It is well-known that traditional 3-phase electrical circuits present 2 topologies: 3 wires or 4 wires (if a neutral wire is present). Power engineers have tools to analyze these circuits in both time or phasor domain (Symmetrical components, Clarke transformation, etc). This is not a major problem.
Let's now suppose that we have a "black box" supply and a "black box" load. They are linked by 4 wires. Should we consider the system a 3-phase 4-wire circuit or a 4-phase 4-wire circuit?
What are the implications? is a 3-phase 4-wire circuit a special case of an asymmetrical and unbalanced 4-phase 4-wire circuit? Do 3-phase and 4-phase Symmetrical Components lead to the same results?
Of course, this can be generalized to n-phase (n+1)-wires....
Hi Paco,
Check this one out first:
Willems, J. (2010). Terminals and Ports. IEEE Circuits and Systems Magazine, 10(4), 8–26. doi:10.1109/mcas.2010.938635
This work sheds a pretty general light on the question of how to define energy and power in a multi-terminal circuit.
Best regards,
Dimitri
Hello Francisco G. Montoya ,
In the US, we have a residential AC power topology known as the split phase configuration in which the two ends of the distribution transformer's secondary winding provides 120 VAC with respect to the center tap of the secondary winding (the neutral); the two 120 VAC hot leads are 180 degrees out of phase with respect to one another. If one measures the RMS voltage difference between the two ends of the secondary winding, one gets 240 VAC, while a measurement between either end and the center tap of the same winding yields 120 VAC RMS voltage difference. The 240 VAC configuration can be used to power electric water heaters, ranges (stoves = burners + oven), etc. The 240 VAC configuration can use either 3-wires (two hots, & a neutral) or 4-wires (two hots, a neutral, & a safety ground); the 4-wire system is used with modern stoves because the burners need 120 VAC, while the oven heating element needs 240 VAC. Note, in older stoves the oven element, which is connected across the two hot wires, is switched off by breaking only one of the two hot wires leading to a very serious safety issue, if you are unaware of it - as I was. The 120 VAC configuration can be used to power lights, receptacles for small appliances, etc. This 120 VAC configuration can use either 2-wires (hot, & neutral), which is only found in older homes, or the more common and up to modern electrical code 3-wires (hot, neutral, & safety ground). Both the 120 VAC and 240 VAC configuartions are considered single phase (or split phase) systems no matter how many wires they employ. But more to the point, you cannot simply connect a 120 VAC load to a 240 VAC source, both from an overload (too much current and/or voltage breakdown) perspective and a safety (mixing up the neutral with the safety ground) perspective. In other words, your load and source cannot be black boxes, unless you want a potential disaster. I would think the same cautions would hold for a 3-wire or 4-wire 3-phase configuration.
Anyway, this is my simple minded view of the matter.
Regards,
Tom Cuff
Thank you Thomas Cuff for your reply. Yes, the split-phase configuration is a nice example of a 2-phase 3-wire circuit. Again, if no information is provided, it's not possible to know if it is really a 3-phase 3-wire circuit (regardless of the line voltage) or not.
For example, if you measure voltages and currents at supply/load terminals, then you need to decide what SC version to use. should you see 2D or 3D Fortescue matrix?
Thank you for the nice paper Dimitri Jeltsema. I read it carefully and it is quite interesting for the power/energy flow field. The concepts of port and terminals are clearly explained. Indeed, both (n+1) and n-wire circuits can be considered 1 port of KCL
Hello Francisco G. Montoya ,
If I form a load using three identical value resistors in a star configuration (one lead from each resistor attached together, and the free ends of the resistors connected to the 3-wire source), then I should be able to distinguish a 3-wire split-phase source from a 3-wire 3-phase source with a clamp-on current probe. In the case of the 3-wire split-phase source, one of the leads of the load should have zero current, while in the case of the 3-wire 3-phase source, all three leads of the load should read the same nonzero current.
Regards,
Tom Cuff
This is not alway true because a high asymmetrical and unbalanced load can lead to the same readings!! What is the limit?
Think for example in a line to ground fault....
Hello Francisco G. Montoya ,
I agree with your previous statement, but only if your original question is amended to explicitly state that the investigator is not allowed to completely disconnect the black box load from the black box source. Otherwise, a voltmeter should be sufficient to distinguish the phases from one another and from the neutral (if it is present) and/or ground (if it is present). In a real world power system, the ability to disconnect all the phases - but not the neutral and/or ground - would usually be required by the electrical code for safety reasons. With regard to your previous statement and your original question, there is an implied absence of any over current protection, which would clear a phase to gound fault, for example. I am not trying to be difficult, here. I am just asking for clarification of the rules implicit in your original question, or as ISO would put it: say what you mean, and mean what you say.
I won't take up anymore of your time. Thanks for an interesting question.
Regards,
Tom Cuff
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