1. Power Measurement Chapter 6

2. Outline POWER Power? Power in DC and AC Circuits Power Measurements
Power Instrumentation (Wattmeter)
ENERGY
Energy?
Energy Instrumentation
Energy Meter
Single Phase
Three Phase

4. Power measurements
DC circuits
AC circuits
Three-phase systems
High-frequency power measurements
Energy measurements
Example: Power and energy measurements in motor drives

5. Concept of Electric POWER
Power can be defined as the time rate of energy transfer or energy dissipation in a load.
Power is the rate of using or supplying energy.
The rate at which work is done to maintain an electric current in a circuit is termed ELECTRIC POWER.
Electric power is measured in watts (W).
The SI unit of power is the watt (W), where W = 1 J/s.
The kilowatt is a commonly used unit where
I kilowatt = 1000 watts.

6. Electric POWER Formula
Normally electric power is useful, making a lamp light or a motor turn.
ELECTRIC POWER equals the product of the current I and the potential difference V.

7. If P is positive, the component absorb power.
If P is negative, the component produces power.

8. POWER in DC Circuits P = I × V = I² × R = V² / R where:
The POWER in DC circuit is equal to the product of voltage and current. [Power = Current × Voltage]
When the system voltage is constant, ammeter readings are almost a sufficient indication of the POWER taken.
The POWER is calculated by using voltmeter and ammeter or wattmeter.
P = I × V = I² × R = V² / R
where:
P = power in watts (W)  I  = current in amps (A)  R = resistance in ohms ( )  V = voltage in volts (V)

9. DC circuits
Ammeter measures current which flow into the voltmeter and load
Voltmeter measures voltage drop across the ammeter in addition to that dropping across the load

10. Digital wattmeter (up to 100 kHz)
Advantages:
High-resolution
Accuracy
Several techniques (multiplication of signals)
Electronic multiplier is an analog system which gives as its output a voltage proportional to the power indication required  A/D conversion

11. Hall-power meter
Coil generates magnetic field which is proportional to load current
The sensor excitation current passes through R1 and is proportional to the load voltage
 Hall voltage is proportional to load power
Problems: offset and linearity

12. Example
How much power is used in a circuit which is 110 volts and has a current of amps?

13. Example
The work done by a heater is 100 joules for time 4 seconds. Find out the electric power of the heater.
Solution:
Given,
Work done by a heater (W)=100 joule
Time taken by a heater (t)=4 seconds
Therefore the electric power of the heater
P = W/t
=100/4
=25 watt

14. Example
The electric power of the electrical bulb is 50 watt. Then at how much time required to the electrical bulb to performed the work of 150 joules.
Solution:
Given,
Electric power (P)=50 watt or 50 joules/second
Work done by a bulb (W)=150 joules
We know that P=W/t
                        t=W/P = 150/50
               Time, t = 3 seconds

15. Examples
Label on TV state 720W/120V. Find the current supply to this TV.
A heater has 30 resistor connected to voltage source 120V. Find the total power which changed to heat .

16. Introduction to Measurement of Power:
In a DC (direct current) circuit: The power in DC circuit is provided by
P = V * I
The power can be calculated basically with the help of just Ammeter and voltmeter. The below diagram shows the circuit diagram for measuring power in DC (direct current) circuit.

17. Total power (P) = Voltmeter meter reading * Ammeter reading

18. In one-phase AC circuit:
Power in 1-phase AC circuit is provided by P = VICosφ,
Wattmeter is employed to calculate power in AC circuits.
Wattmeter consists of two coils:
(i) Current coil (CC)
(ii) Potential coil (PC)
The circuit diagram is displayed in the diagram below;
Total power (P) = Wattmeter reading
= VI Cos φ.
From this power factor can be measured as follows;
Cos φ = P/ VI
Power measurement in 1-phase AC circuit

19. 3-phase AC circuit 1) One wattmeter method: Single wattmeter method
of power measurement
in 3-phase circuit
For balanced 3-phase load that is ZR = ZY = ZB, single wattmeter might be connected into any one phase as displayed in the above diagram. This wattmeter will point out the power in that phase only. Because the load is balanced, the entire power in the 3-phae circuit will be calculated by
Total power = 3 *Wattmeter reading

20. ii) Two-wattmeter method:
This is most the general method for calculating power in a 3-phase, 3-wire system because it can be employed for both unbalanced loads (ZR ≠ ZY≠ ZB) and balanced (ZR = ZY = ZB) connected in either star/delta. The current coils are connected to any two of the lines, and the voltage coils are connected to another line, the one with no current coil connection, as displayed in the below diagram.
Total power = W1+ W2
Two wattmeter method of power measurement in 3-phase circuit

21. POWER in AC Circuits
In AC circuits the voltage and current are changing their magnitude and polarities with reference to time.
The electric power in the circuit at any instant is equal to the product of the current and the voltage across its terminals at that instant.[p = vi]
The instantaneous power,

22. Average Power The mean power
V and I are rms value of voltage and current and to calculate power, we should know the power factor of the load in AC circuit.
Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle of current with respect to voltage.

