Three phase Over current relays; Over current relay characteristics

Depending upon the time of operation the overcurrent relays are categorized as :-

1.       Instantaneous over-current relays

2.       Inverse time-current relays

3.       Inverse definite minimum time (IDMT) Over-current relay

4.       Very inverse relay and

5.       Extremely inverse relay

Now let us study the same one by one:-

1.       Instantaneous Over-current relay:-

This relay as clear from it’s name is that it has instantaneous tripping without any delay. Time of operation of such relay is about 0.1 sec. This type of characteristic can be achieved by using hinged armature relays.

2.       Inverse time-current relay:-

In that type of relays operating time reduces as the actuating quantity ,i.e. current In case of over-current ,increases in magnitude. More pronounced the effect more inverse will be the characteristics. They are normally more inverse near the pick up value of the actuating quantity and become less inverse as it is increased. This type of characteristic can be achieved with induction type relays by using suitable core which doesn’t saturate for large value of fault current. If saturation occurs at very early stage, the time of operation remains the same over the working range. Characteristic for the same in diagram as (a )

Characteristics of Over current Relay

3.       Inverse definite minimum time (IDMT) Over-current relay:-

In that type of relay operating time is approximately inversely proportional to the fault current near pick up value and becomes substantially constant slightly above the pick up value of the relay as shown (b). This is achieved by using a core of the electromagnet which get saturated for current slightly greater than the pickup current.

4.       Very inverse relay:-

In this relay saturation of the core occurs at later stage, characteristic is shown in (c ). The time current characteristic is inverse over greater range and after saturation rends to definite time.

5.       Extremely inverse relay:-

In this relay saturation occur even at later stage. Same is shown in (d) curve. The equation describing the curve is K= I²t , where I is the operating current and t is operating time.

Single phase and Three phase formula's used in electrical engineering

Electrical Formulas

Electrical engineering required certain formula which must be known for an electrical engineer and even a non engineer person so to know certain parameters of appliances around everyone.

Lets discuss 1^st about basic parameters used in electrical systems:-

I = Amperes

E = Volts

kW = Kilowatts

kVA = Kilo volt-Amperes

HP = Horsepower

% eff. = Percent Efficiency

pf = Power Factor

For Single-Phase load here are the formula’s as below:-

TO FIND:-

§  Amperes when kVA is known –>   I = kVA x 1000 / E

§  Amperes when horsepower is known –>  ( HP x 746) / ( E  x  % eff.  x pf )

§  Amperes when kilowatts are known –>  ( kW x 1000 ) / ( E x pf )

§  Kilowatts  –>  ( I x E x pf ) /1000

§  Kilovolt-Amperes  –>  ( I x E ) / 1000

§  Horsepower  –>  ( I x E x % eff. x pf  ) / 746

§  Watts   –>  E x I x pf

§  Energy Efficiency  –>  Load Horsepower x 746 / Load Input kVA x 1000

§  Power Factor  @ cos θ –>  Power Consumed /Apparent Power ( W / VA ) @ ( kW / kVA)

Two-Phase

TO FIND :-

§  Amperes when kVA is known –>   I = ( kVA x 1000 )  / ( E x 2 )

§  Amperes when horsepower is known –>  ( HP x 746) / ( E  x  2  x % eff.  x pf )

§  Amperes when kilowatts are known –>  ( kW x 1000 ) / ( E x 2 x pf )

§  Kilowatts  –>  ( I x E x 2 x pf ) /1000

§  Kilovolt-Amperes  –>  ( I x E x 2 ) / 1000

§  Horsepower  –>  ( I x E x 2 x % eff. x pf  ) / 746

§  Watts   –>  E x I x 2 x pf

§  Energy Efficiency –>  Load Horsepower x 746 / Load Input kVA x 1000

§  Power Factor @ cos θ –>  Power Consumed /Apparent Power ( W / VA ) @ ( kW / kVA)

For findingThree-Phase parameters formula’s are as below:-

TO FIND :-

§  Amperes when kVA is known –>   I = ( kVA x 1000 )  / ( E x 1.73 )

§  Amperes when horsepower is known –>  ( HP x 746) / ( E  x  1.73  x % eff.  x pf )

§  Amperes when kilowatts are known –>  ( kW x 1000 ) / ( E x 1.73 x pf )

