Transformer Loading:
- Thread starter rattus
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- Wisconsin
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- PE (Retired) - Power Systems
Re: Transformer Loading:
Let me get this straight.
VA is not a vector quantity.
Wow, and I always thought that VA was made up of two components P(watts) and Q(vars)?
Let me get this straight.
VA is not a vector quantity.
Wow, and I always thought that VA was made up of two components P(watts) and Q(vars)?
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- Mission Viejo, CA
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- Professional Electrical Engineer
Re: Transformer Loading:
Jim,
rattus is right that power (energy/unit time) is not a vector. Instantaneous current and voltage are vectors. Watts (Joules/sec) are the scalar(dot)product of the instantaneous current and voltage vectors; "power factor" being the cosine of the angle between them.
It is mathematically convenient to represent RMS values of voltage, current and power in three-phase systems as pseudo-vectors, but there is no "direction" of an RMS value; it only has magnitude.
While the math "works" conveniently for RMS values, it doesn't change the instantaneous physics.
Jim,
rattus is right that power (energy/unit time) is not a vector. Instantaneous current and voltage are vectors. Watts (Joules/sec) are the scalar(dot)product of the instantaneous current and voltage vectors; "power factor" being the cosine of the angle between them.
It is mathematically convenient to represent RMS values of voltage, current and power in three-phase systems as pseudo-vectors, but there is no "direction" of an RMS value; it only has magnitude.
While the math "works" conveniently for RMS values, it doesn't change the instantaneous physics.
Re: Transformer Loading:
OK Jim, I will admit that you can look at power this way, but it is not a vector quantity in the usual sense. I have never seen power expressed with a phase angle.
Straight from the Internet, I can't get to my books right now:
"Also note that the waveform for power is not at the same frequency as the voltage or current! Rather, its frequency is double that of either the voltage or current waveforms. This different frequency prohibits our expression of power in an AC circuit using the same complex (rectangular or polar) notation as used for voltage, current, and impedance, because this form of mathematical symbolism implies unchanging phase relationships. When frequencies are not the same, phase relationships constantly change.
As strange as it may seem, the best way to proceed with AC power calculations is to use scalar notation, and to handle any relevant phase relationships with trigonometry."
You can split apparent power into watts and VARs, but the current still heats up the transformer, and the real power is dissipated in the load.
Furthermore, in a resistive load for example, the product of v(t) x i(t) produces a waveform which is always positive, at twice the frequency, and which is not sinusoidal. No way to convert this waveform to a vector quantity.
[ March 11, 2005, 12:20 PM: Message edited by: rattus ]
OK Jim, I will admit that you can look at power this way, but it is not a vector quantity in the usual sense. I have never seen power expressed with a phase angle.
Straight from the Internet, I can't get to my books right now:
"Also note that the waveform for power is not at the same frequency as the voltage or current! Rather, its frequency is double that of either the voltage or current waveforms. This different frequency prohibits our expression of power in an AC circuit using the same complex (rectangular or polar) notation as used for voltage, current, and impedance, because this form of mathematical symbolism implies unchanging phase relationships. When frequencies are not the same, phase relationships constantly change.
As strange as it may seem, the best way to proceed with AC power calculations is to use scalar notation, and to handle any relevant phase relationships with trigonometry."
You can split apparent power into watts and VARs, but the current still heats up the transformer, and the real power is dissipated in the load.
Furthermore, in a resistive load for example, the product of v(t) x i(t) produces a waveform which is always positive, at twice the frequency, and which is not sinusoidal. No way to convert this waveform to a vector quantity.
[ March 11, 2005, 12:20 PM: Message edited by: rattus ]
- Location
- Mission Viejo, CA
- Occupation
- Professional Electrical Engineer
Re: Transformer Loading:
Where I lived in Africa, the homes were wired 380/220. The water heaters were wired on one phase and "controlled" by a local contactor. As an energy conservation method the "water-heater" phase was opened periodically by the local utility. The process was rotated throughout the city.
Re: Transformer Loading:
rattus
Tony requested that you put your caculations for us to view.
You responded to my request as follows:
"Bob, I have done this more than once, and no one took note. I am asking you and Jim to do it yourselves. Anyone proficient in AC system design can do it blindfolded". I would like to see the caculations. Tell me where they are. What page?
[ March 11, 2005, 01:50 PM: Message edited by: bob ]
rattus
Tony requested that you put your caculations for us to view.
