How to Draw Potier Triangle/ZPF characteristics ?

Regulation by Zero Power Factor ( ZPF) method  of Alternator:

During the operation of the alternator, resistance voltage drop IaRand armature leakage reactance drop IaXL are actually emf quantities and the armature reaction reactance is a mmf quantity. To determine the regulation of the alternator by this method OCC, SCC and ZPF test details and characteristics are required.

-As explained earlier OC and SC tests are conducted and OCC and SCC are drawn.

-ZPF test is conducted by connecting the alternator to ZPF load and exciting the alternator in such way that the alternator supplies the rated current at rated voltage running at rated speed.
-To plot ZPF characteristics only two points are required. One point is corresponding to the zero voltage and rated current that can be obtained from scc and the other at rated voltage and rated current under zpf load.
-This zero power factor curve appears like OCC but shifted by a factor IXL vertically and horizontally by armature reaction mmf as shown below in figure. 

Following are the steps to draw ZPF characteristics:

-By suitable tests plot OCC and SCC. Draw air gap line. Conduct ZPF test at full load for rated voltage and fix the point B.

-Draw the line BH with length equal to field current required to produce full load
current on short circuit..
-Draw HD parallel to the air gap line so as to cut the OCC. Draw DE perpendicular to HB or parallel to voltage axis.
-Now, DE represents voltage drop IXL and BE represents the field current required to overcome the effect of armature reaction.
-Triangle BDE is called Potier triangle and XL is the Potier reactance. Find E from V, IRa, IXL and .
-Use the expression E =√ (V cos  Ø+ IRa)² + (V sin ) + IXL)² to compute E. Find field current corresponding to E. Draw FG with magnitude equal to BE at angle (90+ ) from field current axis, where is the phase angle of current from voltage vector E (internal phase angle).
-The resultant field current is given by OG. Mark this length on field current axis. From OCC find the corresponding E0. Find the regulation.

Auto Transformer Principle of Operation,Working & Applications

An auto transformer is a electrical transformer having only single winding which acts as both primary and secondary,so in input and output connected to shared single winding.

Why we need to go for Auto Transformer ?

We have some advantages of auto-transformer over normal two winding transformer.
1.Auto transformers usually smaller in size,because one winding is eliminated. size is small cost also low(so cheap in cost) the winding is same so leakage reactance will be less.
4.increased kVA rating.

Auto Transformer

Construction, Principle of Operation Of Auto Transformer: 

In Auto Transformer, one single winding is shared as primary winding as well as secondary in transformer copper wire wound on silicon shown in the figure input connected at fixed positions.but on other side we employ some tapping to get variable output voltages.Variable turns ratio at secondary can be obtained by changing the tappings of the winding.

Auto Transformer

Copper Savings in Auto Transformer:

If we compare conventional two winding transformer and  auto transformer the amount of copper needed for auto transformer is less.weight of copper of any winding depends upon its length and cross - sectional area.and length depends on no.of turns,cross - sectional area varies with rated current.

Auto Transformer

copper in the section AC proportional to, 


weight of copper in the section BC proportional to


Hence, total weight of copper in the winding of auto transformer proportional to,

In similar way it can be proved, the weight of copper in two winding transformer is proportional to,

=2N1I1(Since, in a transformer N1I1=N2I2)

Let's assume, Wa and Wtw are weight of copper in auto transformer and two winding transformer respectively,

∴ Saving of copper in auto transformer compared to two winding transformer,
∴ Wtw -Wa=kWtw 

9 Advantages of Three Phase System Over Single Phase System

Three Phase System Advantages 

In modern power generation, transportation, distribution we use poly-phase system over single phase system.In poly-phase AC system it  might be two , three or more individual circuits, operate at same frequency, their voltages and currents are out of phase from one another.But when it comes to practical scenario three phase system considered as poly-phase system.It is most reliable and efficient compared to all poly phase systems.Single phase system has some limitations and drawbacks so it's been replaced by three-phase system.Here we listed out major reasons why 3 phase/poly-phase system is better than single phase system.
8 Advantages of Three Phase System Over Single Phase System

Advantages of polyphase systems over single phase systems are

1. A polyphase/3 phase transmission line requires less conductor material than a single phase line for transmitting the same amount power at the same voltage.

2. For a given frame size a polyphase/3 phase machine gives a higher output than a single-phase machine. For example output of a 3-phase motor is 1.5 times the output of single-phase motor of same size.

3. Polyphase/3 phase motors have a uniform torque where most of the single-phase motors have a pulsating torque.

4. Polyphase/3 phase induction motors are self-starting and are more efficient. On the other hand single-phase induction motors are not self-starting and are less efficient.

6. Per unit of output. the polyphase/3 phase machine is very much cheaper.

7. Power factor of a single-phase motor is lower than that of polyphase motor of the same rating.

8. Rotating field can be set up by passing polyphase current through stationary coils.

9. Parallel operation of polypahse alternators is simple as compared to that of single-phase alternators because of pulsating reaction in single-phase alternator.

