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# Directional protection characteristic angle

=C2=A9 Copyright 2012 Rod Hughes Consulting Pty Ltd

Note - if the navigation pane on the left of this window is not visible,= click the 2-pane icon on the top bar

Directional protection requires the setting of an appropriate Relay Char= acteristic Angle  (RCA) to define what direction the relay is "looking= " to define half of the plane as the operating zone and the other half as t= he blocking zone.

The first training course I received on this back in 1982 provided a cop= y of "Sonnemann's paper" (and was referred to as such with highly revered s= tatus as you will see why).  It was published in an AIEE Transactions = back in 1950 so the copy I was given itself seemed to be a "copy of a copy"= .  As you can see Sonnemann's paper gives an extensive mathematical an= alysis of various fault conditions and the different 90, 60 (#1 and #2) and= 30 degree connections. I would say "good luck with reading that in its entirety!!"  But tr= y to get through it as much as you can.

However the subject deserves some additional explanation as follows whic= h may "bridge the gap" / "fill in the missing pieces of the puzzle" for you= , although in itself is not short either.

# Definitions=

There are two aspects to defining a Directional Relay application :

1. (Angle of the) Relay Connection
The a= ngle by which the current applied to the relay (at unity power factor) is r= elative to the voltage applied to the relay as the polarising voltage.=
e.g. Ia and Vbc is a 90=C2=B0 or Quadrature connection.
2. Maximum Torque Angle (MTA) / Relay Characteristic Angle (RC= A)
The angle by which the current applied to the relay= must be displaced from the voltage applied to the relay to produce maximum= torque
e.g. If the setting is MTA/RCA =3D +30=C2=B0, it means = that it is operating on the MTA/RCA when the actual current is leading the = polarising voltage by +30=C2=B0.
Hence, if it is a Qua= drature connection Ia and Vbc,, when Ia is leading Vbc by +30=C2=B0= , therefore Ia is lagging Van by 60=C2=B0, the system pha= se angle of Ia relative to Van is -60=C2=B0  at MTA/RCA,.

The discussion is in two parts - Phase Fault Overcurrent Relays and Eart= h Fault Relays.  Both sections use an example of a phase-to-earth faul= t.

# Phase Fault Overcurrent Relay Application

## (Angle of the) Relay Connection

I can recall in my early years being annoyed that this first term could = easily and inadvertently be called =E2=80=9CRelay Connection Angle=E2=80=9D= =E2=80=93 whilst that is understandable, as an acronym, that can easily be= confused with RCA being officially the Relay Characteristic Angle as the e= lectronic relay equivalent of MTA!!

So please be careful when referring to the =E2=80=9CAngle of the Relay C= onnection=E2=80=9D versus the "Relay Characteristic Angle"

Considering this =E2=80=9CAngle of the Relay Connection=E2=80=9D, Sonnem= ann defines four possible connections of voltage and current to the relay.<= /p>

The "old school" electromechanical rotating induction cup directional el= ements, e.g. the GEC CCD directional cup unit and CDD combined directional = and overcurrent/earth fault, were physically "per phase" elements so you ha= d to be very specific with the CT and VT wiring to get the right inputs to = each element.

With modern multifunction devices with the 3 phase-to-neutral voltage co= nnections and the three phase currents,  effectively every "connection= " option is available to the directional element as required by setting.&nb= sp;

However if we consider what are the required inputs to a particular dire= ctional calculation for one phase, we can consider those inputs in the gene= ric sense of a "connection".

If we just consider the A=E2=80=91phase directional overcurrent element,= with

• zero degrees of the Van phasor at the 12 o=E2=80=99clock pos= ition
and
• unity Power Factor

we get the following four connections to a directional element for= the A phase.

NOTE: at this stage we have not yet determined the required MTA/RCA for = the required protection zone!

