Objectives
Introduction
An instrument that is used to measure either quantity of electricity or energy, over a period of time is known as energy meter or watt-hour meter. In other words, energy is the total power delivered or consumed over an interval of time t may be expressed as:
If v(t) is expressed in volts, i(t) in amperes and t in seconds, the unit of energy is joule or watt second. The commercial unit of electrical energy is kilowatt hour (KWh). For measurement of energy in a.c. circuit, the meter used is based on “electro-magnetic induction” principle. They are known as induction type instruments. The measurement of energy is based on the induction principle is particularly suitable for industrial or domestic meters on the account of lightness and robustness of the rotating element. Moreover, because of smallness of the variations of voltage and frequency in supply voltage, the accuracy of the induction meter is unaffected by such variations. If the waveform of the supply is badly distorted, the accuracy, however, is affected. Basically, the induction energy meter may be derived from the induction watt-meter by substituting for the spring control and pointer an eddy current brake and a counting train, respectively. For the meter to read correctly, the speed of the moving system must be proportional to the power in the circuit in which the meter is connected.
Construction of induction type energy meter
Induction type energy meter essentially consists of following components (a) Driving system (b) Moving system (c) Braking system and (d) Registering system.
Basic operation
Induction instruments operate in alternating-current circuits and they are useful only when the frequency and the supply voltage are approximately constant. The most commonly used technique is the shaded pole induction watt-hour meter, shown in fig.44.1 (b).
The rotating element is an aluminium disc, and the torque is produced by the interaction of eddy currents generated in the disc with the imposed magnetic fields that are produced by the voltage and current coils of the energy meter.
Let us consider a sinusoidal flux φ (t) is acting perpendicularly to the plane of the aluminium disc, the direction of eddy current ie by Lenz’s law is indicated in figure Fig.44.2. It is now quite important to investigate whether any torque will develope in aluminium disc by interaction of a sinusoidally varying flux φ (t) and the eddy currents induced by itself.
where φ and Ie are expressed in r.m.s and β ≈0 (because the reactance of the aluminium disc is nearly equal to zero). Therefore, the interaction of a sinusoidally varying flux φ (t) and its own eddy current ie (induced) cannot produce torque any on the disc.
So in all induction instruments we have two fluxes produce by currents flowing in the windings of the instrument. These fluxes are alternating in nature and so they induce emfs in a aluminium disc or a drum provided for the purpose. These emfs in turn circulate eddy currents in the disc.
As in an energy meter instrument, we have two fluxes and two eddy currents and therefore two torques are produced by
i) first flux(φ1 ) interacting with the eddy currents ( Ie2 ) generated by the second flux (φ2) , and
ii) second flux (φ2) interacting with the eddy currents ( Ie1 ) induced by the first flux (φ1).
In the induction type single phase energy meter, the flux produced by shunt magnet (pressure or voltage coil current) Φsh lags behind the applied voltage V by almost 90°. The flux φse is produced by the load current I and se Φ is in the direction of I (see Fig.44.3).
Let the supply voltage v(t) = Vmax sin (ω t ) and load current i(t) = Imax sin (ω t−θ ) . So, the fluxes are :
(i) Flux generated by current coil
Φse= kImax sin (ω t −θ ) = Φmax (se) sin (ω t −θ )
(ii) Flux generated by voltage coil
(note: and k and k′ are constants.)
The eddy e.m.f , induced by fluxΦse is
Eddy current generated in disc by the current coil
where Z is the eddy current path impedance and α is the phase angle. In general, the angle is negligible because X ≈0 .
Also, note that
Eddy current generated in disc by the voltage coil
The instantaneous torque on the disc is then proportional to
where Φ sh is the flux generated by the voltage coil, Φ se is flux generated by the current coil, ish is the eddy current produced in the disc by the voltage coil, and ise is the eddy current produced in the disc by the current coil. The relative phases of these quantities are shown in fig.44.3.
The flux generated by the current coil is in phase with the current and flux generated by the voltage coil is adjusted to be exactly in quadrature with the applied voltage by means of the copper shading ring on the voltage or shunt magnet. Theory of shaded pole is discussed in Appendix. The average torque acting upon the disc
∞ VI cosθ = power in the circuit
One can write average torque expression directly from the phasor diagram shown in fig.44.3
∞ VI cosθ = power in the circuit
where and I are all expressed as r.m.s.
Remarks : (i) The torque expression shows that for a large torque the eddy current path resistance must be low which in turn the value of cosα will be nearly equal to 1. Consideration of the torque-weight ratio shows that the choice of aluminium disc will be superior to copper and further it can be improved by properly selecting aluminium disc thickness. (ii) Note, that the torque expression does not involve ω t and it has same value at all instants of time. (iii) The resultant torque will act on the disc in such away so that it will move from the pole with the leading flux towards the pole with lagging flux.
Opposing or Brake Torque:
Now the breaking torque is produced by the eddy currents induced in the disc by its rotation in a magnetic field of constant intensity, the constant field being provided by the permanent magnet (called brake magnet, see fig. 44.1(a) & (b)). The eddy current ib produced in the aluminium–disc by the brake magnet flux φb is proportional to the speed ( N ) of rotation of the disc N , as shown in fig.44.4.
Thus braking torque
where r = eddy current path resistance
Since Φb is constant, this implies that Tb ∞ N
where N = speed of rotation of disc.
Now when the speed becomes steady, driving and braking torques become Td =Tb (see fig.44.4).
