What is Electrodynamometer Wattmeter?
The Electrodynamometer Wattmeter is a type of electrical measuring instrument that is used to measure the power of both AC and DC circuits. It works on the principle that a current-carrying conductor placed in a magnetic field experiences a mechanical force. The magnitude of this force is proportional to the product of the current and the magnetic field strength.
The instrument consists of two coils, one fixed and one moving. The fixed coil is connected in series with the load and the current to be measured passes through it. The moving coil is positioned in close proximity to the fixed coil and is mounted on a pivot. The current to be measured also flows through the moving coil.
When current flows through the fixed coil, it creates a magnetic field which in turn induces a current in the moving coil. This induced current creates its own magnetic field which interacts with the magnetic field of the fixed coil. The interaction between these two fields creates a mechanical force on the moving coil which deflects the pointer.
The deflection of the pointer is proportional to the product of the current and the magnetic field strength. This product is also known as the power and is measured in watts. The instrument is calibrated such that the pointer deflects to a certain position on the scale for a known value of power.
Why PMMC Instruments cannot be used for a.c. measurements?
PMMC (Permanent Magnet Moving Coil) instruments are designed to measure direct current (DC) or constant currents. They rely on the interaction between a permanent magnet and a moving coil to measure the current flowing through the circuit. The permanent magnet creates a constant magnetic field in the air gap, and the moving coil, which is connected to a pointer, is positioned in this field. The current flowing through the coil creates a magnetic field that interacts with the magnetic field of the permanent magnet, causing the coil and pointer to move, indicating the current flowing through the circuit.
However, when an alternating current (AC) is applied to a PMMC instrument, the current flowing through the circuit is constantly changing direction. This causes the magnetic field in the coil to change direction as well, creating an alternating torque on the moving coil and pointer. Due to the moment of inertia of the moving system, the pointer is unable to follow the rapidly changing alternating torque and fails to show any reading.
On the other hand, Electrodynamometer type instruments, instead of using a permanent magnet, use the current under measurement to produce the necessary field flux. The current flowing through the circuit is used to create a magnetic field in the air gap, which is proportional to the current. As the current changes direction, the magnetic field in the air gap also changes direction, keeping the torque on the moving coil and pointer constant, allowing the pointer to follow the rapidly changing alternating torque, making it possible to measure alternating current.
Construction of electrodynamometer Wattmeter:
The Electrodynamometer Wattmeter is a type of power measuring instrument that is used to measure both AC and DC power in electrical circuits. The instrument works by utilizing the reaction between the magnetic field of moving and fixed coils.
- Fixed Coil: The fixed coil is connected in series with the load and is considered as the current coil because the load current flows through it. For ease of construction, the fixed coil is divided into two parts which are parallel connected to each other. The fixed coil produces a uniform electric field which is essential for the working of the instrument. The current coil of the instrument is designed to carry a current of approximately 20 amperes to save power.
- Moving Coil: The moving coil is considered as the pressure coil of the instrument. It connects in parallel with the supply voltage and the current flowing through it is directly proportional to the supply voltage. The pointer is mounted on the moving coil and the movement of the pointer is controlled by a spring. The current flowing through the coil increases its temperature, which is controlled by a resistor connected in series with the moving coil.
- Control: The control system provides the controlling torque to the instrument. The Electrodynamometer wattmeter uses a spring control system for the movement of the pointer. This system is used to provide the necessary torque to move the pointer.
- Damping: Damping is the effect that reduces the movement of the pointer. In this wattmeter, the damping torque is produced by air friction. Other types of damping are not used in the system because they destroy the useful magnetic flux.
- Scales and Pointers: The instrument uses a linear scale because the moving coil moves linearly. The instrument uses a knife-edge pointer to remove the parallax error caused by oversight.