23. Current B lags the voltage by 45 degrees so the vector points down and to the right (see below). Current A leads by 45 degrees (it's happening 45 degrees ahead of voltage) so it points up and to the right. Since the peak currents are 1 Amp, the RMS currents are Amps.

24. Example
The real power is 700 W and the phase angle () between voltage and current is 45.6°.
The power factor = cos(45.6°) =
The apparent power = 700 W / cos(45.6°) = 1000 VA

25. The power output rating of motors is usually expressed in a power unit call the horsepower (hp)
The relation between horsepower and watts is
1hp = 746W
Electric motors and other systems have an efficiency () of operation

26. Examples
Calculate the power for a 12V battery supply 250A to a starter motor.
Find the current drawn from a 115V line by a DC electric motor that delivers 1hp by assuming 100% efficiency of operation.
What is the operating efficiency of a fully loaded 2hp DC electric motor that drawn 19A at 100V?

27. POWER Measurement
A wide variety of instrumentation and transducers for the measurement of POWER in AC and DC circuit.
Important primarily for the testing, monitoring and maintenance of the energy supply network and electrical equipment.
Required in high frequency and low power circuits.
A wattmeter suitable used for power meter measurement in DC and AC systems, which will give the same angle of deflection for a given power.

28. Why Wattmeter Needed?
Ammeter measures load current IL and there is voltage drop VA across ammeter.
VL=V – VA
Pdc= VL IL = (V – VA)IL = VIL – VAIL
[Power measured by meters] = [Power consumed by load] [Power loss in ammeter]
The product of ammeter and voltmeter does not give correct power consumed by load

29. If voltmeter shifted across the load to measure the load voltage, it measures VL correctly but ammeter measures current I.
I = IL + IV
Pdc= VL IL = VL (I - IV)= VL I – VL IV
[Power measured by meters] = [Power consumed by load] [Power loss in voltmeter]
Power measured is higher than power actually consumed by load.

30. Wattmeter Errors 1) Error Due to Inductance of Pressure Coil:
Inductance of pressure coil may cause an error in the wattmeter reading.
The instrument gives high reading on lagging pf and low reading on leading power factor and true power.
Pressure coil inductance causes wattmeter to read more power than actual .
To reduce this error capacitance is connected in parallel with PC.

31. 2) Error Due to Capacitance of Pressure Coil:
The wattmeter reads less power
Both inductance and capacitance are present in the pressure coil circuit and, therefore, cancel the effect of each other. 
If the capacitive reactance (XC) = inductive reactance (XL) in the pressure coil circuit, then, the error will be completely eliminated.
3) Error Due to Eddy Currents:
The alternating magnetic fields of current coil induce eddy currents in the solid metal parts nearby the current coil.
These  eddy currents set up their own magnetic field and thus alter the magnitude and phase of the magnetic field causing deflection.
Thus the error is introduced in the instrument readings. 

32. 4) Error Due to Power Loss in Pressure Coil or Current Coil @ error due to method of connection:
There are two methods of connecting wattmeter in the circuit for measurement of power. 
In one method the pressure coil (PC) of the wattmeter is connected on the supply side of current coil (CC) whereas in second method the PC is connected on load side of CC. 
In the former method the wattmeter reads the small copper loss (I2Rc) in addition to the load power i.e. wattmeter reads W + I2Rc. In the second method the wattmeter reads W + I2 p(R+rp).
First method is adopted for measurement of power in circuits carrying small currents while the latter one is adopted for measurement of power in the circuit carrying large currents.

33. Connection to the supply side
The voltage coil is connected to the supply side of the field coils so that only the load current flows through the field coils. However, the voltage applied to the series-connected moving coil and multiplier is E + EF (the load voltage plus the voltage drop across the field coils). Now the wattmeter indicates load power (El) plus an additional quantity (EFl). In high-voltage circuits, where the load voltage is very much larger than the voltage drop across the field coils, the error may be insignificant. In low-voltage conditions, this error may be serious.

