The Physics of... Electrical Power

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Thread Starter

Phil Corso, PE

Post Scope.
A number of postings related to electrical power generation contain misunderstood concepts, expressions, and definitions as related to generated power. My goal, for those members of this forum (especially newbies) that choose to accept, is to provide some enlightenment, without malice, without scorn, without prejudice! And, for those who don’t accept my goal, so be it!
Who cares as long as you’re happy!

Background.
Non-electrical engineers and technicians are caught on the horns of a dilemma! They are/were taught that power is defined as the rate of doing work. Since work is defined as force x distance, then power = force times distance divided by time. In other words power is something tangible, something measurable, something that is useful. For example: Hp; BTU/minute; lb(f)-ft/second; kg(f)-m/sec; Watts; etc. The dilemma is that when talking about synchronous generators conflicting terms have arisen. First, there is apparent-power referred to as Volt-Amperes (VA). Second, there is active-power called Watts (W). And last, there is reactive-power called Volt-Amps-reactive (VAr.) Confusion arises because neither the first expression VA, nor the third VAr, meets the physics definition of power!

History (at least how I remember it.)
In the early days of DC power generation it was easy to determine power - simply the product of Volts and Amps. Then, AC power brought with it terms like inductive reactance, capacitive reactance, amperes-in, amperes-out, lagging-current, leading-current, and power-factor! All of which muddied the waters of understanding. Non-electrical engineers struggled (some EEs still do!) Eventually, as generators were inter-connected to form networks it was realized that system improvement could be effected by manipulating a generator’s excitation, so that some of the networks’ lagging-current could be negated! Ah-ha, said the bean counters, “Perhaps we can sell power-factor improvement!” Still understanding faltered! This led to the adoption of the expression, Watt-less power. Now, a generating company could sell both Watts and Watt-less power! (Of course, only those-in-the-know, knew the latter was an oxy-moron!) Just imagine the confusion when the un-initiated were told, “Although
Watt-less, it still causes losses!” Eventually, the latter term morphed into the adumbrated entity called reactive-power! It was alive! It could even be measured by meter! More importantly, it eliminated “loss-talk!” And, if measurable it could be priced, and then sold!

Apparent-power, Active-power, and Reactive-power Relationship.
What then, is the difference between apparent-, active-, and reactive-power? Of course, most of you with a mathematical bent understand that voltage and current waves are sinusoidal in form, having like-frequencies but unlike-amplitudes. The use of vectors (those of you bothered by the term can use the newer term, phasors) was introduced to explain it. It is nothing more than a mathematical-artifice representing the time-relationship between corresponding points on the voltage and current waves, as follows:
S (apparent power) = |V| x |A|.
W (active-power) = |V| x |A| x Cos(f), with (f) the time-offset (in deg) between V & I, the power-factor angle.
VAr (reactive-power)= |V| x |A| x Sin (f).

The Closing.
I believe the problem many of the forum engineers, technicians, and others have is one of semantics! The watt-less term applies only to the reactive-element, i.e., inductor or capacitor in the circuit, not the source or supply. Also, for purposes of simplicity let’s ignore non-linear loads. Following is the introduction to the white paper on Armature Reaction I presented in Jan ’07. It lists terms or phases to describe “Reactive-Power” as well as my "hapless" goal to curtail the continued use of inconsistent phases:
“Adjectives that described Reactive-Power are plentiful, some even inventive, but most miss the point! Here are some pairs that were culled from A-List and Off-List responses: adds-subtracts; additive-subtractive; absorbs-produces; augments-negates; crowds-expands; decreases-increases; flows-in; flows-out; overcomes-replaces; overtakes-fights; magnetizes-demagnetizes; supports-opposes; strengthens-weakens; and swells-shrinks. There have been and certainly will be others! Thus far, no-one has used adjectives such as: encourage; discourage; thwart; or tweak! I hope this paper will curtail (hmm, a synonym I hadn’t noticed earlier) the seemingly growing list of adjectives.”

My final point is this - call the “various powers” whatever you want to if it works for you! But, always remember that a generator supplies only two quantities, volts, and amps! Whether a generator’s current is resistive, reactive, or some combination of the two, is determined by the phase-displacement of the generator’s line-current, relative to the generator’s terminal-voltage. Just remember it’s the story of the bear and the wall!

Regards,
Phil Corso, PE ([email protected])
 
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Bruce Durdle

It's my turn to disagree with Phil Corso - this time on the subject of "reactive power". Reactive power is the power that must flow in a circuit to supply energy to energy storing devices such as capacitors and inductors. The energy supplied during one quarter-cycle is taken out on the next, but the circuit still has to be able to handle the required current (assuming a parallel connection). Over a full cycle the reactive power supplied is zero, but over a quarter-cycle starting at a current or voltage zero it will have a measurable value. If a capacitor and inductor are connected in parallel, the reactive power will flow in to the capacitor during the quarter-cycle it is coming out of the inductor. The peak value of this power is (V x I)/2 so it is equivalent to the active power (which also has an instantaneous significance but in addition has an average value).

