Protective Relays

Protective Relays 

Introduction

In a power system consisting of generators, transformers, transmission and distribution circuits, it is inevitable that sooner or later some failure will occur somewhere in the system. When a failure occurs on any part of the system, it must be quickly detected and disconnected from the system. Protection scheme required for the protection of power system components against abnormal conditions such as faults essentially consists of protective relaying and circuit breaker. The proper operation of the power system requires an efficient, reliable and fast acting protection scheme, which basically consists of protective relays and switching devices. A protective relay, acting as a brain behind the whole system, senses the fault, locates it, and sends a command or signal to appropriate circuit breaker to isolate only the faulty section, thus keeping the rest of the healthy system functional. It detects abnormal conditions on a power system by constantly monitoring the electrical quantities of the system, which are different under normal and abnormal (fault) conditions. The basic electrical quantities which are likely to change during abnormal conditions are current, voltage, phase angle (direction) and frequency.

Relay operation

Pic source:Electrical Concepts 

Fundamental requirements of relaying 

• Selectivity
• Speed
• Sensitivity
• Reliability
• Simplicity
• Economy

Classification of Relays

In a power system control and protection schemes, various types of relays are used which can be categorized as follows:

– According to functions

– According to construction

– According to speed of operation

– According to their generation of development

– According to the method of connection

– According to the method of action 

According to functions

Relays can be divided into three classes according to the function, they are;

• – Main relay: These relays operate according to the information received from the power system i.e. they operate when there is a change in the actuating quantity which may be current, voltage or power.
• – Auxiliary Relays: These relays operate after the operation of main relays and are used to perform some auxiliary functions such as introducing time delay for the operation of the breaker.
• – Signal Relays: These are the relays used to indicate the operation of main relays. It is also used to energize a signal or an alarm circuit to make the operators alert to take the necessary actions immediately.

According to construction

Protective relay can be broadly classified into the following three categories, depending on the technology they use for their construction and operation.

– Electromechanical Relay

– Static Relay

– Numerical Relay

Electromechanical Relay

Electromechanical relays are further classified into two categories i.e.

• – electromagnetic relays,
• – thermal relays.
• Electromagnetic relays work on the principle of either electromagnetic attraction or electromagnetic induction.
• Thermal relays utilize the electro thermal effect of the actuating current for their operation.
• First of all, electromagnetic relays working on the principle of electromagnetic attraction were developed. These relays were called attracted armature-type electromagnetic relays. This type of relay operates through an armature which is attracted to an electromagnet or through a plunger drawn into a solenoid. Plunger type electromagnetic relays are used for instantaneous units for detecting over current or over voltage conditions. Later on, induction type electromagnetic relays were developed. These relays use electromagnetic induction principle for their operation, and hence work with ac quantities only. Electromagnetic relays contain an electromagnet and a moving part. When the actuating quantity exceeds a certain predetermined value, an operating torque is developed which is applied on the moving part. This causes the moving part to travel and to finally close a contact to energies the trip coil of the circuit breaker.

Static Relay

A static relay refers to a relay in which there is no armature or other moving element and response is developed by electronic components without mechanical motion. These type of relays perform switching actions by changing the state of serially connected solid-state component from non-conducting to conducting or vice versa, without any physical movement of any of relay. They are more versatile, reliable and faster than electromagnetic type. Static relays contain electronic circuitry which may include transistors, ICs, diode and other electronic components. In such type of relays, the output is obtained by the static components like magnetic and electronic circuit etc. The relay which consists static and electromagnetic relay is also called static relay because the static units obtain the response and the electromagnetic relay is only used for switching operation.The instrument transformer is connected to the transmission line, and its output is given to the rectifier. The rectifier rectifies the input signal and pass it to the relay measuring unit.

