The 67 directional relay can detect the direction of the input current using impedance and torque which are calculated for their respective elements. The relay consists the following elements for detecting the current direction: Positive sequence voltage polarized phase directional (DIRP), negative sequence voltage polarized directional element (DIRQ) and for detecting ground current direction (DIRQG), zero sequence voltage polarized ground current directional element (DIRV), zero sequence current polarized neutral current directional element (DIRI), and zero sequence voltage polarized neutral current directional element (DIRN). The last 4 elements are used to detect the direction for ground currents. This relay can be used in conjunction with overcurrent relays (5051, or 50, 51) to either block a trip signal or permit it from them depending on the application. So, the output of this relay is only the current direction for the aforementioned elements.

That main source for designing this relay was the manual for SEL relays, specifically: SEL-351R [2], SEL-351-5-6-7 [3], SEL-751 [4].

Description

This section describes the different elements in the model: DIRP, DIRQ, DIRV, DIRN, DIRI.

Positive-sequence voltage polarized phase directional element (DIRP)

The phase directional element (DIRP) uses the positive sequence impedance () based on the ratio of () to determine the location of the fault. It is used for three phase faults. If the positive sequence impedance falls between  plus or minus 90 degrees of Z1ANG, which is the characteristic angle of the line, then the relay declares the direction as forward. The line-to-line currents must exceed a pickup current (50P32P) set by the user to enable this element. The unit for 50P32P is amperes and it has a range determined by the secondary transformer side current. The positive sequence voltage must be higher than 0.5 threshold value. If it drops, the value from 3 cycles ago will be used.

It should be noted that phase directional is disabled if there is a strong negative-sequence current and so that element (DIRQ) is enabled. The negative-sequence directional element has priority over phase directional [2]. 

The outputs of the directional element itself are: FDIRP and RDIRP which show forward and reverse phase current respectively.

The FDIRP and RDIRP are routed and compared with directions from the negative-sequence element (FDIRQ and RDIRQ). If either of them is 1, the direction for phase is detected as forward (DIRPF), or reverse (DIRPR). This will be explained more in the following sections.

• Equation for calculating the positive sequence impedance:

• Conditions for declaring the fault as forward:

• Pickup current condition:

• Forward and reverse areas in X-R plane based on Z1ANG are shown in the figure below:
  
  

Negative-sequence voltage polarized ground and phase current directional element (DIRQ, DIRQG)

The negative-sequence element calculates Z2 from negative sequence current and voltage to determine the fault. It is used for sensing unbalance faults.

This element controls the negative-sequence overcurrent elements. Along with positive-sequence voltage polarized directional elements, it controls the phase overcurrent directional element (DIRQ). Along with zero-sequence ground or neutral currents, it controls the ground or neutral directional elements (DIRQG). The negative-sequence element has priority over phase directional element and if it is enabled, it will disable the phase directional element.

Based on the settings and conditions, the direction of the current might be detected as forward (F) or reverse (R). That is true for both negative sequence directional element for phase direction and for ground direction. So the directions detected by the element are: FDIRQ, RDIRQ, FDIRQG, RDIRQG

Here are the features and characteristics of this element:

• To use the negative-sequence element for ground directional detection, the ground directional option has to be set to DIRQG.
• To enable the negative sequence element, first the negative sequence current, I2 must be higher than the pickup current for forward and reverse direction: 50QFP, 50QRP.

It should be noted the enabling of negative sequence element is for both phase directional and ground directional.

• As an extra security measure, two restraints are applied to the negative-sequence current: positive sequence restraint (a2) and zero-sequence restraint (k2). The following conditions have to be met so the element is enabled.

• The negative sequence impedance, Z2 is calculated from  which is shifted by Z1ANG. Z1ANG is the characteristic angle of the line. 

          The * sign means it is the conjugate of the complex value. 

• Z2 must be lower than the forward threshold calculated from the parameter Z2F to detect the current direction as forward. Z2 must be higher than the reverse threshold calculated from the parameter Z2R to detect the current direction as reverse. Z2F and Z2R are set by the user can based on them, the forward and reverse threshold are calculated as the following equations:

Forward threshold Z2 Forward direction FDIRQ, FDIRQG

Z2 Reverse threshold Reverse direction RDIRQ, RDIRQG

If Forward threshold  

If  Forward threshold

If Reverse threshold  

If  Forward threshold

• The operating areas based on Z2 and the thresholds are shown in the figure below:

• The directions FDIRQG and RDIRQG are routed along with other elements to determine the direction of the ground directional element (DIRGF or DIRGR) and neutral ground directional element (DIRN). 

