Electrical Engineering ⇒ Topic : Measurement of Power

Power in single-phase ac circuits is measured in a number of ways.

Three methods commonly used are:

1. Three voltmeter method.
2. Three ammeter method.
3. Wattmeter method.

These three methods are briefly discussed in this section

Three Voltmeter Method

The circuit for the measurement of single-phase power using three volt meters is given in Fig. (a). The load is assumed to be inductive as shown. The series resistance R is also assumed to be purely non-inductive.Then from the circuit, the voltage equation can be written as

                               V₁ = V₂ + V₃                                                     (1)  

The phasor diagram of these voltages is drawn as shown in Fig. (b) by taking the current I as the reference phasor. V₂ will be in-phase with I while

          FIGURE  Measurement of single-phase power by the three voltmeter method

V₃, the voltage across the inductive load will lead the current I by an angle 0.

Using the parallelogram law, we get

                     (2)

Power in the load =                                 (3)

and the power factor of the load can be obtained from Equation (2) as

                                            (4)

The overall accuracy of this method of power measurement will depend on the errors in the three voltmeters which are generally high. Therefore, this method is not very accurate. Also, it is difficult to obtain a purely non inductive resistance R in practice.

Three-ammeter Method:-

The circuit diagram for the measurement of single-phase power by using three ammeters is shown in Figure(a). The resistance R is assumed to be purely resistive. Using Kirchhoff's current law, we can write

                                                                   (1)

The phasor diagram of the currents is drawn with the voltage as the reference phasor as shown in Fig. (b). The current 1₂ is in phase with the supply voltage V. Current 1₃ lags behind V by an angle Φ . From the phasor diagram,we have

                FIGURE  Measurement of single-phase power by the three ammeter method.

                                (2)

                                    (3)

and, power factor of the load [from Equation(2)] is

                                                         (4)

Wattmeter Method

Power in a single-phase circuit can be measured using a dynamometer type of wattmeter connected as shown in Figure. The current coil (C.C.) is connected in series with the load and the pressure coil (P.C.) is connected across the load. The load current must pass through the current coil and the voltage across the load must appear across the pressure coil to facilitate accurate reading of the wattmeter. The reading on the wattmeter when multiplied by the multiplication factor gives the power in the load. If W is the wattmeter reading in Watts, then

                                                                                   (1)

and power factor of the load,

                                                                                       (2)

                      FIGURE  Measurement of single-phase power using a wattmeter

MEASUREMENT OF POWER

When the load takes power from the DC supply, the product of readings of ammeter and voltmeter gives the power. The circuit connection is shown in Figure (1).

                                                              figure (1) Measurement of DC power

Ammeter and voltmeter need power for their operation. Combination of Figures 2 (a) and 2(b) may be used to measure the power taken by the load. In Figure 14.20(a), the ammeter is connected between the voltmeter and load. So the reading of the voltmeter will not only indicate the voltage drop across the load but also the voltage drop of ammeter.

                                               figure (2) Connection of ammeter and voltmeter

Let R_a is the resistance of the ammeter, R_v is the resistance of the voltmeter, V_a is the voltage drop across the ammeter, and V_v is the voltage drop across the voltmeter.

From Figure 2(a),

                                                             V_a, = IR_a

In Figure 2(b), voltmeter is connected between load and ammeter Ammeter will measure the load current as well as the current in the voltmeter.

Current through the voltmeter is given by

                                                                                                                      ............ (1)

Power consumed by the load is given as:

                                                                            ............. (2)

                          = Power indicated by instruments  - Power loss in voltmeter

Thus, Eq. (1) and Eq. (2) show that the power indicated by the instruments is equal to the power consumed by the load plus power consumed by the instrument nearest to the load.