It has been found that the above advantages are best realized in the case of three-phase systems.Consequently, the electric power is generated and transmitted in the form of three-phase system.

Final Points :
Single Phase SupplyThree Phase supply
power delivered is pulsatingPower delivered is constant
Single Phase induction motors are not self starting as it does not have starting torque.Three phase induction motors are self starting.
Parallel operation is not easy.Parallel Operation is easy.
Efficiency of single phase motor is lesser.High efficiency.
Single phase motors have pulsating torque.Three phase motors have uniform torque.
Single phase motors have lower power factor.Three phase motors have higher power factor.
disadvantages of three phase system
advantages of 3 phase system pdf
disadvantages of three phase supply
why is 3 phase power more efficient
difference between single phase and three phase supply pdf
advantages and disadvantages of single phase transformer
necessity of three phase system

Current Differential Relay Working || Types of Differential Relays

Current Differential Relay Working || Types of Differential Relays

What is differential relay?

In the over-current relays, a current is sensed but such relays are not very sensitive as these relays cannot distinguish between heavy loads and minor fault conditions. in such castes. differential relays can be need.

A differential relay in defined an the relay that operates when the phasor drill-me of two or more similar electrical quantities exceeds a predetermined value,

Thus a current differential relay operates on the result of comparison between the phase angle and magnitudes of the currents entering and leaving the system to be protected. Under normal conditions. the two currents are equal in phase and magnitude hence relay is inoperative. But under fault conditions. this condition no longer exist.
The relay is connected in such a manner that the difference between current entering and current leaving flows through the operating coil.If this differential current exceeds a preset value then the relay operates and opens the circuit breaker.

Almost any type of relay when connected in a certain way can be made to operate as a differential relay.

Types of differential relays:

1. Current differential relay.
2. Biased beam relay or percentage differential relay.
3. Voltage balance differential relay.

Current differential relay working:

Most of the differential relays are at current differential type. Consider an over current relay connected in the circuit so as to operate as the current differential relay. This it shown in the figure.
Two current transformers are used having same ratio are connected on the either  side of the section to be protected.The secondaries of current transformers are  connected in series, so they carry induced currents in the same direction. Let current I is flowing through the primary of current  transformers towards the external fault. As the current transformers are identical, the secondaries of current transformers will carry equal currents. Due to the connection of relay, no current will flow through the operating coil for the relay, Hence relay will remain Inoperative. So relay cannot operate if there is an external fault.

The current flows through the fault from both sides. The two secondary currents through C.Ts are not equal. The current flowing through the relay coil  is now i1+i2. This high current causes the relay to operate.
It should be noted that the fault current need not always flow to the fault from both sides. A flow on one side only or even some current flowing out of one side while a large current entering  the other side can cause differential relay to operate. Thus the amount of current flowing through a relay coil depends upon the way the fault is being fed‘

Disadvantages of current differential relay:

1. The current transformers are connected through cables called pilot cables. The impedance of such pilot cables generally causes a slight difference between the currents at the ends of the section to be protected, A sensitive relay can operate to a very small difference in the two currents, though there is no fault existing.
2. The relay is likely to operate inaccurately with heavy through current flows.This is because the assumed identical current transformers may not have identical secondary currents due to the constructional errors and pilot cable impedance.
3. Under severe through fault conditions,. the current transformers may saturate and cause unequal secondary currents. The difference between the currents may approach the pick value to cause the inaccurate operation for the relay.
4. Under heavy current flows. pilot cable capacitance may cause inaccurate operation of the relay.
All these disadvantages are overcome in biased beam relay.

What is Creeping in Energy Meters ?

Creeping in Energy Meters: 

In some energy meters a slow but continuous rotation of the disc is obtained when the pressure coils are energized and there is no load current passing through the current coil i.e. current coil is not energized.The main reason for creeping is over-compensation the aluminium disk to over come the static friction of disk and another reason is over voltage across the shunt magnet.Due to this creeping consumers suffers from high tariff. This may be due to incorrect friction compensation to vibration, to stray magnetic field or to the fact that the supply voltage is in excess of the normal voltage. This unwanted effect is called as "creeping in energy meter".

Read Here : How Energy Meter Works?

How to reduce creeping error in energy meter?

To prevent such creeping of the meter two holes or slots are cut in the disc on opposite sides of the spindle. The disc tends to remain stationary when one of the holes comes under one of the poles of the shunt magnet. In some cases a small piece of iron wire is attached to the edge of the disc. The force of attraction of the brake magnet upon this iron wire is sufficient to prevent the creeping of the disc under no load condition.

