Electrical Engineering is a free introductory textbook to the basics of electrical engineering. See the editorial for more information....  # Measurement of Three-Phase Power by Two-Wattmeter Method

Author: E.E. Kimberly

If in Fig. 9-5 (a) the three meter potential coil terminals at 0 be kept joined, but be removed from the neutral of the system, the readings of all wattmeters will be unchanged, because the wattmeter potential coils themselves form a balanced Y-connected circuit and so the voltage across every potential coil remains unchanged. This method of measurement is called the "floating neutral" method and is accurate on a three-phase three-wire or four-wire system regardless of power factor or load unbalance. Fig. 9-6. Measurement of 3-Phase Power by Two-Wattmeter Method

If, then, the junction of the potential leads be moved and connected to one of the line wires, as at x on line 1, the sum P1 + P2+P3 will be unchanged, although the power read from wattmeter W1 will be zero. Thus, it is possible and feasible to measure three-wire, three-phase power in the circuit in Fig. 9-4 (a) by using only the two wattmeters W1 and W3. This is called the two-wattmeter method and may be used with convenience on any three-wire system, whether Y-connected or Δ-connected and whether balanced or unbalanced, as in Fig. 9-6.

A proof of the correctness of the two-wattmeter method in measuring balanced three-phase loads is as follows. For convenience Fig. 9-7 is drawn for a Y-connected circuit. In the vector diagram,

V01 V02, and V03 are phase voltages; V12, V23, and V31 are line voltages;

θ = displacement angle between a current and its respective phase-to-neutral voltage. Fig. 9-7. Vector Diagram of Two-Wattmeter Method

By the three-wattmeter method,

P = P1 + P2 + P3

or
 P = V01I1cosθ + V02I2cosθ + V03I3cosθ [a]

By the two-wattmeter method,

P = Pa + Pb

or
 P = V12I2cos(30°+θ) + V13I3cos(30°-θ) [b]

Since the right-hand members of equations (a) and (b) must be equal, if both methods are to give the same results, But Since this equation is an identity, it follows that Last Update: 2010-10-05