The relaying quantity (output of PT, CT or transducer) is rectified by a rectifier. The rectified output is supplied to a measuring unit. The output of the measuring unit is amplified and fed to the output device. The output unit energizes the trip coil. Static relays possess the advantages of having

• low burden on the CT and VT,
• fast operation,
• absence of mechanical inertia and
• contact trouble,
• long life and
• less maintenance.
• Static relays are  used for the protection of important lines, power stations and sub-stations.

Numerical Relay

Numerical relays are the latest development in this area. These relays acquire the sequential samples of the ac quantities in numeric (digital) data from through the data acquisition system, and process the data numerically using an algorithm to calculate the fault discriminant and make trip decisions. Numerical relays have been developed because of tremendous advancement in VLSI and computer hardware technology. (Very large scale of integrated circuit) They are based on numerical (digital) devices, e.g. microprocessors, micro controllers, Digital Signal Processors (DSP) etc. At present microprocessor/micro controller based numerical relays are widely used. The main features of numerical relays are their economy, compactness, flexibility, reliability, self-monitoring and self-checking capability, multiple functions, low burden on instrument transformers and improved performance over conventional relays of electromechanical and static types.

According to speed of operation

Protective relays can be generally classified by their speed of operation as follows:

– Instantaneous relays

– Time-delay relays

– High-speed relays

• Instantaneous relays: In these relay, complete operation takes place after a very short time duration from the incidence of the current or other quantity resulting in operation.The time of operation of such relays is lesser than 0.2 second.
• Time-delay relays: In these relays, an intentional time delay is introduced between the relay decision time and the initiation of the trip action.
• High-speed relays: These relays operate in less than a specified time. The specified time in present practice is 60 milliseconds (3 cycles on a 50 Hz system).

According to their generation of development

Relays can be classified into the following categories, depending on generation of their development.

i) First-generation relays: Electromechanical relays

ii) Second-generation relays: Static relays

iii) Third-generation relays: Numerical relays.

According to their functions

Protective relays can be classified into the following categories, depending on the duty they are required to perform:

– Overcurrent relays

– Undervoltage relays

– Impedence Relays

– Underfrequency relays

– Directional relays

According to the method of connection

As per the method of connection to the power system, the relays may be classified into

– primary relays

– secondary relays.

• Primary relays: primary relays are those whose sensing elements are directly connected to the power lines, which they protect.
• Secondary relays: Secondary relays are those whose sensing element are connected to the power lines through instrument transformers. Normally, these types of relays are used in power system protection because of high values of voltages and currents of the power circuit.

According to the method of action

On the basis of the action of relays on circuit breakers, they are classified into;

– Direct-acting relays

– Indirect acting relays.

• Direct acting relay: These relays are connected mechanically with the tripping mechanism of the breakers and their control elements acts directly to operate the breaker.
• Indirect acting relays: These relays acts indirectly i.e. instead of acting directly on the breaker’s operating mechanism, they perform switching actions to supply the power from an auxilliary d.c. source to the trip coil of the operating mechanism. The most relays are used in practice of these kinds.

Electromechanical Relay

Electromechanical relays operate by mechanical forces generated on moving parts due to electromagnetic or electrothermic forces created by the input quantities. Most electromechanical relays use either electromagnetic attraction or electromagnetic induction principle of their operation. Such relays are called electromagnetic relays. Depending on the principle for their operation the electromagnetic relays are of two types:

i) attracted armature relays

ii) induction relays.

Some electromechanical relays also use electrothermic principle for their operation and are based upon the forces created by expansion of metals caused by temperature rise due to flow of current. Such relays are called thermal relays. Most of the present day electromechanical relays are of either induction disc type or induction cup type.

Types of electromechanical relays

• Electromagnetic relays

– Attracted armature relays

– Induction relays

• Thermal relays  

Attracted armature relays

Attracted armature relays are the simplest type which respond to ac as well as dc. These relays operate through an armature which is attracted to an electromagnet or through a plunger which is drawn into a solenoid. All these relays use the same electromagnetic attraction principle for their operation. The electromagnetic force exerted on the moving element i.e. the armature or plunger, is proportional to the square of the flux in the air gap or the square of the current. In dc relays this force is constant. The following are the different types of construction of attracted armature relays.

