These terms can be misunderstood ... so just to help you out a bit, lets go back to the start and develop the terms and their meanings "in context" 👌

No apology to the "boffins" and "gurus" who may think "yeah I know all that ...", they may indeed still find something they didn't know 👏🤞. 

For the rest I have tried to explain in detail and at length, i.e. some may be able to do the same thing in much fewer words, but I didn't want to presume any "short hand" was understood by everyone.

If something is still not clear, please let me know - you can contact me using the link in the right-hand panel.

Understanding the relativity of direction.

We use the term "direction" in lots of different ways in every day life.
An example from a non-electrical "domain" is that we would say Israel, Egypt etc are in the Middle East, Japan in the Far East, .... but east of what ... east of Greenwich England purely because that is where 0° longitude line running from North Pole to South Pole was (eventually) arbitrarily set. 
On the other hand we would say that England and France are both part of the "western world", whilst places like Australia and New Zealand are also part of the "western world" despite being further east than the Far East!

(Aside: Of course why Greenwich is 0° is interesting in itself because of the early days of sailing ships at the height of the English "great global empire" exploring the world. To sail the seas, you needed to synchronise your clock by the Greenwich Ball Drop as they sailed away - knowing what time it was in Greenwich allowed you to calculate how far around the globe east/west you had travelled.  So seeing the ball drop on the Observatory roof was better than waiting to hear a canon fired because speed of light vs speed of sound gave better accuracy and coherency for all ships wherever they were at all times of day.  So whilst the New York Times Square New Years Eve ball drop is "cute", Christopher Columbus needed that 0° point of reference defined by the Greenwich Observatory Ball Drop to synchronise his ship's chronometer be able to map how far west America was!)

A subtle epiphany is therefore that "direction" is always RELATIVE  (... mmm .... thinking) ... maybe I should write some sort of universal physical Law about relativity and "frames of reference" .... I could become famous and be called a genius. 🤔

Since direction is relative to a reference, we could say that it is arbitrary because I can simply change my point of reference at any time - Paris is "in an easterly direction" if the reference is London, but it is "in a westerly direction" if the reference is Berlin.

In any wire, the current can ONLY flow along that wire one way or the other i.e. if we are looking side–on to see both ends of a horizontal wire, current can only flow left or right.

However, in an a.c. system the Direction of Current also depends on what exact instant in time I look at that wire!
At one instant without any other frame of reference, I could look at that wire and the current is flowing to the right
Half a cycle later and I look at that wire again, it is flowing to the left.

Confusing?

Furthermore, if we turn the wire vertical, we can say the "direction", and hence the arrow, changes to up or down even though the flow of charge through the wire stays the same.

The "way" .. the direction of current flow ... is defined in IEC 60375 BY CONVENTION as the flow of the positive charge.
That Standard also goes on to emphasize the point that the flow of electric current is the opposite direction to net flow of "free carriers of negative electric charge" i.e. opposite to the flow of electrons.
In an ac system where the electrons oscillate from one half cycle to the next, so the electrons don't "go anywhere" overall, we STILL only consider the Direction of Current flow to be left or right as it would in one half cycle.

We can therefore assign an arrow to that Direction of Current flow on that horizontal wire to represent if it ("it" being the positive charge) is flowing to the left or to the right!

Considering that flow of current, NO relay simply "measures" whether such arrow (Direction of Current) is pointing left or right.

A standard non-directional overcurrent 50/50TD/51 relay is just a MAGNITUDE ONLY based device which operates for currents of magnitudes between the operating setting (noting most relays actual trip operating current is higher than the specific pickup/threshold setting) and the maximum fault level current. 

Indeed a 50/50TD/51 function does not NEED any voltage input ... and it may be just a single phase element with no idea of what is happening on other phases. 
Modern relay often do have voltage inputs but that is for other purposes than the 50/50TD/51 functions, so you could leave the voltage terminals disconnected and the 50/51 would still work correctly.
Furthermore if we have a single current input to a particular element and we swap the connections to the two terminals, the relay still works exactly the same.
A 50/50TD/51 function truly has no concept of "direction" - it has no change in operation even if we reverse the Direction of Current through the terminals!
That 50/50TD/51 element does not care if the current is flowing left or right, or indeed what power factor is involved.
It ONLY considers Magnitude of Current.

