Blondel's Theorem And Three Phase Measurement - Electro Industries Shark 200 Installation & Operation Manual

1: Three-Phase Power Measurement

1.1.3: Blondel's Theorem and Three Phase Measurement

In 1893 an engineer and mathematician named Andre E. Blondel set forth the first
scientific basis for polyphase metering. His theorem states:
If energy is supplied to any system of conductors through N wires, the total power in
the system is given by the algebraic sum of the readings of N wattmeters so arranged
that each of the N wires contains one current coil, the corresponding potential coil
being connected between that wire and some common point. If this common point is
on one of the N wires, the measurement may be made by the use of N-1 Wattmeters.
The theorem may be stated more simply, in modern language:
In a system of N conductors, N-1 meter elements will measure the power or energy
taken provided that all the potential coils have a common tie to the conductor in
which there is no current coil.
Three-phase power measurement is accomplished by measuring the three individual
phases and adding them together to obtain the total three phase value. In older ana-
log meters, this measurement was accomplished using up to three separate elements.
Each element combined the single-phase voltage and current to produce a torque on
the meter disk. All three elements were arranged around the disk so that the disk was
subjected to the combined torque of the three elements. As a result the disk would
turn at a higher speed and register power supplied by each of the three wires.
According to Blondel's Theorem, it was possible to reduce the number of elements
under certain conditions. For example, a three-phase, three-wire delta system could
be correctly measured with two elements (two potential coils and two current coils) if
the potential coils were connected between the three phases with one phase in com-
mon.
In a three-phase, four-wire wye system it is necessary to use three elements. Three
voltage coils are connected between the three phases and the common neutral con-
ductor. A current coil is required in each of the three phases.
In modern digital meters, Blondel's Theorem is still applied to obtain proper metering.
The difference in modern meters is that the digital meter measures each phase volt-
age and current and calculates the single-phase power for each phase. The meter
then sums the three phase powers to a single three-phase reading.
#
Electro Industries/GaugeTech Doc E149701 1-6
The Leader In Power Monitoring and Smart Grid Solutions