– Hinged armature type

– Plunger type

– Balanced beam type

– Polarised moving-iron type

– Reed type

Hinged armature type

• The coil is energized by an operating quantity proportional to the system current or voltage.
• The attractive force increases as the armature approaches the pole of the electromagnet.
• This type of relay is used for the protection of small machines, equipment etc. It is also used for auxiliary relays, such as indicating flags, slave relays, alarm relays etc.
• The actuating quantity of the relay may be either ac or dc.
• In dc relay, the electromagnetic force of attraction is constant.
• In the case of ac relays, sinusoidal current flows through the coil and hence the force of attraction is given by

Fe= KI^2

= K (Imax sin ωt)^2

= K (Imax^2 – Imax^2 cos 2ωt)

It shows that the electromagnetic force consists of two components,one constant independent of time (1/2KImax^2) and another dependent upon time and pulsating at double the supply frequency(1/2KImax^2cos 2ωt).The total electromagnetic force,therefore pulsates at double the supply frequency.

Plunger Type relay

In this type of relay, there is a solenoid and an iron plunger which moves in and out of the solenoid to make and break the contact. The movement of the plunger is controlled by a spring. This type of construction has however become obsolete as it draws more current.

Balanced Beam Relays

It consists of a beam carrying two electromagnets at its ends. One gives operating torque while the other restraining torque. The beam is supported at the middle and it remains horizontal under normal conditions. When the operating torque exceeds the restraining torque, an armature fitted at one end of the beam is pulled and its contacts are closed. Though now obsolete, this type of a relay was popular in the past for constructing impedance and differential relays.

Polarized moving iron relay 

The sensitivity of the hinged armature relays can be increased for dc operation by the addition of a permanent magnet. This type of relay is known as polarized moving iron relay. These employ leaf spring supported armatures

Reed Relays 

• A reed relays consists of a coil and nickel strips (reeds) sealed in a close glass capsule.
• The coil surrounds the reed contact. When the coil is energized, a magnetic field is produced which causes the reeds to come together and close the contact.
• Reed relays are very reliable and are maintenance free.
• They are used for control and other purposes, and also used in protective relays.
• Their input requirement is 1 W to 3 W and they have speed of 1 or 2 m sec.
• They are completely bounce free and are more suitable for normally closed application.
• Heavy duty reed relays can close contacts carrying 2 kW at 30 A maximum current or at a maximum of 300 V dc supply.

Advantages and disadvantages

Advantages

• Can be used for both ac and dc
• They have fast operation and fast reset
• These are almost instantaneous

Disadvantages

• The relay can operate during transients
• Directional feature is absent

Applications

• Protection of various ac and dc equipment
• Over/under current and over/under voltage protection
• Differential protection
• Can be used as auxiliary relay

Induction Relays

Induction relays use electromagnetic induction principle for their application. Their principle of operation is same as that of a single phase induction motor, so used for ac currents only. Two types of construction of these relays.

– Induction disc type

– Induction cup type

In both types of relays, the moving element (disc or cup) is equivalent to the rotor of the induction motor. The moving element acts as a carrier of rotor currents, where as the magnetic circuit is completed through stationary magnetic elements. In order to produce an operating torque, the two fluxes must have a phase difference between them.

In watt metric type construction, φ1 is produced by upper magnet and φ2 by the lower magnet. A voltage is induced in a coil wound on the lower magnet by the transformer action. The Current flowing in this coil produces flux φ2 . In case of the cup type construction φ1 and φ2 are produced by pairs of coil.

Induction Relay torque 

Phasor diagram for an induction relay

Force produced in Induction Relay

The current produced by the flux interacts with other flux and vice versa.

