Directional Over Current Relay - Maximum Torque Angle

EHV lines operates in grid. We can understand the changes in protection system when EHV feeders operates either in parallel or grid with the help of following example.

Consider a part of the 132kV power system as shown above. Here sub-station A is source sub-station and a 132kV double circuit line is feeding the radial sub-station B. The double circuit line under consideration is being protected by four circuit breakers controlled by four over current relays R1, R2, R3 and R4 as shown above. Upon observing the circuit and with common logic we can guess that time of operation for relays will be as below-

1.    R1 -          500 ms,          R2 -                 500 ms

2.    R3 -          300 ms,          R4 -                 300 ms

Now let the fault on circuit-I as shown in the figure. For this fault both relays R3 and R4 at Bus-B will experience the same fault current and as we have to set its time of operation same both will operate simultaneously. Thus selective tripping of only faulty circuit will not be possible.

This difficulty can be overcome if only relay R3 responses for the shown fault of Circuit-I. As seen from the diagram this discrimination can be done by sensing the direction of power flow through the circuit controlled by respective relay. We can see that relay R3 is experiencing fault in forward direction (as it is protecting the Ckt-I) while relay R4 experiences the fault in reverse direction. To have selective tripping of the faulty circuit; only the relay experiencing fault in forward direction shall responds to fault and operates the breaker. 

This type of relaying scheme is shown here by adopting direction arrow convention. However at EHV level it is not necessary to represent directional relay explicitly by arrow symbol as shown here because all relays used in protection of EHV network are directional only.

Basics of Direction Sensing

In above examples we have mentioned that the fault is in forward direction with respect to relay R3. Here we have decided this by observing the position of the relay with respect to fault and source. However in actual practice relay has to discriminate between forward and reverse direction fault. How this can be achieved is discussed in next sections.

Direction of AC current flow.

The name “alternating current” suggests that there is no specified physical direction of current flow. To elaborate this let us compare measurement of alternating current and direct current by clip on meter as shown in following figures.

 
DC clip on meter has either arrow marking or polarity marking on jaw of the meter. If the direction of current flow is reverse with respect to this marking it is indicated by –Ve sign by clip on meter display. Thus current flowing from A to B displayed as 17.32 A and it is  -17.32 A if flowing from B to A.

  However for AC tong tester there is neither such marking nor any –Ve sign for displayed current. Whether current flowing from A to B or B to A display will be +Ve only.

Though the change in direction of current flow in case of A.C. system does not changes sign for clip on meter display still it is wide practice to show currents in A.C system by direction. Obviously then someone may ask the question that; what is the meaning of showing the direction of current flow in AC system?; and answer to this is; it is actually direction of active power flow. Obviously to determine power flow in circuit we require current as well as voltage. How this is achieved is explained in next section. 

Direction of power flow

As mentioned in previous section to determine physical direction of current flow (power flow) we require additional quantity; this additional quantity is voltages causing current (respective phase voltage). The meaning of direction of AC current flow (power flow) can be best understood with the help of power system as shown in figure.

As shown here consider a SLD for three bus power system feeding the lagging power factor load. Let direction sensing devices D_A and D_C are connected to Line-AB and Line-BC at Bus-B. Bus-B CT and PT connections are shown in the figure as per common conventions listed below.

1)    Connect PT secondary terminal “a” to device and “n” to earth

2)    CT shall be installed such that its primary P1 terminal shall be towards Bus

3)    Connect CT secondary terminal S1 to relay and S2 to earth (with other phase CT S2 terminal)

Let us consider an instance where Bus-A is positive. Thus as per CT polarity the current flowing through CT primary and secondary has the directions as shown in the figure.

Now as seen from the figure direction of instantaneous current and voltage for device D_C is same (conventionally both entering into the device). Thus current phasor shown lagging behind voltage phasor by the power factor angle of the load.

While for device D_A direction of instantaneous current and voltage is opposite (conventionally current is leaving the device while voltage is entering into the device). Thus here current phasor is reversed.

By observing the vector representation of voltage and current in the figure (as shown below respective device) we can easily conclude that; if standard connection convention followed then-

Whenever angle between voltage and current is less than 90⁰ (lagging or leading) physically direction of power (current) flow is away from bus.

AND

Whenever angle between voltage and current is more than 90⁰ (lagging or leading) physically direction of power (current) flow is towards bus.

Maximum Torque Angle

The word Maximum Torque Angle has its roots in use of electromagnetic relays. In previous section direction sensing explained by considering generic devices D_A and D_C. Historically these devices were electromagnetic devices; where torque get developed as a result of tow magnetic fluxes developed by tow electrical quantities displaced by certain angle. Depending upon the direction of torque produced direction of power (current) can be decided.

