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 = P_a + P_b

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