Set up an experiment with a 3? source and load... and of course 3 conductors. In each of the 3 conductors insert an ammeter biased with negative to the source an positive to the load. Energize the system and take a plethora of instantaneous readings at regular intervals during at least the first cycle of current. If we choose to use the negative to positive current flow convention, when an ammeter is reading positive, current is flowing from the source to the load, and conversely when an ammeter is reading negative, current is flowing from the load to the source.
That would be using electron flow notation. Thanks to Ben Franklin, the other way is called conventional flow notation and uses hole flow. We are taught both, but the conventional notation is used in most electrical engineering texts. Either one works fine although electron flow might make more sense when studying the motion of electrons.
The above is regarding the pure physics of the system. Now when you enter the realm of mathematical analysis you have to choose to include direction or adopt the positive-negative convention as a substitute for direction.
We are fishing from the same boat here.
Under the former premise, it is obvious all currents do not flow from source to load. Under the latter, you can say all currents all currents flow from source to load because you have adopted an extra convention which permits you to do so.
Again, we must distinguish between the physical world and the way we measure the physical world.
Quite easy to do for DC, but the arrows change direction and magnitudes vary in AC circuit analysis.
We use instantaneous currents. In relaying and power systems, it is common to look at the current direction to be direction of flow in the positive 1/2 cycle using conventional notation.
Mivey, this universal constraint you speak of is only in your mind. I have stated no such thing. Under a particular mode of mathematical analysis I stated adopting the positive-negative convention is unnecessary. Quit stretching my words to mean something else.
Then I failed to see your point. In post
#82 you assert that of the three ways to state KCL, only one is correct. By saying that two of the three representations of KCL are wrong, you are constrained to using only the remaining one.
Perhaps the appearance of your supporting and then un-supporting certain conventions clouded your points. I am now thinking one of your points must be that when using vector notation, your measurements should always be based on all of the currents flowing in the same sense relative to the node?
You start out supporting the equation that sums all currents entering a node (could also be summing all currents leaving a node): From
#17: "The true vector base formula is Ia + Ib + Ic + In = 0". This equates to all of the meters having the same reference direction relative to the node.
In post
#48 you seem to say that there is something wrong with choosing arrows in an opposing direction (the same as using a negative sign): "To write your form of the equation, you have to adopt the convention that all currents flowing into a node are positive and all current flowing out of the node are negative. I refuse to adopt any convention that is totally unnecessary." Then your own diagram in post
#59 shows an adoption of both methods.
You show one system supporting the method of assuming positive flow for all currents leaving a node. All of the arrows face away from node 2 and show a positive needle deflection. To be clear, this is positive for leaving, negative for entering (In + I1 + I2 +I3 = 0)
You also show a system supporting the other convention. The three arrows associated with the phase currents face away from node 1 and show a positive needle deflection for current leaving. The neutral shows a negative deflection for current leaving (In = I1 + I2 + I3).
You also state there is no need to decide whether or not current is entering or leaving. The way you connect your meters makes those very assumptions. It matters a whole lot if you are feeding these currents into a relay as you may have to pick a positive or negative deflection for the instantaneous current leaving a node. Reversing the meter leads adds a negative sign (i.e. adds 180 degrees).
There is not some amorphous equation out there for a particular node under inspection. To inspect or analyze the system, we must choose some sign conventions and one method is not always better than the other.