Is it Single or Two Phase?

[rattus]

But, for the sake of general electrcial theory consistency, why would you say that the current caused by a purely resistive circuit is 180 degrees out of phase with the voltage?

I still find it easier to describe a 120/240V system as two 120V circuits connected +-+- rather than as +--+.

Jim, I don't think I said that, but one might think so if one does not pay close attention to phase angles, references, and the sense of the current.

Agreed, for a simple 1-ph problem your method is easier and quicker.

But, for a 3-ph problem, none of the voltages is the negative of another, therefore you have to use the individual phase angles. I contend that this is the general approach if there is one.

Whatever, it is perfectly acceptable to label V2 as 120V@180 (re N of course). And, yes it is a 180 degree phase difference from V1. Any argument to the contrary is baseless.

 

[jim dungar]

Rattus,

My point is, with your description, you have shown that for a purely resistive circuit the current in a transformer winding is 180 degrees out of phase with the voltage across that winding. While this may be nothing but a "game of math signs", it is not consistent with general electrical concepts and explanations.

 

[Smart $]

...

But, for a 3-ph problem, none of the voltages is the negative of another, therefore you have to use the individual phase angles...

Please forgive my intrusion of this wonderfully delightful and inspiring discussion... but I believe there to be an error in your approach to 3? using phasors. You stated earlier:

The rotating phasor is of the form:

1) v(t) = Vpk[cos(wt + phi) +jsin(wt + phi)]

where (wt) is the independent variable in radians and phi is the phase shift in radians.

Vpk is the magnitude of the peak value of the sinusoid

The real part of this expression provides the instantaneous value.

By definition the rotating phasor describes a pure sinusoid. Any argument to the contrary is baseless.

The error comes when you seem to be using the conventionally-dubbed phase angle in your formula, namely 120? and 240?. When you process the math to its fullest degree, you have to use the negative value of these angles to arrive at the absolute correct answer. Please bear with me...

When we discuss say the 120? phase we are referring to a sinusoidal waveform that lags the 0? and reference waveform by 120? into its full cyclic period of 360?. If we evaluate voltage (V) trigonometrically strictly as a function of time (t) the formula is:

V(t) = Vpk ∙ cos(t + Φ)​

or when evaluated as relative voltage:

V(t) = cos(t + Φ)​

...where Φ is the angular delay [EDIT: "delay" should be "shift"] of the waveform to the reference waveform of 0?.

If we plot this function in Cartesian format, cos(t + 120?) results in a waveform that lags the reference waveform by 240? rather than the anticipated 120?. However, if we use the negative of the value, or rewrite our formula solely for this purpose as:

V(t) = cos(t – Φ)​

...the result is correct and as expected.

View attachment 70

 

[rattus]

Nonsense:

Nonsense:

Smart,

I can't follow your argument at all.

Furthermore, cos(t) is invalid. The units of "t" are seconds. You can only take the cosine of an angle.

 

[Smart $]

"t" in this sense is relative time (I apologize for not pointing that out) and calculated in cycle degrees. It has no unit of measure other than cycle degrees. It would only have a unit of measure if frequency is added as a calculation constant. If the frequency were to be stated in Hz, then the X axis would become "seconds", and "cycle degrees" would be correlative.

Besides, it doesn't really matter what variable is used. The point is that when plotting a sinusoidal waveform, the phase shift is determined by adding a constant "phi" to the variable. A negative value for "phi" is required for a delayed waveform. A positive value advances the waveform. When we say (in conventional manner) a phase shift of 120?, we empirically mean the waveform is delayed by 120?.

 

[winnie]

As I understand Smart $'s point, the convention used in electrical power systems is that phase B lags phase A by 120 degrees, and phase C lags phase B by 120 degrees.

This _convention_ is not consistent with _adding_ 120 degrees to the omega*t term in the voltage equation. When you add 120 degrees to your omega*t term, you are causing a leading phase shift.

So which is it:
V_A = cos(\omega t)
V_B = cos(\omega t + 2\pi /3)
V_C = cos(\omega t + 4\pi /3)
or is it:
V_A = cos(\omega t)
V_B = cos(\omega t - 2\pi /3)
V_C = cos(\omega t - 4\pi /3)

IMHO using _either_ approach is equally reasonable, as long as we either agree which approach to use, or at least make sure that we are individually self consistent. IMHO the second approach is more common; most people would understand 'phase sequence ABC' to mean that over the course of a cycle, A is positive, then B, then C.

On _convention_, the point has been made several times that the magnitude of a vector is always _positive_, and that the use of negative magnitudes is wrong. I submit that this is also a _convention_, one which is roughly the equivalent of saying that 'improper fractions' (fractions in which the numerator are greater than the denominator) are wrong. The mathematics works out just fine if you permit negative magnitudes, or even if you were to _require_ that magnitudes always be negative and call positive magnitudes wrong.

-Jon

 

[mpross]

shift

shift

...A negative value for "phi" is required for a delayed waveform. A positive value advances the waveform. When we say (in conventional manner) a phase shift of 120?, we empirically mean the waveform is delayed by 120?.

I think this is backwards. For a negative valueof phi, the waveform shifts to the right with respect to time (positive t to the right), and for a positve phi, it shifts to the left.

Anyone else?

-Matt

 

[mpross]

shift again

shift again

OK,

I can see what you mean if a delay means that the wave is further along in time (shifted right) for negative value of phi...