Type

System Phasors

Connected Phasors

Current:  I= a

Voltage:  Vbc Figure 1 Figure 2 Figure 3

60=C2=B0 Type 1

Current:   Ia= =E2=80=93 Ib

Voltage:  Vac

(This CT arrangemen= t
may have been
associated with
so-called Z-connection
CT s= chemes which
only has two elements
for OC and EF and the
rel= ay is presented with
just (Ia-Ib) Figure 4 =

Figure 5 Figure 6

60=C2=B0 Type 2

Current:   Ia=

Voltage:  -Vcn Figure 7 <= /span>

Figure 8 =

Figure 9

30=C2=B0

Current:  Ia

Voltag= e:  Vac Figure 10 Figure 11 Figure 12

As most texts would agree, the most common = and practical form is the 90=C2=B0 Quadrature Connection for various techni= cal reasons of sensitivity as described by Sonnemann.  Whilst I have s= hown the direct physical connections for the various directional options, (= numerical relays can make the changes by settings), the remainder of this d= issertation is based on Quadrature Connection as per Figure 3 connecti= ons.

## Maximum Torque Angle (MTA) / Relay Character= istic Angle (RCA)

MTA and RCA are the same thing.  You may find "oldies" like me refe= r to MTA, when we should really now be using RCA in most cases.

Maximum Torque Angle refers to electromechanical relays like the old GEC= CCD and CDD where the cup mechanism literally rotated depending on whether= the fault was seen in the operating zone.
The Torque refers to the forc= e on the directional unit to swing one way or the other, which would then e= ither allow or block the other relay function, i.e. a simple operating deci= sion based on the fault being in the nominal range -90=C2=B0 to += 90=C2=B0 of the MTA.  The =E2=80=9Ctorque=E2=80=9D was important as at= low values of voltage, the operating zone would collapse inwards at the ou= ter boundaries centred at the MTA.
However but even at say 80=C2=B0 from= MTA, it would still swing in the ring direction.

RCA was introduced as the new term for electronic relays because there w= as no mechanical torque inside the relay.  This also means that the ef= fect of low voltages on the =C2=B1 degree range of the operating zone is mu= ch reduced. Nevertheless, the need to define the centre of the operating zo= ne remains.

This second term of MTA/RCA is a little tricky in the wording used in th= e above definition:
=E2=80=9CThe angle by which the current applied = to the relay must be displaced from the voltage applied to the relay to pro= duce maximum torque=E2=80=9D

In the Quadrature Connection, we know what voltage is applied, that is V= bc
So for a +30=C2=B0 RCA, we have to place a fault current phasor Ia=E2= =80=99 at +30=C2=B0 relative to Vbc =E2=80=A6. Note: it is NOT relative to = Va
So MTA is when Ia=E2=80=99 is here Figure 13

So what that means is the current Ia=E2=80=99 is effectively at 60 laggi= ng from the Va phasor, i.e. it is 0.5 power Factor lagging Figure 14

Hence MTA of +30=C2=B0 is achieved when the system Phase Angle =3D -60= =C2=B0 i.e. phase current Ia lags phase voltage Vn by 60=C2=B0 i.e. at Powe= r Factor 0.5 lagging.

Unfortunately due to printing fonts &/or typo errors, some texts ref= er to this Quadrature connection with 30=C2=B0 MTA/RCA which may appear as:=
90=C2=B0-30=C2=B0
The dash can be mis-interpreted as a MINUS sign, i= mplying the MTA/RCA is -30=C2=B0 which is not correct.

However this dash is not a minus sign, but is intended to be merely a te= xt separator between the two angles and hence is intended to be read as bei= ng =E2=80=9C90=C2=B0 connection with a +30=C2=B0 polarising voltage rotatio= n=E2=80=9D.
It may be better to reference this using a colon for better = clarity:
90=C2=B0 ; 30=C2=B0

There is some possibility of confusion due to the official MTA/RCA defin= ition uses a current compared to a voltage, but it is not our usual sense o= f such relativity which is the phase angle of Ia with respect to Va,

This is somewhat evident in the text book =E2=80=9CProtective Relays: Pr= inciples and Applications=E2=80=9D by Blackburn and Domin ISBN 10-1-57444-7= 16-5 and ISBN 13-978-1-57444-716-3.
In Table 3.1, connection number 5 as= Ia and Vbc is referenced as a =E2=80=9C90=C2=B0 -60=C2=B0=E2=80=9D connect= ion
But you will see in the definitions in the preceding paragraph that = the angle of -60=C2=B0 (and it is correctly a MINUS 60 in this definition) = is
=E2=80=9Cthe angle by which the system current lags the system v= oltage=E2=80=9D
i.e. they use PHASE ANGLE, not MTA/RCA to def= ine the arrangement .. it is still an accurate identification of the arrang= ement but just using different definitions based on the usual terminology o= f current with respect to voltage as being the System Phase Angle from whic= h we calculate Power Factor.

