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## Two Watt Meter Method For Power Measurement

Two watt meter method is used for measuring power in 3 phase 3 - wire star or delta connected systems either with balanced or unbalanced load. Let us discuss two watt meter method for 3 phase power measurement  with star and delta connection in detail.

### Measurement of power by two watt meter method in star connection:

In this method we use two watt meters and the current coils of these watt meters are connected in series with two lines and potential coils are connected across these two lines  and load is connected in star as shown in the following figure.

From figure

The instantaneous current flowing through the watt meter W1 is Ir

The voltage across the potential coil of watt meter W1 is

Instantaneous power measured by the watt meter, W1 is given by,

The instantaneous current flowing through the watt meter W2 is Iy

The voltage across the potential coil of watt meter W2 is
Instantaneous power measured by the watt meter, W2 is given by
The total 3 phase power will be sum of power measured by watt meters W1 and W2

Adding equations 1 and 2 we get following results.

Where P is the total 3 phase power consumed by load.

### Measurement of power by two watt meter method in delta connection:

In this method also we use two watt meters and the current coils of these watt meters are connected in series with two lines and potential coils are connected across these two lines and load is connected in delta as shown in the following figure.

The instantaneous current flowing through the watt meter W1 is,

The voltage across the potential coil of watt meter W1 is Erb

Instantaneous power measured by the watt meter, W1 is given by,

The instantaneous current flowing through the watt meter W2 is,
The voltage across the potential coil of watt meter W2 is Eyb

Instantaneous power measured by the watt meter, W2 is given by,
The total 3 phase power will be sum of power measured by watt meters W1 and W2

Adding equations 3 and 4 we get following results.

Where P is the total 3 phase power consumed by load.

Note : The power measured by watt meter is average power because of the inertia of their moving system.

In this post we have discussed about measurement of three phase power using two watt meter method.

## Three phase energy meter  working,construction

An energy meter is used to measure the energy consumed in the kilowatt hours. This is used in each and every house and industry for calculating the energy consumed by them. A 3-phase energy meter has same elements as in case of a single-phase energy meter. We see each of them in detail in this post.

### Construction of three phase energy meter:

A 3-phase energy meter has following systems. This systems are same for both single phase and three phase energy meters. They are:

1. Driving System.

2. Moving System.

3. Breaking System.

4.Registering or Counting System.

#### Driving System:

This consists of a coil wounded on central limb of a shunt electro magnet which acts as pressure coil also known as voltage coil. This coil should have high inductance which means that inductance to resistance ratio of this coil is very high. Because of this inductive nature the current , flux will lag behind supply voltage by 90° approximately.

Copper shading bands are provided on the shunt magnet's central limb to get 90° phase angle displacement between magnetic field set up by the shunt magnet and supply voltage. We have another series electro magnet on which current coil is wounded. This current coil is in series with the load so load current will flow through this.The flux produced by series magnet is proportional to and in phase with the load current. The driving system of 3-phase energy meter comprises of these elements.

#### Moving system:

On a vertical spindle or shaft a light rotating aluminium disc is attached. With the help of a gear arrangement aluminum disc is attached to the clock mechanism on front side of meter which helps to measure the energy consumed by load.

Eddy currents are induced due to time varying flux produced by series and shunt magnets. A driving torque is set up due to interaction between these two magnetic fields and eddy currents.

Therefore  number of rotations of the disk is  proportional to the energy consumed by the load in a certain time interval and is measured in kilowatt-hours (Kwh).

#### Breaking system:

To damp aluminium disc we keep a small permanent magnet diametrically opposite to both the ac magnets(parallel,series). Now this disc moves in the magnet field crossing air gap. When this happens eddy currents are induced in aluminium disc which interacts with the magnetic field and produces breaking torque.

The speed of the rotating disc can be controlled by changing the position of the brake magnet or diverting some of the flux.

#### Counting system:

It has a gear system to which pointer is attached. This is connected to aluminium disc which drives this pointer. This pointer moves on the dial and gives number of times the is disc rotated.

These can be seen in the diagram given below:

A 3-phase induction motor has same four systems but they are arranged in a different way as shown in the figure given below.