The force produced are:

As these forces are in opposition, the resultant force is

If the same current produces ₁ and  ₂ the force produced is given by

Where is the angle between ₁ and _2. If two actuating currents M and N produced is

Induction Relay 

• There are two types of construction of induction disc relays:

– The shaded pole type

– Watt hour meter type

In shaded pole type construction, a C-shaped electromagnet is used. One half of each pole of the electromagnet is surrounded by a copper band known as the shading ring. The shaded portion of the pole produces a flux which is displaced in space and time with respect to the flux produced by the unshaded portion of the pole. Two alternating fluxes displaced in space and time cut the disc and produce eddy current in it. Torques are produced by the interaction of each flux with the eddy current produced by the other flux. The resultant torque causes the disc to rotate.

shaded pole induction disc relay

• Robust & reliable Construction
• Time current characteristics are inverse characteristics
• Current setting can be changed by taking suitable no. of turns
• Eddy currents in disc
• Brake magnet to avoid over run
• Used for over current protection
• Used for slow speed relays

Wattmetric type Induction Disc Relay

It consists of an E shaped electromagnet and an U shaped electromagnet with a disc free to rotate in between .The E shaped electromagnet carries two windings primary and the secondary. The primary winding carries relay current I1 while the secondary winding is connected to the winding of U shaped electromagnet. The primary current induces emf in the secondary and so circulates a current I2 in it. The flux ɸ2 induced in the U shaped electromagnet will lag behind flux ɸ1 by an angle θ Driving torque is developed on the disc proportional to ɸ1ɸ2sinθ .It can provide higher phase angle between ɸ1 and ɸ2 and thus higher torque.

Induction Cup Relay

The relay has two, four or more electromagnets energized by the relay coil. A stationary iron core is placed between these electromagnets. The rotor is hollow metallic cylindrical cup which is free to rotate in the gap between the electromagnets and the stationary iron core. The rotating field is produced by two pairs of coils wound on four poles as shown. The rotating field induces currents in the cup causing it to rotate in the same direction. These relays have inverse time characteristics. Such relays are very fast in operation and may have an operating time of less than 0.01 second

Buchholz Relay 

Buchholz relay in transformer is an oil container housed in the connecting pipe from main tank to conservator tank. It has mainly two elements. The upper element consists of a float. The float is attached to a hinge in such a way that it can move up and down depending upon the oil level in the Buchholz relay Container. One mercury switch is fixed on the float. The alignment of mercury switch hence depends upon the position of the float. The lower element consists of a baffle plate and mercury switch. This plate is fitted on a hinge just in front of the inlet (main tank side) of Buchholz relay in transformer in such a way that when oil enters in the relay from that inlet in high pressure the alignment of the baffle plate along with the mercury switch attached to it, will change.

Overcurrent relay

A protective relay which operates when the load current exceeds a preset value, is called an overcurrent relay. The value of the preset current above which the relay operates is known as its pickup value. Overcurrent relays offer the cheapest and simplest form of protection. These relays are used for the protection of distribution lines, large motors, power equipment, industrial systems etc. A scheme which incorporates overcurrent relays for the protection of an element of a power system, is known as an over current protection scheme or overcurrent protection.
At present electromechanical relays are widely used for overcurrent protection.

Time current characteristics

A wide variety of time-current characteristics is available for overcurrent relays.

– Instantaneous overcurrent relay
– Inverse-time overcurrent relay
– Definite-time overcurrent relay
– Inverse definite minimum time (IDMT) overcurrent relay
– Very inverse – time over current relay
– Extremely inverse – time over current relay

Instantaneous overcurrent relay
Intentional time delay is not provided for operation. The relay contacts are closed immediately after the current in the relay coil exceeds the operating value. Although there will be a short time interval between the instant of pick up value and the closing of the relay contacts, no intentional time delay is provided.This characteristic can be achieved with the help of the hinged armature relay. This relay has a unique advantage of reducing the time of operation to a minimum for faults very close to the sourcewhere the fault current is the greatest.The instantaneous relay is effective where the impedance between the relay and source is small.

Application:

Such type of relay is used for controlling earth fault and other types of circulating current protection.