34. Connection to the load side
The moving coil (or voltage coil) circuit is connected in parallel with the load, the field coils pass a current, the sum of the load current and the moving-coil current. This results in the wattmeter indicating the load power (VI), plus a small additional quantity (VIc). Where the load current is very much larger than Ic, this error may be negligible. In low-load-current situations, the error may be quite significant.

35. 5) Error Due to Friction:
The frictional error becomes relatively important in such an instrument due to availability of small deflecting torque.
6) Error Due to Heating:
This error is mainly due to pressure coil circuit, which carries a current proportional to the pd across its terminals and inversely proportional to its impedance.  Such an error is usually very small.
7) Error Due to Stray Fields:
External fields may cause serious errors in the ordinary types of non-astatic dynamometer wattmeter unless shielded, either by means of an iron case or by a laminated shield.

37. Energy Measurement

38. What is Energy?
The electric energy produced by the source of emf is dissipated in the circuit in the form of heat.
Electrical energy is converted to heat whenever a current flows through a resistance and this can be a problem if it makes a device or wire overheat.
In electronics the effect is usually negligible, but if the resistance is low the current can be sufficiently large to cause a problem.

39. In a circuit of resistance R, the rate at which electrical energy is converted to heat energy is given by
P = IV
but V = IR, then P = I(IR) =I2R
where I2R is known as JOULE HEATING.
From the equation P = I² × R that for a given resistance the power depends on the current squared, so doubling the current will give 4 times the power.
The standard unit for energy is the joule (J), but 1J is a very small amount of energy for mains electricity. so kilo Joule (kJ) or Megajoule (MJ) are sometimes used in scientific work.

40. The kilowatt hour (kWh) is commonly energy used to represent electric energy production and consumption for 1 hour where
1 kWh = 3.6 x 106 J.
The amount of energy used (or supplied) depends on the power and the time for which it is used.
Energy (kWh) = Power (kW) × Time (hours)
A low power device operating for a long time can use more energy than a high power device operating for a short time.

41. Example 1 Calculate energy for a 60W lamp switched on for 8 hours
Solution
Energy uses = Power × Time
= 0.06kW × 8h
= 0.48kWh
= 1728kJ.

42. Example 2 Calculate energy for 3kW kettle switched on for 5 minutes.
Solution
Energy uses = Power × Time
= 3kW × (5/60)h
=0.25kWh
= 900kJ.

43. Example 3
The current flowing through an appliance connected to a 120V source is 2A. How many kilowatt-hours of electrical energy does the appliance use in 4 hours?
Solution

44. Example 4
The work done by a heater is 100 joules for time 4 seconds. Find out the electric power of the heater.
Solution
Given,
Work done by a heater (W)=100 joule
Time taken by a heater (t)=4 seconds
Therefore the electric power of the heater
P = W/t
=100/4
=25 watt

45. Example 5
The electric power of the electrical bulb is 50 watt. Then at how much time required to the electrical bulb to performed the work of 150 joules.
Solution
Given,
Electric power (P)=50 watt or 50 joules/second
Work done by a bulb (W)=150 joules
We know that P=W/t
                        t=W/P = 150/50
               Time t = 3 seconds

46. Energy Meter Instrumentations
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.
Energy meter is an integrating instrument.
Energy is the total power delivered or consumed over an interval of time t may be expressed as:
Where
v(t) is expressed in volts, i(t) in amperes and t in seconds,

47. Single Phase Energy Meter

48. Induction Type Energy Meter
Construction of energy meter

49. Single Phase Energy Meter

51. Single Phase Energy Meter
The operating mechanism in a energy meter
Driving system
Moving system
Braking system
Registering system

52. Driving System consisting of two electromagnets
A coil having large number of turns of fine wire is wound on the middle limb of the shunt magnet.
This coil is known as “pressure or voltage” coil and is connected across the supply mains.
This voltage coil has many turns and is arranged to be as highly inductive as possible (produces a high ratio of inductance to resistance).
This causes the current, and the flux, to lag the supply voltage by nearly 90 degree.

53. An adjustable copper shading rings are provided on the central limb of the shunt magnet to make the phase angle displacement between magnetic field set up by shunt magnet and supply voltage is approximately 90degree.
The copper shading bands are also called the power factor compensator or compensating loop.
The series electromagnet is energized by a current coil, which is connected in series with the load so that it carry the load current.
The flux produced by this magnet is proportional to, and in phase with the load current.