- Shielding: Shielding in an electrodynamometer wattmeter is a technique used to protect the instrument from external magnetic fields that may affect its accuracy. The field produced by this instrument is relatively weak and can easily be disrupted by stray magnetic fields, which can cause errors in the reading. To overcome this problem, the instrument is encased in a high permeability material such as iron or steel. This material has the ability to channel external magnetic fields away from the instrument, thereby reducing the impact of stray fields on the instrument's accuracy. The shielding also helps to maintain a consistent and stable magnetic field within the instrument, which is essential for accurate measurements. In summary, shielding in electrodynamometer wattmeter is a technique to protect the instrument from external magnetic fields and maintain a stable magnetic field within the instrument, resulting in more accurate measurement.
Working of electrodynamometer Wattmeter:
The Electrodynamometer wattmeter is an instrument used to measure the power consumption in an electric circuit. It works based on the principle that a current-carrying conductor placed in a magnetic field experiences a mechanical force. This mechanical force deflects the pointer which is mounted on the calibrated scale.
The instrument has two types of coils: the fixed coil and the moving coil. The fixed coil is connected in series with the circuit whose power consumption is to be measured. The current flowing through the circuit also flows through the fixed coil, creating a magnetic field. The supply voltage is applied to the moving coil, and the current flowing through it also creates a magnetic field.
The moving coil is connected in parallel with the supply voltage, and the current flowing through it is directly proportional to the supply voltage. The pointer is mounted on the moving coil and is placed between the fixed coils. The interaction of the magnetic field created by the fixed coil and the magnetic field created by the moving coil deflects the pointer.
The deflection of the pointer is directly proportional to the power flowing through the circuit. The current flowing through the moving coil is controlled by a resistor that is connected in series with it. This helps to maintain the stability of the instrument.
The instrument also uses a spring control system for the movement of the pointer, and air friction is used to provide damping, which helps to reduce the movement of the pointer. The Electrodynamometer wattmeter uses a linear scale and a knife-edge pointer to remove parallax errors caused by oversight.
Expression for Torque:
In an electrodynamometer instrument, there are two coils: a fixed coil and a moving coil.
The current flowing through the fixed coil is represented as = i1,
The current flowing through the moving coil is represented as = i2.
The self-inductance of the fixed coil is represented as = L1,
The self inductance of the moving coil is represented as = L2
There is a mutual inductance between the fixed and moving coils, represented as = M.
When the electrodynamometer instrument is in operation, it can be represented by an equivalent circuit, as shown in the figure. This circuit shows how the current flowing through the fixed and moving coils, along with the self and mutual inductances, affect the overall operation of the instrument.
The principle of conservation of energy states that energy cannot be created or destroyed, but only transferred or converted from one form to another. In the case of an electrodynamometer wattmeter, energy is input into the device in the form of electrical power, and some of that energy is stored in the device's coils. The remaining energy is converted into mechanical energy, which is used to move the pointer on the instrument's display.
This relationship can be represented by the following formula:
Energy input = Energy stored + Mechanical energy
Mechanical energy = Energy input - Energy stored
The energy that is used to move the pointer of an electrodynamometer instrument is equal to the product of the current in the fixed coil (i1), the current in the moving coil (i2), and the mutual inductance (M) between the two coils, multiplied by the change in the deflection of the pointer (dθ). This can be represented by the formula:
Mechanical energy = Mechanical work done
i1 x i2 x dM = Ti dθ
Mechanical energy = i1 x i2 x dM
Ti = i1 x i2 x dM/ dθ
Where L1 and L2 are constant, so dL1 and dL2 are zero and Ti is the instantaneous deflecting torque.
This is the expression for the instantaneous deflection torque.
D.C. operation : For d.c current of I1 and I2,
The controlling torque is provided by springs
When the electrodynamometer instrument is used to measure alternating current (a.c.), the deflection of the pointer is not constant but changes over time. To get the overall measurement, we need to integrate the instantaneous deflection torque (Ti) over one complete period of the a.c. current.
For AC:
The Average deflecting torque over one cycle is,
Now if two currents are sinusoidal and displaced by a phase angle then
where i1, i2 are the r.m.s. values of the two currents as,
An electrodynamometer instrument is a type of moving coil instrument that is used to measure both direct current (d.c.) and alternating current (a.c.) quantities. The deflection of the pointer in the instrument is determined by the product of the root mean square (r.m.s.) values of two currents, the cosine of the phase angle (power factor), and the rate of change of mutual inductance.
