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Three Phase Power Measurement
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 Objective : Three Phase Power Measurement by Two Wattmeter Method.

 

 

 

                                                                              Fig.1.  Three Phase Power measurement circuit by Two Wattmeters Method.  

 

 The connection diagram for the measurement of power in three phase power measurement circuit using two wattmeter's method is shown in Fig.1.This is irrespective of the circuit connection star or delta. The circuit may be taken as balanced or unbalanced one, balanced type being only a special case.  Please not the connection of two wattmeter's. The current coil  of the wattmeter's 1 and 2 in series with R and B phase with the pressure voltage coils being connected across R-Y and B-Y respectively. Y is the third phase in which no current coil is connected. 

 If star connected circuit is taken as an example the total instantaneous power consumed in the circuit is, 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»W«/mi»«mo»=«/mo»«msub»«mi»I«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«msub»«mi»V«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»+«/mo»«msub»«mi»I«/mi»«mrow»«mi»Y«/mi»«mi»N«/mi»«/mrow»«/msub»«msub»«mi»V«/mi»«mrow»«mi»Y«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»+«/mo»«msub»«mi»I«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«msub»«mi»V«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»(«/mo»«mn»1«/mn»«mo»)«/mo»«/math»

 Each of the terms in the above expression equ. (1) is the instantaneous power consumed by the phases. From the connection diagram, the circuit in and  the voltages across the respective (current, pressure or voltage) coils in the wattmeter, W1 are «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»I«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«/math» and «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»V«/mi»«mrow»«mi»R«/mi»«mi»Y«/mi»«/mrow»«/msub»«mo»=«/mo»«msub»«mi»V«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»-«/mo»«msub»«mi»V«/mi»«mrow»«mi»Y«/mi»«mi»N«/mi»«mo».«/mo»«mo»§nbsp;«/mo»«/mrow»«/msub»«/math» so the instantaneous power measured by the wattmeter W1 is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»W«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«msub»«mi»I«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»*«/mo»«msub»«mi»V«/mi»«mrow»«mi»R«/mi»«mi»Y«/mi»«/mrow»«/msub»«/math».

Similarly the instantaneous power measured by the wattmeter W2 is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»W«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«msub»«mi»I«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«msub»«mi»V«/mi»«mrow»«mi»B«/mi»«mi»Y«/mi»«/mrow»«/msub»«mo»=«/mo»«msub»«mi»I«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»(«/mo»«msub»«mi»V«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»-«/mo»«msub»«mi»V«/mi»«mrow»«mi»Y«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»)«/mo»«/math».

 Some of the two readings as given above is,

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«msub»«mi»W«/mi»«mn»1«/mn»«/msub»«mo»+«/mo»«msub»«mi»W«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«msub»«mi»I«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»(«/mo»«msub»«mi»V«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»-«/mo»«msub»«mi»V«/mi»«mrow»«mi»Y«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»)«/mo»«mo»+«/mo»«msub»«mi»I«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»(«/mo»«msub»«mi»V«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»-«/mo»«msub»«mi»V«/mi»«mrow»«mi»Y«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»)«/mo»«/mtd»«/mtr»«mtr»«mtd»«mfenced open=¨§nbsp;¨»«mrow»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»=«/mo»«msub»«mi»I«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«msub»«mi»V«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»+«/mo»«msub»«mi»I«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«msub»«mi»V«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»-«/mo»«msub»«mi»V«/mi»«mrow»«mi»Y«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»(«/mo»«msub»«mi»I«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»+«/mo»«msub»«mi»I«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»)«/mo»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»(«/mo»«mn»2«/mn»«/mrow»«/mfenced»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§nbsp;«/mo»«msub»«mi»I«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»+«/mo»«msub»«mi»I«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»+«/mo»«msub»«mi»I«/mi»«mrow»«mi»Y«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»=«/mo»«mn»0«/mn»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«mi»p«/mi»«mi»p«/mi»«mi»l«/mi»«mi»y«/mi»«mi»i«/mi»«mi»n«/mi»«mi»g«/mi»«mo»§nbsp;«/mo»«mi»i«/mi»«mi»n«/mi»«mo»§nbsp;«/mo»«mi»e«/mi»«mi»q«/mi»«mi»u«/mi»«mi»a«/mi»«mi»t«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mo»§nbsp;«/mo»«mfenced»«mn»2«/mn»«/mfenced»«mo»,«/mo»«/mtd»«/mtr»«mtr»«mtd»«mfenced close=¨§nbsp;¨ open=¨§nbsp;¨»«mfenced close=¨§nbsp;¨ open=¨§nbsp;¨»«mfenced close=¨§nbsp;¨ open=¨§nbsp;¨»«mfenced close=¨§nbsp;¨ open=¨§nbsp;¨»«mrow»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mrow»«/mfenced»«/mfenced»«/mfenced»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mfenced close=¨§nbsp;¨ open=¨§nbsp;¨»«mfenced close=¨§nbsp;¨ open=¨§nbsp;¨»«mfenced close=¨§nbsp;¨ open=¨§nbsp;¨»«mfenced close=¨§nbsp;¨ open=¨§nbsp;¨»«mfenced close=¨§nbsp;¨ open=¨§nbsp;¨»«mo»§nbsp;«/mo»«/mfenced»«/mfenced»«/mfenced»«/mfenced»«/mfenced»«msub»«mi»W«/mi»«mn»1«/mn»«/msub»«mo»+«/mo»«msub»«mi»W«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mfenced close=¨§nbsp;¨ open=¨§nbsp;¨»«mrow»«msub»«mi»I«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«msub»«mi»V«/mi»«mrow»«mi»R«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»+«/mo»«msub»«mi»I«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«msub»«mi»V«/mi»«mrow»«mi»B«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»+«/mo»«msub»«mi»V«/mi»«mrow»«mi»Y«/mi»«mi»N«/mi»«/mrow»«/msub»«/mrow»«/mfenced»«msub»«mi»I«/mi»«mrow»«mi»Y«/mi»«mi»N«/mi»«/mrow»«/msub»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»-«/mo»«mo»(«/mo»«mn»3«/mn»«mo»)«/mo»«mo»§nbsp;«/mo»«/mtd»«/mtr»«/mtable»«/math»

  Equation (1) is compared with equ. (3)  gives the total instantaneous power consumed in the circuit . They are found to be same. 

 Phasor Diagram of three phase balanced star connected circuit:

 

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