54. Moving System
Consists of a light rotating aluminium disk mounted on a vertical spindle or shaft.
The shaft that supports the aluminium disk is connected by a gear arrangement to the clock mechanism on the front of the meter to provide information that consumed energy by the load.
The time varying (sinusoidal) fluxes produced by shunt and series magnet induce eddy currents in the aluminium disc.
The interaction between these two magnetic fields and eddy currents set up a driving torque in the disc.
The number of rotations of the disk is proportional to the energy consumed by the load in a certain time interval and is commonly measured in killowatt-hours (Kwh).

55. Braking System Consisting of a permanent magnet.
Damping of the disk is provided by a small permanent magnet, located diametrically opposite to the AC magnets.
The disk passes between the magnet gaps.
The movement of rotating disc through the magnetic field crossing the air gap sets up eddy currents in the disc that reacts with the magnetic field and exerts a braking torque.
By changing the position of the brake magnet or diverting some of the flux there form, the speed of the rotating disc can be controlled.

56. Registering System Consisting of gear train and counter.
Driven either by worm or pinion gear on the disc shaft, which turns pointers that indicate on dials the number of times the disc has turned.
The energy meter thus determines and adds together or integrates all the instantaneous power values so that total energy used over a period is thus known.
Therefore, this type of meter is also called an “integrating” meter.

57. Errors in Energy Meter (Induction Type)
Phase displacement error
Frictional Error
Creep
Effect of Temperature Variation

58. Phase Displacement 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).
Required coil winding should be design highly inductive, has resistance and iron losses in core are small.
To avoid this effect, copper shading bands provide around the central limb of the shunt magnet and properly adjusting it by the methods of compensation.

59. Adjustable of shading band
By adjusting the position of the copper shading band in the central limb of the shunt magnet this error can be eliminated.
Phase error correction.

60. Frictional Error Due to friction between spindle and bearings.
An additional amount of driving torque is required to compensate this error by low load adjustment.
The two shading bands on the outer limbs are adjusted to cause a phase displacement between the enclosed flux and main flux which create this extra torque exerted on disc.

61. Creep
Creep is a phenomenon that can adversely affect accuracy, that occurs when the meter disc rotates continuously with potential applied and the load terminals open circuited.
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 (creep error).
This slow motion may be due to
incorrect friction compensation
vibration
to stray magnetic field
for over voltage across the voltage coil.

63. Effect of Temperature Variation
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.

64. Testing of Energy Meter
RSS Phantom Loading
Energy measured by energy meter =
Energy measured by RSS meter =
% Error =

65. Energy meter constant K is defined as
In commercial meters the speed of the disc is of the order of revolutions per hour at full load

66. Example 1
A 240V single phase watt-hour meter has correctly adjusted having a meter constant of 600revs/kWh. Determine the speed of the disc for current of 10A at a power factor of 0.8 lagging in 1 minute.
Solution
Energy consumed in 1 min,
Revolution in 1 min =

67. Example 2
An energy meter revolves 100 revolutions of disc for unit of energy. Find the number of revolutions made by it during an hour when connected 20A at 210V and 0.8 power factor leading.
If energy meter revolves 350 revolutions, calculate the percentage of error. 

68. Example 3
Explain in brief why energy meter reads energy while wattmeter does not. An energy meter has a registration constant of 100rev/kwh if the meter is connected to a load drawing 20A at 230V and 0.8 power factor for 5 hours. Find the number of revolution should be made by it of it is actually made 1800 revolutions. find the
% error and explain it from consumer point of view?

69. Answer.
An energy meter is fitted with some type of registration mechanism whereby all the instantaneous reading of power are summed over a definite period of time.
ENERGY = POWER X TIME
So, an energy meter can read energy. Whereas, a wattmeter indicates the value of power at a particular instant when it is read and hence it can not read energy.
Registration constant= 100 rev/Kwh
I = 20 A,     V = 230 V,     cos φ = 0.8

70. Measurement of Power & Energy
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.

71. Advantages of Instrument Transformers
Single range instrument can be used to cover a wide range.
Indicating instrument can be located at some distance from the circuit. This is a great advantage particularly for high voltage situation.
By use of CT with split core or hinged core, the current in heavy current bus bar can be measured without breaking the circuit.

72. END