§  Kilowatts  –>  ( I x E x 1.73 x pf ) /1000

§  Kilovolt-Amperes  –>  ( I x E x 1.73 ) / 1000

§  Horsepower  –>  ( I x E x 1.73 x % eff. x pf  ) / 746

§  Watts   –>  E x I x 1.73 x pf

§  Energy Efficiency  –>  Load Horsepower x 746 / Load Input kVA x 1000

§  Power Factor  @ cos θ –>  Power Consumed /Apparent Power ( W / VA ) @ ( kW / kVA)

Others Formula

§  kW = hp x .746

§  Torque in lb-ft = hp x 5250 / rpm

§  Motor synchronous speed in rpm = 120 x Hz / number of poles

§  Three-phase full-load amp= hp x .746 / 1.73 x kV x effi ciency x power factor

§  Rated motor kVA = hp (.746) / efficiency x power factor

§  kW loss = hp (.746) (1.0 – effi ciency) / efficiency

§  kVA in-rush = percent in-rush x rated kVA

§  Approximate voltage drop (%) = motor kVA in-rush x transformer impedance / transformer kVA

§  Stored kinetic energy in kW-sec = 2.31 x (total Wk2) x rpm2 x 107

§  Inertia constant (H) in seconds = stored kinetic energy in kW-seconds / hp (.746)

§  Conversion factors: CV = (metric hp) = 735.5 watts = 75 kg-m/sec Wk2 (lb-ft) = 5.93 x GD2 (kg-m2)

§  Ventilating-air requirements: 100-125 cfm of 400C air at 1/2-in. water pressure for each kW of loss

§  Degrees C = (Degrees F-32) x 5/9

§  Degrees F = [(Degrees C) x 9/5 ] + 32

Comparison between Three Phase Overhead and Underground cables

Power can be transferred through Overhead cables or Underground cables. In overhead lines inductance is predominant and in case of underground cables capacitance is predominant.

There are always advantages of Overhead transmission lines in comparison to underground cables:-

1.     The conductor used in Overhead transmission lines is less expensive as size of cable required in overhead lines is less than underground cables. As overhead lines have better heat dissipation than underground cables.

2.     Insulation cost in case of underground cables is more than overhead lines. Overhead lines use bare conductors which are well supported and provide sufficient spacing between conductors. But in underground cables insulation is provided by various high grade paper tapes. A metal sheath is also provided so that moisture doesn’t enter the cable. Oil and inert gas is inserted so as to fill voids. Also storage vessels are needed to be installed after some intervals so to makeup the voids created during expansion and contraction of oil or gas in cables.

3.     Also erection cost of overhead line is much less than underground cables.

4.     It is easy to do capacity addition in overhead lines than underground cables.

There is some advantages of underground transmission than overhead transmission:-\

1. Underground cables provide safety to public.

2. Underground cable doesn't give interference and also underground cables provide better looks to surroundings.

Skin Effect Three phase lines; Factors effecting skin effect; Why skin effect not occur on DC?

Skin effect occurs in transmission lines due to unequal distribution of current over the entire cross section of the conductor being used for long distance power transmission. Skin effect usually occur in Alternating current not in Direct current flow. As Direct current is uniformly distributed across the section so skin effect doesn't takes place.But in alternating current current flow is non-uniform, where outer filaments of conductor takes more current than filament closer to the center. This will leads to higher resistance in conductors due to uneven distribution at alternation current then Direct current.

The inner filament carrying currents gives rise to flux which links to inner filaments only where as flux due to current carrying outer filaments enclose both the inner as well as the outer filaments. The flux linkages per ampere to inner strands is more as compared to outer strands. Hence the inductance/impedance of the inner strands is greater than those of the outer strands which results in more current in the outer strands as compared to the inner strands.

Lets understand the same more thoroughly :-


Having understood the phenomena of skin effect let us now see why this arises in case of an AC system. To have a clear understanding of that look into the cross sectional view of the conductor during the flow of alternating current given in the diagram below.

Let us initially consider the solid conductor to be split up into a number of annular filaments spaced infinitely small distance apart, such that each filament carries an infinitely small fraction of the total current.

Like if the total current = I

Lets consider the conductor to be split up into n filament carrying current ‘i’ such that I = n i .

