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Distance relays are characterised by having two input quantities proportional to the voltage and current at a particular point in the power system, referred to as the relaying point. Ideal static distance relays have characteristics independent of actual magnitudes of voltage and current but dependent only on their ratio and phase angle between them.

The versatile family of distance relays includes impedance relays, reactance relays and mho relays. The measurement of impedance, reactance or admittance is done by comparing input current and voltage. Hence distance relays have voltage and current as input quantities.

In a static distance relay it is necessary that the two input quantities are similar i.e., voltage/voltage or current/current because they are not electrically separate as they are in case of electromagnetic relays (in an impedance relay magnets are energized by voltage and currents). In electromagnetic relays the net effect required is a force on a moving mechanism and it can be equally obtained either by a voltage or a current which is not true in case of static relays.

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So the comparators employed in static distance relays can be of either voltage comparator or current comparator. In a voltage comparator line current is converted into equivalent voltage V_{A} by passing it through an impedance Z_{R }∠θ and the voltage drop I Z_{R} is then compared with the line voltage V. Z_{R} ∠θ is the design impedance or a replica of the impedance of the line to be protected on a secondary basis. Distance relay based on voltage comparison.

Similarly in case of a current comparator, a current is derived from CT and the voltage from PT is converted into equivalent current V/Z_{R} by connecting replica impedance in series with secondary of PT. The current in secondary of PT corresponds to V/Z_{R} which is compared with I.

Sometimes it may be convenient to compare the two voltages V and IZ_{R} in a current comparator which is accomplished by connecting resistance in series with each voltage.

The arrangements of inputs for two input comparators- (i) with voltage inputs and (ii) with current inputs are shown in Fig. 4.20.

It is to be noted that the transient dc component of current passing through line impedance produces a faithful voltage waveform which is derived from line PT and the secondary current of line PT(V/Z_{R}) has faithful transient. The comparator compares V/Z_{R} and I, both having identical transient (assuming faithful reproduction). Hence the effect of transients is cancelled out from impedance measurement. So use of replica impedance is not only convenient but permits fast tripping also as it eliminates error due to transients in the fault current.

A rectifier bridge current comparator, shown in Fig. 4.21, receives two current inputs (operating current I_{0} and restraining current I_{r}). The output of comparator is applied to a permanent magnet coil relay or a static level detector.

In distance relays I_{0} and I_{r} may be supplied either by the CT or by a PT through series impedance or by both sources in a particular combination to have particular relay characteristic. If the restraining current I_{r} is supplied by PT and operating current I_{0} is supplied by CT, as shown in Fig. 4.21, the relay operates when the ratio V/I is less than a certain value and is, therefore, a minimum impedance relay.

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A practical static distance protection scheme includes a starting, measuring and timing elements made up of solid state devices. The output unit is usually a moving coil relay. The starting element is usually an overcurrent relay. The output is given to the measuring element. Phase comparators are employed in the measuring devices. The measuring device determines whether the fault is within the protected zone or not. Correspondingly a tripping signal is initiated in case the fault is within the protected zone. In case the fault is outside the protected zone, the timer unit starts. This initiates zone-wise protection.

A block diagram of a distance relay based on current comparison principle is given in Fig. 4.22. The line PT secondary is connected to auxiliary PT and the output of auxiliary PT is converted into current and this current is compared with the output of the auxiliary CT.

Static distance relays do not have any moving part so they operate much faster (operating time of the order of some milliseconds) and without risk of incorrect tripping as compared to electromagnetic relays. With semiconductor devices it is possible to obtain other distance characteristics than the conventional ones. Static distance relays are accurate over a wider range of fault currents and line lengths and require much lower burden as compared to their counterparts in electromagnetic relays. Static distance relays are compact in size and have better stability under power swing conditions.

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The main problem with impedance relays is smoothening of one of the inputs so that the pickup does not vary from zero to infinity during the cycle as first the voltage and then the current passes through zero. Normally, the voltage is smoothened as it is easier to do so as compared to the smoothening of current. This is done by a phase-splitting circuit.

Static distance relays are extensively used for protection of medium and long transmission lines, parallel feeders and unit backup protection as well as interconnected and T-connected lines.

**Static Distance Relay Characteristics****: **

Distance relay characteristics are normally drawn on an R-X diagram but sometimes it becomes convenient to draw them on G-B diagram as well.

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**While discussing and deriving the characteristics of distance relays (impedance, reactance and mho relays), including those of directional relay the following points are worth remembering: **

1. While comparing only single term quantities corresponding to the current and voltage of the circuit under protection the characteristic obtainable will be either a straight line passing through the origin or circle with its centre at the origin depending on whether it is a phase or amplitude-comparison and whether the characteristic is plotted on R-X diagram or G-B diagram.

2. In case one quantity is compared with the sum or difference of the two quantities, the circle passes through the origin and the straight line is offset from the origin. Directional relay is a mathematical dual of impedance relay.