This is a two element 3-phase energy meter. On a common spindle two discs are mounted and each disc has its own break magnet. Moving system drives a gear  Each unit is provided with its own copper shading ring, shading band, friction compensator, etc., to make adjustments for obtaining correct reading.

This gives construction of a 3 phase energy meter.

### Working of three phase energy meter:

Now let us see how a 3 phase energy meter works.

For same power/energy the driving torque should be equal in both elements. For adjusting torque in both the elements we have two current coils connected in phase opposition and two potential coils connected in parallel. Full load current passes through current coil and this arrangement causes two torques to be in opposition and the disc doesn't move if torques are equal. Magnetic shunt is adjusted if there is inequality in torques to make the disc to stand still. Before testing a 3 phase energy meter torque balance is obtained in this way.

Aluminium discs are acted upon by the two coils one is voltage coil and the other is current coil. Voltage coil produces magnetic flux proportional to voltage and current coil produces magnetic flux proportional to current. The voltage coil field lags by 90 degrees by using a lag coil.

Due to this two torques eddy currents are produced in the aluminium discs and discs rotate on a common shaft. Force exerted on the aluminium disc is proportional to product of instantaneous current and voltage. To this shaft a gear arrangement is made and a needle is attached to this gear so when discs rotates this needle moves on dial and counts the number of rotations of the disc.

A permanent magnet is used to produce a force in opposition and proportional to the speed of disc. When power is switched off this acts as break and makes the disc to stop rotating instead of rotating faster. Disc rotates at a speed proportional to power consumed.

Instantaneous power can be calculated by using below formula

Pi = (3600 * N) / (T * R)

where
Pi = Real power being used at that point in time in kW
T = Time (in seconds) for the disc to rotate through the N rotations or part of a rotation
N = The Number of full rotations counted.
R = The number of revolutions per Kilowatt hour (rev/kWh) of the meter being used.

In this way we use a three phase energy meter to calculate the energy consumed by the load.

Related to three phase energy meter:

3 phase energy meter connection diagram
3 phase energy meter price list
3 phase energy meter principle
l&t energy meter price list
3 phase energy meter specifications
3 phase energy meter l&t
3 phase electric meter price india
3 phase energy meter working

## Working principle, construction , torque equation and extending range of electrostatic type instruments

Hello readers, In this post we are going to discuss about construction principle and torque equation of electrostatic type instruments.

### Working principle of electrostatic type instruments:

Working principle of electrostatic type instruments is electrostatic effect.

#### What is meant by electrostatic induction??

To understand clearly about electrostatic effect see the below circuit.

1.Here the two plates are being charged by a high voltage battery.

2. Due to this one of the plate gets positive charge and the other plate gets negative charge.

3. Here the deflecting torque is produced by this static electrical field due to attraction present between these opposite charges.

4. The plates move because of the electrostatic force(attraction between plates) that has been produced because of this induced charges.

This effect is called electrostatic effect.

### Construction of electrostatic type instruments:

1. Linear type electrostatic instruments.

2. Rotatory type electrostatic instruments.

### Linear type electrostatic instruments:

1. Here one of the plates is fixed and the other plate is movable and these plates are charged as shown in the above circuit. So one of the plate gets positive charge and the other plates gets negative charge. Due to this there will be force of attraction between the plates so the movable plate moves towards the fixed plate until movable plate gains maximum amount of electrostatic energy. Fixing pointer to the movable plate we can measure the voltage. These are called linear type electrostatic instruments.

### Rotatory type electrostatic instruments:

2. Here we have a rotatory plate. Due this movement of rotatory plate there may be force of attraction or repulsion between the plates. These are called rotatory type electrostatic instruments.

### Torque equation of electrostatic type instruments:

Now let us see torque equation of both linear type electrostatic instruments and rotatory type electrostatic instruments.

### Torque equation of linear type electrostatic instruments:

Let us see in detail about torque equation of liner type electrostatic instruments.

Observe the following diagram.

1.Here plate A is fixed and it is positively charged and plate B is movable and it is negatively charged.