Time current characteristics

Definite time overcurrent relay
• Definite time overcurrent relay operates after a predetermined time when the current exceeds its pick-up value.
• The operating time is constant, irrespective of the magnitude of the current above the pick up value.
• The desired definite operating time can be set with the help of an intentional time delay mechanism provided in the relaying unit.

Application:
• Back up protection of distance relay of transmission line with time delay.
• Back up protection to differential relay of power transformer with time delay.
• Main protection to outgoing feeders and bus couplers with adjustable time delay setting.

Inverse time overcurrent relay

In such type of relay, the operating current isapproximately inversely proportional to themagnitude of the actuating quantity.At values of current less than pick up value,the relay never operates. At, higher values,the operating time of the relay decreaseregularly with the increase of the current.The inverse time relay is of three types.

Inverse Definite Minimum Time Relay

• In this relay, the operating time is inversely proportional to the fault current near pick-up value.
  • The relay becomes considerably constant slightly above the pickup value of the relay as shown in the figure.
  • This is achieved by using a core of the electromagnet which gets saturated for current slightly greater than
  the pick-up current.

Application:
• The relay is used for the protection of the distribution line.

Very Inverse Relay
• In such relay, the saturation of the current occurs at a still later stage.
• The time-current characteristic is inverse over a greater range and after saturation tends to the definite time.
• The relay is used in the places where there the magnitude of the short-circuit current fall rapidly because of the large distance from the source.

Application:
• Relays with very inverse time characteristic are
employed on feeders and long sub-transmission lines.

Extremely Inverse Relay
• The characteristic time of the relay is extremely large as compared to the IDMT and the Very inverse relay.
• In this type of relay, the core saturation occurs at the very large stage.
• The relay can operate instantly when the pickup value of the current is more than the relay setting time. The relay provides faster operation.

Application:
• This relay is used for protecting the cable, transformer, etc. It is used for sensing the overheating of the machines.
• The inverse time relay is used in the distribution networks and the power plants.

Time current characteristics

IDMT characteristics

Induction type overcurrent relay

Pic source:engineering note india

There are two structures of the induction disc type overcurrent relay:

1. Shaded pole structure
2.  Watt-hour meter structure.

Most of the induction relays are of watt-hour meter structure. The construction of this relay is similar to the watt-hour or the AC energy meter.It consists of two electromagnets. The upper electromagnet carries two winding; primary winding and the secondary winding.The advantage of this type of construction is that it can provide a larger phase angle between the two fluxes and hence a higher torque. An important feature of this type of relay is that its operation can be controlled by opening or closing the secondary winding.If the circuit is opened, no torque will be produced and thus the relay is made inoperative.The relay has two electromagnets. The upper electromagnet has two winding; one of these is primary and is connected to the secondary of a CT in the line to be protected and is tapped at intervals. The tapping are connected to a plug setting bridge by which the no. of turns in use can be adjusted thereby giving the desired current setting.The plug bridge is usually arranged to give seven sections of tapping to give overcurrent range from 50% to 200% in steps of 25%. If the relay is required to response for earth faults the steps are arranged to a range from 10% to 70% or 20% to 80% in steps of 10%. The values assigned to each tap are expressed in terms of percentage of full load rating of CT with which the relay is associated and represents and value above which the disc commences to rotate and finally closes the trip circuit.The pickup current equals the rated secondary current of CT multiplied by current setting. For example suppose that an overcurrent relay having a current setting of 150% is connected to a supply circuit through a CT of 500/5 A. The rated secondary current of CT is 5 A and therefore the pick-up value will be 1.5 x 5 = 7.5 A.  It means that with above current setting, the relay will actually operate for a relay current equal to or greater than 7.5 A.The second winding is energized by induction from the primary and is connected in series with the winding on the lower magnet. By this arrangement, the leakage fluxes of upper and lower electromagnets sufficiently displaced in space and phase to set up a rotational torque on the aluminium disc suspended between the two magnets. This torque is controlled by the spiral spring or by a permanent magnet brake on disc.The torque is given by the expression

T=K1Irms^2-K2

where Irms is the current through the coil and K2 is the restraining torque of the spring.