Polar phasor diagrams are a snapshot in time of the rotating phasors V and/or I.
They are not two-axis as horizontal and vertical .. they are not like a map north-south vs east-west.
They are the overall r.m.s. (root mean square) magnitude calculated over the cycle and the angle relative to a particular reference angle - they are therefore circular.
They represent quantities that vary in instantaneous magnitude in a sinusoidal nature.

For convenience/convention, we first define the reference angle 0°of the polar circle as “horizontal to the right” and we would (generally, but perhaps not always for any obscure reason) say that corresponds to t=0.

This lines up nicely with the formula of sinewave being:

sin(ωt)

For electricity, we have two waveform formulas that are true at any instant in time (assuming you correctly juggle the mathematics between using Radians or Degrees in your calculation method – “for on screen display” here I will use degrees for angle although ω implies radians)

V(t) = |V| x sin(ωt + a°)

I(t) = |I| x sin(ωt + b°)

Note so far, I have not specifically defined which phase current Ir, Iy, Ib is I; or which phase‑to‑neutral Vrn, Vyn, Vbn or phase‑to‑phase voltage Vry, Vyb, Vbr is the V(t) I am referring to.

We can take a snapshot of the V and I waveforms at any point in time and represent their position on that polar diagram – V and I are always in the same angle relativity of “a” relative to “b”.

It is to note, that at all of times, the PQS vectors are "fixed" on the P:Q plane because we use S = VI*
I* being the complex conjugate of I(t). 
In other words, because the PQ vector plane is not a time-referenced diagram, the overall "direction" of P and Q flow do not change throughout the cycle, even though the instantaneous V times I phasor would rotate at twice the system frequency.

Non-Directional Overcurrent Function

IEEE C37.2 lists two generic Non-Directional Overcurrent elements (annoyingly they refer to a "relay" when most modern "relays" comprises multiple elements which individually can be any device number)

1. device 50 as an instantaneous operation,
   1. device 50TD as a Definite (fixed) Time operation,
2. device 51 as a time-based operation inversely proportional to the current relative to the current setting

So let's now focus on say only the A-phase current as applied to a single-phase Non-Directional  Overcurrent element (50, 50TD or 51 as the case may be) ... and for the sake of simplicity, but not specifically relevant to a single input current element, we will assume Unity Power Factor.

As discussed above, in principle we can draw a phasor diagram at an instant throughout the cycle knowing that the angular relationship between V and I remains the same so the position of that snapshot can have both the V and I phasor at some angle relative to the zero degree axis, hence the "pure form" of the equations where no specific phasor is adopted as the reference are:

Vrn(t) = |Vrn| x sin (ωt + a°)

Ir(t) = |I| x sin(ωt + b°)

We can further derive that the phase‑to‑phase voltage between Yellow and Blue is in quadrature to the Vrn phasor.

Vry(t) = |Vry| x sin (ωt + a° -90°)

At Unity Power Factor, Vrn and Ir are in phase so a = b, therefore a-b = 0

Cos (a-b) = 1

We "normally" assign a certain phasor as the reference phasor at 0° horizontal.
However as shown in the above four time phasor diagrams at different times, there is nothing "stopping" me drawing the Unity Power Factor Phasor Diagram of just the single current phasor when the current phasor happens to be at 45° to the horizontal 0°.

Therefore returning to the phasor diagram showing ONLY the current phasor, we can see that a 50/50TD/51 element has a "donut" operating zone .. inner edge of the donut is the pickup setting magnitude, and the outer edge is the max fault current magnitude.
If the current phasor (red arrow) sits anywhere within the green shaded zone on the phasor diagram, the 50/50TD/51 will (eventually) trip.