This dash in this instance is truly a minus sign is a clear confusion be= tween the previous note where the dash in "90=C2=B0-30=C2=B0" is specifical= ly NOT a minus sign.

At the risk of being presumptuous of =E2=80=9Credefining the entire worl= d=E2=80=9D, I would suggest to re-word the definition of MTA/RCA without re= ference to current, after all it is all about defining the location of the = polarising voltage with respect to the applied voltage as follows:
= =E2=80=9CThe angle by which the polarising voltage of the relay lead= s the applied voltage to the relay=E2=80=9D =

Figure 15

Now that would seem to make more sense that you get =E2=80=9Cmaximum tor= que=E2=80=9D when the connected current is in phase with Vpolarising.

Perhaps the following comparison examples w= ill help clarify the terms.

Consider a Directional Overcurrent element = with a 90=C2=B0 quadrature connection.
It has a certain pickup current <= u>magnitude that the red current phasor must exceed to operate .. that = is the smaller semi-circular boundary.
The red phasor magnitude by defin= ition cannot exceed the max fault current at that location .. that is the o= uter semi-circular boundary.
It also has a setting for the MTA/RCA .. th= e two examples are for +30=C2=B0 and +10=C2=B0 respectively (why&= nbsp;10=C2=B0 .. no reason, just to demonstrate!) .
The zones of operati= on are therefore bounded by =C2=B190=C2=B0 of the respective MTA/RCA a= nd referenced RELATIVE to the POLARISING VOLTAGE.
If the red current pha= sor falls with the green zone, the protection will operate.

90= =C2=B0 Quadrature Connection (Ia and Vbc)
MTA/RCA =3D +30=C2=B0
(PLUS 30=C2=B0)

MTA/RCA =3D +10=C2=B0
(PLUS 10=C2=B0) =

Figure 16 Figure 17

However, as an alternative choice, if the p= olarising arrangement is not Quadrature, but Angle of Relay Connect= ion is 30=C2=B0 (Ia and Vac), we get the same zones as follows by = changing the MTA/RCA to suit:

30= =C2=B0 Connection (Ia and Vac)
MTA/RCA =3D -30=C2=B0
(MINUS 30=C2=B0)
MTA/RCA =3D -50=C2=B0
(MINUS 50=C2=B0) Figure 18 Figure 19

If you compare the two blue background exam= ples, you can see the same zone coverage for the two different Connections = by choosing appropriate MTA/RCA to suit.

Similarly, the two fawn background examples= are the same zone coverage according to the Connection Angle and the MTA/R= CA to suit.

Published Document Error 1

Some of the misunderstandings of these angles is due to typographical fo= rmatting in published documents.

An example of this is the well known PRAG/NPAG/PAAG published at va= rious times by GEC, Alstom, AREVA, Schneider and GE.

If we have a look at the 1975 Edition 2, section 9.17.6 (see Figure= 20) has two examples titled:

90=C2=B0-30=C2=B0 characteristic (3= 0=C2=B0 MTA)

90=C2=B0-45=C2=B0 characteristic (4= 5=C2=B0 MTA) Figure 20 PRAG 1975 edition 2

Some others have ERRONEOUSLY simplified this apparent numerical referenc= e as a MINUS sign and therefore to simply be "60=C2=B0" and "45=C2=B0".
= But not so!!

The printed "-" dash is NOT= a mathematical MINUS sign ... it is just a text separator!= !

"90=C2=B0-30=C2=B0 characteristic (= 30=C2=B0 MTA)" is short-hand publishing notation for:
"90=C2=B0 Quadrature connection with a PLUS = 30=C2=B0 MTA/RCA relative to the Vbc Polarising Voltage"
This bec= omes clear(er) when you read the first sentence in each example:
The A phase relay is supplied with Ia and Vbc voltage displaced by 30=C2=B0 in an anti-clockwise d= irection. ...  the relay maximum torque is produced when the curren= t lags the system phase to neutral voltage by 60=C2=B0.

