Mathematical Vs Power Engineering convention (Power Factor) 1

[ppaya]

I see that some of us are more familiar to mathematical convention. Therefore motor load is described as "consuming WATTS" and "Generating VARs (or consuming negative VARs)". This means power factor is negative and lagging.

Engineers would conviniently say motor load consume both. Power factor is lagging, and positive.

There seems to be both conventions in use. Any thoughts what convention to apply ?

 

[Bung]

This is a great subject for messing with people's minds. I tend to shy awaya from it by thinking of it all in terms of the phase relationship between the V and the I. The idea of "generating" or "consuming" VArs is a bit misleading, at least to my tiny mind. Does a generator (machine with active mechancial power applied, and which supplies active energy to another machine) generate or consume VArs? If the real power is zero, and you have 100kVAr of capacitors and 100kVAr of inductors connected, does it make sense to say that the generator is doing nothing except apply a voltage? Are the capacitor and inductor happily acting as a source and sink supplying each other with VArs?

It's all just a convention, so stick with the one you like. The power station types seem to use one convention, and industrial types use the other.

Bung
Life is non-linear...

 

[alehman]

I've always thought of induction motors with lagging power factor (I lagging V) as consuming watts and consuming vars.

 

[jghrist]

See thread237-114077

 

[weh3]

The pf of a synchronous generator depends on the load, unless you are paralleled with utility, in which case, the voltage regulator determines the pf.

But even with supposedly equal capacitive and inductive loads, there has to be some magnetization. When the quadrature current just swings back and forth between you and the utility or between L and C, how can you really say that one is generating and the other is consuming? It all has to do with your point of view (motor or utility) and the phase relationships. I believe Bung points out the same above.


William

 

[jghrist]

From a mathematical standpoint, the normal power convention is for inductive vars to be positive. Complex power is defined as S=V·I*, where I* is the complex conjugate of I (same as I except with the sign of the angle reversed). So if V=1+j·0 and I=0.6-j·0.8 (80% lagging power factor), then S=0.6+j·0.8

 

[Bung]

Assuming generator action (ie current away from the + terminal of the 'source'):
P is +, emf supplies poower
P is -, emf absorbs power
Q is +, emf supplies VArs (I lags E)
Q is -, emf absorbs VArs (I leads E)

Assuming motor action (ie current into the + terminal of the 'source'):
P is +, emf absorbs power
P is -, emf supplies power
Q is +, emf absorbs VArs (I lags E)
Q is -, emf supplies VArs (I leads E)

source : Stevenson, Elements of Power system analysis, 3rd ed, p24.

Bung
Life is non-linear...

 

[electricpete]

I would agree with everyone this is a potential for immense confusion of terminology. Now that I have been educated in the thread linked above, I would say there is still a great mixture of terms which certainly creates ambiguity even though the user is 100% correct in their terminology.

Bung you said:
"Assuming generator action (ie current away from the + terminal of the 'source'):
....
P is -, emf absorbs power
Q is +, emf supplies VArs (I lags E).."

Let's say we have that combination P is - and Q is + with current defined per your assumption. Then the angle between voltage and your defined current is between 90 and 180. I think using the terminology defined in the previous linked thread (which makes sense to me), most people would search for the angle between 0 and 90 and therefore redefine the current direction for this case and call it leading. Both are right... terminology immensely varying.

The original power factor talked about power factor lagging and positive for a motor. Does that mean there is a negative power factor? I can see there may be a math basis for it but it would not be common terminology and would require clarification of the assumptions.

jgrist - what is an inductive var. Vars can flow into or out of machines without ever calling the var inductive or reactive. (the device is inductive or reactive... the direction of var flow into or out of the device helps us characterize a device as inductive or reactive, but the poor var only knows which way it's flowing... not what type of device is attached).

I am not meaning to disagree with anyone. I'm sure all in this thread understand the math basis for their own terminology and use it consistently. Only once again pointing out this terminology is a tricky subject when communicating among people who have different math basis underlying their terminology.

