Electronics Protection - Summer 2017 - 18

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A single phase AC power source requires two conductors while a three-phase
source can transmit three times the power using only one extra conductor. This
means that a 50 percent increase in transmission cost yields a 200 percent increase
in transmitted power. Three-phase connections, such as the three-phase motors
shown in Figure 4, are connected in either WYE (upper schematic) or DELTA (lower
schematic) configurations.
The Voltages Van, Vbn, and Vcn in the WYE connection are called phase voltages.
Voltages marked Vab, Vbc, and Vac are line voltages. The currents Ia, Ib, and Ic are
phase currents. The total power dissipated by the load is the sum of the individual
phase current-voltage products in the WYE connection. Note the bold text indicates
vector operations: Pt = Ia*Van + Ib* Vbn + Ic*Vcn
Generally, power is calculated using the line voltages rather than the phase voltages. Figure 5 shows a phasor diagram of the phase voltage, phase current, and line
voltages. Voltage calculations are performed vectorially.

Figure 4. The two types of threephase connections.

The magnitudes of the line voltages in a balanced system are equal
to 3 times the phase voltage. Note that the phase voltages precede
the line voltages by 30 degrees. This is a result of the vector subtraction used to compute the line voltages from the phase voltages. High
voltage differential probes are used to measure the line and phase
voltages, they attenuate the signal by 100:1. The resulting phase voltages at the digitizer input are 1.69 V peak (3.38 Vpk-pk). These voltages are scaled by a factor of 100 due to the use of a ÷100 probe.
This will result in phase voltages reported as 169 Vpk (338 Vpk-pk).
This is 120 Vrms. The line voltages are √3 times the phase voltage,
or 208 Vrms. This is the nominal three-phase voltage in the United
States. We can verify this by acquiring the phase voltages on the digitizer and then computing the line voltages as shown in Figure 6.
Channels Va, Vb, and Vc are the measured phase voltages. Vab, Vbc,
and Vca are the computed line voltages (nominally 586 Vpk-pk). The
phase difference between the phase voltage and its adjacent line
voltage is 30 degrees as confirmed by the cursor measurement in
the zoom trace in the leftmost grid. The line voltage, Vab lags the
phase voltage, Va, by 1.38 ms out of a period of 16.67 ms. Phase
differences between the line voltages are 120 degrees.
The current phasors in Figure 5 are shown with a general phase
difference, Θ, from the phase voltages. This angle, Θ, represents
reactive components that can possibly be incorporated in the
motor windings. Our experiment uses a pure resistive load resulting in Θ being equal to 0 degrees.

Figure 5. Relationships of phase voltage, phase current, and line voltages.

Figure 6. Line voltages computed from phase voltages.

Figure 7, shows the phase voltages (Va, Vb, and Vc), the phase
currents (Ia, Ib, and Ic), and the phase power dissipation (Pa, Pb, and Pc) for a WYE-connected load (where we have
access to both the phase and line voltages). Multiply the phase voltage by its related phase current and the result is
the instantaneous power in each phase. The mean value of the instantaneous power is the real power component.
The sum of all three-phase power readings is the total real power of the load.
This measurement is referred to as the three-wattmeter power measurement. In order to make this measurement
using external differential probes to measure the voltages, it will require six channels. If single ended probes are used
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Table of Contents for the Digital Edition of Electronics Protection - Summer 2017