2. As the forces are opposite we have attraction between plates. So there will be linear motion between these plates.

3. As there is force between these plates at equilibrium electrostatic force will be equal to spring force.

4.Now electrostatic energy stored in the plate is given by,

5.Now let us increase the voltage by a small amount let it be dv due to this there will be displacement of plate let the displacement be dx. So work done against the spring force due to displacement of  plate B be F.dx.  Relation between current and applied voltage is given by,

6. Now the input energy from this value of electric current is given by,

7. Now the change in this stored energy is given by,

8. Now apply principle of energy conservation by neglecting the higher order terms in the expression.

Input energy to the system = increase in the stored energy of the system + mechanical work done by the system.

By substituting all the values we get,

Now the equation of force from the above equation is given by,

### Torque equation of rotatory type electrostatic instruments:

Let us see in detail about torque equation of rotatory type electrostatic instruments.

Observe the following diagram.

1. By replacing F, dx in equation (1)  by Td , dA respectively we get deflecting torque of rotary type electrostatic instruments.

2. So the deflecting torque is given by,

3.At steady state we have controlling torque is given by, Tc = K × A. Where A is the deflection and it is given by,

As the deflection is directly proportional to square of voltage we have non- uniform scale.

Hence we have derived  torque equation of  electrostatic type instruments i.e for liner type electrostatic instruments and  rotatory type electrostatic instruments.

Generally electrostatic type instruments are used for measuring high voltages.

The main advantage of using electrostatic type instruments as voltmeters is we can extend the range of voltage that is to be measured.

### Methods to extend the range of voltage to be measured for electrostatic instruments:

1. Resistance potential dividers.

2.Capacitor multiplier technique.

### Resistance potential dividers to extend the range of voltage to be measured for electrostatic instruments:

Now let us see how to extend the range of voltage to be measured by using resistance potential dividers.

To understand it see the below circuit.

### Circuit diagram of resistance potential dividers to extend the range of voltage to be measured for electrostatic instruments:

The following diagram shows the circuit to extend the range of voltage to be measured by
electrostatic instruments using resistance potential dividers.

### Procedure to extend the range of voltage to be measured by electrostatic instruments using resistance potential dividers:

1. Across r which is total resistance apply the voltage which is to be measured.

2. Across R which is a part of total resistance r connect an electrostatic capacitor.

3.Make one assumption that the capacitor which is connected is having infinite leakage resistance in case if we apply dc voltage. Here the multiplying factor is ratio of resistances i.e, r/R. Multiplying factor in ac case is same as dc case.

### Capacitor multiplier technique to extend the range of voltage to be measured for electrostatic instruments:

Now let us see how to extend the range of voltage to be measured by electrostatic instruments
using capacitor multiplier technique.

To understand it see the below circuit.

### Circuit diagram of capacitor multiplier technique to extend the range of voltage to be measured for electrostatic instruments:

The following diagram shows the circuit to extend the range of voltage to be measured by electrostatic instruments using capacitor multiplier technique.

### Procedure to extend the range of voltage to be measured by electrostatic instruments  using capacitor multiplier technique:

Let us calculate the multiplying factor.

1. From diagram we have series combination of capacitors. The equivalent capacitance is given by

2. Voltmeter impedance is given by Z1 = 1/jÏ‰C1 . Now total impedance is given by,

3.Multiplying factor is given by,

Z/Z1 = 1 + C2 / C1.

In this way we can extend the range of voltage to be measured by electrostatic instruments with the help of  resistance potential dividers and capacitor multiplier technique.

### Advantages of electrostatic type instruments:

1. As the deflection torque is directly proportional to square of voltage we can measure both a.c and d.c voltages by using electrostatic type instruments.

2.High values of voltage can be measured  using electrostatic type instruments.

3. Current drawn by electrostatic type instruments  is low so power consumption of electrostatic type instruments is low.

### Disadvantages of electrostatic type instruments:

1.Electrostatic type instruments have non uniform scale.

2.Electrostatic type instruments are larger in size.

3.Electrostatic type instruments are costlier compared to other type of instruments.

4.Various operating forces present in electrostatic type instruments are small in magnitude.

Today we have learnt working principle, construction , torque equation and extending range of electrostatic type instruments.

## Differences Between Instrument and Power Transformers

In this article differences between power transformer and instrument transformer are discussed.Current transformer and Potential transformers come under instrument transformers.

