Blondel’s theorem | Power in Poly-Phase System

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.

power-measurement-in-3-phase-3-wire-system
Fig. 1 Power measurement in a 3-phase, 3 wire system

The current coils (CC) of wattmeters (W1, W2, W3) 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 = v1i1 + v2i2 + v3i ………………..(1)

Now

Reading of wattmeter W1 , t1= vAi1

Reading of wattmeter W2 , t= vBi2

Reading of wattmeter W3 , t= vCi3

Since

v1 = v + vA

v2 = v + vB

v3 = v + vC

Therefore,

t1= (v1 − v)i1

t= (v2 − v)i2

t= (v3 − v)i3

Sum of 3 wattmeter readings = t1 + t2 + t3

= (v1 − v)i+ (v2 − v)i+ (v3 − v)i3

= v1i1 + v2i2 + v3i− v(i+ i+ i3)

Apply KCL at node O,

i+ i+ i= 0

Therefore,

Sum of wattmeter readings = v1i1 + v2i2 + v3i3    ……………(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.

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