Now during the flow of an alternating current, the current carrying filaments lying on the core has a flux linkage with the entire conductor cross section including the filaments of the surface as well as those in the core. Whereas the flux set up by the outer filaments is restricted only to the surface itself and is unable to link with the inner filaments.Thus the flux linkage of the conductor increases as we move closer towards the core and at the same rate increases the inductor as it has a direct proportionality relationship with flux linkage. This results in a larger inductive reactance being induced into the core as compared to the outer sections of the conductor. The high value of reactance in the inner section results in the current being distributed in an un-uniform manner and forcing the bulk of the current to flow through the outer surface or skin giving rise to the phenomena called skin effect in transmission lines.skin effect



Factors Affecting Skin Effect in Transmission Lines

The skin effect in an ac system depends on a number of factors like:-

1) Shape of conductor.

2) Type of material.

3) Diameter of the conductors.

4) Operational frequency.

Corona Loss in Transmission Lines; Hissing sound in transmission lines

Corona Effect

Corona phenomenon is the ionization of the surrounding air near power conductor. Free electrons are always present in free space because of radioactivity and cosmic rays. As the potential between the conductors is increased, the gradient around the surface of the conductor increase. The free electrons will move with certain velocity depending upon the field strength.These free electrons will collide with molecules of air and in-case they have high velocity they will dislodge the electrons from molecules and which will leads to increase in no. of electrons. This will form a electron avalanche. 

In case the ratio of spacing between conductors to the radius of conductor is less than 15, flashover will occur between conductors before ionization.

Corona loss occurs with hissing sound which is very clearly listened in HT lines. There sound is even very clearer during rainy seasons.

Corona loss is given by formula as below:-

Corona loss= 241X10^-5 f+25 (r/d)^1/2    (Vp-Vo) ²

                                                       d            

d= air density correction factor

Corona loss directly proportional to (Vp-Vo) ²

Vo= rgd (ln d/r)

Where g= Dielectric strength and is equal to 30 KV/cm peak at NTP

So v is directly proportional to diameter

also corona loss is  proportional to (r/d)^1/2

So by combining both effects we see that corona loss reduces as conductor diameter increases

Corona Effect in Transmission Line

When an alternating electric current is made to flow across two conductors of the transmission line whose spacing is large compared to their diameters, then air surrounding the conductors (composed of ions) is subjected to di-electric stress. At low values of supply end voltage, nothing really occurs as the stress is too less to ionize the air outside. But when the potential difference is made to increase beyond some threshold value of around 30 kV known as the critical disruptive voltage, then the field strength increases and then the air surrounding it experiences stress high enough to be dissociated into ions making the atmosphere conducting. This results in electric discharge around the conductors due to the flow of these ions, giving rise to a faint luminescent glow, along with the hissing sound accompanied by the liberation of ozone, which is readily identified due to its characteristic odor. This phenomena of electrical discharge occurring in transmission line for high values of voltage is known as the corona effect in power system. If the voltage across the lines is still increased the glow becomes more and more intense along with hissing noise, inducing very high power loss into the system which must be accounted for.

Factors Affecting Corona Effect in Power System.

As mentioned earlier, the line voltage of the conductor is the main determining factor for corona in transmission lines, at low values of voltage (lesser than critical disruptive voltage) the stress on the air is too less to dissociate them, and hence no electrical discharge occurs. Since with increasing voltage corona effect in a transmission line occurs due to the ionization of atmospheric air surrounding the cables, it is mainly affected by the conditions of the cable as well as the physical state of the atmosphere. Let us look into these criterion now with greater details :

Atmospheric Conditions for Corona in Transmission Lines

It has been physically proven that the voltage gradient for di-electric breakdown of air is directly proportional to the density of air. Hence in a stormy day, due to continuous air flow the number of ions present surrounding the conductor is far more than normal, and hence its more likely to have electrical discharge in transmission lines on such a day, compared to a day with fairly clear weather. The system has to designed taking those extreme situations into consideration.

Condition of Cables for Corona in Transmission Line.

This particular phenomena depends highly on the conductors and its physical condition. It has an inverse proportionality relationship with the diameter of the conductors. i.e. with the increase in diameter, the effect of corona in power system reduces considerably.