"90=C2=B0-45=C2=B0 characteristic (45=C2=B0 MTA)"  is short-hand pu= blishing notation for:
"90=C2=B0 Qu= adrature connection with a PLUS 45=C2=B0 MTA/RCA relative to the Vbc P= olarising Voltage".
This becomes clear(er) when you read the firs= t sentence in each example:
The A p= hase relay is supplied with Ia and Vbc voltage displa= ced by 45=C2=B0 in an anti-clockwise direction.

If we go back to the previous 1966 Ed= ition 1 of the PRAG, the title "90=C2= =B0-30=C2=B0 characteristic (30=C2=B0 MTA)" was actually segregated = in two paragraphs: =

Figure 21 PRAG 1966 edition 1<= /p>

As you can see, the 'clarity" of this= two-part reference is lost when it is "simplified" for "publishing purpose= s" into something which looks mathematical= : "90=C2=B0-30=C2=B0 characteristic (30=C2=B0 MTA)".=

Pe= rhaps these short hand representations should have said something like:

90=C2= =B0 Connection : +30=C2=B0 MTA/RCA

or

90=C2=B0= Connection with=  +30=C2=B0 MTA/RCA

Bottom Line = of this Warning: Please be careful of short hand publishing typographical formattin= g!

Published Document Error 2

A further example of possible "terminology confusion" ...

A somewhat old electronic relay - the ASEA RXPE 42, defined its overcurr= ent relay as a "-30=C2=B0 directional overcurrent".

RXPE direction= al.pdf Figure 22

However the text of that brochure goes on to say Figure 23

This current leading voltage reference seems to be a PLUS 30 degree refe= rence.

It then goes on to refer to MINUS 30 degree characteristic angle =F0=9F= =A4=A6=E2=80=8D=E2=99=82=EF=B8=8F=F0=9F=A4=B7=E2=80=8D=E2=99=82=EF=B8=8F Figure 24

and the diagram shows the voltage reference as effectively Vbc Figure 25

Consequently if maximum sensitivity is current leading the reference Vbc= voltage by 30, then the current lags the phase-to-neutral by 60 degrees.

Published Document Error 3

I have also recently come across a technical web site which states that = the MTA and the RCA are two different things either side of the Maximum Tor= que line.

They have fallen into the trap as per the PRAG typographical error menti= oned above of thinking that "90 - 30" is a mathematical formula =F0=9F=98= =9E=F0=9F=91=8E = The corrected diagrams would be  I am hoping they will heed my corrections

# Earth Fault Relay Application

The trick there is that the zero sequence directional element needs Vo and In as the connected quantities.  Clearly ther= e is no "angle of connection" as V0 would be zero in a balanced = load un-faulted condition.

The Van voltage phasor will reduce in magnitude due to the fa= ult to earth and shift slightly yielding the system voltage phasors and the= resultant V0 output of the delta winding VT as follows:&nb= sp; Figure 26

With the extreme short circuit right at the VT terminals, Van would be z= ero so V0 would be pointing straight down.

Also to note is that relative to the TF winding, Ia is flowin= g away from the TF and In is flowing towards the TF.  Hence In =3D =E2=80=93Ia.

In =3D 3 x I0 Figure 27

The inputs to the directional earth fault element need to be V0 and I0

As per Figure 27, we can get V0 from an open delta VT ... the= output of that is by definition Va + Vb + Vc =3D 3 x V0

As for the zero sequence current, we can either use the direct neutral C= T as per Figure 27, or the residual connection of the three line CTs connec= ted in Holmgren, or a Core Balanced CT, or opposite of the A phase current = since I0 =3D In/3 =3D  -Ia/= 3.

In any case, we now see that the Zero Sequence Current as the directiona= l element applied current is LAGGING the Polarising V0 voltage.<= /p>

Hence Earth Fault MTA/RCA would generally be expected to be NEGATIVE ang= le with respect to the Polarising quantity. Figure 28 Figure 29

.

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