The disc spindle carries a moving contact which bridges two fixed contacts (trip circuit contacts) when the disc has rotated through a preset angle. The angle can be set to any value between 0 degree and 360 degree. This adjustment is known as time setting multiplier. The multiplier setting is generally in the form of an adjustable back stop which decides the arc length through which the disc travels, by reducing the length of travel the operating time is reduced.The time setting multiplier is calibrated from 0 to 1 in steps of 0.05. this figure don’t represent the actual operating time but are multiples to be used to convert the time known from the relay name plate curve (time – PSM curve) into the actual operating time. Thus if time setting is 0.2 and the operating time obtained from the time – PSM curve of the relay is 5 seconds, then actual operating time of the relay will be equal to 0.2 x 5 = 1 second. Since the time required to rotate the disc through a preset angle depends upon the torque which varies as current in the primary circuit, therefore, more the torque lesser will be the time required. So the relay has inverse time characteristics.

Distance or Impedance Relay

This is one type of relay which functions depending upon the distance of fault in the line. More specifically, the relay operates depending upon the impedance between the point of fault and the point where relay is installed. These relays are known as distance relay or impedance relay.

Classification of Distance Relays

Distance relays used for the protection of power circuits may be divided into two groups:

• Definite distance relays and
• Time-distance relays.

Definite distance relays operate instantaneously when the impedance (reactance or admittance) falls below a specified value. These relays may be of impedance, reactance or mho type.

Time-distance relays have the time of operation dependent upon the value of impedance (reactance or admittance) i.e., upon the distance of the fault from the relay point. A fault nearer to the relay will operate it earlier than a fault farther away from the relay. These relays may be of impedance, reactance or mho type.

Impedance Type Distance Relay

Consider the impedance relay is placed on the transmission line for the protection of the line AB. The Z is the impedance of the line in normal operating condition. If the impedances of the line fall below the impedance Z then the relay starts working. Let, the fault F1 occur in the line AB. This fault decreases the impedance of the line below the relay setting impedance. The relay starts operating, and it sends the tripping command to the circuit breaker.

Electromagnetic Type Impedance Relay

The solenoid B is excited by the voltage supplied of the PT. This voltage develops the torque in the clockwise direction, and it pulls the plunger P₂ in the downward direction. The spring connects to the plunger P₂ apply the restraining force on it.This spring generates the mechanical torque in the clockwise direction. The solenoid A generates the other torque in the clockwise direction and thus moves the plunger P₁ The solenoid one is excited by the CT of the lines. This torque is called the deflecting or pick up torque. When the system is free from fault, the contacts of the relay become open. When the fault occurs in the protective zone, the current of the system rises because of which the current across the relay also increases. The more torque developed on the solenoid A. The restoring torque decreases because of the voltage decreases. The balance arms of the relay start rotating in the opposite direction, thus closed their contacts. 

Induction Type Impedance Relay

The upper electromagnet has two separate windings. The primary winding is connected to the secondary coil of the current transformer. The current setting of the winding is varied by the help of the plug bridge placed below the relay. The flux induce between the electromagnets produces the rotational torque, which rotates the aluminum disc of the relay. In normal operating conditions the force exerted on the armature is more than the induction element which keeps the trip contacts open. When the fault occurs in the system, then the aluminum disc starts rotating, and their rotation is directly proportional to the current of the electromagnet. The rotation of the disc-wound the spring.

Impedance Type Distance Relay

The voltage and the current operating elements are the two important component of the impedance relay. The current operating element generates the deflecting torque while the voltage storage element generates the restoring torque. The torque equation of the relay is shown in the figure below

The -K₃ is the spring effect of the relay. The V and I are the value of the voltage and current. When the relay is in normal operating condition, then the net torque of the relay becomes zero.