Therefore, VI cosθ ∞ N i.e. speed of the disc is proportional to the power consumed by the load. The total number of revolution i.e. ∫ Ndt =∫ V I cosθ dt ∞ Energy consumed. This means that the speed of rotation of the disc is proportional to the average power. The integral of the number of revolutions of the disc is proportional to the total energy supplied. The disc is connected via a gearing mechanism to a mechanical counter that can be read directly in watt-hours.
Remarks: (i) For a given disc and brake magnet, the braking torque varies with the distance of the poles from the center of the disc. The maximum braking torque occurs when the distance of the center of the pole faces from the center of the disc is equal to 83% of the radius of the disc. (ii) a movement of the poles of brake magnet towards the center of the disc reducing the braking torque (as the distance of brake magnet reduces from the center of the disc), and vise versa.
Errors in the energy meter:
Assuming the supply voltage and frequency constant, the induction type energy may have the following errors:
i. Speed error: Due to the incorrect position of the brake magnet, the braking torque is not correctly developed. This can be tested when meter runs at its full load current alternatively on loads of unity power factor and a low lagging power factor. The speed can be adjusted to the correct value by varying the position of the braking magnet towards the centre of the disc or away from the centre and the shielding loop. If the meter runs fast on inductive load and correctly on non-inductive load, the shielding loop must be moved towards the disc. On the other hand, if the meter runs slow on non-inductive load, the brake magnet must be moved towards the center of the disc.
ii. Meter phase error: An error due to incorrect adjustment of the position of shading band results an incorrect phase displacement between the magnetic flux and the supply voltage (not in quadrature). This is tested with 0.5 p.f. load at the rated load condition. By adjusting the position of the copper shading band in the central limb of the shunt magnet this error can be eliminated.
iii. Friction error: An additional amount of driving torque is required to compensate this error. The two shading bands on the limbs are adjusted to create this extra torque. This adjustment is done at low load (at about 1/4th of full load at unity p.f.).
iv. Creep: In some meters a slow but continuous rotation is seen when pressure coil is excited but with no load current flowing. This slow revolution records some energy. This is called the creep error. This slow motion may be due to (a) incorrect friction compensation, (b) to stray magnetic field (c) for over voltage across the voltage coil. This can be eliminated by drilling two holes or slots in the disc on opposite side of the spindle. When one of the holes comes under the poles of shunt magnet, the rotation being thus limited to a maximum of . In some cases, a small piece of iron tongue or vane is fitted to the edge of the disc. When the position of the vane is adjacent to the brake magnet, the attractive force between the iron tongue or vane and brake magnet is just sufficient to stop slow motion of the disc with full shunt excitation and under no load condition.
1800
v. Temperature effect: Energy meters are almost inherently free from errors due to temperature variations. Temperature affects both driving and braking torques equally (with the increase in temperature the resistance of the induced-current path in the disc is also increases) and so produces negligible error. A flux level in the brake magnet decreases with increase in temperature and introduces a small error in the meter readings. This error is frequently taken as negligible, but in modern energy meters compensation is adopted in the form of flux divider on the break magnet.
Energy meter constant K is defined as
K =No. of revolutions/ kwh
In commercial meters the speed of the disc is of the order of 1800 revolutions per hour at full load
Extension of Instrument Range:
We have seen earlier M.C. instrument’s range can be extended by properly designed non inductive shunts and multipliers in cases of ammeter and voltmeter respectively. Similarly for MI instruments shunts and multipliers can be designed for extension of range. Sometimes transformers are used in ac systems for the measurement of the basic quantities such as current, voltage and power. The transformers used in connection with the instruments for measurement purpose are referred to as Instrument Transformers. They are classified as Current Transformer (C.T.) used for current measurement and potential Transformer (P.T.) used for voltage measurement. These transformers are used not only for extension of the range of the instrument, but also for isolating the instrument from a high current or voltage line. The advantages of these transformers are
Appendix
Theory of shielded pole shunt magnet:
Fig. 44.5(a) shows that a shielding coil C (single turn) surrounds the pole face of the core of a magnet that is magnetized by the supply voltage V . The flux Φ at the pole face is taken as a reference vector in the phasor diagram as shown in fig. 44.5(b).
No load magnetizing current I0 and ampere turns NI0 for the magnetic circuit are in same phase. The phasor OA = NI0 represents magnetizing ampere turns slightly in advance of the flux Φ owing to core loss in the magnetic circuit. The e.m.fs induced in exciting and shielding coils are represented by OE and OEs respetively and they are lagging by with respect to the flux Φ.The current in shielding coil and also ampere-turns due to this coil are represented by the phasor OIs .Hence, the effective ampere-turns to be provided by the exciting coil are represented by OT which is equal to the phasor sum of ampere-turms . The phasor OP represents balancing ampere-turns due to the shielding coil C . The resultant exciting current is represented by OI . The applied voltage to the exciting coil is then can be found out by adding the induced e.m.f OEp to the resistance and reactance voltage drops of the exciting coil. Now, in the induction energy meter, the applied voltage OV must lead the flux phasor Φ by 900 . An inspection of phasor diagram shows that by adjusting the ampere-turns of the shielding coil one can obtain 900 phase difference between applied voltage OV and flux Φ.The ampere-turns of the shielding coil being effected either by alternation of the resistance of the shielding coil or by altering its axial position.
57 docs|62 tests
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1. What is a single-phase induction type energy meter or watt-hour meter? |
2. How does a single-phase induction type energy meter work? |
3. What are the advantages of using a single-phase induction type energy meter? |
4. Can a single-phase induction type energy meter measure reactive power consumption? |
5. How can I ensure the accuracy of a single-phase induction type energy meter? |
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