedance, real part and imaginary part. The key here is he is assuming a damped oscillation. However, I do not see a mistake in his math and the real part of the impedance is affected by the circuits reactance. Remarkable, isn't it?

As far as perpetual motion, I have some thoughts on that but prefer not to share them here. It goes well beyond EE and into physics. I could make an argument either way with well known physics.

[IanB]

However, I do not see a mistake in his math and the real part of the impedance is affected by the circuits reactance.

In which equation do you see this? Or where do you see any words to this effect in the text?

Also, there is a huge, glaring omission in the whole of the chapter. Can you point out what it is?

[DejanC]

I see in the equation I posted in the OP that shows U = 0 and the two subsequent equations. What is the omission?

[IanB]

I see in the equation I posted in the OP that shows U = 0 and the two subsequent equations. What is the omission?

That equation simply states that a particular mathematical variable "U" under certain conditions is equal to zero. If you read any more into it than that, then you are extrapolating beyond the text.

The omission I refer to is the explicit inclusion of time as a variable in the system analysis.

If you take an isolated RLC network and analyze it in a modern manner, you get a second order differential equation that has a solution of the form x = f(t) (where x can be any variable in the system). You can solve this differential equation in various ways, perhaps by the use of Laplace transforms.

To consider the decaying system, you consider the particular solution of this differential equation where the initial condition could be an impulse given by the Dirac delta function. In the under-damped case this solution evolves into a decaying sine wave.

Now consider the definition of impedance: Z = V/I, or in this case the apparent impedance U = V/I. For U to be zero it means V must be zero, and therefore the current I is present with no superimposed voltage. How is this? It is because the driving force for the current comes from the stored energy in the system, which is gradually dissipating, cycle by cycle. Therefore you can have current flowing with no externally imposed voltage.

Steinmetz has performed a pseudo-static analysis where he considers the decay ratio as an algebraic property of the system, and thus the stored energy is slightly obscured by the analysis. He does, however, refer to stored energy in the text to explain what is going on.

[jonpaul]

See both Charles Proteus Steinmetz's landmark books


Theory and Calculation of Alternating Current Phenomena 1900

Theory And Calculation Of Transient Electric Phenomena And Oscillations 1907

Jon

[DejanC]

Thank you for your analysis. I agree with it in general however I am not reading into it saying that the impedance is zero. He specifically states that and follows it by saying U = 0, so obviously U is the impedance. You even used it in your equation as such.

I just think its a very interesting phenomenon and shows an instance where the reactance plays a role in the real part of the impedance and power. This case is usually ignored and it shouldn't be. We are always drilled that reactance is always VAR and not Watts. And that is not true. I wonder why this is studied more in detail.

I don’t believe Steinmetz made any omission really.

[IanB]

The decrease in stored energy over one cycle is exactly equal to the real power dissipated by the resistance R in the system. You have "loss of stored energy" (negative) plus "real power dissipated" (positive) equals zero. If you want to say the reactance plays a role in the real part of the impedance and power, then the reactance is where the energy is stored, and that energy is real, and can contribute to real power dissipation.

We are always drilled that reactance is always VAR and not Watts. And that is not true. I wonder why this is studied more in detail.

The fact that reactive devices like capacitors and inductors store energy is elementary, and is studied in detail in foundational material.

Being drilled is unfortunately learning by rote, and does not contribute to understanding.

AC circuit theory is a simplified analysis where amplitude and frequency are invariant with time. It is therefore a form of "steady state" analysis, where the steady state is a cyclic steady state in which the average behavior over time is always the same. In the special case of AC circuit theory you have that reactance is VAR and not watts, because there is no change in the average amount of stored energy over time. Therefore all power flows are due to transfer through the system, and are not due to accumulation or discharge of energy in the system.

However, AC circuit theory is very much a special case, and not the general case. The general case is transient analysis, such as when a motor is switched on, or a transformer is energized, or when a circuit breaker trips. AC circuit theory does not work for these cases, and you have to solve the differential equations for the transient.

Steinmetz considered one kind of transient analysis, which he chose to call "oscillating currents", only he omitted to write the differential equations for the system. Whether he did this because he thought the reader would not be familiar with differential equations, or for some other reason, remains unclear. However, it can apparently lead to such questions as appear here.

[DejanC]

Actually, the differential equations are written there in the text I shared and attached to this post. How do you think he derived the equations otherwise? Hope you get a chance to see it. He knows about di/dt and dv/dt.

What astonished me is the hubris onto which we all think we know every aspect of electrical theory. HFHV conditions are for example very unique and not much is known there. This post was an example of uncommon knowledge.

[IanB]

Yes, he writes some derivatives and some integrals, but he does not write the complete differential equation for the system.

Here is a contemporary analysis of such a system, approached using the formulation and solution of the differential equation:

https://math.libretexts.org/Bookshelves/Differential_Equations/Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)/06%3A_Applications_of_Linear_Second_Order_Equations/6.03%3A_The_RLC_Circuit

What astonished me is the hubris onto which we all think we know every aspect of electrical theory.

When you say "we all", who exactly are you referring to? How can you speak for anyone except yourself?

[DejanC]

To counter that, I can list some unexplained electrical phenomenon.

First I will give you your chance. What phenomenon is not explained by our understanding? What are some EE mysteries? That way you can show that we indeed do not have hubris in this regard.

[IanB]

A few salient points from this topic:

• AC Circuit theory is a simplified method of analysis that can be applied when the amplitude and frequency of the current is steady and does not vary with time, and when the arithmetic mean value of the waveform is zero.
• Within AC circuit theory, it is possible to define a quantity called AC impedance, which is the impedance to current flow through the device or subsystem under consideration.
• If the amplitude and/or frequency are varying with time, then AC circuit theory is no longer applicable, and transient analysis is used.
• Since transient analysis falls outside AC circuit theory, then AC impedance is not something that can be defined in the traditional way.
• Similarly, real power and reactive power are also not defined according to their AC circuit usage.

What I do find interesting is that the technical note referenced is dated from 1897. It is remarkable that all the fundamentals required for electrical engineering were thoroughly known at that time, when widescale industrial adoption of electricity was in its infancy.

[IanB]

To counter that, I can list some unexplained electrical phenomenon.

First I will give you your chance. What phenomenon is not explained by our understanding? What are some EE mysteries? That way you can show that we indeed do not have hubris in this regard.

There's a difference between "not explained" and "not explainable".

I can confidently say that all observable phenomena can be explained, given sufficient information about the observation.

There may be some things that remain unexplained so far, but that is typically due to lack of information, or due to doubts about the veracity of the observations or reports.

[IanB]

And don't ask to explain "magnetism", because someone tried that on Richard Feynman once, and it didn't go well.

[ejeffrey]

Maybe another approach will be better.

Can you explain *why* you think this statement is particularly interesting or exciting?  What does it help you understand or predict?

As near as I can tell this is just some mathematical noodling trying to make equivalent circuit parameters to the standard linear elements but using decaying oscillations as the basis set rather than the more conventional steady sin/cos.  It might be handy for certain problems but it clearly hasn't taken the world by storm.  I couldn't say why, maybe it's not particularly useful maybe it would be useful but not enough people know about it to try?  Or maybe it is actually used in some disciplines that people here aren't familiar with?

[coppercone2]

I think its a very interesting observation.

[DejanC]

Basically anything pertaining to videos like these:

https://youtu.be/n0yt2B2B6Zc?si=B-jMl75h4UuUKgLP

If this is covered by any conventional explanation, please share. I have more examples...