Note if we "happen" to look at this system just half a cycle later, the same operating zone is still true ... BUT we do not say that the Direction of Current has changed! 
We just have to realise that the point of relativity in respect of TIME has changed.  

Clearly the Direction of Current as defined by IEC 60375 has not changed, but the phasor position moves around depending on the "point of relativity" in time that we take the snapshot of that phasor.

Directional Current Elements

IEEE C37.2 defines Device 67  is (specifically an a.c.) DirectionAL Overcurrent element - I emphasis the "AL".

Note carefully, it does not say it is a "Direction OF Current" relay!

The use of the term "DirectionAL" implies there is some aspect that is associated with a "direction".

Also to note that taking the above example in the Non-Directional element section of swapping the connections to the two terminals of that directional element, we do in fact see that the relay, still subject to magnitude, either ceases to try operate, or does try operate!

What's that I hear you say .... "aha! Contradicting yourself from earlier on this page when you said <<NO relay simply "measures" whether such arrow is pointing left or right>>, yet clearly a 67 operates for the arrow in one direction but not the other!! "

Sigh! 
I suppose at first thought that could be a fair observation ... but I just again highlight ... direction is relative!!!

Lets first consider a primary conductor passing through a series of CT cores.
The same current (load or fault) is flowing on the primary through all cores.

The first "point of relativity reference" is that I am going to ARBITARILY decide that for this section of the power system, the FORWARD direction relative to the CT location is at the right-hand edge of the image.  I (or you) could have chosen the left-hand edge, but it just suits me to choose the right-hand edge!

The second "point of relativity reference" to check is the CT wiring.

The third is the CT polarity.

The fourth is the relay polarity.

.. and now with modern numerical relays, the FIFTH "point of relativity reference" is the relay polarity setting.

Depending on all those FIVE independent but critical relativities, the relay must interpret that the left-to-right flow of current on the primary to be considered FORWARD but which is seen in the left most configuration as current flow left-to-right through terminal 1-to-2, or in other combinations as as right-to-left through terminals 2-to-1!! 

Indeed as we move through the power system we may well find different organisation have different Forward/Reverse definition and different CT polarity specification:

• Forward = away from the generator
• Forward = towards the (usually) net load
• Forward = away from the busbar, i.e. flow is in opposite directions swaps either side of a busbar
• Forward = into the busbar for a bus incomer and out of the busbar for a feeder

Then consider a line connecting substations of two different organizations where they have defined direction differently at each end of the line!

Or where CT polarity is specified differently

• P1 towards Bus, S2 Star away from Bus
• P1 towards Bus, Star (S1 or S2) towards protected plant
• P1 away from protected plant, S2 star towards protected plant

So back to whether I contradicted myself .... we need to challenge what wire swap means ... is it truly a change in Direction of the Current, or was it a change in point of relative reference??
Clearly the change is NOT a change in the Direction of the primary current - load or fault as the case may be!

As direction is relative (arbitrary), we need to precisely define what thing's direction are we talking about ... the Direction Of Primary Current through the CT ... or the Direction of Secondary Current through the Relay?  Which is THE point of reference?

So I have not contradicted myself.
For the same Direction Of Primary Current through the CT, in the absence of making any other relativity changes, swapping the Direction of Secondary Current through the Relay does in fact swap the operation or non-operation of the protection element.
So provided we do our job correctly for the design drawings to the wiring to the settings and adjust the combination of the connections, polarities and the settings, there would be NO change in operation of that DirectionAL relay!
Of course, do that job incorrectly and you have mayhem!

Operating Direction of a Directional Overcurrent Element.

So considering the donut operating zone of a Non-Directional Overcurrent element, what can we say about the operating zone of a Directional Overcurrent element?

Once again we have to consider our point of reference of what that DirectionAL zone actually means.

It is a little tricky and still confuses many .. including some of the text-book type attempts of explanation.

Hence I have dedicated a separate page Directional protection characteristic angle describing how we get the "half donut" operating zone on the phasor diagram 👌  

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