### Differences Between Instrument and Power Transformers

Power Transformers Instrument Transformers
1. Mainly used to change voltage levels in
a power system.
1. Mainly used to extend the ranges of the
instruments while measuring parameters like
voltage,current,power etc.
2. They are required to transform huge amount
2. They are required to transform very small power
as their loads are generally delicate moving elements
of the instruments.
3. They can be used to step up or step down the
voltage.
3. They are basically step down transformers and
used along with devices such as protective
relays,indicators etc.
4. The exciting current is a small fraction of the
4. As the load it self is small, the exciting current is
of the order of the secondary winding.
5. The cost is main consideration in the design
while efficiency and regulations are secondary
considerations.
5. Accuracy is the main consideration while designing
to keep ratio and phase angle errors minimum.
Cost is the second consideration.
6. As they handle large power, the heat
dissipation is the major consideration and
cooling method is necessary.
6. The power output is very small as loads are light.
Hence heating is not severe.
7. The limitation on the load is due to temperature
issue.
7. Accuracy is the main load limitation factor and not
the temperature rise.
8. Example : Distribution transformer used in
transmission.
8. Example : Current transformer and Potential
transformer

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## Differences Between Moving Coil (MC) And Moving Iron (MI) Instruments

Let us have a comparison between two major type of electrical measuring instruments they are moving coil (MC) and moving iron (MI) instruments.In this article all major differences between moving iron and  moving coil   instruments are discussed.When you go viva or interview most often question on electrical measurements is what is the difference between mi and mc type instruments?.In this article you will get answer to all differences between MI & MC typ instruments.

### Differences Between Moving Coil (MC) And Moving Iron (MI) Instruments

M.C Instruments M.I Instruments
1. MC type instruments are more accurate. 1. MI type are less accurate than MC type.
2. Manufacturing cost is high. 2. Cheap in cost.
3. Reading scale is uniformly distributed. 3. Non-uniform scale
(scale cramped at beginning and finishing)
4. Very sensitive in construction & for input. 4. Robust in construction.
5. Low power consumption 5. Slightly high power consumption.
6. Eddy current damping is used. 6. Air friction damping is used.
7. Can be used only for D.C measurements. 7. Can be used for A.C as well as for D.C
measurements.
8. Controlling torqure is provided by spring. 8. Controlling torque is provided by
gravity or spring
9. Deflection proportional to current.( Î¸ Î± I ). 9. Deflection proportional to square of current.
( Î¸ Î± I² ).
10. Errors are set due to aging of control
springs,permanent magnet (i.e. No Hysteresis loss)
10. Errors are set due to hysteresis and stray fields.
(i.e. hysteresis loss takes place).

In this comparison between MC and MI Instruments we shared top points.

Tags:
difference between moving coil and moving iron instruments
difference between moving coil and moving iron instruments pdf

## Torque Equation Of Moving Iron Instruments

In previous tutorial on Moving Iron Instrument Operation construction & working principle was discussed. In this post moving iron instrument torque equation will be derived.

### Torque Equation of Moving Iron Instruments

Consider a small increment in current supplied to the coil of the instrument. due to this current let dÎ¸ be the deflection under the deflecting torque Td. Due to such deflection, some mechanical work will be done.
Mechanical Work = Td .dÎ¸

There will be a change in the energy stored i the magnetic field due to the change in inductance. This is because the vane tries to occupy the position of minimum reluctance. The inductance is inversely proportional to the reluctance of  the magnetic circuit of coil.

Let   I = initial current
L = instrument inductance
Î¸ = deflection
dI = increase in current
dÎ¸ = change in deflection
dL = change in inductance

In order to effect an increment dL in the current, there must be an increase in the applied voltage given by,

e = d(L*I)/dt
= I * dL/dt + T * dI/dt     as both I and L are changing.

The electrical energy supplied is given by

eIdt = { I * dL/dt + T * dI/dt }Idt
=I²dL + ILdI
The stored energy increases from 1/2*(LI²) to 1/2*[(L+dL)(I+dI)²]
Hence the change in stored energy is given by,
1/2*[(L+dL)(I+dI)²] - 1/2*(LI²)
Neglecting higher order terms,this becomes ILdI +  1/2 * I² dL
The energy supplied in nothing but increase in stored energy plus the energy required for mechanical work done.

