Design Feature: September 1, 1995

An old technique updated for modern requirements allows you to measure all three line currents in a three-phase system. You perform this measurement using two current transformers (CTs) and three ammeters. The original technique appeared in Alternating-Current Machines by George Mueller (McGraw-Hill, 1952). The method works equally well with modern current sensors. Figs 1 and 2 illustrate the technique. The operation of the circuit depends on the fact that the vector sum of the three line currents in a three-phase system equals 0. I_A+I_B+I_C=0; hence, I_A+I_B= I_C.

This relationship exists regardless of whether the line currents are balanced. The vector sum of the current-sensor outputs is also 0, as long as the output signals are in phase with the respective line currents. Thus, V_A+V_B+V_C=0; hence, V_A+V_B= V_C. The circuit uses these relationships to derive the third voltage signal, V_C. Eliminating one current sensor results in a considerable savings. (The current sensor here costs $17.30.)

The op amp is connected as an inverting summing amplifier. When resistors R₁, R₂, and R₃ are of equal value, the op amp acts as a one-to-one inverter with respect to each input. V_OUT= (V_A+V_B)=V_C. The current sensors are rated at 1.6V rms maximum undistorted output. For highest accuracy, you should keep the signal levels below that figure. For the component values shown, a 0- to -10A range is a good choice. You can increase the sensitivity by increasing the load resistances or by passing the line conductors through the CTs more than once.