Electrical Engineering is a free introductory textbook to the basics of electrical engineering. See the editorial for more information.... 
Home Polyphase Circuits Interpretation of Wattmeter Readings  
Search the VIAS Library  Index  
Interpretation of Wattmeter Readings in TwoWattmeter MethodAuthor: E.E. Kimberly If θ in Fig. 97 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. 96) remove the potential coil wire of the lowerreading wattmeter and touch it on the line containing the other wattmeter. If, then, the needle of the lowerreading 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 92.  The meters in the line to a threephase 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 (94),
Thus, Power factor = 75.8%
The power factor for a balanced load may also be found from the equation
(95)
Example 93.  Calculate the readings of wattmeters W_{1} and W_{3} in Fig. 94 (a) and the total power.
First Solution.  The wattmeter readings are: The total power is As a check,
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 W_{1} in Fig. 94 is the product of V_{21} (the voltage on the potential coil) and I_{1} cos α, where α is the angular displacement of I_{1} from V_{21}. There is an advantage, therefore, in taking the x axis of reference through V_{21} and also in rotating the vector diagram so that V_{21} is horizontal and runs from left to right as viewed by the student. The diagram will then appear as in Fig. 98. To solve for the reading of wattmeter W_{3} the diagram would be used as in Fig. 94, with V_{23} along the x axis of reference. The simplified vector diagram for computing the reading of W_{3} is shown in Fig. 99. With the axis taken through V_{21}, as in Fig. 98, the reading of wattmeter W_{1} can be found by computing only the inphase or cosine components of current and then multiplying their sum by V_{21}. Thus,To calculate the reading of wattmeter W_{3}j the work follows:
It is important to note that the reading of the wattmeter W_{3} is positive because its potential coil is connected across lines 3 and 2 in such a way that the vector  V_{32} is used in the vector diagram. It must also be recognized that wattmeters W_{1} and W_{3} 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.


Home Polyphase Circuits Interpretation of Wattmeter Readings 