I²dL + ILdI = ILdI + 1/2*(I²)dL +Td.dÎ¸
Td.dÎ¸ =  1/2( I².dL )

Td = 1/2  I²dL/dÎ¸

While the controlling torque is given by,
Tc = KÎ¸
where K = spring constant
KÎ¸ = 1/2  I²dL/dÎ¸
Î¸ = 1/2  I²dL/dÎ¸ * 1/K      under equilibrium

Thus the deflection is proportional to the square of the current through the coil. And the instrument gives square law response.

## Moving Iron Instrument Working Operation

### Moving Iron Instruments or MI Instruments

In our previous article we have discussed PMMC Instrument Working Opeartion. In this tutorial on Moving Iron Instrument Working Operation we go through the construction & basic principle of MI type instrument.

The moving iron instruments are classified as:
i) Moving iron attraction type instruments
ii) Moving iron repulsion type instruments

### Moving Iron Attraction Type Instrument Working Operation

Moving Iron Instrument Working Principle : The basic working principle of these instruments is very simple that a soft iron piece if brought near magnet gets attracted by the magnet.

The construction of the attraction type moving iron instrument is shown in the below figure.

lt consists of a fixed coil C and moving iron piece D. The oil is flat and has narrow slot like opening. The moving iron is a flat disc which is eccentrically mounted on the spindle. The spindle is supported between the jewel bearings. The spindle carries a pointer which moves over a graduated scale.The number of turns of the fixed coil are dependent on the range of the instrument. For passing large current through the coil only few turns are required.

The controlling torque is provided by the springs but gravity control may also be used for vertically mounted panel type instruments.

The damping torque is provided by the air friction. A light aluminium piston is attached to the moving system. it moves in a fixed chamber. The chamber is closed at one end. it can also be provided with the help of vane attached to the moving system.

The operating magnetic field in moving iron instruments is very weak. Hence eddy current damping is not used since it requires a permanent magnet which would affect or distort the operating field.This is the reason Why why eddy current damping is not used in moving iron instrument.

### Moving Iron Repulsion Type Instrument

Moving iron repulsion Type instruments have two vanes inside the coil. the one is fixed and other is movable. When the current flows in the coil, both the vans are magnetized with like polarities induced on the same side. Hence due to the repulsion of like polarities, there is a force of repulsion between the two vanes causing the movement of the moving vane. The repulsion type instruments are the most commonly used instruments.

The two different designs of repulsion type instruments are:
ii) Co-axial vane type

#### Radial Vane Emulsion Typo Instrument

Below shows the radial vane repulsion type instrument. Out of the other moving iron mechanisms, this is the moat sensitive and has most linear scale.

The two vanes are radial strips of iron. The fixed vane is attached to the coil. The movable vane is attached to the spindle and suspended in the induction field of the coil. The needle of the instrument is attached to this vane.

Even-though the current through the coil is alternating, there is always repulsion between the like poles of the fixed and the movable vane. Hence the deflection of the pointer is always in the same direction. The deflection is effectively proportional to the actual current and hence the scale is calibrated directly to read amperes or volts. The The calibration is accurate only for the frequency for which it is designed because the impedance is different for different frequencies.

#### Concentric Vane Repulsion Type Instrument

Figure shows the concentric vane repulsion type instrument. The instrument has two concentric vanes. One is attached to the coil frame rigidly while the other can rotate co-axially inside the stationary vane.

Both the vanes are magnetized to the same polarity due to the current in the coil. Thus the movable vane rotates under the repulsive force. As the movable vane is attached to the pivoted shaft, the repulsion results in a rotation of the shaft. The pointer deflection is proportional to the current in the coil. The concentric vane type instrument is moderately sensitive and the deflection is proportional to the square of the current through coil. Thus the instrument said to have square low response. Thus the scale of the instrument is non-uniform in nature. Thus whatever may be the direction of the current in the coil, the deflection in the moving iron instruments is in the same direction. Hence moving iron instruments can be used for both a.c. and d.c. measurements. Due to square low response, the scale of the moving iron instrument is non-uniform.