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[electricpete]

To address Bung's terminology a little closer I pull from the other thread the definition that we call it leading if real and reactive power flow in same direction, lagging if opposite directions.

The case I selected above generator with real power flowing in and reactive power flowing out we would call leading. You call lagging soley based on Q.

The discrepancy in terminology only applies for generator operating with real power in or motor with real power out. Not very common I agree but you have specifically allowed for it by listing those cases.


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[jghrist]

By inductive var, I mean the reactive volt-amperes that would flow into a passive inductive element (inductor), as opposed to capacitive vars that would flow into a capacitor.

To me, saying real power flows into a generator does not make sense. If real power flows into a machine, it is acting as a motor not as a generator.

 

[electricpete]

Hi jghrist. Thanks again for your comments in the other thread. I am happy to accept your very logical definition of leading and lagging based on whether reactive and real power flow in the same or opposite direction.

I hope you don't mind me taking lighthearted disagreement with your inductive var terminology... once again making the point that some groups of terminology are not consistent with outher groups of terminology. Anyway, inductive and capaacitve vars are not terms that I have heard before. We can look at a transmission diagram and talk about MW flowing in a certain direction without saying whether it is a "generator MW" or a motor "MW". Why do we have to give an inductive or capacitive label to vars? It serves no purpose to my knowledge because we will still have to identify the direction of flow. By your terminology one would say that we add capacitors to a transmission system to remove capacitive vars? I think most would rather simply say we are adding vars to support the voltage. The terminology vars in and vars out has been used for years to describe generator operation at my plant. I guess instead of those two modes we should have four: inductive vars in, inductive vars out, capacitive vars in and capacitive vars out? Only how do I tell the difference between inductive vars out and capacitive vars in? Just kidding. I know what you meant but it's different than what I hear.

There are in this world motor-generator sets that serve to transmit real power in two directions and could reverse real power direction. They are not common. If not for the fact that Bung listed "P is -, emf absorbs power
Q is +, emf supplies VArs (I lags E)" under generator, I would not have commented.


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[Rodmcm]

In both motor and generator cases lagging pF is when the real power and reactive power are flowing in the same direction, and leading pF is if they are not. Hence a 'lagging' generator can supply a 'lagging' motor

 

[jghrist]

electricpete,

I think you're right about the vars. It is better not have only volt-amperes reactive (vars). Thinking of capacitive vars flowing into a capacitor confuses the issue. Better to say that a capacitor supplies vars, that is, positive vars flow out of a capacitor. Likewise, if a generator is supplying an inductive load, the current out of the generator (with positive direction defined as the same direction as real power) lags the voltage. The generator is supplying vars.

So what I meant before by inductive vars was simply vars.

 

[weh3]

This post is summarized at the bottom, if you don't want to read the whole thing.

It is not correct to speak of vars or currents flowing in a certain direction, because all they do is circulate back and forth. The conventions have to do with what happens during a positive voltage cycle.

The real current (Ip, in-phase component) for a power-consuming device must be understood to be in the same orientation as the voltage. For a generator it is the opposite: current flows OUT of the device when the terminal voltage is positive.

In a spreadsheet, graph the voltage, phase-shifted current, and the resulting real and quadrature currents. Make it so that changing a single cell adjusts the phase angle. Watch what happens as you move the phase around. If you want more detail on this, I can provide it.

When you go over 90 deg phase, the real current and the voltage waveforms go 180 deg out of phase, indicating that the power flow has reversed. The quadrature current stays the same.

V*Ip is a waveform with an offset of half its amplitude. The offset is the RMS power. The ratio of this amplitude to the Itotal is the pf. The direction of real power flow is whether this is centered above or below the axis, and this power never changes direction.

V*Iq is a waveform with no offset.

Say that a synchronous generator is supplying a motor that takes 45 lagging. The generator is also at 45 lagging. The reason for this is that the magnetizing current peaks 45 degrees after the voltage for either device.

Leading and lagging indicate the phase relationship between the magnetizing current waveform and voltage waveform when the voltage is oriented in such a way that the real current and voltage are in phase.