When two magnetic fluxes are derived from two different electrical quantities the torque produced by these fluxes will depend upon phasor relationship of these two quantities. Obviously for energy meter and Watt Meter; for correct functioning of the devices; torque will be maximum when applied voltage and current are in phase; while for VAR meter for capacitor it would be maximum if current leads voltage by 90⁰ and for VAR meter for reactor it would be maximum if current lags voltage by 90⁰. This angle of applied current with respect to applied voltage at which maximum torque get produced is called as Maximum Torque Angle.     

However situation explained above entirely changes in case of a device which can discriminate direction of current in case of fault (Directional Overcurrent Relay) due to following two reasons

1)    The voltage of faulty phase decreases drastically

2)    Angle between voltage and current of faulty phase is nearly 90⁰

Hence direction decision making in case of fault becomes very difficult. How to overcome these difficulties depends upon type of fault. There are mainly two types of fault in electrical system a) Line-Line fault and b) Line-Ground fault. Direction decision making philosophy and thus requirement of MTA (Maximum Torque Angle) in case of each type of fault is entirely different and we will discuss it in next section.

NOTE: Now a days use of numerical relays become very common; where direction decision making done numerically; by sampling voltage and currents many times during each cycle and by using proper algorithm. However use of the word Maximum Torque Angle carried forward as it is by most of the relay manufacturer. Some relay manufacturer uses RCA (Relay Characteristic Angle) instead of MTA due to this technological change. 

MTA for Line-Line Fault

Consider a part of the power system as shown in the figure. Let there be Line-Line fault at point A and let direction decision to be made by the relay at point B.

  

When there is no fault; vector diagram representing voltage and current is as shown in figure.

For R-Y fault R-Ph and Y-Ph source voltage will decrease and will approach close to each other and R-Ph current will lag approximately 90⁰ with respect to R-Y Phase voltage thus during fault vector diagram will be as shown in figure.

Thus depending up on nature of load and fault impedance R-Phase current may be anywhere as shown by shaded area for figure.

Obviously voltage selected for this direction decision making will be of healthy phases. That means if we are considering direction decision making in respect of R-Ph current then we have to choose V_YB voltage as our reference voltage as shown in figure.

To include all this probable area for R-Ph current it is necessary to redefine zone of forward direction with respect to polarizing voltage V_YB. Thus line AB is selected as new dividing line for operating direction (Forward) and Non-Operating direction (Reverse). Perpendicular line to this dividing line is line C-D. Now we can see that line CD leads V_YB. For electromagnetic relays this angle use to be 45⁰. Now for numerical relay this angle is settable still recommended value is +45⁰.

MTA for Line-Ground Fault

Consider R-Ph to ground fault. During this fault R-Ph voltage will decrease and R-Ph current will be lagging to R-Ph voltage nearly by 90⁰ as shown in the figure-1.

However Earth fault relay current I_n will be 180⁰ out of phase with respect to R-Ph current as shown in figure-2

Thus depending up on fault impedance R-Phase current may be anywhere as shown by red shaded area and thus corresponding earth fault relay current may be anywhere as shown by green shaded area for figure-3.

As there may be the fault on any phase and as during fault; volatge of faulty phase reduces nearly to zero it is not desirable to consider volatge of faulty phase for deciding the direction of fault current. It is obvious choice to use residual voltage V₀ (vector sum of Vr, Vy and Vb) for deciding the direction of fault current as shown in the figure.

To include all this probable area for earth fault current it is necessary to redefine zone of forward direction with respect to polarizing voltage V₀. Thus line AB is selected as new dividing line for operating direction (Forward) and Non-Operating direction (Reverse). Perpendicular line to this dividing line is line C-D. Now we can see that line CD lags V₀. For electromagnetic relays this angle use to be -45⁰. Now for numerical relay this angle is settable still recommended value is -45⁰.

Conclusion

For protection of EHV lines generally directional overcurrent and earth fault relays are used. In case of directional relay it is necessary to set correct MTA for over current as well as earth fault relay. Maximum Torque Angle depends upon factors such as source impedance and method adopted for earthing of generators and transformers. In transmission system generally solidly earthed transformers are used. Hence it is common to use following settings for MTAa.   For Overcurrent Relay MTA = +45⁰ or 45⁰ leading
b.   For Earth Fault Relay MTA = -45⁰ or 45⁰ lagging