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## Permanent Magnet Moving Coil Type (PMMC) Instrument-Working Principle

### Permanent Magnet Moving Coil Type (PMMC) Instrument Working Principle

The basic principle of operation is that when a current carrying conductor is brought in a magnetic field (they should not be parallel to each other) a torque on the conductor is produced. The Permanent Magnet Moving Coil instrument consists of a rectangular coil pivoted so that its sides lie in the air gap between the two poles of a permanent magnet and a soft-iron cylinder. The air gap between the magnet poles and iron core is small and the flux density is uniform and is in a radial direction, so that the flux lines are always at right angle to the current carrying conductor and hence when current passes through the coil, a deflecting torque is produced owing to the interaction between the two fluxes, one due to permanent magnet and the other due to the magnetic field of the coil. This is shown in Fig.1.

### constructions of permanent magnet moving coil instruments

 Fig.1.
If I is the current flowing in the moving coil in the direction shown, forces F, F will act on the two sides of this coil, the direction of force being determined by Fleming's left-hand rule and is in the direction for this system as shown in Fig.1. The torque causing the coil to rotate is given as F.2r where r is the mean distance of the wires forming the sides of the coil, from the axis of rotation.Now, if N is the no. of turns in the coil, B the magnetic flux density due to permanent magnet, I the current in the coil, l the effective length, the force acting on the coil is given by

F = NBil Newton .. . (4.1)
Hence the torque on the coil is
T = NBil. 2r N-m ... (4.2)

### Control torque & Damping torque in  PMMC Instrument

In any measuring (electromagnetic) instrument there are three torques acting on the moving mechanism to which a pointer is connected which moves on the dial of the instrument and indicates the reading of the quantity being measured. One of the three torques is the deflecting torque which we have just studied. The other torques are (i) control torque (ii) Damping torque. In case of PMMC instruments spring made of phosphor bronze provides control torque. The spring also serves as leads to the moving coil. When deflecting torque acts on the coil, both the control torque and damping torques come into action. The control torque restrains the rotation of the coil whereas the deflecting torque tries to rotate the coil. At balance, if the coil has moved through an angle  Î¸ and if k is the spring constant, we have

as NEZ.2r are constant of a particular meter. Hence equation (4.5) suggests that the current is proportional to Î¸. Thus the scale is uniformly divided i.e. it is a linear scale i.e. if for I amp the deflection is through an angle Î¸, for 2I amps the deflection would be 2Î¸.Now if damping torque were absent, the pointer will keep on oscillating around the mean value and an exact reading cannot be recorded. These oscillations are damped out by the damping torque. The moving coil is wound on an aluminium former which is placed in the magnetic field.As the coil rotates eddy currents are induced in the aluminium former and these eddy currents would try to oppose the cause i.e. the deflecting force and finally when the pointer comes to its actual value being measured, damping is provided by eddy currents and the coil (the pointer) remains stationary at its actual value.

### Torque Equation of PMMC Instrument

The equation for the developed torque can be obtained from the basic low of the electromagnetic torque. The deflecting torque is given by,

Td   = NBAI
where  Td  = deflecting torque in N-m
B = flux density in air gap, Wb/m2
N = number of turns of the coil
A = Effective coil area m2
I = Current in the moving coil, amperes
Td  = GI
where G = NBA = constant
The controlling torque is provided by the springs and is proportional to the angular deflection of the pointer.
Tc  = kÎ¸
where  Tc  = controlling torque
K = spring constant, Nm/rad or Nm/deg
Î¸ = angular deflection
for the final steady state position,
Td   = Tc
GI = KÎ¸
Î¸ = (G/K) I
I = (K/G)Î¸

Note: Thus the deflection is directly proportional to the current passing through the coil in Permanent Magnet Moving Coil Type (PMMC) Instrument.

### Advantages of Permanent Magnet Moving Coil Type  or PMMC instruments

(a) Low power consumption
(b) High Torque/weight-ratio
(c) Uniformity of the scale and the possibility of a very long scale
(d) Perfect damping provided by eddy currents induced in the metal former of the moving coil. The metal used is aluminium as it is light in weight
(e) The possibility of a single instrument being used with shunt and resistance to cover a large range of both currents and voltages.
(f) Freedom from errors due to stray magnetic fields.

Tags:PMMC Torque Equation,PMMC instrument wikipedia,permanent magnet moving coil (PMMC),permanent magnet moving coil  (PMMC) mechanism,Working operation