Power Measurements in DC Circuits

Measurement of electric power is essential in both commercial industrial applications and domestic applications. Prior estimation and subsequent measurements of instantaneous and peak power demands of any installation are mandatory for design, operation and maintenance of the electric power supply network feeding it.

How Power Measurements in DC circuits are done using an Ammeter and Voltmeter

Electric power (P) consumed by a load (R) supplied from a dc power supply (V_S) is the product of the voltage across the load (V_R) and the current flowing through the load (I_R), thus:

P = V_R x I_R

Therefore, power measurements in a dc circuit can be carried out using a voltmeter (V) and an ammeter (A) using anyone of the arrangements as shown below:

Note that, both the voltmeter and the ammeter require power for their own operations. In the first arrangement above i.e. Figure (a), the voltmeter is connected between the load and the ammeter. The ammeter thus, measures the current flowing into the voltmeter, in addition to the current into the load.

Power consumed by the load = Power indicated by the instruments – Power loss in the voltmeter

Thus, power indicated = Power consumed + Power loss in voltmeter.

In the second arrangement above shown in Figure (b), the voltmeter measures the voltage drop across the ammeter in addition to the voltage dropping across the load.

Voltage drop across the ammeter, V_A= I_R x R_A (where R_A is the internal resistance of the ammeter)

Power consumed by the load the load = V_R x I_R = (V_S – V_A) x I_R

= V_s x I_R – V_A x I_R

= V_s x I_R – I²_R  x R_A    (Equation 2)

= Power indicated by instruments – Power loss in the ammeter

Therefore, Power indicated = Power consumed + Power loss in Ammeter

Theoretically, if we consider voltmeter to have infinite internal impedance and ammeter to have zero internal impedance, then from equation 1 and equation 2, you can observe that the power consumed by the respective instruments goes down to zero. Therefore, in ideal cases, both the two arrangements can give correct indication of the power consumed by the load. Under practical conditions, the value of power loss in instruments is quite small, if not totally zero, as compared with the load power, and hence, the error introduced on this account is small.

Power Measurement in DC Circuits using a Wattmeter

Power in dc circuits can also be measured by a wattmeter. Wattmeter can give direct indication of power and there is no need to multiply two readings as shown in the arrangements above where the ammeter and voltmeter are used.

The commonly used wattmeter for power measurement is the dynamometer. It consists of two fixed coils, connected in series, and positioned coaxially with space between them and a moving coil placed between the 2 fixed coils and fitted with a pointer.

It can be shown that the torque produced by the dynamometer is proportional to the product of the current flowing through the fixed coils times that through the moving coil.

The fixed coils (current coils), carry the load current while the moving coil (Voltage coils), carries a current that is proportional, via the multiplier resistor R_V, to the voltage across the load R. Hence, the deflection of the moving coil is proportional to the power consumed by the load. In this construction of the wattmeter, the insertion error (as with the previous arrangements with ammeters and voltmeters) still exists. Relative β positioning of the current coil and the voltage coil with respect to the load, introduce similar V_s errors in the measurement of the actual power. By connecting the voltage coil between A and C, the current coils carry the surplus current flowing through the voltage coil conversely, by connecting the moving coil between B and C, this current error can be avoided,  but now the voltage measures the surplus voltage drop across the current coils.

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• Testing Power and Distribution Transformers
• Overhead vs. Underground Power Distribution Systems
• Supervisory Control and Data Acquisition in Power Systems