Also the presence of dirt or roughness of the conductor reduces the critical breakdown voltage, making the conductors more prone to corona losses. Hence in most cities and industrial areas having high pollution, this factor is of reasonable importance to counter the ill effects it has on the system.

Spacing between Conductors

As already mentioned, for corona to occur effectively the spacing between the lines should be much higher compared to its diameter, but if the length is increased beyond a certain limit, the di-electric stress on the air reduces and consequently the effect of corona reduces as well. If the spacing is made too large then corona for that region of the transmission line might not occur at all.

Induction Motors Torque Equation; Torque equation

Torque equation for the Induction motor is as given below:-

As we see from the above that Torque equation is Directly proportional to square of the voltage.

Factors affecting the speed-torque characteristics of an Induction motor : The speed-torque characteristics are affected by various factors like applied voltage, R₂’ and frequency.

(a) Applied voltage : We know that T µ V². Thus not only the stationary torque but also the torque under running conditions changes with change in supply voltage.


(b) Supply frequency : The major effect of change in supply frequency is on motor speed. The starting torque is reduced with increase in frequency.

(c) Rotor resistance : The maximum torque produced does not depend on R₂’. However, with increase in R₂’, the starting torque increases. The slip at which T_max is reached increases too which means that T_max is obtained at lower motor speeds.

Slip Ring induction motors starting; Slip ring induction motor starter

Starting Of Slip Ring Induction Motors

Slip ring Induction motors had external resistance connected in line. These motors are usually started with full line voltage applied across its terminals. During starting of slip ring induction motors the value of starting current is adjusted or kept minimum, by increasing the resistance of the rotor circuit.  The external resistance is connected in star and kept at maximum during starting so to minimize starting current. By increasing the rotor resistance it will not only reduces the rotor current but the stator current too.

This means that whenever a resistance is added in rotor circuit that will leads to reduced starting current. Thus because of this, the starting torque is increased due to the improvement in power factor.

Usually resistance is added during starting and slowly made out of circuit when motor attains the speed and this resistance is disconnected by using a contactor in line.  Slip ring can be taken in line by using manually also. The 3-phase supply to the stator has a switching contactor along with over-load and no or low-voltage protective devices. There might be also an interlock provided to ensure the proper sequential operation of the control gear and starting devices.

Slip ring motors circuit diagram is as shown above.

Torque curve of Slip ring motors is shown above

As per torque formula

Torque is directly proportional to resistance.

So as the resistance is high in slip ring motors torque is also high during starting.

As these motors have considerably high starting torque with low starting current, these motors can be started on load. The external resistance is used only for the starting purpose, after which the motor gradually picks up the speed, the resistance gradually cut-off. These rings are isolated after the motor reaches its rated speed. The carbon brushes are lifted and the rings are short circuited thus making them very similar to squirrel cage motors.

Applications of Slip Ring Induction Motors

These motors are used where the load is intermittent and comes on very sharply for brief periods, such as a punching machine. A heavy flywheel is fitted in the drive, preferably between the work and any speed-reduction gears. The flywheel shares the load with the motor, thus enabling a motor of lower rating to be employed. For load sharing to take place automatically, the motor speed should drop considerably as the load increases and this is ensured by using a motor having a high full-load slip, say for example 10%.

Characteristics Of Slip Ring Induction Motor

As other induction motors consists of Stator and Rotor circuits slip ring motors also have same Stator circuit there is only difference in rotor circuit. Rotor circuit consists of external resistance in the circuit. The stator circuit is slip ring motors is rated as same in the squirrel cage motor, but the rotor is rated in frame voltage or short circuit current. The frame voltage is the open circuit voltage when the rotor is not rotating and gives the measure of turns ratio between the stator and rotor. The short circuit current is the current flowing when the motor is operating at full speed, with the slip rings shorted and the full load applied to the motor shaft.

Advantages of Slip-Ring Motors:

1. These are used where there are high Inertia loads  as these motors have excellent starting torque.

2. These motors have low starting current then other induction motors.

3.  It is easy to control the speed of the motor from 50% to 100% of the full speed,

Disadvantages of Slip Ring Motors

1. Higher brush and slip ring maintenance required,

2. As the brush wears out, it may lead to intermittent contact, and thus heavy sparking.

3. Also speed control of motor comes along with increased losses as heat comes across resistance.