Bruce
 
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Phil Corso, PE

Bruce, although you disagree, I hope you're still happy! I'll keep my reply brief:

1) I said that the term Reactive-Power does not meet the physics definition of 'power'!

2) I said name it whatever you want if it works for you!

3) I agree with you that simple non-inductors and capacitors store energy in one-half cycle, and then return it the next-half cycle. But, a simple dimension check of the equations will reveal that, in SI terms, the units are those for energy, not power!

Phil
 
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Bruce Durdle

The energy has got to get in in one quarter-cycle and out again the next - and the rate of flow of energy is power.
 
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Phil Corso, PE

Bruce, power tells you how fast work is being done OR how fast energy is being transferred. I'm sure you will agree that an inductive-current lags its supply voltage by 90 deg while a capacitive-current leads its voltage by 90 deg. I’m also sure you will agree that electric power is given as VxIxCos(phi). And, because the angle phi is 90 deg, its cosine is zero, Hence power in the inductive circuit is zero, as it is in the capacitive circuit.

Regarding energy, it is true that energy is transferred in for 1/4-cycle, then out the next 1/4-cycle. But, no power is delivered (and then returned) because no work is being done! Unless, however, the inductor or capacitor contained dissipative elements, i.e., their connecting leads!

Phil
 
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Bruce Durdle

One of the good things about this discussion group is that it often forces us to examine the things we had rammed down our throats during the formative education process and have taken for granted ever since. Phil Corso's statement that the units of reactive power are in fact energy has forced me to go back and revisit the area of fundamental AC theory.

For a capacitor with applied voltage V sin wt, the current is I cos wt. The instantaneous power is VI sin wt cos wt. Using the standard trig identity this is equal to VI/2 sin 2wt. The **average** value of this is zero. But the **RMS** value is non-zero, and equals VI/(2 x sqrt2). So the units are the same as those for active power - volts x amps.

Just in case anyone quibbles that the average is zero over a cycle so it can't be important, just look at the average value of alternating current over a cycle. (Perhaps if Edison had thought of that argument we'd be freed of all the hassle about active vs. reactive power).

Incidentally, this partially answers the question about why we have to pay for reactive power - just as the average value of current in the line is zero but the line still needs to be able to handle the current peak requirement, so he average value of reactive power is zero but the supply system must be able to provide the peak reactive power requirement (an this will not appear on energy bills). Let's hope we can now put this one to bed - all this digging into stuff I had to learn a loooong time ago and promptly forgot is making my head hurt!

Bruce
 
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Phil Corso, PE

Bruce,

To assuage the pain you’re experiencing from what I view as a semantic problem, how about the following definition:

“In an inductor, energy taken from the source as current increases is returned to the source as current decreases. Thus, the average energy taken by the inductor is zero. That is, no power is absorbed or delivered by the inductor. Instead, that energy is converted to heat (power) in all resistive elements between the source and the inductor!”
 
I congratulate Mr. Corso for opening a new topic to allow forum contributors to relax and "cool their jets". I also needed time to reflect.

I also wish to express my thanks to Bruce Durdle for his eloquence.

I observed a post stating that many Non-electrical engineers and technicians are caught on the horns of a dilemma. Perhaps they are not. Perhaps, they realize that a VAr must affect the generator in some fashion. After all; a generator can only supply volts and amps. Reduce voltage and current must increase. V=IR (Ohms Law). AC has a different aspect to R; yet the basic law remains.

Many engineers/technicians have also been schooled in the Eli the Ice Man relationship (E=LC). Again; I must concur with the physics of electrical power. The LC relationship is energy and is not defined as work.

My 1979 calculus book still resides on my desk. I do not refer to it very often.

I can still do the math; although I rather not.

The physics of electrical power. If one does not maintain the speed of the generator in relation to the number of poles(no dynamos allowed).... etc., one will not be able/allowed to produce watts on a controlled frequency grid.

I will CONCEDE; as I have in nearly all of my posts that MANY things are happening in the same instant of time. These many things: AVR, Torque In/ Torque Out... etc.. only add to this delicate and dynamic energy balance.

CTTech
 
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Phil Corso, PE

Responding to CCTech’s 02-Jul (00:44): what are you talking about? The phrase “ELI the ICE man” helps one remember that the phase relationships of current and voltage for purely inductive and purely capacitive circuits are opposite. That is, with ‘E’ representing voltage and ‘I’ representing current, then for the inductance ‘L’ case voltage (E) leads current (I). Similarly, ICE means that for the capacitor case current (I) leads voltage (E)! Now, what does E=LC stand for?

Regards, Phil
 
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Bruce Durdle

Hi Phil,

It's all in the use of words... semantics, as you say. But some of the distinctions are important in an engineering sense. As electrical engineers in a world where the (technical) illiterati are starting to take an interest in matters of electrical supply, I feel quite strongly that we need to be careful how we use words. Power is different from energy. Energy is stored and can flow from one part of a system to another - power is the rate of energy flow. Electrical energy is not "heat" - in the thermodynamic sense, it can be used to lift a weight against gravity and is therefore "work". The average energy absorbed by an inductor during a complete cycle is zero, and the same with the capacitor. But power factor effects occur when we connect capacitors (leading power factor) with inductors (lagging power factor). In that case, during a cycle, we can have energy moving from the inductor to the capacitor and back again. The electronics guys use the effects as resonant circuits, where the "Q" factor indicates the proportion of energy lost through resistance during a cycle to the proportion initially stored.