If the spring control effect becomes neglected, the equation becomes

Operating characteristic of impedance relay

Reactance Relay

The reactance relay is a high-speed relay. This relay consists of two elements an overcurrent element and a current-voltage directional element. The current element develops positive torque and a current-voltage developed directional element opposes the current element depending on the phase angle between current and voltage. Reactance relay is an overcurrent relay with directional limitation. The directional element is arranged to develop maximum negative torque when its current lag behind its voltage by 90°.It has a four-pole structure carrying operating, polarizing, and restraining coils. The operating torque is developed by the interaction of fluxes due to current carrying coils, i.e., the interaction of fluxes of 2, 3 and 4 and the restraining torque is produced by the interaction of fluxes due to poles 1, 2 and 4. The operating torque will be proportional to the square of the current while the restraining torque will be proportional to VI cos (Θ – 90°). The desired maximum torque angle is obtained with the help of resistance-capacitance circuits. Reactance type relay is very suitable as a ground relay for ground fault. The operating torque will be proportional to the square of the current while the restraining torque will be proportional to VI cos (Θ – 90°). The desired maximum torque angle is obtained with the help of resistance-capacitance If the control effect is indicated by –k₃, the torque equation becomes

T = K₁I² – K₂ VI cos(θ – 90⁰) – K3

where Θ, is defined as positive when I lag behind V. At the balance point net torque is zero, and hence

The spring control effect is neglected in the above equation, i.e., K₃ = 0.

Operating characteristic of a reactance relay

The operating characteristic of a reactance relay is shown in the figure. X is the reactance of the protected line between the relay location and the fault point, and R is the resistance component of the impedance. The characteristic shows that the resistance component of the impedance has no consequence on the working of the relay, the relay reacts solely to the reactance component. The point below the operating characteristic is called the positive torque region.

Mho Relay

A mho Relay is a high-speed relay and is also known as the admittance relay.In this relay operating torque is obtained by the volt-amperes element and the controlling element is developed due to the voltage element.It means a mho relay is a voltage controlled directional relay.The operating torque is developed by the interaction of fluxes due to pole 2, 3, and 4 and the controlling torque is developed due to poles 1, 2 and 4. At balance point, the net torque is zero, and hence the equation becomes

If the spring controlled effect is neglected i.e., k₃ = 0.

The diameter of the circle is practically independent of V and I, except at a very low magnitude of the voltage and current when the spring effect is considered, which causes the diameter to decrease. The diameter of the circle is expressed by the equation as

Z_R= K₁ / K₂

₌ohmic setting of the relay

The relay operates when the impedance seen by the relay within the circle. The operating characteristic showed that circle passes through the origin, which makes the relay naturally directional.The impedance angle of the protected line is normally 60º and 70º which is shown by line OC in the figure. The arc resistance R is represented by the length AB, which is horizontal to OC from the extremity of the chord Z. By making the τ equal to, or little less lagging than Θ, the circle is made to fit around the faulty area so that the relay is insensitive to power swings and therefore particularly applicable to the protection of long or heavily loaded lines.For a given relay the τ is constant

The operating torque for a Mho relay is by V-I element and restraining torque is by voltage element.

Therefore, a Mho relay can be called as a voltage restrained directional relay.

T = K₁ VI Cos (Φ – τ) –K₂V², neglecting the effect of the spring.

K₂V² < K₁VI Cos (Φ – τ)

K₂V < K₁I Cos (Φ – τ)

(V/I Cos (Φ – τ)) < K₁/K₂

or (V/I) < (K₁/K₂) Cos (Φ – τ)

or Z < (K₁/K₂)Cos (Φ – τ)

At balance conditions, the operating torque is equal to restraining torque.

i.e., K₁VICos (Φ – τ) = K₂V²

(I/V)Cos (Φ – τ) = (K₂K₁) = K

(1/Z) = (K / Cos (Φ – τ)) = Y

Y = K / Cos (Φ – τ) = admittance in mho.