For d.c. use, the deflection of the pointer is proportional to the square of the current, resulting in a non-uniform and crowded scale at the ends. However, for a.c. use, the instantaneous torque is proportional to the square of the instantaneous current. As the current varies, the deflecting torque also varies, but due to the inertia of the moving system, the meter cannot follow rapid variations, and thus the final reading is the average torque. This means that the deflection is a function of the mean of the squared current, and the scale is calibrated in terms of the square root of the average current squared, which is the r.m.s value of the a.c. quantity being measured.
If the electrodynamometer instrument is calibrated with a d.c. current of 1 A, and the pointer indicates 1 A d.c. on the scale, then on a.c., the pointer will deflect up to the same mark, but 1 A in this case will indicate the r.m.s value. Because of this direct connection between a.c. and d.c., the instrument is often used as a calibration instrument.
In terms of sensitivity, the instrument can be used as an ammeter to measure currents up to 20 A, while using it as a voltmeter it can have low sensitivity of about 10 to 30 Ω/v, which means that it can measure voltages across low resistance ranges.
Controlling torque in electrodynamometer Wattmeter:
In an Electrodynamometer wattmeter, the controlling torque is provided by two control springs. These control springs are connected to the moving coil and provide the necessary force to move the pointer on the calibrated scale. The control springs act as a lead to the moving coil and provide the necessary force to balance the torque produced by the interaction of the magnetic fields of the fixed and moving coils. The controlling torque helps to keep the pointer in a stable position, and any change in the power consumption is indicated by a deflection of the pointer. The controlling torque is necessary for the accurate measurement of power consumption and can be adjusted by adjusting the tension of the control springs. The controlling torque ensures that the pointer is not affected by any external forces and the measurement is accurate and stable.
Damping in Electrodynamometer wattmeter:
Damping in an Electrodynamometer wattmeter is a mechanism that helps to reduce the movement of the pointer and stabilize the reading on the scale. The purpose of damping is to prevent the pointer from oscillating or overshooting the actual reading after the current or voltage in the circuit changes.
One method of providing damping in an Electrodynamometer wattmeter is through air friction. This is achieved by attaching aluminum vanes to the spindle at the bottom of the instrument. These vanes are positioned in such a way that they are exposed to the air as the spindle rotates. The movement of the pointer creates a drag force due to the interaction of the vanes with the surrounding air. This drag force acts as a damping torque and helps to slow down the movement of the pointer, allowing it to settle at the correct reading more quickly.
It is worth noting that other types of damping methods such as mechanical damping (using a dashpot) or electrical damping (using a damper winding) may also be used but these methods may not be suitable for Electrodynamometer wattmeter due to the fact that they may destroy the useful magnetic flux. Air friction damping is the most common method of damping used in Electrodynamometer wattmeter.
Deflecting Torque in electrodynamometer wattmeter:
The deflecting torque in an Electrodynamometer wattmeter is produced by the interaction of the magnetic fields generated by the fixed and the moving coils. The fixed coil is connected in series with the circuit whose power consumption is to be measured and the moving coil is connected in parallel with the supply voltage.
The current passing through the fixed coil (I1) generates a magnetic field, and the current passing through the moving coil (I2) also generates a magnetic field. The flux density (B) of the magnetic field generated by the fixed coil is proportional to the current passing through it (I1). Mathematically, B = K*I1 where K is a constant.
The force experienced by each side of the moving coil is given by NBI2*l, where N is the number of turns in the moving coil, B is the magnetic flux density, I2 is the current passing through the moving coil and l is the length of the moving coil.
The torque produced on the whole of the moving coil is given by NBI2lb, where b is the breadth of the moving coil. This can be written as Td = NKI1I2A, where A is the area of the moving coil.
This shows that the deflecting torque (Td) is proportional to the product of the currents passing through the fixed and moving coils (I1*I2).