-Matt

 

[rattus]

Tangents:

Tangents:

How did this thread become so tattered?

I said that none of the 3-phase voltages is the negative of another, therefore you cannot solve 3-phase problems as Jim likes to do with 1-ph systems.

In the rotating vector, the angle "phi" can be any value between 0 and pi. "phi" is in radians; "wt" is in radians. It is incorrect to write cos(t). And I hope we all know that a positive value of "phi" means a phase lead, and a negavtive value means a phase lag.

I prefer to describe 3-ph voltages with the phase angles 0, -120, & -240 degrees. Convert those angles to radians if you wish.

And "negative magnitude" is a contradiction in terms. You may negate the whole expression, but the magnitude, by definition, is always positive.

.

 

[rattus]

3-ph Problem:

3-ph Problem:

Jim,

How would you compute the currents in a 3-ph wye with one phase open and 120V loads on each of the other two phases and a 240V load between them.

 

[LarryFine]

Jim,

How would you compute the currents in a 3-ph wye with one phase open and 120V loads on each of the other two phases and a 240V load between them.

I would use 208 volts in my calculation. You?

 

[kingpb]

Good point Jon.

Just for clarification, the power system always rotates in a counterclockwise rotation. For a positive sequence, your statement that B lags A by 120 deg, and C lags B by 120 is correct.

However, there are utility systems that use what is called negative sequence which means they label there phases in the order of ACB. in that case, C lags A by 120 deg, and B lags C by 120 deg. The formulas still are the same.

 

[rattus]

I would use 208 volts in my calculation. You?

Fine Larry, (that's a joke son!) but how do you compute the 208V; how do you calculate the phase and neutral currents? How do you calculate the phase angles?

 

[LarryFine]

Fine Larry, (that's a joke son!)

So was my "208".

I will respond to the question soon. (Not correctly, maybe, but adamantly.)

 

[engy]

Rattus,

My point is, with your description, you have shown that for a purely resistive circuit the current in a transformer winding is 180 degrees out of phase with the voltage across that winding. While this may be nothing but a "game of math signs", it is not consistent with general electrical concepts and explanations.

While sometimes a "game of math signs", it is also sometimes the real world:

With a load on two phases of a 280Y120, the current is out of phase with the voltage of both phases.

 

[winnie]

How did this thread become so tattered?

Because we have about 6 zillion different but related things to discuss. I should have started my essays (another thread) with a sentence along the lines of 'This is my understanding of the situation, please correct them so that I can learn.' And started a separate thread for separate components of the question (Voltage, RMS, Phase, etc.). Instead I started to write what I hoped was a complete text...which is just too large for a single thread, as shown here

In the rotating vector, the angle "phi" can be any value between 0 and pi. "phi" is in radians; "wt" is in radians. It is incorrect to write cos(t). And I hope we all know that a positive value of "phi" means a phase lead, and a negavtive value means a phase lag.

The angle phi can be anything from - to + infinity. Since this is a cyclic system, any value from - to + infinity can be mapped to the range 0 to 2pi, but equivalently -pi to +pi or -2pi to 0 can be used.

I prefer to describe 3-ph voltages with the phase angles 0, -120, & -240 degrees. Convert those angles to radians if you wish.

Showing your own preference to not use the range above zero

And "negative magnitude" is a contradiction in terms. You may negate the whole expression, but the magnitude, by definition, is always positive.

The magnitude of a vector may be _defined_ as always positive, and I won't disagree with this. I claimed above, however, that this definition is a convention that is not required by the mathematics of the situation. The math works just fine with -Vpk or -omega or -phi. When you say '-V at 0 degrees is wrong but V at 180 degrees is correct', that is by convention only; mathematically they mean exactly the same thing.

Going North at -10 miles per hour is the equivalent of going South at 10 miles per hour, and while I agree that there is a clear linguistic contradiction, the _math_ works out just fine.

-Jon

 

[rattus]

Correction:

Correction:

The angle "phi" can be anywhere in the range of +/- pi. "wt" can be any value, but we usually assume a single period.

In practice "phi" usually falls between +/- pi/2.

 

[rattus]

The Fixed Phasor:

The Fixed Phasor:

The fixed phasor is a complex number comprising the RMS magnitude and phase angle of a sinusoidal voltage or current. It is usually written in polar form:

V = Vrms/phi

which corresponts do,

V = Vrms[cos(phi) + jsin(phi)]

Fixed phasors may be added or subtracted to obtain line/phase voltages/currents and neutral currents in 3-ph systems.

If we stretch the definition to include impedances, fixed phasors may be divided and/or multiplied to obtain currents and voltages.

 

[Smart $]

The angle "phi" can be anywhere in the range of +/- pi. "wt" can be any value, but we usually assume a single period.

In practice "phi" usually falls between +/- pi/2.

+/- pi/2? That's only ? 90? !!!

I agree with Jon that the value of Φ is unlimited. The effective range, however, is 0? ? 360?, or 0 ? 2Pi radians, when discussing phase shift, as the reference waveform is considered to be at Φ = 0 and an out-of-phase waveform can either lead or trail by up to 360? while being within or at the extents of the reference period.

 

[rattus]

Phase Shift:

Phase Shift:

I would argue that "phase shift" is commonly used to indicate current lead or lag which is limited to +/- pi/2 in practice.

If we are describing 3-ph voltage or current relative to zero, phi can be any value in the cycle but must be less than 2pi.