CHAPTER 2: ELECTRICAL BACKGROUND
Another common delta connection is the four-wire, grounded delta used for lighting loads. In this connection the center point of one winding is grounded. On a 120/240 volt, four- wire, grounded delta service the phase-to-ground voltage would be 120 volts on two phases and 208 volts on the third phase. The phasor diagram for the voltages in a three- phase, four-wire delta system is shown below.
| Vca |
120 V | Vnc |
| Vbc |
120 V | Vbn |
| Vab |
FIGURE 2–5: Three-Phase, Four-Wire Delta Phasors
2.2.4Blondell's Theorem and Three-Phase Measurement
In 1893 an engineer and mathematician named Andre E. Blondell set forth the first scientific basis for poly phase 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 watt-meters 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 analog meters, this measurement was made 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 Blondell'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 common.
