Interpretation of Wattmeter Readings in Two-Wattmeter Method

If θ in Fig. 9-7 were greater than 60°, then the angle (30°+θ) would be greater than 90° and its cosine would be negative. Hence, the reading of wattmeter W_a would be negative and the power P_a would be negative.

It should be noted that, for all cases when the current is lagging arid when θ is greater than 0° and less than 90°, Wb will give a higher reading than W_a. If the currents were leading - rather than lagging - their respective phase voltages, W_a would be greater than W_b for values of θ between 0° and 90°.

A good method of determining whether the low meter reading on a balanced load should be taken as positive or negative is as follows: From the common line (at C, Fig. 9-6) remove the potential coil wire of the lower-reading wattmeter and touch it on the line containing the other wattmeter. If, then, the needle of the lower-reading wattmeter reverses, the reading is to be taken as negative. If the needle does not reverse, then the reading is to be taken as positive. Return the moved wire to its original position.

Example 9-2. - The meters in the line to a three-phase motor being tested indicate the following values:

What are the power and the power factor?

Solution. - The power is

The power factor is, by equation (9-4),

Thus, Power factor = 75.8%

Example 9-3. - Calculate the readings of wattmeters W₁ and W₃ in Fig. 9-4 (a) and the total power.

First Solution. - The wattmeter readings are:

The total power is As a check,

Fig. 9-8. Rotated Vector Diagram for Computing Reading of Wattmeter W₁ in Example 9-3

Second Solution. - In the calculation of power in problems of this type, when the actual values of line currents are not needed, some students run less risk of error in sign or position of current components if the power indicated by each meter is computed on a different reference axis, instead of being computed on one common axis. For example, the reading of wattmeter W₁ in Fig. 9-4 is the product of V₂₁ (the voltage on the potential coil) and I₁ cos α, where α is the angular displacement of I₁ from V₂₁. There is an advantage, therefore, in taking the x axis of reference through V₂₁ and also in rotating the vector diagram so that V₂₁ is horizontal and runs from left to right as viewed by the student. The diagram will then appear as in Fig. 9-8. To solve for the reading of wattmeter W₃ the diagram would be used as in Fig. 9-4, with V₂₃ along the x axis of reference. The simplified vector diagram for computing the reading of W₃ is shown in Fig. 9-9.

With the axis taken through V₂₁, as in Fig. 9-8, the reading of wattmeter W₁ can be found by computing only the in-phase or cosine components of current and then multiplying their sum by V₂₁.

Thus,

To calculate the reading of wattmeter W₃j the work follows:

Fig. 9-9. Simplified Vector Diagram for Computing Reading of Wattmeter W₃ in Example 9-3

It is important to note that the reading of the wattmeter W₃ is positive because its potential coil is connected across lines 3 and 2 in such a way that the vector - V₃₂ is used in the vector diagram. It must also be recognized that wattmeters W₁ and W₃ do not actually measure power, but produce two readings which, when added algebraically, give a sum which is equal to the power. The mathematical proof of this fact is given here.