**Statement**

**Blondel’s theorem** states that if a network is supplied through P conductors, the total power is measured by adding the readings of **P** wattmeters so arranged that a current element of a wattmeter is in each line and the corresponding voltage element is connected between that line and a common point.

**Note:** If the common point is located on one of the lines, then the total power may be measured by **P−1** wattmeters.

Let us take a simple example of a 3-phase 3 wire system for power measurement. The diagram for such system is shown in figure 1.

The current coils (CC) of wattmeters (W_{1}, W_{2}, W_{3}) are connected to respective line conductors. The potential coils (PC) are connected to common point G. Star load is connected to the system.

v = potential of point G w.r.t. neutral point O.

Instantaneous power consumed by the load = v_{1}i_{1} + v_{2}i_{2} + v_{3}i_{3 } ………………..(1)

**Now**

Reading of wattmeter W_{1} , t_{1}= v_{A}i_{1}

Reading of wattmeter W_{2} , t_{2 }= v_{B}i_{2}

Reading of wattmeter W_{3} , t_{3 }= v_{C}i_{3}

Since

v_{1} = v + v_{A}

v_{2} = v + v_{B}

v_{3} = v + v_{C}

Therefore,

t_{1}= (v_{1} − v)i_{1}

t_{2 }= (v_{2} − v)i_{2}

t_{3 }= (v_{3} − v)i_{3}

Sum of 3 wattmeter readings = t_{1} + t_{2} + t_{3}

= (v_{1} − v)i_{1 }+ (v_{2} − v)i_{2 }+ (v_{3} − v)i_{3}

= v_{1}i_{1} + v_{2}i_{2} + v_{3}i_{3 }− v(i_{1 }+ i_{2 }+ i_{3})

Apply KCL at node O,

i_{1 }+ i_{2 }+ i_{3 }= 0

Therefore,

Sum of wattmeter readings = v_{1}i_{1} + v_{2}i_{2} + v_{3}i_{3} ……………(2)

Since equation (1) and (2) are equal. Hence the total instantaneous power measured by the three wattmeters is equal to the total power consumed in the load.