I am quite happy with your statement that no energy is absorbed or delivered by the inductor - provided we are talking about a complete charge/discharge cycle, and the average power flow over a cycle is zero. What I am trying to say is that, in circuit terms, even if the average power to an inductor or capacitor is zero, we still have to engineer the system to handle the instantaneous power needed to get the energy into and out of the reactive elements. The average of water flow into and out of a tidal channel during a tidal cycle is also zero, but that doesn't mean the flow can be ignored. A power factor correcting capacitor can be thought of as providing negative reactance to compensate for the positive reactance of the motor windings, of taking a leading current which is 180 deg out of phase with the motor reactive current, of drawing leading reactive power and balancing the lagging reactive power of the motor, or of "generating" reactive power which is "absorbed" by the motor. All of these can be defended in terms of the physics, starting with Kirchoff's laws, and all are of use in different situations. Each of the concepts is just as "real" as the others.

Cheers,

Bruce
 
Phil,

Just having some fun. It seemed that the discussion of the basics for newbies was the topic. Just ascertaining if you remembered the basics from Elec 101. That was back when we learned resistors (Bad boys... Willingly). Even AC reverts back to some basic DC laws after we apply mathematics. Someone suggested that technicians do not understand. I suppose that a VAR is not a VAr. Semantics! Lighten up.

Best regards,

CTTech
 
Something less than E=MC^2, probably.

Don't induction motors cause the voltage and current sine waves to shift away from each other?

And, to keep watts flowing (watts do flow don't they?) most efficiently on the grid isn't it desirable to keep the voltage and current sine waves more closely aligned with each other?

So, if there is zero whatever flow be it power or energy when the power factor is less than 1.0, why does a synchronous generator have to be operated in an overexcited condition in order to shift the voltage and current sine waves back towards each other?

And doesn't that excitation consume real power, in the form of watts, since current is flowing through a conductor in the rotating field of the synchronous generator?

As Ricky Ricardo said to Lucille Ball many times, "'Splain it to me, Lucy!"
 
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Phil Corso, PE

Responding to CCTech’s 04-Jul (00:38):
A1) As a matter of fact my basic course was Electricity 01!
A2) No, as any technocrat will tell you, VAR and VAr aren’t the same!

Responding to CSA’s 04-Jul (00:55):
A1) As Stan Laurel said to Oliver Hardy, “Coitainly, Ollie!”
A2) E=mc^2, exactly! Refer to A2) above!
A3) Yes, there is an analogous condition!
A4) In fact, Watts does not “flow!” Nor does “current!”
A5) Excellent question! Yes, excitation uses real power. And, while it’s included in the generator’s efficiency calculation, it (as power) hardly impacts the generator’s load!

Now, if either or both of you really want answers to your questions, search the List Archives. Some 50+ topics covering the VAr and Syn Gens have been submitted! If you are unable to find an answer to suit you, then submit a new post!
(BTW, the definition of technocrat can also be found in the archives!)

Have a great 4th!

Regards, Phil
 
hi all,

power is always flow high potential to low potential. so When active/reactive power flow there will be a voltage drop (I^2*r).
(Active power always flow high voltage end to low voltage end, if there is not any setup transformer).

And my question is can reactive power flow from low voltage end high voltage end?

Is it possible that active power flowing to one direction when reactive power flow to opposite direction?
can some one please explain it?
 
WATT...

an excellent question! It is really the crux of Super-Grid problem … transferring both power and VAr, over a myriad of interconnections (see http://www.control.com/thread/1026242714 for my bear & wall story!)

First, the answer to your seemingly simple question... Yes, VAr 'flow' can be in either direction thru a system-interconnection! Consider three power plants, A, B, C, each connected at the vertex of a triangular-shaped transmission system.

Local loads are Sa, Sb, Sc, respectively. Load Sa=Pa+Qa,, Load Sb=Pb+Qb, Load Sc=Pc+Qc, , where: S represents the Apparent load in VA; P represents the Real component in kW; and Q the Reactive component in VAr (for simplicity I’ve omitted the 'j' operator!) Furthermore, the voltage at each station bus is set to 100%!

Obviously, the Ps and Qs are different, but sum of P's is controlled by the speed(s) of each generator’s prime-mover! Now what about the sum of Q's? Because the bus-voltage are equal there is no high-pot to low-pot differences... what then, determines VAr 'direction'?

The answer is simple but getting it, ain’t! Stated another way, it’s like asking someone to, "Explain how a Ratchet works without using your hands!" But, here is my answer... VAr 'direction' is determined by altering the each generator's excitation (field-current) thus changing the generator's Power-Factor angle (no, not its torque-angle!) The math is quite complicated, probably requiring EXA-iterations for the Super-Grid!

There is a simpler alternative to the "Super-Grid" but that's another Thread!

Regards,
Phil Corso
 
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