You responded to my request as follows:
"Bob, I have done this more than once, and no one took note. I am asking you and Jim to do it yourselves. Anyone proficient in AC system design can do it blindfolded". I would like to see the caculations. Tell me where they are. What page?
[ March 11, 2005, 01:50 PM: Message edited by: bob ]
Re: Transformer Loading:
Bob, try page one. That is the place where you informed me that resistance does not carry a phase angle. There is another post on the Oregon thread I believe with numbers.
If you and Jim would just concede that power is a scalar quantity and cannot be added vectorially, this discussion would be at an end.
A BTU is a BTU is a BTU irrespective of the load configuration. Heat is not a vector quantity either.
Now where is the vector diagram I requested?
Bob, try page one. That is the place where you informed me that resistance does not carry a phase angle. There is another post on the Oregon thread I believe with numbers.
If you and Jim would just concede that power is a scalar quantity and cannot be added vectorially, this discussion would be at an end.
A BTU is a BTU is a BTU irrespective of the load configuration. Heat is not a vector quantity either.
Now where is the vector diagram I requested?
Re: Transformer Loading:
rattus
I went back over all the posts and did not see your caculations. However I am not sure what I am looking for. Jim Dungar is the only one I found that had any caculations of any significance. Did not look at the other post. Please list yours so we can see.
several of my references and found no angle associated with power.
[ March 11, 2005, 07:15 PM: Message edited by: bob ]
rattus
I went back over all the posts and did not see your caculations. However I am not sure what I am looking for. Jim Dungar is the only one I found that had any caculations of any significance. Did not look at the other post. Please list yours so we can see.
I don't think I had any comment on this. I checked
several of my references and found no angle associated with power.
[ March 11, 2005, 07:15 PM: Message edited by: bob ]
physis
Senior Member
Re: Transformer Loading:
I'm not interested in being involved in the debate, I'd have to do the math and I really don't feel like it.
I don't recall who it was, but I saw I think on the last page, I'm pretty sure, a specific statement regarding working with power vectorially.
And Rattus, if your going to debate math, you must use equations to do it.
I'm not interested in being involved in the debate, I'd have to do the math and I really don't feel like it.
I don't recall who it was, but I saw I think on the last page, I'm pretty sure, a specific statement regarding working with power vectorially.
And Rattus, if your going to debate math, you must use equations to do it.
Re: Transformer Loading:
OK Sam, equations you want, equations you get:
First let the phase voltages be:
Van = 120V @ 0
Vbn = 120V @ 120
Vcn = 120V @ -120
Then,
Vac = Van - Vcn = 208V @ 30
Now connect a resistor of 20.8 Ohms across Vac.
Then,
Iload = 208V @ 30/20.8 Ohms @ 0 = 10A @ 30
In = 0
Now consider separate loads across Van and Vcn:
12 Ohms @ -30 load across Van,
Ia = 120V @ 0 / 12 Ohms @ -30 = 10A @ 30
12 Ohms @ 30 load across Vcn.
Ic = 120V @ -120 / 12 Ohms @ 30 = 10A @ -150,
In = 0
Now for the tricky part:
Ic is the current out of Vcn, but we want the current into Vcn, so we must take the negative, i.e.,
-Ic = 10A @ 30;
You will find that the currents are exactly the same in both cases, but the xfrmr does not know the difference, nor does it care. It only knows it is being saddled with 1200VA per winding, not 1040VA.
So, it is illogical to say that the load is 2400VA in one case and 2080 in the other! The heating effect is the same!
To those who would say, "who cares?", I would reply that this is a mind exercise to help one to better understand ratings and phase angles.
I think I understand ratings and angles. I do not understand however why it takes so much argument to get across the simple point that for a given current and voltage, the heating effect is the same in the transformer irrespective of the load configuration.
[ March 12, 2005, 08:52 AM: Message edited by: rattus ]
OK Sam, equations you want, equations you get:
First let the phase voltages be:
Van = 120V @ 0
Vbn = 120V @ 120
Vcn = 120V @ -120
Then,
Vac = Van - Vcn = 208V @ 30
Now connect a resistor of 20.8 Ohms across Vac.
Then,
Iload = 208V @ 30/20.8 Ohms @ 0 = 10A @ 30
In = 0
Now consider separate loads across Van and Vcn:
12 Ohms @ -30 load across Van,
Ia = 120V @ 0 / 12 Ohms @ -30 = 10A @ 30
12 Ohms @ 30 load across Vcn.
Ic = 120V @ -120 / 12 Ohms @ 30 = 10A @ -150,
In = 0
Now for the tricky part:
Ic is the current out of Vcn, but we want the current into Vcn, so we must take the negative, i.e.,
-Ic = 10A @ 30;
You will find that the currents are exactly the same in both cases, but the xfrmr does not know the difference, nor does it care. It only knows it is being saddled with 1200VA per winding, not 1040VA.