**i. Directional Relay****: **

**Phase Comparison: **

Directional relay is basically a phase comparator which compares the phase relation between V and I and the relay will operate for the condition -90° ≤ θ ≤ 90°. The inputs in case of static directional relay are V and I Z_{R} and the characteristic is –

Z Z_{R} cos (ɸ – θ) ≥ 0

Where, Z is the fault impedance and is equal to ratio of V and I, Z_{R }is the replica impedance in the relay, ɸ is the phase angle between V and I and θ is the relay characteristic angle.

Since Z and Z_{R} cannot be zero.

∴ cos (ɸ – θ) ≥ 0 or ɸ – θ = ± π/2

**Amplitude Comparison: **

The inputs for amplitude comparison will be –

V + I Z_{R} and V – I Z_{R }

For operation of relay –

|V + I Z_{R}| > |V – I Z_{R}|

or |Z + Z_{R}| > |Z – Z_{R}|

and for no operation |Z + Z_{R}| < |Z – Z_{R}|

**ii. Impedance Relay****: **

**Amplitude Comparison: **

Impedance relay is inherently an amplitude comparator and the inputs are I Z_{R }and V.

For operation of relay –

|I Z_{R}| >|V|

or |Z| < | Z_{R}|

or R + jX < Z_{R}

For threshold condition R + jX = Z_{R} which is an equation of a circle on impedance (R-X) diagram.

The circle having radius equal to Z_{R} and centre at the origin, as illustrated in Fig. 4.24 (a), is the characteristic of the impedance relay.

**Phase Comparison: **

The inputs are (V + I Z_{R}) and (V – I Z_{R}). The characteristic is given in Fig. 4.24 (b). It can be seen that as long as Z_{R} lies along the circumference of the circle with radius Z_{R}, the two quantities (Z + Z_{R}) and (Z – Z_{R}) make an angle of ± 90°. This gives the same characteristic as shown in Fig. 4.24 (a).

**iii. Angle Impedance Relay****: **

**Amplitude Comparison: **

The two input quantities are (2 I Z_{R} – V) and V and for operation of relay –

|2 I Z_{R} – V| >|V|

or |2 Z_{R} – Z| >|Z|

The characteristic is shown in Fig. 4.25 (a).

**Phase Comparison: **

The two input quantities are (I Z_{R} – V) and I Z_{R} and for operation of relay the phase angle between (Z_{R} – Z) and Z_{R} should be within ± 90°. It can be seen that the characteristic is a straight line normal to Z_{R}. As long as Z lies below the line, the angle between (Z_{R} – Z) and Z lies within the limits of ± 90° [Fig. 4.25 (b)].

**iv. Reactance Relay****: **

**Amplitude Comparison: **

This relay is a particular case of an angle impedance relay in which the reactance component of the impedance is measured and, therefore, for operation of relay –

|2X_{r} – Z| > |Z|

The two inputs are V and (2 I Z_{R} – 2 I R_{r} – V) where R_{R} is made equal to resistance of Z_{R}, thus leaving only its reactive component X_{R}.

**Phase Comparison: **

The two inputs are I Z_{R} and (I Z_{R} – V) as in case of an angle impedance relay. The relay will trip when Z is below the characteristic i.e., when (Ψ + θ) < 180°. For Z to be purely reactive Ψ would be 90° under threshold condition and the relay would trip when Z sin ɸ is less than X_{R} on the R-X diagram.

**v. Mho or Angle Admittance Relay****: **

This is the inverse of the angle impedance relay. The two relays are dual of each other. The equation of one type on an impedance diagram corresponds to the equation of other type on admittance diagram and vice versa. The characteristic for mho or admittance relay is a straight line offset from the origin on G-B diagram while on R-X diagram it will be a circle passing through the origin.

**Amplitude Comparison: **

The two inputs are |I Z_{R}| and |2V – I Z_{R}|.

For relay operation-

|2 V – I Z_{R}| <|I Z_{R}|

or |2 Z – Z_{R}| < |Z_{R}|

The characteristic is illustrated in Fig. 4.27. The relay will operate as long as the fault impedance Z lies within the circle having diameter Z_{R}.

**Phase Comparison: **

The two inputs are |I Z_{R} – V| and V and the relay will operate when the phase angle between them is less than 90° i.e., when 90° > Ψ > – 90°.

Since mho relay is inherently directional relay, phase comparator is the more convenient construction.

**vi. Offset Mho Relay****: **

Use of a comparator as an offset mho relay is shown in Fig. 4.28. The inputs are fed to the comparator through a mixing transformer. The circuit is designed such that the relay operates when V and I have phase angle within certain limits and ratio V/I is less than a certain value of Z_{n}, impedance setting of the relay.

However, if the direction of power flow is reversed, the phase angle between I and V changes and then the relay operates when ratio V/I is less than K Z_{n} which is less than unity. The characteristic of such a relay is called offset-mho and it is a circle whose circumference encloses the origin and is slightly offset when drawn on impedance plane.