The instrument is spring controlled, and the restoring or controlling torque is proportional to the angular deflection (θ). Mathematically, Tc = K2*θ where K2 is another constant.
As the deflecting torque is equal to the controlling torque, the angular deflection produced in the instrument is proportional to the product of the currents passing through the fixed and moving coils (θ ∝ I1*I2). This means that the deflection of the pointer on the instrument is directly proportional to the power flowing through the circuit being measured.
Errors in Electrodynamometer Wattmeter:
- Pressure Coil Inductance: The pressure coil in an Electrodynamometer wattmeter has some inductance, which means that it has a tendency to resist any changes in the current flowing through it. This inductance can cause the current in the pressure coil to lag behind the voltage, which means that the power factor of the wattmeter becomes lagging. This results in the meter reading a higher value than the actual power consumption.
- Pressure Coil Capacitance: Along with inductance, the pressure coil also has capacitance. Capacitance is the ability of a component to store electrical energy in an electric field. The capacitance of the pressure coil can increase the power factor of the instrument, which can lead to errors in the reading.
- Error due to Mutual Inductance Effect: The mutual inductance between the pressure and current coils can also produce errors in the reading. Mutual inductance is the phenomenon where the changing current in one coil induces a voltage in another coil. This can affect the accuracy of the reading.
- Eddy Current Error: Eddy currents are circulating currents that are induced in a conductor when it is exposed to a changing magnetic field. These currents can create their own magnetic field which can affect the main current flowing through the coil. This can cause errors in the reading.
- Stray Magnetic Field: Any external magnetic field that is present in the vicinity of the wattmeter can disturb the main magnetic field of the instrument. This can affect the accuracy of the reading.
- Temperature Error: Variations in temperature can change the resistance of the pressure coil. This can also affect the movement of the spring, which provides the controlling torque, leading to errors in the reading. As the temperature increases, the resistance of the pressure coil increases, and the movement of the spring decreases, leading to a decrease in the reading. Conversely, as the temperature decreases, the resistance of the pressure coil decreases, and the movement of the spring increases, leading to an increase in the reading.
- Torque to weight ratio: The torque to weight ratio is an important factor in the design of an electrodynamometer wattmeter. The torque is the force that causes the moving coil to rotate and is proportional to the product of the current flowing in the fixed and moving coils. The weight of the moving coil, on the other hand, is a function of the number of turns in the coil. To have a reasonable deflecting torque, the mmf (magnetomotive force) of the moving coil must be large enough. The mmf is equal to the product of the number of turns in the coil and the current flowing through it. To increase the mmf, the current flowing through the moving coil should be high or the number of turns should be large. However, the current cannot be made very high as it may cause excessive heating of the springs, so the only option is to have a large number of turns. This increases the weight of the coil, reducing the torque to weight ratio and causing frictional errors in the reading.
- Frequency errors: Another error that can occur in an electrodynamometer wattmeter is the frequency error. The frequency of the current passing through the fixed and moving coils can affect the self-inductance of the coils, which in turn can cause errors in the reading. The frequency error can be reduced by having equal time constants for both fixed and moving coil circuits. This means that the time constant of the fixed coil circuit should be equal to that of the moving coil circuit. This helps to ensure that the self-inductance of the coils is not affected by changes in frequency and that accurate readings are obtained.
Advantages of Electrodynamometer Wattmeter:
- They are free from hysteresis and eddy current losses.
- They can be used on both AC and DC.
- They are used as transfer instruments.
- They have a precision grade accuracy.
- They are useful for measuring accurate r.m.s values of voltage, regardless of the waveform.
- They have low power consumption.
- They are lightweight.
Disadvantages of Electrodynamometer Wattmeter:
- They have a low sensitivity due to a low torque to weight ratio.
- They are more expensive than other types of instruments.
- They are sensitive to overload and mechanical impacts.
- They have a nonuniform scale.
- They have a weak magnetic field, resulting in a large operating current.
- They are sensitive to errors caused by pressure coil inductance, capacitance, and mutual inductance.
- They are affected by temperature changes, which can cause errors in the readings.