Single Phase Induction Type Energy Meter Working, Construction & Creeping

Single Phase Induction Type Energy Meter Construction,Working Principle,Operation,Creeping,Torque Equation

The measurement of energy is the same process as measurement of power except that the instrument not merely indicates the power or rate of supply of energy but must take into account also the length of time for which the rate of energy is continued. There are basically three types of energy meters.
(a) Electrolytic meters
(b) Motor meters
(c) Clock meters.
Out of the above, motor meters are very widely used and among motor meters also induction type watt-hour meters are more commonly used and will be dealt with here. Single phase induction type energy meter working explained including constructional details.
READ HERE : PMMC Working & Operation

Single Phase Induction Type Energy Meter Construction

The construction of this meter is more or less similar to induction type watt-meter. The main alterations are the provision of only one pressure coil upon the central limb of the shunt magnet and only one copper shading band upon this limb. In addition there are two copper bands placed obliquely on the other two limbs of this magnet, their objective is to provide compensation against friction error in the energy meter (see figure).

In this meter the moving system is allowed to revolve continuously instead of being allowed merely to rotate through a fraction of one revolution as in an indicating instrument. The speed of revolution is proportional to the power in the circuit. It follows, therefore, that the no. of revolutions made by the revolving system in any given time is proportional to the energy supplied. The number of revolutions made by the meter is recorded by a counting mechanism consisting of a train of wheels to which the spindle of the rotating system is geared.

Single Phase Induction Type Energy Meter Working

The control of speed is brought about by a permanent magnet called the brake magnet.The magnet is placed opposite to the electromagnet used for providing deflecting torque and it induces currents in the disc which produces retarding torque proportional to their magnitude which latter is proportional to the speed of the rotating system. This system attains a steady speed when the retarding torque exactly balances the driving torque produced by the power in the circuit. The braking torque produced by the brake magnet depends upon the strength of the magnet.

Torque Equation:

If  φ is the flux of the brake magnet, i the current induced by the rotation of the moving system in the field of the brake magnet and TB is the braking torque, then
T ∝ i.φ
If n is the speed of the rotating system (disc) and e the voltage induced in the disc of the meter.
∝ n.φ
Let r be the resistance to the path of eddy current i in the disc, hence i = e/r.
and  T φ.(e/r)
∝ φ².(n/r)

This braking torque equals the constant driving torque TD when a steady speed of the disc
is attained. Thus if N be the steady speed of the meter

T' ∝ φ².(N/r)
and at balance T'B = T∝ φ².(N/r)  or N  ∝ (r/φ²).TD

Hence the steady speed attained by the meter for a constant driving torque TD is directly proportional to the resistance of the path of the induced eddy currents and inversely proportional to the square of the flux of the brake magnet. Therefore, it can be seen that it is very important for brake magnet to have constant magnetic strength throughout the use of the energy meter. It is to be noted that the spring control and pointer of the watt-meter have been replaced in the energy meter by a brake magnet which provides braking torque as explained above.

Using the theory of induction watt-meter.
Operating or driving torque ∝ VI cosφ
where V is the supply voltage across the shunt coil and ! the load current through the series coil of the meter and φ the p.f. angle between V and I.
Now the braking torque has been shown to be proportional to the speed N of the disc i.e.
Since for a steady speed N, the driving torque TD is equal to TB, we have N  VI cosφ or power is proportional to speed N.Thus the total no. of revolutions which equals N.dt is proportional to VI cosφ dt   i.e. proportional to energy supplied.

The speed of the disc can be adjusted by suitably positioning the brake magnet with respect
to the spindle of the disc. If the brake magnet is moved towards the spindle the braking torque
decreases and if taken away from the spindle the braking torque increases.
An energy meter is rated in terms of the supply voltage, the full load current and number
of revolutions of the disc per kWhr (also known as constant of the energy meter). These are
marked on the dial of the energy meter.

What is creeping in energy meter?

Creep:In some meters a slow but continuous rotation of the disc is obtained when the pressure coils are energized and there is no load current passing through the current coil i.e. current coil is not energized. This may be due to incorrect friction compensation to vibration, to stray magnetic field or to the fact that the supply voltage is in excess of the normal voltage.

To prevent such creeping of the meter two holes or slots are cut in the disc on opposite sides of the spindle. The disc tends to remain stationary when one of the holes comes under one of the poles of the shunt magnet. In some cases a small piece of iron wire is attached to the edge of the disc. The force of attraction of the brake magnet upon this iron wire is sufficient to prevent the creeping of the disc under no load condition.

Friction Compensation In Energy Meter:
The two shading bands embrace the flux contained in the two outer limbs of the shunt magnet and thus eddy currents are induced in them which cause a phase displacement between the enclosed flux and the main gap flux. As a result a small driving torque is exerted on the disc, this torque being adjusted by variation of the position of these bands to compensate for friction torque in the instrument.
The friction compensation can be checked whether it is correct or not by connecting light load under which condition it should run at the correct speed.

Energy Meter Phase Angle Error:
It is desired that the phase angle between the applied voltage to the pressure coil and the shunt magnet flux should be at 90° which is adjusted with the help of shading band on the shunt magnet. An error due to incorrect adjustment of the position of this shading band will be evident when the meter is tested on a load whose p.f. is less than unity. An error on the "fast" side under these conditions can he eliminated hy bringing the shading hand further drawn the limb of the shunt magnet i.e. nearer to the disc.

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