To summarize:

Real power flow is determined by the conventions used at the terminals of the device:

Motor: Ip is in phase with V
Generator: Ip is 180 deg out of phase with V

Irrespective of the terminal convention:

A device has a lagging power factor if magnetizing current lags the total current by an angle between 0 and 90.

A device has leading power factor if the magnetizing current leads the total current by an angle between 0 and 90.



Regards,
William

 

[polyphase]

weh3, I would appreciate seeing more regarding your spreedsheet graphing.

 

[weh3]

Here are the cell contents (MS Excel):

The angle value that can be changed on the fly:
C1: 45 (the pf angle)

Column Headings:
A2: "N" (a sequential number for building a sine wave)
B2: "V" (Voltage)
C2: "It" (Total current)
D2: "S" (Apparent power)
E2: "Ip" (Real current)
F2: "Iq" (Reactive or magnetizing current)
G2: "P" (Real power)
H2: "Q" (Reactive power)

A3 - A33: the numbers 0 thru 30 (I used 30 because it fit on the screen)

Formulas (copy them down through row 33):
B3: =SIN(A3/30*2*PI())
C3: =SIN(A3/30*2*PI()-$C$1*PI()/180)
D3: =B3*C3
E3: =COS($C$1*PI()/180)*SIN(A3*2*PI()/30)
F3: =-SIN($C$1*PI()/180)*COS(A3*2*PI()/30)
G3: =B3*E3
H3: =B3*F3

The minus sign in F3 is needed because we are using the sin as a reference and not the cos.

Graph columns from B through H. Watch what happens as you change the angle in C1.

Have fun,
William

 

[cuky2000]

Check page 4 in the enclose site

http://www.legacypower.net/Documents/Training PDF/System Power Calculations.pdf

 

[weh3]

I evidently forgot to take the conjugate of I in my formulas, which is probably why I needed the extra minus sign in one spot.

If everyone agrees on the definition that capacitors generate vars and inductors consume them, then that is OK with me, but I have a hard time with the physical sense of it.

Regards,
William

 

[electricpete]

Reactive power represents instanteous power changing direction every half-cycle as you say.

But there is a different between reactive power associated with an inductive device and reactive power associated iwth a capacitive device. We can choose to describe it in phase relationship between current and voltage as you have. Or we can choose an alternate description of direction of reactive power flow.

There are some advantages to considering reactive power as something that flows from one point to another within a system. We have various supplies of vars and we have various demands of vars and they must total to zero. By following the var flow we can also begin to analyse the voltage drop. Under idealized (approximate) conditions of decoupled load flow, the voltage drop through series inductances associated with transmission lines is proportional to the reactive power flow (the other half of that decoupled approximation is that the real power flow is proportional to the phase difference across the line).

Reactive power flowing through series inductance creating voltage drop is easy for EE's to conceptualize as analogous to dc current flowing through resistances creating a dc voltage drop. (similar analogy again for real power flowing through series inductance creating phase drop).

If we redefined vars in an opposite sense flowing from inductance to capacitance, then we would no longer have a situation analogous to dc ohms law (or we would have to reverse something else to compensate).

Consider if you add capacitors to a transmission system at a certain location you will almost invariably increase the voltage at that location (and adding inductance decreases the voltage). It is easy to imagine that adding a "source" increases the voltage and adding a "load" decreases the voltage. If we redefined it in the opposite manner this intuitve behavior would disappear.

I have no disagreement with your characterizations of power flow. I don't agree with your conclusion that any of the other responses is wrong... just alternate terminology with assumptions necessary in any terminology we choose.


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[cuky2000]

Enclose is a site with a helpfull audio-visula tool to see the physical meaning of reactive power flow

http://eknowledge.pjm.com/Lesson1/Intro1.htm

[sub] Please proceed as follow:
a- Go to menu
b- Click on Lesson 4 (Integrating Real & Reactive power Flows)
c- Click “Flow Patterns”
d- Proceed to see Cases 1 to 8. [/sub]

I hope this could help you to visualize the physical sense of the Vars power flow.