Dear Friends,
We make Transformers at Jhansi. We use three wattmeter method for measuring No-Load and Load-Losses of a three phase transformer. We some time come across a situation that one of the wattmeter reads negative.

I would like to know from my more learned friends what is the reason for this?

Do we add all the three reading irrespective of the sign or should we subtract the power which is negative?

How can power in any phase be negative for a passive machine like a transformer?

Please throw some light.

Regards and thanks to all.
Rajeev Agarwal

 

Responding to Rajeev's May 8, 6:34pm query. A lot more information is required. As a start:

Q1) Does the sum of 3-single phase measurements, using the same wattmeter and taken one phase at a time, equal the algebraic sum of the 3-simultaneous measurements?

Regards,
Phil Corso, PE {Boca Raton, FL, USA}
[[email protected]] ([email protected])

 

perhaps you have discovered the secret of limitless power.

my guess is you have the meters hooked up wrong.

 

Further to my May 9, 8:50pm response to Rajeev:

Assuming that the three transformer windings are relatively balanced, and this were a 2-wattmeter measurement with one showing a negative reading, then, it is due to the power factor being less than 0.5. But, a
negative reading in a 3-wattmeter measurement should not occur unless the voltage/current-coil connections are asymmetrical. This leads to the following questions:

Q2) How is the test stand setup? Case a) For a 3-phase, 3-wire, delta-connected load? Or Case b) for a 3-phase, 4-wire, wye-connected load?

Q3) If the 3-p, 3-w Case a), are the current-coil leads connected "inside" the delta? Furthermore, where are the voltage-coil leads connected?

Q4) If the 3-p, 4-w Case b), are the common voltage-coil leads connected together?

Q5) Is it possible to send a schematic diagram of your test setup?

Regards,
Phil Corso, PE {Boca Raton, FL, USA}
[[email protected]] ([email protected])

 

Is this John Galt?

 

This is not an uncommon occurence.The magnetic asymmetry of the 3 limb core (while this is considered a symmetrical core, this in fact is an asymmetrical core) causes asymmetrical magnetising currents (and hence asymmetrical mmf's). Also, this mmf has take care of quite long lenghts of magnetic circuit, that do not have any turns on them.

The sum of the instantatneous powers indicated by the 3 wattmeters represent the total power consumed (sum of the powers indicated by N wattmeres for an N phase system always gives the total power; Blondell's thorem ??). In fact, there are reported cases, where a second reversal has occured, rendering this power once again positive.

The following may be a possible explanation. We have to look at this in terms of shifting magnetic neutrals, one at top where the 3 fluxes converge and one at bottom where the three fluxes diverge (total flux being zero at these magnetic neutrals, since this is a 3 phase system). This is representative of the spiracore construction, where the yokes at top and bottom converge at a point in a star like formation(magnetic neutrals). Hence there is symmetry in core.

But the conventional 3 limb core is rendered assymmetricl, because it is a departure from the spiracore construction and the magnetic length to be traversed by the three fluxes are not equal any more. Another way of looking at this is that the central limb of a spiracore construction is pushed in so that it is in line with the other two limbs. Now this core can be viewed more as a delta configuration than star configuration (spiracore). As a point of interest, the delta type spiracore is still being manufactured by some companies.

Due to this assymmetry that has been introduced, there is significant change in the individual reluctances. Due to this, the two magnetic neutrals shift more and more to one side of the core and in special cases may be located within one limb itself, say at the top and bottom. Then for the three fluxes to be 0, the flux (and hence the no-load loss) in this third leg (let us call this Phase C for convenience) will be only for the height between the two fictitious neutrals, as rest of this limb is covered by the resultant of the other two fluxes. Hence the no-load loss for this portion of 3rd limb, not travesed by its own flux will be part of the losses measured by the other two wattmeters (phases A and B). At the transition point (where the two magnetic neutrals have shifted so much that they coincide), the flux in C Phase due to excitation of C phase is zero. Hence the power indicated is zero. The extreme case is where these two fictitious neutrals cross each other, there by reversing the flux in phase C, to make the total flux zero, which results in phase C acting like a source of power(in reality, it is measuring power in a part of core where the polarity of potential applied to wattmeter has reversed). The power in the overlapping area is already measured by the wattmeters of phases A and B. What wattmeter of phase C is measuring is the same power in the overlapping zone, but as a negative value.

