What are the principles of analog single phase wattmeter?

An analog single-phase wattmeter is a device which measures the power transmitted from source to load in the circuit.

The simplest type is an ammeter whose scale is calibrated watts. This device can provide satisfactory indications of power generated or consumed if:

A) The line voltage is known and varies little under any conditions where an indication is needed, and

B) The circuit uses direct current (DC), or alternating current (AC) where the load is purely resistive.

An application where such a meter would provide useful indications of power consumed is a circuit connected to a well-regulated 120 volt source, AC or DC, has a load consisting of incandescent lamps and/or heating elements and the meter is calibrated to 120 volts. If the line current is 9 amperes, the meter indicates 1080 watts. It works on the formula E x I = P, where E is the electromotive force in volts, I is the line current in amperes and P is the power, in watts.

This type of meter has a number of shortcomings. If the mains voltage varies, such as when few loads are connected the voltage may be higher than 120 and the instrument will underestimate the power. When the mains are heavily laden, the reverse is true. If the voltage is well-regulated, this error may be small enough to ignore as it can be less than that of the meter movement, especially where the effort and expense of obtaining precise readings is not justified.

If the circuit operates from a AC source and the load is an electric motor, this type of instrument will indicate the apparent power, in volt-amperes but this will differ from the true power, measured in watts.

The cause of this difference is the inductance, or opposition to change in current flow inherent in magnetic devices such as motors or iron-core fluorescent lamp ballasts. In motor circuits, the current will lag in time behind the voltage and the amount of this lag depends on a number of factors, chiefly the type of motor and the torque demanded from it. In the case of lamp ballasts, the lag is affected by ballast design, ambient temperature, age of the bulb, etc.

We can calculate the difference, or power factor, between apparent power and true power if we know the lag angle (360 degrees = 1 cycle):

Watts = VA x Cos(q)

or,

True Power = Apparent Power x Power Factor.

One way determine the lag angle is with an oscilloscope, which can indicate the amplitude of the voltage, current and their phase relationship. This method is rarely used for AC power circuits as an oscilloscope is costly, requires a skilled operator and these three values must then be plugged into a formula to determine the true power.

The method long used for practical measurements is the dynamometer-type wattmeter. This is a meter movement which has one coil which is in series with one conductor to the load, usually it induces a magnetic field in the stator and has relatively few turns of large-diameter wire. The second coil is attached to the pointer and suspended in the magnetic gap of the stator. It has many turns of fine wire and is connected parallel to the load. A magnetic field in either coil by itself will produce no movement of the pointer, as its flux is unopposed. The torque produced, and the degree of deflection of the pointer is the result of the interaction both of amplitude and of phase of the two magnetic fields, one related to current and the other to voltage. Thus it remains accurate for variable voltages, currents and phase relationships.

An example of this instrument's value: A certain home has a central air conditioner. On a muggy evening, the homeowner measures the current at 21 amperes using a clamp-on type ammeter and the voltage at 234 VAC, for an apparent power of 4194 VA. On a sweltering summer afternoon the compressor demands more torque from the motor driving it, so 23 amperes and 228 VAC is seen for 5244 VA.

Now let's check that power factor. In the first case the lag angle is 45 degrees so the true power is 2966 watts. As more torque is demanded from the motor the lag angle changes much more than the current, so in the second case if the lag angle is only 15 degrees, the true power is 5065 watts.

As we can see from this example, the ammeter can provide us with useful information on choosing the size of the conductors, Transformers, alternator windings or circuit breaker ratings for motor circuits but only a very rough guess as to the actual energy consumption.

Incidentally the electric meter which the utility company uses to determine the monthly household electrical use is a variation of the dynamometer wattmeter movement and the rotation of the wheel is in proportion to true, not apparent power.

Recent advances in microelectronics allow construction of dynamometers using semiconductor devices to measure voltage, current and phase relationship and such a device may be less expensive to construct than the traditional meter. Also they can provide a digital display, eliminating parallax and scale interpretation error.