Zero-sequence voltage polarized ground current directional element (DIRV)

This element calculates from zero sequence voltage and residual ground current () along with shifting them by Z0ANG. Like DIRQG, it is used for unbalance and ground faults. is the residual current from three phase currents:

By choosing ground directional element to DIRV, if certain conditions are met, the element is enabled and fault current direction is detected as being forward (FDIRV) or reverse (RDIRV). These values are routed along with directions from other elements (DIRI, DIRQG) to determine the direction for the ground directional element (DIRG). 

Here are the conditions and calculations that are made in this element:

• Ground directional element is set to DIRV.
• The residual ground current has to be higher than ground directional pickup current for forward direction and reverse direction (50GFP, 50GRP) which are settings made by the user:

• As an extra measure of security, a positive sequence restraint is applied to the zero-sequence current. This factor is a0 and the condition is the following:

• Z0 is calculated from zero sequence voltage and ground current shifted by Z0ANG. Z0ANG is the zero-sequence impedance characteristic angle and is set by the user.

• Z0 has to be lower than the forward threshold calculated from the setting Z0F so the direction is forward. Z0 has to be higher than the reverse threshold calculated from the setting Z0R so the direction is reverse. Z0F and Z0R are zero sequence threshold settings that are changed by the user.

Forward threshold Z0 Forward direction FDIRV

Z0 Reverse threshold Reverse direction RDIRV

If Forward threshold  

If  Forward threshold

If Reverse threshold  

If  Forward threshold

• The operating areas of Z0 based on the thresholds are shown in the figure below:

• The directions FDIRV, RDIRV are routed along with directions from other elements to detect for ground overcurrent directional element (DIRGF or DIRGR) and neutral ground overcurrent directional element (DIRN). 

Zero-sequence current polarized neutral current directional element (DIRI)

Unlike other elements which calculate the impedance to detect the direction, this element calculates torque from neutral current (IN) and residual ground current (IG). The angle between them is shifted by INMTA which is set by the user.

The condition for enabling this element is similar to zero sequence voltage polarized ground directional (DIRV) but with a few extra security measures. The nominal neutral current and nominal current which can be chosen by the user to be 1 or 5 A, are used to calculate the threshold.

The direction from this element can be detected as forward (FDIRI), or reverse (RDIRI). They are routed along with other elements to determine the direction for ground directional (DIRG).

Here are the conditions and calculations related to this element:

• Ground directional is set to DIRN.
• Just like for DIRV, the ground current has to be higher than 50GFP and 50GRP pickup currents and there is a positive restraint on I0. These are the conditions to also enable the current polarized element.
• A Neutral Restraint factor (KGN) is applied on the ground current. The following condition is an extra security measure to enable the current opalized directional element.

• The channel IN current from the input to the relay is the neutral current directly from a CT. To enable this element, IN must to be higher than a neutral current threshold which is calculated from the nominal IN current which is set by the user.

IN Nominal can be set to 1 or 5 A.

• The torque which is used to detect the fault direction is calculated from IG and IN shifted by INMTA. INMTA is the maximum torque angle and is set by the user.

• If T is higher than the forward threshold, the direction is forward. If T is negative and lower than the reverse threshold, the direction is reverse. The thresholds are calculated from the nominal phase current and nominal neutral current.

T Forward threshold Forward direction FDIRI

Reverse threshold T Reverse direction RDIRI

Forward threshold (Channel IN nominal current) (Phase nominal current)  

Reverse threshold -1 * (Channel IN nominal current) (Phase nominal current)  

• FDIRI and RDIRI are routed along with directions from other elements to detect the direction for ground overcurrent directional element (DIRGF or DIRGR) and neutral ground overcurrent directional element (DIRN)

Zero-sequence voltage neutral current directional element (DIRN)

This element is very similar to DIRV as it also calculates Z0 to determine the direction. The difference is it calculates Z0 from the channel neutral current IN and zero-sequence voltage. This element is also used to detect ground faults.

Here are the conditions and calculations related to this element:

• Ground directional element is set to DIRN.
• The neutral current or channel IN current (IN) must be higher than ground directional pickup current for forward direction and reverse direction (50GFP, 50GRP) divided by 10. This is because this element is more sensitive than those for detecting ground current directions. 50GFP and 50GRP are set by the user.

• Z0 is calculated from zero sequence voltage (V0) and neutral current (IN) shifted by Z0ANG. Z0ANG is the zero-sequence impedance characteristic angle which is set by the user.

• If Z0 is lower than the forward threshold, calculated from Z0F, the direction is forward (FDIRN). If Z0 is higher than the reverse threshold which is calculated from Z0R, the direction is reverse (RDIRN). Z0F and Z0R are settings for Z0 threshold which can be changed by the user.

Forward threshold Z0 Forward direction FDIRN

Z0 Reverse threshold Reverse direction RDIRN

If