Mathematically, in this extreme condition, phases A and B registered the power for the entire core plus the small region of overlap. Hence the power measured is the sum of the three wattmeters, due care being accorded to the sign. The loss in this overlap region needs to be subtracted. The three mmfs have to exist as they are the very reason why the situation exists

But this trend is less and less noticeable at the normal flux densities encounetered in modern day core materials, partly due to improved material charcteristics and partly due to step-lap construction. But, even in these modern cores, at higher flux densities, we can still see significant unbalances in the three individual readings, with power in one phase moving towards very low values (approaching zero).

Regards

 

Further to the details I sent earlier, I would like to add the following, as there was an error in one of the paragraphs which wrogly referred to potential rather than current:

The errant paragraph is repeated as:

"Then for the three fluxes to be 0, the flux (and hence the no-load loss) in this third leg (let us call this phase C for convenience) will be only for the height between the two fictitious neutrals, as rest of this limb is covered by the resultant of the other two fluxes. Hence the no-load loss for this portion of 3rd limb not traversed by its own flux will be part of the losses measured by the other two wattmeters (phases A and B). At the transition point, (where the two magnetic neutrals coincide), the flux in C phase due to excitation of C phase is zero. Hence the power indicated is zero. The extreme case is where these two fictitious neutrals cross each other (which condition requires a reversal of flux in phase C for the total flux to be zero), there by reversing the flux in phase C, which results in phase C acting as if it is a source of power (in reality, the potential applied to the wattmeter is reversed, there by registering negative power). The power in the overlapping area is already measured by the wattmeters of phases A and B. What wattmeter of phase C is measuring is the power in this overlapping zone of the core."

Please replace this with:

"Then for the three fluxes to be 0, the flux (and hence the no-load loss) in this third leg (let us call this phase C for convenience) will be only for the height between the two fictitious neutrals, as rest of this limb is covered by the resultant of the other two fluxes. Hence the no-load loss for this portion of 3rd limb not traversed by its own flux will be part of the losses measured by the other two wattmeters (phases A and B). At the transition point, (where the two magnetic neutrals coincide), the flux in C phase due to excitation of C phase is zero. Hence the power indicated is zero. The extreme case is where these two fictitious neutrals cross each other (which condition requires a reversal of flux in phase C for the total flux to be zero), there by reversing the flux in phase C, which results in phase C acting as if it is a source of power. In reality, depending on the flux density in the core (which has to be reversed to counteract the last condition where the magnetic neutrals crossed each other), the phase displacement between current and voltage in C phase will have to be greater than 90 deg (which will require reversal of the current coil of the wattmeter as there is change in power component direction) and this is seen as a negative power in the wattmeter connected to particular phase (C phase). The power in the overlapping area is already measured by the wattmeters of phases A and B. What wattmeter of phase C is measuring is the power in this overlapping zone of the core.

It must be remembered that the resultant flux density in the various parts of core at all times will be will be the designed flux density only."

Please make the above change. Sorry about this error that inadvertently crept in.

Regards

 

Dear Friends,

Power is given by P= V*I*Power factor. However,
if the load is inductive or capacitive there occurs a phase difference in V and I. Now assume when V is positive, I is negative or otherwise V is negative and I is positive. In both cases the product V * I * power factor is negative.

If lag or lead is small say P.F > 0.6, over the total cycle, in spite of above phenomenon for majority of period both V and I are either both positive or both negative. And hence average value is positive.

But if P.F is too low, i.e. P.F < 0.6, effect of
V +ive, I -ive (or vice-versa) is larger than
both positive or negative. which makes the average value negative.

Ram Kumar Tiwari