How to measure power with two wattmeters

At power measurement in three-phase circuits two wattmeters, it is possible not only to save one wattmeter, but also to roughly estimate from their readings power factor value three-phase electrical receiver.

For example, if the load in the phases is active and symmetrical, then the readings of the two wattmeters will be the same. This can be seen from the vector diagram (Fig. 1, c).

The currents coincide in direction with the phase voltages (receiver connected to a star): current AzA with voltage UA, and current AzV with voltage UBsince the load is active. Injection ψ1 between UAC and AzA is equal to 30O, and the angle ψ2 between UBC and AzB is also equal to 30O.

Rice. 1... Scheme of connecting two wattmeters to a three-wire network (a, b) and vector diagrams of voltages and currents at cos f = 1 (c) and cos f = 0.5 (d).

Power values ​​measured with wattmeters are determined by the same expressions:

Pw1 = UACAzAcosψ1= UlIl cos30 °,

Pw1 = UBC AzBcosψ2 = UlIl cos30 °

If the load is active-inductive character and cosine phi is equal to 0.5, that is, the angle φ = 60 °, then the angle ψ1= 30 °, and the angle ψ2 = 90 ° (Fig. 1, d).

The wattmeter readings will be as follows:

Pw1 = UlIl cos30 °

Pw1 = UlIl cos90 °

If the readings on one of the wattmeters become zero, this means that the cosine phi has decreased to 0.5.

The diagram also shows that if the cosine phi in the network becomes less than 0.5, that is, the angle φ will be greater than 60 °, then the angle ψ2 will become more than 90 ° and this will lead to the fact that the readings on the second wattmeter will become negative, the needle of the device will start to deviate in the other direction (usually modern wattmeters have a switch for the direction of the current in the moving coil). The total power in this case is equal to the difference between the readings of the wattmeters.

If the load is symmetrical, then according to the readings of two wattmeters, you can accurately calculate the value of cos φ according to the formula

cos φ = P / S = P / (√P2 + Q2),

where P = Pw1 + Pw2 — active power three-phase electrical receiver, W, Q = √3(Pw1 + Pw2) — reactive power of a three-phase electric receiver. The last expression shows that if the difference between the readings of two wattmeters is multiplied by √3, you get the reactive power three-phase electrical receiver.