So, it is illogical to say that the load is 2400VA in one case and 2080 in the other! The heating effect is the same!
To those who would say, "who cares?", I would reply that this is a mind exercise to help one to better understand ratings and phase angles.
I think I understand ratings and angles. I do not understand however why it takes so much argument to get across the simple point that for a given current and voltage, the heating effect is the same in the transformer irrespective of the load configuration.
[ March 12, 2005, 08:52 AM: Message edited by: rattus ]
- Location
- Wisconsin
- Occupation
- PE (Retired) - Power Systems
Re: Transformer Loading:
rattus,
I never said power (P) was a vector. I said VA was a vector made up of scalar components P and Q.
And after reviewing your calculations, you are correct it is "tricky", I never new that the inverse of Ic=10A @ -150?, was -Ic=10A @ -30?.
I always believed that it was,
10 @ -150? - 180? = 10 @ 30?,
which would make the current into Vcn equal to the current leaving Van satisfying almost every network analysis I know of.
[ March 12, 2005, 08:34 AM: Message edited by: jim dungar ]
rattus,
I never said power (P) was a vector. I said VA was a vector made up of scalar components P and Q.
And after reviewing your calculations, you are correct it is "tricky", I never new that the inverse of Ic=10A @ -150?, was -Ic=10A @ -30?.
I always believed that it was,
10 @ -150? - 180? = 10 @ 30?,
which would make the current into Vcn equal to the current leaving Van satisfying almost every network analysis I know of.
[ March 12, 2005, 08:34 AM: Message edited by: jim dungar ]
Re: Transformer Loading:
It illogical to say it is different for different load configurations. It should be obvious to anyone who knows anything that we are in effect talking of a current rating and that does not change because the line to line voltage is 208V instead of 240V.
How do you justify this thinking?
The standard methods simply do not apply to special cases such as this.
I hope by now that even Bob the consultant will admit there is a PF in the secondaries. But the real issue is, "What is the loading on the transformers?"
It illogical to say it is different for different load configurations. It should be obvious to anyone who knows anything that we are in effect talking of a current rating and that does not change because the line to line voltage is 208V instead of 240V.
How do you justify this thinking?
The standard methods simply do not apply to special cases such as this.
- Location
- Wisconsin
- Occupation
- PE (Retired) - Power Systems
Re: Transformer Loading:
rattus, I apologize, after all we all make typos.
But I still can not accept your conclusion.
In both of your situations the current through each winding is equal and in the same direction, or else there would be a residual current In. If the vector current in each winding is the same then the VA loading of the transformer must be the same.
Also, this is not a uniquely special case. Wye connected transformers are routinely severely unbalanced.
rattus, I apologize, after all we all make typos.
But I still can not accept your conclusion.
In both of your situations the current through each winding is equal and in the same direction, or else there would be a residual current In. If the vector current in each winding is the same then the VA loading of the transformer must be the same.
Also, this is not a uniquely special case. Wye connected transformers are routinely severely unbalanced.
- Location
- Wisconsin
- Occupation
- PE (Retired) - Power Systems
Re: Transformer Loading:
No, I am not switching sides. The transformer winding loading is always 1200VA each and the total transformer loading is 2080VA. If there is no neutral current then the two series connected loads must be identical in loading to a single load.
No, I am not switching sides. The transformer winding loading is always 1200VA each and the total transformer loading is 2080VA. If there is no neutral current then the two series connected loads must be identical in loading to a single load.
Re: Transformer Loading:
It is the internal resistance of the windings that partly determines the rating--not the load resistance.
Let's say each transformer has an effective series resistance of 1 Ohm. Then 100W is dissipated in each set of windings. Now how does the neutral current, phase angle, or anything else change that fact? Power is a scalar quantity, as you admit, and must be added arithmetically.
Jim, please support that argument with some sort of physical principle or law.
It is the internal resistance of the windings that partly determines the rating--not the load resistance.
Let's say each transformer has an effective series resistance of 1 Ohm. Then 100W is dissipated in each set of windings. Now how does the neutral current, phase angle, or anything else change that fact? Power is a scalar quantity, as you admit, and must be added arithmetically.
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